University of Amsterdam
MSc Physics and Astronomy
Track: Astronomy & Astrophysics
Master Thesis
Search for Giant Pulses from
nearby pulsars
by
Angana Chakraborty
12199966 (UVA)
August 21, 2020
60 ECTS
October 1, 2020 - August 21,2020
Supervisors:
Ralph wijers
Antonia Rowlinson
Examiners
Ralph Wijers
Antonia Rowlinson
Anton Pannekoek
Institute
Acknowledgements
The work done towards this thesis over the past year would not have been possible without the help and support of several people. I am extremely grateful to them and wish to thank all of them for their sincere efforts.
I wish to express my sincere appreciation to my supervisor, Professor Ralph Wijers, who guided me enthusiastically and encouraged me. Your insightful feedback pushed me to sharpen my thinking and brought my work to a higher level. Without your persistent help, the goal of this project would not have been realized. I had a great time doing this project and learnt a lot from you. I also wish to express my deepest gratitude to my co-supervisor, Dr. Antonia Rowlinson, who not only provided valuable guidance to me but also helped me believe in myself.
I would like to pay my special regards to Dr. Mark Kuiack whose “You can do it yourself approach” helped me learn a lot more than I normally would have. I am also thankful to Kelly Gourdji, Alex Cooper, Jelle Meijn who often helped me by providing useful feedback. My sincere thanks also goes to our API Transients group for numerous stimulating and insightful discussions. I thank my fellow classmates with whom work never felt like work. I got my motivation more from coffee breaks with them than any other resources. Even with the lockdown taking place, we had quizzes, online game sessions and numerous Zoom calls without which I wouldn’t have been able to deal with the pandemic. I am also thankful to API for hosting a caring and supportive environment.
With the onset of pandemic, a lot of things changed. Amidst all the chaos and confusion, I am really lucky to have had a flatmate and best friend like Sumedha Biswas. Our stargazing sessions will be missed very much. There are countless times I am sure I would not have succeeded had you not been there, struggling along with me. I thank my family for always supporting me. I can’t thank them enough for for giving me the solid foundation upon which everything else is built. Lastly, I would like to express my gratitude towards the universe being full of wonders. The mysteries of the universe give purpose and meaning to my life. I hope our relationship lasts a lifetime.
Abstract
Evidence now exists that atleast 16 pulsars emit, besides their regular periodic pulses, rare and unusual so-called ’Giant Pulses’ which are distinct in multi-ple ways. Giant Pulses (GP) from pulsars are considered to be 10 or more times stronger than the average pulse emitted by the pulsar. The emission mechanism of these pulses are not fully understood yet. In order to get a bet-ter understanding of the giant pulse generation mechanism, analysis of giant pulses at low frequencies is important. Combining the findings across a range of frequencies will help in putting constraints on the mechanisms responsible for the emission.
There has been detection of extreme giant pulses (GPs) from the highly variable PSR B0950+08 (Kuiack et al. 2020), using the Amsterdam-ASTRON Radio Transient Facility And Analysis Centre (AARTFAAC), a parallel transient de-tection instrument based on the LOw Frequency ARray (LOFAR). A method has been developed to search for giant pulses from nearby pulsars using AART-FAAC wide-field radio survey. A targeted search for giant pulses from known GP emitters was carried out. Incoherent de-dispersion method was to remove the dispersion effects which are prominent at low frequencies.
We will present results of the method from the known GP emitters. We measure the sensitivity of AARTFAAC to giant pulses detected from the target sources. We find two promising candidates, B0301+19 and B1237+25 which emit pulses that should be detectable by AARTFAAC.
Summary
A massive star explodes at the end of its life. The explosion is called a super-nova. After the explosion, the core of the star collapses to become an ultradense object with the mass of the sun packed into a ball the size of a city. This rem-nant of the giant star is called neutron star. It is the densest object astronomers can observe directly. One sugar cube of neutron star material would weigh as much as a mountain on Earth.
Millions of neutron stars populate our galaxy, the Milky Way. Many neutron stars are undetectable because they do not emit enough energy. They are called ’pulsars’ when they generate regular pulses of electromagnetic radiation including radio, optical, X-ray and gamma-ray wavelengths that streams from their magnetic poles. As the pulsars spin, these streams point at Earth once every rotation. They sweep over our planet Earth like fleeting lighthouse beams, and telescopes pick up each one as a pulse.
Some pulses have been observed that are monstrously enormous compared to other pulses. These pulses were first observed from the Crab Pulsar in 1968. The Crab pulsar is a relatively young neutron star which is the central star in the Crab Nebula, a remnant of the supernova SN 1054, which was observed everywhere on Earth in the year 1054 AD.
These pulses are called giant pulses. In the simplest words, giant pulses are those that have energy at least 10 times more than the average pulse emitted by the pulsar. It is not known so far what causes the pulsars to emit giant pulses. It is a mystery that remains to be solved. The majority of studies to date have focused on radio observations at high frequencies.
Giant pulses were observed from the pulsar PSR B0950+08 in 2018 using the Amsterdam-ASTRON Radio Transient Facility And Analysis Centre (AART-FAAC) based on the LOw Frequency ARray (LOFAR), situated in the Nether-lands. This is a great opportunity to observe and study giant pulses at low frequencies. If we combine the findings from several frequencies, we will inch closer to finding the reasons behind what is causing these giant pulses.
I develop a method that enables me to search for giant pulses after I have got rid of most of the unwanted noise from the data I obtained from AARTFAAC.
I targeted those stars that have already emitted giant pulses in the past. I use statistics to analyse the data and interpret the results. On comparison with the information known about the giant pulses in the literature, I measured the sensitivity of AARTFAAC to detect these giant pulses. Two promising candidates were found as a result of the targeted search. Future research is needed to observe giant pulses from the candidates.
