MSP Evolution
Constraints on Pulsar Evolution: The Joint Period-Spindown Distribution of Millisecond Pulsars
We calculate the joint period-spindown (P−Pdot) distributions of millisecond radio pulsars (MSRP) for the standard evolutionary model in order to test whether the observed MSRPs are the unequivocal descendants of millisecond X-ray pulsars (MSXP). The P−Pdot densities implied by the standard evolutionary model compared with observations suggest that there is a statistically significant overabundance of young/high magnetic field MSRPs. Taking biases due to observational selection effects into account, it is unlikely that MSRPs have evolved from a single coherent progenitor population that loses energy via magnetic dipole radiation after the onset of radio emission. By producing the P−Pdot probability map, we show with more than 95% confidence that the fastest spinning millisecond pulsars with high magnetic fields, e.g. PSR B1937+21, cannot be produced by the observed MSXPs within the framework of the standard model.
The P−Pdot distribution of millisecond pulsars for the standard model:
- The P-Pdot distribution of millisecond radio pulsars evolved from a progenitor population consistent with the observed millisecond X-ray pulsars. The probability map is a produced by seeds sampled from a discrete progenitor millisecond X-ray pulsar population.
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- In this case, the probability map is a produced by seeds sampled from a continuous millisecond X-ray pulsar progenitor population consistent with the observed millisecond X-ray pulsars.
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The color contours are the expected MSRP distribution for the observed MSXPs, with red representing the highest density. Any MSRP outside of the color contours cannot be produced by the observed MSXPs with more than 95% confidence. The dashed red line is the 68% confidence limit of the expected P−Pdot distribution taking the observed MSXPs as the progenitor population. MSRPs within the shaded region maybe produced by MSXPs with spin distributions different than what is observed. The area shaded with lines assumes a maximum spin frequency Vmax=619Hz, which the fastest spinning observed MSXP (i.e. 4U1608−52). The shaded area extends to the dotted region if the maximum spin frequency for MSXPs is allowed to be Vmax=760Hz which is the theoretical upper limit predicted by Chakrabarty etal. (2003). The blue and red filled circles are the observed MSRPs in single and binary systems respectively. The area outside of the shaded region is not sensitive to the prior, i.e. the observed MSRPs outside of the shaded area cannot be produced consistently by the standard model for any MSXP spin distribution with more than 95% confidence. The spindown values for the observed MSRPs are corrected for secular acceleration (Shklovskii 1970; Camilo et al. 1994). The spin-up line (dotP~mdot*P_0^4/3) for mdot=Mdot_Edd and the characteristic age line for τ_c=10^10 yrs are shown with dashed and dash-dotted lines.
The "Relaxed Multidimensional Kolmogorov-Smirnov Filter":
The relaxed 2D K-S filter allows additional acceptance of populations with 0.05<P(2DK−S)<0.2 by oversampling the extreme outliers of the P-Pdot distribution in order to probe for possible contaminations and extreme fluctuations. The distribution also shows how optimally the P-Pdot parameter space is sampled with a peak sampling rate around the nominal acceptance value of P(2DK−S)~0.2. The dotted line is the relaxed 2DK-S filter for the synthetic populations that is used to construct the predictive distribution in fig2. The solid line is the conventional K-S filter that would only accept strictly consistent P-Pdot samples.
Millisecond pulsars in LMXBs:
