Comments on the Paper " Bare Quark Matter Surfaces of Strange Stars and E
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+ e − Emission " We would like to point out here that although the idea expressed in the above mentioned paper [1] that the bare surface of a hot strange star may be a strong source of e + e − pairs of luminosity L e ± ∼ 3 × 10 51 ergs s −1 for a duration of ∼ 10 s appears to be novel and exciting, it is, unfortunately unlikely to work because of several reasons. It is true that, it has already been hypothesesized by previous authors [2] that the bare surface of a strange star may be endowded with a superstrong electrostatic field of magnitude E ∼ 5 × 10 17 V cm −1 ∼ 1.5 × 10 13 statvolt cm −1. Although such estimates, in general, could be fairly uncertain, let us momentarily assume that there is indeed such a field on the surface of the strange star over a height of ∆R ∼ 10 −10 cm. As correctly envisaged in ref. 1, such a strong value of E >> E cr = 1.3 × 10 16 V cm −1 is likely to convert the virtual pairs of the QED vacuum into real ones, i.e, create real e + e − pairs. For the sake of illustration, let us consider the region of the electric field as a parallel plate capacitor where the electrons comprise the negatively charged plate sitting on top of the positively charged stellar surface. If the number of electrons on the top plate is N e , the vacuum discharge will be quenched after the generation of N e real pairs-the N e positrons thus created will move upward and tend to neutralize the preexisting negative charge whereas the freshly produced N e electrons will move downward to neutralize the stellar surface and eventually the field would cease to exist. The maximum value of the total energy liberated by the discharge of the capacitor, in the form of pairs and photons, would be the stored electrostatic energy of the capacitor : W s = E 2 8π (4πR 2)∆R ∼ 10 28 ergs (1) where we have taken R ∼ 10 6 cm. In fact, in realistic cases, the system would adjust itself in such a manner that, atleast in a steady state situation, the value of E would be well below E cr even if is assumed that momentarily …
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