Atmosphere In Radiative Equilibrium Research Articles

Magnetospheric return-current-heated atmospheres of rotation-powered millisecond pulsars

We computed accurate atmosphere models of rotation-powered millisecond pulsars in which the polar caps of a neutron star (NS) are externally heated by magnetospheric return currents. The external ram pressure, energy losses, and stopping depth of the penetrating charged particles were computed self-consistently with the atmosphere model, instead of assuming a simplified deep-heated atmosphere in radiative equilibrium. We used exact Compton scattering formalism to model the properties of the emergent X-ray radiation. The deep-heating approximation was found to be valid only if most of the heat originates from ultra-relativistic bombarding particles with Lorentz factors ofγ ≳ 100. In the opposite regime, the atmosphere attains a distinct two-layer structure with an overheated optically thin skin on top of an optically thick cool plasma. The overheated skin strongly modifies the emergent radiation: It produces a Compton-upscattered high-energy tail in the spectrum and alters the radiation beaming pattern from limb darkening to limb brightening for emitted hard X-rays. This kind of drastic change in the emission properties can have a significant impact on the inferred NS pulse profile parameters as performed, for example, by Neutron star Interior Composition ExploreR. Finally, the connection between the energy distribution of the return current particles and the atmosphere emission properties offers a new tool to probe the exact physics of pulsar magnetospheres.

Mathematical Assessment of Physical and Chemical Processes from the Middle B to the Early F Type Main Sequence Stars

AbstractThe middle B to the early F Main Sequence stars have some of the most quiet stellar atmospheres. In this part of the HR diagram we find stars with atmospheres in radiative equilibrium. They lack the convective circulations of the middle F and cooler stars and the massive stellar winds of hotter stars. When stars of different mass evolve off the Main Sequence in this part of the HR Diagram their evolutionary paths do not cross initially. Thus stars with the same effective temperature and surface gravity have the same luminosity and mass. By comparing their elemental abundances, we might be able to identify physical processes which cause any differences in their abundances. Here we begin with stars whose effective temperatures and surface gravities are similar, and which have been analyzed by us using spectra obtained from the Dominion Astrophysical Observatory (DAO). Improvements in our knowledge of the energy distributions of stars (for example via GAIA measurements) should lead to improved estimates of stellar effective temperatures and surface gravities.

The energy of waves in the photosphere and lower chromosphere

Most static 1D atmosphere models in the quiet Sun predict a rise of the gas temperature at chromospheric layers, but numerical simulations only yield an increase in the brightness temperature. We investigate the thermal structure in the solar chromosphere as derived from an LTE inversion of Ca II H spectra in QS and active regions. We investigate the temperature stratifications on differences between magnetic and field-free regions in the QS, and between QS and ARs. We determine the energy content of individual calcium bright grains (BGs). The rms temperature fluctuations are below 100 K in the photosphere and 200-300 K in the chromosphere. The average temperature stratification in the QS does not exhibit a clear chromospheric temperature rise, opposite to the AR case. We find an energy content of about 7*10E18 J for BGs that repeat with a cadence of about 160 secs. The precursors of BGs have a vertical extent of about 200 km and a horizontal extent of about 1 Mm. The comparison of observed with synthetic NLTE profiles confirms that the solar chromosphere in the QS oscillates between an atmosphere in radiative equilibrium and one with a moderate chromospheric temperature rise. Two-dimensional x-z temperature maps exhibit nearly horizontal canopy-like structures with a few Mm extent around photospheric magnetic field concentrations at a height of about 600 km. The large difference between QS regions and ARs, and the better match of AR and non-LTE reference spectra suggest that magnetic heating processes are more important than commonly assumed. The temperature fluctuations in QS derived by the LTE inversion do not suffice on average to maintain a stationary chromospheric temperature rise. The spatially and vertically resolved information on the temperature structure allows one to investigate in detail the topology and evolution of the thermal structure in the lower solar atmosphere.

