“Anti-glitches” in the Quark-Nova model for AXPs II

Abstract

We investigate the “antiglitch” AXP 1E 2259+586 experienced between MJD=56031 and 56045 in the context of the Quark-Nova model in which an AXP is a quark star surrounded by a degenerate Keplerian disk. In a companion paper we assumed the “anti-glitch” to be instantaneous, whereas in this paper we consider the quark star to undergo a period of enhanced spin-down over several days. We find that the Quark-Nova model can account for the spin-down and at the same time the enhanced 2–10 keV observed flux without introducing any new physics to the model.

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Fig. 1
Fig. 2

Notes

  1. 1.

    Alternate mechanisms involving accretion of matter onto a neutron star have been proposed by Katz et al. (1994) and Brook et al. (2013) with specific application to the current event by Katz (2013).

  2. 2.

    In our companion paper (Ouyed et al. 2013) we consider a retrograde ring. In this case the angular momentum transfer will spin down the QS during step 2 above instead of spinning it up. The rest of the steps will proceed as normal, including the removal of the atmosphere and enhanced spin down rate.

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Acknowledgements

This work is funded by the Natural Sciences and Engineering Research Council of Canada. N. Koning would like to acknowledge support from the Killam Trusts.

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Appendix: Mass loss due to wind

Appendix: Mass loss due to wind

The mass loss from the ring atmosphere is given by equation B.6 in Ouyed et al. (2007b):

$$ \dot{m}(t) \approx1.66 \times10^{18}\mbox{ gm}\,\mbox{s}^{-1} \frac{R_{\mathrm{in},25}^3 T_{\mathrm{ring}, \mathrm{keV}}^3}{\mu_{\mathrm {{atm}}}(t)^{3/2} M_{\mathrm{QS},1.5}} $$
(A1)

where R in,25 is the inner radius of the ring in units of 25 km, T ring,keV is the temperature of the ring in units of keV, and M QS,1.5 is the mass of the QS in units of 1.5 M. The mean molecular weight of the atmosphere, μ atm(t), evolves in time after a burst according to equation 27 in Ouyed et al. (2007b):

$$ \mu_{\mathrm{{atm}}}(t) = \biggl[\frac{1}{\mu_q} + \biggl(\frac{1}{\mu_b}- \frac{1}{\mu_q} \biggr)e^{-t/\tau} \biggr]^{-1} $$
(A2)

where μ q and μ b are the mean molecular weight of the atmosphere in quiescence and during the burst respectively. τ is given by equation 26 in Ouyed et al. (2007b):

$$ \tau= 2.52 \times10^{7} \mbox{ s} \frac{M_{\mathrm{QS},1.5}^4}{\eta _{0.1}^3 R_{\mathrm{in},25}^6} $$
(A3)

where η 0.1 is the wall accretion efficiency in unis of 0.1. If we assume a fraction of the mass-loss, β, is removed as the wind then (1−β) is available for accretion onto the QS giving an accretion luminosity of:

$$\begin{aligned}& L_{\mathrm{{acc}}}(t) = 1.5 \times10^{38} \mbox{ erg}\,\mbox{s}^{-1} \\& \hphantom{L_{\mathrm{{acc}}}(t) =} {}\times \eta_{0.1} (1-\beta) \biggl[\frac{R_{\mathrm{in},25}^3 T_{\mathrm {ring}, \mathrm{keV}}^3}{\mu_{\mathrm{{atm}}}(t)^{3/2} M_{\mathrm{QS}, 1.5}} \biggr] \end{aligned}$$
(A4)

Equation B.13 in Ouyed et al. (2007b) then gives the equilibrium temperature of the ring:

$$ T_{\mathrm{ring}, \mathrm{keV}}(t) = 0.8\mbox{ keV} \frac{(1-\beta)\eta_{0.1} R_{\mathrm{in},25}}{\mu_{\mathrm{{atm}}}(t)^{3/2} M_{\mathrm {QS},1.5}} $$
(A5)

Substituting Eq. (A5) into (A1) (and multiplying by β) we get the mass loss rate due to the wind:

$$ \dot{m}_{\mathrm{{wind}}}(t) \approx3.9 \times10^{17}\mbox{ gm}\,\mbox{s}^{-1} \beta(1-\beta)^3 \frac{R_{\mathrm{in},25}^6 \eta_{0.1}^3}{\mu _{\mathrm{{atm}}}(t)^6 M_{\mathrm{QS},1.5}^4} $$
(A6)

The total mass lost due to the wind from the time of the burst, t b , to time t is:

$$\begin{aligned}& \Delta m_{\mathrm{{wind}}}(t) \approx3.9 \times10^{17}\mbox{ gm}\,\beta (1-\beta)^3 \\& \hphantom{\Delta m_{\mathrm{{wind}}}(t) \approx} {}\times \frac{R_{\mathrm{in},25}^6 \eta_{0.1}^3}{\mu_{\mathrm {{atm}}}(t)^6 M_{\mathrm{QS},1.5}^4} \biggl[\int_{t_b}^{t} \mu_{\mathrm{{atm}}}(t)^{-6} dt \biggr] \end{aligned}$$
(A7)

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Koning, N., Leahy, D. & Ouyed, R. “Anti-glitches” in the Quark-Nova model for AXPs II. Astrophys Space Sci 350, 701–705 (2014). https://doi.org/10.1007/s10509-014-1787-0

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Keywords

  • Stars: neutron
  • Stars: individual (1E 2259+586)
  • X-Rays: bursts