Contents
1 Introduction 2
1.1 Pulsars . . . 3
1.1.1 Pulsar emission . . . 5
1.1.2 Giant pulse emission . . . 6
1.1.3 Giant pulses at low frequencies . . . 9
1.2 Propagation effects . . . 11
1.2.1 Dispersion . . . 12
1.3 Goals and outline of the thesis . . . 13
2 Observations and data preprocessing 15 2.1 Observations with AARTFAAC . . . 15
2.1.1 Radio Frequency Interference . . . 16
2.2 Target selection . . . 16
2.3 Stacking and incoherent de-dispersion . . . 21
3 Data analysis and results 22 3.1 TraP pipeline . . . 22
3.1.1 Search for giant pulses using pipeline . . . 23
3.1.2 Flux scaling . . . 24
3.2 Flux density distribution . . . 26
4 Discussion 35 4.1 Giant pulse emission rates . . . 35
5 Conclusions 39 5.1 Future work . . . 40
List of Figures
1.1 Evolution of pulsars diagram . . . 3 1.2 The lighthouse model of a pulsar . . . 5 1.3 Comparison of giant pulse with average pulse . . . 8 1.4 Cumulative probability distribution of pulse amplitudes of pulsar
PSR B1937+21. . . 8 1.5 A giant pulse detected from the Crab pulsar at several low
fre-quencies. . . 10 1.6 Pulse dispersion of pulsar B1356–60 . . . 12 2.1 Time-frequency plot of some of the giant pulses observed from
PSR B0950+08 observed on 2018-04-14 . . . 18 2.2 Range of dispersion measure which is optimum for AARTFAAC
time resolution . . . 20 2.3 P-Pdot diagram of known GP emitters amongst all radio pulsars 20 2.4 De-dispersed pulse obtained using incoherent de-dispersion method 21 3.1 Light curve showing background variability due to ionospheric
scintillation which was then subtracted . . . 25 3.2 Lightcurve of PSR B1112+50 for de-dispersed time series . . . . 28 3.3 Lightcurve of PSR B1112+50 for raw data . . . 29 3.4 Plot of the histogram of flux values taken from de-dispersed time
series of the source PSR B1112+50. . . 29 3.5 Plot of the histogram of flux values taken from raw data of the
source PSR B1112+50. . . 30 3.6 Modeling the noise with a Gaussian distribution for de-dispersed
time series of source PSR B1112+50 . . . 30 3.7 Modeling the noise with a Gaussian distribution for raw data of
source PSR B1112+50 . . . 31 3.8 The distribution of peak intensities of individual pulses from PSR
B1112+50 . . . 31 3.9 Plot of the peak flux distribution of the single pulses for PSR
B1112+50. . . 32 iv
List of Figures 3.10 Plot of the inverse cumulative flux density distribution of flux
values from the source PSR B1112+50 and the background . . . 33 3.11 Distributions of pulses with peak flux densities from B0301+19
Kazantsev et al.(2019). . . 34 4.1 Rate of the emission of GPs of pulsars with low magnetic field
List of Tables
2.1 List of Pulsars with GRPs (Kazantsev & Potapov 2018) . . . 19 4.1 Rate and clusters of GP generation for some of the pulsars
Chapter 1
Introduction
Exploring the transient universe at radio wavelengths has been on the fron-tier of research for the past decade. Transients are astronomical objects whose intensity varies on timescales that range from seconds to several years. The progenitors of such sources are most likely locations of explosive or dynamic events and probing them is a great opportunity to study extremes of grav-ity, magnetic fields, velocgrav-ity, temperature, pressure, and density. They usually represent a range of events, such as supernovae, novae, dwarf nova outbursts, gamma-ray bursts, and tidal disruption events, as well as gravitational mi-crolensing transits, eclipses, and comets. Transients can be classified into slow transients and fast transients. Slow transients have timescales of hours to years whereas fast transients have timescales of nanoseconds to minutes. Slow tran-sients usually emit via incoherent emission. Fast trantran-sients usually emit via coherent emission. Slow transients require imaging on a wide range of time integration while fast transients require time-domain signal processing of data sampled at high time and frequency resolutions. This thesis aims to use the Amsterdam-ASTRON Radio Transient Facility And Analysis Center (AART-FAAC), an instrument exclusively designed to detect bright transients at low radio frequencies. Using AARTFAAC, we will look into extreme pulses from nearby pulsars in more details. These extreme pulses have a very short dura-tion.
Pulsars
Fig. 1.1 – Spin period – period derivative diagram of all pulsars excluding millisecond pulsars are shown in the figure. New-born pulsars are in the top left hand side of the diagram and spin down to longer periods within a few million years. When they eventually cease radiating, they are classified as extinct. The death line delineates the dead pulsars whose emission is too faint to be detected.
1.1
Pulsars
A pulsar is a highly magnetized rotating neutron star that emits beams of electromagnetic radiation out of its magnetic poles. We can observe the elec-tromagnetic radiation if it is along our line of sight while the pulsar is spinning. In order to visualize this, we can picture a lighthouse which appears to blink when seen by a sailor on the ocean. As the pulsar rotates, the beam of light sweeps across the Earth, then swings out of view and then swings back around again. This emission appears in the form of pulses. The reason for which we see pulsed emission from pulsars is that the pulsar’s beam of light is not aligned with the pulsar’s axis of rotation. Due to the misalignment, we observe
Pulsars
odic short pulses of radio waves at the same rate as the rotation of the pulsar. So the rate of the pulses also reveals the rate at which the pulsar is spinning. Their rotation periods range from milliseconds to seconds.
Pulsars belong to a class of objects called neutron stars that form when stars much more massive than the Sun run out of fuel in its core and collapses in on themselves. The stellar death typically leads to a massive explosion called a supernova. The neutron star is the dense object that is left over after the explo-sion. Young pulsars spin very fast because the rotation rate of the core-collapse increases enormously through conservation of angular momentum. Over the next few million years, their spin periods increase with time. The rotation pe-riod is slowed because the rotation of the magnetic field causes magnetic dipole radiation emission which slows down the neutron star’s rotation. Eventually, the rotation rate reaches a point where the pulsar ceases to emit radio emission and is no longer detectable from Earth. The pulsar is now said to be dead(1.1). Millisecond pulsars, also called recycled pulsars, are created by accretion of matter from the companion. So as the companion evolves, mass and angular momentum are transferred from the companion to the pulsar. This causes the pulsar to spin up and the magnetic field strength is reduced.
Pulsars are the only astrophysical objects accessible to observations that en-able astrophysicists to study strong electric and magnetic fields together. The discovery of the first pulsar is accredited to Jocelyn Bell Burnell and her col-leagues. She made the discovery during a low-frequency (ν =81 MHz) survey of extragalactic radio sources (Hewish et al. 1968). Pulsars served as the first evidence that neutrons stars exist in the real world and not just in theory. The electromagnetic radiation emitted by a pulsar carries information about these objects and what is happening inside them. Pulsars are known for their precise pulse emission. Any irregularity or change in the pulse emission can in-dicate what is happening in its surroundings. The radiation from pulsars passes through the interstellar medium (ISM) before it reaches Earth. The interaction of the radiation with the ISM causes propagation effects which are discussed in more detail in section 1.2. Thus, pulsars also serve as valuable probes of the ISM.
Another way pulsars are useful tools is via pulsar timing. The arrival times of the radio pulses are accurately tracked. This can help scientists detect grav-itational waves which changes the space-time metric during its propagation. As a result, the arrival times are changed slightly. Millisecond pulsars in tight binary systems can cause strong space-time deformation that results in rela-tivistic effects and help in constraining theories of gravity in the strong field limit.
Pulsars
Fig. 1.2 –Here we see the dipole magnetic field configuration centered at the pulsar. The magnetic axis is not aligned with the rotation axis and thus electromagnetic beams can be observed as pulses with regular rotational periods. The light cylinder, outlined in green, is the radius out to which the co-rotation speed of the magnetic field approaches the speed of light.
1.1.1
Pulsar emission
Pulsars can radiate across the entire electromagnetic spectrum. The emission observed at higher frequencies is created closer to the neutron star than that re-ceived at lower frequencies. This implies emission heights depend on frequency. Pulsar emission has been studied and observed for decades but we still have many open questions about the nature of the pulsar emission.
The rotating magnetic field of a pulsar accelerates energetic charged particles that then stream along the field lines. So plasma near the neutron star rotates with it because of the strong magnetic fields. The distance where the rotation
Pulsars
velocity of the field lines reach the speed of light defines the light cylinder as shown in the figure 1.2. The magnetic field lines inside the light cylinder are closed while those which would close outside but cannot since plasma would exceed the speed of light are called open field lines.
The accelerated energetic charged particles move along the open field lines and produce radiation that triggers a cascade of additional radiating particles. The radiation is beamed in the direction of the motion of the particles because the particles are moving relativistically. The pulsar’s radio emission is mainly produced at some particular height above the magnetic pole and is confined to a narrow beam defined by the orientation of the field line at that height. As the pulsar rotates, if this beam crosses the path of the observer, it is seen as a radio pulse.
Studies are still going on to pinpoint where the particles create this radio emis-sion in the open field region. While there are many models that suggest the emission is formed close to the poles, recent studies indicate that it may occur closer to the edges of the light cylinder. Further studies are ongoing to better understand the details of the process.
