Scintillation studies of PSR B

Transcription

1 University of Bielefeld Faculty of Physics BACHELOR THESIS Scintillation studies of PSR B Hauke Jung November 12, 2014 Supervisor and first referee: JProf. Dr. Joris Verbiest Second referee: Dr. Stefan Os lowski

2 Contents 1 Introduction & Theory Supernovae Pulsars Discovery Basic properties PSR B Pulsar Timing LOFAR Interstellar scintillation Description & Techniques PSRCHIVE RFI zapping Standard templates Times of Arrival TEMPO Spectral Analysis Dynamic Spectrum Secondary spectrum and scintillation arcs Analysis & Results Data Timing DM variations Scintillation Conclusion & Outlook 23 1

3 Chapter 1 Introduction & Theory In the last ten years, a massive resurgence in low-frequency radio astronomy has come about. With telescopes like LOFAR (the LOw Frequency ARray), the LWA (Long Wavelength Array) and the MWA (Murchison Widefield Array) coming into operation, low-frequency radio astronomy research is enabled at far higher sensitivity than ever before. One key area of interest, is that of pulsar astronomy and in particular the study of pulsar emission at low frequencies. This is particularly beneficial for studies of the ionised interstellar gas, since effects from this ionised medium on the radio pulses of pulsars, are most powerful at the lowest frequencies. In this thesis we investigate how LOFAR data can be used to investigate pulsar scintillation in the bright and nearby pulsar PSR B (J ). In the following, we will briefly introduce pulsars in general, their origin (Section 1.1 and PSR B in specific (Section 1.2), explain the basics of the LOFAR telescope (Section 1.4) and finally describe how interstellar scintillation affects pulsar timing (Section 1.3) and pulsar radiation at LOFAR frequencies (Section 1.5). Software dedicated to pulsar analysis made research remarkably easier. Two important standard software packages were used in this thesis and will be introduced in sections 2.1 and 2.2 along with a description on data processing as well as dynamic and secondary spectra (Section 2.3). Chapter 3 will provide the results and analysis of the work and chapter 4 gives a short summary and an outlook on possible future work with this pulsar. 2

4 1.1 Supernovae A massive (more than 8 M 1 ) star has nearly finished its life when it doesn t have enough hydrogen left to keep up the hydrogen fusion process. The helium atoms resulting from the fusion process then will fuse and this process is continued until the resulting fusion product is iron. No energy can be gained by fusing iron atoms. Therefore the fusion process stops and gravity makes the core collapse. It will continue to collapse until the electron degeneracy pressure doesn t allow further collapse to happen. The falling outer layers get shocked by the sudden halt and cause a rebound which is observable to us as a nebula. During the explosion the brightness is rises up to a billion times compared to the regular brightness of the star, the outer shells of the star are blown away and the only remaining part is the core. For core masses beyond the Chandrasekhar mass ( 1.39M ) electron degeneracy pressure is insufficient to sustain the core and it will further collapse until electron degeneracy pressure is large enough to prevent a further collapse. In this case a neutron star is formed. For masses above the Tolman Oppenheimer Volkoff limit (ill-defined: 1.5-3M ) even electron degeneracy pressure provides insufficient support the core and it will further collapses into a black hole. These values hold for cores before they go supernova. At the end neutron stars will have masses between 1 and 2 M. The difference is the 1.2 Pulsars In this section we will give a short historical note on the discovery of pulsars and an introduction to pulsars and their properties Discovery In 1967, Jocelyn Bell discovered a highly periodic signal while searching the sky for radio sources. She and her doctoral advisor Anthony Hewish first thought this could be artificial, sent out by other civilizations. Therefore they first named this radio source LGM1 (Little Green Men 1). They published their results in the Nature magazine ( Observation of a Rapidly Pulsating Radio Source, Hewish et al., 1968). Pulsars are radio sources and due to their strong magnetic field, they continuously emit radio waves from the magnetic poles. As the pulsar also rotates around its rotation axis which differs from the magnetic axis, we see an effect that is best described as a lighthouse in the sense that the continuous emission is seen as a series of pulses. Pulsar is the short form for pulsating source of radio emission. The star itself doesn t pulsate, but the signal we see is pulsating. Pulsars were found to be fast rotating neutron stars. These have been predicted by Baade and Zwicky (1934) but were not expected to be observable. The rapid rotation of pulsars is explained by the huge but slowly rotating progenitor star. Conservation of angular momentum leads to a rapidly rotating pulsar if the size decreases. 1 solar masses, the mass of the sun 3

