Two-photon annihilation in the pair formation cascades in pulsar polar caps

The importance of the photon-photon pair production process ($\gamma+ \gamma^{\prime}\to e^{+}+e^{-}$) to form pair production cascades in pulsar polar caps is investigated within the framework of the Ruderman-Sutherland vacuum gap model. It is found that this process is unimportant if the polar caps are not hot enough, but will play a non-negligible role in the pair formation cascades when the polar cap temperatures are in excess of the critical temperatures, $T_{cri}$, which are around $4\times 10^6K$ when $P=0.1$s and will slowly increase with increasing periods. Compared with the $\gamma-B$ process, it is found that the two-photon annihilation process may ignite a central spark near the magnetic pole, where $\gamma-B$ sparks can not be formed due to the local weak curvatures. This central spark is large if the gap is dominated by the ``resonant ICS mode''. The possible connection of these central sparks with the observed pulsar ``core'' emission components is discussed.Comment: 7 pages, 3 Postscript figures, LaTex, accepted for publication in Astronomy and Astrophysic

Is Gamma-ray Absorption by Induced Electric Fields Important in the Pulsar Magnetospheres?

Although the unified formula for gamma-ray absorption process involving both the magnetic field and a perpendicular electric field derived by Daugherty & Lerche (1975) is correct, we argued in this paper that their conclusion that the induced electric fields are important in the pair formation process in the pulsar magnetospheres is wrong and misleading. The key point is that usually the direction of a gamma photon at the emission point observed in the laboratory frame should be (v/c, 0, [1-(v/c)^2]^{1/2}) rather than (0, 0, 1), where v is the co-rotating velocity. This emission direction is just the one which results in zero attenuation coefficient of the gamma photon. Calculation shows that after the photon has moved a distance, its direction lead to the result that the induced electric field is also of minor importance. Thus only gamma-B process is the important mechanism for the pair production in the pulsar magnetospheres. The implications of the modification by ejecting the induced electric field are also discussed.Comment: 4 pages, 2 Postscript figures, LaTeX, some miscomments on the references of Harding et al are modified, Accepted for publication in Astronomy and Astrophysics Letter

What if pulsars are born as strange stars?

The possibility and the implications of the idea, that pulsars are born as strange stars, are explored. Strange stars are very likely to have atmospheres with typical mass of $\sim 5\times 10^{-15}M_\odot$ but bare polar caps almost throughout their lifetimes, if they are produced during supernova explosions. A direct consequence of the bare polar cap is that the binding energies of both positively and negatively charged particles at the bare quark surface are nearly infinity, so that the vacuum polar gap sparking scenario as proposed by Ruderman & Sutherland should operate above the cap, regardless of the sense of the magnetic pole with respect to the rotational pole. Heat can not accumulate on the polar cap region due to the large thermal conductivity on the bare quark surface. We test this ``bare polar cap strange star'' (BPCSS) idea with the present broad band emission data of pulsars, and propose several possible criteria to distinguish BPCSSs from neutron stars.Comment: 31 pages in Latex. Accepted by AstroParticle Physic

Deformation and KK-theoretic Index Formulae on Boundary Groupoids

Boundary groupoids were introduced by the second author, which can be used to model many analysis problems on singular spaces. In order to investigate index theory on boundary groupoids, we introduce the notion of {\em a deformation from the pair groupoid}.Under the assumption that a deformation from the pair groupoid $M \times M$ exists for Lie groupoid $\mathcal{G}\rightrightarrows M$, we construct explicitly a deformation index map relating the analytic index on $\mathcal{G}$ and the index on the pair groupoid. We apply this map to boundary groupoids of the form $\mathcal{G} = M_0 \times M_0 \sqcup G \times M_1 \times M_1 \rightrightarrows M=M_0\sqcup M_1$, where $G$ is an exponential Lie group, to obtain index formulae for (fully) elliptic (pseudo)-differential operators on $\mathcal{G}$, with the aid of the index formula by M. J. Pflaum, H. Posthuma, and X. Tang. These results recover and generalize our previous results for renormalizable boundary groupoids via the method of renormalized trace