Searching for Millisecond Pulsars in Gamma-ray Data Using the Fermi Lat

When professor Antony Hewish of Cambridge University set out with his graduate student Jocelyn Bell to study the effects of interplanetary scintillation in the latter part of 1967 he had no idea they would make one of the most important astronomical discoveries of their time. The association of their discrete radio signal with a Pulsar, then only a theorized entity, initiated an era of great interest in interstellar space. As further analysis was conducted a need for telescopes to monitor radiation at other energies became quite evident. Soon the first space based telescopes were launched in order to study high energy radiation, which is absorbed by the atmosphere. Although not the first probe into the gamma-ray sky, the Energetic Gamma Ray Experiment Telescope, or EGRET, aboard the Compton Gamma Ray Observatory (CGRO) lead to the discovery of a great many point sources of gamma-rays, many of which remained unidentified during its lifetime. Its successor, and in many ways superior, the Gamma Ray Large Area Space Telescope (GLAST), later renamed Fermi, was launched in June of 2008 and now allows for an even greater and more detailed exploration of the gamma-ray sky. One of the major science goals associated with the new telescope is the resolution of many unidentified point sources of gamma rays and the discovery of new pulsars. With more and better data, new search techniques have been implemented to find pulsars, most notably a time-differencing technique (Atwood et al. 2006, Ziegler et al. 2008). Using this technique and data from the Fermi telescope, blind searches have been performed to detect neutron star pulsations. Here I review the history and relevant science of pulsars as well as the telescopes used in their discovery. I also discuss the timedifferencing technique and its use in the discovery of new pulsars. Finally, I provide analysis of the possibility for discovery of a new millisecond pulsar, a special class of rapidly rotating pulsars, in gamma-ray data alone. Millisecond Pulsar Searches With Fermi 3 1 – Pulsar Discovery Although Jocelyn Bell's discovery of a periodic radio signal in August of 1967 lead to the first confirmed discovery of a pulsating source of radio (PSR), or pulsar, the seeds for such a discovery were laid by Walter Baade and Fritz Zwicky in 1934 (Baade and Zwicky 1934). They suggested the existence of a neutron star, a possible endpoint in stellar evolution: ...a supernova represents the transition of an ordinary star into a neutron star, consisting mainly of neutrons. Such a star may possess a very small radius and an extremely high density (Baade and Zwicky 1934) It was also suggested by Pacini in 1967, prior to the discovery of the pulsar, that a highly magnetized, rapidly rotating neutron star may be the source of energy in the Crab Nebula (Pacini 1967). The 250-ft. radio telescope at Jodrell Bank in Manchester, U.K. had the ability to discover a pulsar about 10 years prior to the actual discovery; however, periodic fluctuations in the radio signal were either overlooked or not recognized as such. The implementation at Cambridge of a large receiving antenna with a longer wavelength (3.7 m) by Hewish allowed their telescope to be sensitive to weak discrete radio sources (Lyne and Graham-Smith 2005). The initial discovery of large signal fluctuations at similar times on successive days was dismissed as possible terrestrial interference until a recorder with a faster response time was used and, in November of 1967, a pulse with a period of 1.337 seconds was recorded (Lyne and Graham-Smith 2005). Millisecond Pulsar Searches With Fermi 4 Figure 1: The left is the original recording of the first pulsar B1919+21 and the right is the fast recording. In the original you can see where the fluctuations were labeled as interference (Lyne and GS 2005, taken from Hewish et al. 1968). The discovery was announced in a Nature article of February 1968. The initial publication contained a great deal of analysis of the signal, first suggesting the source must lie outside the solar system due to Doppler effect observations on the pulsar periodicity (Lyne and Graham-Smith 2005). They reasoned that the short period of the signal implied its association with a compact object, either a white dwarf or neutron star. Initially, there were three proposed models for the source of such periodic signals: radial pulsations, orbital motion, and rotation. Radial pulsation and orbital motion were ruled out because of the short period, which was increasing with time. A rotating neutron star became the only possible candidate due to its stability at such a short period, low enough luminosity at closest pulsar distances, and small enough radius (Manchester and Taylor 1977). The first pulsar was named PSR B1919+21. The B stands for the location in 1950 coordinates while the numbers give the location in the sky. All pulsars published after 1993 are designated by a J, for J2000 coordinates, and have numbers referring to their right ascension and declination. Some older pulsars, therefore, are listed with two different names for the two systems (Lyne and Graham-Smith 2005). Millisecond Pulsar Searches With Fermi 5 2 – Pulsar Properties In the first year following the discovery by Bell and Hewish a great deal of work was published concerning pulsars and when the dust settled it was generally accepted that pulsars are strongly magnetized and rapidly rotating neutron stars. Although theorized years before their discovery, much of what is now known about pulsars has been confirmed by observation and population statistics. In order to understand how pulsars came to be it is important to first break down the components which make them special, namely the formation of neutron stars, the role of their strong magnetic fields, and the nature of their evolution. I will also discuss the evolution of binary and millisecond pulsars, a class with somewhat distinct development and physical properties. 2.1 – Neutron Star Formation Neutron stars are one of the possible endpoints in stellar evolution, along with black holes and white dwarfs. A star “dies” when it ceases to to generate energy through nuclear fusion in its core. More massive stars may be able to continue through the nuclear cycle to the burning of iron; however, others will be disrupted by hot flashes when the core begins to burn other elements such as oxygen (the “oxygen flash”). Without the thermal pressure due to nuclear energy generation the star cannot withstand the internal compression due to gravity and will collapse. This collapse occurs first in the inner core of the star, releasing enormous amounts of energy which blow way the outer layers of the star. Once the supernova explosion has occurred, gravity begins to pull the remaining stellar material in upon itself until another means of pressure support allows for an equilibrium state. Neutron stars are one example of this equilibrium, gaining the needed quantum mechanical neutron degeneracy pressure from the non-interaction of neutrons which, as fermions, are only allowed to have one particle occupying a given quantum mechanical state. Similarly, white dwarfs, another possible equilibrium Millisecond Pulsar Searches With Fermi 6 endpoint in stellar evolution, are supported by electron degeneracy pressure. Although it is impossible to know for sure what progenitor star formed each compact object, population statistics show that neutron stars likely evolved from 4-10 solar mass stars, often via a supernova explosion (Longair 1994). Neutron stars have an average mass of 1.4 solar masses (2.8 * 10 kg), although their mass can range between 0.2 and 2.0 solar mases. They have an average radius of 1.4 km, leading to a central density on the order of 10-10 g/cm. Neutron stars consist of a neutron super-fluid interior housed within a crystalline solid crust and while its strong magnetic fields only minimally affect its interior makeup, playing a small role in the composition of the crystal structure of the crust, they are dominant in the region outside the star (Lyne and Graham-Smith 2005). Figure 2: An example neutron star cross section (Manchester and Taylor 1977). The association with supernovae has lead to realization of a number of important facts concerning pulsars. Supernova explosions explain pulsar's high transverse velocities, gaining kicks due to asymmetry in the explosion. These high drift velocities help explain pulsars being found away from Millisecond Pulsar Searches With Fermi 7 supernova remnants (SNRs) although likely being born in the same region. While most supernova remnants have a lifetime of about 10 years, pulsars are known to “live” (be detectable) for about 10 years (Longair 1994, Bhattacharya and Heuvel 1991). The Galactic pulsar birthrate has been estimated at about one per fifty years from statistics of supernovae. Furthermore, the predominant existence of pulsars as solitary objects while most other stars are members of binary systems is most likely due to disruption from the supernova explosion (Bhattacharya and Heuvel 1991). 2.2 – Pulsar Magnetic Fields Pulsars have extremely strong magnetic fields associated with them which greatly affect the physical conditions far beyond the surface of the star. The magnetic field is also responsible for the loss of angular momentum due to magnetic dipole radiation. This loss of energy and angular momentum is what causes pulsar periods to lengthen over time. The magnetosphere is a region outside the surface of the pulsar but within the speed-of-light cylinder, a space with a radius such that a particle located at its edge and co-rotating with the pulsar would be traveling at the speed-of-light (Bhattacharya and Heuvel 1991). This co-rotation is due to the fact that the magnetosphere is coupled to the ions of the star's crust by the strong magnetic fields (Manchester and Taylor 1977). Magnetic field lines cannot close beyond the speed-of-light cylinder and thus remain as “open” field lines. It is along these open field lines that the plasma of charged particles is accelerated as a pulsar “wind.” The region around the magnetic poles on the surface of the pulsar between closed field lines are known as the polar “caps,” while the region further out, beyond the last closed magnetic field line is known as the outer magnetospheric “gap.” It is from these regions that the beams of radiation originates, through an electron-positron cascade and secondary plasma of charged particles. Primary charged particles are accelerated along open field lines by strong electric fields