Luminosity Dependent Changes of Cyclotron Resonance Energies in Binary X-ray Pulsars

Transcription

1 Luminosity Dependent Changes of Cyclotron Resonance Energies in Binary X-ray Pulsars Motoki Nakajima Department of physics. Graduated School of Science, Nihon University, Tokyo, Japan Submitted to the Collage of Science and Technology, Nihon University on January 31, 2006, in partial fulfillment of the requirements for the degree of Doctor of Philosophy February 23, 2006

2 i Abstract Neutron star is a highly magnetized degenerate star. The existence of this object was predicted by Baade and Zwicky in 1934, and the observational confirmation was achieved by Bell and Hewish (1967). The emission from the neutron star is observed as a pulse-like signal which is generated by the neutron star rapid rotation. Therefore, the neutron star is occasionally called Pulsar. Since the discovery, a number of observations have been performed with various wavelength, and the various nature of the pulsars have been revealed; having a mass of g and a radius of 10 6 cm. Special mention on a pulsar, it possess a much more intense magnetic field on its surface; the typical field strength is Gauss. The origin of the intense magnetic fields of the pulsars are still unknown. To investigate the origin, we need to precisely measure the number of pulsar field strength. In order to estimate the magnetic field on the pulsar surface, several methods have been used. One of a method is to observe the cyclotron resonant scattering feature (CRSF) in X-ray spectra. This feature energy directly provide us the field strength. This method is usually applied to the accretion-powered pulsars which exist in the binary systems. Using this method, the first systematic observations were performed by Japanese X-ray Satellite Ginga in 1990 s. In these observations, the peculiar object was found, named 4U A binary X-ray pulsar 4U is known to have multiple CRSFs in the spectrum. The double CRSFs of 4U (the fundamental energy at 11 kev and the second harmonic at 23 kev) have been observed by several missions in typical recurrent outbursts. However, with Ginga observation, a single CRSF at 16 kev was obtained in a minor outburst in 1991, of which the luminosity was 1/7 of those of typical ones. In order to investigate how the CRSFs depend on the source luminosity, we analyzed the RXTE data of 4U obtained in 39 observations. In addition, we analyzed the data of the other accretion-powered pulsar, X , when the source exhibited the large flux change. Accordingly, we have clearly revealed that the CRSFs depend on the source X-ray luminosity in each analysis case; as the source is bright, the low resonance energy is observed, and as the source is faint, the high resonance energy is observed. The luminosity-dependent cyclotron resonance energy may be understood as a result of a decrease in the height where the CRSFs is produced, in response to a decrease in the mass accretion rate. From this, we can conclude that the observed change of the magnetic field is just appearance, not change of the real field strength. Furthermore, we can infer that the observed magnetic field, when the source flux is faint, is the real field strength of the pulsar surface.

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4 Contents 1 Introduction 1 2 Review Brief History of X-ray Astronomy Neutron Stars and Pulsars The classification of pulsars Rotation powered pulsars Accretion powered pulsars Magnetic Fields of Pulsars Cyclotron Resonant Feature Change of Resonance Energy U Other examples Instrumentation Rossi X-ray Timing Explorer Pointed Instruments Proportional Counter Array High Energy X-ray Timing Experiment (HEXTE) All Sky Monitor Observations The criterion of targets and observations selection U Overview ASM light curves PCA and HEXTE pointings iii

5 iv CONTENTS 4.3 X Overview ASM light curves PCA and HEXTE pointings Data Analysis and Results on 4U Light curve of PCA and HEXTE The representative spectra CRSF variation in date-sorted spectra CRSF variation in intensity-sorted spectra Result of all PCA and HEXTE spectra NPEX model multiplied by CYAB factors fitting The change of cyclotron resonance energy Behavior of other CRSF parameters Data Analysis and Results on X Light curve of PCA and HEXTE Representative pulse-phase averaged spectra Result of all PCA and HEXTE spectra Spectral fitting with our model The change of cyclotron resonance energies in X spectra Behavior of other CRSF parameters Discussion Luminosity Dependent Cyclotron Resonance Energy Change The latitude change The height change Other CRSF Parameters Conclusion 99 A All spectra 101 A.1 Spectra of 4U A.2 Spectra of X

6 Chapter 1 Introduction In this thesis, we study the magnetic field on an enigmatic celestial object, Neutron Star. The neutron star is one of the end product of a massive star evolution. The existence of this object was predicted by Walter Baade and Fritz Zwicky (1934), two years after the discovery of the neutron by James Chadwick in However, a neutron star was not discovered by observations for thirty years. In 1962, the X-ray emission from the neutron star which belongs to the Low Mass X-ray Binary (hereafter LMXB) system, named Sco X-1, was detected by the rocket experiment performed by R. Giacconi and his collaborators (1962). Five years later, Bell and Hewish (1967) at Cambridge radio astronomy group discovered a radio pulsar, and subsequently an X-ray pulsar was found in 1971 (Giacconi et al. 1971). This series of discoveries of pulsars revealed the existence of the neutron star. Now a days, hundreds radio pulsars (e.g. Lyne & Graham-Smith 1998) and about a hundred X-ray pulsars (e.g. Bildsten et al. 1997; Liu, van Paradijs & van den Heuvel 2000) are known to be neutron stars. The pulsar observations have been performed at various wavelength, radio, optical, X-ray, γ-ray and so on. According to these observations and theoretical researches, the physical parameters of typical neutron stars, masses M NS and radiuses R NS, are inferred as g and 10 6 cm, respectively. In addition, it was revealed that some neutron stars have strong magnetic fields, typically G. Several methods have been used to measure intense magnetic fields of pulsars, The representative method in radio pulsars is to utilize the pulse period and its derivative (see Section 2.3) assuming magnetic dipole radiation. Using this method, we can infer that the magnetic field strength on pulsar poles are G. In contrast, another method is used for accreting X-ray pulsar. If the pulsar has G, it is expected that the electron cyclotron resonance on the polar caps of pulsars is observed in X-ray band. We can confirm this phenomenon in 1

7 2 CHAPTER 1. INTRODUCTION X-ray spectra as absorption feature, and the resonance energy directly provides us the magnetic filed strength (see Section 2.4). It is widely considered that the location where the cyclotron resonance occurs is close to the pulsar surface. In 1990 s, Japanese third X-ray satellite Ginga performed the first systematic observation to search for the cyclotron feature in X-ray spectra of accreting pulsars (e.g. Mihara 1995). The observations revealed that the 11 accreting X-ray pulsar have cyclotron resonance feature in their X-ray spectra, and the obtained magnetic filed strength are G. This directly obtained field strength is in a good correspondence with the result of radio pulsar observations. So far, it had been believed that the observed resonance energies are unchanged. However, one of the transient accreting pulsar, named 4U , exhibited the resonance energy change by a factor of 1.5 when the source luminosity changed by a factor of 1/7. In order to explain this phenomenon, a model was proposed in the previous researches (e.g. Mihara et al. 2004), but the model was not able to describe the change well. Moreover, the details of the cyclotron resonance change is still unknown, since the observations were only twice. The aim of this thesis is to reveal the change of the magnetic field strength in detail. According to the previous study, it might be considered that the large X-ray luminosity change acts a significant role on the change of the magnetic filed strength. Thus, we concentrate on the data analysis when the source exhibits the large flux change. Here, we analyze two accreting X-ray pulsars, 4U and X , acquired with RXTE. In Chapter 2, we review the brief history of X-ray astronomy, X-ray pulsars and the electron cyclotron resonance. The instruments utilized in this thesis is explained in Chapter 3. The description of observational information appears in Chapter 4. The Chapter 5 and 6 are dedicated to the analysis of X-ray pulsars, 4U and X , respectively. The discussions are described in Chapter 7, and summary is in Chapter 8.

8 Chapter 2 Review In this chapter, we first review a brief history for X-ray Astronomy. Second, we outline highly magnetized neutron stars, which are the main subject of this thesis. 2.1 Brief History of X-ray Astronomy Before the mid 20th century, it was unknown that celestial objects except the sun emit X-rays. Ricald Giacconi and his collaborators first attempted to observe the fluorescent X-rays from the moon with Geiger counter onboard an Aerobee rocket on 1962 June 18. Unfortunately their attempt did not succeed, but more fortunately they discovered the X-ray emission from the source outside the solar system (Giacconi et al. 1962). Subsequently, this source was identified with Sco X-1 which is well known as the brightest X-ray source. This discovery led to start the X-ray astronomy, and Giacconi received Nobel prize for physics in Since then about 40 celestial objects were discovered with rocket and balloon X-ray experiments by the end of 1960 s. Next decade, the new observational attempt was carried out. On 1970 December 12, the first X-ray satellite, UHURU, was launched into earth orbit (Giacconi et al. 1971a). Using two proportional counters with collimator onboard UHURU, the all-sky survey observations were performed, and the discovered 339 X-ray sources were listed as the 4U catalog (Forman et al. 1976). In addition, the first imaging capability spacecraft, named Einstein, was launched on 1978 November 12. This satellite allowed us to observe extended celestial objects, for example, supernova remnants. Now a days, several X-ray satellites, Japanese fifth X-ray satellite Suzaku, Chandra, XMM Newton, INTEGRAL, Swift, HETE-II and RXTE which is the main instruments in this thesis, are op- 3

9 4 CHAPTER 2. REVIEW erated. 2.2 Neutron Stars and Pulsars In 1932, James Chadwick first discovered neutron, as predicted by Rutherford. After the discovery, two astrophysicists, Walter Baade and Fritz Zwicky, tentatively proposed the new idea in 1934; a very small object mainly composed of neutrons is left after the supernova which is the last phenomenon of stellar evolution. The existence of the neutron star had been not confirmed for 30 years. This is because the predicted neutron star size is small (R NS 10 km), so it was considered that the optical flux is too faint to observe. In 1967 July, radio astronomers, Hewish and Bell, started to search for the fluctuation of radio signals caused by solar wind. In order to detect the short time scale variation, the temporal resolution of the instruments were improved drastically. When the observations were started with this instruments, Bell found the periodic radio signals in the recorder charts. Subsequent observations showed that the periodic radio signals occurred with s period, as shown in Figure 2.1. This object was named pulsar by shortening pulsating radio source, and it was identified as a rotating neutron star (e.g. Hewish at al. 1968). Subsequent observations made by UHURU confirmed the existence of X-ray pulsars (Giacconi et al. 1971b). Figure 2.1: The chart of the first pulsar observation. The thick line represents the radio flux from the pulsar.

10 2.2. NEUTRON STARS AND PULSARS The classification of pulsars The pulsars are divided into two group, according to whether the radiation energy is extracted from rotation, or the mass accretion from companion star. The former type is called rotation powered pulsar, and the later is accretion powered pulsar. Below, we briefly outline the two class of pulsars Rotation powered pulsars Most pulsars belong to this group, and over 700 pulsars are known (e.g. Taylor et al. 1993; Lyne & Graham-Smith 1998). Since they emit the radio signals, they are called radio pulsar. The rotation periods of rotation powered pulsars are widely distributed from millisecond order to several seconds. Pulsars with a shorter period does not exist due to destruction of a star by centrifugal force, and are with longer pulse period is not observed due to too weak radiation. Using rotational energies and magnetic fields, they emit non-thermal electromagnetic radiation which is pulsed at their rotation periods. The rotation powered pulsars always exhibit the spin down, and is considered that the radiation energy is extracted from the rotation energy. When the radiation occurred through the magnetic dipole radiation, the radiation luminosity L d is described as L d = 2 ( ) BR 3 2 (2π ) 4 NS sin 2 θ 3c 3 2 P = ( B G ) 2 ( ) 6 RNS P 4 erg s 1, (2.1) 10 6 cm where c is the speed of light, B is magnetic field strength at pulsar surface, R NS is radius of pulsar, P is pulse period, and θ is an angle between rotation axis and magnetic axis. In the second line, θ is assumed π for simplicity. On the other hand, the loss of rotation energy 2 Ėrot with a typical moment of inertia I g cm 3, is described as Ė rot = 4π2 IP P 3 ( ) = I g cm 3 ) ( ) P 3 ( 1 s P s s 1 erg s 1, (2.2) where P is the time derivative of P. When the L d is equal to Ėrot, a magnetic field strength B is described as B G = (P P) 1 2 = 3.1 ( P s s 1 ( I g cm 3 ) 1 2 ( ) P 1 ( 2 1 s ) 1 ( 2 R NS 10 6 cm I g cm 3 ) 3 ) 1 2 ( R NS 10 6 cm ) 3. (2.3)

11 6 CHAPTER 2. REVIEW Thus, by measuring a pulse period and its time derivative, we can infer a surface magnetic field of a rotation powered pulsar. Since the typical P and P of radio pulsars are s and s s 1, respectively, the estimated radio pulsar magnetic fields are in the G range Accretion powered pulsars The first observational confirmation of the existence of the accretion-powered pulsars was made by UHURU (Giacconi et al. 1971b). Cen X-3, which is the first discovered accretion-powered pulsar, showed X-ray pulsations, and it was considered that the modulation of the pulse period is generated by its orbital motion of the pulsar (Schreier et al. 1972). In subsequent optical observation, the binary companion of Cen X-3 was identified as O6-O8 type supergiant, V779 Cen (Krzeminski 1974; Hutchings et al. 1979). Since then 100 accretion-powered pulsars have been found. Since they exhibit X-ray pulsation, they are called X-ray pulsar. The summary of the fundamental studies of accretion-powered pulsars are described in some articles (e.g. White et al. 1983; Bildsten et al. 1997). As mentioned above, accretion-powered pulsars exist in closed binary systems. The pulsar accretes the matters from binary companion via the stellar wind or through the Roche lobe overflow. Through these processes, the accretion disk is formed around the pulsar. Due to sufficient high temperature (typically 10 7 K) of the accretion disk, accreted matters are completely ionized. As the matter approaches the pulsar, the accretion stream is disrupted by the intense magnetic field of the pulsar. This occurs at a certain radius, called Alfven radius r A. At this radius, these two forces, ram pressure p ram and magnetic pressure p mag, become equal; p ram = ρv 2 (2.4) p mag = B2 ( 8π B 2 = s 8π ) (RNS r ) 6, (2.5) where ρ is a mass density, v is a infall velocity, B s is magnetic field strength at a pulsar surface. The infalling velocity v from the infinite at radius r is described as v = (2GM NS /r) 1/2, where G is the gravitational constant and M NS is mass of the neutron star. In addition, assuming the spherical mass accretion, the mass accretion rate M is given 4πr 2 ρv. Thus, Alfven radius r A