1.1.2
Giant pulse emission
Every pulsar has a unique pulse profile and pulse period. However, most ra-dio pulsars show pulse-to-pulse intensity fluctuations. These individual pulses differ in shape and intensity since each of them is a result of complicated pro-cesses taking place in the pulsar magnetosphere. They are also unstable due to instability in the emission process and as a result of perturbation effects on the interstellar medium. Despite this, the average pulse profile is quite stable since it is obtained from the summation of thousands of individual pulses. It is quite challenging to detect individual pulses from most radio pulsars because of their low flux density. However, the first exception to this was the detection of exceptionally bright pulses from PSR B0531, or the Crab pulsar (Staelin & Reifenstein 1968). This pulsar emitted strong individual pulses regularly and the pulses had flux densities that exceeded the average level by at least an order of magnitude. These pulses came to be known as Giant Pulses(GPs). For a long time after that, no other pulsar showed this kind of pulses until an-other millisecond pulsar, PSR B1937+21, was found to emit similar giant pulses (Wolszczan et al. 1984; Cognard et al. 1996). The giant pulses were found to occur at the trailing edge of both the pulse and the interpulse (Soglasnov et al. 2004). In every rotation of the pulsar, two peaks were observed, main pulse and interpulse (Backer 1984).
Pulsars The working definition of giant pulses is that i) The fluence (pulse integrated flux density) of a giant pulse should be at least 10 times greater than that of the average pulse (AP) ii) it has a narrower pulse width compared to the average pulse profile as can can be seen in figure 1.3 iii) it occurs in a narrow phase window of the average pulse. If the effects of interstellar scintillation are ignored, the flux density of normal pulses usually never exceeds the average flux density by a factor more than 10. Giant pulses are anomalous in that sense. The earliest sources to exhibit giant pulses had a strong magnetic field strength at the light cylinder, BLC. Six of the ten pulsars with the highest measured
BLC are GP emitters. This initially led to the speculation that there might
be a correlation between giant pulse emission and BLC, suggesting that the
mechanism may depend on the conditions at the light cylinder (Cognard et al. 1996). However, with discovery of giant pulses from pulsars, B0950+08 (Singal 2001) and B0031-07 (Kuzmin & Ershov 2004), the conjecture was dismissed. As seen in Table2.1, many pulsars exhibiting giant pulses have BLC lower than
1000 G.
These rarely observed strong pulses stand out from the background noise and ordinary individual pulses. The time scales for these individual giant pulses are too short for them to be due to either diffractive or refractive scintillation effects. Thus, it is an intrinsic effect.
Giant pulses have been observed in various types of pulsars having a wide range of periods, luminosity, magnetic field at the light cylinder and broad frequency range. There is no correlation between pulsar properties and the GP phenomenon.
The emission mechanism is thought to be a broadband, nonlinear plasma pro-cess (Eilek & Hankins 2016) and the emission can be detected from radio to γ-ray frequencies. Crab giant pulses appear to be a broadband phenomenon, detectable across the full observing bandwidth in most observations (Popov et al. 2009, 2006). The giant pulses are not always expected to be detected si-multaneously over multiple widely separated frequency bands (Oronsaye et al. 2015). Simultaneous dual frequency observations of GPs from PSR B1937+21 at 2210-2250 and 1414-1446 MHz (Popov & Stappers 2003) don’t reveal any GPs which occur simultaneously in both frequency ranges. Simultaneous dual frequency observations of GPs in PSR B0031-07 at 111 and 40 MHz reveal only a few common GPs (Kuzmin & Ershov 2004). The giant radio pulses observed in PSR B1937+21 are phase aligned with the X-ray pulses (Kinkhabwala & Thorsett 2000). This suggests that they might constitute the radio component of high energy emission. Phase alignment of X-ray and radio pulses was also observed for PSR B1821-24 (Romani & Johnston 2001).
Pulsars
Fig. 1.3–We see here GP (solid line) in comparison with an AP (dotted line) for the pulsar PSR B1937+21.(Kuzmin 2007)
Fig. 1.4–Cumulative probability distribution of pulse amplitudes of pulsar PSR B1937+21. At low intensities, the observed pulse strength distribution is dominated by Gaussian back-ground noise whereas for amplitudes above the noise, the pulse strength distribution show power law distribution. (Cognard et al. 1996)
Pulsars The fluence of a giant pulse is calculated by integrating flux density over the entire time duration of the giant pulse. It has been found from long term observations of giant pulses from different sources that the the pulse intensity distribution is not straightforward in nature1.4. At low intensities of ordinary pulses, the pulse strength distribution is Gaussian one, but above a certain threshold the pulse strength of GPs is roughly power-law distributed. Normal pulse energies exhibit exponential or log-normal distribution (Burke-Spolaor et al. 2012) while giant pulse energies follows a power-law distribution (Cognard et al. 1996;Argyle & Gower 1972). The physics responsible for producing these coherent bursts of radio emission is not completely known.
The giant pulses are associated with non-thermal high energy emission. They may occur in different altitude of the magnetosphere compared to regular radio emission. Thus, observations of GPs can be used to probe a pulsar’s emission region. Normal radio pulse emission for many pulsars is considered to origi-nate from lower altitudes in the magnetosphere or polar caps. According to model by Lyutikov (Lyutikov 2007), GPs originate from closed magnetic field lines. Regular emission originates from open magnetic field lines. High density plasma is trapped in the closed field lines near the light cylinder and if the resonance condition is met, coherent radiation is emitted. The resonance con-dition depends on the magnetic field at the location, the plasma density and the angle between the line of sight and the local magnetic field. This could explain why GPs are observed in narrow phase windows. The model also argues that since it is rare for the resonance condition to be fulfilled, few pulsars show GP phenomenon. It is also able to explain that pulse-to-pulse variation in location of emission bands is due to fluctuations of the plasma density.
There could be multiple mechanisms causing GPs. In the figure 2.3, we see that there are roughly two groups of sources emitting GPs, type I and type II GPs (Kuzmin 2007). It might suggest that there are categories of GP emitting pulsars where the pulses originate from different regions of the magnetosphere (Wang et al. 2019). Of these two types of GP emitters, Type I can be connected to high energy emission from the outer gap (see 1.2). Type II GPs are emitted from a hollow cone over the polar cap instead of LC. Some difference can be seen between these two types of GP emitters with respect to timescale, energy distribution
1.1.3
Giant pulses at low frequencies
Low frequency studies of pulsars help in characterizing the effects of multi-path propagation through the interstellar medium. Combined with simultaneous
Pulsars
Fig. 1.5 – The above figure shows a single giant pulse detected from the Crab pulsar at several low frequencies.
observations at higher frequencies helps in analyzing pulse morphologies across a range of frequencies. This helps in constraining theories of the pulsar emission mechanism. Thus in order to get a whole picture of the giant pulse generation mechanism, it is important to analyze weak giant pulses at low frequencies. Simultaneous observations of individual pulses spanning frequencies above and below the 100 MHz spectral turnover will be particularly useful in characterizing the complex nature of giant pulse emission.
At lower radio frequencies, pulses emitted from a source will undergo multi path propagation as fluctuation in the electron density of the ISM. The shapes of the pulses are therefore different from the intrinsically narrow pulses observed in the high frequency ( >1 GHz) regime. In figure 1.5 we see that the pulse shapes are characterized by a rapid rise followed by an exponential decay at low frequencies.
