Observationally inferred superburst ignition depths are shallower than models predict. We address this discrepancy by reexamining the superburst trigger mechanism. We first explore the hypothesis of Kuulkers et al. that exothermic electron captures trigger superbursts. We find that all electron capture reactions are thermally stable in accreting neutron star oceans and thus are not a viable trigger mechanism. Fusion reactions other than 12C + 12C are infeasible as well since the possible reactants either deplete at much shallower depths or have prohibitively large Coulomb barriers. Thus we confirm the proposal of Cumming & Bildsten and Strohmayer & Brown that 12C + 12C triggers superbursts. We then examine the 12C + 12C fusion rate. The reaction cross-section is experimentally unknown at astrophysically relevant energies, but resonances exist in the 12C + 12C system throughout the entire measured energy range. Thus it is likely, and in fact has been predicted, that a resonance exists near the Gamow peak energy ~ 1.5 MeV. For such a hypothetical 1.5 MeV resonance, we derive both a fiducial value and upper limit to the resonance strength and find that such a resonance could decrease the theoretically predicted superburst ignition depth by up to a factor of 4; in this case, observationally inferred superburst ignition depths would accord with model predictions for a range of plausible neutron star parameters. Said differently, such a resonance would decrease the temperature required for unstable 12C ignition at a column depth 10^12 g/cm^2 from 6 x 10^8 K to 5 x 10^8 K. Determining the existence of a strong resonance in the Gamow window requires measurements of the 12C + 12C cross-section down to a center-of-mass energy near 1.5 MeV, which is within reach of the proposed DUSEL facility.
Deep Dive into Possible Resonances in the 12C + 12C Fusion Rate and Superburst Ignition.
Observationally inferred superburst ignition depths are shallower than models predict. We address this discrepancy by reexamining the superburst trigger mechanism. We first explore the hypothesis of Kuulkers et al. that exothermic electron captures trigger superbursts. We find that all electron capture reactions are thermally stable in accreting neutron star oceans and thus are not a viable trigger mechanism. Fusion reactions other than 12C + 12C are infeasible as well since the possible reactants either deplete at much shallower depths or have prohibitively large Coulomb barriers. Thus we confirm the proposal of Cumming & Bildsten and Strohmayer & Brown that 12C + 12C triggers superbursts. We then examine the 12C + 12C fusion rate. The reaction cross-section is experimentally unknown at astrophysically relevant energies, but resonances exist in the 12C + 12C system throughout the entire measured energy range. Thus it is likely, and in fact has been predicted, that a resonance exists n
Superbursts are long, energetic, and rare thermonuclear flashes on accreting neutron stars in low-mass X-ray binaries. Their durations (∼ hours), fluences (∼ 10 42 ergs), and recurrence times (∼ years) distinguish superbursts from their typical hydrogen-and helium-triggered counterparts (for reviews, see Kuulkers 2004;Cumming 2005;Strohmayer & Bildsten 2006). As of this writing, astronomers have detected 15 superbursts from 10 sources (Kuulkers 2004;in't Zand et al. 2004;Remillard et al. 2005;Kuulkers 2005;Keek et al. 2008, and references therein).
The proposal (Cumming & Bildsten 2001;Strohmayer & Brown 2002) that thermally unstable 12 C fusion (Woosley & Taam 1976;Taam & Picklum 1978;Brown & Bildsten 1998) triggers superbursts offers a reasonable explanation of their origin. Cooling model fits to superburst light curves (Cumming & Macbeth 2004;Cumming et al. 2006) as well as observed fluences and recurrence times (e.g. Keek et al. 2006) suggest ignition column depths Σ ign ≈ 10 12 g cm -2 , where Σ ≡ ρ dz is the radially integrated density. Previous superburst ignition models (Cumming & Bildsten 2001;Strohmayer & Brown 2002;Cumming 2003;Brown 2004;Cooper & Narayan 2005;Cumming et al. 2006;Gupta et al. 2007) demonstrated Electronic address: rcooper@kitp.ucsb.edu; steinera@pa.msu.edu; ebrown@pa.msu.edu that 12 C ignites at Σ ≈ 10 12 g cm -2 only if 12 C is abundant and the ocean temperature T ≈ 6 × 10 8 K at that column depth; within existing models of nuclear heating in the neutron star crust, such a large temperature requires an inefficient neutrino emission mechanism in the neutron star core and a low thermal conductivity in the neutron star crust, so that the crust is much hotter than the core.
