It is widely believed that pulsar glitches require the presence of the solid crust and a superfluid component weakly bound to the crust. The analysis of macroglitches indicates (§ 9.7) that the fractional crustal moment of inertia exceeds 10"2. However, as we have seen in § 8.16, the maximum fractional crustal moment of inertia of strange stars with M > 0.5 Mq is lower than 10"4.2 Therefore, it was stated long ago, that strange stars with the crust cannot explain pulsar macroglitches; glitching pulsars are not strange stars (Alcock et al., 1986; Alpar, 1987). Of course, it was obvious from the very beginning, that the standard two-component model of pulsar glitches (§ 9.7), in which superfluid neutrons in the inner crust transfer an accumulated excess of angular momentum to the rest of the pulsar body, does not apply to strange stars. As noted by Alpar (1987), a large value of AQ/|Q| ~ 10"3 — 10"2 in glitches requires the existence of a strange star component distinct from the quark matter. The effective moment of inertia Id of this component should satisfy Id/I — AQ/1Q l However, the moment of inertia of the strange star crust is two orders of magnitude smaller. This statement of Alpar (1987) is based on observational estimates for macroglitches, AQ/Q ~ 10"6 — 10"5 < AQ/|Q|. According to Alpar, such estimates indicate that glitches are produced by the angular momentum transfer from the non-quark matter to the rest of the star coupled to the magnetosphere. In his model macroglitches are not associated with sudden changes of the moment of inertia.
The lower bound on Icrust/I might be weakened, if one uses the arguments based exclusively on conservation of the total angular momentum J during a glitch (Glendenning & Weber, 1992). A tacit assumption is that the angular momentum transferred during a glitch comes from a sudden decrease of the moment of inertia of the crust in a so called crust-quake, AIcrust = —/Icrust, where / is the fraction of the decreasing moment of inertia. Notice that this assumption is just the opposite to that made by Alpar (1987). Retaining only terms linear in AQ, we see that conservation of the total angular momentum implies AJ = AQI0 — Q/Icrust = 0, where I0 is the moment of inertia of the strange star component accelerated during the quake. This results in /Icrust/I0 ~ AQ/Q ~ 10"6 for macroglitches, while from the strange star models Icrust ~ 10"5 I. All matter constituents (quarks, electrons, as well as nuclei in the crust) are charged and rather strongly coupled by Coulomb forces, so that I0 ~ I. Therefore, one should require / ~ 0.01 — 0.1 for macroglitches. In view of the low shear modulus (§ 3.7) and the associated low critical elastic strain of the outer crust, such an amplitude of crust quakes seems unrealistically high.
2Strictly speaking, this is true for strange stars with M > 0.5 Mq and spin periods longer than 1 ms. We do not consider too low-mass strange stars rotating close to the Keplerian limit, where /crust // can be as high as KT3 (Glendenning & Weber, 1992; Zdunik etal., 2001).
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