Diffusive Nuclear Burning Research Articles

The effect of diffusive nuclear burning in neutron star envelopes on cooling in accreting systems

ABSTRACT Valuable information about the neutron star (NS) interior can be obtained by comparing observations of thermal radiation from a cooling NS crust with theoretical models. Nuclear burning of lighter elements that diffuse to deeper layers of the envelope can alter the relation between surface and interior temperatures and can change the chemical composition over time. We calculate new temperature relations and consider two effects of diffusive nuclear burning (DNB) for H–C envelopes. First, we consider the effect of a changing envelope composition and find that hydrogen is consumed on short time-scales and our temperature evolution simulations correspond to those of a hydrogen-poor envelope within ∼100 d. The transition from a hydrogen-rich to a hydrogen-poor envelope is potentially observable in accreting NS systems as an additional initial decline in surface temperature at early times after the outburst. Second, we find that DNB can produce a non-negligible heat flux, such that the total luminosity can be dominated by DNB in the envelope rather than heat from the deep interior. However, without continual accretion, heating by DNB in H–C envelopes is only relevant for <1–80 d after the end of an accretion outburst, as the amount of light elements is rapidly depleted. Comparison to crust cooling data shows that DNB does not remove the need for an additional shallow heating source. We conclude that solving the time-dependent equations of the burning region in the envelope self-consistently in thermal evolution models instead of using static temperature relations would be valuable in future cooling studies.

Diffusive nuclear burning in cooling simulations and application to new temperature data of the Cassiopeia A neutron star

A critical relation in the study of neutron star cooling is the one between surface temperature and interior temperature. This relation is determined by the composition of the neutron star envelope and can be affected by the process of diffusive nuclear burning (DNB), which occurs when elements diffuse to depths where the density and temperature are sufficiently high to ignite nuclear burning. We calculate models of H-He and He-C envelopes that include DNB and obtain analytic temperature relations that can be used in neutron star cooling simulations. We find that DNB can lead to a rapidly changing envelope composition and prevents the build-up of thermally stable hydrogen columns y$_H$ > 10$^{7}$ g cm$^{-2}$, while DNB can make helium envelopes more transparent to heat flux for surface temperatures $T_s$ > 2 $\times 10^6$ K. We perform neutron star cooling simulations in which we evolve temperature and envelope composition, with the latter due to DNB and accretion from the interstellar medium. We find that a time-dependent envelope composition can be relevant for understanding the long-term cooling behaviour of isolated neutron stars. We also report on the latest Chandra observations of the young neutron star in the Cassiopeia A supernova remnant; the resulting 13 temperature measurements over more than 18 years yield a ten-year cooling rate of $\approx$ 2%. Finally, we fit the observed cooling trend of the Cassiopeia A neutron star with a model that includes DNB in the envelope.

DIFFUSIVE NUCLEAR BURNING OF HELIUM ON NEUTRON STARS

Diffusive nuclear burning of H by an underlying material capable of capturing protons can readily consume H from the surface of neutron stars (NSs) during their early cooling history. In the absence of subsequent accretion, it will be depleted from the photosphere. We now extend diffusive nuclear burning to He, motivated by the recent observation by Ho \& Heinke of a carbon atmosphere on the NS in the Cassiopeia A supernova remnant. We calculate the equilibrium structure of He on an underlying $\alpha$ capturing material, accounting for thermal, mass defect, and Coulomb corrections on the stratification of material with the same zeroth order $\mu_e = A/Z$. We show that Coulomb corrections dominate over thermal and mass defect corrections in the highly degenerate part of the envelope. We also show that the bulk of the He sits deep in the envelope rather than near the surface. Thus, even if the photospheric He abundance is low, the total He column could be substantially larger than the photospheric column, which may have implications for rapid surface evolution ($\approx 1$ yr timescales) of neutron stars. When nuclear reactions are taken into account, we find that for base temperatures $\gtrsim 1.6 \times 10^8$ K, He is readily captured onto C. As these high temperatures are present during the early stages of NS evolution, we expect that the primordial He is completely depleted from the NS surface like the case for primordial H. We also find that magnetic fields $\lesssim 10^{12}$ G do not affect our conclusions. Armed with the results of this work and our prior efforts, we expect that primordial H and He are depleted, and so any observed H or He on the surfaces of these NS must be due to subsequent accretion (with or without spallation). If this subsequent accretion can be prevented, the underlying mid-Z material would be exposed.