5 1.2.2 Basic properties In Figure 1.1 we can see the pulse period derivative vs. the pulse period derivative. The first thing to notice is that there are two groups of points in the figure. The second thing is the range of the y-axis which goes from approximately to This means, a typical pulse period derivative P for the group at the lower left is and for the other group These two main groups correspond to normal (slow) pulsars at the upper right and fast spinning millisecond pulsars (MSPs) at the lower left. Normal pulsars have a spin period (the time they need to do a complete spin around its rotational axis) of several seconds down to 30 ms. If pulsars have a companion, they can accrete matter from it. This increases their rotational momentum and therefore they accelerate their spin. Pulsars which have gone through this scenario are called MSPs and have pulse periods down to approximately 1 ms. Figure 1.1: P P diagram (Source: Kramer, 2005) Lorimer and The life of a newborn pulsar begins at the upper left of the diagram and will move downwards according to the diagonal lines denoting the age. Normal pulsars have a typical age of 10 million years. The emission of magnetic dipole radiation causes the pulsar to lose energy. Consequently the pulsar slows down (pulse period is getting longer), represented by a shift to the right in the diagram. When the spin period gets too long, the emission process becomes inefficient, so that we can no longer detect the pulsar and it is declared radio-quiet. In the diagram it falls into the gray graveyard area. When a companion recycles a pulsar it moves from the graveyard to the lower left group of MSPs. In the process of recycling its spin increases and its magnetic field gets weaker, causing less dipole radiation (i.e. lower P - the period gets more constant). Since their discovery, continuous observations across a wide range of observing frequencies have uncovered a vast amount of information about pulsars. Consequently, we now know that their masses cover a much wider range than expected from the work by Baade and Zwicky (1934) from less than 1.17M (Janssen et al., 2008) at the low end, to more than 2.01M (Antoniadis et al., 2013) at the high end. Based on these values and models for equations of state for extremely dense matter (Lattimer and Prakash, 2004), the radii of these objects are predicted to be of the order of 10 km. Finally, while still primarily studied at radio frequencies, pulsars have now been detected across the entire electromagnetic spectrum 4

6 1.2.3 PSR B This section gives a short overview of the basic properties of this special pulsar. Specifically, we will explain why this pulsar is a good choice for scintillation studies. PSR B is a nearby ( 430pc) and very bright 2 pulsar. Therefore it is easy to detect. It is a normal pulsar with a rotational period 2 of 1.29 s and moves with a transverse velocity 2 of km /s with respect to the solar system. With a declination of +74 it is circumpolar in Europe. That means that a continuous 24-hour observation is possible. Most pulsars are in the plane of the galaxy while PSR B is not. The pulsar is nearby, but outside of the so-called local bubble which is a cavity in the interstellar medium (ISM) where the density of dust and electrons is very low. Our Solar System resides in the local bubble. If we now observe this pulsar we could expect to see scintillation right from the edge of the local bubble. Most pulsars have multiple peaks in their profile and they differ from pulse to pulse. In contrast the peaks of PSR B have a regular pattern and are constant in width and height (van Leeuwen et al., 2003). In Rickett et al. (2000) the authors also deal with the scintillation of PSR B exclusively. They try to find out where the scattering of the waves that causes the scintillation happens. Nulling & drifting PSR B has features like nulling and drifting which are interesting to investigate and are briefly explained below. Nulling is a sudden lack of a signal for one or more pulse periods. An instrumental failure is not the cause of this. The pulsar stops emitting and after a short time it starts again. In the case of PSR B the nulling fraction (percentage of nulls) is 1.4% (van Leeuwen et al., 2003). Drifting is a periodic change in arrival time of the pulse. For a characteristic time (called P 3 ) the pulse is coming earlier or later each pulse. After that the pulse comes again at the time where it started drifting before. This is repeated indefinitely. Many normal pulsars are nulling but the nulling fraction is different for each pulsar. Some are not nulling at all whereas some only turn on for a short time (i.e. they are mostly nulling). Pulsars that fall into the last category are called rotating radio transients (RRATS, see McLaughlin et al., 2006) Figure 1.2: An example for nulling and drifting in our observation. 2 see ATNF Pulsar Catalogue at 5

7 An example of both nulling and drifting is shown in Figure 1.2. The null can be seen approximately at the edge of the lower third of the figure. The drifting is the slope of the pulse from the bottom right to the top left, repeated multiple times. Carousel model The question about the cause for drifting pulses leads to the carousel model. It currently is the most favored model to explain the drifting phenomenon. In Figure 1.3 we can see an illustration of the emission geometry that is proposed for the carousel model. It assumes that we don t have one compact beam which is emitted from one single place but instead there are multiple subbeams emitted from different regions. Theses are depicted as circles in the figure. Adding to that the emitting regions aren t static but moving in a circle like a carousel does. Each drifting band (length of P 3 as depicted in the figure) is from the same subbeam but comes at a slightly different phase every pulse period because the carousel has shifted slightly. Rankin and Rosen (2014) recently confirmed the carousel model is good in explaining the drifting behavior for PSR B Unfortunately it is a phenomenological model which doesn t give any physical insight. Figure 1.3: Illustration of the carousel mechanism. Source: van Leeuwen et al. (2003) 6