12 2.2. NEUTRON STARS AND PULSARS 7 Figure 2.2: A schematic of pulsar magnetosphere and accretion disk (Ghosh & Lamb 1972). is given as ( ) 4/7 ( ) 1/7 ( ) 12/7 ( ) 2/7 r A Bs MNS RNS M. (2.6) G g 10 6 cm g s 1 Figure 2.2 shows a schematic cross-section view of the accretion disk and pulsar magnetosphere. Within Alfven radius, accretion matter is forced to follow the field lines, and finally falls onto magnetic poles. When the accreting plasma reaches at the surface of the neutron star, it gains considerable kinetic energy, and the energy is released as radiation. Accretion luminosity L acc is written as L acc = GM NSM R NS ( ) ( M NS 10 6 ) cm M erg s 1. (2.7) g Although the luminosity becomes bright as the mass accretion rate increase, there is a certain upper limit on luminosity. If the spherical mass accretion occurs, the outgoing radiation pressure is not negligible; Thomson scattering become important for the accreted matter, electrons. The radiation pressure at distance from the pulsar center r is described as σ T L/(4πr 2 c), where σ T is the Thomson cross section, cm 2, and L is a source luminosity. This radiation pressure is transferred to the protons by the electrostatic forces between the proton and the electron. Then the inward gravitational force is described as GM NS (m p +m e )/r 2 GM NS m p /r 2, where m p and m e are the proton and electron mass, respectively. At low luminosity, the gravitational forces which acts upon the accretion materials are greater than the radiation pressure, and the accretion stream is not disrupted. When the luminosity become a certain R NS level, called Eddington luminosity, these two forces become equal, Lσ T 4πr 2 c = GM NSm p r 2, (2.8)

13 8 CHAPTER 2. REVIEW Figure 2.3: This figure shows the accretion flow near the stellar surface showing the infalling material, shock, settling mound material and emergent radiation. The figure from Burnard et al. (1991). L Edd = 4πGM NSm p c σ T = ( MNS g ) erg s 1. (2.9) (2.10) When the source flux reaches the Eddington luminosity, the accretion materials are blown up away by the intense radiation pressure, and can not fall onto pole. In case of the highly-magnetized pulsars, the accretion flows concentrate in the small fraction of the pole (Figure 2.2), the resulting maximum luminosity might become smaller than L Edd. Assumed such a situation on the magnetic pole is shown in Figure 2.3. Although the maximum luminosity is assumed to be smaller than L Edd to upward, in fact, the radiation can escape sideways without exerting too much pressure on the infalling materials. Thus, the source can radiate over Eddington luminosity level sideways. The mass accretion does not always occur in all accretion-powered pulsars. Some of accretion-powered pulsars, for example Cen X-3 and second discovered accreting pulsar Her X-1 (Tananbaum et al. 1972), exhibit the continuous mass accretion, that is to say continuous X-ray emission occurring. This type of accretion-powered pulsars have approximate circular

14 2.2. NEUTRON STARS AND PULSARS 9 Figure 2.4: The broadband energy spectrum of Her X-1 is shown as the representative spectrum of the accretion powered pulsar. The cyclotron absorption feature is seen around 40 kev. The data was observed with BeppoSAX, and figure from dal Fiume et al. (1998). orbits and the pulsars go around near the companion star. These pulsars are persistent sources and the pulsars can accrete the matters continuously, and these typical luminosities are erg s 1. In contrast, there is another type of sources which occasionally exhibit the X-ray emission. This type is called transient pulsar. The transient pulsar usually has an eccentric orbit around a companion star. When the pulsar approach the companion star, the pulsar can accrete the matters from the companions star and form the accretion disk. At periastron passage, the transient sources emit large X-ray and the X-ray outburst will be observed. When the pulsar leaves periastron for apastron, the provision of the material is suspended and the mass accretion rate M decreases. Accordingly, the source luminosity becomes faint and then the source keeps low flux level until the next periastron passage. The most of accretion-powered pulsars emit X-rays. The representative X-ray spectrum of the accretion powered pulsar is shown in Figure 2.4. As shown Figure 2.4, X-ray spectra of the accretion powered pulsars are generally characterized by flat shape, steep cutoff at higher energy band and cyclotron absorption feature. And also, the spectrum often exhibits the photoelectric absorption below several kev. These X-ray spectra are traditionally modeled with power-law times exponential cutoff model (PLCUT; e.g. White at al. 1983) as { 1 (E P LCUT (E) = AE Γ Ecut ) exp( N H σ(e)) exp( E Ecut E fold ) (E > E cut ) (2.11)

15 10 CHAPTER 2. REVIEW Here E is the X-ray energy, Γ is the photon index, E cut is the energy where the spectrum breaks ( cutoff energy ), E fold is folding energy describing the cutoff steepness, N H is the equivalent hydrogen column density and σ(e) is the cross section of photoelectric absorption due to the cold matter of cosmic abundance (Morrison and McCammon 1983). In addition to the continuum, X-ray pulsar spectrum often exhibits the fluorescent iron K-lines at 6.4 kev for K α and 7.05 kev for K β (Makishima et al. 1986; Nagase 1989). This model (Equation 2.11), however, cannot reproduce the data completely at E = E cut (Makishima et al. 1990b). Thus, the improved model was proposed, called FDCO model, by Tanaka (1986) as F DCO(E) = AE Γ exp( N H σ(e)) exp {(E E cut )/E fold }. (2.12) Though this model is similar to Fermi-Dirac distribution function, it is purely an empirical one. Mihara (1995) proposed a new continuum model of accretion powered pulsars. It is composed of two power-laws, as ( NP EX(E) = exp( N H σ(e)) (A 1 E α 1 + A 2 E +α 2 ) exp E ), (2.13) kt where A 1, α 1, A 2, α 2 and kt are positive parameters, and k is Boltzmann constant. Thus, the model consists of Negative and Positive power-laws with EXponential cutoff, and hence this model is called NPEX model. In contrast to previous model, this NPEX model has physical meanings; kt represents the typical temperature of the X-ray emitting region, and positive power-law with α 2 = 2.0 describes a Wien peak (Rybicki & Lightman 1979). The detail explanations of this model is described in Mihara (1995) and Makishima et al. (1999). In this thesis, we utilize this model for the continuum of the accretion-powered pulsars. 2.3 Magnetic Fields of Pulsars As mentioned in Section 2.2, it have been believed that pulsars possess surface magnetic fields of an order of G. This consideration based on the magnetic flux conservation when the formation of the pulsar occur by the supernova collapse (Woltjer 1964; Hoyle, Narlikar & Wheeler 1964; Pacini 1967). During supernova collapse the suppercurrent is induced in the neutron star crust (e.g. Lamb 1991), and it is considered that the suppercurrent is decayed by ohmic dissipation. Hence, the evolution of the magnetic fields have been considered that pulsars are born with intense magnetic fields and the magnetic fields decay with time (van den Heuvel 1991). Although the above evolution scenario is widely accepted, the other scenarios

16 2.4. CYCLOTRON RESONANT FEATURE 11 are proposed (e.g. Srinivasan 1990; Jones 1991). In order to make this point clear, we need to perform further observations of magnetic field of neutron stars. In order to estimate the surface magnetic field strength from observations, several methods have been used so far. As described in Section 2.2.2, the field strength of rotation-powered pulsars have been inferred with the pulse period and its time derivative (see Equation 2.3). However, this method estimates an approximate field strength, and it can not apply to the accretion-powered pulsars, because the pulse periods of accretion-powered pulsars are spun up or down by the momentum of the accreted matters (e.g. Bildsten et al. 1997). To estimate the magnetic fields of the accretion-powered pulsars, Ghosh & Lamb (1979) proposed Accretion torque theory. If the accretion is in an equilibrium, this model can estimate the magnetic fields with observed pulse periods and the measured X-ray luminosity, as µ 30 P 7/6 L 1/2 37 R 1/2 NS M 1/3, (2.14) where µ 30 is magnetic moment in unit of G cm 3 and L 37 is X-ray luminosity in unit of erg s 1. However, this model is applied only the condition when the angular velocity, with which the magnetic fields rotate rigidly with the pulsar, is equal to the Keplerian angular velocity at Alfven radius. A direct way to estimate the magnetic fields from observations is to measure the cyclotron absorption energies in the X-ray spectra as described in the next section. 2.4 Cyclotron Resonant Feature In the accretion column which is formed on the pulsar pole, a certain energy photon is scattered by the electrons in material. This phenomenon appears as an absorption line feature in the X-ray spectrum. The feature energy provides us the magnetic field strength on the pulsar pole. This cyclotron resonant phenomenon have been well studied by many authors (e.g. Meszaros 1992; Nagel 1980). Here, we briefly explain the electron cyclotron theory. Electrons in an uniform magnetic field can move along the field lines, while the motion perpendicular to the fields is constrained to a circular orbit. Its radius r cyc is given as r cyc = v ω cyc = m ev eb, (2.15) where ω cyc is the cyclotron frequency, m e is the electron mass, v is the velocity perpendicular to the magnetic fields, e is the charge of electron and B is the field strength. Under the typical

17 12 CHAPTER 2. REVIEW field strength ( G) on the pulsar pole, r gyration gets smaller, and this value becomes close to de Brogile wavelength as λ de Brogile = h mv, (2.16) where h is the rationalized Plank constant. Then the effect of the quantum mechanics become important in such condition, and the kinetic energy of an electron perpendicular to the field is quantized discrete levels called Landau levels. The n-th Landau level is described as E n = (n + 1 ) 2 + s E a (n = 0, 1, 2,...), (2.17) where s = ± 1 2 is the electron spin. E a1 is the cyclotron energy as Thus the n-th cyclotron energy is given as E a = hω cyc = heb m e, (2.18) E a n = ne a (n = 1, 2, 3,...) = n heb m e E a n [kev] = 11.6 n B G. (2.19) The life time of the electrons excited into higher Landau level is very short; the typical radiative-decay time scale is s (Latal 1986). An excited electron immediately de-excites by emitting a photon with hω cyc = E a n as it falls to ground level (n = 0). The resonant energy E a1 is usually called the fundamental resonance energy, and E a2, E a3 are called second, third resonance energy, respectively. Since the photon is immediately emitted after being absorbed by the electron, this process is a scattering rather than an absorption. Therefore, these features are designated as Cyclotron Resonant Scattering Features (hereafter CRSFs). In some case, electron in the higher harmonics (n = 2, 3,,) decays by fundamental transitions (cascade). Then higher harmonics absorption or emission line appears at the fundamental energy. Since the electron cyclotron scattering occur near the pulsar surface, the effect of the gravitational redshift becomes important. The observed cyclotron resonance energy is less than true energy, as E obs a n = E a n (1 + z g ) 1, (2.20) where ( (1 + z g ) 1 = 1 2GM NS R NS c 2 ) 1 2. (2.21)

18 2.4. CYCLOTRON RESONANT FEATURE 13 Figure 2.5: Cyclotron scattering cross sections for a magnetic field strength of 0.04B cr which corresponds to G. The µ represents cos θ. The θ is the angle between the photon propagation and the magnetic field. As the angle θ decrease, in other wards increasing ν, the cross sections become broad and shallow feature. It is considered that the thermal motion of the electron along the field lines caused this feature. This figure from Araya & Harding Using Equation 2.21 with M NS = g and R NS = 10 6 cm, we obtain (1 + z g ) 1 = Therefore, the observed magnetic field strength is 20 30% less than true field strength at the pulsar surface. In relativistic regime, the n-th Landau levels are described as (Harding & Daugherty 1991) E n = m ec 2 { ( ) } B sin n sin 2 θ 1, (2.22) θ Bcr where θ is angle of the incident photon to the magnetic field and B cr is the critical magnetic field strength as B cr = m2 c c3 he = G. (2.23)

19 14 CHAPTER 2. REVIEW Figure 2.6: The result of Monte Carlo simulations by Araya-Góchez & Harding (2000). Above panels show the comparison between cone and isotropic injection for coin shape and cylindrical geometries. The source spectrum is shown as dotted lines, the emergent spectrum as solid lines. On each panel, four lines represent different cos θ (from top to bottom): cos θ > 0.75, 0.75 > cos θ > 0.5, 0.5 > cos θ > 0.25, and cos θ < This formula indicates that the observed resonance energy decreases with increasing the angle θ by several %. Figure 2.5 shows the cyclotron scattering cross section (Araya & Harding 1999). This cross section depends on the angle between the photon propagation and the magnetic field, the polarization of the incoming and outgoing photon. Using these calculations of the cyclotron cross sections, many authors (Araya & Harding 1999; Araya-Góchez & Harding 2000) attempt to predict the shape of the cyclotron resonant features, as shown in Figure 2.6. According to these simulations, the cyclotron features show a much more complicated behavior depending on the various condition, such an angle of incident photon to magnetic field.

20 2.4. CYCLOTRON RESONANT FEATURE 15 These simulations have shown that the shape of the cyclotron resonant features in the X- ray spectra are strongly affected by the magnetic fields strength, source geometries, and the viewing angle. In order to reproduce the cyclotron resonant features in the observed X-ray spectra, several analytic CRSF models have been used in the X-ray spectral analysis. One of the CRSF models is Gaussian absorption model (GABS) (e.g. Coburn et al. 2002) as GABS(E) = τ c { exp 1 2 ( ) E 2 } Ec, (2.24) σ c where E c is the cyclotron resonance energy, σ c is the cyclotron line width, and τ c is the optical depth at resonance. This function is multiplied to the continuum model as I(E) I 0 (E) exp {GABS(E)}. (2.25) Another analytic form of the CRSF feature is the CYclotron ABsorption model or CYAB model (Mihara 1995; Makishima et al. 1999) described as CYAB(E) = D (W E/E a) 2 (E E a ) 2 + W 2, (2.26) where E a1 is the cyclotron resonance energy, W is the width of the cyclotron feature, and D is the depth of the resonance. This model also modifies the continuum spectrum as exp {CYAB(E)}, same as GABS model. In this thesis, we utilize this model for the CRSFs. This Lorentzian-like shape function is derived from the consideration which is based on the Thomson/Compton cross sections in a magnetized cold plasma (Ventura 1979; Rybicki & Lightman 1979). In a cold plasma, W is purely the natural width. By applying E t = h, W can be estimated to be 10 ev. However, W obtained from the observations is larger than it. A reason would be the thermal Doppler effects or the geometrical effects might make the absorption feature broad. The first observational confirmation of the evidence of the cyclotron resonance feature was made by Balloon-HEXE experiment (Trümper et al. 1978). The second discovered X-ray pulsar, Her X-1 (Tananbaum et al. 1972), showed a remarkable feature at 40 kev in the X-ray spectrum, as shown in Figure 2.7. As shown in the figure, the cyclotron features were first recognized as the emission lines around 50 kev. However, the following observations made by HEAO-1 (Voges et al. 1982) and Ginga (Mihara et al. 1990) revealed that the cyclotron lines in the spectrum of Her X-1 were not emission features but absorption features. After the discovery of the CRSF in Her X-1, the recurrent transient source, 4U , exhibited the cyclotron feature at 20.1 kev in absorption, detected by HEAO-1 A4 (Wheaton et al. 1979). Subsequent detailed re-analysis with A2 instrument, White et al. (1983) revealed that 20 kev feature is in fact the second harmonic feature, and the fundamental resonance

21 16 CHAPTER 2. REVIEW Figure 2.7: The count rate spectra of Her X-1. The prominent cyclotron feature is seen around 40 kev. Arrows represent the lower-threshold due to the atmospheric absorption. This figure from Trümper et al. (1978). feature exists at 11.5 kev. Until the mid-1980s, these cyclotron features were discovered from only two accretion-powered pulsars, so the CRSFs were considered to be rare phenomena. In early 1990s, Japanese 3rd X-ray satellite Ginga performed the first systematic search for the CRSFs in the X-ray spectra of accreting pulsars (Mihara 1995). Accordingly, 11 cyclotron sources were newly discovered and the CRSFs are recognized as the common phenomena in accretion-powered pulsars. Following X-ray satellite missions, for example RXTE (see Chapter 3), BeppoSAX (e.g. Boella et al. 1997) and INTEGRAL, search for the cyclotron features in accretion powered pulsars. So far, the evidence of 14 cyclotron sources are discovered, and 3 cyclotron candidate sources are found. The summary of the observational results are given in Table 2.1.

22 2.4. CYCLOTRON RESONANT FEATURE 17 Figure 2.8: The pulse-phase-resolved spectrum of 4U observed with RXTE (Heindl et al. 2004). The cross marks in the upper panel represent the count spectrum, and the solid line is the unfolded model curve. The five cyclotron resonant features are clearly observed. Although new cyclotron sources are not discovered from recent observations, the study of the CRSFs parameters have been advanced. Many authors examine the correlations between the CRSFs parameters (e.g. Mihara 1995; Makishima et al. 1999; Coburn et al. 2002; Kreykenbohm et al. 2004), and the interesting relations have been found. In addition, the source which exhibit five cyclotron resonant features was found by RXTE and BeppoSAX (Heindl et al. 1999; Santangelo et al. 1999). Figure 2.8 shows the pulse-phase-resolved spectrum of 4U In the following sections, we investigate the peculiar behavior of 4U

23 18 CHAPTER 2. REVIEW Table 2.1: Summary of all cyclotron resonance energies. Object name Ea References (instrument) kev 4U , 24.1, 34.5, Wheaton et al. (1979, HEAO-1) Heindl et al. (1999b, RXTE) Santangelo et al. (1999, BeppoSAX) 4U , 38 Makishima et al. (1992, Ginga) Cusumano et al. (1998, BeppoSAX) 4U Clark et al. (1990, Ginga) Vela X-1 24, 52 Kendziorra et al. (1992, Mir-HEXE) Kreykenbohm et al. (2002, RXTE) X , 49, 74 Makishima et al. (1990, Ginga) Coburn et al. (2005, RXTE) Kreykenbohm et al. (2005, INTEGRAL) Cep X-4 28 Mihara et al. (1991, Ginga) Cen X-3 29 Santangelo et al. (1998, BeppoSAX) Heindl & Chakrabarty (1999c, RXTE) X Per 29 Coburn et al. (2001, RXTE) MX Heindl et al. (2003, RXTE) XTE J Heindl et al. (2001, RXTE) 4U Orlandini et al. (1998, BeppoSAX) Heindl & Chakrabarty (1999c, RXTE) GX Mihara (1995, Ginga) Her X-1 41 Trümper et al. (1978, Ballon-HEXE) A , 110 Kendziorra et al. (1992, 1994, HEXE) Kretschmar et al. (2005, INTEGRAL) Wilson & Finger (2005, RXTE) Inoue et al. (2005, Suzaku) GS ? Mihara (1995, Ginga) OAO ? Orlandini et al. (1999, BeppoSAX) LMC X-4 21?, 100? Mihara (1995, Ginga) Barbera et al. (2001, BeppoSAX)

24 2.5. CHANGE OF RESONANCE ENERGY Change of Resonance Energy By HEAO-1, Ginga, BeppoSAX and RXTE, a number of pulsars which have cyclotron features in their spectra were discovered. So far, it have been believed that the cyclotron feature energies are unchange, because the magnetic field strength is proper to a neutron star and the resonant scatterings occur near the neutron star surface. However, an exception was found by Ginga in 1991 (Mihara et al. 2004) U As described in Section 2.4, 4U is the second accretion powered pulsar exhibiting the cyclotron resonance. Since the CRSF discovery made by HEAO-1, this source has been observed with many satellites, and the fundamental resonance energy has been measured repeatedly at 11 kev. The example of the count spectrum of 4U observed with LAC on board Ginga in 1990 is shown in the left panel of Figure 2.9 (Mihara et al. 2004). The residuals shown in the bottom panel are yielded by fitting the spectrum with the continuum model without incorporating cyclotron absorption model. In April 1991, 4U caused a small outburst whose peak intensity corresponded to 1/7 of regular outburst. Ginga observed this event, and a drastic change in the CRSF was detected: instead of the familiar double absorption features at 11 kev and 22 kev, it exhibited a single deep and wide absorption at 16 kev as shown in the right panel of Figure 2.9 (Mihara 1995; Mihara et al. 1998; Makishima et al. 1999; Mihara et al. 2004). Figure 2.10 shows the cyclotron resonance energies of 4U and 2 60 kev luminosities observed so far (White et al. 1983; Nagase et al. 1991; Tamura et al. 1992; Heindl et al. 1999; Santangelo et al. 1999; Mihara et al. 2004). All of the plotted data in Figure 2.10 are evaluated with Gaussian absorption model (see Equation 2.24). Although the source have been observed at the different luminosities in each observation, the fundamental and second harmonic resonance energies did not change except for the result observed on 1991 April. Mihara et al. (2004) tentatively concluded that the fundamental resonance energy, at 11 kev in normal outbursts, increased to 16 kev, and the reason of the change is that a lower luminosity would make the accretion column shorter, and hence increase the magnetic field intensity at the column top. However, there has remained an alternative possibility that the second harmonic resonance, normally at 22 kev, decreased to 16 kev in the 1991 outburst. Furthermore, even if the former interpretation is correct, the observed change in E a1 was considerably larger than is predicted by an accretion column model by Burnard et al. (1991).

25 20 CHAPTER 2. REVIEW Figure 2.9: The pulse-phase averaged spectra of 4U observed with LAC on board Ginga (Mihara et al. 2004). (Left) The 1990 spectrum fitted with a continuum model. (Right) The 1991 spectrum fitted with a continuum model. Figure 2.10: The fundamental and second harmonic cyclotron resonance energies and 2 60 kev luminosities of 4U The resonance energies were evaluated with Gaussian absorption model. This figure from Mihara et al. (2004).

26 2.5. CHANGE OF RESONANCE ENERGY Other examples In addition to the case of 4U , Ginga observed 4 accretion-powered pulsars, X , Cep X-4, Her X-1 and 4U , when the sources exhibited the different luminosities (Mihara et al. 1998). The summary of the previous observational results are shown in Table 2.2. In these observations, X only showed the fundamental resonance energy change together with the X-ray luminosity except for 4U The fundamental resonance energy of X increased from 27 kev to 30 kev as the source luminosity decreased. In contrast, the other sources, Cep X-4, Her X-1 and 4U , did not exhibit the resonance energy change when the source X-ray luminosity changed. On the other hand, Gruber et al. (2001) analyzed the long monitored Her X-1 data observed with RXTE and HEAO-1, and he reported that the fundamental resonance energy of Her X-1 exhibited 23% historical change instead of the luminosity related change. Thus, the resonance energy change mechanism is still ambiguous. Table 2.2: The cyclotron resonance energies with luminosities. The table from Mihara et al. (1998). Objects count rate E a1 Lx date [c s 1 ] [kev] [10 37 erg s 1 ] 4U kev 1990/2/ ± 0.6/22.1 ± /4/ ± X kev 1989/10/ ± a 1989/9/ ± a Cep X kev 1988/4/ ± /4/ ± /4/ ± Her X kev 1990/7/ ± /6/ ± /6/ ± /5/ ± U kev 1988/3/ ± /7/ ± a Estimated with the assumed distance 3 kpc.

27 22 CHAPTER 2. REVIEW Figure 2.11: This plot shows the observed cyclotron resonance energies and X-ray luminosities extracted from Table 2.2.

28 Chapter 3 Instrumentation In this chapter, we describe the instruments utilized in this analysis. Our purpose is as described in the end of Chapter 1 to reveal how the cyclotron resonant scattering features (CRSFs) observed in X-ray spectra of binary pulsars behave as the source luminosities change. For that purpose, data observed at various X-ray luminosity levels are needed. In addition, the data have to be obtained by a detector which have a broad-band energy sensitivity to cover the cyclotron resonance energies, typically 10 to 50 kev (Table 2.1). One of the scientific satellites satisfying our requirement is Rossi X-ray Timing Explorer (hereafter RXTE). 3.1 Rossi X-ray Timing Explorer RXTE, launched into a circular orbit of altitude 580 km and 23 inclination on 1995 December 30, was constructed to observe the rapid variations of the celestial objects; black holes, white dwarfs, pulsars and so on. RXTE also aims for the repeated monitoring of variability of transient sources in long term. This satellite was named Rossi after Bruno B. Rossi, who is a astrophysicist and discovered the first cosmic X-rays with his collaborators. The schematic view of RXTE is shown in Figure 3.1. RXTE have two types of scientific instruments; the pointed instruments, named PCA and HEXTE, and another is the all-sky monitor camera, named ASM. The detailed descriptions of these instruments will be appeared in next sections. RXTE employs the short-term observations on many sources within a day. In order to perform this operation, RXTE can maneuver as quickly as 6 /minute. Also, the rotatable solar panels onboard RXTE enable the spacecraft to observe any region of the sky, except for the area within 30 of the sun. This performance meet the requirement for our purpose. The pointing accuracy is < 0. 1, with knowledge of aspect from star trackers and gyroscopes to 1. 23

29 24 CHAPTER 3. INSTRUMENTATION Figure 3.1: RXTE schematic view The observed data is put in temporary storage with capacity of 906 Mbits. Those data are sent via NASA s TDRSS (the Tracking Data Relay Satellite System) or the communications with the ground high-gain antennas. The downlink rates are 20 kbps for TDRSS and 256 or 512 kbps for the high-gain antennas. The communication between the spacecraft and TDRSS or the ground station is 24 hours or 30 min a day, respectively. It is known that there are some radiation and particle belts, named van Allen belts, around the earth. These belts with altitude from 2,000 to 10,000 km were discovered by the first American satellite (e.g. van Allen et al. 1958). These belts seriously affect the instruments onboard X-ray satellites. Since RXTE was launched into low earth orbit, which is under the lowest belt, RXTE is not exposed to the intense particles and radiations. However, there are another radiation anomaly zone around the the south Atlantic, southeast off the coast of Brazil, due to the different magnetic field configurations. RXTE passes through this zone, named South Atlantic Anomaly (SAA) several times per day. During the spacecraft passes through the SAA, the detectors onboard RXTE turn off until the spacecraft emerges from the SAA. The effects of the SAA for the detectors are explained in next Section. Although ten years from the launch have caused, some problems on the instruments, the current status of RXTE is good overall.