Propagation effects telescopes need to be powerful and sensitive enough to detect these weak giant pulses. This was impossible until two decades ago. The majority of studies on giant pulses have focused on high time resolution radio observations at several GHz. At such high frequencies, the effects of dispersion and scattering do not degrade the intrinsic nano to microsecond time resolution of detected pulses. Recently with the advent of sensitive telescopes around the world, more research has been done on giant pulses and the effects of multi-path propagation at low frequencies (Kazantsev & Potapov 2018; Oronsaye et al. 2015; Karuppusamy et al. 2012).
1.2
Propagation effects
The radio sky is dynamic. All sources exhibit significant variations in their brightness when viewed over long duration. This variability cab be due to intrinsic emission of the source but usually they are due to extrinsic factors. The emitted radiation from the source travels as plane waves. The radiation traveling from the pulsars experience propagation effects as they traverse the ionized and magnetized interstellar medium (ISM). If the intervening medium were uniform, the radiation would not be affected. However, that is not the case. The interstellar medium is clumpy on a variety of scales. Due to density inhomogeneities causing differences in the refractive index of the medium, vari-ations are introduced in the phase velocity along the plane of the wave. This leads to brightness variations of the source in the plane of the observer. Thus the apparent variability of the source flux density in our telescope, called scin-tillation, depends on if the scattering screen along our line of sight is moving due to transverse velocity of the medium, antenna or source. The propagation effects include i) dispersion; ii) scattering; iii) scintillation. The interstellar medium imparts a number of propagation effects onto the properties of the radio signal which can be summarized by the following equation:
I(t) = grgdS(t) × hd(t) × hDM(t) × hRx+ N (t) (1.1)
where the I(t) is the observed signal, gr and gd represent the refractive and
diffractive scintillation, S(t) is the emitted signal, hDM(t) is due to the
disper-sion, hd(t) is scattering, hRx(t) is Faraday rotation and N(t) is the instrumental
noise. We do not consider effects due to Faraday Rotation here. At low frequen-cies, scattering becomes profound. Scintillation causes amplitude modulations in time and frequency. Scintillation timescales are generally too large to be relevant to detecting fast transients. however for long duration of observations,
Propagation effects
they need to be taken into account. They cause variability in the background, which needs to be rectified. For more information on the removal of background variabilty, see section 3.1.1.
Fig. 1.6–Pulse dispersion of pulsar B1356–60. The dispersion measure is 295 cm3 pc. The quadratic frequency dependence of the dispersion delay is clearly visible. (Lyne & Graham-Smith 2012)
1.2.1
Dispersion
Pulses emitted at higher radio frequencies travel faster and arrive before lower radio frequencies due to the frequency dependence of group velocity of radio waves as they propagate through the ionized component of the ISM (see figure
1.6). The delay in the pulse arrival times is inversely proportional to the square of the observing frequency and this constant of proportionality is known as the
Goals and outline of the thesis dispersion measure (DM). We can write the group velocity of a pulse as
vg = c r 1 −ν 2 p ν2 (1.2)
where c is the speed of light, ν is the observing frequency and νp is the plasma
frequency given by νp = s nee2 πme ≈ 104Hz r ne 1cm−3 (1.3)
Here, e is the electron charge, me is the electron mass and ne is the electron
density. Dispersion measure is the line-of-sight column density of free electrons which is written as,
Z d
0
nedl (1.4)
Here, d is the distance to the pulsar. Using the above equation, we can derive the time delay of the radio wave due to the dispersion measure;
tDM(ν) = e2 2πmecν2 DM ≈ 4.15 ms DM ν2 GHz (1.5) The dispersion process broadens the pulse significantly (proportional to δν/ν3)
when it is detected over a finite bandwidth. Thus, it decreases the energy contained in the signal causing the signal to noise ratio (SNR) to decrease. Also if this effect is unaccounted for then not only the pulse shapes will be distorted but the times of arrival will be affected. Thus, the pulses need to be corrected or de-dispersed. There is a benefit of this propagation effect. Dispersion helps in distinguishing Radio Frequency Interference from astrophysical signals (see section 2.1.1). Here, we used incoherent de-dispersion method which is the simplest way to compensate the effects of pulse dispersion. It involves shifting each frequency channel in time according to the dispersion delay equation. For more details, please see 1.5. We choose not to discuss coherent de-dispersion method here since it is not used for the data analysis.
1.3
Goals and outline of the thesis
Giant pulses from pulsars have so far remained an elusive and unexplained phe-nomenon. Giant pulses from PSR B0950+08 observed in Kuiack et al.(2020),
Goals and outline of the thesis
opens the prospect for searching extreme fluence pulses from nearby pulsars at low frequencies. In order to get a better understanding of the giant pulse generation mechanism, analysis of giant pulses at low frequencies is crucial. The analysis of pulse morphologies across a range of frequencies, will help in providing constraints on the mechanisms responsible for giant pulse emission. The goal of my thesis is to see if AARTFAAC can detect giant pulse emission from more pulsars that are preferably at nearby distances. Individual pulsars from distant pulsars will be too faint to detect. Propagation effects are more profound at low frequencies so they were first removed from the data before it was was further processed. A single pulse search method was then developed to find giant pulses in the data obtained. Finally, we measured the sensitivity of AARTFAAC to detect these giant pulses.
Only a handful of pulsars have exhibited extreme pulses so far. If more pulsars are found to emit giant pulses then we might have a better understanding of the physical processes that leads to this kind of emission. The method can be used for other sources that can potentially emit giant pulses. Other than shedding light on the possible emission mechanism, the giant pulses can also be used to probe the magnetosphere of the pulsars.
Chapter 2 explores the instrument used for obtaining data for the thesis and the target selection methods. Chapter 3 discusses the methods employed to find giant pulses and the results of the search. Chapter 5 discusses the rate of the giant pulses from various sources found so far. We present the conclusions and summary in chapter 5.
Chapter 2
Observations and data
preprocessing
2.1
Observations with AARTFAAC
The data for the thesis is obtained from the Amsterdam-ASTRON Radio Tran-sients Facility and Analysis Center (AARTFAAC) (Prasad et al. 2016) which is based on Low Frequency Array (LOFAR) (van Haarlem et al. 2013). The AARTFAAC instrument is an all-sky radio transient detector operating primar-ily in LOFAR’s low band (30–80 MHz). It surveys most of the locally visible sky for transients and variable sources. It continuously tries to detect radio transients that might have originated from some of the most energetic events in the universe. There are two modes of operations for LOFAR, which are beam-forming and correlation. Beamforming uses multiple antennas to receive signals after adjusting the magnitude and phase of individual antenna signals appropriately. In correlation method, the signals between different baselines are cross-correlated. The Fourier transform of this will result in images. AART-FAC uses both beamforming and correlation when imaging. All signals from a station are first summed into one or more beams, and then images are obtained by correlating the station beams. AARTFAAC shares the six core stations, known as the Superterp, with LOFAR and by combining data from these sta-tions, it generates 1 second images via aperture synthesis. These stations offer the optimum combination of imaging quality and sensitivity. They are ideal for wide-field imaging since they form a densely sampled UV plane, giving a good instantaneous uv-coverage, that are co-planar to high accuracy. The wide-field, fast imaging is possible since AARTFAAC has a large field of view and fine time resolution. Though it draws data from LOFAR antennas, it processes
Target selection
these data independently of LOFAR. The data obtained from AARTFAAC con-sists of 16 separate sub-bands which have a bandwidth of 195.3 kHz. They are calibrated and are integrated in 1 second time intervals. The targeted search for giant pulses is done by incoherent de-dipersion and subsequent stacking of images generated by AARTFAAC (sec2.3). The images generated are of 1024 x 1024 pixels. The transient sources analyzed by AARTFAAC must have dec-lination greater than 0◦. This is because the sensitivity of dipoles drops near the horizon as the noise increases below the celestial equator.
