[Paper Review] Rapid uniform rotation of protoneutron stars

J. O. Goussard, P. Haensel+1 more|ArXiv.org|Oct 31, 1996

Pulsars and Gravitational Waves Research1 references16 citations

TL;DR

This paper investigates rapid uniform rotation of protoneutron stars using general relativistic models with realistic dense matter equations of state. It finds that the maximum rotation frequency is well-approximated by the empirical formula used for cold neutron stars, and that the minimum rotation period of solitary pulsars is significantly longer than for cold neutron stars due to thermal and lepton-rich effects in protoneutron stars.

ABSTRACT

Rapid uniform rotation of newborn neutron stars (protoneutron stars) is studied for a range of internal temperatures and entropies per baryon predicted by the existing numerical simulations. Calculations are performed using general relativistic equations of hydrostatic equilibrium of rotating, axially symmetric stars. Stability of rotating configurations with respect to mass shedding and the axially symmetric perturbations is studied. Numerical calculations are performed for a realistic dense matter equation of state, under various assumptions concerning neutron star interior (large trapped lepton number, no trapped lepton number, isentropic, isothermal). For configurations with baryon mass well below the maximum one for the non-rotating models, the mass shedding limit depends quite sensitively on the position of the ``neutrinosphere''. The absolute upper limit on rotation frequency is, to a good approximation, obtained for the maximum baryon mass of rotating configurations. Empirical formula for the maximum rotation frequency of uniformly rotating protoneutron stars is shown to be quite precise; it actually coincides with that used for cold neutron stars. Evolutionary sequences at fixed baryon mass and angular momentum, which correspond to evolution of protoneutron stars into cold neutron stars are studied, and resulting constraints on the maximum rotation frequency of solitary pulsars are discussed.

Motivation & Objective

• To determine the maximum rotation frequency of uniformly rotating protoneutron stars under realistic dense matter equations of state.
• To assess how thermal energy, trapped lepton number, and neutrinosphere structure affect rotational stability and mass shedding limits.
• To evaluate the implications of protoneutron star evolution for the maximum spin period of isolated neutron stars (solitary pulsars).
• To test the validity of the empirical formula for maximum rotation frequency in hot, lepton-rich protoneutron stars.
• To examine the role of secular instabilities and thermal structure in limiting rotation rates during protoneutron star evolution.

Proposed method

• Solves general relativistic equations of hydrostatic equilibrium for uniformly rotating, axially symmetric stars.
• Uses a realistic equation of state for dense matter including nucleons and leptons, with varying assumptions on trapped lepton number and temperature profiles.
• Applies an approximate method to locate the deformed, spheroidal neutrinosphere, which affects mass shedding limits.
• Performs numerical calculations across a range of baryon masses, temperatures, and entropies consistent with existing simulations of protoneutron stars.
• Evaluates stability against mass shedding and axially symmetric perturbations to determine rotational limits.
• Traces evolutionary sequences at fixed baryon mass and angular momentum to model protoneutron star cooling into cold neutron stars.

Experimental results

Research questions

• RQ1 How does the maximum rotation frequency of uniformly rotating protoneutron stars depend on temperature, entropy, and trapped lepton content?
• RQ2 To what extent does the shape and location of the neutrinosphere influence the mass shedding limit in rapidly rotating protoneutron stars?
• RQ3 Does the empirical formula for maximum rotation frequency—previously validated for cold neutron stars—hold for hot, dense protoneutron stars?
• RQ4 What constraints does protoneutron star evolution place on the minimum spin period of isolated neutron stars?
• RQ5 How do secular instabilities and thermal structure affect the upper limits on rotation frequency in protoneutron stars?

Key findings

• The maximum rotation frequency of protoneutron stars is well-approximated by the empirical formula used for cold neutron stars, with high precision.
• The mass shedding limit depends sensitively on the neutrinosphere position at low baryon masses, but this dependence weakens as mass increases.
• The absolute upper limit on rotation frequency is achieved for the maximum baryon mass of rotating configurations.
• For protoneutron stars with baryon mass below the maximum for non-rotating models, the minimum rotation period is significantly longer than for cold neutron stars.
• The inclusion of secular instabilities would further reduce the maximum rotation frequency, strengthening the conclusion that solitary pulsars cannot spin as fast as cold neutron stars.
• The results are robust to approximations in thermal structure and neutrinosphere location, suggesting the main conclusions are insensitive to these simplifications.