arXiv subjects

Lars Bildsten

Publications and source records attributed to Lars Bildsten.

At least 73 records · Page 4Linked to original sources

arXiv2017

The Importance of Urca-process Cooling in Accreting ONe White Dwarfs

We study the evolution of accreting oxygen-neon (ONe) white dwarfs (WDs), with a particular emphasis on the effects of the presence of the carbon-burning products $\mathrm{^{23}Na}$ and $\mathrm{^{25}Mg}$. These isotopes lead to substantial cooling of the WD via the $\mathrm{^{25}Mg}$-$\mathrm{^{25}Na}$, $\mathrm{^{23}Na}$-$\mathrm{^{23}Ne}$, and $\mathrm{^{25}Na}$-$\mathrm{^{25}Ne}$ Urca pairs. We derive an analytic formula for the peak Urca-process cooling rate and use it to obtain a simple expression for the temperature to which the Urca process cools the WD. Our estimates are equally applicable to accreting carbon-oxygen WDs. We use the Modules for Experiments in Stellar Astrophysics (MESA) stellar evolution code to evolve a suite of models that confirm these analytic results and demonstrate that Urca-process cooling substantially modifies the thermal evolution of accreting ONe WDs. Most importantly, we show that MESA models with lower temperatures at the onset of the $\mathrm{^{24}Mg}$ and $\mathrm{^{24}Na}$ electron captures develop convectively unstable regions, even when using the Ledoux criterion. We discuss the difficulties that we encounter in modeling these convective regions and outline the potential effects of this convection on the subsequent WD evolution. For models in which we do not allow convection to operate, we find that oxygen ignites around a density of $\log(ρ_{\rm c}/\rm g\,cm^{-3}) \approx 9.95$, very similar to the value without Urca cooling. Nonetheless, the inclusion of the effects of Urca-process cooling is an important step in producing progenitor models with more realistic temperature and composition profiles which are needed for the evolution of the subsequent oxygen deflagration and hence for studies of the signature of accretion-induced collapse.

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arXiv2017

Electron Captures on $^{14}{\rm N}$ as a Trigger for Helium Shell Detonations

White dwarfs (WDs) that accrete helium at rates $\sim 10^{-8} \, M_\odot \, \rm yr^{-1}$, such as those in close binaries with sdB stars, can accumulate large ($\gtrsim 0.1 \, M_\odot$) helium envelopes which are likely to detonate. We perform binary stellar evolution calculations of sdB+WD binary systems with MESA, incorporating the important reaction chain $^{14}{\rm N}(e^-, ν) {^{14}{\rm C}} ( α, γ) {^{18}{\rm O}}$ (NCO), including a recent measurement for the ${^{14}{\rm C}} ( α, γ) {^{18}{\rm O}}$ rate. In large accreted helium shells, the NCO reaction chain leads to ignitions at the dense base of the freshly accreted envelope, in contrast to $3α$ ignitions which occur away from the base of the shell. In addition, at these accretion rates, the shells accumulate on a timescale comparable to their thermal time, leading to an enhanced sensitivity of the outcome on the accretion rate history. Hence, time dependent accretion rates from binary stellar evolution are necessary to determine the helium layer mass at ignition. We model the observed sdB+WD system ${\rm CD}\,-30^\circ 11223$ and find that the inclusion of these effects predicts ignition of a $0.153 \, M_\odot$ helium shell, nearly a factor of two larger than previous predictions. A shell with this mass will ignite dynamically, a necessary condition for a helium shell detonation.

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arXiv2017

Accretion-Induced Collapse From Helium Star + White Dwarf Binaries

Accretion-induced collapse (AIC) occurs when an O/Ne white dwarf (WD) grows to nearly the Chandrasekhar mass ($M_{\rm Ch}$), reaching central densities that trigger electron captures in the core. Using Modules for Experiments in Stellar Astrophysics ($\texttt{MESA}$), we present the first true binary simulations of He star + O/Ne WD binaries, focusing on a $1.5 M_\odot$ He star in a 3 hour orbital period with $1.1-1.3 M_\odot$ O/Ne WDs. The helium star fills its Roche lobe after core helium burning is completed and donates helium on its thermal timescale to the WD, $\dot{M}\approx3\times10^{-6} M_\odot$/yr, a rate high enough that the accreting helium burns stably on the WD. The accumulated carbon/oxygen ashes from the helium burning undergo an unstable shell flash that initiates an inwardly moving carbon burning flame. This flame is only quenched when it runs out of carbon at the surface of the original O/Ne core. Subsequent accumulation of fresh carbon/oxygen layers also undergo thermal instabilities, but no mass loss is triggered, allowing $M_{\rm WD}\rightarrow M_{\rm Ch}$, triggering the onset of AIC. We also discuss the scenario of accreting C/O WDs that experience shell carbon ignitions to become O/Ne WDs, and then, under continuing mass transfer, lead to AIC. Studies of the AIC event rate using binary population synthesis should include all of these channels, especially this latter channel, which has been previously neglected but might dominate the rate.

