All Figures

$\begin{figure} \par\includegraphics[width=8cm,clip]{5241fig1.ps} \end{figure}$ Figure 1: Constraints on quark core parameters obtained from superbursters (solid) and the soft X-ray transient Aql X-1 (dashed) assuming slow neutrino cooling for both. $Q_{\rm SQM}$ is given as a function of $Q_\nu$ for different choices of K. Thin lines show non-isothermal constraints from Eq. (6) with $K=10^{19},~ 10^{20},~ 10^{21},~ 10^{22}\mbox{ cgs}$ from the bottom up. Non-isothermal constraints for Aql X-1 are nearly indistinguishable from those for superbursters. Thick lines show isothermal constraints from Eq. (7). We take $\dot{m}=0.3 \dot{m}_{\rm Edd}$ for the superbursters.
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In the text

$\begin{figure} \par\includegraphics[width=16.8cm,clip]{5241fig2.ps} %\end{figure}$ Figure 2: Left: comparing cooling by a non-isothermal (dashed and dot-dashed; cf. Eq. (12)) and isothermal (dashed-doubledot and solid; cf. Eq. (14)) core to the observations in Table 1. For Cen X-4 the quoted temperature intervals overlap. Right: the "mixed'' case with non-isothermal superbursts and isothermal soft X-ray transients (dashed and solid; cf. Eq. (16)) and photon cooling (dotted) assuming a pure blackbody with $Q_{\rm SQM}$ as labelled for each curve.
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In the text

$\begin{figure} \par\includegraphics[width=17.6cm,clip]{5241fig3.ps} %\end{figure}$ Figure 3: Left: comparing combined photon and neutrino cooling of an isothermal core (solid; cf. Eq. (22)) to the observations in Table 1 with $Q_{\rm SQM}$ as labelled for each curve. For reference we also show curves with neutrino cooling only (dashed; cf. Eq. (14)) and photon cooling only (dotted). The curves assuming $Q_{\rm SQM}=100$ MeV and neutrino cooling only are nearly identical. For Cen X-4 the quoted temperature intervals overlap. Right: corresponding curves for a non-isothermal core.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{5241fig4.ps} \end{figure}$ Figure 4: Plot of Eq. (24) assuming $e\phi _{\rm e}(R_S)=20$ MeV and ¹⁰⁶Ge at the crust boundary. Note that for this barrier height the gap width goes to zero and $\tau$ to 1 somewhat below the neutron drip density, which can then not be reached.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{5241fig5.ps} \end{figure}$ Figure 5: A crude model of Cen X-4. Crust mass in a system accreting with 10 day long accretion outbursts separated by quiescent intervals of 30 years and an average accretion rate of $1.9\times 10^{-11}~{M}_\odot~{\rm yr}^{-1}$ . The inset shows a few equilibrium cycles. The peaks seen here have a flat top which is not resolved in time on the scale shown.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{5241fig6.ps} \end{figure}$ Figure 6: A crude model of Aql X-1. Crust mass in a system accreting with 10 day long accretion outbursts separated by quiescent intervals of 220 days and an average accretion rate of $10^{-10}~{M}_\odot~{\rm yr}^{-1}$ . The inset shows a few equilibrium cycles.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{5241fig4.ps} \end{figure}$	Figure 4: Plot of Eq. (24) assuming $e\phi _{\rm e}(R_S)=20$ MeV and ¹⁰⁶Ge at the crust boundary. Note that for this barrier height the gap width goes to zero and $\tau$ to 1 somewhat below the neutron drip density, which can then not be reached.
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{5241fig5.ps} \end{figure}$	Figure 5: A crude model of Cen X-4. Crust mass in a system accreting with 10 day long accretion outbursts separated by quiescent intervals of 30 years and an average accretion rate of $1.9\times 10^{-11}~{M}_\odot~{\rm yr}^{-1}$ . The inset shows a few equilibrium cycles. The peaks seen here have a flat top which is not resolved in time on the scale shown.
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{5241fig6.ps} \end{figure}$	Figure 6: A crude model of Aql X-1. Crust mass in a system accreting with 10 day long accretion outbursts separated by quiescent intervals of 220 days and an average accretion rate of $10^{-10}~{M}_\odot~{\rm yr}^{-1}$ . The inset shows a few equilibrium cycles.
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