induced by the rotation of the highly magnetized neutron star (Bhattacharya and Heuvel 1991). The inclination of the magnetic dipole with Millisecond Pulsar Searches With Fermi 8 respect to the rotation axis in pulsars gives rise to a lighthouse effect, lending to their pulsed nature. Furthermore, the two emission regions lead to multiple beam patterns for the different emission frequencies: a narrow radio beam and a wider gamma-ray beam. Figure 3: Pulsar schematic detailing essential features. The velocity of light cylinder is represented by the vertical dashed lines and the polar caps are the cross hatched regions (Lyne and Graham-Smith 2005). Magnetic field strengths in young pulsars can reach 10 Gauss, but among “normal” pulsars, population statistics tell us that those with longer periods (older) tend to have smaller average field strengths. An interesting value is the ratio of the gravitational to electrostatic forces on an electron near the surface of a pulsar. For the Crab Pulsar, the ratio GMm r / e rB c is about 10 -12 (21-22 Lyne and G-S). A measure of the strength of the magnetic field of a pulsar at its surface can be computed using its spin period and spin-down rate: B s= 3c I 8 R P Ṗ  1 /2 , where I is the moment of inertia and R the neutron star radius. These strong magnetic field strengths are generated in the collapse following supernova of a normal star with a field strength B of about 100 Millisecond Pulsar Searches With Fermi 9 Guass, the magnetic flux being conserved into compressing stellar material (Lyne and Graham-Smith 2005). Most calculations suggest that pulsar magnetic fields decay on a time scale of about 10-10 years, based upon the time constant for field decay: B=4 R /[m1c] , where σ is conductivity, R the stellar radius, and m an integer set to zero for a dipolar magnetic field (Manchester and Taylor 1977). A decrease in magnetic field strength is generally thought to accompany the increasing period of a pulsar over time; however, the exact nature of the decay has been debated. A plot of field strength versus spin-down, or characteristic, age τ, defined as =2P/ Ṗ , shows a decrease in field strength with increasing τ. Another indicator of the age of a pulsar is called its kinetic age. This is defined as t k= z / ż where z is the distance the pulsar has migrated away from the galactic plane. Transverse velocity data indicate that pulsars have high velocities, with a population average of about 200 km/s. This allows them to travel great distances from the plane of our galaxy even though most are born very near to it. The magnetic field can be estimated from the spin period and spin-down rate suggesting the spin-down age τ is a good indicator of the true age if the magnetic field does not decay. However, when comparing the spin-down age τ to the kinetic age tk, τ is on average two orders of magnitude larger. This means that “the spin-down age increases much faster than the true age, exactly as would be expected from a decay of the field strength” (Bhattacharya and Heuvel 1991). Further evidence suggesting the true age of pulsars is given by the characteristic age is found in observing characteristic ages for pulsars with associated supernova remnants. That of the Crab pulsar, 1,240 years, is close to the 955 years elapsed since its progenitor supernova; furthermore, the characteristic age of the Vela pulsar, 1.1 · 10 years, is in agreement with estimates of 1-3 · 10 years (Manchester and Taylor 2005). Millisecond Pulsar Searches With Fermi 10 In reality, a difference in kinetic versus spin-down age suggests a decline in the spin-down torque on the pulsar given by: N= I ̇= 2 3 c B s 2 R sin , where Ω is the angular velocity and α the angle of inclination (Bhattacharya and Heuvel 1991). The similarly defined “radiation reaction torque” is given by: N=−2msin 2 3c  , where m is the magnetic dipole moment (Manchester and Taylor 2005). This has lead to theories which point to precession, or reduction of inclination α, of the magnetic dipole over time, leading to a decreased magnetic field (or magnetic moment) M due to alignment while the field strength B remains unchanged. Strong electric fields generated by the rapid rotation of the highly magnetized star give rise to a potential of 10-10 volts. Before the realization that pulsars radiate a beam of radiation with two distinguishable components estimates of the dipole inclination angle α were impossible. This knowledge allows estimates of α to be made using the width of the core beam or the shape of the Scurve traced out by the rotating polarized beam (Bhattacharya and Heuvel 1991). However, no statistics showing a systematic trend in dipole inclination angle α have been found leading researchers to believe a decrease in magnetic field strength B is responsible for torque reduction (Bhattacharya and Heuvel 1991, Lyne and Graham-Smith 2005). A good description of the life of a pulsar, and its magnetic field, can be found in analysis of a fieldperiod (or B-P) diagram. Figure 6 below shows a B-P (field strength versus period) diagram and gives a good visual representation of the evolutionary life of most pulsars. They begin in the upper left corner and have strong magnetic fields and short periods and end lower and to the right with depleted Millisecond Pulsar Searches With