Magnetospheric Emission From Isolated Pulsars

The lines shown correspond to L_x = dE/dt - a hard upper limit to the magnetospheric emission - and L_x = 2.5 X 10^{-17} (dE/dt)^1.39, an empirical relationship derived by Seward and Wang (1988) based upon Einstein results; a similar relationship was derived by Ogelman (1994) based upon Einstein and ROSAT results.

Figure 1: Click here for plot of Lx vs. dE/dt.

Clearly a simple interpretation with x-ray luminosity scaling as some power of the spindown energy loss does not hold for all pulsars, although the general correlation is clear. In particular, there appear to be a number of pulsars for which the x-ray emission, relative to available spin-down power, exceeds that characteristic of the majority. This is suggestive of a second emission component - perhaps associated with cooling emission from the NS surface. This suggestion is strengthened by observation of a distinct soft emission component, consistent with the cooling scenario, from several of these pulsars. Other pulsars fall distinctly below the curve, perhaps indicating geometrical effects which limit the x-ray emission. Note, however, that the luminosity for each pulsar is derived on the basis of a particular spectral model, and that this varies from point to point.

The general view of pulsar magnetospheres derives from the model of Goldreich and Julian (1969) who showed that within the star and magnetosphere, the component of E along B must vanish because any nonzero component would result in charge flow which would rearrange the charge density until the field was canceled. The dynamics produce a charge-separated, corotating magnetosphere. In regions where the charge density is zero (the so-called ``gap regions''), however, no charge redistribution is possible, and regions with large E · B may be formed. For sufficiently large rotation rates and magnetic fields, these large fields can result in e± production generating a pair plasma which effectively ``shorts'' the circuit; the charges are accelerated along the field lines, resulting in curvature radiation of gamma-rays, and ensuing photon-particle cascades. Models for such gap sites have concentrated on regions just above the magnetic polar caps (Sturrock 1971, Ruderman and Sutherland 1975), and on regions in the outer magnetosphere (``outer gaps'' - e.g. Cheng, Ho, \& Ruderman 1986a,b: Chiang \& Romani 1994; Romani \& Yadigaroglu 1995). The models are not mutually exclusive, and each invokes potential drops along the magnetic field associated with the rotational dynamo action of the pulsar magnetic field.

Figure 2: Click here for sketch of pulsar magnetosphere.

In outer gap models, the x-ray and gamma-ray emission from the more luminous pulsars are accommodated by an acceleration site where the magnetic field is low enough for pair-production via photon-photon interactions to dominate the process. The gap is formed in the outer magnetosphere between the Omega · B = 0 surface (which defines the charge-separated regions) and the light cylinder, along the last closed field line (see Figure 2).

Three important regions contribute to the emission mechanism in a bootstrap manner. In region I, electrons and positrons are accelerated by the large potential difference across the gap, radiating curvature gamma-rays and/or boosting soft photons via inverse Compton scattering. These primary gamma-rays move away from the closed-field-line region and collide with ambient photons to produce secondary e± pairs in region II, just above region I. These energetic particles produce synchrotron radiation in the ambient magnetic field (and/or boost photons by inverse Compton scattering), covering energies from optical to gamma-rays. These photons limit the growth of region I above the last closed field line. The secondary photons move beyond region II to form tertiary pairs in region III. These pairs have insufficient energy for formation of x-ray or gamma-rays, but provide a sea of infrared and optical photons which illuminate the entire open magnetosphere. These photons refuel the gap so that the mechanism in region I can continue.

For young pulsars such as the Crab, a relativistic wind produced by the pulsar can be confined by the circumstellar material representing the ejected envelope of the progenitor. The result of this confinement is a synchrotron nebula which is x-ray luminous due to the interaction of the relativistic electrons with the ambient magnetic field (Pacini and Salvati 1973, Helfand and Becker 1987). For older pulsars, any such circumstellar envelope has long since dissipated; however, confinement of the electron wind can still result from the ram pressure associated with the pulsar proper velocity into the interstellar medium (Cheng 1983). The pulsar wind expands relativistically near the pulsar, but encounters a reverse shock at R_s ~< 0.1 R_N where R_N is the radius of the confining volume. The synchrotron emission region lies beyond the reverse shock, and extends to ~R_N; between the reverse shock and the pulsar, the emission is underluminous. The size of the confinement volume relates wind parameters to the pulsar motion and the density of the ISM. This model has been successfully applied to pulsar-core region of the SNR CTB80, where the young pulsar PSR~1951+32 seems to be generating a wind-driven synchrotron nebula (Kulkarni \etal 1988, Hester and Kulkarni 1988).