Sandra de Jong. August 16, 2010

Transcription

1 The neutron-star low-mass X-ray binary 4U -6: distance measurements, timing and spectral analysis and discovery of a kilo-hertz Quasi-periodic Oscillation Sandra de Jong August 6,

2 Contents Introduction. The Rossi X-ray Timing Explorer Structure of the source and emission processes Thermonuclear X-ray s What happens in a burst? Photospheric radius expansion bursts X-ray Colours Hardness Diagrams Colour-colour diagram Power density spectra Data analysis and Results 5. s Visual identification Spectral fitting Distance determination Colour-colour and colour-intensity diagrams Hardness-diagrams and hardness-intensity diagrams... Colour-colour diagram Timing analysis Discovery of a kilohertz QPO Hysteresis Discussion 5. Calculation of the distance Colour analysis Timing analysis Conclusions 6 A Data 4 B properties: profiles 4 C properties: duration and peaks 47 D fits 48 E Crab Soft colour over the years 8 F QPO fits 8 G Power spectrum fits 8

3 Introduction An X-ray binary is a binary system with a compact object (white dwarf, neutron star or black hole) and a main-sequence companion star. The compact object accretes matter from the secondary via an accretion disk, generating a lot of energy. In 964 already, Salpeter [] suggested that accretion might be the the energy source in quasars. The idea of accretion onto a compact object as a power source was first suggested by Shklovsky in 967 [4]. We discern High Mass X-ray Binaries (HMXB) and Low Mass X-ray Binaries (LMXB), depending on the mass of the secondary. Another difference is the main source of radiation. In LMXB the optical light is dominated by the X-ray-heated accretion disk whereas in HMXB the optical light is dominated by the companion star []. The source 4U -6 is an LMXB with a neutron star primary. The source was first detected by Uhuru (Forman et al, 978 [6]) and Ariel V (Warwick et al., 98 [7]). The source exhibits irregular type X-ray bursts (van der Klis et al., 984 [8], 985 [9]) (more about bursts in section.) and periodic intensity dips (van der Klis, 985 [9], Parmar, Gottwald & van der Klis, 989[] (more about dips in section.4). The distance to the source is constrained to between kpc using burst properties (Parmar et al., 989 []). The dips indicate that the binary is seen at a high inclination, i = 6 8 (Frank, King& Lasota, 987 [7]). I will try to constrain this distance better using a possible photospheric radius expansion burst (see section..). Furthermore, this source has a reported Quasi-Periodic Oscillation (QPO) at Hz (Jonker, van der Klis & Wijnands, 999 [6]) and I have discovered a QPO at around 5 Hz (more information about QPOs in section.5 and the discovery of the khz QPO in section..). The Rossi X-ray Timing Explorer The data I used in this thesis have been taken with the Rossi X-ray Timing Explorer (RXTE). This satellite was launched in 995 into a low-earth orbit (6 km) with on board three instruments: the Proportional Counter Array (PCA), the High Energy X-ray Timing Experiment (HEXTE) and an All-Sky Monitor (ASM, Jahoda et al., 6 [8]). I have used data taken with the PCA, which consists of 5 Proportional Counter Units (PCUs). Each PCU has a collecting area of 6 cm and has channels ranging from to 56, covering a (nominal) energy range from to 6. The time resolution is microsecond. The detector consists of several layers: a mechanical collimator with a FWHM of o, an aluminized Mylar window, a propane-filled veto volume, a second Mylar window and a xenon-filled main counter. The main counter is further divided into

4 layers and each xenon layer is divided into left and right. (Jahoda et al., 6 [8]). An incident photon with a certain energy hits the main counter and triggers a chemical reaction which changes the voltage in the detector. To convert the voltage change into the original photon energy a response matrix is used. This gives the information about the probability that an incident photon of a particular energy will be observed in a particular instrument channel. The information from the PCA goes to the Experiment Data System (EDS). The EDS bins the data using six Event Analyzers. There are seven basic modes possible, and within these modes there are several possible configurations. For all observations two Event Analyzers are dedicated to the standard modes: Standard- and Standard-. The Standard- configuration has a time resolution of.5 seconds and no energy resolution, all 56 channels are combined. The Standard- data have a time resolution of 6 seconds ( seconds if the source is bright) and uses 9 energy channels. In this research (except for the standard modes) I used the Good Xenon mode (where available) and Event mode. Good Xenon mode has the highest time and energy resolution, it combines information from two Event Analyzers. Good Xenon mode uses all 56 energy channels and has a time resolution of.95 microseconds. The Event data has a time resolution of 5 microseconds and uses 64 energy channels, covering the full band of the PCA. The data have been taken over several years. The first observations are from 997 during days (Obs Id=66). Two years later, in 999, observations were made with an interval of a month in between (ObsId=44). The next set of observations was made during day in (ObsId=75). The last data were taken in 4 during days (ObsId=96). A more detailed list of when the data were taken, the observation time and the time resolution can be found in the Appendix.. Structure of the source and emission processes To understand the processes of emission and accretion I will describe the most common model of the accreting X-ray binaries in more detail. As mentioned before matter is accreted via an accretion disc around the compact object. Around this there is probably some kind of corona, consisting of hot, low-density gas. Occasionally there is also a jet present that is oriented perpendicular to the accretion disc. For neutron stars a jet has been observed only in LMXB, where the magnetic field of the compact object is weak (Kaufmann Bernadó& Massi 7 [6], []). Accreting matter can form a disc if the angular momentum J is too large to hit the accretion object directly. This means that the circularization radius, the radius where matter would orbit if it lost energy but not angular momentum: R = J GM, where M the mass of the accreting object, is larger 4

5 than the effective size of the accretor ([]). This condition always holds for accretion via Roche lobe overflow. The rotation in the accretion disc is differential, the angular velocity depends on the radius and increases when the radius decreases. This differential rotation causes viscous shear within the disc which causes the gas to lose energy by radiation (Pringle 98[5], []). Assuming the disk is cooled such that the local Kepler speed v K = (GM R) / is supersonic, I can use the thin disc approximation: the height H cs v K R R, where R is the radius of the disc and v K the local Kepler speed. This means that the vertical and radial components of the disc are decoupled. In a steady state, the local effective temperature distribution becomes (assuming the disc is optically thick in the vertical direction): T eff = ( ) /4 [ GM Ṁ 8πσR β ( Rin R ) / ] /4 () Here Ṁ is the mass accretion rate and β a dimensionless quantity depending on the boundary conditions of the inner edge radius R in (β is for a non-rotating star with R in equal to the stellar radius, Pringle 98 [5], []). The strength of the magnetic field of the compact object is important for the behaviour of the accretion flow near the compact object. Generally compact objects in HMXB have a strong magnetic field, around Gauss, whereas compact objects in LMXB have a low magnetic field, < Gauss (Done, Gierliński & Kubota, 7 [4]). Black holes do not have a magnetic field since they have no surface, but I will not expand on the black hole physics in this report, I will focus on neutron stars only. If the magnetic field is strong, the accretion disc is truncated and the accretion flow will be channeled onto restricted regions of the compact object. For weak magnetic fields the disc will reach further inwards. For slowly rotating stars, with ω < Ω K, (where Ω K = (GM R ) / is the Kepler angular velocity) with a weak magnetic field the inner parts of the accretion disc cannot spin at the Kepler angular velocity when hitting the surface of the neutron star, since the star is spinning slower than Ω K. This means that between the disc and the surface there will be a boundary layer, where the accretion flow is no longer Keplerian, to adjust the angular velocity of the material before it is accreted onto the compact object. The boundary layer must release energy via dissipation and kinetic energy in the form of infalling material on the compact object (Mitsuda et al 984 [5]). If the angular velocity of the compact object is similar to the Kepler velocity there is no boundary layer (Balsara 9 [5]). The magnetic field can be measured directly in, for example, pulsars or indirectly by looking for features from the inner accretion disc. If there are features that arise from close to the neutron star, like kilo-hertz quasiperiodic oscillations (more about those in section.5), the magnetic field is not strong since the disc is not truncated. The pulsar method of measuring 5