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arXiv2017

Modules for Experiments in Stellar Astrophysics (MESA): Binaries, Pulsations, and Explosions

We substantially update the capabilities of the open-source software instrument Modules for Experiments in Stellar Astrophysics (MESA). MESA can now simultaneously evolve an interacting pair of differentially rotating stars undergoing transfer and loss of mass and angular momentum, greatly enhancing the prior ability to model binary evolution. New MESA capabilities in fully coupled calculation of nuclear networks with hundreds of isotopes now allow MESA to accurately simulate advanced burning stages needed to construct supernova progenitor models. Implicit hydrodynamics with shocks can now be treated with MESA, enabling modeling of the entire massive star lifecycle, from pre-main sequence evolution to the onset of core collapse and nucleosynthesis from the resulting explosion. Coupling of the GYRE non-adiabatic pulsation instrument with MESA allows for new explorations of the instability strips for massive stars while also accelerating the astrophysical use of asteroseismology data. We improve treatment of mass accretion, giving more accurate and robust near-surface profiles. A new MESA capability to calculate weak reaction rates "on-the-fly" from input nuclear data allows better simulation of accretion induced collapse of massive white dwarfs and the fate of some massive stars. We discuss the ongoing challenge of chemical diffusion in the strongly coupled plasma regime, and exhibit improvements in MESA that now allow for the simulation of radiative levitation of heavy elements in hot stars. We close by noting that the MESA software infrastructure provides bit-for-bit consistency for all results across all the supported platforms, a profound enabling capability for accelerating MESA's development.

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arXiv2016

The Effects of Magnetic Fields on the Dynamics of Radiation Pressure Dominated Massive Star Envelopes

We use three dimensional radiation magneto-hydrodynamic simulations to study the effects of magnetic fields on the energy transport and structure of radiation pressure dominated main sequence massive star envelopes at the region of the iron opacity peak. We focus on the regime where the local thermal timescale is shorter than the dynamical timescale, corresponding to inefficient convective energy transport. We begin with initially weak magnetic fields relative to the thermal pressure, from 100-1000G in differing geometries. The unstable density inversion amplifies the magnetic field, increasing the magnetic energy density to values close to equipartition with the turbulent kinetic energy density. By providing pressure support, the magnetic field's presence significantly increases the density fluctuations in the turbulent envelope, thereby enhancing the radiative energy transport by allowing photons to diffuse out through low density regions. Magnetic buoyancy brings small scale magnetic fields to the photosphere and increases the vertical energy transport with the energy advection velocity proportional to the Alfvén velocity, although in all cases we study photon diffusion still dominates the energy transport. The increased radiative and advective energy transport causes the stellar envelope to shrink by several scale heights. We also find larger turbulent velocity fluctuations compared to the purely hydrodynamic case, reaching $\approx$ 100 km/s at the stellar photosphere. The photosphere also shows vertical oscillations with similar averaged velocities and periods of a few hours. The increased turbulent velocity and oscillations will have strong impacts on the line broadening and periodic signals in massive stars.

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arXiv2016

PTF1 J082340.04+081936.5: A hot subdwarf B star with a low mass white dwarf companion in an 87 minute orbit