2.1.1
Radio Frequency Interference
AARTFAAC detects a large number of transient sources that are not of astro-physical importance. These sources include terrestrial radio frequency interfer-ence(RFI), airplanes or satellites. Any interference that is caused by an exter-nal source and is within the observed frequency band is called RFI. Thus, they are not caused due to astrophysical sources themselves. There could be many sources of RFI such as cars, electrical fences, powerlines and wind turbines. RFI increases the false detection rate so and we get few genuine astrophysical signals. However, only a small fraction of AARTFAAC data is affected by RFI. Bright RFI is not a concern since the time periods corrupted by heavy RFI can be easily flagged and eliminated. In order to deal with these unwanted signals, there is a multi stage filtering process in action. Weak RFI can be filtered with TraP pipeline. RFI caused due to airplanes and satellites visibly appear on the images and therefore such bad images can be flagged and removed. RFI signals are much stronger than astrophysical signals so usually brightest detections are considered to be RFI spikes and subsequently filtered. This poses a challenge for sources with low DM since brightest giant pulses can be flagged as RFI. For sources with larger dispersion measure, it is easy to spot RFI. Radiation from pulsars is dispersed after propagating through ISM. The data is de-dispersed by adjusting time delays appropriately and then the the data is summed over all frequencies accordingly. Since RFI is terrestrial in nature, it has DM = 0 and and thus in de-dispersed data, it will be easy to identify them. They will appear extremely bright and are then flagged and filtered.
2.2
Target selection
Since the discovery of giant pulses from B0531+21 in 1968, 15 more sources have shown giant pulse emission (see Table 2.1). Amongst all the sources, five of the sources have declination less than 0◦ and so they are not visible to
Target selection AARTFAAC’s field of view(FOV). These sources are B0031−07, B0540−69, B1820−30A, B1821−24A, B0529−66. AARTFAAC has a time resolution of 1 second. The duration of giant pulses vary from microsecond to nanoseconds. Though AARTFAAC does not have a time resolution of the order of millisec-onds, giant pulses are exceptionally bright and they should be visible in the images generated. Thus, AARTFAAC is perfect to detect these bright and rare events. Amongst the remaining candidates, I have excluded B0531+21 (Crab pulsar) as a candidate since AARTFAAC does not have the required spatial resolution to observe giant pulses from the source. It has a spin rate of 30 times per second. The Crab Nebula is also very bright thereby it is not suitable for most interferometric radio observations. The light curves of the source show strong contamination from the surrounding nebula. Another candidate that I have excluded from my targeted search of giant pulses is the first discovered millisecond pulsar, PSR B1937+21. The flux density of the giant pulses emitted by PSR B1937+21 are the brightest radio emission ever observed (Soglasnov et al. 2004). However, the source lies too close to the galactic plane and there-fore, the light curves are contaminated with noise and it will not be a suitable candidate for single pulse search.
The goal of the research is to search for giant pulses from nearby pulsars. In order to find the range of dispersion measure which can be probed with AARTFAAC, I plotted the dispersion delay relation as seen in figure 2.2. The optimum dispersion range extends till 122 pc cm−3. Most of the candidates have pulse period less than 1 second which is AARTFAAC’s resolution. For the pulsars with pulse period of the order of millisecond, it is impossible to resolve the pulses into time bins accordingly. However, giant pulses from the known sources are exceptionally bright and so these pulses should be visible in the images as was seen for the source PSR B0950+08 shown in figure 2.1.
Target selection
Fig. 2.1 – Time-frequency plot of some of the giant pulses observed from PSR B0950+08 observed on 2018-04-14. Some of the images show bright pulses. (Kuiack et al. 2020)
Target selection
Table 2.1 List of Pulsars with GRPs (Kazantsev & Potapov 2018)
Pulsar name Period DM BLC References
[s] [pc cm3] [G]
B0950+08 0.253065 2.97 141 Singal (2001)
B1133+16 1.187913 4.84 11.9 Kazantsev and Potapov (2015b) B1112+50 1.65644 9.19 4.24 Ershov and Kuzmin (2003) B1237+25 1.382449 9.25 4.14 Kazantsev and Potapov (2015a) B0656+14 0.384929 13.94 765 Kuzmin and Ershov (2006) B0301+19 1.387584 15.66 4.76 Kazantsev et al. (2017) B1957+20 0.001607 29.12 3.76×105 Johnston and Romani (2003)
J1752+2359 0.409051 36.2 71.1 Ershov and Kuzmin (2006) B0531+21 0.033392 56.77 9.55 ×105 Staelin and Reifenstein (1968) J0218+4232 0.002323 61.25 3.21 ×1005 Joshi et al. (2004)
B1937+21 0.001558 71.02 1.02 ×106 Wolszczan et al. (1984)
B0031-07 0.942951 10.922 7.02 Kuzmin et al. (2004) B0540-69 0.0506 146.5 3.62×105 Johnston and Romani (2003)
B0529-66 0.975725 103.2 39.7 Crawford et al. (2013) B1820-30A 0.0054 2.47 ×105 Knight et al. (2005)
B1821-24 0.0031 119.8 7.25 ×105 Johnston and Romani (2003)
Target selection
Fig. 2.2 – Time resolution is limited by dispersion. AARTFAAC has 1 second time res-olution. By plotting the dispersion delay relation, we can find the range of DM which is optimum for AARTFAAC time resolution. In this case, the cutoff DM is 122 pccm−3
Fig. 2.3–The location of radio pulsars that have shown giant pulses are shown in the
Stacking and incoherent de-dispersion
2.3
Stacking and incoherent de-dispersion
Pulsar radiation is dispersed. The time delays introduced due to the prop-agation effects need to be rectified to obtain proper pulse arrival times from the source. Astrophysical signals are usually faint. The images that were gen-erated by AARTFAAC were stacked in order to increase the signal to noise ratio . Stacked image will have much smoother background thus, improving the image quality and reinforcing faint source fluxes. Before stacking, the data is de-dispersed(see Sec 1.2.1). This is done using incoherent de-dispersion in which each frequency channel is shifted in time (Cordes & McLaughlin 2003), according to Equation 1.5. While incoherent de-dispersion is computationally efficient, there will still be some residual intra-channel dispersion smearing (see figure 2.4. Compared to giant pulse fluxes, these losses are not significant and can be neglected. This method is only an approximation but it works very well for single pulse search.
Fig. 2.4–The time delays for different frequency channels are adjusted till they are aligned and then summed along several frequencies to get a de-dispersed pulse
Chapter 3
Data analysis and results
3.1
TraP pipeline
The low frequency radio sky is dominated by bright sources. AARTFAAC searches for transients in the images. This is not an easy task since astronom-ical sources are variable due to ionospheric effects or there might be instru-mental noise or RFI activity. The stacked images are processed for further analysis using the LOFAR Transient Pipeline (TraP ; (Swinbank et al. 2015)). The pipeline allows searches for transient astronomical sources in the images from AARTFAAC observations. TraP is useful for a variety of purposes that range from finding sources and their possible associations in each image to esti-mating source detection significance. TraP creates a running catalogue of each individual astronomical source detected in a given set of images. When a new measurement is made, the source association procedure searches for counter-parts in the running catalogue. The detection threshold of the sources is set at 8σ and for the sources detected, the analysis threshold is 3σ. This ensures that only astronomical sources are analysed and their light curves are extracted. All pixels that fall below the threshold 8σ from the median value are rejected, where σ is the standard deviation of the distribution.
The steps involved in how the pipeline process the images can be summarized as follows:
• Sources above 8σ are detected in the first image.