Fermi 11 magnetic fields and extended periods. The stronger a pulsar's magnetic field at birth the faster its period will increase, especially initially. After a few million years of emission, the magnetic field begins to decay and the increase in period halts, since spin-down rate decreases with decreased magnetic field. Within about ten million years the polar cap voltage will decrease sufficiently that the pulsar will cease to radiate and become “invisible.” This accounts for the lack of low B and long P pulsars, below the “death line” in the diagram. There is evidence to suggest that magnetic fields of pulsars do not decay completely but reach a minimum of no less that 10 Gauss. Some pulsars are spun-up through accretion and are found in the lower left of the diagram. These are the binary (circled) and millisecond pulsars and will be discussed in more detail in later sections. Figure 4: A B-P diagram showing the derived magnetic fields of 403 pulsars plotted against spin period (Bhattacharya and Heuvel 1991). 2.3 – Pulsar Emission Pulsar emission emanates from two principal regions, core emission from the polar caps and cone emission from the outer gap. The development of the core beam of particles is dependent upon surface flow from the pulsar, either thermal or field emission, or as a result of a reverse flow of oppositely charged particles. Whatever the cause, a stream of particles with relativistic energies γ of about 10-10 Millisecond Pulsar Searches With Fermi 12 is excited along magnetic field lines above the surface. This primary beam develops a broader cascade of charged particles through pair production. The electrons (or positrons) produced are restricted to following magnetic field lines, which are generally curved. As the particle is transversely accelerated it radiates gamma rays in a process known as curvature radiation. The cascade creates a secondary plasma of charged particles which has lower energy and higher density due to the emitted pairs. Since this takes place in a region of closed magnetic field lines, gamma rays produced continue to interact with the magnetic field, creating electron-positron pairs, and furthering the cascade. The resulting plasma of accelerated charged particles is responsible for the core radio emission from the polar cap region, explaining the much narrower radio beam produced by pulsars. Radiation from the outer magnetospheric gap, the region bounded by the last closed field line and extending to the velocity of light cylinder, emanates in a similar cascade. The difference is that the electric field extends further, accelerating electrons and positrons to highly relativistic energies, without the damping effect of the plasma. As in the polar cap, curvature radiation is created by the charged particles moving along open field lines; however, the subsequent gamma rays produced may escape to be observed as high energy pulsar radiation or continue to aid in a particle cascade. The emission from the outer gap is responsible for a nearly constant beam pattern over more than ten decades of the Crab pulsar high-energy spectrum due to the geometrically restricted emitting region (Lyne and GrahamSmith 2005). Although the processes in these two regions are very similar, the details of their emission differ greatly. The figures below detail the emission regions and cascade processes. Millisecond Pulsar Searches With Fermi 13 Figure 5: Schematic diagram of a pulsar detailing emission regions, notably the locations of the polar cap and outer magnetospheric gap (Chiang and Romani 1992). Figure 6: The left is an image detailing the cascade process in the polar cap region and the right is a similar representation of cascade process in the outer magnetospheric gap (Lyne and Graham-Smith 2005). As previously noted, pulsars, although predominantly detected via radio emission, radiate energy through the full range of the electromagnetic spectrum. Optical pulses from the Crab Pulsar were discovered by Cocke, Disney, and Taylor on 16 January 1969 using a cathode-ray rube. Soon after, a stroboscopic photograph was taken at Lick Observatory using a new television technique. Also in 1969, two separate rocket flights successfully detected X-ray emission from the Crab Pulsar with radiated power more than 100 times greater than in the visible region (Lyne and Graham-Smith 2005). These discoveries provided many answers concerning details of pulsar emission and laid the Millisecond Pulsar Searches With Fermi 14 groundwork for further research into high energies as well as into binary and millisecond pulsars, common emitters of high energy radiation. High energy emission is most commonly associated with younger pulsars, although older millisecond pulsars are capable of high energy emission as well. The key source of energy fueling the emission is the rate of loss of rotational energy, given by: Ė=−I ̇=−4 I v v̇=4 I Ṗ /P . Clearly, the high energy output of young and millisecond pulsars is due to their very low spin periods and, in the case of young pulsars, large period derivatives. Since the inertia is mostly independent of the neutron star model adopted, and varies little with mass, the period and period derivative are important in determining energy output. For the Crab pulsar the energy loss rate is Ė = 4.5 · 10 erg s. Much, at least 1.5 · 10 erg s, must be absorbed in the surrounding Crab Nebula in order to account for observed radiation. Non-thermal X-rays, generated by synchrotron (or magnetic bremsstrahlung) radiation, where charged particles are accelerated to relativistic energies in a magnetic field, are seen as pulsed emission (Lyne and Graham-Smith 2005). Both the X-ray and gamma-ray emission are emitted from the outer magnetospheric gap as a wide cone of emission. The highest energy gamma-rays, of up to TeV energies, are emitted furthest out in the outer gap, where the magnetic field is weakest and pair production is less limited (Lyne and Graham-Smith 2005). 