We present the discovery of the hot subdwarf B star (sdB) binary PTF1 J082340.04+081936.5. The system has an orbital period P$_{\rm orb}=87.49668(1)$ min (0.060761584(10) days), making it the second-most compact sdB binary known. The lightcurve shows ellipsoidal variations. Under the assumption that the sdB primary is synchronized with the orbit, we find a mass $M_{\rm sdB}=0.45^{+0.09}_{-0.07}$ M$_\odot$, a companion white dwarf mass $M_{\rm WD}=0.46^{+0.12}_{-0.09}$ M$_\odot$ and a mass ratio $q = \frac{M_{\rm WD}}{M_{\rm sdB}}=1.03^{+0.10}_{-0.08}$. The future evolution was calculated using the MESA stellar evolution code. Adopting a canonical sdB mass of $M_{\rm sdB}=0.47$ M$_\odot$, we find that the sdB still burns helium at the time it will fill its Roche lobe if the orbital period was less than 106 min at the exit from the last common envelope phase. For longer common envelope exit periods the sdB will have stopped burning helium and turned into a C/O white dwarf at the time of contact. Comparing the spectroscopically derived log(g) and $T_{\rm eff}$ with our MESA models, we find that an sdB model with a hydrogen envelope mass of $5\times10^{-4} M_\odot$ matches the measurements at a post-common envelope age of 94 Myr, corresponding to a post-common envelope orbital period of 109 min which is close to the limit to start accretion while the sdB is still burning helium.

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arXiv2016

Convection Destroys the Core/Mantle Structure in Hybrid C/O/Ne White Dwarfs

A hybrid C/O/Ne white dwarf (WD) -- an unburned C/O core surrounded by an O/Ne/Na mantle -- can be formed if the carbon flame is quenched in a super-AGB (SAGB) star or white dwarf merger remnant. We show that this segregated hybrid structure becomes unstable to rapid mixing within 2,000 years of the onset of WD cooling. Carbon burning includes a weak reaction that removes electrons, resulting in a lower electron-to-baryon ratio ($Y_{\rm e}$) in the regions processed by carbon burning compared to the unburned C/O core, making the O/Ne mantle denser than the C/O core as the WD cools. This is unstable to efficient mixing. We use the results of $\texttt{MESA}$ models with different size C/O cores to quantify the rate at which the cores mix with the mantle as they cool. In all cases, we find that the WDs undergo significant core/mantle mixing on timescales shorter than the time available to grow the WD to the Chandrasekhar mass ($M_{\rm Ch}$) by accretion. As a result, hybrid WDs that reach $M_{\rm Ch}$ due to later accretion will have lower central carbon fractions than assumed thus far. We briefly discuss the implications of these results for the possibility of Type Ia supernovae from hybrid WDs.

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arXiv2016

Turbulent Chemical Diffusion in Convectively Bounded Carbon Flames

It has been proposed that mixing induced by convective overshoot can disrupt the inward propagation of carbon deflagrations in super-asymptotic giant branch stars. To test this theory, we study an idealized model of convectively bounded carbon flames with 3D hydrodynamic simulations of the Boussinesq equations using the pseudospectral code Dedalus. Because the flame propagation timescale is much longer than the convection timescale, we approximate the flame as fixed in space, and only consider its effects on the buoyancy of the fluid. By evolving a passive scalar field, we derive a {\it turbulent} chemical diffusivity produced by the convection as a function of height, $D_{\rm t}(z)$. Convection can stall a flame if the chemical mixing timescale, set by the turbulent chemical diffusivity, $D_{\rm t}$, is shorter than the flame propagation timescale, set by the thermal diffusivity, $κ$, i.e., when $D_{\rm t}>κ$. However, we find $D_{\rm t}<κ$ for most of the flame because convective plumes are not dense enough to penetrate into the flame. Extrapolating to realistic stellar conditions, this implies that convective mixing cannot stall a carbon flame and that "hybrid carbon-oxygen-neon" white dwarfs are not a typical product of stellar evolution.

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arXiv2016

Thermal Runaway During the Evolution of ONeMg Cores towards Accretion-Induced Collapse

We study the evolution of degenerate electron cores primarily composed of the carbon burning products oxygen, neon, and magnesium (hereafter ONeMg cores) that are undergoing compression. Electron capture reactions on A=20 and A=24 isotopes reduce the electron fraction and heat the core. We develop and use a new capability of the Modules for Experiments in Stellar Astrophysics (MESA) stellar evolution code that provides a highly accurate implementation of these key reactions. These new accurate rates and the ability of MESA to perform extremely small spatial zoning demonstrates a thermal runaway in the core triggered by the temperature and density sensitivity of the Ne-20 electron capture reactions. Both analytics and numerics show that this thermal runaway does not trigger core convection, but rather leads to a centrally concentrated (r < km) thermal runaway that will subsequently launch an oxygen deflagration wave from the center of the star. We use MESA to perform a parameter study that quantifies the influence of the magnesium mass fraction, the central temperature, the compression rate, and uncertainties in the electron capture reaction rates on the ONeMg core evolution. This allows us to establish a lower limit on the central density at which the oxygen deflagration wave initiates of $ρ_c > 8.5 \times 10^9\, \textrm{g cm}^{-3}$. Based on previous work and order-of-magnitude calculations, we expect objects which ignite oxygen at or above these densities to collapse and form a neutron star. Calculations such as these are an important step in producing more realistic progenitor models for studies of the signature of accretion-induced collapse.