• A source finding algorithm, Python Source Extractor(PySE; (Carbone et al. 2018)) scans the image for sources and creates catalogue entries for each source in a database. This pipeline measures the rms (root mean
TraP pipeline square) noise in the inner 18th of the images.
• For successive images, the sources that are detected above the detection threshold are matched and added to existing database entries associated with the sources. These measurements help in making lightcurves (flux density as a function of time) of the sources.
• If a new source is detected then a new catalogue entry is created. Measure-ments are also performed at the locations of sources which were detected in previous images.
• The entire database of monitored source-catalogues can be accessed via Banana which is a web interface to the database designed to explore the TraP outputs.
The source monitoring feature forces extraction of light curves at the positions manually specified which aids in targeted searches for giant pulses. TraP also enables monitoring of background position(s) within a few beamwidths from the source. This is helpful in modelling background variability as discussed in section3.1.1. Along with the sources, a monitoring list of background locations were also inputted so that the background light curves can also be extracted and further analyzed for comparison with source light curves.
Before ingesting images into the pipeline, the images are run through a python script, TraP fits QC.py. The script measures the root mean square(RMS) values for all images where 4σ is the sigma clipping threshold used to calculate the RMS. This is the value used in TraP settings. A Gaussian is fitted to all the RMS values. The images are sorted into good/bad images after the sigma thresholds are calculated. The sigma clipping threshold used to reject images is 3σ. So images above the threshold are rejected. The good images are written into images to process.py which can be ingested directly into TraP. This ensures that images corrupted by RFI are flagged and removed. TraP outputs light curves for the monitored sources which can be accessed via the Banana web interface.
3.1.1
Search for giant pulses using pipeline
To search for giant pulses, it is necessary to know the dispersion measure (DM) of the sources. The sources used for my research have known dispersion mea-sure values which helps in monitoring them. While running the images through TraP, a list of source monitoring locations can be specified where forced extrac-tion of lightcurves are attempted, allowing for better detecextrac-tion of sources near
TraP pipeline
to the faint limit. As mentioned previously, after applying the appropriate de-lay to each frequency channel, the frequency channels were summed (see section
2.3). The entire de-dispersed observation data set was then searched for peaks. The detection of astronomical signals is possible when the de-dispersed signal power is high enough compared to statistical variations in the noise power. As the source moves across the sky, its apparent brightness is modulated due to the varying sensitivity of the antennae. The flux density scaling needs to be corrected for each image separately (see section 3.1.2). In order to discern the pulses from the background, I performed a comparative analysis of the flux density distributions of the sources and their nearby background. The analysis helps in removing the variability of the background introduced due to ionospheric scintillation. Ionospheric scintillation modulates the brightness of the source by 10-30% on timescales of 10–20 minutes. At low radio frequencies, the background sky shows both positive and negative flux. The negative flux is the result of synthesis imaging and taking finite Fast Fourier Transforms (FFT) which produces a ringing around sources in the sky. Bright sources will typically have negative bowls around them. The background variability occurs on a time scale of 10–20 min. These variations need to be subtracted from the light curve through low-pass filtering of the light curve. The de-dispersed time-series is convolved with a box-car function of suitable width to smoothen the data. The width is taken to be 2 minutes in this case for two reasons: extreme pulses will not significantly dominate the rolling mean and the variability will be removed from the light curve. If the width is very short then extreme pulses might significantly shift the value of the rolling mean and if it very long then the smoothed light curve cannot follow the ionospheric variations. After subtracting the background variability by using the rolling boxcar mean of two minutes width (Kuiack et al. 2020), the data no longer show variation in the light curves due to the ionosphere (see 3.1).
3.1.2
Flux scaling
The measured flux values of the sources need to be scaled appropriately into flux units. The flux scaling in the images is calculated for every image sepa-rately by using a linear least-squares fit of the instantaneous brightness of all detected sources extracted with the help of PySE (Carbone et al. 2018) in the AARTFAAC catalogue to their catalogued flux values (Kuiack et al. 2019). By comparing many flux density measurements from persistent sources in the im-age to the AARTFAAC catalogue, the method has been proved credible. The average uncertainty in the flux values is largely due to ionospheric variability
TraP pipeline
Fig. 3.1 – The figure shows light curve for one of the sources monitored; B1112+50. The observation is taken from May 2nd, 2020. On the x-axis, we have the flux values in arbitrary
units and the original light curve is shown in blue dots. We can see that it shows a lot of variation which needs to be subtracted. After subtracting the background variability, we get the subtracted light curve which is shown in red. This can then be used for further data analysis.
and measurement error and is estimated at 30%.
Flux density distribution
3.2
Flux density distribution
In order to discern giant pulses in the observation dataset, I performed several tests to the extracted light curves of the monitored sources. First of all, if a particular source emits giant pulse in a given observation session, then it should be visible by eye. As mentioned before, giant pulses stand out from the back-ground if they are well above the noise. They have very high fluence compared to average pulses. If there are no such conspicuous pulses then the next step would be to search for them statistically, by looking for an excess of bright events at the location of the pulsar. Though I have targeted nearby pulsars so that AARTFAAC has a better chance of detecting these bright giant pulses but the giant pulses can also fall below the detection threshold of AARTFAAC, so in that case they will not be visible in the de-dispersed light curve.
One needs to be careful with assessing any extreme events, if visible, since they can also be due to random noise, RFI, or an instrumental error. A good method to check this is by comparing raw data with de-dispersed time series for the same source. The raw data retains all the propagation effects so if we find a giant pulse in the de-dispersed time series, it should not be there at the same timing location in the raw data. If it is in both datasets, then it is probably due to some random noise.
Next, we try to model the noise with a Gaussian distribution. A Gaussian distri-bution is usually an accurate model for noise. We find more bright events than expected by comparing the expected number from a Gaussian distribution with the real number of events, using Poisson statistics (since these are independent events and no two events can occur simultaneously). This serves as statistical evidence to the fact that we might have detected something significant.
We perform the same analysis on the un-dedispersed signals and on the back-ground. If we find more bright events there as well, it means they are not accredited to GPs. Rather, the noise is a little bit non-Gaussian. Therefore, we need to prove the presence of GPs from the pulsar by comparing the background data with the pulsar data. The background is chosen where no AARTFAAC source has been detected. A comparison between the two will help eliminate false positives. When a giant pulse is present in the observation dataset, then there will be flux excess in the de-dispersed time series but not in the raw data. For this, we compute the excess above a chosen threshold (3.5σ) in the back-ground and take this as the expectation for the excess in the pulsar data. Then we measure the excess in the pulsar data and see whether it is significantly greater than in the background (again using Poison statistics.)
Flux density distribution from the mean, the number of events you expect to see there by random noise decreases strongly, and so you need to see fewer events there before you can call them a significant signal. For all the sources, I chose a threshold of 3.5σ since below that events are most likely due to random noise. The total noise can be approximated by a Gaussian and so with the mean and width of the distribution, I then calculated how many events one can expect and how many real events are there above 3.5σ threshold. We can find the Poisson probability which is given by the formula as follows:
P (Nreal; Nexpected) =
e−NexpectedNNreal
expected
Nreal!
(3.1) The formula helps in finding out if the events are due to random statistical fluctuations or not. If the probability is high then it is most likely due to random noise. The Poisson probability is calculated for both source light curves and backgrounds. It is also calculated for both raw data and de-dispersed time series.
For events that are above 2σ, the inverse cumulative probability distribution of fluences can be plotted for both source and background and compared. This will give final proof of whether there is giant pulse emission from the source or not. If the distribution is similar for both then it means there has been no giant pulse emission detected from the source.