3.6 AND 4.5 μm PHASE CURVES AND EVIDENCE FOR NON-EQUILIBRIUM CHEMISTRY IN THE ATMOSPHERE OF EXTRASOLAR PLANET HD 189733b

We present new, full-orbit observations of the infrared phase variations of the canonical hot Jupiter HD 189733b obtained in the 3.6 and 4.5 micron bands using the Spitzer Space Telescope. When combined with previous phase curve observations at 8.0 and 24 micron, these data allow us to characterize the exoplanet's emission spectrum as a function of planetary longitude. We utilize improved methods for removing the effects of intrapixel sensitivity variations and accounting for the presence of time-correlated noise in our data. We measure a phase curve amplitude of 0.1242% +/- 0.0061% in the 3.6 micron band and 0.0982% +/- 0.0089% in the 4.5 micron band. We find that the times of minimum and maximum flux occur several hours earlier than predicted for an atmosphere in radiative equilibrium, consistent with the eastward advection of gas by an equatorial super-rotating jet. The locations of the flux minima in our new data differ from our previous observations at 8 micron, and we present new evidence indicating that the flux minimum observed in the 8 micron is likely caused by an over-shooting effect in the 8 micron array. We obtain improved estimates for HD 189733b's dayside planet-star flux ratio of 0.1466% +/- 0.0040% at 3.6 micron and 0.1787% +/- 0.0038% at 4.5 micron; these are the most accurate secondary eclipse depths obtained to date for an extrasolar planet. We compare our new dayside and nightside spectra for HD 189733b to the predictions of models from Burrows et al. (2008) and Showman et al. (2009). We find that HD 189733b's 4.5 micron nightside flux is 3.3 sigma smaller than predicted by the Showman et al. models, which assume that the chemistry is in local thermal equilibrium. We conclude that this discrepancy is best-explained by vertical mixing, which should lead to an excess of CO and correspondingly enhanced 4.5 micron absorption in this region. [abridged]

A magnetar strength surface magnetic field for the slowly spinning down SGR 0418+5729

The observed upper bound on the spin down rate of the otherwise typical Soft Gamma-ray Repeater SGR 0418+5729 has challenged the interpretation of this source as a neutron star with ultrastrong magnetic fields. Current limits imply a dipole magnetic field strength of less than 7.5 x 10^{12} G (Rea et al. 2010), which is significantly smaller than that of a typical SGR. Independent of the properties inferred from X-ray timing, the X-ray spectra of neutron stars allow a measurement of their magnetic field strengths because they are distorted from pure blackbodies due to the presence of a magnetic field in a radiative equilibrium atmosphere. In this paper, we model high signal-to-noise XMM-Newton spectra of SGR 0418+5729 to place constraints on the strength of the magnetic field at the surface of the neutron star. Our analysis shows that neutron star atmosphere models with moderate magnetic field strengths (10^{12-13} G) cannot fit the X-ray spectra, whereas, models with stronger magnetic fields are able to account for the observations. We find that the strength of the magnetic field at the surface is 1.0 x 10^{14} G. This value, although lower than all of the other SGRs analyzed to date, is still high enough to generate the observed X-ray bursts from the source. In connection to the spindown limits, it also implies a significantly non-dipolar structure of the magnetic field. We discuss the results of our spectral modeling and compare them with other SGRs.

The energy of waves in the photosphere and lower chromosphere

Acoustic waves are one of the primary suspects besides magnetic fields for the chromospheric heating process to temperatures above radiative equilibrium (RE). We derived the mechanical wave energy as seen in line-core velocities to obtain a measure of mechanical energy flux with height for a comparison with the energy requirements in a semi-empirical atmosphere model. We analyzed a 1-hour time series and a large-area map of Ca II H spectra on the traces of propagating waves. We analyzed the velocity statistics of several spectral lines in the wing of Ca II H, and the line-core velocity of Ca II H. We converted the velocity amplitudes into volume and mass energy densities. For comparison, we used the increase of internal energy necessary to lift a RE atmosphere to the HSRA temperature stratification. We find that the velocity amplitude grows in agreement with linear wave theory and thus slower with height than predicted from energy conservation. The mechanical energy of the waves above around z~500 km is insufficient to maintain the chromospheric temperature rise in the semi-empirical HSRA model. The intensity variations of the Ca line core (z~1000 km) can be traced back to the velocity variations of the lowermost forming spectral line considered (z~ 250 km). The chromospheric intensity, and hence, (radiation) temperature variations are seen to be induced by passing waves originating in the photosphere.