30 3.2. POINTED INSTRUMENTS Pointed Instruments RXTE carries two type of pointed instruments, Proportional Counter Array and High Energy X-ray Timing Experiment. Those two instruments are co-aligned to the identical pointing field of view. Below, we describe the basic properties of two instruments Proportional Counter Array Figure 3.2: The PCA assembly (Left), and a schematic cross section of a PCU (Right). The Proportional Counter Array (hereafter PCA; Jahoda et al. 1996) was constructed by NASA s Goddard Space Flight Center. The PCA assembly is shown in the left of Figure 3.2. The PCA is composed of 5 co-aligned identical proportional counter units (PCUs). In order to extend the detector life time, some of the PCUs were not operated in observations. The nominal energy sensitivity of the PCA is 2 60 kev with energy resolution of < 18 % at 6 kev. The right of Figure 3.2 shows the cross-section view of one PCU. The PCU consists of a hexagonal collimator of beryllium copper and a multi-anode proportional counter (the basic theories of the proportional counters are summarized in a numerous articles. e.g. Charpak and Sauri. 1979; Knoll 1979). Each PCU have 241 Am source which provide the calibration line. The field-of-view of PCU is collimated to a 1, and the unabsorbed X-ray detecting area is 1600 cm 2. The Xenon (90%) which act as a main absorber and Methane (10%) gas are contained with 860 torr in a PCU at 22 C. In addition, propane layer which is put above Xenon volume acts as a Veto layer. The Xenon volume is divided into three layers, as shown in the right of Figure 3.2. Approximately 90 % of low energy (< 10 kev) photons are absorbed within the top layer. Figure 3.3 shows the effective area of the PCA. In order to avoid the effect of Xe K-edge

31 26 CHAPTER 3. INSTRUMENTATION around 30 kev, we use < 30 kev data in our analysis Effective Area (cm 2 ) 10 3 All Layers Top Layer Energy (kev) Figure 3.3: The effective area of PCA. The solid line indicates the effective area of all layer, while the dashed line is only top layer. Around 30 kev dip is effect of Xe K-edge, and low efficiency at low energy side is caused by Propane layer. The PCA background is composed of three components; the charged particles, the internal background, and the diffuse cosmic X-ray background. The charged particles events depend on the location of the satellite and the time. The internal backgrounds are induced by charged particles or high-energy γ-rays, and it is especially enhanced during the SAA passage. The diffuse cosmic X-ray background is believed to consist of unresolved AGN and other weak X- ray sources within 1 field-of-view. The charged particles events are sufficiently reduced by the effective anti-coincidence schemes, including side and rear veto chambers and top propane layer. The rest of two component events are left upon the acquired data, and are to be determined by a model. The background model is computed based on parameters measured at the time of the blank-sky observations, and describing the condition and the position of the spacecraft and also the exponential decay of the activation materials after the SAA passage. Figure 3.4 shows the estimated PCA background spectrum. The remarkable features around 4 and 30 kev are due to the Xe L and K-edge. The diffuse cosmic X-ray component is included in the shape of power-law. All event acquired from PCA passes to Experiment Data System (EDS). The EDS is composed of 8 independent computers as Event Analyzers (EAs). The six EAs are dedicated to the PCA, and the other two EAs are All Sky Monitor. The two of EAs dedicated to the PCA produce the PCA standard mode data. One EA generate the data which has a temporal res-

32 3.2. POINTED INSTRUMENTS 27 Figure 3.4: PCA Background spectrum which is composed of cosmic X-ray background and unrejected instrument background. The line-like structure around 5keV is caused Xe L-edge, and also the Xe K-edge feature appears around 30 kev. The other line-like features are caused by the activated various material of the spacecraft. olution of sec and no spectral information, called Standard-1 data. Another data, called Standard-2 data, has a temporal resolution of 16 sec and 129 pulse height analyzer for each PCU. In our analysis, we employ the Standard-2 data mode and the top-layer only. Table 3.1: The properties of the PCA Energy range 2 60 kev Energy resolution < 18% at 6 kev Time resolution 1µsec Spatial resolution 1 degree FWHM Collecting area 6500 cm 2 Sensitivity 0.1 mcrab Background 2 mcrab

33 28 CHAPTER 3. INSTRUMENTATION High Energy X-ray Timing Experiment (HEXTE) The High Energy X-ray Timing Experiment (hereafter HEXTE; Rothschild et al. 1998) was built by the High Energy Astrophysics group at the Center for Astrophysics and Space Sciences of University of California. The whole HEXTE assembly is shown in the left of Figure 3.5. The HEXTE consists of two set of clusters of detectors, named cluster A and cluster B. The nominal energy range is kev with energy resolution of 15.4% at 60 kev. The net open area of the two clusters of detector is 1600 cm 2. One cluster consists of four NaI/CsI scintillation counters with a 1 field-of-view. A cutaway illustration of 1 counter is shown in the right of Figure 3.5. One scintillation counter is composed of a lead honeycomb collimator, the NaI/CsI crystal and a photomultiplier tube. Figure 3.5: The HEXTE assembly (Left), (Right) The nominal effective area of one cluster is 800 cm 2, however, one of the pulse height analyzer in cluster B failed on 1996 March 21, so that the effective area of cluster B is 3/4 of nominal value. The present effective area of both clusters are given in Figure 3.6. The HEXTE background is composed of two components; the internal background induced by charged particles or high-energy γ-ray, and the diffuse cosmic X-ray background. The HEXTE acquires the real time background information by rocking the cluster subsystem. The moving direction of each cluster is shown in Figure 3.5.

34 3.2. POINTED INSTRUMENTS Effective Area (cm 2 ) 10 2 Cluster A Cluster B 100 Energy (kev) Figure 3.6: The effective area of two clusters. Table 3.2: The properties of the HEXTE Energy range kev Energy resolution 15% at 60 kev Time resolution 8 µsec Spatial resolution 1 degree FWHM Collecting area 800 cm 2 per one cluster Background 50 count/sec per one cluster Figure 3.7: background spectra of HEXTE.

35 30 CHAPTER 3. INSTRUMENTATION FOVs on sky Timing of Rocking Cycle + +Bkg + SRC Src Bkg Cluster A Cluster B Rocking Phase 1.0 Figure 3.8: HEXTE rocking interval. Figure from Coburn (2001).

36 3.3. ALL SKY MONITOR All Sky Monitor The All Sky Monitor (hereafter ASM; Levine et al. 1996) was built by the center for Space Research at the Massachusetts Institute of Technology. The ASM has been monitoring the fluxes of about 150 bright X-ray sources. Also, the ASM can identify the transient sources, both known and previously unknown, when the sources have gone into outburst. The ASM is also able to examine the source spectrum with few energy channels. Then, the unidentified source newly discovered can be inferred whether a neutron star or black hole. The observed data are immediately archived via World Wide Web (e.g. weather/). 6 cm P a rtitio 1 D M a s k, 5 0% o p e (6 s e g me ts ) 30cm 7 5 cm B e w i d o w 8 P o s itio s e s i g s ig a l a o d e s E le ctro ics 1 2 a tico i cid e ce a o d e s X e p ro p o rtio a l co u te r (d ra w o v e rs iz e ) Figure 3.9: Left diagram shows entire ASM view. Three SSCs are mounted on rotating assemblies. The centers of FOVs of two SSCs are co-aligned perpendicular to the other SSC. Right shows a schematic view of a major component of SSC. The counters are filled with a Xenon (95%) and CO 2 (5%) gas mixture at a total absolute pressure of 1.2 atm. The ASM consists of three Scanning Shadow Cameras (SSCs) mounted on motorized rotating assemblies, as shown in Figure 3.9. While the data of ASM are accumulated (typically 90 seconds), the rotating assemblies and the attitude of RXTE are fixed. During orbital and assemblies rotation, 80 % of the sky will be surveyed within a day, and also the sources randomly chosen are scanned typically five to ten times per day. One SSC is composed of the position-sensitive proportional counter and the 1-dimensional coded mask with 6 90 field-of-view. The centers of field-of-views of two SSCs are co-aligned

37 32 CHAPTER 3. INSTRUMENTATION perpendicular to the other SSC. Two SSCs are also pointed perpendicular to the field-of-views of the other instruments (PCA and HEXTE). The substantial effective area of one SSC is 30 cm 2 (at 5 kev), and the nominal energy range is kev. Figure 3.10 shows the principle of a position determination. The positions of celestial objects are able to be inferred by measuring the histograms upon the proportional counters. For the bright sources, the ASM can provide the accurate positions within Figure 3.10: The principle of ASM position determination. Energy range On-axis effective area Enclosed gas Fields of View Table 3.3: The properties of the ASM kev 10cm 2, 30cm 2 and 23cm 2 at 2, 5 and 10 kev, respectively Xe (95%) and CO 2 (5%) (total pressure 1.2 atm) 6 90

38 Chapter 4 Observations 4.1 The criterion of targets and observations selection The changes of the resonance energies of the cyclotron resonant scattering features (CRSFs) have been observed in a few sources. Previous researches (e.g. Mihara et al. 1998) suggested dependency on the source luminosities. In order to reveal how the CRSFs behave against the luminosities, we chose such targets as, targets with CRSF in their X-ray spectra, and exhibited the different resonance energies in previous researches targets which exhibited the large luminosity change, such as an outburst In this thesis, we have selected accretion powered pulsar 4U as a representative object. This source showed the large resonance energy change and frequent outbursts at intervals of few years. In addition, we have also selected accretion powered pulsar X which shows outbursts at intervals of 10 years. The details of these sources are described in following sections U Overview Here, we summarises the basic property of 4U reported by previous observations. This source was discovered by the first X-ray satellite UHURU (Giacconi et al. 1971a), and it was recognized the recurrent transient (Forman et al. 1976). Following observations made by 33

39 34 CHAPTER 4. OBSERVATIONS HEAO-1 A-2 experiment (Rothschild et al. 1979) and Ariel V All-Sky Monitor (Holt 1976), the 3.6 second pulsations were detected, and the orbital period of 24.3 days was evaluated from the Doppler variations of pulses (Rose et al. 1979, and references there in). The optical counterpart, V635 Cas, was found in the combined SAS 3 (Clark & Cominsky 1978) and HEAO-1 (Johns et al. 1978a) error boxes for 4U (Johns et al. 1978b). Further optical observation was performed by Unger et al. (1998), and V635 Cas was identified as O9e star. The distance to 4U is estimated as 7 kpc (Negueruela and Okazaki 2001). The HEAO-1 A-4 experiment (Matteson 1978) observation discovered the cyclotron resonant feature with energy of 23 kev (Wheaton et al. 1979). The detection of the cyclotron feature was the second example following Her X-1 (Section 2.3). Using the HEAO-1 A-2 experiment data obtained in the same outburst, White et al. (1983) suggested that the 23 kev feature is in fact the second harmonic resonance, with the fundamental resonance at 11 kev. This double harmonic resonant features were reconfirmed with Ginga by Nagase et al. (1991) in 1990 outburst. Next year, Ginga detected a small outburst whose peak intensity is less than 1/7 of 1990 outburst, and a single cyclotron resonance feature with the energy of 16 kev was found (Mihara et al. 1998, 2004, and Section 2.4). In 1999 outburst, the third harmonic feature was found with RXTE by Heindl et al. (1999a), and forth harmonic harmonic with BeppoSAX by Santangelo et al. (1999). Subsequently, the evidence of the fifth harmonic was suggested in pulse-phase resolved spectrum (Heindl et al. 1999b). In the RXTE data, the resonance energies were 11.8, 24.1, 34.5, 47.0 and 66.5 kev. 4U thus is the only source showing five cyclotron resonant features ASM light curves The upper panel of Figure 4.1 shows the activity of 4U in the ASM 2 12 kev energy band. Most of time, the source have been in the quiescent state. In this state, the source is not able to be observed by the pointed instruments on board RXTE. Since the RXTE observation started, the ASM have detected three outbursts with the peak intensity mcrab. This source tends to cause the periodic outburst at an intervals of few years. In this thesis, we utilize the outburst data acquired on 1999 March.

40 4.2. 4U Figure 4.1: Upper panel shows the light curves of 4U observed with RXTE ASM for 9 years. The horizontal dashed line corresponds to 250 mcrab. Enlarged light curve of 1999 outburst is shown in bottom. The vertical dashed lines indicate times of the periastron passage.

41 36 CHAPTER 4. OBSERVATIONS PCA and HEXTE pointings During this outburst, total 51 times pointing observations were made with PCA and HEXTE. The first pointing observation was performed on 1999 March 3 and the last one was on April 25. Most of the exposure time of these observations are less than 1 ksec. In order to acquire the good time intervals, we have defined the criterion of observation time, as the earth elevation angle was > 10, the offset angle of the source to the field of view center was < 0.02, and the spacecraft was not within 30 minutes of an entrance to the South Atlantic Anomaly (see Section 3.1). The variation of those parameters are shown in Figure 4.2. Also, we avoid to use the data which show the high electron contamination rate. The threshold of the electron contamination rate is recommended as < 0.1 counts s 1 by the RXTE instrument team, but its rate is sometimes corrupted by the high-rate real X-ray events. So, we visually inspected the electron-rate light curves as shown in bottom panel of Figure 4.2, and have defined it < 0.12 counts s 1. Figure 4.2 shows those examples. After the data screenings, some of the data extremely loose the exposure time. We eliminated the data whose exposure time of PCA is less than 100 s. Accordingly, we have discarded 12 data set, and the rest of the observations are summarized in Table 4.1. They also indicated as arrows on bottom of Figure 4.1. As shown in Table 4.1, some of the PCUs were not operated at each observation (see Section 3.2.1). In order to reduce the statistical uncertainties, we use the all PCUs available in each observation.

42 4.2. 4U Figure 4.2: The time-dependent variations of the earth elevation angle, offset angle, time since the spacecraft enters the SAA and the electron contamination rate. This example is extracted from March 12 observation.

43 38 CHAPTER 4. OBSERVATIONS Table 4.1: The log of good RXTE observations of 4U in the 1999 March April outburst. PCA HEXTE cluster A cluster B No. Date Observation ID Start/End Time a PCU. Exposure Exposure b Exposure b (1999) (UT) No. [ks] [ks] [ks] 1 Mar :35/03:49 all Mar :08/13:41 0,1, Mar :35/20:57 all Mar :47/20:56 all Mar 7a :57/10:54 all Mar 7b :40/20:55 all Mar :22/06:36 0,2,3, Mar 11a :41/09:40 0, Mar 11b :21/00:01 all Mar :02/07:30 all Mar :58/19:41 0,2,3, Mar :44/06:56 0,2, Mar :53/08:17 0, Mar :33/09:46 0, Mar :49/08:05 0,2,3, Mar 19a :26/06:13 0,2, Mar 19b :51/13:12 0, Mar :34/03:57 0, Mar 21a :27/08:33 0,2,3, Mar 21b :48/13:27 0,2,3, Mar :22/05:28 0, Mar :53/11:01 all Mar :04/08:12 all Mar 29a :12/03:01 0,1,2, Mar 29b :15/11:17 0,1, Mar :11/06:24 0,2, Apr :27/04:19 0,1, Apr :09/06:14 all Apr :30/02:45 0,2, Apr :08/06:11 all Apr :09/11:27 0,2, Apr :25/04:28 all Apr :13/03:27 0,2,3, Apr :59/06:05 all Apr :16/04:28 0,1,2, Apr :14/03:22 all Apr :58/22:12 0,1,2, Apr :56/22:10 0,2,3, Apr :14/01:34 all a Start and end time (UT) of the PCA observations. b On-source time after screenings.