3 – Binary and Millisecond Pulsars X-ray emission from X-ray binary pulsars is usually generated during the accretion of mass from one star onto another. Before the class of X-ray binaries and the nature of their emission can be discussed, however, it is important to understand how they are formed and what separates them from “normal” Millisecond Pulsar Searches With Fermi 15 pulsars. From a statistical standpoint, there are many factors which differentiate the population of binary and millisecond pulsars, related by their method of formation, from the majority of the population of pulsars. Both binary and millisecond pulsars tend to have much weaker magnetic fields and much shorter periods than the bulk of pulsars. Furthermore, about half of millisecond pulsars lie in binary systems, while about 92% of pulsars in general are solitary (Manchester et al. 2005). Finally, as will be discussed, the formation of millisecond pulsars, both solitary and binary, is closely related to the evolution of binary pulsar systems and share important traits with a particular class of X-ray binaries. Although binary and millisecond pulsars represent a minority of the pulsar population, their study has done a great deal to further knowledge of neutron stars and their magnetic fields (Bhattacharya and Heuvel 1991). Since the discovery of discrete X-ray sources many have displayed periodic variations in both optical and X-ray emission suggesting they are members of close binary systems. Optical observations also allow for a more complete analysis of the system to be made, including the masses of the separate components. A spectroscopic Doppler shift observation of the radial velocity of the visible star also allows measurements of the orbital periods of binary systems to be made and are often on the order of a few days, suggesting a system close enough for mass transfer. When the velocity curve of the visible star is resolvable it can be combined, along with Newtonian mechanics for elliptical orbits, to yield the mass function: f m p ,mc , i = 4 G asini Pb 2 = mc sini mpmc 2 where mp is the primary star (pulsar) mass, mc the companion mass, i the inclination of the orbit with respect to the plane of the sky, Pb the period of the binary orbit, and G the gravitational constant. In most cases, when velocity curves for the sources are obtained, separate mass can be determined for Millisecond Pulsar Searches With Fermi 16 each member of the system and are generally about 2-30 solar masses for the visible companion and 13 solar masses for the primary X-ray source, determined to be a pulsar by the same logic used for the radio emitters (Manchester and Taylor 1977, Lyne and Graham-Smith 2005). 3.1 – Accretion in X-ray Binaries Data indicate the majority of X-rays from discrete sources are due to accretion of matter from the massive companion star onto the compact primary. This is thought to be the principal process producing X-ray emission in X-ray binaries; however, solitary X-ray emitters have been found and their emission is likely due to rotation of the neutron star as in most pulsar emission. Still, other X-ray emitters have been found with long period emission (6-12 s), extremely strong magnetic fields (1010 Gauss), and high luminosity. However, their spin-down energies I ̇ are far too low to account for their luminosities and the nature of their emission is unknown, lending to the name anomalous X-ray pulsar (AXP). Similar to AXPs is a class of radio pulsars which also have very strong magnetic fields, together they form a class known as 'magnetars', with the source of the X-ray energy being stored in the magnetic field in the interior of the neutron star. Isolated X-ray emitters have also been detected through soft emission of thermal X-rays from the surface of the neutron star, the source of which is most likely energy stored in the gravitational collapse (Manchester and Taylor 1977, Lyne and Graham-Smith 2005). Millisecond Pulsar Searches With Fermi 17 Figure 7: Matter streams onto the compact neutron star from the massive companion, transferring angular momentum in the process (Francis Graham-Smith 1992). The primary emission mechanism of interest is that due to accretion in a binary star system, shown above. The X-ray luminosity of the pulsar is approximately equal to the rate of potential energy loss of the accreting material: Lx≈ G M Ṁ R , where M and R are the mass of the compact star and Ṁ is the accretion rate. The maximum X-ray luminosity is known as the Eddington luminosity LEdd, and is derived from an equilibrium between gravitational forces and the radiation pressure, using the relation: GM r 2 = Lel 4 r m p c ,