8 1.3 Pulsar Timing Pulsar timing is the process obtaining a pulsar s accurate measurements of its period and other intrinsic properties through repeated observations. A model for a pulsar includes multiple properties that affect the arrival times of its pulses on earth. The first property is derived by initially pointing the telescope at the pulsar. From there we already get the right ascension and declination. By watching the pulses for some time we can get the periodicity and from their frequency dependence the dispersion measure (which will be discussed in section 3.2.1). If we have such a timing model we can calculate what the model predicts for when the pulses should arrive and compare the prediction to the actual observations. Figure 1.4 shows an illustration of how this could possibly look like, if the pulse period is wrong. The actual pulses (in red) come later than expected. The difference between predicted and actual pulse is called a timing residual. The linearly increasing residuals shown in the illustration describe a wrong period in the model. Every wrongly described parameter in the model results in its own characteristic timing signature. 1.4 LOFAR LOFAR is the low frequency array. As the name already suggests, it is an array of low frequency antennas. The project consists of multiple stations in Europe. The majority of the stations are in the Netherlands. It consist of several hundreds of immovable antennas detecting the radio waves at the very Figure 1.4: Illustration of how a deviation from the model looks in case the pulse period is incorrect in the timing model. lowest frequencies detectable from the earth right before the atmospheric cut-off as seen in Figure 1.5. Stations have low-band antennas (LBA) which operate from MHz ( m wavelength) and high-band antennas (HBA) operating from MHz ( m). This means that the LOFAR array is placed right of the telescope depicted in Figure 1.5. LOFAR can be used to observe with all stations simultaneously, with a subset of all stations or just with one single station. The data used in this thesis were taken with the station located in Effelsberg, Germany. All antennas are static, therefore they wouldn t be able to track objects in the common way where telescopes are moved. Instead LOFAR is a digital telescope. This means, if the wave arrives at the station coming from an angle not perpendicular to the surface, the wave arrives slightly later at the far end of the antenna field. Using this difference, the incoming wave can be combined from all antennas in phase, which effectively points the telescope to the source. For pulsar observations this is how LOFAR is used and so it essentially does not matter where the telescopes are placed. The resolution of LOFAR is dependent on the longest baseline between LOFAR antennas. This is the reason some LOFAR stations are located very far from the rest of the LOFAR network (as far as 7

9 central France, southern Sweden and soon Ireland and Poland). Further details on the LOFAR system are given by van Haarlem et al. (2013). 100 % Gamma rays, X-rays and ultraviolet light blocked by the upper atmosphere (best observed from space). Visible light observable from Earth, with some atmospheric distortion. Most of the infrared spectrum absorbed by atmospheric gasses (best observed from space). Radio waves observable from Earth. Long-wavelength radio waves blocked. Atmospheric opacity 50 % 0 % 0.1 nm 1 nm 10 nm 100 nm 1 µm 10 µm 100 µm 1 mm 1 cm 10 cm 1 m 10 m 100 m 1 km Wavelength Figure 1.5: Atmospheric electromagnetic opacity by NASA (original); vectorized by User:Mysid; Source: electromagnetic_opacity.svg Figure 1.6: Low band (left, W. Reich, MPIfR Bonn) and high band (right, ASTRON Dwingeloo ) LOFAR dipole antenna. 8