Exact results in modeling planetary atmospheres—II. Semi-gray atmospheres

We solve the radiative transfer equation for a semi-gray planetary atmosphere in radiative equilibrium, in an attempt to define an entirely analytical non-gray model atmosphere of finite optical thickness. The salient feature of the model is that the incident solar radiation is partitioned between two adjacent spectral domains—the “visible” and the “infrared”—in each of which the atmosphere's (effective) opacity is assumed to be independent of frequency (the semi-gray assumption). We envisage a plane-parallel atmosphere illuminated by a beam of parallel radiation and bounded below by a partially reflecting and emitting ground. The former emits infrared radiation, induced by the absorption of radiation both visible and infrared, deriving from the external irradiation as well as from the emission of the planet's surface layer. For an atmosphere with given single-scattering albedos and optical thicknesses in both the visible and infrared domains, we compute the temperature at every depth of the atmosphere, as well as the ground's temperature.

Exact results in modeling planetary atmospheres—I. Gray atmospheres

An exact model is proposed for a gray, isotropically scattering planetary atmosphere in radiative equilibrium. The slab is illuminated on one side by a collimated beam and is bounded on the other side by an emitting and partially reflecting ground. We provide expressions for the incident and reflected fluxes on both boundary surfaces, as well as the temperature of the ground and the temperature distribution in the atmosphere, assuming the latter to be in local thermodynamic equilibrium. Tables and curves of the temperature distribution are included for various values of the optical thickness. Finally, semi-infinite atmospheres illuminated from the outside or by sources at infinity is dealt with.

K. Schwarzschild's problem in radiation transfer theory

We solve exactly the problem of a finite slab receiving an isotropic radiation on one side and no radiation on the other side. This problem—to be more precise the calculation of the source function within the slab—was first formulated by K. Schwarzschild in 1914. We first solve it for unspecified albedos and optical thicknesses of the atmosphere, in particular for an albedo very close to 1 and a very large optical thickness in view of some astrophysical applications. Then we focus on the conservative case ( albedo = 1 ) , which is of great interest for the modeling of grey atmospheres in radiative equilibrium. Ten-figure tables of the conservative source function are given. From the analytical expression of this function, we deduce (1) a simple relation between the effective temperature of a grey atmosphere in radiative equilibrium and the temperature of the black body that irradiates it, (2) the temperature at any point of the atmosphere when it is in local thermodynamical equilibrium. This temperature distribution is the counterpart, for a finite slab, of Hopf's distribution in a half-space. Its graphical representation is given for various optical thicknesses of the atmosphere.

Possible descent across the “Tropopause” in Antarctic winter

Descent of air from stratosphere to troposphere in Antarctic winter is proposed to be feasible, because of forcing from above by subsidence plus wave-breaking, together with suction from below to resupply the katabatic winds which flow down the slopes of the Antarctic Plateau in the boundary layer. In Antarctic winter, there is no real tropopause to prevent such descent, hence the quotes in the title: the temperature profile is often that of a radiative equilibrium atmosphere. Such descent would be important because the dryness and low precipitation over the Antarctic Plateau would be less altered during global warming, because there would be an alternative fractionation pathway for H 2O 18 and HDO in Antarctic ice-cores, and because the ozone budget in the unpolluted troposphere of the southern hemisphere would be significantly different. Each of these features could have a major impact on climate or on the study of climate.