I monitored several sources out of which the source B1112+50 has been observed the longest (≈ 49000 pulsar periods). GPs were first discovered from the source byErshov & Kuzmin(2003) at a frequency of 111 MHz. Around 126 GPs were detected in 105 observation sessions in the cited work. This translates to 0.67 percent of the full quantity of the pulsar’s periods (see figure 3.8). The pulsar has a pulse period of 1.65644 seconds (Kazantsev & Basalaeva 2020) and its dispersion measure is 9.19 pc cm−3 (Manchester et al. 2005).
I extracted light curves for both raw data and de-dispersed time series for this source (see figure 3.2 and figure 3.3 respectively). The observation was taken on 2nd May, 2020. A visual inspection of both the images reveal no conspicuous giant pulses. The histogram of both datasets reveal that the flux values are well fitted by a Gaussian. For raw data, there were 9 events above the threshold of 3.5σ and for de-dispersed data there were 9 events above the threshold. The expected number of events for such a threshold is 3. Using the equation 3.1, the poisson probabilities for raw data and de-dispersed data turned out to be 0.00317 and 0.00336 respectively
Flux density distribution
Fig. 3.2 – The extracted light curve for de-dispersed time series of the source PSR B1112+50. On the x-axis, we have time and on the y-axis we have flux in Jy. The ob-servation is taken on May 02, 2020.
The source flux values were compared with the background as can be seen in the figure3.7 and figureure3.6. From the figure, we see that there is more data around the mean. Repeating the same method as for source fluxes, we find that the number of events for raw data and de-dispersed time series above the threshold is 11 and 10 respectively. The poisson probability of events above the threshold given the expected number of events is 0.00024 and 0.00048976 respectively.
The flux distribution for the source and background were plotted (see figure
3.10). They both look quite similar and this goes on to imply that in this case, no giant pulse emission has been detected. From previous studies, it is found out that the fluence of giant pulse from B1112+50 is 720 Jy ms at 111 MHz. At 60 MHz, it would approximately convert to 1.4 Jy s. The highest datapoint detected is 18.715 Jy s. Thus, the previously seen giant pulses are too faint to be detected with AARTFAAC.
I repeated the same method for other sources. For the observations taken on 2nd
May, 2020, other sources that were analyzed include PSR J0218+4232, PSR B0301+19 and PSR B0656+14. Their pulse periods and dispersion measure values are given in Table 2.1. It is seen that for the source J0218+4232, the mean pulse energy from August, 2004 observation is 18 Jy µs at 857 MHz as
Flux density distribution
Fig. 3.3 –The extracted light curve for raw data of the source PSR B1112+50. The light curve is dominated by propagation effects which have not been rectified. On the x-axis, we have time and on the y-axis we have flux in Jy. The observation is taken on May 02, 2020.
Fig. 3.4 – Plot of the histogram of flux values taken from de-dispersed time series of the source PSR B1112+50. On the x-axis we have flux values in Jy. On the y-axis, we have the probability density of the flux values. The mean and standard deviation of the source fluxes are given in the box. The Gaussian is not a proper fit as we can see that there are many values that are not fitted with a Gaussian.
Flux density distribution
Fig. 3.5 – This is the histogram of flux values taken from raw data of the source PSR B1112+50. A guassian has been fitted to the data. On the x-axis we have flux values in Jy. On the y-axis, we have the probability density of the flux values.
Fig. 3.6 –On the x-axis we have flux values in Jy. On the y-axis, we have the probability density of the flux values. The noise is modeled by fitting a Gaussian. Both background and source fluxes are shown together for a comparative analysis. There is more noise at the mean.
reported in Knight et al. (2006). This means that at lower frequencies, the fluence of giant pulses will be less than 1 Jy s. The highest fluence value found
Flux density distribution
Fig. 3.7 –On the x-axis we have flux values in Jy. On the y-axis, we have the probability density of the flux values. Both background and source fluxes are shown together for a comparitive analysis. The noise is modeled by fitting a Gaussian. There is more noise at the mean.
Fig. 3.8 – The distribution of peak intensities of individual pulses from PSR B1112+50 (Ershov & Kuzmin 2003). On the x-axis, we have R which represents the ratio of GP peak flux density to AP peak flux density. On the y-axis, we have the ratio of the number of GPs to the total number of pulses observed.
Flux density distribution
Fig. 3.9–Plot of the peak flux distribution of the single pulses for PSR B1112+50 ( Karup-pusamy et al. 2011). The dashed line represents 10×Sav,peak.
from AARTFAAC observations is 14.92 Jy s. We did not find any ultra-bright pulses from PSR J0218+4232 down to a flux density of 18 Jy; the previously known ’normal GPs’ are too faint to see in our data. Similarly for source, PSR B0656+14, the observed fluence value inKuzmin & Ershov(2006) is 600 Jy ms at 111.870 MHz. At AARTFAAC frequencies, it is challenging to detect giant pulses from the source. However, for source B0301+19, the highest fluence value found from the observations is 20.7765 Jy. In Kazantsev et al. (2019), the fluence of giant pulses was 6930 Jy ms at 111 MHz. Thus, AARTFAAC has potential to detect giant pulses from this source. The pulsar B0301+19 is an isolated second-period pulsar with a relatively high integrated flux density. Thus, it is among the 150 most powerful pulsars. It has a low magnetic field at its light cylinder. The flux density distribution of giant pulses have been found complex in the sense that it shows a lognormal part (typical for regular pulses), a power law part (typical for GRPs) and a long tail at high energies (see3.11). On 7th July, I observed two more sources, B1237+25 and B1133+16. The highest fluence value for both sources found from AARTFAAC observations is 21.56 Jy s and 17.5 Jy s respectively. For B1133+16, the previously observed fluence is ∼ 8 Jy s, so these pulses are too faint to see in our data. On the other hand, the previously observed fluence for B1237+25 is 55 Jy s so we might detect giant pulses from the source in future if we monitor the source more.
Flux density distribution
Fig. 3.10– The inverse cumulative flux density distribution of flux values from the source and the background are quite similar. On the x-axis, we have fluence values in Jy s units and on the y-axis, we have cumulative number of pulses that are atleast 2 standard deviation above the mean.
Flux density distribution
Fig. 3.11–Distributions of pulses with peak flux densities greater than 4σ from B0301+19 (Kazantsev et al. 2019). In the top panel, flux densities are in in absolute units and in bottom panel, the values represent the flux densities divided by average flux density values.
Chapter 4
Discussion
4.1
Giant pulse emission rates
Emission rate statistics help in studying the emission physics of GPs. Since the emission mechanism causing giant pulses is unknown and may be variable, analyzing the rate of giant pulse generation can help us learn more about du-ration and nature of the mechanism, and measure the expected time between two giant pulses. It is desirable to know the rates of giant pulse emission from known GP emitters because it can elucidate on the dynamical behavior of GP generation mechanism. The rate of giant pulse emission also helps in comparing statistical properties of GPs with regular pulses. We focus on the pulsars those are within AARTFAAC’s field of view.
