The cooling rate of neutron stars after thermonuclear shell flashes

Abstract

Thermonuclear shell flashes on neutron stars are detected as bright X-ray bursts. Traditionally, their decay is modeled with an exponential function. However, this is not what theory predicts. The expected functional form for luminosities below the Eddington limit, at times when there is no significant nuclear burning, is a power law. We tested the exponential and power-law functional forms against the best data available: bursts measured with the high-throughput Proportional Counter Array (PCA) onboard the Rossi X-ray Timing Explorer. We selected a sample of 35 "clean" and ordinary (i.e., shorter than a few minutes) bursts from 14 different neutron stars that 1) show a wide dynamic range in luminosity; 2) are the least affected by disturbances by the accretion disk; and 3) lack prolonged nuclear burning through the rp-process. We find indeed that for every burst a power law is a better description than an exponential function. We also find that the decay index is steep, 1.8 on average, and different for every burst. This may be explained by contributions from degenerate electrons and photons to the specific heat capacity of the ignited layer and by deviations from the Stefan-Boltzmann law due to changes in the opacity with density and temperature. Detailed verification of this explanation yields inconclusive results. While the values for the decay index are consistent, the predicted dependency of the decay index with the burst time scale, as a proxy of ignition depth, is not supported by the data.

NuSTAROBSERVATION OF A TYPE I X-RAY BURST FROM GRS 1741.9-2853

“…and setting the time of the first point in the fit t 0 = 110 s (C 0 is the count rate at t 0 , and t s is the time of the burst onset), we find a decay index α = 2.25 ± 0.03. As noticed by in't Zand et al (2014), α is strongly correlated with t s , however we estimate that the error on t s cannot exceed ±0.2 s, which leads to a systematic error on α lower than ±0.002. Despite some variability, the interval from 75 s to 95 s seems to match with the extrapolation of the exponential decay.…”

The evolution of X-ray bursts in the ‘Bursting Pulsar’ GRO J1744–28

“…In particular, the 'dip' we see after Normal Bursts has previously been interpreted as being caused by the inner disk refilling after a sudden accretion event (e.g. Younes et al 2015). As these dips are also seen after some Minibursts, we could also interpret Minibursts as being caused by a similar cycle.…”

“…During the main part of Outburst 3, Swift, XMM-Newton and Suzaku made one pointed observation each, Chandra made four observations, and NuSTAR made three observations. The Chandra observation on March 3 2014 was made simultaneously with one of the NuSTAR observations (see Younes et al 2015). After the main part of the outburst, the source was not well-monitored, although it remained detectable by Swift/BAT, and it is unclear whether any rebrightening events occured.…”

“…(iii) A 'dip': a period during which the count rate falls below the persistent level, before exponentially decaying back up towards the pre-burst level (e.g. Younes et al 2015).…”

“…Where t is time, t 0 is the start time of the dip, a d is the amplitude of the dip, d is the time at the local dip minimum and λ is the dip recovery timescale. This function is based on the finding by Younes et al (2015) that dip count rates Burst in which count rates have been normalised by the persistent emission count rate during the observation from which each burst was observed. As the bursts are on average closer to the average pulse profile in this metric, this suggests that the intensity of a burst is roughly dependent on the persistent emission rate.…”