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arXiv2016

Carbon Shell or Core Ignitions in White Dwarfs Accreting from Helium Stars

White dwarfs accreting from helium stars can stably burn at the accreted rate and avoid the challenge of mass loss associated with unstable Helium burning that is a concern for many Type Ia supernovae scenarios. We study binaries with helium stars of mass $1.25 M_\odot\le M_{\rm{He}} \le 1.8 M_\odot$, which have lost their hydrogen rich envelopes in an earlier common envelope event and now orbit with periods ($P_{\rm orb}$) of several hours with non-rotating $0.84$ and $1.0 M_\odot$ C/O WDs. The helium stars fill their Roche lobes (RLs) after exhaustion of central helium and donate helium on their thermal timescales (${\sim}10^5$yr). As shown by others, these mass transfer rates coincide with the steady helium burning range for WDs, and grow the WD core up to near the Chandrasekhar mass ($M_{\rm Ch}$) and a core carbon ignition. We show here, however, that many of these scenarios lead to an ignition of hot carbon ashes near the outer edge of the WD and an inward going carbon flame that does not cause an explosive outcome. For $P_{\rm orb} = 3$ hours, $1.0 M_\odot$ C/O WDs with donor masses $M_{\rm He}\gtrsim1.8 M_\odot$ experience a shell carbon ignition, while $M_{\rm He}\lesssim1.3 M_\odot$ will fall below the steady helium burning range and undergo helium flashes before reaching core C ignition. Those with $1.3 M_\odot \lesssim M_{\rm He} \lesssim 1.7 M_\odot$ will experience a core C ignition. We also calculate the retention fraction of accreted helium when the accretion rate leads to recurrent weak helium flashes.

astro-ph.HE↗

arXiv2016

Asteroseismic signatures of evolving internal stellar magnetic fields

Recent asteroseismic analyses have revealed the presence of strong (B $\gtrsim 10^5$ G) magnetic fields in the cores of many red giant stars. Here, we examine the implications of these results for the evolution of stellar magnetic fields, and we make predictions for future observations. Those stars with suppressed dipole modes indicative of strong core fields should exhibit moderate but detectable quadrupole mode suppression. The long magnetic diffusion times within stellar cores ensure that dynamo-generated fields are confined to mass coordinates within the main sequence convective core, and the observed sharp increase in dipole mode suppression rates above $1.5 \, M_\odot$ may be explained by the larger convective core masses and faster rotation of these more massive stars. In clump stars, core fields of $\sim10^5 \, {\rm G}$ can suppress dipole modes, whose visibility should be equal to or less than the visibility of suppressed modes in ascending red giants. High dipole mode suppression rates in low-mass ($M \lesssim 2 \, M_\odot$) clump stars would indicate that magnetic fields generated during the main sequence can withstand subsequent convective phases and survive into the compact remnant phase. Finally, we discuss implications for observed magnetic fields in white dwarfs and neutron stars, as well as the effects of magnetic fields in various types of pulsating stars.

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arXiv2016

Late-time Spectroscopy of Type Iax Supernovae

We examine the late-time (t > 200 days after peak brightness) spectra of Type Iax supernovae (SNe Iax), a low-luminosity, low-energy class of thermonuclear stellar explosions observationally similar to, but distinct from, Type Ia supernovae. We present new spectra of SN 2014dt, resulting in the most complete published late-time spectral sequence of a SN Iax. At late times, SNe Iax have generally similar spectra, all with a similar continuum shape and strong forbidden-line emission. However, there is also significant diversity where some late-time SN Iax spectra display narrow P-Cygni features and a continuum indicative of a photosphere in addition to strong narrow forbidden lines, while others have no obvious P-Cygni features, strong broad forbidden lines, and weak narrow forbidden lines. Finally, some SNe Iax have spectra intermediate to these two varieties with weak P-Cygni features and broad/narrow forbidden lines of similar strength. We find that SNe Iax with strong broad forbidden lines also tend to be more luminous and have higher-velocity ejecta at peak brightness. We estimate blackbody and kinematic radii of the late-time photosphere, finding the latter an order of magnitude larger than the former. We propose a two-component model that solves this discrepancy and explains the diversity of the late-time spectra of SNe Iax. In this model, the broad forbidden lines originate from the SN ejecta, while the photosphere, P-Cygni lines, and narrow forbidden lines originate from a wind launched from the remnant of the progenitor white dwarf and is driven by the radioactive decay of newly synthesized material left in the remnant. The relative strength of the two components accounts for the diversity of late-time SN Iax spectra. This model also solves the puzzle of a long-lived photosphere and slow late-time decline of SNe Iax. (Abridged)