The rate of GP generation is not constant in all pulsars as shown inKazantsev & Basalaeva (2020). Rates of some of the pulsars are given in Table 4.1. The pulsars in the table are ordinary pulsars with low values of the magnetic field at the light cylinder. Of all the sources listed in table4.1, PSR B0950+08 and B1112+50 show a very stable rate of GP generation (see figure 4.1. For PSR B0301+19 and B1133+16, there were several sessions of non-detections. PSR B0301+19 show a fairly low GP generation rate, 5 GPs per hour on average. Since it emits giant pulses that can be potentially detected with AARTFAAC, we can take longer observation sessions in future to increase the chances of de-tecting giant pulses from the source. PSR B1112+50 showed the longest array of giant pulses. This suggests that the processes causing GPs is of prolonged duration. The variability in the rates indicate that the mechanism generating these bright giant pulses is not stable. Of course, increased observational du-ration might help better in rate measurement. It is interesting to note that
Giant pulse emission rates
pulsars with similar parameters show different rates of GP rates. The same can be said for GP clustering. Only pulsars PSR B0950+08 and PSR 1112+50 showed a considerable number of clusters of more than 2 GPs. Other pulsars do not have more than two consecutive GPs.
Table 4.1 Rate and clusters of GP generation for some of the pulsars (Kazantsev &
Basalaeva 2020)
Pulsar name Maximum Average 2 GPs > 2 GPs min−1 min−1 B0950+08 3.10 0.51 29 4 B1133+16 0.30 4.84 1 0 B1112+50 0.70 0.07 95 7 B1237+25 0.38 0.07 3 0 B0301+19 0.59 0.09 1 0
The observations, used to search for detectable giant pulses, are taken on 28th April, 29th April, 2 May and 7th July. All 4 total observation sessions (∼ 32
hours) contained no detectable giant pulses. PSR B1112+50 has been observed the longest. It has been observed on all dates. Ershov & Kuzmin (2003) observed 126 GPs in 105 observation sessions where each session equalled 5 minutes. This represents about 0.67 percent of the full quantity of the pulsar’s periods. In our research, we did not find any exceptionally pulses from the pulsar down to a fluence of 1.4 Jy s.
The sources, B1133+16, J0218+4232 and B0656+14 have been observed for nearly 15 hours. While we did not detect very bright pulses from B1133+16, J0218+4232 and B0656+14, we detected bright pulses from B0301+19 which lie well within the detection threshold of AARTFAAC. Kazantsev & Potapov
(2018) reported that 80 out of the sample of 3160 individual pulses detected were more than 4σ noise by amplitude and were classified as giant pules. The average profile was becomes more detectable only at the time the GPs were generated. So the source should be monitored for a longer observation session so that AARTFAAC can detect emission during periods of extreme pulse activity. We observed the source on 2 May for a little more than 3 hours. As given in Table4.1, the source was found to be emitting 5 GPs per hour on average at 111 MHz. The Poisson probability of detecting null events in this case is 0.67%. In
Kazantsev et al.(2019), 40150 pulsar periods were observed out of which 3160 pulses exceeded the 4σ threshold. Of the 3160, only 2.53% pulses pulses had peak flux densities 30 times more than the mean pulses. Thus, it is an entirely
Giant pulse emission rates possible scenario that we didn’t detect any GPs in our observation session. We might have been observing during quiescent period. There is also uncertainty in observing at different frequencies which might influence the detection of giant pulses.
For the source B1237+25, observations carried out in Kazantsev & Potapov
(2017) reported 3.8% (518 events) of the 13617 pulses studied had peak flux density, Sind > 10 Savg. With the long term study by Kazantsev & Basalaeva
(2020), it was found out that GPs are detected in 70% of the observational sessions, where the total observation duration is 37.92 hours. On average, PSR B1237+25 generates approximately 4 giant pulses per hour. The maximum value of the rate was 22 pulses per hour. The Poisson probability of detecting null events in this case is 1.8%. In my 5 hours of observation on 7th July, we did not detect any exceptionally bright pulse from the source. However, we need more observations to increase our chances of detecting giant pulses from the source.
Pulsars such as the Crab pulsar show a relatively high rate of giant pulse emission. Its rate does not change much on short-term scale but changes on a long term scale. This suggests that while the efficiency of the giant pulse emitting process appears to vary in time scale of a few days, intrinsic properties of the underlying process itself does not change. The intrinsic properties of the process may however evolve over longer time-scales as discussed in Rudnitskii et al. (2017). Unfortunately, AARTFAAC cannot extract lightcurves for the Crab pulsar since it doesn’t have the required spatial resolution to observe giant pulses from the source. PSR J0218+4232 has a much lower rate of giant pulse emission than other giant pulse emitters. The giant pulses of PSR J0218+4232 are aligned in phase with the peaks of the X-ray profile and roughly coincide with the minima of the integrated pulse profile in the radio band. This strong correlation between X-ray and radio properties confirms that the two emission processes originate in similarly defined regions of the pulsar magnetosphere. For PSR B0656+14, Ershov & Kuzmin (2003) observed approximately one giant pulse in 1000 observed periods.
Giant pulse emission rates
Fig. 4.1 –Rate of the emission of GPs of pulsars with low magnetic field strength at BLC.
Chapter 5
Conclusions
Search for extreme GPs are motivated by the detection of such pulses from PSR B0950+08. Observations of 7 pulsars in the Northern Hemisphere were carried out using AARTFAAC at 60 MHz in order to search for GPs. While we have not conclusively detected giant pules from any of the candidates, these searches illustrate the methodology that can be used to detect giant pulse emission from nearby pulsars and the issues and challenges that occur in these type of searches. We also probed AARTFAAC’s sensitivity to giant pulse emission. In doing so, we found promising candidates, B0301+19 and B1237+25, which produce giant pulses that can be detected with AARTFAAC.
Giant pulse emission is still poorly understood theoretically, even more so than normal pulsar radio emission. Much confusion prevails over whether giant pulse emission is the same or different than regular pulse emission. In order to get a whole picture of giant pulse emission, more observations need to be taken at low frequencies. Propagation effects are significant at low frequencies. Previously, due to limitations imposed either due to low sensitivity of observing systems or insufficient removal of dispersion, fewer giant pulses were detected at low frequencies (Bhat et al. 2007;Popov et al. 2006). This is not the case anymore. AARTFAAC which is based on LOFAR, has the necessary sensitivity to detect bright giant pulsars from some of the pulsars.
I developed a method to search for giant pulses from nearby pulsars which have dispersion measure less than 122 pc cm−3. I removed the propagation effects from the data, especially dispersion effects which are significant at the frequencies AARTFAAC operate. I ingested the de-dispersed images into the TraP pipeline which processed the images to give me light curves of the can-didate sources I was monitoring. There were no conspicuous giant pulses so I used statistical methods to help me search for giant pulses. After comparing
Future work
with previously known fluence values, I found two promising candidates that emits AARTFAAC detectable giant pulses. With more observations, we will definitely succeed in detecting giant pulses from the source.
At the moment, it is not known if the phenomenon is ubiquitous or rare. While only a handful of pulsars showed giant pulses, it could be simply that the telescopes were not sensitive enough to detect giant pulses or they were not observing in the time period that the pulsar was emitting giant pulses. It is also possible that perhaps the emission from a particular source is observable at different frequencies than the one AARTFAAC operates at. Giant pulses exist in various types of pulsars spanning wide range of periods, magnetic field at the light cylinder and broad frequency range. So far, there is no proof of correlation between pulsar properties and the phenomenon.
5.1
Future work
With the wealth of data available from AARTFAAC, we have the perfect op-portunity to search for giant pulses from different sources. For candidates B0301+19 and B1237+25, longer observation session will help in detecting gi-ant pulses during periods of extreme pulse activity. Once we find gigi-ant pulses from other sources besides PSR B0950+08, we can turn our attention to other sources that have not emitted giant pulses in the past. We can also observe many more giant pulses from known GP emitters, improving the statistics and allowing better characterization of giant pulsar emission. The pulsar science stands to benefit from further research in this field.