44 4.3. X X Overview The system of X is similar to 4U This source sometime exhibits large X-ray outbursts. The first outburst with the intensity of 1 Crab was caught by Vela 5B in 1973 (Terrell & Priedhorsky 1984). The second outburst was detected by Tenma and EXOSAT in 1983 (Tanaka et al. 1983; Stella et al. 1985). During this outburst, the EXOSAT observation revealed that the source displayed stable pulsations with a period of 4.4 second and an orbital period of days with a moderate eccentricity of 0.31 ± Following the EXOSAT and Tenma observations, the observations with optical band were performed by several observatories, and the 15 mag star BQ Cam was identified as the optical counterpart of X (Argyle et al. 1983). The discovery of Hα emission and infrared excess made BQ Cam a Be star (Coe et al and references therein). Negueruela et al. (1999) reported further investigation that the spectral type of BQ Cam is classified as O8 9Ve star, and the distance to X was estimated as 7 kpc. The evidence for the cyclotron resonance was first suggested by the Tenma observation (Makishima et al. 1990a), but the cyclotron feature appeared at the higher edge of the energy band of the GSPC onboard Tenma, so that the result was not made reliable. This feature was substantially confirmed by the Ginga observation during 1989 outburst (Makishima et al. 1990b). The source exhibited the prominent CRSF at 28.5 ± 0.5 kev and the hint of presence of the second feature at 53 kev (Makishima et al. 1990b; Mihara 1995). This discovery made X made the forth X-ray pulsar which have the CRSF. After 15 years of quiescence, X caused the outburst (Swank et al. 2004) in 2004 December. During this outburst, a lot of observations were made with RXTE and INTEGRAL. The RXTE observations revealed that the source has the three cyclotron resonant features with energies 26.34±0.03, 49.1± and 74±2 kev (Coburn et al. 2005; Pottschmidt et al. 2005). In the INTEGRAL observations, Kreykenbohm et al. (2005) confirmed the presence of three CRSFs with energies 24.9 ± 0.1, 50.5 ± 0.1 and at the declining phase. Furthermore, Mowlavi et al. (2005) reported that the parameters of CRSF, such resonance energy, line width and line depth, change together with time.

45 40 CHAPTER 4. OBSERVATIONS Figure 4.3: The ASM light curve of X The arrows indicate the pointing observations. The vertical dotted lines indicate the periastron passage day (Zhang et al. 2005) ASM light curves Figure 4.3 shows the whole 2 12 kev ASM light curve of outburst. The flux started to increase on 2004 November 23 (Swank et al. 2004), and reached the maximum level of 1.2 Crab on December 22 (Remillard & ASM team. 2004). The day of the periastron passage corresponds to the time when the flux reached the peak and the outburst started (Zhang et al. 2005). This trend resembles the outburst light curve of 4U The flux then decayed with an exponential timescale as, Flux exp[ t/(15.9days)]. Here, t is the days (Qu et al. 2005) PCA and HEXTE pointings During this outburst, total 109 pointing observations were made with PCA and HEXTE. Most of observations were scheduled by the proposed plans, and those data are not released within a year. Thus, we have mainly analyzed the 24 public data summarized in Table??. We use the all PCUs operated at each observation. In contrast of the 4U case, only the data

46 4.3. X observed with HEXTE cluster B are used in our analysis. Because HEXTE cluster A did not modulate its rocking position until 2005 January 14. During this periods, the cluster A position was fixed between the 1. 5 off-source position and the on-source position (e.g. Pottschmidt et al. 2005). Although the cluster A was in trouble, cluster B functioned normally. By rebooting the relevant systems, cluster A returned to the full function. There is no evidence of any hardware or software damage, and the cluster s behavior was back in normal. We have performed the data reduction with the same way as 4U In case of 4U , we set the threshold of the electron rate as < 0.12 counts s 1 based on the visually inspections. In order to set the new electron contamination thresholds, we again examine the electron-rate light curves, and we define the new threshold at each observation as shown in Table 4.2. After the data screening, we discard a low-exposure data set. The rest of 23 observations we have selected are summarized in Table 4.2. Figure 4.4: The electron rate of each observation. The solid lines represent the electron rate, and dashed lines are the threshold we defined. The electron rate tends to change together with the real X-ray counts. The two dips in Jan. 18b are the source eclipse by the earth.

47 42 CHAPTER 4. OBSERVATIONS Table 4.2: The log of RXTE observations of X in the outburst. PCA HEXTE cluster B No. Date Observation ID Start/End Time a electron rate PCU. Exposure Exposure b (2004/2005) (UT) [counts s 1 ] No. [ks] [ks] 1 Dec G 05:28/06:21 < ,1,2, Dec 29a :52/06:30 < ,2,3, Dec 29b :52/22:29 < ,2,3, Dec :35/14:20 < ,2, Jan :39/00:55 < 0.35 all Jan 6a :23/06:38 < ,1,2, Jan 6b :15/16:04 < ,1, Jan :43/15:59 < ,2, Jan 15a :28/04:33 < 0.2 0,2, Jan 15b :19/15:14 < 0.2 0,2, Jan 15c G 22:28/03:59 < ,2, Jan :33/02:12 < ,2, Jan 17a :31/13:00 < ,2, Jan 17b :10/00:13 < ,2, Jan 18a :08/12:58 < ,2, Jan 18b :17/01:24 < ,2, Jan :39/08:41 < ,2, Feb 12a :23/04:10 < 0.1 0,2, Feb 12b :04/21:06 < 0.1 0, Feb 13a :12/08:18 < 0.1 0,2, Feb 13b :45/14:10 < 0.1 0,2, Feb 13c :01/19:01 < 0.1 0,2, Feb :07/14:56 < 0.1 0,2, a Start and end time (UT) of the PCA observations. b On-source time after data selection.

48 Chapter 5 Data Analysis and Results on 4U In this chapter, we describe the data analysis and results on 4U In the analysis performed in this thesis, we utilize the software, HEADAS version for data analysis and XSPEC version 11.3 for spectral analysis. These software are the common tools in X-ray astrophysics and are distributed by NASA Goddard Space Flight Center ( All of the errors appeared in this thesis are 90 % confidence levels. 5.1 Light curve of PCA and HEXTE As mentioned in Section 4.2.3, we have selected 39 PCA and HEXTE pointing observation data. As we already showed the ASM 2 12 kev light curve of the outburst in Figure 4.1, here we show the light curves at higher energy band with PCA and HEXTE in Figure 5.1. The count rates are summarized in Table 5.1. The three light curves exhibit the similar trend in the increasing phase. In the decline phase, each light curve decayed with an exponential timescale at the first half, and its decayed with linear timescale at the end of the decline phase, as shown in Figure 5.2. Comparing with the PCA light curve, the light curve of the HEXTE cluster A rapidly decayed until April 10. In order to quantify the decay timescales, we fitted the data from March 27 to April 10 with the exponential function as, F lux exp[ t/(t [days]) ], where t is the time and T is the decay timescale. The solid lines in Figure 5.2 represent the functions, and we obtained the exponential timescales of 14.3 days for PCA and of 8.7 days for HEXTE light curve. 43

49 44 CHAPTER 5. DATA ANALYSIS AND RESULTS ON 4U The difference of the time scale between the PCA and the HEXTE is obviously confirmed in the hardness ratio, as shown in the bottom panel of Figure 5.2. The hardness ratio is almost constant until March 27, and it turned to decreasing on March 28. It kept decreasing until April 10, and turned to being constant again. From this, we can infer that the continuous change of the shapes of X-ray spectra occurred during this period. In next section, we advance the spectral analyses in these period. Figure 5.1: Above three panels show the light curves of PCA, HEXTE cluster A and B individually. The plotted data are the average count rate in one data set after background subtraction. The count rates are listed in Table 5.1.

50 5.1. LIGHT CURVE OF PCA AND HEXTE 45 Figure 5.2: Same as Figure 5.1, but the data are plotted with log scale. The bottom panel shows the hardness ratio. In this panel, the significant change occurred on March 27.

51 46 CHAPTER 5. DATA ANALYSIS AND RESULTS ON 4U Next we examine the light curve observed within a one day observation. Figure 5.3 shows the representative PCA light curves, acquired on March 11b, 27 and April 10. March 11b is located near the outburst peak, and the March 27 and April 10 are the start and end point of the hardness ratio change, respectively. The three data shown in Figure 5.3 were obtained with all PCUs. According to the Figure 5.3, it can be confirmed that the flux of 4U varied considerably even within a day. The light curve on March 11b clearly showed Quasi-Periodic Oscillation (hereafter QPO; van der Kils 2004 and references therein) with 500 sec period. This QPO was already reported as milli-hertz QPO by Heindl et al. (1999), and such a low-frequency variations have been observed in some accretion powered pulsars (Shirakawa & Lai 2002, and references therein). Some explanations have been proposed for this phenomenon, however, the exact model is not yet constructed. Figure 5.3: The 2 60 kev PCA light curves on March 11b, March 27 and April 10. The blank regions appeared in each data are due to the passage of the SAA. The 3.6 second pulses are smeared in the plots.

52 5.1. LIGHT CURVE OF PCA AND HEXTE 47 Table 5.1: Summary of the PCA and HEXTE background-subtracted count rates of 4U in the 1999 March April outburst. PCA HEXTE cluster A cluster B No. Date Rate a Rate b Rate b (2004/2005) [c s 1 PCU 1 ] [c s 1 ] [c s 1 ] 1 Mar ± ± ± Mar ± ± ± Mar ± ± ± Mar ± ± ± Mar 7a ± ± ± Mar 7b ± ± ± Mar ± ± ± Mar 11a ± ± ± Mar 11b ± ± ± Mar ± ± ± Mar ± ± ± Mar ± ± ± Mar ± ± ± Mar ± ± ± Mar ± ± ± Mar 19a ± ± ± Mar 19b ± ± ± Mar ± ± ± Mar 21a ± ± ± Mar 21b ± ± ± Mar ± ± ± Mar ± ± ± Mar ± ± ± Mar 29a ± ± ± Mar 29b ± ± ± Mar ± ± ± Apr ± ± ± Apr ± ± ± Apr ± ± ± Apr ± ± ± Apr ± ± ± Apr ± ± ± Apr ± ± ± Apr ± ± ± Apr ± ± ± Apr ± ± ± Apr ± ± ± Apr ± ± ± Apr ± ± ± 0.6 a In the 3 30 kev energy range. b In the kev energy range.

53 48 CHAPTER 5. DATA ANALYSIS AND RESULTS ON 4U The representative spectra As mentioned in Section 5.1, the hardness ratio of 4U changed between March 27 and April 10. This would imply that the changes of the spectral shapes occurred during this period. In order to reveal how the spectra of 4U change with the flux getting faint, we first selected the representative data sets acquired on March 12 which corresponds to the outburst peak, March 27 and April 10. Those data sets were observed with all PCUs for a long duration. For each dataset, we accumulated 3 30 kev PCU data into a single spectrum, and kev HEXTE data into the other. Each of the background spectrum was estimated with the supplied model and the calibration file, so called bright background model, described in Chapter 3. Figure 5.4 shows the background-subtracted PCA+HEXTE spectra. In order to grasp the shapes of the cyclotron resonant features, we attempted to fit the spectra with a continuum model. As described in Section 2.2.3, the typical continuum spectra of accreting binary pulsars can be approximated with a power-law times exponential cutoff model. In this thesis, we selected its updated version called NPEX (Negative and Positive power-laws with EXponential) model (Equation 2.13 in Section 2.2.3). First we fitted the background-subtracted spectra with the NPEX model. We need to notice that the PCA background estimations are only good to a few percent. The spectra might be slightly over- or under-subtracted because the uncertain estimations of the backgrounds. In order to take into account possible over- or under-subtraction of background, we allowed the background normalization to vary (as described in the RXTE cook book), so as to minimize the fit chi-squared. We found the optimum normalization factor to be less than several percents, with 1.0 being the nominal value. Even allowing this correction, the model left the significant residuals as shown in the bottom panels of Figure 5.4. The fits remained unacceptable with χ 2 ν 158, 62 and 18 for the March 12, 27 and April 10 spectra, respectively. Indeed, the March 12 and 27 spectra exhibit two negative deviations at 12 and 22 kev from the NPEX fit, while that of April 10 shows only one negative feature around 16 kev. These results confirmed the previous observation with Ginga (Section 2.5.1). The 12 and 22 kev features are regarded as the fundamental and the second harmonic cyclotron resonant features respectively. In contrast, the 16 kev feature has alternative possibility, fundamental or second harmonic feature. In order to evaluate the parameters of the cyclotron resonant features, next we introduced a CRSF model into the spectra. As described in Section 2.4, two models, Gaussian absorption (GABS) model (Equation??) and cyclotron absorption (CYAB) model (Equation 2.26), have been used to represent the CRSFs in the spectra. In this thesis, we have selected to use the

54 5.2. THE REPRESENTATIVE SPECTRA 49 Figure 5.4: The pulse-phase averaged spectra of 4U on March 12 (left), March 27 (center) and April 10 (right). The cross-marks represent the background-subtracted spectra of PCA and HEXTE, and the histogram represents the NPEX model in the top panels. The bottom panels show the residuals. CYAB model. This is because the present results are to be compared with the previous result observed with Ginga and CYAB model (Mihara et al. 2004, and references therein). We fitted the spectra on March 12 and 27 with the NPEX continuum multiplied by two CYAB factors (hereafter NPEX CYAB2 model), in which all the NPEX and CYAB parameters are left free except that the second CRSF energy is fixed at twice the fundamental energy. For the spectrum on April 10, we applied the NPEX multiplied by a single CYAB factor (hereafter NPEX CYAB model). The PCA+HEXTE data were fitted simultaneously with the same parameters, but using another free parameter to adjust relative normalizations of the two instruments. The background normalization was again allowed to vary, by up to ±8 % for the March 12 data and 1 % for March 27 and April 10 data. As shown in the right panel of Figure 5.5, the NPEX CYAB model has successfully reproduced the PCA+HEXTE data on April 10, yielding reduced chi-squared of 0.9. The derived resonance energy on April 10 is kev at an X-ray luminosity of erg s 1. This resonance energy corresponds to the result acquired with Ginga in 1991 (Mihara et al. 2004).

