Envelopes Of Neutron Stars Research Articles

How bright can old magnetars be? Assessing the impact of magnetized envelopes and field topology on neutron star cooling

ABSTRACT Neutron stars cool down during their lifetime through the combination of neutrino emission from the interior and photon cooling from the surface. Strongly magnetized neutron stars, called magnetars, are no exception, but the effect of their strong fields adds further complexities to the cooling theory. Besides other factors, modelling the outermost hundred meters (the envelope) plays a crucial role in predicting their surface temperatures. In this letter, we revisit the influence of envelopes on the cooling properties of neutron stars, with special focus on the critical effects of the magnetic field. We explore how our understanding of the relation between the internal and surface temperatures has evolved over the past two decades, and how different assumptions about the neutron star envelope and field topology lead to radically different conclusions on the surface temperature and its cooling with age. In particular, we find that relatively old magnetars with core-threading magnetic fields are actually much cooler than a rotation-powered pulsar of the same age. This is at variance with what is typically observed in crustal-confined models. Our results have important implications for the estimates of the X-ray luminosities of aged magnetars, and the subsequent population study of the different neutron star classes.

AT 2018lqh and the Nature of the Emerging Population of Day-scale Duration Optical Transients

Abstract We report on the discovery of AT 2018lqh (ZTF 18abfzgpl)—a rapidly evolving extragalactic transient in a star-forming host at 242 Mpc. The transient g-band light curve’s duration above a half-maximum light is about 2.1 days, where 0.4/1.7 days are spent on the rise/decay, respectively. The estimated bolometric light curve of this object peaked at about 7 × 1042erg s−1—roughly 7 times brighter than the neutron star (NS)–NS merger event AT 2017gfo. We show that this event can be explained by an explosion with a fast (v ∼ 0.08 c) low-mass (≈0.07 M ⊙) ejecta, composed mostly of radioactive elements. For example, ejecta dominated by 56Ni with a timescale of t 0 ≅ 1.6 days for the ejecta to become optically thin for γ-rays fits the data well. Such a scenario requires burning at densities that are typically found in the envelopes of neutron stars or the cores of white dwarfs. A combination of circumstellar material (CSM) interaction power at early times and shock cooling at late times is consistent with the photometric observations, but the observed spectrum of the event may pose some challenges for this scenario. We argue that the observations are not consistent with a shock breakout from a stellar envelope, while a model involving a low-mass ejecta ramming into low-mass CSM cannot explain both the early- and late-time observations.

Plasma screening of nuclear fusion reactions in liquid layers of compact degenerate stars: a first-principle study

ABSTRACT A reliable description of nuclear fusion reactions in inner layers of white dwarfs and envelopes of neutron stars is important for realistic modelling of a wide range of observable astrophysical phenomena from accreting neutron stars to Type Ia supernovae. We study the problem of screening of the Coulomb barrier impeding the reactions by a plasma surrounding the fusing nuclei. Numerical calculations of the screening factor are performed from the first principles with the aid of quantum-mechanical path integrals in the model of a one-component plasma of atomic nuclei for temperatures and densities typical for dense liquid layers of compact degenerate stars. We do not rely on various quasi-classic approximations widely used in the literature, such as factoring out the tunnelling process, tunnelling in an average spherically symmetric mean-force potential, usage of classic free energies and pair correlation functions, linear mixing rule, and so on. In general, a good agreement with earlier results from the thermonuclear limit to Γ ∼ 100 is found. For a very strongly coupled liquid 100 ≲ Γ ≤ 175, a deviation from currently used parametrizations of the reaction rates is discovered and approximated by a simple analytic expression. The developed method of nuclear reaction rate calculations with account of plasma screening can be extended to ion mixtures and crystallized phases of stellar matter.