astro-ph.HE↗

arXiv2016

Rapidly Rising Transients in the Supernova - Superluminous Supernova Gap

We present observations of four rapidly rising (t_{rise}~10d) transients with peak luminosities between those of supernovae (SNe) and superluminous SNe (M_{peak}~-20) - one discovered and followed by the Palomar Transient Factory (PTF) and three by the Supernova Legacy Survey (SNLS). The light curves resemble those of SN 2011kl, recently shown to be associated with an ultra-long-duration gamma ray burst (GRB), though no GRB was seen to accompany our SNe. The rapid rise to a luminous peak places these events in a unique part of SN phase space, challenging standard SN emission mechanisms. Spectra of the PTF event formally classify it as a Type II SN due to broad Halpha emission, but an unusual absorption feature, which can be interpreted as either high velocity Halpha (though deeper than in previously known cases) or Si II (as seen in Type Ia SNe), is also observed. We find that existing models of white dwarf detonations, CSM interaction, shock breakout in a wind (or steeper CSM) and magnetar spindown can not readily explain the observations. We consider the possibility that a "Type 1.5 SN" scenario could be the origin of our events. More detailed models for these kinds of transients and more constraining observations of future such events should help better determine their nature.

astro-ph.CO↗

arXiv2016

Seismology of Rapidly Rotating Accreting White Dwarfs

A number of White Dwarfs (WDs) in cataclysmic binaries have shown brightness variations consistent with non-radial oscillations as observed in isolated WDs. A few objects have been well-characterized with photometric campaigns in the hopes of gleaning information about the mass, spin, and possibly internal structural characteristics. The novel aspect of this work is the possiblity to measure or constrain the interior structure and spin rate of WDs which have spent gigayears accreting material from their companion, undergoing thousands of nova outbursts in the process. In addition, variations in the surface temperature affect the site of mode driving, and provide unique and challenging tests for mode driving theories previously applied to isolated WD's. Having undergone long-term accretion, these WDs are expected to have been spun up. Spin periods in the range 60-100 seconds have been measured by other means for two objects, GW Lib and V455 And. Compared to typical mode frequencies, the spin frequency may be similar or higher, and the Coriolis force can no longer be treated as a small perturbation on the fluid motions. We present the results of a non-perturbative calculation of the normal modes of these WDs, using interior thermal structures appropriate to accreting systems. This includes a discussion of the surface brightness distributions, which are strongly modified from the non-rotating case. Using the measured spin period of approximately 100 seconds, we show that the observed pulsations from GW Lib are consistent with the three lowest azimuthal order rotationally modified modes that have the highest frequency in the stellar frame. The high frequencies are needed for the convective driving, but are then apparently shifted to lower frequencies by a combination of their pattern motion and the WD rotation.

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arXiv2015

Magnetar Driven Shock Breakout and Double Peaked Supernova Light Curves

The light curves of some luminous supernovae are suspected to be powered by the spindown energy of a rapidly rotating magnetar. Here we describe a possible signature of the central engine: a burst of shock breakout emission occurring several days after the supernova explosion. The energy input from the magnetar inflates a high-pressure bubble that drives a shock through the pre-exploded supernova ejecta. If the magnetar is powerful enough, that shock will near the ejecta surface and become radiative. At the time of shock breakout, the ejecta will have expanded to a large radius (~10^{14} cm) so that the radiation released is at optical/ultraviolet wavelengths (T ~ 20,000 K) and lasts for several days. The luminosity and timescale of this magnetar driven shock breakout are similar to the first peak observed recently in the double-peaked light curve of SNLSQ14BDQ. However, for a large region of model parameter space, the breakout emission is predicted to be dimmer than the diffusive luminosity from direct magnetar heating. A distinct double peaked light curve may therefore only be conspicuous if thermal heating from the magnetar is suppressed at early times. We describe how such a delay in heating may naturally result from inefficient dissipation and thermalization of the pulsar wind magnetic energy. Without such suppression, the breakout may only be noticeable as a small bump or kink in the early luminosity or color evolution, or as a small but abrupt rise in the photospheric velocity. A similar breakout signature may accompany other central engines in supernovae, such as a black hole accreting fallback material.