Analytical investigation of the atmospheric radiation limits in semigray atmospheres in radiative equilibrium

We model the wavelength-dependent absorption of atmospheric gases by assuming constant massabsorption coefficients in finite-width spectral bands. Such a semigray atmosphere is analyticallysolved by a discrete ordinate method. The general solution is analyzed for a water vapor saturatedatmosphere that also contains a carbon dioxide-like absorbing gas in the infrared. A multiple stableequilibrium with a relative upper limit in the outgoing long-wave radiation is found. Differing fromprevious radiative–convective models, we find that the amount of carbon dioxide strongly modifiesthe value of this relative upper limit. This result is also obtained in a gray (i.e., equal absorption ofradiation at all infrared wavelengths) water vapor saturated atmosphere. The destabilizing effect ofcarbon dioxide implies that massive carbon dioxide atmospheres are more likely to reach a runawaygreenhouse state than thin carbon dioxide ones. DOI: 10.1034/j.1600-0870.2003.00023.x

The Effect of Vacuum Polarization and Proton Cyclotron Resonances on Photon Propagation in Strongly Magnetized Plasmas

We consider the effects of vacuum polarization and proton cyclotron resonances on the propagation of radiation through a strongly magnetized plasma. We analyze the conditions under which the photons evolve adiabatically through the resonant density and find that the adibaticity condition is satisfied for most photon energies of interest, allowing for a normal-mode treatment of the photon propagation. We then construct radiative equilibrium atmosphere models of strongly magnetized neutron stars that includes these effects, employing a new numerical method that resolves accurately the sharp changes of the absorption and mode-coupling cross sections at the resonant densities. We show that the resulting spectra are modified by both resonances and are harder at all field strengths than a blackbody at the effective temperature. We also show that the narrow absorption features introduced by the proton cyclotron resonance have small equivalent widths. We discuss the implications of our results for properties of thermal emission from the surfaces of young neutron stars.

Analytical investigation of the atmospheric radiation limits in semigray atmospheres in radiative equilibrium

We model the wavelength-dependent absorption of atmospheric gases by assuming constant massabsorption coefficients in finite-width spectral bands. Such a semigray atmosphere is analyticallysolved by a discrete ordinate method. The general solution is analyzed for a water vapor saturatedatmosphere that also contains a carbon dioxide-like absorbing gas in the infrared. A multiple stableequilibrium with a relative upper limit in the outgoing long-wave radiation is found. Differing fromprevious radiative’convective models, we find that the amount of carbon dioxide strongly modifiesthe value of this relative upper limit. This result is also obtained in a gray (i.e., equal absorption ofradiation at all infrared wavelengths) water vapor saturated atmosphere. The destabilizing effect ofcarbon dioxide implies that massive carbon dioxide atmospheres are more likely to reach a runawaygreenhouse state than thin carbon dioxide ones.

CHALLENGES TO UNDERSTAND STELLAR CHROMOSPHERES AND STELLAR ACTIVITY: THE LIMIT CASE OF LATE-A AND EARLY-F STARS

The onset of chromospheric activity appears at late-A and early-F stars where theories predict atmospheres in radiative equilibrium and shallow or non-existent convective zones. The detection of Ly-α emission cores in several A and F stars, first with the IUE satellite and then with the HST, gives evidence for the presence of chromospheric layers in these stars up to B-V=0.m19 (Catalano et al. 1986). Semiempirical chromospheric models for Altair allowed us (Freire et al. 1995) to explain the observed emission profiles taking into account normal HI IS absorption. However, due to the very high rotational velocity we analyzed alternative hypotheses like the formation of Ly-α emissions into a corotating expanding wind, but we ruled out this alternative because we obtained inconsistent results. In addition, X-ray emission (originated surely in a corona) strengthen the presence of a chromosphere. Here we place the problem of chromospheric activity of late-A and early-F stars in the general context of the formation of over-photospheric stellar layers, comparing them with late-type star and solar cases.