10 1.5 Interstellar scintillation Interstellar scintillation is an effect that causes variations in the measured intensity of electromagnetic waves (e.g. radio waves coming from pulsars) at the telescope. It is similar to the twinkling of the stars which is observable in the night sky. While the scintillation of (visible) stars is caused by air turbulence in the atmosphere, the interstellar scintillation of radio sources is caused by the interstellar medium between Earth and the radio source. From basic physics we know the concept of diffraction & interference: a point source emits a wave and the wave is sent out isotropically (uniformly in all directions). If the wave then hits an object it will be diffracted. The diffracted wave can then interfere with a wave coming from the point source or other density inhomogeneities. If we then measure the intensity at a line perpendicular to the direction in which the wave traveled we can see an interference pattern. This concept can be applied to interstellar scintillation. Pulsars are very small and therefore can be treated as point sources. The radio waves coming from their magnetic poles traverse space and at some point they will interact with the free electrons of the ionized interstellar medium. The waves will be diffracted and then can interfere with each other at the observer on Earth. Since the Earth moves through space we can observe the scintillation pattern. Because the ISM is responsible for the interference pattern, we can study the ISM due to this diffraction. As the line of sight (the line connecting the pulsar and the observer at Earth) sweeps through the inhomogeneous and turbulent ISM, the interference pattern changes. The inhomogeneous ISM is often approximated by a thin-screen model. The large scale of the ISM can theoretically be condensed into a thin wall. Then only this thin screen is responsible for the interference. This model (contrary to what one might believe) is able to explain the basic effects of the observed scintillation. Depending on the scale of the distance between two interfering waves we can distinguish two different types of scintillation: diffractive (DISS) and refractive (RISS) interstellar scintillation. DISS takes place if closely spaced waves scattered from the thin screen interfere with each other and create an interference pattern with small maxima (also called scintles ) and minima at the observer (also seen in Figure 1.7). RISS corresponds to larger scales in the scattering screen. This causes long term intensity modulations. Figure 1.7: Illustration of the thin screen model and scintillation (Source: Lorimer and Kramer, 2005, after Cordes, 2002). 9

11 The free electrons in the ISM also delay the waves in a strongly frequency-dependent way. This physical principle is called dispersion and says, that the group velocity of a wave is dependent of the wavelength (and therefore the frequency 2 ). See section for a more detailed description of this particular phenomenon. 10

12 Chapter 2 Description & Techniques In this chapter we discuss the processing techniques and software that were used for the data analysis. In particular, we describe the PSRCHIVE package (Section 2.1) which was used for data optimization (2.1.1) and generation of pulse-arrival-times (2.1.2 and 2.1.3); the TEMPO2 package (Section 2.2) which was used to derive the derived pulse-arrival-times; and MatLab (Section 2.3.2) which was used for investigation of the scintillation properties of the pulsar. 2.1 PSRCHIVE PSRCHIVE 1 is an open-source package with the sole purpose of providing tools and algorithms for pulsar data analysis. It consist of several command-line programs as well as graphical interfaces. The parts of the package that were relevant to our work will be briefly explained in the following sections. An introduction to PSRCHIVE can be found in van Straten et al. (2012) RFI zapping As LOFAR is designed to observe at low frequencies, there is a high chance that it also detects radio broadcasts, military radar and other types of artificial, man-made radio waves which are emitted near the telescope. These signals are orders of magnitude higher in intensity than the astronomical signals and therefore they can outshine the pulsars. Depending on the signal we can remove these disturbing signals by deleting or zero-weighting different chunks of data. If there is a continuous stream of radio-frequency interference (RFI) at a well-defined frequency, this can be easily dealt with by zapping (i.e. removing) the relevant frequency channel. An example of this kind of RFI is shown in Figure 2.1. Another possibility is an impulsive signal consisting of small bursts which may be radar. Other sources can be satellite or point-to-point communication. All of this RFI needs to be removed as well as possible. This is done by zapping scripts and manually with the pazi program which is an interactive program that displays either frequency vs. pulse phase or time vs. pulse phase. The data files are stored with information about frequency, time (pulse phase), polarization and intensity. To be able to plot this information in a 2D graph the data needs to be scrunched (i.e. averaged over the dimension that is not plotted). A screenshot of pazi is shown in Figure 2.1. Here we see the frequency vs. pulse phase view and two types of RFI. One is seen at MHz and slightly below. Here we see, that one complete frequency channel is distorted MHz is the international aircraft emergency frequency

13 Apparently there was an emergency call during a short time of this observation. We can easily delete that particular frequency channel and keep the rest of the data. As noted in the last paragraph in section 1.5, radio waves are dispersed. Waves with higher frequency arrive earlier than those with lower frequency. PSRCHIVE can correct for these inter-channel delays and align the pulses (and at will disperse the pulses again). If we now have a short burst of RFI this would result in a straight vertical line. But as we correct for dispersion by shifting the frequency channels, the former straight line becomes a parabolic line. The sloped lines in the figure are this kind of short, impulsive RFI. Sometimes there are multiple lines and it s not feasible to get rid of all of them. In those cases we only deleted the RFI with highest intensity. Figure 2.1: Example of two different kinds of RFI, displayed in pazi Standard templates After the RFI is finally zapped we can create a so-called standard template. It is an analytic model of the average pulse shape. The tool paas from PSRCHIVE can create such a model by interactively fitting multiple von Mises functions to the pulse shape. Using standard templates is a quite new approach. The method commonly used before was to use the best observation as a template to time against. By doing this the best observation needs to be excluded from the dataset. To exclude the best observation is not favorable. The standard template containing a composition of multiple von Mises functions is beneficial here. In Figure 2.2 we see a stacked, aligned and color-coded view of all four templates with the 114 MHz-template in black, 137 MHz in red, 161 MHz in green and 185 MHz in blue. It is visible that the pulse shape changes slightly with frequency. This may be due to interstellar scattering or it can be intrinsic to the pulsar. 12