astro-ph.HE↗

arXiv2015

Asteroseismology Can Reveal Strong Internal Magnetic Fields in Red Giant Stars

Internal stellar magnetic fields are inaccessible to direct observations and little is known about their amplitude, geometry and evolution. We demonstrate that strong magnetic fields in the cores of red giant stars can be identified with asteroseismology. The fields can manifest themselves via depressed dipole stellar oscillation modes, which arises from a magnetic greenhouse effect that scatters and traps oscillation mode energy within the core of the star. The Kepler satellite has observed a few dozen red giants with depressed dipole modes which we interpret as stars with strongly magnetized cores. We find field strengths larger than $\sim\! 10^5 \,{\rm G}$ may produce the observed depression, and in one case we infer a minimum core field strength of $\approx \! \! 10^7 \,{\rm G}$.

astro-ph.SR↗

arXiv2015

Population of post-nova supersoft X-ray sources

Novae undergo a supersoft X-ray phase of varying duration after the optical outburst. Such transient post-nova supersoft X-ray sources (SSSs) are the majority of the observed SSSs in M31. In this paper, we use the post-nova evolutionary models of Wolf et al. to compute the expected population of post-nova SSSs in M31. We predict that depending on the assumptions about the WD mass distribution in novae, at any instant there are about 250-600 post-nova SSSs in M31 with (unabsorbed) 0.2-1.0 keV luminosity L_x>10^36 erg/s. Their combined unabsorbed luminosity is of the order of ~10^39 erg/s. Their luminosity distribution shows significant steepening around log(L_x)~37.7-38 and becomes zero at L_x~2x10^38 erg/s, the maximum L_x achieved in the post-nova evolutionary tracks. Their effective temperature distribution has a roughly power law shape with differential slope of ~4-6 up to the maximum temperature of T_eff~1.5x10^6 K. We compare our predictions with the results of the XMM-Newton monitoring of the central field of M31 between 2006 and 2009. The predicted number of post-nova SSSs exceed the observed number by a factor of ~2-5, depending on the assumed WD mass distribution in novae. This is good agreement, considering the number and magnitude of uncertainties involved in calculations of the post-nova evolutionary models and their X-ray output. Furthermore, only a moderate circumstellar absorption, with hydrogen column density of the order of ~10^21 cm^-2, will remove the discrepancy.

astro-ph.SR↗

arXiv2015

Local Radiation Hydrodynamic Simulations of Massive Star Envelopes at the Iron Opacity Peak

We perform three dimensional radiation hydrodynamic simulations of the structure and dynamics of radiation dominated envelopes of massive stars at the location of the iron opacity peak. One dimensional hydrostatic calculations predict an unstable density inversion at this location, whereas our simulations reveal a complex interplay of convective and radiative transport whose behavior depends on the ratio of the photon diffusion time to the dynamical time. The latter is set by the ratio of the optical depth per pressure scale height, $τ_0$, to $τ_c=c/c_g$, where $c_g \approx$ 50 km/s is the isothermal sound speed in the gas alone. When $τ_0 \gg τ_c$, convection reduces the radiation acceleration and removes the density inversion. The turbulent energy transport in the simulations agrees with mixing length theory and provides its first numerical calibration in the radiation dominated regime. When $τ_0 \ll τ_c$, convection becomes inefficient and the turbulent energy transport is negligible. The turbulent velocities exceed $c_g$, driving shocks and large density fluctuations that allow photons to preferentially diffuse out through low-density regions. However, the effective radiation acceleration is still larger than the gravitational acceleration so that the time average density profile contains a modest density inversion. In addition, the simulated envelope undergoes large-scale oscillations with periods of a few hours. The turbulent velocity field may affect the broadening of spectral lines and therefore stellar rotation measurements in massive stars, while the time variable outer atmosphere could lead to variations in their mass loss and stellar radius.

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