Constraints on Thermal Emission Models of Anomalous X‐Ray Pulsars

Thermal emission from the surface of an ultramagnetic neutron star is believed to contribute significantly to the soft X-ray flux of the anomalous X-ray pulsars (AXPs). We compare the detailed predictions of models of the surface emission from a magnetar to the observed spectral and variability properties of AXPs. In particular, we focus on the combination of their luminosities and energy-dependent pulsed fractions. We use the results of recent calculations for strongly magnetized atmospheres in radiative equilibrium to obtain the angle- and energy-dependence of the surface emission. We also include in our calculations the significant effects of general relativistic photon transport to an observer at infinity as well as the effects of interstellar extinction. We find that the combination of the large pulsed fractions and the high inferred luminosities of AXPs cannot be accounted for by surface emission from a magnetar with two antipodal hot regions or a temperature distribution characteristic of a magnetic dipole. This result is robust for reasonable neutron star radii, for the range of magnetic field strengths inferred from the observed spin down rates, and for surface temperatures consistent with the spectral properties of AXPs. Models with a single hot emitting region can reproduce the observations, provided that the distance to one of the sources is ~30% less than the current best estimate, and allowing for systematic uncertainties in the spectral fit of a second source. Finally, the thermal emission models with antipodal emission geometry predict a characteristic strong increase of the pulsed fraction with photon energy, which is apparently inconsistent with the current data. The energy-dependence of the pulsed fraction in the models with one hot region shows a wider range of behavior and can be consistent with the existing data. Upcoming high-resolution observations with Chandra and XMM-Newton will provide a conclusive test.

The outer atmosphere of Tau -- III. Inhomogeneities deduced from cold CO fluorescence

Ultraviolet spectra of α Tau obtained with the Goddard High Resolution Spectrograph (GHRS) on the Hubble Space Telescope show clusters of CO emission lines which are excited by the O i (uv2) multiplet near 1304 A. Identifications of these fluorescent lines and their pumping routes are presented. The absolute intensities of the CO lines and their ratios cannot be explained by the one-dimensional chromospheric model based on collisionally excited lines. The excitation temperature of the CO is found to be only ≃2000 K, lower than that of the minimum value in the chromospheric model. The CO line intensities are used to deduce the O i radiation field, linewidths and opacity where the CO is pumped. The low opacity deduced implies that the O i radiation and CO molecules must be in close proximity, implying a two-component atmosphere. Although a combination of regions of traditional ‘chromosphere’ within a cool radiative equilibrium atmosphere cannot yet be excluded, the uv spectrum could instead be accounted for, in principle, by shocks within such a cool atmosphere.

Formation of Solar Calcium H and K Bright Grains

We have simulated the generation of Ca II H2V bright grains by acoustic shocks. We employ a one-dimensional, non-LTE radiation-hydrodynamic code, with six-level model atoms for hydrogen and singly ionized calcium. We drive acoustic waves through a stratified radiative equilibrium atmosphere by a piston, whose velocity is chosen to match the Doppler shift observed in the Fe I 396.68 nm line in the H line wing, formed at about 260 km above τ500 = 1. The simulations closely match the observed behavior of Ca II H2V bright grains down to the level of individual grains. The bright grains are produced by shocks near 1 Mm above τ500 = 1. Shocks in the mid-chromosphere produce a large source function (and therefore high emissivity) because the density is high enough for collisions to couple the Ca II populations to the local conditions. The asymmetry of the line profile is due to velocity gradients near 1 Mm. Material motion Doppler-shifts the frequency at which atoms emit and absorb photons, so the maximum opacity is located at—and the absorption profile is symmetric about—the local fluid velocity, which is shifted to the blue behind shocks. The optical depth depends upon the velocity structure higher up. Shocks propagate generally into downflowing material, so there is little matter above to absorb the Doppler-shifted radiation. The corresponding red peak is absent because of small opacity at the source function maximum and large optical depth due to overlying material. The bright grains are produced primarily by waves from the photosphere that are slightly above the acoustic cutoff frequency. The precise time and strength of a grain depend upon the interference between these waves near the acoustic cutoff frequency and higher frequency waves. When waves near the acoustic cutoff frequency are weak, then higher frequency waves may produce grains. The 5 minute trapped p-mode oscillations are not the source of the grains, although they can slightly modify the behavior of higher frequency waves.