6 the magnetic field is by the evolution of the spin rate of pulsars. The spin of isolated pulsars will decrease over time since rotational energy is emitted via magnetic dipole radiation, giving B = Ic PP 8π R, with period P, period 6 derivative P, moment of inertia I and radius of the object R (Gunn & Ostriker 97 [6]). For accreting pulsars in a binary, the situation is slightly different since the radiation energy comes (partly) from the accretion. In this case, however, magnetic fields can be inferred from cyclotron lines seen in the X-ray spectrum (Clark, Woo, Nagase, Makishima & Sakao 99 [9]). Generally the emission from X-ray binaries can be described very well by a blackbody for the thermal emission arising from the disc, and a power law to account for a high energy component (a possible mechanism for this component is inverse Compton scattering: photons from the disc or neutron star will gain energy by scattering with high energy electrons). Here I will describe in a bit more detail the types of emission we can expect from different components of the source. The disc is assumed to be geometrically thin (as explained earlier) and optically thick. This means the disc will behave as a blackbody at each radius where the effective temperature is defined in Eq. (). Furthermore the disc will emit reprocessed X-rays from the inner disc. In the cooler outer regions of the disc this will be optical and UV radiation. For HMXB the emission at optical/uv is dominated by the companion OB star, so absorption features from the companion star can be found in the optical/uv spectra. The inner accretion disc emits blackbody radiation as well, but since the temperature here is higher than in the outer regions of the disc, instead of UV radiation soft X-rays are emitted in the range of.5.5. If the compact object is a neutron star, it will also emit X-rays (few ) from its surface. This is influenced by the accretion rate and different states of the binary (low/hard & soft states, see Section.4.). LMXB objects with high inclinations can be obscured by their companion star, but still radiation from the compact object can be detected. Generally the radiation from the compact object has a lower luminosity but a higher energy. This would point to some vertically extended structure. One theory is that an accretion disc corona (ADC) is visible, a dense optically thick gas that forms by the photoionization of the upper atmosphere of the accretion disc by X-rays from the inner accretion disc and neutron star (See Fig ). In the ADC photons can be upscattered by inverse Compton processes. Some LMXBs show emission lines in their spectra, which could be originating from the ADC since it is optically thick and emission lines can be formed efficiently in an X-ray photo-ionized gas (Ko & Kallman, 994 [8]). Another theory is that sources have a corona with hot gas around the compact object (See Fig ). The X-rays from the inner disc will inverse Compton scatter photons to higher energies. The temperature of electrons in the corona is a few up to a few tens (for the low/hard state of some 6

7 Figure : Schematic impressions of the corona (left) and the accretion disc corona (ADC, right). In the middle of each picture is the neutron star (NS) with around it the accretion disc. The corona can be seen around the neutron star and the inner part of the disc, while the ADC is visible only above and below the accretion disc. atoll sources, Paizis et al. 6 [7]). For HMXB it is not clear if there is a corona as well. If there is a jet present in the source, it will emit radio radiation via synchotron processes. Some sources also emit diffuse radio emission. HMXBs with neutron stars have no detectable radio emission. For LMXBs Z-sources are stronger radio emitters than atolls (Paizis et al, 6 [7], Z- and atoll sources are explained in Section.4.).. Thermonuclear X-ray s As noted before, X-ray binaries have a compact object that accretes matter via an accretion disk from their companion star. For HMXB the matter is transferred onto the accretion disk via stellar winds. In LMXBs this wind is less strong since the companion star is of lower mass and accretion happens via overflow of the Roche lobe, the gravitational potential lobe. X-ray bursts have only been observed in LMXB. Furthermore, if an LMXB shows X-ray bursts, the compact object is a neutron star, since a surface is needed for the bursts to develop [][]. We discern between two types of bursts, the regular bursts or type I (these are meant when bursts are named without number) and the type II bursts. Type I bursts are due to burning of accreted material on the surface of the neutron star and have been observed in many LMXB. Type II bursts are thought to be related to spasmodic accretion and have so far only been observed in two sources[]... What happens in a burst? The transferred matter, mainly hydrogen and helium, falls via the accretion disk onto the neutron star and forms a thin shell. We define the accretion 7

8 rate per unit area as ṁ = Ṁ/A acc, where Ṁ is the accreted material and A acc is the surface covered by the accreted material. The accreted matter becomes part of the neutron star and undergoes hydrostatic compression as new material is piled on top of it. The temperature and density rises and the material ignites. The hydrogen burning process goes via the CNOcycle. This is thermally stable for high ṁ (> g cm s ), but not for lower ṁ (< 9g cm s ), so a burst can occur []. For high ṁ the helium burning is not stable, there is a high temperature dependence for the helium burning rate, making it susceptible to thin shell instabilities causing a burst. For values of ṁ between 9 gcm s the hydrogen completely burns before the helium ignites, but this can still lead to a burst []. The thermal instability develops into a burst. The temperatures during the thermal instability are very high and produce elements beyond iron via the rapid-proton (rp) process (Heger, Cumming, Galloway & Woosley, 7 [9], []). This process burns the hydrogen via proton-captures and β-decay, which indicates that the energy release of the burst last for - seconds after the start of the burst. In the case of a pure helium burst the burst lasts shorter, in the order of 5- seconds[]. In appendix B all burst profiles found in 4U -6 are shown. Some sources show double bursts, two bursts with short interval times (7 s to s), where the second bursts is much less luminous (Galloway et al., 8 [], Keek, Galloway, in t Zand & Heger [7]). There are also instances of triple and even quadruple bursts (Boirin et al., 7 [], Keek et al. [7]). The short recurrence time between these bursts is not sufficient to accumulate enough fuel to allow ignition by unstable burning. The fuel is either a leftover unburnt material from the previous burst or newly accreted... Photospheric radius expansion bursts The maximum luminosity that can be achieved by accretion is the Eddington luminosity or Eddington limit which is: L Edd, = 8πGm PM NS c[ + (α T T eff ).86 ( ] GM ) / NS ζσ T eff ( + X) Rc () ( ) =.5 8 MNS + (αt T eff ).86 ( GM / ) NS M ζ( + X) Rc () Here M NS is the mass of the neutron star, T eff the effective temperature of the atmosphere, α T a coefficient parametrizing the temperature dependence of the electron scattering opacity (. 9 K ), X the mass fraction of hydrogen in the atmosphere (.7 for cosmic abundances) and ζ accounts for the possible anisotropy in the burst emission []. For a neutron star with a mass of.4m, a radius of km and X =, this gives L edd 8 M M ergs/s 8