55 50 CHAPTER 5. DATA ANALYSIS AND RESULTS ON 4U Figure 5.5: Same as Figure 5.4, but the data are fitted with the different models, NPEX CYAB2 and NPEX CYAB. The background correction factor turned out to be 1.0 %. In contrast, the March 12 and 27 spectra were not reproduced successfully (χ 2 ν 7.0 and 2.0) even by the NPEX CYAB2 model. This is because the negative residuals remain kev in these spectra. In order to reproduce the March 12 and 27 spectra, we introduced a third CYAB factor. Accordingly, these negative features were removed, and the derived centroid energies are kev for the March 12 spectrum and kev for the March 27 spectrum. Since these energies are close to three times the typical fundamental cyclotron-resonance energy, the features can be identified with the third harmonic resonances detected from the same outburst (Heindl et al. 1999; Santangelo et al. 1999). This model, hereafter called NPEX CYAB3 model, successfully reproduced the March 12 and 27 spectra with χ 2 ν 1.2 and 1.1. The acquired fundamental resonance energy, E a1, on March 12 is 10.9 ± 0.1 kev at an X-ray luminosity of erg s 1, while that of March 27 is 10.5 ± 0.1 kev at erg s 1. The derived parameters from these model fittings are summarized in Table 5.4 for the NPEX CYAB3 models and Table 5.3 for the NPEX CYAB model. Although the X-ray luminosity changed from to erg s 1 between March 12 and 27, there was no significant change in the fundamental resonance energy, E a1, and the other CYAB

56 5.2. THE REPRESENTATIVE SPECTRA 51 Figure 5.6: The pulse-phase averaged spectra on March 12 (left) and 27 (right). The crossmarks represent the background-subtracted spectra of PCA and HEXTE, and the histogram represents the NPEX CYAB3 model in the top panels. The bottom panels show the residuals. parameters. On the other hand, the drastic change occurred in the CRSFs between March 27 and April 10. The resonance energy has thus increased by a factor of 1.4 as the luminosity decreased by a factor of 3, although there still remains a possibility that the single CRSF at 15.1 kev on April 8 is in reality the second harmonic.

57 52 CHAPTER 5. DATA ANALYSIS AND RESULTS ON 4U Table 5.2: Summary of the best-fit parameters of the NPEX CYAB3 model, on March 12 and 27. a 10 3 Date Mar 12 Mar 27 A 1 (ph s 1 kev 1 ) α ± A a 2 (ph s 1 kev 1 ) kt (kev) Ea1 b (kev) 10.9 ± ± 0.1 W 1 (kev) τ W 2 (kev) τ E b a3 (kev) W 3 (kev) τ L c x χ 2 ν b The second resonance energy Ea2 was fixed at 2 E a1. c erg s 1 in 3 50 kev Table 5.3: Summary of the best-fit parameters of the NPEX CYAB model, on April 10. Date Apr 10 A 1 (ph s 1 kev 1 ) 0.06 ± 0.01 a 10 3 b erg s 1 in 3 50 kev α A a 2 (ph s 1 kev 1 ) kt (kev) E a (kev) W (kev) τ 1.18 ± 0.10 L b x 2.02 χ 2 ν 0.95

58 5.3. CRSF VARIATION IN DATE-SORTED SPECTRA CRSF variation in date-sorted spectra In order to investigate how the CRSFs change together with the source flux decreasing, we analyze the daily-averaged spectra between March 27 and April 10. For the moment, we mainly concentrate on the study of the 3 30 kev PCA spectra, because this energy range is sensitive to the CRSFs. And also, to eliminate the energy response uncertainties and the gain differences in each detector, we used the data acquired only with PCU 0, PCU 2 and PCU 3. During that period, 13 pointing observations with different PCU sets were performed as shown in Table 4.1, while observations were made with PCU 0, 2 and 3. The data on March 29b is mainly acquired with PCU0, 1 and 2, but PCU3 functioned in short duration, 2.6 ksec. So, we use this data and analyzed the total 12 data sets (March and April 2 10). Figure 5.7: Date-sorted PCU0+PCU2+PCU3 spectra of 4U from March 12 to April 10. For the presentation, the spectra are shifted vertically by a factor of 0.5 for each observation. Figure 5.7 shows 12 date-sorted PCU0+PCU2+PCU3 spectra. In order to resolve the

59 54 CHAPTER 5. DATA ANALYSIS AND RESULTS ON 4U drastic spectral change between March 27 to April 10, we applied the NPEX model (without incorporating CYAB factors) to the daily-averaged PCU0+PCU2+PCU3 spectra over this period. The left panel of Figure 5.8 shows residuals of the data to the best-fit NPEX model, which allow us to grasp the spectral changes objectively. The PCA background normalizations were corrected in the way as described in Section 5.2. Since the residuals on March 27, 28, 29a and 29b show almost the same shape as the residuals of Figure 5.4, we may consider that the two CRSF persisted at least until March 29b. On March 31, the second CRSF became less clear, and on April 2 onward, the residuals reveal only a single absorption. The fundamental resonance initially observed at 11 kev moved to higher energies, up to 15 kev, while there is no opposite trend such as the two features drifting toward lower energies. In order to quantify the results of these visual inspections, we have fitted the same set of spectra with the NPEX CYAB2 (or NPEX CYAB) model. The obtained best-fit parameters are summarized in Table 5.4, and the residuals are plotted in the right panel of Figure 5.8. The spectra from March 27 through April 2 required the two CYAB factors, because the double CYAB fit gave a significantly better reduced chi-square ( ) than the single CYAB fit ( 2). On April 3, the spectrum is roughly reproduced by the single CYAB model. The successful single CYAB fit continued to the end, on April 10. These results quantitatively reveal that the fundamental CRSF energy increased from 10 to 15 kev over this 14 day period, although details of the change are not yet resolved clearly.

60 5.3. CRSF VARIATION IN DATE-SORTED SPECTRA 55 Figure 5.8: (left) Date-sorted PCU0+PCU2+PCU3 spectra of 4U from March 27 to April 10, normalized to the respective best-fit NPEX models. For the presentation, the results are shifted vertically at 10 for each observation. (b) The same as left panel, but the fitting model is NPEX CYAB2 (March 27 through April 2) or NPEX CYAB (April 4 and later).

61 56 CHAPTER 5. DATA ANALYSIS AND RESULTS ON 4U Table 5.4: Summary of the best-fit parameters of the NPEX CYAB( CYAB) model, determined by the date-sorted PCA spectra from March 27 thorough April 10. Date A1 α1 A a 2 kt E a1 b W1 D1 W2 D2 L c x χ 2 ν (ph s 1 kev 1 ) (ph s 1 kev 1 ) (kev) (kev) (kev) (kev) Mar Mar Mar 29a Mar 29b Mar Apr Apr Apr Apr Apr Apr Apr a b The second resonance energy Ea2 was fixed at 2 E a1. c erg s 1 in 3 30 kev

62 5.4. CRSF VARIATION IN INTENSITY-SORTED SPECTRA CRSF variation in intensity-sorted spectra As mentioned in Section 5.1, 4U exhibited significant intra-day intensity variations. Figure 5.9 shows the light curve from March 27 to April 10. Because of the intensity variation within one day, the spectra of one observation are an average over a wide luminosity range. In order to see the luminosity dependence more clearly, we sorted the PCA data from March 27 to April 10 into 14 intensity intervals, as notes from f1 to f14 in Figure 5.9. We again used data from PCU 0, 2 and 3, which worked throughout this period. Then, we have repeated the same analysis as performed in Section 5.3. The left panel of Figure 5.10 shows the residuals of these intensity-sorted spectra to their best-fit NPEX models, to be compared with Figure 5.8. The two CRSFs, at 11 kev and 22 kev, are thus observed clearly in the higher six intensity levels, f1 through f6. As the intensity decreased, the second CRSF gradually became shallower. Finally, the second CRSF disappeared at level f9, and the fundamental CRSF started to move from 11 to 15 kev over levels f8 through f14. From these results, we confirm that the 15 kev single structure results from an upward shift of the 10 kev fundamental CRSF. The spectral changes revealed here is consistent with, but clearer than, those seen between April 2 and April 4 in the date-sorted spectra. Using the NPEX CYAB2 (or NPEX CYAB) model, we quantified the CRSF parameters as a function of the intensity. The fitting results are summarized in Table 5.5, and the residuals are shown in the right panel of Figure The full fitting results are displayed in Figure 5.11 and The two CYAB factors have been required by the f1 to f8 spectra. The second CRSF is not clearly visible in the f8 residual (Figure 5.10 and Figure 5.11), but a large χ 2 ν ( 2.4) was obtained by the single CYAB fitting. We therefore applied the NPEX CYAB2 model to the f8 spectrum, and obtained a fully acceptable fit (Table 5.5). The f9 through f14 spectra have been fitted successfully by the NPEX CYAB model. From f1 through f8, τ 2 decreased; that is, the second harmonic feature became shallower. Although this behavior is absent in the day-sorted results except the data on April 2 (Table 5.5), the difference can be attributed to the fact that each day-average spectrum is a mixture of different spectra corresponding to different intensities. These results unambiguously show that the center energy of the fundamental CRSF moved from 10 to 15 kev as the luminosity decreased. Thus, we can conclude that the 16 kev spectral structure of 4U observed by Ginga (1991) and this work is the fundamental CRSF, rather than the second harmonic resonance which moved toward lower energies. The threshold

63 58 CHAPTER 5. DATA ANALYSIS AND RESULTS ON 4U Figure 5.9: The PCU light curve of 4U observed from March 27 to April 10, plotted with 16 sec binnings. The horizontal dashed lines indicate boundaries of the intensity sorting. between the single and double CRSF structures is found at a 3 30 kev luminosity of erg s 1.

64 5.4. CRSF VARIATION IN INTENSITY-SORTED SPECTRA 59 Figure 5.10: (left) The same as left panel of Figure 5.8, but for the intensity-sorted spectra defined in Figure 5.9. (right) The intensity-sorted PCA spectra, each normalized to the bestfit NPEX CYAB2 (f1-f8) or NPEX CYAB (f9-f14) model. Data are presented in the same manner as right panel of Figure 5.8.

65 60 CHAPTER 5. DATA ANALYSIS AND RESULTS ON 4U Figure 5.11: The PCU light curve of 4U observed from March 27 to April 10, plotted with 16 sec binnings. The horizontal dashed lines indicate boundaries of the intensity sorting from f1 to f14.

66 5.4. CRSF VARIATION IN INTENSITY-SORTED SPECTRA 61 Figure 5.12: The PCU light curve of 4U observed from March 27 to April 10, plotted with 16 sec binnings. The horizontal dashed lines indicate boundaries of the intensity sorting.

67 62 CHAPTER 5. DATA ANALYSIS AND RESULTS ON 4U Table 5.5: Summary of the best-fit parameters of the NPEX CYAB2 (of CYAB) model, determined by the intensity-sorted PCA spectra from f1 to f14. Date A1 α1 A a 2 kt E a1 b W1 D1 W2 D2 L c x χ 2 ν (ph s 1 kev 1 ) (ph s 1 kev 1 ) (kev) (kev) (kev) (kev) f f f f f f f f f f f f f f a (fixed) b The second resonance energy Ea2 was fixed at 2 E a1. c erg s 1 in 3 30 kev

68 5.5. RESULT OF ALL PCA AND HEXTE SPECTRA Result of all PCA and HEXTE spectra As mentioned in Section 5.3 and 5.4, we revealed that the cyclotron resonance energies change together with the X-ray luminosities through March 27 to April 10. We here proceed to the analysis of the entire PCA and HEXTE data NPEX model multiplied by CYAB factors fitting In order to know how the cyclotron features appear in the spectra at each observation, we first attempted to fit the all of PCA and HEXTE background-subtracted spectra with NPEX model (all of NPEX model fitting results are shown in Appendix A.1). The background normalizations are corrected again in same method as described in Section 5.2. The NPEX fitting for all spectra yield the single or multiple negative deviations around kev. Next we applied the CYAB model to the negative deviations. Since the data on March 3 and 4 exhibit the single negative residuals at 15 kev, we applied the NPEX CYAB model to these data. The data on March 4 was reproduced by the NPEX CYAB model 1 well. In contrast, the fit for the March 3 data was still unacceptable (χ 2 ν 1.7). Then, we fitted the March 3 data with the NPEX CYAB2 model, and obtained reasonable fit with χ 2 ν 1.1. After March 4, the data were generally well described with the NPEX CYAB2 model until April 2. By jointly analyzing the PCA and HEXTE data, the second CRSF parameters have been significantly better constrained than using the PCA data alone. The derived parameters are listed in Table 5.6 and 5.7. In some fits, however, rather large values of χ 2 ν were left. For example, the NPEX CYAB2 fits were rather poor (χ 2 ν 2.0) on March 7a, 11b, 12, 15, 19a, 21a, 22, 27, 28, 29a and 29b, often having negative residuals at 35 kev. As in Section 5.2, these residuals can be removed by multiplying the model with the third CYAB factor. Thus, we applied the NPEX CYAB3 model (see Section 5.2) to these data. In contrast to Section 5.2, to converge the fittings, the third CRSF energy was fixed to the three times of the fundamental energy. The third harmonic persisted in the spectra for about 20 days from March 7a, with relatively constant parameters, till March 29b when it became unconstrained presumably due to insufficient data statistics in higher energies. Meantime, the second CRSF stayed around at 22 kev. The data from April 3 to the end did not show the higher harmonics, with the NPEX CYAB 1 In Nakajima et al. (2006), the data on March 4 was reproduced by the NPEX CYAB2 model. This discrepancy is probably yielded by using the different version of the analysis software. HEADAS version is used for the present analysis, while HEASOFT version 5.2 was used for Nakajima et al. (2006).

69 64 CHAPTER 5. DATA ANALYSIS AND RESULTS ON 4U model giving acceptable fits ( 1.4). In order to estimate the upper limits on the second harmonic feature, we attempted to fit the data obtained from April 3 to April 10 with the NPEX CYAB2 model. Here the second CRSF width W 2 was tied to W 1, because W 2 is close to W 1 (except for April 1 and 2) when the spectrum exhibits the double features. The obtained upper limits on D 2 are given in Table 5.7.