14 2.1.3 Times of Arrival Figure 2.2: Templates aligned and colored to see differences. Now that we have the RFI-zapped data and the analytic model we can do the pulsar timing described in section 1.3. First we use the standard template to determine the ToAs (Times of Arrival). These are the times at which the different pulses arrive at the LOFAR-station. Normally, multiple pulses get averaged before an averaged ToA is derived, but in case of PSR B individual pulses were possible to use because it is very bright. The command pat from PSRCHIVE creates a tim -file containing the ToAs. Now, if we measure at two different times, the radio wave will reach us at two different points in time. Considering that the Earth moves around the Sun, the waves reach us at a different point in time than if the earth would stand still. This would affect the ToAs. A conversion to a barycentric arrival time (which is the time at which the wave would arrive at the barycenter 2 of the Solar System), is needed. This is called the Roemer delay correction and is the biggest correction needed to be made. This is an important step when analyzing pulsar data. Other steps include corrections for offsets between the telescope clock and the international time standard, corrections for the rotation of the Earth (and the Doppler shift caused by this) and corrections for space-time distortions induced by the major planets (mostly Jupiter). The data is prepared now and can be analyzed with TEMPO2. 2 center of mass 13

15 2.2 TEMPO2 TEMPO2 3 is a software package designated for pulsar timing. It was mainly developed by George Hobbs & Russell Edwards and significantly enhanced by Joris Verbiest and various pulsar astronomers subsequently. It is based on the TEMPO software package and is written in C/C++. Designed to be expandable through plugins it is now used as the global standard. If no plugins are loaded it will output values of variables characteristic to pulsar (e.g. rotational frequency and derivative, dispersion measure, eccentricity) as well as statistical values of the fit algorithms. These values are derived from the input ToAs and timing model. Output values can be altered and expanded by the user to include more information. A very important plugin is called plk and provides the possibility to plot the ToAs with uncertainties as a function of different variables (e.g. frequency, time, position angle) as well as fitting the timing model parameters to the residuals. An example image of what the plk plugin looks like is shown in Figure 2.3. The plottable variables for the x- and y-axes are at the left side and the timing model variables that can be fitted are at the top. Figure 2.3: Example (color inverted) image of the TEMPO2 plugin plk. 3 Hobbs, Edwards, and Manchester (2006) 14

16 2.3 Spectral Analysis In this section we will describe what the dynamic and secondary spectra are and show how they were investigated Dynamic Spectrum The dynamic spectrum is a frequency vs. time plot in which you can see the frequency spectrum for each subintegration 4. That means, in this plot we see how intense the received radio waves are at a given frequency and time. If we have scintillation or other changes in the ISM we are able to see these in the dynamic spectrum in the form of intensity fluctuations. In the dynamic spectrum we are able to see so-called scintles if scintillation is present. Scintles are areas of higher intensity. The goal of this thesis is to measure the size of these scintles and to investigate how they change with frequency. Naively one could suggest to just measure the size e.g. by counting the pixels of the image. But there is a more sophisticated quantitative method described by Cordes et al. (1986) and Rickett (1990). At first, a 2D autocorrelation of the dynamic spectrum is generated. Then we take a slice at the middle frequency and middle time-step. We now have two functions and we will take the half-width at half-maximum for the time-slice and the half-width at 1 for the frequency-slice. e The value for the time-slice corresponds to the decorrelation bandwidth (size of the scintles in the frequency dimension) and the value for the frequency slice corresponds to the decorrelation time or scattering broadening time (size of the scintles in the time dimension). Autocorrelation function The autocorrelation function is a function which shows a measure of the correlation of a function or signal with itself. It is created by shifting the signal by a value τ and then integrating over the product of the original signal and its shifted version. The value τ is called the time lag. Because the dynamic spectrum is a matrix of intensities and not a one-dimensional function of intensities, we need to do a 2D-autocorrelation. In practice this can be detained using the Convolution theorem and the Wiener-Khinchin-Theorem, resulting in: ACF = abs {(fftshift(ifft2 [(fft2(m) conj(fft2(m))]))} /(n m) (2.1) where M is the matrix of intensity values, n and m are this dimensions of the matrix, ifft2 is the two-dimensional inverse fourier transformation, conj(fft2(m)) is the conjugate of the fourier transformation and fftshift shifts the center lags to the middle of the matrix. We then want to fit the theoretical predicted functions to our derived ACFs. The functions are (following Coles et al. (2010) and Lorimer and Kramer (2005)): ( ρ(τ) = exp ( τ ) ) 5 3 (2.2) τ ( 0 ρ(ν) = exp ln 2( ν ) ) (2.3) ν 0 where τ 0 and ν 0 are the decorrelation time and bandwidth. 4 A subint essentially means averaging of multiple pulse. While this is needed for many pulsars to be able to actually see the pulse, it was not necessary for this thesis because PSR B is so bright that we can see individual pulses. 15