9 (Kuulkers et al., []). At this limit the outwards radiative pressure is balanced by the gravitational force inwards. During a burst, the spectrum can be fit very well with a blackbody function, a function of temperature T and radius R: L BB = 4πR σt 4 eff (4) When the luminosity equals the Eddington luminosity it cannot increase anymore. To cool down the outer layers of the star, the photosphere, are lifted. This increase in radius causes the effective temperature to drop since they are related via the black body relation in Eq.(4). This is called a photospheric radius expansion burst (PRE burst). PRE bursts can be detected by either their flux or the evolution of the hard colour of the source (see for definition of colours Section.4). Some PRE bursts show double peaked profiles in the light curves. As the temperature lowers, the flux shifts (at least partially) out of the detectable frequency range of the instrument (sometimes even below the X-ray band). Strong events sometimes show a precursor, a fast increase in X-ray intensity that lasts only for a few seconds before it falls back to the persistent level for a few seconds. After that, the burst starts. Sometimes the light curve does not show a convincing PRE burst, but the PRE nature of a burst can still be deduced by modelling the burst with a blackbody or by studying the hard colour of the burst as the amount of soft photons will increase compared to the amount of hard photons[][]. Due to the upper limit to luminosity that PRE bursts provide, they are used as standard candles. Since there are some assumptions in the mass of the neutron star and the nature of the accreted matter, the errors of this method are within 5% (Kuulkers et al., []). Besides for the distance to the source, PRE bursts can also be used to find the mass and radius of the neutron star by measuring the effective temperature when the luminosity is Eddingon-limited (the result is independant of the distance to the source). A draw-back is the dependence on a model to convert the observed colour temperature into an effective temperature (Fujimoto & Taam, 986 [44]..4 X-ray Colours X-ray instruments generally do not have a good spectral resolution. A way to do spectral analysis is by looking at the emission of a source in different energy bands. Changes in spectral components will reflect into changes in the colours. The hardness ratios, or colours, are defined by splitting the entire energy band into (typically) four parts. The intensity in the second part is divided by the that of the first and is called the soft colour. The intensity of the fourth part is divided by that of the third and is called the hard colour. The soft colour is mainly influenced by absorption effects, whereas the hard colour is less affected by interstellar absorption and more by changes in the high-energy continuum (Schultz, Hasinger & Trümper, 9

10 989 [5]). Another advantage of using colours is that statistics are improved since several energy channels are averaged together. This is especially useful for faint sources, where the count rate per individual energy channel is very low which give bad statistics. Also, since X-rays sources are very variable, the time interval taken to measure a spectrum cannot be too large to avoid mixing several states into the same spectrum. X-ray colours offer in this case a working solution to characterise the source properties over short time intervals with good statistics. Furthermore, the use of colours gives a quantitative view of different components, like the disc and the power law, without the need to use complex models to describe the data. Events like dipping (see below) are also easier to identify in colour-diagrams than in individual spectra..4. Hardness Diagrams One way to study a source is by plotting the hard or soft colour against time to see how the spectral properties of the source evolve. This is a way to study the dipping behaviour. During a dip the luminosity drops and the spectrum hardens. The dipping phase is periodic and is thought to be caused by an obscuration of the central source by material located in the outer regions of the accretion disc (White & Swank, 98 []). This means that the source has to have a high inclination (i = 6 8, Frank, King & Lasota, 987 [7]). Generally the amount of soft photons from the disc decreases because they are blocked by the obscuration. The hard photons originating from the corona are still observed. For 4U -6 the dipping phase lasts for 4 % of the.94-hour orbital cycle (Ba lucínska-church et al., 999[]). can happen during the dipping phase, but they have an apperant lower count rate compared to the bursts outside of dips (Ba lucínska-church et al., 999[]). To study the dipping we can make hardness-diagrams, in which the hard colour is plotted against time. Hardness-Intensity diagrams (HID) show the relation between the Intensity over the whole band versus the hard colour. HIDs can be used together with colour-colour diagrams (see.4.) to distinguish certain states of the source. Using HIDs, it is possible to see the behaviour of the source during dipping and how this relates to the normal state..4. Colour-colour diagram The plot of the soft colour versus the hard colour is called a colour-colour diagram (CCD). The CCD can be used to study the behaviour of a source; it shows the changes in spectral shape independent of the overall intensity. We can discern two distinct patterns shown by LMXB in the CCD and clas-

11 sify sources on the basis of this pattern: atoll- and Z-sources (Hasinger & van der Klis, 989 []. The difference between these two types is thought to be caused by the difference in the rate of mass transfer, where the rate is higher in Z-sources;.5 L edd, compared to.. L edd in normal atoll sources (there are atoll sources that accrete at higher rates, up to.5 L edd []). Therefore Z-sources are more luminous []. Figure shows the pattern of an atoll source (4U 68-5) in the CCD. The atoll shape consists of the lower and upper banana branches, an island-state and some times an extreme island-state. The atoll shape is traced in weeks to months (Muno, Remillard & Chakrabarty, [4]), where the source moves quicker through the banana state (hours to a day) than through the islands (days to weeks)[]. The motion of the sources through the diagram is smooth, following the pattern instead of jumping from one state to another. However, since atoll sources trace the pattern over a long time span the data do not always show all transitions []. In the island state atoll sources can show hysteresis; the source returns to the same point in the CCD but following a different path. In the banana branch hysteresis has not been observed []. Figure shows the pattern of a Z-source (Cyg X-). A typical Z-pattern consists of a horizontal, normal and flaring branch (as indicated in the picture). This shape is traced in timescale of hours to days (Muno et al, [4]). There is no evidence for hysteresis in Z-sources []. The motion of these sources in the CCD is thought to be caused by changes in accretion rate. For atoll sources the accretion rate goes up as the source transits from the (extreme) island state via the lower banana to the upper banana. For Z-sources the accretion rate increases from the horizontal branch through the normal branch to the flaring branch []. There is also a correlation between the state of a source and its X-ray luminosity L X, which is connected to the mass accretion rate. This correlation is better on short time scales, from hours to days, than on longer time scales. The correlation is only within a source and not across sources []. The reason that luminosity does not entirely correlate with the accretion rate is probably because the luminosity is affected by changes in the geometry of the accretion flow (van der Klis et al., 99 []). For atolls the Island state has the hardest spectrum and the lowest luminosity (few tens of, therefore it is also called the low/hard state), the luminosity increases as the source becomes softer and moves through the banana state (few, soft state). For Z-sources the luminosity increases with the mass accretion rate as well (here the horizontal branch is called the hard state, overall the spectra are very soft (few, Paizis et al. 6 [7]). The behaviour of bursts is also driven by the accretion rate and will change throughout the CCD. The duration of the burst (defined as the ratio between total energy emitted during the burst and the burst peak luminosity) decreases as the accretion rate increases (van Paradijs, Penninx & Lewin, 988

12 Figure : An example of the colour-colour diagram of an atoll-source, 4U Each point represents 8s of data. In the picture the states are labeled. Sometimes there is also an extreme island state visible above the island state. The typical error bars of the banana and island branch are included. The hard colour is defined as the count rate ratio in the bands / and the soft colour as /..5. Picture adapted from Méndez et al. (999) []). This is linked to the composition of the accreted material. When the mass accretion rate increases, the amount of hydrogen available for unstable burning during bursts decreases, because at high accretion rates the accreted hydrogen is burnt stably into helium before unstable burning switches on []. The average burst temperature increases when the accretion rate increases (Bloser et al., [])..5 Power density spectra A power density spectrum is calculated from the Fourier transform of the data, in which the power per frequency is plotted versus frequency, visualizing the variability of a source. A power spectrum can show two types of structures: noise (broad features) and quasi-periodic oscillations (QPOs and periodic pulsations []) which are narrow features. There are different types of noise: power-law noise which follows a power law (P ν α ; where α is typically between and ) and includes white noise (α = ), /f -noise (α = ) and red noise (α =, the word is also used for any other noise where P ν decreases with ν). Another type of noise is band-limited noise,