70 5.5. RESULT OF ALL PCA AND HEXTE SPECTRA 65 Table 5.6: Summary of the best-fit continuum parameters of the NPEX CYABn (n = 1,2,3) model, determined by the date-sorted PCA+HEXTE spectra from March 3 thorough April 20. Date A 1 α 1 A a 2 kt (ph s 1 kev 1 ) (ph s 1 kev 1 ) (kev) L b x χ 2 ν Mar Mar Mar Mar Mar 7a Mar 7b Mar Mar 11a Mar 11b Mar Mar Mar Mar Mar Mar Mar 19a Mar 19b Mar a 10 3 Mar 21a (fixed) (fixed) Mar 21b Mar Mar Mar Mar 29a Mar 29b Mar Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr b erg s 1 in 3 50 kev

71 66 CHAPTER 5. DATA ANALYSIS AND RESULTS ON 4U Table 5.7: Summary of the best-fit cyclotron parameters of the NPEX CYABn (n = 1,2,3) model, determined by the date-sorted PCA+HEXTE spectra from March 3 thorough April 20. Date Ea1 a W 1 D 1 W 2 D 2 W 3 D 3 (kev) (kev) (kev) (kev) Mar Mar Mar Mar Mar 7a Mar 7b Mar Mar 11a Mar 11b Mar Mar Mar Mar Mar Mar Mar 19a Mar 19b Mar Mar 21a Mar 21b Mar Mar Mar Mar 29a Mar 29b Mar Apr = W = W = W = W = W = W Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr Apr a The second and third resonance energies (E a2 and E a3 ) were fixed at 2 E a1 and 3 E a1, respectively. b erg s 1 in 3 50 kev

72 5.5. RESULT OF ALL PCA AND HEXTE SPECTRA The change of cyclotron resonance energy Sine the PCA and HEXTE spectra are reproduced by the NPEX model multiplied CYAB factors, next we examine how the cyclotron resonance features behave together with the X-ray luminosity through the outburst. We extracted the fundamental resonance energies and X-ray luminosities from the Table 5.6 and 5.7, and the relation between these parameters are given in Figure From this figure, we reconfirmed that the cyclotron resonance energies depend on the X-ray luminosity through the outburst. We have found that the fundamental resonance energy stays constant at higher or lower luminosity region; beyond erg s 1, the E a1 stays 10 kev, and the E a1 stays 16 kev below erg s 1. The fundamental resonance energy shifts from 10 kev to 16 kev, when the 3 50 kev luminosity decreases across a relatively narrow range of (5 ± 2) erg s 1. These results are consistent with those derived in Section 5.4 from the intensity-sorted study of the 3 30 kev PCA spectra. Figure 5.13 also summarizes the fundamental resonance energies, derived through both the date-sorted and intensity-sorted analyses, as a function of the calculated 3 50 kev luminosity at 7 kpc.

73 68 CHAPTER 5. DATA ANALYSIS AND RESULTS ON 4U Figure 5.13: The obtained fundamental cyclotron energies shown against the 3 50 kev luminosity. The open symbols represent the fundamental energy of the multiple absorption features, and the filled symbols the energy of the single CRSF. All the date-sorted data in the brightening (circles) and declining (triangles) are presented together with the intensity-sorted (squares) results. The data are in Table 5.6 and 5.7.

74 5.5. RESULT OF ALL PCA AND HEXTE SPECTRA Behavior of other CRSF parameters Together with the X-ray luminosity, the other CRSF and the continuum parameters, for example line width, depth and NPEX kt, change as well. These relations among the continuum and cyclotron line parameters have been studied by many authors (e.g. Makishima et al. 1990b; Mihara 1995; Mihara et al. 1998; Makishima et al. 1999; Heindl et al. 2001; Coburn et al. 2002; Kreykenbohm et al. 2004). Our work provides how these parameters in a single system change in correlated ways, when the resonance energy varies. Here, we describe some relations between these parameters. The correlation between the X-ray luminosity and CYAB depth D n (n = 1, 2, 3) First, we deal with the CYAB depth parameters, D n (n = 1, 2, 3) which exhibited the peculiar variation as the source X-ray flux changed. The CYAB depth parameters are given in Figure Both date-sorted (Section 5.5.1) and intensity-sorted (Section 5.4) data with 3 50 kev luminosity are plotted in that figure. Up to erg s 1, D 1 stays relatively constant. Beyond erg s 1, D 1 start decreasing clearly, while the second harmonic resonance depth D 2 appears rapidly above erg s 1, as shown in the middle panel of Figure D 3 does not exhibit the change at erg s 1.

75 70 CHAPTER 5. DATA ANALYSIS AND RESULTS ON 4U Figure 5.14: The obtained CYAB depth D n (n=1,2,3) shown against the 3 50 kev luminosity. The fundamental line depth in upper panel, the second line in middle panel and the third line depth in bottom panel. The arrows in middle panel represent the upperlimit of the second cyclotron feature.

76 5.5. RESULT OF ALL PCA AND HEXTE SPECTRA 71 The correlation between the X-ray luminosity and CYAB width W n (n=1,2,3) Next, we examine the relation between the X-ray luminosity L X and the CYAB W. Again, both date-sorted (Section 5.5.1) and intensity-sorted (Section 5.4) data with 3 50 kev luminosity are used. The L X and CYAB W relation is given in Figure The fundamental resonance width W 1 in each date-sorted and intensity-sorted data shows the slight increasing at erg s 1. Beyond erg s 1, W 1 start decreasing clearly. The second resonance width W 2 continuously increased until the maximum luminosity, as shown in the middle panel of Figure The third resonance width W 3 does not exhibit a significant change. Figure 5.15: The obtained CYAB width W n (n=1,2,3) shown against the 3 50 kev luminosity. The fundamental line width in upper panel, the second in middle panel and the third in bottom panel. The filled-circle marks represent the data from date-sorted, and the open-circle marks are the intensity-sorted data.

77 72 CHAPTER 5. DATA ANALYSIS AND RESULTS ON 4U The correlation between the cyclotron resonance energy and NPEX temperature kt The relation between the cyclotron resonance energies and NPEX kt or cut-off energy have been studied for a long time by many authors (e.g. Makishima et al. 1990b; Mihara 1995; Coburn et al. 2002). Figure 5.16 shows the fundamental cyclotron resonance energy E a1 and the NPEX kt derived from the date-sorted and intensity-sorted data. Although the NPEX kt has rather large error, we consider that the NPEX kt stay constant. This result is not consistent with the previous researches which reported that the two parameters have positive correlation. Figure 5.16: The fundamental cyclotron resonance energy and the NPEX kt relation. The fixed kt parameters (Table 5.5 and 5.6) are excluded. The filled-circle marks represent the data from date-sorted, and the open-circle marks are the intensity-sorted data.

78 Chapter 6 Data Analysis and Results on X In this chapter, we describe the data analysis and results on X In Chapter 5, we utilize the software, HEADAS version for data analysis and XSPEC version 11.3 for spectral analysis. 6.1 Light curve of PCA and HEXTE As mentioned in Section 4.3.3, we used 23 data set observed at decline phase of the outburst for our analysis. In the same way as in Section 5.1, we first examine the daily-averaged PCA and HEXTE count rate. The background-subtracted 3 25 kev PCA and kev HEXTE cluster B count rates are given in Figure 6.1. Same as the light curve of 4U , we confirmed the exponential decay in X light curve (Mowlavi et al. 2005). To evaluate the decay time scale, we fitted the data from January 4 to January 19 with the exponential function as, F lux exp[ t/(t [days]) ], where t is the time and T is the decay timescale. The obtained decay time scales are 22 days for PCA (2 25 kev) band, and 28.5 days for HEXTE (20 80 kev) band. In contrast with the case of 4U , the decay time scales of X are longer than the time scale of 4U (14.3 days for PCA band and 8.7 days for HEXTE band). And also, the decay trend of X differs from the case of 4U which exhibited the faster decay in hard band. The different decay time scales are reflected in the hardness ratio as shown in the bottom panel of Figure 6.1. Up to January 19, the hardness ratio mildly increased, and it abruptly increased after February 12. From this figure, we can infer that the continuous spectral change 73

79 74 CHAPTER 6. DATA ANALYSIS AND RESULTS ON X occurred at the outburst decline phase. Figure 6.1: Above three panels show the daily-averaged count rate of PCA and HEXTE cluster B. The bottom panel represents count rate of HEXTE cluster B to PCA ratio (hardness ratio). As shown in Figure 6.1, the data set are divided into 4 data blocks, so we have selected the 4 data set to examine the flux variation within one day observation. Figure 6.2 shows the 2 60 kev PCA light curves acquired on Dec 30, Jan 6b, 18b and Feb 12a. Each data are observed with 3 PCUs, and plotted with 16 sec/bin. As the source flux was bright, the variations of the PCA count rate are 10%. In contrast, the variation level on Feb 12a is relatively large compared to the data observed on Dec 30. The light curve of 4U tends to show that the variation level decreased as the flux becomes faint, while the case of X exhibits the opposite change (Section 5.1).

80 6.1. LIGHT CURVE OF PCA AND HEXTE 75 Table 6.1: Summary of the count rate change of X in the outburst. PCA HEXTE cluster B No. Date Rate a Rate b (1999) [c s 1 PCU 1 ] [c s 1 ] 1 Dec ± ± Dec 29a ± ± Dec 29b ± ± Dec ± ± Jan ± ± Jan 6a ± ± Jan 6b ± ± Jan ± ± Jan 15a ± ± Jan 15b ± ± Jan 15c ± ± Jan ± ± Jan 17a ± ± Jan 17b ± ± Jan 18a ± ± Jan 18b ± ± Jan ± ± Feb 12a ± ± Feb 12b ± ± Feb 13a ± ± Feb 13b ± ± Feb 13c ± ± Feb ± ± 0.3 a In the 3-25 kev energy range. b Count rates of HEXTE cluster B in the kev energy range.

81 76 CHAPTER 6. DATA ANALYSIS AND RESULTS ON X Figure 6.2: PCA light curves observed at each observation. Each time are counted from the observation start time. The plotted data are averaged in 16 sec in each bin.

82 6.2. REPRESENTATIVE PULSE-PHASE AVERAGED SPECTRA Representative pulse-phase averaged spectra The evidence of CRSFs in X spectra are already reported (Coburn et al. 2005; Kreykenbohm et al. 2005; Pottschmidt et al. 2005; Mowlavi et al. 2005) from this outburst, so we here concentrate on the study of the CRSFs evolution along with the X-ray luminosity. As shown in Figure 6.1, the count rate of X changed by a factor of 10 during the observations. First, we examine how the spectral shape change together with the flux. Since the data are divided into 4 blocks with each flux levels, we have selected 4 data sets on Dec 30, Jan 6b, 18b and Feb 12a, as representative spectra at each intensity level. We accumulated all PCUs functioned at each observation into one spectrum, and the HEXTE cluster B data are utilized only in this analysis (see Section 4.3.3). The background spectra of PCA are calculated with same way described in Chapter 3. Figure 6.3 shows the 3 25 kev PCA and kev HEXTE cluster B backgroundsubtracted spectra. Each PCA spectrum are extracted from 3 PCUs. The prominent cyclotron resonant features are seen at 30 kev, and the second harmonic resonance 50 kev (e.g. Kreykenbohm et al. 2005). From the visually inspection of this figure, we consider that the fundamental resonant features moved toward higher energy when the source flux became faint. This tendency is same as 4U (see Section 5.5.2). Figure 6.3: The representative X spectra at 4 flux levels. Each PCA data are accumulated with 3 PCUs. Next we attempted to fit the data with the continuum model. Same as the case of the

83 78 CHAPTER 6. DATA ANALYSIS AND RESULTS ON X analysis of 4U (Section 5.2), we used NPEX model (Equation 2.13 in Section 2.2.3) as an continuum. All fitting parameters are left free. As mentioned in Section 5.2, the PCA background estimation is only good in a few percent, so the background normalization was allowed to vary when the data were fitted with NPEX model. The residuals obtained by the NPEX model fitting are given in Figure 6.4. The remarkable absorption features are seen between 20 and 30 kev through the observations. Figure 6.4: Representative spectra of X , presented in the form of their residuals of NPEX model fitting. The data are shifted vertically for clarity. Since Figure 6.3 and 6.4 provide the approximate change of the CRSFs, next we attempt to quantify the resonance energies at each observation. Since the raw spectra in Figure 6.3 revealed that the source has two CRSFs through the observations, we use the NPEX model multiplied by the two CYAB factors (Equation 2.26 in Section 2.4). Although we fixed the second resonance energy E a2 as 2 E a1 in 4U analysis, all of parameters of CYAB factors are left free for the X analysis. This is because the NPEX CYAB2 model (E a2 = 2 E a1 ) used in the 4U analysis yields the large residual around 50 kev.

84 6.2. REPRESENTATIVE PULSE-PHASE AVERAGED SPECTRA 79 This implies that the fundamental to second resonance energy ratio is not equal to 2.0. In addition, the fluorescent neutral K α iron lines are seen through the observations, so we applied the Gaussian model to the iron feature. The Gaussian model is described as L iron (E) = I iron 2πσ 2 iron exp { (E E iron) 2 }, (6.1) 2σ 2 iron where E iron is the line energy, σ iron is the line width and K is the flux in the line ( photons cm 2 s 1 ). In this analysis, we fixed the line energy E iron at 6.4 kev, and the line width σ iron at 0.5 kev, respectively. Thus, the PCA+HEXTE cluster B data were fitted simultaneously with the NPEX and Gaussian model multiplied by two CYAB factors. And also, we use another free parameter to adjust relative normalizations of the two instruments. Although the two CYAB factors and iron line are incorporated into the model, the large bumps at 20 and 30 kev and a sharp negative peak still remain in the residuals (χ 2 ν 4), as shown in Figure 6.5. We assume that such structure appeared in residuals is yielded due to the sharp and deep cyclotron absorption core. The fundamental resonant feature, however, does exhibit the energy change from 23 to 28 kev as the X-ray luminosity decreases by a factor of 5. Figure 6.5: Upper 4 panels show the representative spectra and folded models. The residuals of the representative spectra to the best-fit models are shown in the bottom panels.