Expanded Atmospheres and Winds in Type I X-Ray Bursts from Accreting Neutron Stars

Abstract We calculate steady-state models of radiation-driven super-Eddington winds and static expanded envelopes of neutron stars caused by high luminosities in type I X-ray bursts. We use flux-limited diffusion to model the transition from optically thick to optically thin, and include effects of general relativity, allowing us to study the photospheric radius close to the star as the hydrostatic atmosphere evolves into a wind. We find that the photospheric radius evolves monotonically from static envelopes (r ph ≲ 50–70 km) to winds (r ph ≈ 100–1000 km). Photospheric radii of less than 100 km, as observed in most photospheric radius expansion bursts, can be explained by static envelopes, but only in a narrow range of luminosity. In most bursts, we would expect the luminosity to increase further, leading to a wind with photospheric radius ≳100 km. In the contraction phase, the expanded envelope solutions show that the photosphere is still ≈1 km above the surface when the effective temperature is only 3% away from its maximum value. This is a possible systematic uncertainty when interpreting the measured Eddington fluxes from bursts at touchdown. We also discuss the applicability of steady-state models to describe the dynamics of bursts. In particular, we show that the sub- to super-Eddington transition during the burst rise is rapid enough that static models are not appropriate. Finally, we analyze the strength of spectral shifts in our models. Expected shifts at the photosphere are dominated by gravitational redshift, and are therefore predicted to be less than a few percent.

Plasma screening enhancement of thermonuclear reaction rates

Plasma screening can enhance the thermonuclear reaction rates significantly. The most pronounced effect takes place in the white dwarf cores and neutron star envelopes; there the enhancement factor can reach as tenths orders of magnitude. Here thermodynamically consistent description of this effect, which does not violate of the detailed balance principle, is discussed.

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.

A NICER Thermonuclear Burst from the Millisecond X-Ray Pulsar SAX J1808.4–3658

Abstract The Neutron Star Interior Composition Explorer (NICER) has extensively monitored the 2019 August outburst of the 401 Hz millisecond X-ray pulsar SAX J1808.4–3658. In this Letter, we report on the detection of a bright helium-fueled Type I X-ray burst. With a bolometric peak flux of (2.3 ± 0.1) × 10−7 erg s−1 cm−2, this was the brightest X-ray burst among all bursting sources observed with NICER to date. The burst shows a remarkable two-stage evolution in flux, emission lines at 1.0 and 6.7 keV, and burst oscillations at the known pulsar spin frequency, with ≈4% fractional sinusoidal amplitude. We interpret the burst flux evolution as the detection of the local Eddington limits associated with the hydrogen and helium layers of the neutron star envelope. The emission lines are likely associated with Fe, due to reprocessing of the burst emission in the accretion disk.

Nonequilibrium Layer in the Crust of Neutron Stars and Nonequilibrium β-Processes in Astrophysics

The formation of the chemical composition of neutron star envelopes, at densities 1010–1013 g cm–3, is considered. As hot matter is compressed in the process of collapse, which leads to the explosion of a core-collapse supernova, the stage of nuclear equilibrium with free neutrino escape, kinetic equilibrium in β-processes, and, as a result, the establishment of limited nuclear equilibrium with a fixed number of nuclei takes place. Cold matter is compressed at a fixed number of nuclei whose atomic weight initially does not change and subsequently decreases. A pycnonuclear reaction of the fusion of available nuclei and a decrease in their number begin at the end. The compression of cold matter is accompanied by an increase in the mass fraction of free neutrons. In this case, the chemical composition of the envelope differs significantly from the equilibrium one and contains a considerable store of nuclear energy. Nonequilibrium β-reactions proceed at densities exceeding the upper bound for the nonequilibrium layer density, which lead to heating, nuclear energy release, and the possible attainment of a state of complete thermodynamic equilibrium. The thermodynamics of nonequilibrium β-processes, which lead to the heating of matter as neutrinos escape freely, is considered.

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.

Gamma-Ray Emission During the Accretion of Matter from a Supernova Envelope onto a Compact Remnant

The aim of this study is to investigate the accretion of matter onto a compact gravitating remnant (neutron star) in the central region of the expanding shell of a Type II supernova. Computations of an explosion with the energetics of a Type II supernova have been performed to derive the structure of matter in the vicinity of the neutron star. The energy of the expanding shell and the parameters of the presupernova correspond to the known values for SN 1987A. This accretion leads to the formation of a layer of fairly dense and hot gas at the surface of the compact remnant, providing the conditions for nucleosynthesis reactions. Thus, one result of the study is to demonstrate the importance of the r and rbc processes, or explosive nucleosynthesis, in the compact envelope of a neutron star. A second result is the production of emission lines from unstable elements formed in the central part of the neutron-star envelope.