Hydrogen Burning on Magnetar Surfaces

We compute the rate of diffusive nuclear burning for hydrogen on the surface of a "magnetar" (soft gamma-ray repeater [SGR] or anomalous X-ray pulsar [AXP]). We find that hydrogen at the photosphere will be burned on an extremely rapid timescale of hours to years, depending on the composition of the underlying material. Improving on our previous studies, we explore the effect of a maximally thick "inert" helium layer, previously thought to slow down the burning rate. Since hydrogen diffuses faster in helium than through heavier elements, we find this helium buffer actually increases the burning rate for magnetars. We compute simple analytic scalings of the burning rate with temperature and magnetic field for a range of core temperatures. We conclude that magnetar photospheres are very unlikely to contain hydrogen. This motivates theoretical work on heavy element atmospheres that are needed to measure the effective temperature from the observed thermal emission and constrains models of AXPs that rely on magnetar cooling through thick light element envelopes.

Evolution of Young Neutron Star Envelopes

We extend our initial study of diffusive nuclear burning (DNB) for neutron stars (NSs) with hydrogen (H) atmospheres and an underlying layer of proton-capturing nuclei. Our initial study showed that DNB can alter the photospheric abundance of hydrogen on surprisingly short timescales (102-104 yr). Significant composition evolution impacts the radiated thermal spectrum from the NS as well as its overall cooling rate. In this paper, we consider the case when the rate-limiting step for the H consumption is diffusion to the burning layer rather than the local nuclear timescale. This is relevant for NSs with surface temperatures in excess of 106 K, such as young (<105 yr) radio pulsars and accreting NSs in quiescence. When downward diffusion is the limiting rate in DNB, the rate of H consumption is suppressed by 1-2 orders of magnitude compared to a DNB estimate that assumes diffusive equilibrium. In order to apply our ongoing study to young neutron stars, we also include the important effects of strong magnetic fields (B ~ 1012 G). In this initial study of magnetic modifications to DNB, we find that the H-burning time is lengthened by 2-3 orders of magnitude for a 1012 G field. However, even for NSs with dipole field strengths of 1012 G, we find that all of the H can be burned before the pulsar reaches an age of ~105 yr, thus potentially revealing the underlying proton-capturing elements. Finally, we conclude by providing an overview of what can be learned about fallback and pulsar winds from measuring the surface composition of a young NS.

Diffusive Nuclear Burning in Neutron Star Envelopes

We calculate the rate of hydrogen burning for neutron stars (NSs) with hydrogen atmospheres and an underlying reservoir of nuclei capable of proton capture. This burning occurs in the exponentially suppressed diffusive tail of H that extends to the hotter depths of the envelope where protons are rapidly captured. This process, which we call diffusive nuclear burning (DNB), can change the H abundance at the NS photosphere on timescales as short as $10^{2-4}$ years. In the absence of diffusion, the hydrogen at the photosphere (where $T\approx 10^6 {\rm K}$ and $\rho\sim 0.1 {\rm g cm^{-2}}$) would last for far longer than a Hubble time. Our work impacts the understanding of the evolution of surface abundances of isolated NSs, which is important to their thermal spectrum and their effective temperature-core temperature relation. In this paper, we calculate the rate of H burning when the overall consumption rate is controlled by the nuclear timescales, rather than diffusion timescales. The immediate application is for H burning on millisecond radio pulsars and in quiescence for the accreting NS Cen X-4. We will apply this work to young radio pulsars and magnetars once we have incorporated the effects of strong $B>10^{12} {\rm G}$ magnetic fields.