85 80 CHAPTER 6. DATA ANALYSIS AND RESULTS ON X In order to reproduce the deep fundamental cyclotron resonant feature well, we introduce another cyclotron absorption model, so-called GABS (Equation 2.24 in Section 2.4). The NPEX and iron line model multiplied by two GABS factors for the fundamental and the second features is applied to the spectra. However, the bumps at 20 kev still remain with this model and the χ 2 ν values are unacceptable ( χ2 ν 2.0 ). Since either cyclotron absorption model cannot reproduce the sharp and deep fundamental cyclotron feature, next we attempt to fit the composite cyclotron absorption model as, NPEX model multiplied by two CYAB factors and single GABS (hereafter NPEX CYAB2 GABS model). All of the NPEX, CYAB and GABS parameters are left free except that the GABS line energy E c is fixed at 1.2 times of the fundamental energy. This is because the CYAB factor becomes maximum at E a1 + W 2 1 E a1, and this value corresponds to 1.2 E a1 in our case. Thus, we applied the NPEX CYAB2 GABS model to the 4 spectra. Again the PCA background normalizations were corrected in a same way as described in Section 5.2, and the obtained correction factors are less than 10 %. The NPEX CYAB2 GABS model well describes the 3 spectra on Dec 30, Jan 6b and 18b. On February 12a data, the second resonance energy does not converge presumably due to insufficient data statistics in higher energies. Then we fixed the parameter E a2 as 2 E a1, and fit again the data with the model. Finally, we acquired an acceptable χ 2 ν value on February 12a. The best-fit parameters of NPEX CYAB2 GABS model are summarized in Table 6.2. All of the representative spectra with the best-fit models are shown in Figure 6.6. From this model fitting, we confirmed that the fundamental cyclotron resonance energy, in this case E a1, changed from to kev when the source flux became faint.

86 6.2. REPRESENTATIVE PULSE-PHASE AVERAGED SPECTRA 81 Figure 6.6: Same as Figure 6.5, but the folded models are NPEX CYAB2 GABS. GABS is added to represent the sharp core of the fundamental cyclotron structure. Table 6.2: Summary of the best-fit NPEX CYAB2 GABS model, determined by the 4 representative PCA+HEXTE spectra on December 30, January 6a, 18b and February 12a. Date A 1 α 1 A a b 2 kt I iron L c x χ 2 ν (ph s 1 kev 1 ) (ph s 1 kev 1 ) (kev) (ph s 1 cm 2 ) Dec Jan 6b Jan 18b Feb 12a CYAB GABS Date E a1 W 1 D 1 E a2 W 2 D 2 σ τ (kev) (kev) (kev) (kev) (kev) Dec Jan 6b Jan 18b Feb 12a (fixed) a 10 3 b 10 2 c erg s 1 in 3 50 kev

87 82 CHAPTER 6. DATA ANALYSIS AND RESULTS ON X Result of all PCA and HEXTE spectra Spectral fitting with our model In Section 6.2, we introduced a simple model; NPEX CYAB2 GABS model to fit the spectra of X Here, we proceed to the spectral analysis to the whole dataset. We applied the the NPEX CYAB2 GABS model for the 30 kev fundamental cyclotron features and the second resonant features at 50 kev, but some authors (Coburn et al. 2005; Kreykenbohm et al. 2005; Pottschmidt et al. 2005; Mowlavi et al. 2005) reported that the source exhibited the 3 CRSFs at energies 25, 50 and 74 kev in long-exposed X-ray spectra. In our case, the significant third CRSF was not detected due to the low statistics in those energy band. Therefore, we concentrate on the study of the fundamental and the second cyclotron feature in this analysis. As mentioned in Section 6.2, the second resonant feature in the latter phase was not constrained due to insufficient data statistics in higher energies. For the data after February 12a, NPEX CYAB2 GABS model is applied with E a2 fixed at 2 E a1. Finally, we can reproduce the entire X spectra with our model. The bestfit parameters are summarized in Table 6.3 for the continuum parameters and Table 6.4 for the cyclotron absorption parameters. The PCA background normalizations are again left free through this analysis. In contrast to the case of 4U , the double CRSFs persisted in the X spectra until February 15.

88 6.3. RESULT OF ALL PCA AND HEXTE SPECTRA 83 Table 6.3: Summary of the best-fit continuum parameters of the NPEX CYAB2 GABS model, determined by the date-sorted PCA+HEXTE spectra from December 28 thorough February 15. Date A 1 α 1 A a b 2 kt I iron L c x χ 2 ν (ph s 1 kev 1 cm 2 ) (ph s 1 kev 1 cm 2 ) (kev) (ph s 1 cm 2 ) Dec Dec 29a Dec 29b Dec Jan Jan 6a Jan 6b Jan Jan 15a Jan 15b Jan 15c Jan Jan 17a Jan 17b Jan 18a Jan 18b Jan Feb 12a Feb 12b Feb 13a Feb 13b Feb 13c Feb a 10 3 b 10 2 c erg s 1 in 3 50 kev

89 84 CHAPTER 6. DATA ANALYSIS AND RESULTS ON X Table 6.4: Summary of the best-fit cyclotron parameters of the NPEX CYAB2 GABS model, determined by the date-sorted PCA+HEXTE spectra from December 28 thorough February 15. CYAB GABS Date E a1 W 1 D 1 E a2 W 2 D 2 σ c τ c (kev) (kev) (kev) (kev) (kev) Dec Dec 29a Dec 29b Dec Jan Jan 6a Jan 6b Jan Jan 15a Jan 15b Jan 15c Jan Jan 17a Jan 17b Jan 18a Jan 18b Jan Feb 12a (fixed) Feb 12b (fixed) Feb 13a (fixed) Feb 13b (fixed) Feb 13c (fixed) Feb (fixed) E c of GABS was fixed to 1.2 E a1

90 6.3. RESULT OF ALL PCA AND HEXTE SPECTRA The change of cyclotron resonance energies in X spectra Since the PCA and HEXTE cluster B spectra are reproduced by the NPEX and iron line model multiplied by two CYAB factors and one GABS, we examine how the cyclotron resonance features behave together with the X-ray luminosity through the decline phase of the outburst. The derived fundamental and second resonance energies from Table 6.4 are plotted in Figure 6.7 against the 3 50 kev X-ray luminosity L X at 7 kpc. We found that the fundamental cyclotron resonance energies depend on the X-ray luminosity at the outburst decline phase, as shown in Figure 6.7(a). The trend of the luminosity dependent change is same as the case of 4U (see Figure 5.13). Figure 6.7: The derived cyclotron resonance energies are plotted against the 3 50 kev X-ray luminosity, (a) The fundamental, and (b) The second resonance, respectively. In the case of 4U , we were not able to find any indication of the change of the second resonance energy. In contrast, the second resonance energies are slightly decreased with luminosity in X , as shown in Figure 6.7(b). From this figure, it is revealed that both the fundamental and the second resonance features exhibit similar luminosity-dependence of CRSF. As the source flux become bright, resonance energy become lower The fundamental

91 86 CHAPTER 6. DATA ANALYSIS AND RESULTS ON X resonance energy shifts from kev to kev, when the 3 50 kev luminosity decreases from to erg s 1, while the second resonance energy shifts from kev to kev. In Figure 6.8, we plotted a ratio of the fundamental resonance energy to the second resonance one. The harmonic ratios, E a2 E a1, decreased from 2.3 to 2.1 as the source luminosity became faint, as shown in Figure 6.8. The harmonic ratio larger than 2 is not observed in other accretion powered pulsars. Figure 6.8: The second resonance to fundamental resonance energies ratios are shown against the 3 50 kev X-ray luminosity. The data acquired after February 12a are excluded since fixed the E a2 to the twice of E a1.

92 6.3. RESULT OF ALL PCA AND HEXTE SPECTRA Behavior of other CRSF parameters As the 4U analysis, here we examine how the other CRSF parameters change together with the flux. The correlation between the X-ray luminosity L X and CYAB depth D n (n = 1, 2) and GABS τ c Since we showed the luminosity-dependent variation of the CYAB depth D n (n = 1, 2, 3) in Section 5.5.3, we again attempt to inspect the L X CRSF depth relation of X We plot the CYAB D 1, D 2 and GABS τ c parameters against the 3 50 kev X-ray luminosities, as shown in Figure 6.9. All cyclotron depths exhibit continuous decrease as the luminosity became bright. In the case of 4U , the fundamental feature depth exhibited the variation at the threshold luminosity which divide whether the spectrum has double CRSFs or single CRSF. On the other hand, there are no peculiar variation in the cyclotron depths of X It is considered that such cyclotron feature depth variation might be yielded by the change of the observed CRSF numbers. Thus, the depth variation does not occur in the case of X The other parameters Figure 6.10 shows the relation between the X-ray luminosity L X and the cyclotron feature widths, W 1, W 2 and σ c. Although the fundamental CRSF widths of 4U exhibited the large variation around the threshold luminosity (Figure 5.16), the cyclotron feature widths of X stays constant value. In addition, we refer to the relation between the fundamental resonance energy E a1 and NPEX kt, It is known that this relation has positive correlation among the several X-ray pulsars. As the case of 4U (Section 5.5.3), we can not find any correlation in E a1 kt in single system.

93 88 CHAPTER 6. DATA ANALYSIS AND RESULTS ON X Figure 6.9: The obtained CYAB depth D n (n=1,2) and GABS depth τ c are plotted against the 3 50 kev luminosity. The fundamental CYAB depth D 1 in upper panel, the second CYAB depth D 2 in middle panel and the fundamental GABS depth τ c in bottom panel.

94 6.3. RESULT OF ALL PCA AND HEXTE SPECTRA 89 Figure 6.10: The obtained CYAB width W n (n = 1, 2) and GABS τ c are plotted against the 3 50 kev luminosity. The fundamental CYAB width W 1 in upper panel, the second CYAB width W 2 in middle panel and the GABS width τ c in bottom panel.

95 90 CHAPTER 6. DATA ANALYSIS AND RESULTS ON X Figure 6.11: The fundamental cyclotron resonance energy E a1 and the NPEX kt relation. The data extracted from Table 6.3 and 6.4.

96 Chapter 7 Discussion In Chapter 5 and 6, we analyzed the 2 X-ray pulsar data observed with RXTE, and we showed that the fundamental cyclotron resonance energy change together with the source X-ray luminosity. In this Chapter, we describe the interpretation of the CRSF energy change. 7.1 Luminosity Dependent Cyclotron Resonance Energy Change We have confirmed that the cyclotron resonance energies acquired from the data analysis of 4U and X depend on the source X-ray luminosity. When the source flux was bright, the cyclotron resonance energy was observed low, and when it was faint, the high resonance energy was high (see Figure 5.13 and 6.7). A possible reason of the change of the resonance energy might be that the location where the CRSF is produced changes with the luminosity. Here, we discuss two possibilities; either the forming region of CRSF shifts from high latitude to low latitude, or the hight of the forming region changes together with the X-ray luminosity The latitude change First, we consider the possibility that the location forming the CRSF changes along the latitude with the X-ray luminosity. By the theory (e.g. Padmanabhan 2001, and classical references therein), the accretion matter falls onto the pulsar pole as a ring like shape, and the radius of ring, R pole (typical value 1 km) is described as R pole ( RNS 91 r A ) 1/2, (7.1)

97 92 CHAPTER 7. DISCUSSION where r A L 2/7 X is Alfven radius (see Section 2.2.3, Equation 2.4). In the case of change of the CRSF energy in 4U , the expected change of R pole between March 27 (L X = erg s 1 ) and April 10 (L X = erg s 1 ) is a factor of 1.2. Then the estimated change of the magnetic field between two data set is several percent. However, the observed CRSF energy increased by a factor of 1.5 from March 27 to April 10. Thus this idea cannot be applied to these cases The height change Second, we consider that the height, where the CRSF is produced, changes along the magnetic fields above the pulsar pole with luminosity. Assuming that the pulsar has dipole magnetic field, the observed fundamental resonance energy E a1, which corresponds to the magnetic field strength, depends on the distance from center of the pulsar r, as r 3. Assuming that the CRSF is formed at a height h r above the neutron star surface in the accretion column (Figure 7.1), we expect E a1 (R NS + h r ) 3 (1 + z g (r)) 1 (7.2) with R NS the radius of the neutron star. The factor (1 + z g (r)) 1 describes the gravitational redshift at distance r from center of the pulsar. Assuming the resonance energy to be observed on the neutron star surface is E 0 R 3 NS(1 + z g (R NS )) R 3 NS. (7.3) Then, the relative resonance height, h r /R NS, can be related to the resonance energy as h r R NS = h r = { } 1/3 Ea (1 + z g (r)) E 0 { } 1/3 Ea (1 + z g (r)) 1 R NS. (7.4) 1.32 E 0 Substituting the observed value of E a1 and the typical R NS = 10 km into Equation 7.4, we have calculated h r as a function of the X-ray luminosity. The results are shown in Figure 7.2 and 7.3. Since there is no a priori knowing of E 0, we employed two sets of different values of E 0 ; 17 kev and 20 kev for 4U , and 27 kev and 30 kev for X (see Figure 5.13 and 6.7). The former value of two E 0 sets are close to the observed maximum value of E a1. Both sources, the height h r increases in a rough proportion to the X-ray luminosity. The h r

98 7.1. LUMINOSITY DEPENDENT CYCLOTRON RESONANCE ENERGY CHANGE 93 Figure 7.1: The schematic view of the accretion column on pulsar pole region. of X exhibits the continuous increasing together with the luminosity, while the case of 4U , h r increases until the luminosity erg s 1 where h r appears to saturate at 2 or 3 km which depend on E 0. In addition, h r may approach certain values of 0.1 or 0.7, as L X decreases below erg s 1. This might be considered that the observed magnetic filed as L X is below erg s 1 is the real field strength of the neutron star surface. The results presented in Figure 7.2 may be compared to a theoretical prediction by Burnard et al. (1991), who estimated the height of the accretion column h top as Here, L eff Edd h top R NS L x L eff Edd H. (7.5) is the Eddington luminosity along the magnetic field which is identical to the conventional Eddington Luminosity for a 1.4M neutron star, L eff Edd = ergs s 1. H is the ratio of the Thomson cross section to the Rosseland-averaged electron scattering cross section for radiation flows across the magnetic fields. The dashed line in Figure 7.2 shows this prediction, assuming H = 1.23 (Mihara et al. 2004) and R NS = 10 km. Except for the observed saturated part in high luminosity, the measured h r is about 70% of the predicted h top. This is quite reasonable, because the resonance energy would sample the magnetic field strength which is measured at, or slightly below, the top of the column (i.e., h r < h top ).