Pulsar glitches: The crust may be enough

Background: Pulsar glitches—the sudden spin-up in the rotational frequency of a neutron star—suggest the existence of an angular-momentum reservoir confined to the inner crust of the neutron star. Large and regular glitches observed in the Vela pulsar have originally constrained the fraction of the stellar moment of inertia that must reside in the solid crust to about 1.4%. However, crustal entrainment—which until very recently has been ignored—suggests that in order to account for the Vela glitches, the fraction of the moment of inertia residing in the crust must increase significantly; to about 7–9 %. This indicates that the required angular momentum reservoir may exceed that which is available in the crust.

Purpose: We explore the possibility that uncertainties in the equation of state provide enough flexibility for the construction of models that predict a large crustal thickness and consequently a large crustal moment of inertia.

Methods: Moments of inertia—both total and crustal—are computed in the slow-rotation approximation using a relativistic mean-field formalism to generate the equation of state of neutron-star matter.

Results: We compute the fractional moment of inertia of neutron stars of various masses using a representative set of relativistic mean-field models. Given that analytic results suggest that the crustal moment of inertia is sensitive to the transition pressure at the crust-core interface, we tune the parameters of the model to maximize the transition pressure, while still providing an excellent description of nuclear observables. In this manner we are able to obtain fractional moments of inertia as large as 7% for neutron stars with masses below 1.6 solar masses.

Conclusions: We find that uncertainties in the equation of state of neutron-rich matter are large enough to accommodate theoretical models that predict large crustal moments of inertia. In particular, we find that if the neutron-skin thickness of ${}^{208}\mathrm{Pb}$ falls within the (0.20–0.26) fm range, large enough transition pressures can be generated to explain the large Vela glitches—without invoking an additional angular-momentum reservoir beyond that confined to the solid crust. Our results suggest that the crust may be enough.

Figure 1

Fraction of the crustal moment of inertia as a function of the neutron-skin thickness of ${}^{208}\mathrm{Pb}$ for a variety of neutron-star masses (in units of the solar mass) as predicted by two “families” of mean-field models. (a) Predictions made with the relatively soft FSU [63] parametrization and (b) with the relatively stiff NL3 interaction [61, 62].

Figure 2

Equation of state in the form of pressure-vs-baryon density as predicted by the four models considered in the text. The insert displays (on a linear scale) the EOS on a more limited range: from the crust-core transition density up to nuclear-matter saturation density. The symbols denote the density and pressure at the crust-core interface.

Figure 3

Crustal contributions to the total mass (a) and radius (b) as a function of neutron-star mass as predicted by the four models considered in the text.

Figure 4

Fraction of the moment of inertia residing in the crust as a function of stellar mass for the four models considered in the text. The horizontal line represents observational constraints from the Vela glitches by assuming no ($\langle m_n^{*}\rangle /m_n=1$) entrainment. In contrast, the uncertainty band accounts for significant crustal entrainment of between 7% [12] and 9.4% [7, 15].

Figure 5

Mass-vs-radius relationship predicted by the four models considered in the text. Also shown are observational constraints on stellar masses [45, 46] and radii [65, 70, 72, 73], as explained in the text.