13 Figure : An example of a typical Z-source, Cyg X-. Each point represents s points of data, typical error bars are shown. HB, NB and FB are, respectively, the Horizontal, al and Flaring Branch. Hard colour is defined as the count rate ratio in the bands 6 /4.5 6, soft colour as 4.5 /. This picture is taken from Hasinger & van der Klis (989). which extends over a broad frequency ranges but then drops steeply toward higher frequencies. QPOs are fluctuations with a preferred frequency (the central frequency) and visible as peaks in the power spectrum ([]). The width of the peak is a measure for the coherence time of the signal. QPOs are thought to be obstacles in the accretion disc (van der Klis, 5[]) and have central frequencies ranging from. Hz. The QPO does not always appear exactly at the same frequency, there is some variation due to source state and luminosity changes, thus mass accretion rate of the source (van der Klis, 5[]). The strength of a QPO is measured in root-mean-squared (rms) amplitude; a way of expressing the strength of a feature using the count rate of the spectrum via: P rms = S + B S + B (5) S Here P is the Fourier power of the feature, S is the flux from the source and B is the background flux (Rms amplitude can be used to express the power of any feature in the power spectrum []). Generally we can describe three types of QPO depending on their central frequency: the kilohertz QPO (ν > Hz), hectohertz QPOs (ν = Hz) and low-frequency QPOs (ν < Hz) (van der Klis, 5[]). The division reflects current ideas about the origin of these different types of QPOs. The khz QPOs are the fastest variability components that have been detected in X-ray binaries. They were first detected in 996 by RXTE; earlier instruments lacked the time resolution, effective area of telemetry rate

14 needed to detect the fast variability. The high frequency of these QPOs indicates they arise from the inner part of the accretion disc, close to the central compact object. This suggests that the magnetic field in the sources where khz QPOs are detected is weak (see also section.). The khz QPOs tend to come in pairs, with a separation of 7 6 Hz (Méndez & Belloni, 7 [9]) depending on the central frequency. The hhz QPOs were first reported in 998. These type of QPOs stand out because of their approximately constant central frequency, independent of other source properties. They appear in atoll sources in most states and the central frequency is quite similar across sources []. Low-frequency QPOs were first mentioned in 98. These types of QPO are thought to be a blockage from the outer parts of the accretion disc, since they have low frequencies that correspond with the Keplerian angular velocity in the outer regions of the accretion disc. Atoll sources show low-frequency QPOs at 6 Hz and khz QPOs at 5 5 Hz (Hasinger & van der Klis, 989[], Psaltis, Belloni & van der Klis, 999 [4]). In the lower left banana state the twin khz QPOs can be observed. The hhz QPO can be seen in almost all states []. Some dipping atoll sources also show a QPO at low frequencies, between.6.4 Hz that has hardly any dependence on photon energy. Other sources have shown a QPO at the upper banana branch in the range of 6 4 Hz. [] Z-sources show 5- Hz and 5-6 Hz low-frequency QPOs and - high-frequency QPOs (Psaltis et al., 999[4]). A 5-6 Hz QPO and a khz QPO are visible at the horizontal branch and upper normal branch. At the lower normal branch there is a QPO at 6 Hz and at the flaring branch there is no really visible QPO, but mostly noise []. The source 4U -6 has a known QPO at Hz, found in the data with ObsId by Jonker, van der Klis & Wijnands, 999 ([6]). The QPO is persistent through bursts and dips. This QPO has an rms amplitude of 9 %, which remains also constant during bursts and dips. 4

15 Data analysis and Results In this section of the report I present the methods I used for the data reduction and results.. s.. Visual identification To find bursts, I started by creating light curves of all the data using the ftools package. This package is designed to be used with the data from RXTE. For each observation I checked which PCUs were on, sometimes a PCU switches off during an observation, causing a drop in the count rate. Another phenomenon that I found mainly in the first datasets are fall-outs, in which the count rate goes to for a few milliseconds. This is due to deadtime effects after the detectors have encountered a high-energy particle[4]. Also I took into account the Good Time Intervals, the times during which data was received (excluding PCA break downs). Figure 4 shows a light curve from the observation with ObsId A double burst can be seen at and seconds from the start of the observation. At 5 and 8 there are normal bursts. Also around 5 seconds there is a drop in count rate, due to one of the PCUs turning off. At two instances ( 45 and 5 seconds) a fall-out is visible. In total I found bursts, of which four are double bursts, during this report I will use S for a single burst and D and D for the two bursts in double bursts. From light curves with more than one burst I could measure the time between bursts, which ranges from 6 seconds to seconds between single bursts. From the second of a double burst to the next single burst the waiting time ranges from 8- seconds. The four double bursts were found in, respectively, ObsIds (two, separation times of 65 and 7 seconds), (one, separation time 7 seconds) and one in (separation time 85 seconds). In the appendix the burst profiles of all bursts can be found as well as the duration and count rates of the bursts. The most luminous burst is in ObsId 75---; this burst has a count rate of 9 counts/pcu/s, whereas most single bursts have a count rate of 4 counts/pcu/s. Generally the rise time is seconds and the burst duration varies between 7 and seconds for single bursts and the first of a double bursts. The second burst in a double does not always have the clear fast rise time and exponential decay as the singe and first bursts of doubles have, which can be seen in the appendix. The total duration of the D bursts is between the and 5 seconds. These times are estimates since it is not easy to find the true end of the burst as it fades out. Here I define the end of a burst as the moment when the post-burst flux is leveled within the persistent emission before the burst within σ. 5

16 Figure 4: The light curve of 4U -6 from one of the observations in 44---, with a time resolution of second. In this light curve there is a double burst visible (the first set) and two single bursts. Also around 5 seconds into the observation one of the PCUs turned off, which is visible as a drop in the count rate. There are two detector drop-outs at 5 and 5 seconds. Here the count rate is zero due to high energy particles. 6

17 .. Spectral fitting None of the bursts looked like PRE-burst in the light curves. To be sure I fitted the spectra of the bursts with a blackbody spectrum. PRE bursts show characteristic behaviour in the spectra, the black-body temperature dips simultaneously to a peak in the effective black-body radius. To model the bursts I used the xspec program. Using the light curve I find a rough estimate of the start and end points of the bursts. Then I extracted spectra from the burst every.5 seconds. I also made a spectrum of the persistent emission just before the burst. This contains data from both the source and the background. The persistent emission is due to continued accretion during the burst, but since the burst is much more luminous I can safely subtract this emission to keep only the burst emission. Using both the burst spectra and the persistent spectra in xspec I can determine the true start and stop of the burst. This is done by subtracting the persistent emission from the burst emission. xspec gives the count rate and error of the persistent-level subtracted emission. If the count rate of the subtracted spectrum is more than σ different from zero, the burst emission is not leveled with the persistent emission. If in the count rate is less than σ different from zero, I assumed that the emission is leveled with the persistent emission. To know which channels correspond to which energy bands I need to create a response matrix. This is not only because the data can be binned in several configurations, but also because the channel-energy relation changes over time. The observed emission (O, per channel ch) is a convolution of the response matrix (R, depending on the energy E and the channel ch) and the real emission (depending on energy E): O(ch) = R(E, ch)i(e)de (6) Which can also be expressed as : O = R I. The observed emission O and the response matrix R are known. However, we cannot invert this equation into R O = I, this will create large errors. xspec will assume I and will create O = R I. O will be compared to O. If they are not the same I will be adapted and the process will be repeated until the difference O O is minimal. Then it can be assumed that I = I and the real emission is known. Creating the response matrix can be done with the tool pcarsp. To use pcarsp one needs to provide a spectrum-file (.pha), an attitude file (needed if the satellite was not pointed directly at the source, not necessary in this case), the layers used (all) and the detectors used (all). In xspec I ignore the energies in the ranges -.5 and 5+ since they are not properly calibrated. The model I used for the fit is a simple absorption 7

18 model (wabs) to account for the interstellar absorption in the direction of the source, times a blackbody spectrum (bbody). The absorption model accounts for the photo-electric absorption the radiation undergoes on the way to the observer. This model has only one parameter, the equivalent hydrogen column N in units of atoms/cm : M(E) = exp( Nσ(E)) (7) The function σ(e) is the photo-electric cross-section and depends on the element abundance in the interstellar medium. Here we assumed solar abundances. The blackbody spectrum models the radiation from the source itself and has two parameters: the temperature (in ) and a normalization constant K: E de A(E) = 8.55K () 4 (8) (exp(e/) ) Where K is defined as K = ( L 9 d ) (9) Here L 9 is the luminosity of the source in units of 9 ergs/s and d is the distance to the source in units of kpc. Earlier measurements found the equivalent hydrogen column towards 4U -6 to be 4 atoms/cm (Parmar et al., 989 []. I ran the fit program twice, once with the equivalent hydrogen column fixed to that value and once letting this parameter free. When calculating the errors for both cases I estimate both the 68% and the 9% confidence levels. If given parameter was not σ or more significant, I calculated the 95 % confidence upper limit. In reality this applies for the equivalent hydrogen column N H and the normalization parameter K. For the temperature parameter, especially in the beginning of the burst, it is possible to get 68% confidence level parameter estimates. For an example of the fitted spectra see Figures 5 and 6. After fitting all the spectra I used Matlab to produce plots of the parameters. In the appendix, Section D are the fits for all bursts. A PRE burst would show a drop in temperature during the bursts. Also the normalization of the blackbody component would go up since it is linked to the radius via the luminosity. However, I was unable to find such a burst... Distance determination I was unable to find a PRE-burst and cannot determine the distance exactly. However, I am able to set an upper limit to the distance using the brightest burst: the second burst in which has a count rate of 9 counts/s/pcu, more than twice the count rate of other bursts. We know this burst has a luminosity less then the Eddington limit. I calculate the 8

19 Figure 5: xspec plot of 4U -6 of the first burst in This spectrum is taken seconds after the burst has started and has an exposure of.5 seconds. The spectrum covers the.5-5. energy range. The fitted model is also plotted. The lower plot shows the residuals to the best-fit model. Figure 6: xspec plot of 4U -6 of the first burst in This spectrum is taken when the burst is almost over, 88 seconds after the burst has started and has an exposure of.5 seconds. The spectrum covers the.5-5. energy range. The fitted model is also plotted. The lower plot shows the residuals to the best-fit model. 9

20 distance to the burst if it did have a luminosity at the peak of the burst equal to the Eddington luminosity to find the upper limit. LEdd d = () 4πF peak I set the luminosity equal to the Eddington limit:.7 8 ergs/s (for a.4m neutron star, Kuulkers et al., []), see section... I can use the value of the normalization parameter K to find the flux: K = L 9 d Here I can substitute for the luminosity: = L d 7 () K = 4πσR T 4 d = 4πF bol () Here F bol is the bolometric luminosity. The value for K from the fit is (8.8±.4), giving a 4πF bol of (8.75±.4) 5 ergs/s/kpc. Now plugging this in the formula with the Eddington Luminosity this gives an upper limit to the distance (since the peak luminosity of the burst is in fact not equal to the Eddington luminosity but less) of.4±.6 kpc. The error only depends on the error in K. The value found is consistent with the previous estimate of the distance being - kpc by Parmar et al (989)[].. Colour-colour and colour-intensity diagrams To study the dipping in the source and to see the behaviour of the source in the colour-colour diagram I create light curves in different energy bands. For this I use the Std- data and a time resolution of 6 seconds. For each observation I produce five light curves:..7,.7 6., , and. 6.. After this I subtract the background in these bands. The background is estimated using the data from PCU in the Std- files, because this PCU is always on. In the Std- files the particle rates are included that are necessary to estimate the background. During the creation of the background deadtime corrections are also taken into account. The background is estimated by using matching background conditions to the observations to models which contain actual background observations. I define the soft and hard colour as respectively.7 6. /..7 and / count rate ratios in these bands. I define the intensity as the entire. 6. band count rate... Hardness-diagrams and hardness-intensity diagrams To study the dipping behaviour of the source I have made hardness-plots. Here I plot the hard colour versus time and compare it with the count rate

21 of all channels versus time. By comparing these plots the dips are easy to recognize, see for example Figure. The dipping properties differ between observations. For ObsId=6 the hard colour during non-dips (persistent emission) is between.7.8 and during dips this goes to.. The bursts have a hard colour of.55, also one burst that happens during a dip. For ObsId=44, the hard colour for the persistent emission is the same.7.8, but the dips have a hard colour of..65. Here the bursts have a hard colour of.55 as well, also the one burst that happens during a dip. For ObsId=75 the hard colour during the persistent phase is.5, which is a drop compared to the previous observations. During dipping the hard colour ranges between and during bursts the hard colour is between.5.. In ObsId=96 the hard colour returns to.7.8 for non-dipping intervals and..9 during dipping. The hard colour during bursts is.45 and two bursts happened during dipping. In total I have found bursts, of which 6 happened during dipping intervals, including of the 4 double bursts. Since the dipping lasts for % of each cycle, one would expect slightly more bursts () to happen during the dipping. The bursts that happen during a dip have a lower average count rate (9.7 counts/pcu/s including D-bursts, 7.4 counts/pcu/s excluding D-bursts) than the average of all bursts (4.6 counts/pcu/s including D-bursts and the largest burst, 77. counts/pcu/s excluding D-bursts, but including the largest burst and 56.4 counts/pcu/s excluding both the D-bursts and the largest burst). For the hardness-intensity plots I use the hard colour as defined before and the intensity in the total. 6. -band. In Fig 7 I plot the sampled data with error bars. In Fig 8 the shape of the data is more visible. Here I have also indicated where the different observations happen. As shown in the plot, the observations are divided in streaks which have a left to right motion and bend slightly down towards the right. ObsId 66, part of ObsId 44 and ObsId 96 are located in the middle streak. The rest of ObsId 44 is visible in the high streak and ObsId 75 is entirely in the lowest streak. I have plotted the dipping behaviour in Fig 9. As expected the dipping is visible in the higher left corner of each observation where the intensity is lower and the hard colour higher.

22 Figure 7: Hard colour versus intensity with error bars for all RXTE observations of 4U -6. Each dot represents data with a duration of 56 seconds. The bursts have been removed from the data set and the colours are normalized by Crab (see text for details)..8 Hard colour / Intensity.-6. Figure 8: Hard colour versus intensity of 4U -6 per observation. Green circles are data from ObsId=6, blue crosses ObsId=44, red plusses ObsId=75 and black stars ObsId=96. Each dot represents data with a duration of 56 seconds Hard colour / Intensity. 6. x

23 Figure 9: Hard colour versus intensity of all data from the RXTE observations of 4U -6. The green points show the dipping phase, which is on the higher left part of each streak, where the hard colour is higher and the overall is intensity lower. Each dot represents data with a duration of 56 seconds.

24 4 Figure : An example of a light curve of 4U -6 combined with a plot of time versus the hard colour. This plot is taken from the observation This observation lasts for.5x 4 seconds and shows 4 bursts and three episodes of dipping. The first burst takes place during the dip. The bursts are clearly seen as peaks in the lightcurve and a small downward excursion in the hard colour. The dips appear as irregular episodes in the lightcurve and as intervals of increased hardness in the hardness versus time plot.