Recent observations, simulations, and experiments have exposed three fundamental problems with this scenario. First and foremost is the inference that the ocean is in fact too cold for 12 C ignition at the inferred column depth Σ ign ≈ 10 12 g cm -2 . This comes from fits (Shternin et al. 2007;Brown & Cumming 2009) to the quiescent cooling of the quasi-persistent transient KS 1731-260 (Wijnands et al. 2002;Rutledge et al. 2002;Cackett et al. 2006), a system that also exhibited a superburst (Kuulkers et al. 2002b). The timescale for the quiescent luminosity to decrease suggests that the crust’s thermal conductivity is high; as a result, the inner crust temperature remains close to that of the core even during the accretion outburst. Cackett et al. (2008) reach the same conclusion for MXB 1659-29 (see also Brown & Cumming 2009). In fact, molecular dynamics simulation results (Horowitz et al. 2007(Horowitz et al. , 2009;;Horowitz & Berry 2009) suggest that the neutron star crust is arranged in a regular lattice and therefore has a high thermal conductivity. Neither shear-induced viscous heating (Piro & Bildsten 2007;Keek et al. 2009) nor deep crustal heating due to electron captures, neutron emissions, and pycnonuclear reactions (e.g., Haensel & Zdunik 2008;Horowitz et al. 2008;Gupta et al. 2008) can account for the heat necessary to raise the ocean temperature to the required level (although see Page & Cumming 2005;Blaschke et al. 2008, who consider heating in strange stars and hybrid stars, respectively).
Second, evidence of heavy-ion fusion hindrance at extreme sub-Coulomb-barrier energies (Jiang et al. 2002(Jiang et al. , 2007(Jiang et al. , 2008) ) implies that the cross-section and thereby the 12 C + 12 C reaction rate may be orders of magnitude smaller than that assumed in the aforementioned superburst ignition models. When included in superburst ignition models, heavyion fusion hindrance increases Σ ign by at least a factor of 2 (Gasques et al. 2007).
Third, the means by which nuclear burning on the stellar surface produces sufficient quantities of 12 C to trigger superbursts is poorly understood. Superburst models require large 12 C mass fractions for ignition (Cumming & Bildsten 2001;Cumming 2003;Cooper & Narayan 2005;Cooper et al. 2006;Cumming et al. 2006). All systems that exhibit superbursts show helium-triggered type I X-ray bursts as well (e.g. Galloway et al. 2008), but theoretical models of such bursts yield 12 C mass fractions far smaller than those required for ignition (Joss 1978;Schatz et al. 2001Schatz et al. , 2003b;;Koike et al. 2004;Woosley et al. 2004a;Fisker et al. 2005Fisker et al. , 2008;;Peng et al. 2007;Parikh et al. 2008). Most systems that exhibit superbursts apparently undergo long periods of stable nuclear burning between successive heliumtriggered bursts (Kuulkers et al. 2002a;in ’t Zand et al. 2003;Keek et al. 2008); stable burning generates much more 12 C than unstable burning, but the calculated yield is insufficient to trigger superbursts in all systems, particularly those accreting at a high rate (Taam & Picklum 1978;Schatz et al. 1999Schatz et al. , 2003b;;Cooper et al. 2006;Fisker et al. 2006).
Detection of a superburst from the classical transient 4U 1608-522 (Remilla
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