Radiative equilibrium in rapidly expanding shells

The equation of radiative equilibrium for rapidly expanding spherical shells including the special relativistic terms is discussed, and a temperature-correction procedure for the solution of this equation is given. The temperature-correction scheme combines a partial linearization approach with the approximate Lambda-operator iteration method. For some test problems, the temperature structures of atmospheres in radiative equilibrium in the Lagrangian frame are calculated. The effects of the velocity field on the temperature stratification and the luminosity are also discussed. We find that the temperature structure of a moving photosphere in radiative equilibrium in the Lagrangian frame differs significantly from that of a static photosphere and that, at least, all first-order terms, in particular the advection and aberration terms, have to be included consistently both in the radiative transfer and the energy equation in studies of supernovae atmospheres and other high-speed radiating flows.

The Structure of a Stationary Atmosphere with a Heat Source or Sink

There are several methods for solving a structure of a stellar atmosphere in radiative equilibrium. Among them, the matrix method (Nariai and Shigeyama 1984, Nariai and Ito 1985) uses only the energy equation at the nodes; therefore, it is easy to extend this method to an atmosphere that is not in radiative equilibrium. The matrix method gives direct solutions for the cases of a gray model or a picket–fence model, and it is so effective that the calculation converges in 3 or 4 iterations in the case of a non-gray atmosphere with scattering even if the starting model is isothermal. In order to simplify the problem, in this paper, however, we will limit ourselves to the case of a gray atmosphere with pure absorption.

Analyses of light-ion spectra in stellar atmospheres. III. Nitrogen in the O stars.

view Abstract Citations (86) References (38) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Analyses of light-ion spectra in stellar atmospheres. Mihalas, D. ; Hummer, D. G. Abstract An analysis of the N iii emission lines in 0 stars has been carried out on the basis of a detailed solution of the coupled statistical-equilibrium and transfer equations for a multiline, multilevel, multi-ion ensemble. Our calculations, using static, plane-parallel models reproduce successfully the observed emission at AA4634, 4640, 4641 (3p 2P -3d 2D) and absorption at AA4097, 4103 (3s 2S-3p 2P ). The multiplet is found to come into emission at the observed temperature for both main-sequence and low-gravity objects. The equivalent widths of the emission lines agree very well with those measured for the class of Of stars thought to have compact atmospheres, i.e., those classified as O((f)) by Walborn. In these stars the basic physical mechanism responsible for this phenomenon is the overpopulation of 3d by means of dielectronic recombinations from the low-lying 2s2p(1P )3d autoionizing states with cascades 3d 3p. The 3p state is drained by the "two-electron jumps" coupling 3p to the 2s2p2 (25, 2p, 2D) states, thus preventing emission in the 3s-3p lines. The possible importance of the Swings mechanism to the fully developed Of stars (in Walborn's sense) is pointed out, and the irrelevance of the Bowen mechanism to all Of stars is firmly demonstrated. The fact that the N iii emission lines can be produced in static nonextended atmospheres in radiative equilibrium has the far-reaching significance that the presence of emission lines in a spectrum is not in itself sufficient evidence for the existence of a stellar chromosphere (i.e., an extended, nonradiatively heated region). Subject headings: atmospheres, stellar - emission-line stars line formation Of-type stars Publication: The Astrophysical Journal Pub Date: February 1973 DOI: 10.1086/151919 Bibcode: 1973ApJ...179..827M full text sources ADS | data products SIMBAD (9) Related Materials (3) Part 1: 1972ApJ...177..115M Part 2: 1973ApJ...179..209M Part 4: 1973ApJS...25..433A