25 .. Colour-colour diagram The colour-colour diagram was made twice. I first made a preliminary CCD using the Std- data as described before. I removed the bursts and plotted the soft against the hard colour. Figure shows the plot. One would expect to see an atoll or Z-shape, but the source traces no visible pattern, but rather random islands. This has several causes; the PCA has changed over time and the channel-to-energy distribution and effective area have changed as well. The five PCU s all behave differently. Also, initially, I did not interpolate in channel space to define fixed energy boundaries for each band. To correct for the gain changes and the differences in effective area, I normalize the colours and intensity of 4U -6 by the corresponding Crab values, using observations that are close in time. The Crab Nebula has a constant X-ray emission over time scales much longer than the spin period of the Crab pulsar of ms (Toor & Seward, 974[4], van Straaten, van der Klis & Méndez () [4]), making it a very useful source to calibrate X-ray instruments. See Fig E (in the appendix) for the evolution of soft colour (defined as.5 6./..5 ) of the Crab versus time. Visible in the figure are the four gain changes, in which the PCU was reset to a new gain. To find the correct count rates in each energy band I interpolated linearly in channel space. To make the final CCD I used corrected data. There is a slight change in the energy bands for this diagram compared to the previous one. The colours are now defined as soft and hard colour as.5 6. /..5 and /6. 9.7, respectively. This CCD can be seen in Figure. Each point represents 56 seconds of data. Without the sampling the shape of the source is less visible due to hysteresis. However, still the source does not show a clear atoll or Z-shape. The first set of observations (ObsId = 66) was taken in 997 during 4 consecutive days, and is located in the middle of the CCD with an average hard colour of.5 and an average soft colour of. The next set (ObsId = 44) was taken in 999 distributed over months; the source started out in the middle of the CCD with average hard and soft colour similar to those in ObsId 66, but during the last observation in this set the source was in the upper right part of the CCD, with an average hard colour of.5 and an average soft colour of. The following set (ObsId = 75) was taken in during one day. The source was then at the lower left part of the CCD, with an average hard colour of and an average soft colour of.5. The last set (ObsId = 96) was taken in 4 during two consecutive days. The source was back again in the middle of the CCD, with hard and soft colour similar to those of the first two observations. One can use this CCD to study bursting and dipping behaviour, by connecting burst and dipping properties to the state of the source. Using the CCD I can track where the bursts happen and check if the bursting behaviour 5

26 Figure : First CCD of 4U -6, of all RXTE data. Here backgroundsubtracted Std- data is used. All points represent the average colours in each separate observation. The hard colour is defined as / and the soft colour as.7 6. /..7. For this plot I have not corrected for the detector gain change and the change in effective area of the detectors over the years. Green circles are data from ObsId=6, blue crosses ObsId=44, red pluses ObsId=75 and black stars ObsId=96. 6

27 Figure : Second CCD of 4U -6, using background subtracted Std- data that is corrected for detector gain changes and effective area and sampled every 56 seconds. The colours are defined slightly different than before: hard colour is defined as / and the soft colour as.5 6. / Hard colour / Soft colour 6.-.5/.-.5 Figure : The CCD of 4U -6. Same data as in Fig but with indication of the observations. Color coding is the same as for Figure ; green circles are data from ObsId=6, blue crosses ObsId=44, red pluses ObsId=75 and black stars ObsId=96. (Error bars left out for clarity, see Fig ) Hard colour / Soft colour.5 6./..5 7

28 Figure 4: The CCD of 4U -6, each point representing 56 seconds of data, where the moment before the burst is indicated. The blue points show where a single burst happens and the green points where a double burst happens. The black dot indicates the brightest burst. can be related to the state of the source. Figure 4 shows the CCD with error bars again, with an indication of the point before a burst happens. In this Figure also the most luminous burst is indicated with a black dot. This burst is the left most burst in the entire plot, but not the softest. I have also indicated the dipping behaviour in Figure 5. The dipping periods are located at the top-right part of each observation isle but is connected to it. The dips do not all happen in the same place of the CCD nor are they completely disconnected from the non-dipping state.. Timing analysis I make the power spectra using the fft xte routine, which takes the FITS files and produces a.tra file. fft xte reads metafiles, where the observations are listed in the metafile. The observations are then put in chronological order and the first point is determined, t. After this the user is asked to select the energy channels for the analysis and to give the time resolution τ. Using the fact that these systems have never shown variability above Hz I set the Nyquist frequency, ν Ny at 48 Hz, a power of. τ = ν Ny () 8

29 Figure 5: The CCD of 4U -6, each point representing 56 seconds of data, where the dipping events are indicated by green crosses. During the dipping the source becomes harder. The dipping events are not completely disconnected from the non-dipping isles Hard colour / Soft colour 6.-.5/.-.5 The Good Xenon files have a time resolution of.95 µs, so I need to rebin the data by a factor 56 to get the wanted resolution. For the Event files the time resolution is 5 µs which needs to be rebinned only twice. I chose the length of the FFT, L FFT, to 6 seconds and averaged the 6-s power spectra within each observation to reduce noise contributions. The length of the intervals, L FFT, determines the lowest frequency reached in the power spectrum, which is /L FFT. So with a length of 6 seconds it is possible to reach a minimum frequency of. Hz. Observations that were close in time were processed together to improve the statistics. After this I use the Clean tra routine to remove bursts. During a burst the persistent emission from the source is overshadowed by the burst emission. To further study the power spectra I use the xana routine, that reads the power spectra. Before I can analyse the spectrum I need to subtract the Poisonnian noise. This noise is due to the random nature of the arrival of photons in the time series. The power spectrum of a Poisson process, when properly normalized (Leahy, 98 [47]), follows a χ -distribution with degrees of freedom. Hence, the expected average power is, and the variance is 4. Because of the averaging of the power spectra of consecutive segments of 6 second duration, the variance of the Poissonian noise is actually 4/N where N is the number of averaged power spectra. Due to dead-time effects the noise level can be above or below. This source is not very bright so the dead-time effects are not that important for this. 9

30 To subtract this Poisson level of the power spectrum I take the very last part of the power spectrum, from 5 Hz to the end. Since I suppose there is only noise here, I fit this with a straight line. I subtract this amount from all bins. In Figure 6 the difference between the raw and Poisson-subtracted power spectrum is shown. Figure 6: Power spectra of ObsId The left panel shows the raw power spectrum, where the power from about Hz seems to be. The right panel shows the power spectrum where the Poissonian noise is subtracted. Visible in this spectrum is the -Hz QPO. Raw spectrum Poisson-subtracted spectrum.. Discovery of a kilohertz QPO After this I fit the power spectra with a power law and Lorentzians which gives the best fit, except for the observations with ObsId=75. The fits for all observations are shown in the appendix. For ObsId=75 I combined the observations and which are very close in time (with a gap of 48s) and fitted them with three Lorentzians only. The results can be found in Table and Figure 7. I could not get a good fit of since it has a low signal to noise ratio (S/N). In Figure 7 the Lorentzians have central frequencies of., 5.8 and 5. Hz. I do not detect the -Hz QPO in this observation with 95% confidence upper limit of 7. % rms amplitude. However, I found the Lorentzian at 5 Hz to be significant with a 7.σ single trial significance; the significance was calculated by comparing the power of the Lorentzian to the power of the poissonian background < P >, which is defined as < P >= ± NW, where N is the number of power spectra and W is the number of frequencies that I averaged in the power spectrum. The rms amplitude of the 5-Hz QPO

31 Figure 7: A -Lorentzian fit to the combined power spectrum of observations and 75---, the Poisson-levels have been subtracted as described in the text. The parameters for the fit can be found in Table. The red line is a Lorentzian with a central frequency of.4h and the green line has a central frequency of 5.8 Hz. The blue line has a central frequency of 5 Hz and fits the khz QPO.

