Term Project: Magnetic Fields of Pulsars

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1 Term Project: Magnetic Fields of Pulsars Jamie Lomax May 14, 2008 Contents Introduction-A brief introduction to pulsars. (Page 1) Observing Pulsars-An example of how pulsars are observed. (Page 1) Magnetic Fields of pulsars-basics about the magnetic fields of pulsars and theorized decay mechanisms. (Page 2) Conclusions (Page 3) Annotated Bibliography (Page 3) Appendix-Includes all figures and tables refered to in paper. (Page 5) Introduction Pulsars are rapidly spinning neutron stars that formed from supernovae. They are called pulsars because, when observed, they seems to blink ; that is, we do not see their emission in radio frequencies continuously. However, pulsars have a regular period, usually on the order of seconds or less. From observations, several quantities can be derived specifically for pulsars. First, we can determine the period of rotation of the pulsar through measurements of how often they blink. The period derivative of the pulsar can also be measured. This quantity gives us an idea of how quickly the period is changing. Then, from both of these values, the characteristic age of the pulsar can also be found and is given by the following equation: τ = P (n 1) P (1 (P 0 P )n 1 ) where n is the bracking index (a measurable quantity that depends on rotation frequency and its first and second derivatives), P 0 is the initial period of the pulsar and P is the current period of the pulsar (Camilo et alt., 2000). Finally it is also possible to estimate the magnetic field of the pulsar too. Observing Pulsars-An Example: How two pulsars were observed by Camilo et al. The Camilo group used the Parkes radio telescope in Australia to discover two pulsars. This telescope is equipped with a multibeam (13 beams) receiver (see Figure 1 for an example picture of a seven beam receiver). This helps to increase the sensitivity of the measurements. Also, each beam takes data in two orthogonal polarizations so the amount of information collected is maximized. 1

2 This is because, given information taken from two orthogonal measurements, the original signal can be reconstructed (everything else must be a linear combination of the two orthogonal signals detected). The group estimates that with this receiver, detection of a pulsar with a period greater than a tenth of a second is possible. Measurements were centered on a frequency of 1374MHz, however a range of frequencies was observed. Data was binned into 288MHz wide channels that were recorded over 35 minutes of observing time. From the resulting data, a pulse profile can be created for the pulsar (Figure 2). These pulse profiles represent one revolution of the pulsar. When the pulsar is on, there is a large spike in the flux density compared to when it is off. Also, several other parameters (period, period derivative, frequency, flux density, etc.) were measured and derived from the data (See Table 1). The two pulsars that Camilo et alt. are reporting their discovery of are important because they are unusual. The first pulsar, PSR J , has the largest period derivative known (as of the year 2000) while the second pulsar, PSR J , has the largest magnetic field of any known pulsar (again, as of the year 2000). Magnetic Fields of Pulsars Basics The magnetic field of a pulsar can be estimated with the following equation B 2 P P Ic 3 ( 4π 2 R 6 ) where I is the moment of inertia of the pulsar and R is the radius (Flowers et alt., 1976). This equation was derived theoretically from an expression that relates the energy a pulsar loses in its pulse emissions and its magnetic field under the assumptions that the field is a dipole and that is is possible to extrapolate the dipole field (which was determined for a large distance from the pulsar) back to the surface of the pulsar. It has been theorized that pulsars must be born with their magnetic field because there is no mechanism in place to fuel a magnetic field of the strengths seen. However, it may be that the magnetic moment of the parent star is aligned with its rotation axis but when the pulsar forms the rotation axis and magnetic moment are no longer aligned. Observations show that older pulsars tend to have a magnetic field on the order of G while younger pulsars have a magnetic field an order of two or three times higher (10 12 G or G) (Goldreich et alt., 1992) so the natural conclusion is that as pulsars age, their magnetic field strength decreases. (For a comparison, the Earth s magnetic field is 0.6G while the Sun and refrigerator magnets are about 50G.) In fact, a large number of studies assume an exponential decay rate of the magnetic field on the order of 10 7 years (Dipankar et alt., 1992) and it has been theorized that this decay could be caused by three different mechanisms, ohmic decay, ambipolar diffusion and Hall drift. Decay Mechanisms Ohmic decay and ambipolar diffusion are dependent on the state of the material in the pulsar. The equations that describe both processes can be derived from the equations of motion of the 2

