[Paper Review] Fall-back crust around a quark-nova compact remnant II: The degenerate torus case with applications to AXPs

Rachid Ouyed, D. A. Leahy+1 more|ArXiv.org|Nov 3, 2006

High-pressure geophysics and materials3 citations

TL;DR

This paper proposes that a degenerate, metal-rich torus formed from quark-nova ejecta can explain key observational features of Anomalous X-ray Pulsars (AXPs), particularly 1E2259+586 and 4U0142+615. The torus, sustained by magnetic pressure and angular momentum, undergoes slow accretion and X-ray bursting due to magnetic field penetration, reproducing quiescent luminosities, blackbody temperatures, burst lightcurve decay profiles, and spin-down glitches. The model estimates a torus mass of ~10⁻⁶ M☉ and suggests optical/infrared emission from 4U0142+615 may originate from this thin degenerate torus.

ABSTRACT

In the first paper of this series we explored the case where a quark-nova ejecta forms a degenerate shell, supported by the star's magnetic field. Herein, we consider the case where the ejecta has sufficient angular momentum to form a Keplerian torus, and we show that the density and temperature of the torus are such that it will remain degenerate throughout it's lifetime. We go on to discuss the evolution of such a torus and apply it to two AXPs, namely 1E2259$+$586 and 4U0142$+$615. As it turns out, using our model we can account for many of the observations of these objects including the quiescent phase luminosity, and blackbody temperatures during quiescence and bursting phases. Furthermore, for 1E2259$+$586 our model explains the steep and slow decay components seen in the burst lightcurve, as well as the rotation period glitches and enhanced spin-down rate. We also estimate the mass of the degenerate torus to be of the order of $10^{-6}M_{\odot}$, and speculate that the observed optical/infrared emission from 4U0142$+$615 might be a signature of the thin degenerate torus we describe here.

Motivation & Objective

• To investigate the formation and evolution of a degenerate torus from quark-nova ejecta when angular momentum prevents shell formation.
• To explain the quiescent and bursting X-ray behavior of AXPs, particularly 1E2259+586 and 4U0142+615, via accretion from a magnetically confined torus.
• To account for observed burst lightcurve decay components, spin-down rate enhancements, and glitches through torus fracturing and differential rotation.
• To estimate the mass and thermal evolution of the torus and assess its contribution to observed emission relative to vortex expulsion.

Proposed method

• Uses angular momentum conservation to model torus formation at the magnetic equilibrium radius, where the quark star's magnetic pressure balances ejecta gravity.
• Applies the propeller mechanism to deflect ejecta into a thin, equatorial torus when the magnetic radius exceeds the corotation radius.
• Models thermal evolution via energy balance: accretion luminosity heats the torus, while blackbody cooling dominates from the sides.
• Derives accretion rate from non-degenerate atmosphere evaporation using thermal velocity and density profiles.
• Solves the heat capacity equation with time-dependent temperature evolution, incorporating Fermi energy and specific heat of degenerate matter.
• Estimates equilibrium temperature and timescales for thermal evolution using dimensionless scaling with mass, radius, and temperature.

Experimental results

Research questions

• RQ1 Can a degenerate torus formed from quark-nova ejecta reproduce the quiescent X-ray luminosity and blackbody temperatures observed in AXPs?
• RQ2 How does magnetic field penetration into the inner edge of a differentially rotating torus lead to X-ray bursting behavior?
• RQ3 Can the model explain the slow, steep decay component in the burst lightcurve of 1E2259+586?
• RQ4 What causes the observed spin-down rate enhancements and glitches in AXPs like 1E2259+586 within this framework?
• RQ5 Is the optical/infrared emission from 4U0142+615 consistent with emission from a thin degenerate torus?

Key findings

• The degenerate torus reaches thermal equilibrium within ~1/A timescale, with equilibrium temperature ~0.52 keV, depending on accretion efficiency, magnetic field, and torus mass.
• The model reproduces the quiescent luminosity and blackbody temperatures of 1E2259+586 and 4U0142+615 through accretion from the torus atmosphere.
• The slow, steep decay in the burst lightcurve of 1E2259+586 is explained by ionization fraction changes in the high-metallicity torus under X-ray irradiation.
• Spin-down rate enhancements and glitches are attributed to differential rotation and fracturing of the torus due to shear forces.
• The torus mass is estimated at ~10⁻⁶ M☉, consistent with observational constraints and torus stability.
• The model suggests that in the oldest AXPs, emission from the torus may exceed that from magnetic vortex expulsion, potentially explaining the optical/infrared emission from 4U0142+615.