32 Table : Results of the fit of and combined using Lorentzians. χ = 4.6/ Lorentzian Central frequency Rms amplitude FWHM.4 ±.9 Hz 4.9 ±. %.4 ±. 5.8 ±.8 Hz. ±.8 %. ±.5 5.± 4. Hz 6.6 ± 4. % 98.4 ± 4. Table : Results of the fit of and combined in the energy ranges -4 and 4- with the 68% confidence level and 95% upperlimit (UL). Energy range All parameters free ν, FWHM fixed ν, FWHM fixed Using the full energy fit Using the best fit -4 rms (68%) 97.9%±5.% 4.%±.9% 98.%±4.9-4 rms (95% UL) 8.7 % 6.7% 4- rms (68%) 8.8%±6.% 8.8%±6.% 8.8%±4.6% 4- rms (95% UL) 7.9% 4.5% is 6.6 ± 4.7 % and the FWHM is 98 ± 4. Hz. I divided the spectra into two energy bands: -4 and 4-, created power spectra of each band and in each band tried to fit Lorentzians to the feature and measure the rms energy spectrum of this QPO. I first tried having all model parameters free. However, I was unable to get significant results, due to the low count rate. After this I fixed the frequency and FWHM to the best-fit values of the full-band spectrum and left only the power free. This is done twice with the parameters from the best fit of the total energy spectrum (here I assume that the frequency and FWHM are energy independent) and the parameters of the best fit of the specific energy spectrum (which were consistent with the values obtained from the fits to the full energy band). The results are given in table. I did not detect a second QPO, even though khz QPOs tend to appear in pairs (Méndez & Belloni, 7 [9])... Hysteresis Since I wanted to study the path of the source in the colour-colour diagram I want to see if the source might be showing hysteresis: this occurs when the source is at the same point several times while following a different path to reach that point each time. I compared the integrated power in the power spectra within a fixed frequency range with the frequency of the QPO at Hz. To measure the -Hz QPO I fit the power spectrum from. Hz to Hz with a power law and one Lorenzian. The results can be found in

33 Table 8. As mentioned before I did not detect the -Hz QPO in the datasets and The spectrum of was difficult to fit since it has a low S/N. In the sets and we found a QPO at.9 Hz and.6 Hz, respectively. Since these values are about twice as high as the values found in the other observations with -Hz QPOs, we argue that in these observations we have detected harmonics of the -Hz QPO. I found a second significant (.-σ) Lorentzian in at.98 Hz, which has less power than the Lorentzian at.86 Hz. For I was unable to find a significant Lorentzian at half the frequency of the.6-hz QPO, but we found a likely one at a frequency of. Hz with a.7 σ significance. To find the rms in a fixed frequency range I added the power in each frequency bin between. and Hz after subtracting the Poisson level. This power is converted into rms amplitude and is plotted versus observation number together with the frequency of the -Hz QPO in Figure 8, where the observations are sorted in time. In this figure the.- Hz integrated power is steady around 5 % rms amplitude for the ObsId=66 (average rms power is 5.5%) and 44 (average rms power is 4.8%), where for ObsId=44---, the observation that is at the right most position in the CCD, is slightly lower at %. After this, the power drops to % for ObsId=75--- (the left most point in the CCD), the average rms power for ObsId=75 is 5.6%. The rms power then increases to 6 % for ObsId=96, where the average is 6.5%. The average frequency of the -Hz QPO is.8 Hz for ObsId=66. In ObsId=44 the average is.6 Hz if the uncertain points and subharmonics are not taken into account. If I do take the subharmonics into account the average is.4 Hz. For ObsId=75 there is no -Hz QPO. In the last set, ObsId=96, the frequency is.8 Hz on average. The observations with ObsId=66, part of ObsId=44 and ObsId=96 have overlapping points in the CCD. If the source is in the same state this would mean the average power and the frequency of the -Hz QPO would be similar. Using the above measurements I can say that ObsId=66 and ObsId=96 are indeed similar states. The power spectra of these observations are also very similar (see Appendix). Even though the average power of the observations with ObsId=44 are similar to the observations in ObsId=66 and ObsId=96, one can clearly see that in the observations in ObsId=44 the source is in a different state. Not only in the frequency of the -Hz QPO but also in the appearance of (sub) harmonics instead of one clear peak. For ObsId=75 the source is clearly in a different state than the rest of the observations. Not only is the -Hz QPO not visible, the average power is very weak compared to the other states. I can conclude that the source indeed shows hysteresis, which, together with the time sampling of observations, may cause the strange shape of the CCD of this source.

34 Figure 8: Evolution of the frequency (black circles with error bars) of the -Hz QPO and the broad-band rms amplitude (between. to Hz, green dashed line) plotted versus the ObsId. The observations are ordered in time. For two observations, and (points 6 and 9 in the plot), I have probably observed an harmonic since the frequency of the peak is about twice as high as the previous and next observations. For I was able to fit a significant Lorentzian to the expected frequency of the QPO based on the harmonic (star) For I could not find a significant Lorentzian. In this case I have plotted a point for the likely QPO frequency based on the harmonic (blue square). The order of the observations: 66---, 66---, 66---, , 66---, 44---, 44---, , 44---, 75---, 75---, 75---, 96---, 96---, Frequency of the Hz QPO 5 RMS amplitude from. Hz to Hz Observations in chronological order, see caption 4

35 Discussion I have analysed the full set of RXTE observations of the neutron-star lowmass X-ray binary 4U -6. For this thesis I carried out both spectral and timing analysis of the observations. I will now discuss my results.. Calculation of the distance I have tried to constrain the distance to the neutron-star low-mass X-ray binary 4U -6 using photospheric radius expansion bursts. Being unable to find such a burst, I used the brightest burst in my sample to find an upper limit to the source distance of.4±.6 kpc. To find this value I made some assumptions: the mass of the star, the chemical composition and the anisotropy of the burst emission. The possible mass of neutron stars range from. M to M, with mass distribution peaks at.7m and.76m for Type II supernovae and. M for type b supernovae (Timmes, Woosley & Weaver, 996 [48]). Without making assumptions of the progenitor event that formed the neutron star, I have assumed a mass of.4m, which fits with both ranges. The chemical compostion ranges between X= for hydrogen poor material to X=.7 for cosmic abundances. Here I have used X=, based on Kuulkers et al., [], who found that the hydrogen-poor composition better fitted the distance measurements to sources with a known distance. We did not take into account the anisotropy of the burst emission. However, since 4U -6 has a high inclination the emission from the source is not expected to be isotropic (Boirin et al, 7 []).. Colour analysis Using colour-colour and hardness-intensity diagrams I have characterised the behaviour of the source in detail. I have correlated the bursting behaviour of the source with the states in the CCD (Figure 4). The double bursts happen in the middle of the CCD and the most luminous burst happens when the source is in the leftmost state. If the source would trace an atoll-like shape, the left most part of the CCD corresponds to the state in which the mass accretion rate is highest among these observations. This can explain the very bright burst at this point. The bursts in this state are also shorter than those in other states (7. seconds compared to 9.9 seconds in the middle state). This is in agreement with the notion that if the mass accretion rate increases the amount of hydrogen in the burning material of the burst decreases (which causes shorter bursts []). The double bursts only happen in the middle part of the CCD. Double (also triple and quadruple) bursts are linked to mixed hydrogen/helium burning, which is thought to happen at low accretion rates (Galloway et al., 8 5

36 []). When the source is in the right most part of the CCD, there are no double bursts, and the bursts that happen in this state have slightly shorter durations than average (. seconds compared to 9.9 seconds), which would point to higher accretion rates than the observations in the middle state of the CCD.. Timing analysis I have discovered a kilo-hertz quasi-periodic oscillation, with a frequency of 5 Hz in this source. The khz QPO is only detected in observations ObsId=75 and not in the other observations, with 95 % upper limits given in Table 7. This is the third high-inclination source in which a khz QPO is discovered, the other sources are 4U 95-5 (Barret et al., 997[46] and EXO (Homan & van der Klis, [45]). Since khz QPOs are supposed to originate at the inner regions of the accretion disc, one would not expect to see them in high inclination systems, where the inner disc is occulted by the outer parts of the disc. This suggests that, although the khz QPO could be produced close to the neutron star, a mechanism related to an extended component (eg. the corona) is needed to make the khz QPO visible. This is consistent with previous results (Berger et al., 996 [49]) that show that the spectrum of the emission responsible for the QPOs is too hard to be attributed to the accretion disc. Also it is interesting that the -Hz QPO is detected in all our observations except in the one where I detected the khz QPO. This is also the case for EXO (Homan & van der Klis, [45]). Furthermore the appearance of the khz QPO and the disappearance of the -Hz QPO happens in the left most state of the CCD. It might be that the -Hz and the khz QPOs are connected, and that there is a physical change in the accretion disc that favors the production of either one or the other. 4 Conclusions In this research I have studied the Low-mass X-ray binary source 4U - 6. I have used thermonuclear X-ray bursts to set an upper limit to the distance using the theory of photospheric radius expansion bursts, assuming a neutron star mass of.4m, hydrogen poor material and isotropic emission. The calculated upper limit to the distance to 4U -6 I found is.4±.6 kpc, which is consistent with earlier constraints to the distance of - kpc (Parmar et al., 989 []). I have also studied the dipping of the source by looking at the time evolution of the hard colour of the source combined with light curves. I have further investigated the connection between the persistent non-dipping phase and the 6