3 particles that make up the pulsar (Goldreich et alt., 1992): m p v p t + m p(v p )v p = µ p m p ψ + e(e + v p c B) m pv p τ pn m p(v p v e ) τ pe m v e e t + m e(v e )v e = µ e e(e + v e c B) m ev e m e(v e v p ) τ en τ ep Ohmic decay is reliant on the electrical conductivity of the matter inside the pulsar. In fact, this is why it is called ohmic decay. A derivation of the decay of a pulsars magnetic field over time using the equations of motion for the particles in the pulsar and Faraday s Law yield a term that resembles Ohm s Law: E = j σ 0. However, theoretically the electrical conductivity (σ 0 ) of the material is extremely large. The result of this is that ohmic decay can not possibly cause a decay in the magnetic field of the magnitudes observed because the time to do so is larger than the age of the known universe (Goldreich et alt., 1992). Ambipolar diffusion seems account for the decay of magnetic fields in a better manner. However, ambipolar diffusion requires that the matter is a homogeneous particle fluid (Goldreich et alt., 1992). It is the result of a build up of charge on the surface of a pulsar. As charge is built up, a charge imbalance is formed which, in turn, makes these particles want to move. This movement is what would cause decay in the magnetic field and particles may even leave the surface of the pulsar. The third possibility, Hall drift, can not be a direct cause of the decay. However, it is theorized that it may be a catalyst to increase ohmic decay to a level that could account for the decay of magnetic fields in a respectable time frame. Hall drift is, most basically, a transport of magnetic flux by the moving electrons give rise to an electrical current (Reisenegger et alt., 2007) and therefore increases the electrical conductivity of the pulsar. Conclusions Even though we have identified three possible mechanisms for the decay of magnetic fields in pulsars it is still not clear if decay actually happens. Some theories suggest that it does while others disagree. It is possible that the number of pulsars whose magnetic fields are known is, at this point, just not great enough for astronomers to reliably say that decay is in fact happening. Our methods for observing and deriving magnetic fields of pulsars may favor older pulsars with weaker magnetic fields and younger pulsars with stronger magnetic fields. Currently more research is needed to settle this debate. A large survey of pulsars in which magnetic fields of pulsars are derived needs to be completed in order to determine which theory is correct or how we must modify our theories to fit what is actually happening. Annotated Bibliography Camilo, F., Kaspi, V.M., et alt, 2000, ApJ, 541, 367. Discovery of Two High Magnetic Field Radio Pulsars The authors of this paper report the discovery of two pulsars which they believe have large magnetic fields. They made their discovery using the Parkes Radio Telescope in Australia. This paper gives a good example of the observation techniques and data analysis used to infer the strength of magnetic fields in a pulsar. 3

4 Dipankar, B., Ralph A.M.J., et alt. 1992, Astron. Astrophys., 254, 198. On the Decay of Magnetic Fields of Single Radio Pulsars The authors of this paper do Monte Carlo simulations of magnetic field decay in pulsars and then compare their results to observations. Their simulations suggest that the amount of time needed for the magnetic field to decay in a single pulsar is greater than the life time of the pulsar. This leads them to suggest that there is no appreciable decay in the magnetic field. Flowers, E. et alt. 1976, ApJ., 302, 215. Evolution of Pulsar Magnetic Fields This paper gives the equation for the magnetic field and suggests the possibility that the magnetic moment and spin axis of the parent stars of pulsars are originally aligned and then drift apart during pulsar formation. Goldreich, P. & Reisenegger, A. 1992, ApJ, 395, 250. Magnetic Field Decay in Isolated Neutron Stars The authors of this paper explore three ways that the magnetic field in neutron stars could decay over time. The first way, ohmic decay, is found to be too slow for any appreciable amount of decay. The other two ways, ambipolar decay and Hall drift, are theorized to cause a more significant decay over the life time of the neutron star. This article gives possible theories that may explain why the magnetic fields of pulsars/neutron stars could to decay over time. Reisenegger, A., et. alt. 2007, A&A, 233, 472. Hall drift of axisymmetric magnetic fields in solid neutron-star matter The authors of this paper give a good definition of Hall drift which clarifies what it is. 4

5 Appendix to Magnetic Fields of Pulsars A B Figure 1: An example of a multibeam receiver. This particular receiver was built by the Australia Telescope National Facility (ATNF), the same organization that operates the Parkes Radio Telescope that Camilo et alt. used in their observations, and is used on the Arecibo Radio Telescope. A) The point spread function of this receiver. B) The underside of the receiver where you can see the seven beams. Figure 2: The pulse profile for pulsars J (top) and J (bottom) at 1374 MHz. (Camilo et alt., 2000). This clearly shows when the pulsar is on and off.

6 Table 1: An example of the parameters that can be found by observing pulsars using the method that Camilo et alt used.