Y RMlx EOS A

where M^a^X and Rmil* are, respectively, the mass and radius of the most massive stable non-rotating star. Equation (9.28) gives the necessary condition for a rotating neutron star with a given EOS to be consistent with the shortest observed pulsar period:

In order to rotate stably with the period ^Obs1, a star must be sufficiently massive and compact.

Figure 9.8. EOS constraints from observation of rapidly rotating pulsars. The dashed line, labeled by SS, corresponds to bare strange stars, studied in § 8.11 (with the EOS of strange quark matter described in § 8.11). Precise condition discussed in the text implies that at a given spin period (1.4 ms, 1 ms, 0.5 ms) a maximum-mass non-rotating star has to lie above a dot-and-dashed line. For M < Mmax this condition becomes approximate.

Figure 9.8. EOS constraints from observation of rapidly rotating pulsars. The dashed line, labeled by SS, corresponds to bare strange stars, studied in § 8.11 (with the EOS of strange quark matter described in § 8.11). Precise condition discussed in the text implies that at a given spin period (1.4 ms, 1 ms, 0.5 ms) a maximum-mass non-rotating star has to lie above a dot-and-dashed line. For M < Mmax this condition becomes approximate.

The theoretical predictions can be confronted with observations of millisecond pulsars (which, by definition, are the pulsars with spin periods P < 30 ms - see Lorimer 2001). By 2006 approximately 150 such pulsars have been discovered. A list of nine fastest rotators, with P < 2 ms, is given in Table 9.8. All of them but IGR J00291+5934 and A1744-361 are observed as radio pulsars, while IGR J00291+5934 and A1744-361 are accreting millisecond X-ray pulsars in binary systems (Galloway et al., 2005; Bhattacharyya et al., 2006). The first millisecond pulsar discovered, PSR B1937+214 (Backer et al., 1982), with P = 1.5578 ms, remained the most rapidly rotating neutron star till 2005. (Until its discovery, the fastest rotation, P = 33.1 ms, was demonstrated by the Crab pulsar.) In 2005 a new spinning champion was discovered, PSR J1748-2446ad, with P = 1.396 ms (Hessels et al., 2006). As seen from Fig. 9.8, the rotational stability curve, above which a pulsar with P = 1.4 ms is stable, lies too low to produce any noticeable constraint on the EOS of dense matter.

A very strong constraint would be given by a much faster submillisecond pulsar, with P = 0.5 ms. Such a pulsar was discovered on January 18, 1998, in a 7 hour optical observation of the supernova remnant 1987A in the Large Magellanic Cloud with the Cerro Tololo 4-meter telescope in Chile. The discovery ruled almost all theoretical EOSs, which were believed to be realistic - they became forbidden by that observation! As the reader can see, the pulsar rules out all EOSs used to calculate the M — R curves in Fig. 9.8. That nightmare for theorists lasted for one year. In that year, all theoretical concepts of dense matter physics were revisited in attempts to construct a realistic EOS which would be able to explain a 0.5 ms pulsar (see, e.g., § 9.8.4), but no convincing resolution of the apparent conflict between theory and observation was found. The story finished in February, 1990, with the discovery of exactly four times more rapid optical oscillations from the Crab pulsar with one of the telescopes of the Las Campanas observatory in Chile, near Cerro Tololo. Both telescopes had similar TV cameras for transmitting images of what the telescopes were seeing to observatory control rooms. In January and February, the hottest summer period in Chile, the TV transmitters could produce falsely modulated signals, the effect that had not been known before. The discovery of 0.5 ms pulsar turned out to be an artifact, and realistic theoretical EOSs were rehabilitated. Nevertheless, the story was a good push to the neutron star theory.

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