17 2.3.2 Secondary spectrum and scintillation arcs A secondary spectrum is the power spectrum of the dynamic spectrum. When investigating the secondary spectrum Stinebring et al. (2001) found that sometimes they contain parabolic features. These scintillation arcs correspond to different scattering screens along the line of sight. An example of scintillation arcs are shown in Figure 2.4. It shows a dynamic spectrum at the top and the corresponding secondary spectrum at the bottom. Scintillation arcs can be seen in the secondary spectrum as two symmetric features drifting away from zero conjugate frequency. We indicated them with the red line. They change with time as the line of sight traverses the ISM. Depending on how inhomogeneous the ISM is and how fast the pulsar moves they can change on timescales from minutes to hours. It should be noted that the intensity color gradient is on a logarithmic scale. This already is a hint that scintillation arcs are not easy to detect. Figure 2.4: Example dynamic (left) and secondary spectrum (right). Original figures taken from Stinebring et al. (2001). Matlab For the calculation of the autocorrelation functions and the secondary spectrum a matlab script originally written by Bill Coles for different types of data, was slightly adapted to our data format to compute the secondary spectrum. 16

18 Chapter 3 Analysis & Results 3.1 Data For this thesis we had a continuous 24-hour set of data files from September It was observed at the LOFAR station in Effelsberg with the higher frequency band. Which means we observed at the spectrum of MHz. The data was already pre-processed. This means, the data we got included files each having 500 subints split into four different frequency bands. They were centered approximately at 114; 137; 161; and 185 MHz. The first thing we then did was deleting as much RFI as possible like described in section Then we concatenated the whole observation into a single file for each four frequency bands and created four standard templates. For further progression, the four standard templates needed to be aligned so that we have one standard template for the whole observation. This can be done with the tool paas from PSRCHIVE. 3.2 Timing We used the process described in section 2.1.2, and 2.2 to derive ToAs which were used to get a dispersion measure and align the pulses for the whole observation DM variations Waves that are scattered by the ISM arrive later at lower frequency. The time delay can be inferred through t = D DM f 2 where the Dispersion Measure, DM, is defined as and the Dispersion constant, D, equals DM = D = l 0 n e dl e2 2πm e c. The DM value has multiple uses. If we have a DM value from observing a pulsar and calculating the time delay between two frequencies, then assuming we have a model of the free electron distribution for the galaxy we can calculate n e and furthermore we can calculate the distance l to the pulsar. 17

19 If we have a DM value and measured the distance e.g. by the parallax method we can update our model for the free electron distribution. We measured the DM based on the time delay across our observing bandwidth at 15-minute Data Data without the lower half 114MHz band DM [pc cm ] Time [MJD ] Figure 3.1: DM variations across the 24h data. intervals, shown in Figure 3.1. The intent for this figure was to see if the DM value changes over time or is constant. Another reason was to check if the DM value is correct. The original value is derived from the ATNF catalogue and we saw that it was incorrect. The effect is that pulses were folded too early at lower frequencies which is also visible in Figure 2.1 where the pulses drift to the left side at lower frequencies. Also obvious are some significant changes in the DM value on short time scales between MJDs and , as well as near MJD and MJD These correspond to rapid changes in the ISM. Because the sensitivity is lower at the frequency band edges, the RFI plays a bigger role. The RFI in the 114 MHz band affected the DM values extraordinarily (DM value is proportional to f 2 - so lower frequencies affect the value more than higher frequencies) and therefore we excluded the lower half of the 114 MHz band. It is visible that the uncertainties are also reduced by that step. 18