Heat blanketing envelopes vs cooling of neutron stars

We discuss the effect of the chemical composition of heat blanketing envelopes of neutron stars (NSs) on the interpretation of the observations of these stars. First we analyze the diffusive fluxes of ions in non-isothermal and non-ideal Coulomb plasmas. Then we outline models of diffusively-equilibrated heat blanketing envelopes composed of binary ionic mixtures and finally we study their effect on the cooling of isolated NSs.

The impact of heat blanketing envelopes on neutron stars cooling

The goal of this work is to investigate the effects of chemical composition of heat blanketing envelopes of neutron stars on their thermal states and thermal evolution. To this purpose, we employ newly constructed models of the envelopes composed of binary ion mixtures (H–He, He–C, C–Fe) varying the mass of lighter ions (H, He or C) in the envelope. The results are compared with those calculated using the standard “onion-like” envelope. For illustration, we apply these results to estimate the internal temperature of the Vela pulsar and to study cooling of neutron stars. We show that uncertainties in the chemical composition of the envelopes can lead up to ~ 2.5 times uncertainty of the internal temperature of the star which significantly complicates theoretical reconstruction of the internal structure of cooling neutron stars from observations of their thermal surface emission.

Flux decay during thermonuclear X-ray bursts analysed with the dynamic power-law index method

The cooling of type-I X-ray bursts can be used to probe the nuclear burning conditions in neutron star envelopes. The flux decay of the bursts has been traditionally modelled with an exponential, even if theoretical considerations predict power-law-like decays. We have analysed a total of 540 type-I X-ray bursts from five low-mass X-ray binaries observed with the Rossi X-ray Timing Explorer. We grouped the bursts according to the source spectral state during which they were observed (hard or soft), flagging those bursts that showed signs of photospheric radius expansion (PRE). The decay phase of all the bursts were then fitted with a dynamic power-law index method. This method provides a new way of probing the chemical composition of the accreted material. Our results show that in the hydrogen-rich sources the power-law decay index is variable during the burst tails and that simple cooling models qualitatively describe the cooling of presumably helium-rich sources 4U 1728-34 and 3A 1820-303. The cooling in the hydrogen-rich sources 4U 1608-52, 4U 1636-536, and GS 1826-24, instead, is clearly different and depends on the spectral states and whether PRE occurred or not. Especially the hard state bursts behave differently than the models predict, exhibiting a peculiar rise in the cooling index at low burst fluxes, which suggests that the cooling in the tail is much faster than expected. Our results indicate that the drivers of the bursting behaviour are not only the accretion rate and chemical composition of the accreted material, but also the cooling that is somehow linked to the spectral states. The latter suggests that the properties of the burning layers deep in the neutron star envelope might be impacted differently depending on the spectral state.

Thermonuclear Bursts with Short Recurrence Times from Neutron Stars Explained by Opacity-driven Convection

Abstract Thermonuclear flashes of hydrogen and helium accreted onto neutron stars produce the frequently observed Type I X-ray bursts. It is the current paradigm that almost all material burns in a burst, after which it takes hours to accumulate fresh fuel for the next burst. In rare cases, however, bursts are observed with recurrence times as short as minutes. We present the first one-dimensional multi-zone simulations that reproduce this phenomenon. Bursts that ignite in a relatively hot neutron star envelope leave a substantial fraction of the fuel unburned at shallow depths. In the wake of the burst, convective mixing events driven by opacity bring this fuel down to the ignition depth on the observed timescale of minutes. There, unburned hydrogen mixes with the metal-rich ashes, igniting to produce a subsequent burst. We find burst pairs and triplets, similar to the observed instances. Our simulations reproduce the observed fraction of bursts with short waiting times of ∼30%, and demonstrate that short recurrence time bursts are typically less bright and of shorter duration.

Few-Body Effects in Neutron Star Matter

Neutron resonances in systems of few nuclei, electron capture reactions with formation of excited nuclei, and density oscillation in the neutron star envelopes are investigated. These results allow to propose the special experiments to verify the neutron resonances in the few-body systems and understand the origin of some processes that are going in the neutron star crusts.

Diffusion in dense non-isothermal Coulomb plasma

We generalize our previous work on diffusion of ions in isothermal plasmas to handle non-isothermal systems. This approach, combined with the method of effective potentials for computing diffusion coefficients, allows us to formulate the diffusion problem in Coulomb systems of arbitrary coupling. The results are applied to study heat-blanketing envelopes of neutron stars in diffusive equilibrium.