37 dipping phase by studying hardness-intensity diagrams (HIDs) and colourcolour diagrams (CCDs). During the dipping phase the source spectrum is harder, and luminosity decreases compared to the the non-dipping phase, but that the two phases are not so different they appear as different states in either the HID or the CCD. The colour-colour diagram of the source shows neither a clear atoll nor Z-shape. This is probably caused by bad sampling, the data has been taken with long (more than weeks) intervals and generally last for one day, and hysteresis, the source moves through the same point in the CCD but traces a different path. I have also studied the variability of the source using Fourier power density spectra. I have detected a 7.-σ significant khz quasi-periodic oscillation (QPO) at 5±4. Hz. This is the first time a khz QPO has been detected in 4U -6 and only the third time a khz QPO is detected in a high inclination source (for the other sources see: Barret et al., 997[46], Homan & van der Klis, [45]). I have connected the behaviour of the known -Hz QPO to the newly discovered khz QPO. In our observations, only one is visible each time; if the -Hz QPO is visible, the khz QPO is not and the other way around. Furthermore I have studied the behaviour of the -Hz QPO and connected this to the power in a fixed frequency range to find whether the source shows hysteresis. Using the data available I conclude that the source indeed shows hysteresis; it moves through the middle state while following (at least) two different paths. References [] Various authors, X-ray binaries, Cambridge Astrophysical Series, No 6, 995 [] Various authors, Compact Stellar X-ray sources,cambridge Astrophycial Series, No 9, 6 [] E.E. Salpeter, ApJ 4:796-8 (964) [4] I.S. Shklovsky, ApJ 48:L-L4 (967) [5] J.E. Pringle, AR&A 9:7-6 (98) [6] W. Forman, C. Jones, L. Cominsky, P. Julien, S. Murray, G. Peters, H. Tananbaum & R. Giacconi, ApJS, 8: 57-4 (978) [7] R. S. N. Warwick et al., MNRAS, 97: (98) [8] M. van der Klis, J. van Paradijs, F.A. Jansen & W.H.G.Lewin, 984, IAU Circ. 96 [9] M. van der Klis, A.N. Parmar,J. van Paradijs, F.A. Jansen, & W.H.G. Lewin, 985b, IAU Circ

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39 [] E. Kuulkers, P.R. den Hartog, J.J.M. van t Zand, F.W.M. Verbunt, W.E. Harris & M. Cocchi, A&A 9:66-68 () [] M. Ba lucińska-church, M.J. Church, T. Oosterbroek, A. Segreto, R. Morley & A.N. Parmar, A&A 49: (999) [] D.K. Galloway, M.P. Muno, J.M. Hartman, D. Psaltis & D. Chakrabarty, ApJSS 79:6-4, 8 December [] G. Hasinger & M. van der Klis, A&A 5:79-96 (989) [4] T. A. Jones, A. M. Levine, E. H. Morgan & S. Rappaport, ApJ 677 Issue :4-47 (8) [5] N.S. Schultz, G. Hasinger & J. Trümper, A&A, 5, (989) [6] M. Kaufmann Bernadó & M. Massi, Mem. S.A. It. Vol. 78, 9 (7) [7] L. Keek, D.K. Galloway, J.J.M. in t Zand & A. Heger, ApJ 78:9-5, July [8] M. Mendéz, M. van der Klis, E.C. Ford, R. Wijnands & J. van Paradijs, ApJ, 5:L49L5, 999 January [9] M. Mendéz & T. Belloni, MNRAS 8: (7) [4] M.P. Muno, R.A. Remillard & D. Chakrabarty, ApJ 568:L5-L9, March [4] D. Psaltis, T. Belloni & M. van der Klis, ApJ 5:6-7, 999 July [4] A. Toor & F.D. Seward, ApJ, 79: (974) [4] S. van Straaten, M. van der Klis & M. Méndez, ApJ 596:55-76, October [44] M.Y. Fujimoto & R.E. Taam, ApJ 5:46-5, 986 June [45] J. Homan and M. van der Klis, ApJ 59:847-85, August [46] D.Barret, J.F. Olive, L. Boirin, J.E. Grindlay, P.F. Bloser, Y. Chou, J.H. Swank, & A.P. Smale, IAU Circ. 679, 997 [47] D.A. Leahy, W. Darbro, R.F. Elsner, M.C. Weisskopf, S. Kahn, P.G. Sutherland & J.E. Grindlay, ApJ 66:6-7, March 98 [48] F.X. Timmes, S.E. Woosley & T.A. Weaer, ApJ 457:84-84, 996 February [49] M. Berger et al., ApJL 496:L-L7 (996) 9

40 A Data Table : A list of all data used Observation name Observation date Time observed (sec) Time resolution /4/ µs /4/ µs /4/ µs /4/ µs /4/ µs // µs // µs // µs // µs /9/ 99 5 µs /9/ 65 5 µs /9/ 5 µs // µs // µs //4 6 5 µs 4

41 B properties: profiles The next figures show the profils of all X-ray bursts observed from 4U - 6 with RXTE. The burst profiles are plotted with a time resolution of second in a time frame of 5 seconds. On the x-axis is I plot the time, and on the y-axis the count rate. In total bursts were found, eight of which were part of a double burst; consisting of a strong burst and a weaker burst following within a short time interval. Observation number: Table 4: profiles per dataset Observation number:

42 Observation number: Observation number: Observation number: Observation number:

43 Observation number: Observation number:

44 Observation number: Observation number:

45 Observation number: Observation number: Observation number: Observation number:

46 Observation number:

47 C properties: duration and peaks Table 5: The properties of the bursts per observation. The total duration is the time from the rise until the point where the burst emission is equal to the persistent emission. D and D are the first and second member of double bursts, S are single bursts. Observation Type Duration to peak Duration total Count rate /PCU/s S s s 8 S s s D 9 s s 48 D 5 s 5 s 78 D 9 s 5 s 4 D s 5 s S s s S s 5 s S s 5 s D 6 s s 8 D 5 s s 44 S s 5 s 5 S 6 s s S s s 5 S s 5 s S 8 s 55 s S 7 s 9 s 8 S s s 7 S s s 5 S s 5 s S 6 s 7 s 4 S 6 s 7 s S s 75 s S s 7 s S s s D s s 85 D 6 s 5 s 5 S s s 5 S s 5 s S s s 47

48 D fits All bursts are fitted are fitted twice using xspec using an absorption model and a black body model (for a detailed describtion see Section..). Here I show all the fitted burst profiles. Where the equivalent hydrogen column,n H, is free, the upper panel shows the count rate during the burst, the second panel the equivalent hydrogen column, the middle panel the evolution, the fourth panel the normalization constant of the blackbody and the lowest panel shows the evolution of χ. If the equivalent hydrogen column is fixed, at 4 atoms/cm (see Section..) the upper panel shows the count rate, the second, the third the normalization parameter and the lowest panels shows the χ of each fit. 48

49 66--- Equivalent Hydrogen Column N H free Equivalent Hydrogen Column N H fixed at 4 atoms/cm Chi Time, offset =

50 66--- Equivalent Hydrogen Column N H free Equivalent Hydrogen Column N H fixed at 4 atoms/cm Chi Time, offset =