20 3.3 Scintillation Frequency [MHz] MJD Figure 3.2: Dynamic spectrum with 10 s subintegrations On of the most interesting images is Figure 3.2. It shows the dynamic spectrum of PSR B for the whole 24-h observation. The x-axis is time and the y-axis is frequency with low frequencies at the top and high frequencies at the bottom. The color gradient is proportional to the intensity measured at the LOFAR station. Quite apparent are the small bright spots that are visible almost everywhere. These are the intensity maxima (or scintles) from the interstellar scintillation described in section 1.5. If we look how the plot changes from left to right we see bright scintles on the left, then fainter scintles and again bright scintles at later times. This structure is caused by the refractive interstellar scintillation (RISS). The period of this scintillation appears to be approximately one day, but that is not necessarily so. This change could also be some instrumental effect, but we verified that it is not caused by the elevation-dependent sensitivity of the antennas. At the top and bottom we can see the intensity vanishing. The cause again is the low sensitivity at the frequency band edges. There is almost no information until approximately 110 MHz and from approximately 190 MHz on. Also there is a gap in the data at the lower right. We don t have data for that frequency band and amount of time because of failure of the recording computers. To improve the data and make the following steps easier we first took the average of the whole dynamic spectrum and subtracted that value from the whole spectrum. 19

21 Autocorrelation functions Next we divided the dynamic spectrum into four separate parts (each consisting of full time resolution and a quarter of the frequency bandwidth) and calculated an autocorrelation function for each of the subset spectra. After that we did the same, but divided the spectrum into 16 parts (quarter time, quarter frequency bandwidth) Furthermore we peak-normalized the obtained ACFs to be in the range from 0 to 1. This way fitting was easier because there is one fitting parameter less. Hence we can see a time and also frequency dependence of the scintillation timescale and frequency scintillation bandwidth. First we fitted the functions 2.2 and 2.3 to all of the ACFs. This was done by writing a gnuplot script for each ACF and setting individual starting conditions for the fitting routine. A selection of the ACFs are shown in Figure 3.3. The top four figures are frequency slices, therefore they have time as a variable (a subint was 10 s). It is visible that the 114 MHz band (subfigures 1 and 5) carries very little small information and does not have scintles at all. Therefore the slices from the 114 MHz band only show the sharp peak (delta function - which is a general characteristic of ACFs). When viewing the slices of the 137 and 161 MHz bands (subfigures 2, 3, 6, and 7) the typical exponential decay becomes apparent. In the 185 MHz band (subfigures 4 and 8) we also see an exponential in the middle which has a triangle shape at the bottom. This is caused by the missing data in the bottom right of the dynamic spectrum but does not effect the other values for the scintillation parameters. All ACFs were fitted and the values for the scintillation timescale and frequency bandwidth were plotted in Figure 3.4 and 3.5 as a function of observing frequency. We see a clear trend in both figures. The theoretically expected frequency-dependence is ν 1.2 for the scintillation timescale and ν 4 for the frequency bandwidth (see Lorimer and Kramer, 2005). There are a few outliers which are far away from the fitted curve. They can possibly be explained by RFI, refractive scintillation and changes over short time scales. Typical values of the scintillation parameters finally are 18.1 min as the median scintillation timescale and 2.55 MHz as the median frequency bandwidth. 20

22 1 F Slice from the ACF of the 1st time and 1st frequency interval exp(-t/t 0 ) ( 5/3)*L 1 F Slice from the ACF of the 3rd time and 2nd frequency interval exp(-t/t 0 ) 5 /3)*L Intensity Intensity Subint # Subint # 1 F Slice from the ACF of the 2nd time and 3rd frequency interval exp(-t/t 0 ) 5 /3)*L 1 F Slice from the ACF of the 4th frequency interval exp(-t/t 0 ) 5 /3)*L Intensity Intensity Subint # Subint # 1 T Slice from the ACF of the 1st time and 1st frequency interval exp(-f/f 0 ))*C 1 T Slice from the ACF of the 3rd time and 2nd frequency interval exp(-f/f 0 ))*C Intensity Intensity Frequency [MHz] Frequency [MHz] 1 T Slice from the ACF of the 3rd time and 3rd frequency interval exp(-f/f 0 ))*C 1 T Slice from the ACF of the 4th time and 4th frequency interval exp(-f/f 0 ))*C Intensity Intensity Frequency [MHz] Frequency [MHz] Figure 3.3: A selection of all autocorrelation functions showing different behavior. Top four are slices through the ACF at the middle frequency (f-slices), bottom four are slices through the ACF at middle time/subint (t-slices). 21

23 Scintillation timescale quarter length full length ν 1.2 fitting curve t [min] ν[mhz] 10 Figure 3.4: Time bandwidth t with 60 s subints and band edges removed. Frequency bandwidth quarter length full length ν 4 fitting curve 5 f [MHz] ν[mhz] 1 Figure 3.5: Frequency bandwidth f with 60 s subints and band edges removed. 22