Cooling of neutron stars with diffusive envelopes

We study the effects of heat blanketing envelopes of neutron stars on their cooling. To this aim, we perform cooling simulations using newly constructed models of the envelopes composed of binary ion mixtures (H--He, He--C, C--Fe) varying the mass of lighter ions (H, He or C) in the envelope. The results are compared with those calculated using the standard models of the envelopes which contain the layers of lighter (accreted) elements (H, He and C) on top of the Fe layer, varying the mass of accreted elements. The main effect is that the chemical composition of the envelopes influences their thermal conductivity and, hence, thermal insulation of the star. For illustration, we apply these results to estimate the internal temperature of the Vela pulsar and to study the cooling of neutron stars of ages of 0.1 - 1 Myr at the photon cooling stage. The uncertainties of the cooling models associated with our poor knowledge of chemical composition of the heat insulating envelopes strongly complicate theoretical reconstruction of the internal structure of cooling neutron stars from observations of their thermal surface emission.

Diffusive heat blanketing envelopes of neutron stars

We construct new models of outer heat blanketing envelopes of neutron stars composed of binary ion mixtures (H - He, He - C, C - Fe) in and out of diffusive equilibrium. To this aim, we generalize our previous work on diffusion of ions in isothermal gaseous or Coulomb liquid plasmas to handle non-isothermal systems. We calculate the relations between the effective surface temperature Ts and the temperature Tb at the bottom of heat blanketing envelopes (at a density rhob= 1e8 -- 1e10 g/cc) for diffusively equilibrated and non-equilibrated distributions of ion species at different masses DeltaM of lighter ions in the envelope. Our principal result is that the Ts - Tb relations are fairly insensitive to detailed distribution of ion fractions over the envelope (diffusively equilibrated or not) and depend almost solely on DeltaM. The obtained relations are approximated by analytic expressions which are convenient for modeling the evolution of neutron stars.

Carbon production on accreting neutron stars in a new regime of stable nuclear burning

Abstract Accreting neutron stars exhibit Type I X-ray bursts from both frequent hydrogen/helium flashes as well as rare carbon flashes. The latter (superbursts) ignite in the ashes of the former. Hydrogen/helium bursts, however, are thought to produce insufficient carbon to power superbursts. Stable burning could create the required carbon, but this was predicted to only occur at much larger accretion rates than where superbursts are observed. We present models of a new steady-state regime of stable hydrogen and helium burning that produces pure carbon ashes. Hot CNO burning of hydrogen heats the neutron star envelope and causes helium to burn before the conditions of a helium flash are reached. This takes place when the mass accretion rate is around 10 per cent of the Eddington limit: close to the rate where most superbursts occur. We find that increased heating at the base of the envelope sustains steady-state burning by steepening the temperature profile, which increases the amount of helium that burns before a runaway can ensue.

THE COOLING OF THE CASSIOPEIA A NEUTRON STAR AS A PROBE OF THE NUCLEAR SYMMETRY ENERGY AND NUCLEAR PASTA

X-ray observations of the neutron star in the Cas A supernova remnant over the past decade suggest the star is undergoing a rapid drop in surface temperature of $\approx$ $2-5.5\%$. One explanation suggests the rapid cooling is triggered by the onset of neutron superfluidity in the core of the star, causing enhanced neutrino emission from neutron Cooper pair breaking and formation (PBF). Using consistent neutron star crust and core equations of state (EOSs) and compositions, we explore the sensitivity of this interpretation to the density dependence of the symmetry energy $L$ of the EOS used, and to the presence of enhanced neutrino cooling in the bubble phases of crustal "nuclear pasta". Modeling cooling over a conservative range of neutron star masses and envelope compositions, we find $L\lesssim70$ MeV, competitive with terrestrial experimental constraints and other astrophysical observations. For masses near the most likely mass of $M\gtrsim 1.65 M_{\odot}$, the constraint becomes more restrictive $35\lesssim L\lesssim 55$ MeV. The inclusion of the bubble cooling processes decreases the cooling rate of the star during the PBF phase, matching the observed rate only when $L\lesssim45$ MeV, taking all masses into consideration, corresponding to neutron star radii $\lesssim 11$km.