24 Chapter 4 Conclusion & Outlook PSR B was the choice to investigate because it is nearby, bright and it is a scintillating pulsar. As this pulsar is thought to be just outside of the local bubble it is expected to see scintillation coming from this place. The DM value was almost constant throughout the observation with just slight changes. It was compared with the value in the ATNF catalogue and a difference was apparent. One reason why we are able to see short time variations in the DM value is that LOFAR is observing at a low frequency. With the LWA and the MWA coming into operation we could get even more sensitive to short time variations. Having a dynamic spectrum with very visible scintillation effects we were hoping to see scintillation arcs coming from the edge of the local bubble. But even with varying sensitivity and resolution we could not see any. Knowing that scintillation arcs are not easy to detect because they come and go frequently, it is recommendable to keep looking. It is also possible to further increase sensitivity by decreasing the subint length. 10 s were chosen because of hardware limitations. The LOFAR data for PSR B enable us to use single pulses ( 1.29 s) although with this short subint length one would need to create dynamic spectra for shorter timescales, or increase computing power. But in essence it would be interesting to keep looking and as far as possible automate this analysis. Also repeating this process on different pulsars could be valuable. Another aspect of continuing to observe is to look for changes in the scintillation parameters. As the pulsar moves, our line of sight traverses the structure of the ISM in between. If the line of sight changes we also see different structures of the ISM because of the scintillation. It would be interesting to see on which scales the scintillation parameters change over time, if at all. 23

25 Bibliography J. Antoniadis, P. C. C. Freire, N. Wex, T. M. Tauris, R. S. Lynch, M. H. van Kerkwijk, M. Kramer, C. Bassa, V. S. Dhillon, T. Driebe, J. W. T. Hessels, V. M. Kaspi, V. I. Kondratiev, N. Langer, T. R. Marsh, M. A. McLaughlin, T. T. Pennucci, S. M. Ransom, I. H. Stairs, J. van Leeuwen, J. P. W. Verbiest, and D. G. Whelan. A Massive Pulsar in a Compact Relativistic Binary. Science, 340:448, April doi: /science W. Baade and F. Zwicky. Cosmic rays from super-novae. Proc. Nat. Acad. Sci., 20: , W. A. Coles, B. J. Rickett, J. J. Gao, G. Hobbs, and J. P. W. Verbiest. Scattering of Pulsar Radio Emission by the Interstellar Plasma. ApJ, 717: , July doi: / X/717/2/1206. J. M. Cordes. Pulsar Observations I. Propogation Effects, Searching, Distance Estimates, Scintillations and VLBI. In S. Stanimirovic, D. R. Altschuler, P. F. Goldsmith, and C. J. Salter, editors, ASP Conf. Ser. 278: Single-Dish Radio Astronomy: Techniques and Applications, pages , San Francisco, Astronomical Society of the Pacific. J. M. Cordes, A. Pidwerbetsky, and R. V. E. Lovelace. Refractive and diffractive scattering in the interstellar medium. ApJ, 310:737, A. Hewish, S. J. Bell, J. D. H. Pilkington, P. F. Scott, and R. A. Collins. Observation of a rapidly pulsating radio source. Nature, 217: , G. B. Hobbs, R. T. Edwards, and R. N. Manchester. Tempo2, a new pulsar-timing package - i. an overview. MNRAS, 369: , June doi: /j x. G. H. Janssen, B. W. Stappers, M. Kramer, D. J. Nice, A. Jessner, I. Cognard, and M. B. Purver. Multi-telescope timing of PSR J : , November doi: / : J. H. Lattimer and M. Prakash. The physics of neutron stars. Science, 304: , D. R. Lorimer and Michael Kramer. Handbook of pulsar astronomy. Cambridge observing handbooks for research astronomers ; 4. Cambridge Univ. Press, Cambridge [u.a.], ISBN URL M. A. McLaughlin, A. G. Lyne, D. R. Lorimer, M. Kramer, A. J. Faulkner, R. N. Manchester, J. M. Cordes, F. Camilo, A. Possenti, I. H. Stairs, G. Hobbs, N. D Amico, M. Burgay, and J. T. O Brien. Transient radio bursts from rotating neutron stars. Nature, 439: , doi: /nature Joanna Rankin and Rachel Rosen. Revisiting the carousel and non-radial oscillation models for pulsar b Monthly Notices of the Royal Astronomical Society, 439: , April 24

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27 Acknowledgements I would like to thank Joris Verbiest for offering the opportunity to write this thesis, for having a solution for almost any problem that came up and for his support throughout the last phase of writing. Secondly I would like to thank Stefan Os lowski for always being helpful when dealing with problems in PSRCHIVE! 26

28 Declaration I hereby declare and confirm that this thesis is entirely the result of my own original work. Where other sources or information have been used, they have been indicated as such and properly acknowledged. I further declare that this or a similar work has not been submitted for credit elsewhere. Hauke Jung 27