Free-free Opacity Research Articles

Opacity calculations for aluminum, hydrogen, and gold using FLYCHK with improved free-free opacity formalism

Opacity is an essential property for understanding the fundamental properties of high-energy-density (HED) and astrophysical plasmas. FLYCHK, a collisional-radiative code, has been used to calculate the opacities of HED plasmas under various conditions because of its simplicity and availability. However, the opacity calculations of FLYCHK have limitations in a strongly coupled region, partly because of the problem of a free-free opacity formalism. In this study, we improved the free-free opacity calculation model of FLYCHK and generated opacities of various materials, including high-Z materials (Al, H, and Au). The FLYCHK opacities were in good agreement over a wide range of conditions with those obtained using the Los Alamos opacity code ATOMIC and the detailed level accounting model.

Few-Femtosecond Dynamics of Free-Free Opacity in Optically Heated Metals

Few-Femtosecond Dynamics of Free-Free Opacity in Optically Heated Metals

Role of opacity at the 9 keV back lighter energy used in measuring the equation of state of boron at pressures up to a Gbar

Many experiments have been conducted at the National Ignition Facility to measure the equation of state Hugoniot of plastic, boron, and diamond at extreme pressures up to a Gbar. The “Gbar” design employs a strong spherically converging shock launched through a solid ball of material using a hohlraum radiation drive. The shock front conditions are characterized using X-ray radiography, typically at energies near 9 keV. In this paper we examine how the opacity of boron at 9 keV changes at high pressures and temperatures. Understanding this is vital to unfolding the density in the shock front as pressures exceed 100 Mbar. We compare opacity calculations from a number of methods including the legacy XSN opacity tables, super transition array (STA), average atom (AVAT), and detailed configuration accounting (DCA) methods. We examine how the changing opacity is correlated with the K-shell occupation calculated using the opacity methods as well as other electronic structure methods such as MECCA, Purgatorio, and an all-electron Kohn-Sham density functional theory calculation that uses optimized all-electron norm-conserving Vanderbilt pseudopotentials (ONCV). We also examine the relative contribution of free-free opacity to the overall opacity, which is dominated by bound-free absorption.

Time-Resolved XUV Opacity Measurements of Warm Dense Aluminum.

The free-free opacity in plasmas is fundamental to our understanding of energy transport in stellar interiors and for inertial confinement fusion research. However, theoretical predictions in the challenging dense plasma regime are conflicting and there is a dearth of accurate experimental data to allow for direct model validation. Here we present time-resolved transmission measurements in solid-density Al heated by an XUV free-electron laser. We use a novel functional optimization approach to extract the temperature-dependent absorption coefficient directly from an oversampled pool of single-shot measurements, and find a pronounced enhancement of the opacity as the plasma is heated to temperatures of order of the Fermi energy. Plasma heating and opacity enhancement are observed on ultrafast timescales, within the duration of the femtosecond XUV pulse. We attribute further rises in the opacity on ps timescales to melt and the formation of warm dense matter.

Ab initio simulations and measurements of the free-free opacity in aluminum.

The free-free opacity in dense systems is a property that both tests our fundamental understanding of correlated many-body systems, and is needed to understand the radiative properties of high energy-density plasmas. Despite its importance, predictive calculations of the free-free opacity remain challenging even in the condensed matter phase for simple metals. Here we show how the free-free opacity can be modelled at finite-temperatures via time-dependent density functional theory, and illustrate the importance of including local field corrections, core polarization, and self-energy corrections. Our calculations for ground-state Al are shown to agree well with experimental opacity measurements performed on the Artemis laser facility across a wide range of extreme ultraviolet wavelengths. We extend our calculations across the melt to the warm-dense matter regime, finding good agreement with advanced plasma models based on inverse bremsstrahlung at temperatures above 10eV.

ASYMMETRIC SHAPES OF RADIO RECOMBINATION LINES FROM IONIZED STELLAR WINDS

Recombination line profile shapes are derived for ionized spherical stellar winds at radio wavelengths. It is assumed that the wind is optically thick owing to free-free opacity. Emission lines of arbitrary optical depth are obtained assuming that the free-free photosphere forms in the outer, constant expansion portion of the wind. Previous works have derived analytic results for isothermal winds when the line and continuum source functions are equal. Here, semi-analytic results are derived for unequal source functions to reveal that line shapes can be asymmetric about line center. A parameter study is presented and applications discussed.

Free-free opacity in dense plasmas with an average atom model

A model for the free-free opacity of dense plasmas is presented. The model uses a previously developed average atom model, together with the Kubo-Greenwood model for optical conductivity. This, in turn, is used to calculate the opacity with the Kramers-Kronig dispersion relations. Comparisons to other methods for dense deuterium results in excellent agreement with DFT-MD simulations, and reasonable agreement with a simple Yukawa screening model corrected to satisfy the conductivity sum rule. Comparisons against the very recent experiments of Kettle et al. for dense aluminum also reveal very good agreement, in contrast to existing models. Weaknesses in the model are also highlighted.

IRON OPACITY BUMP CHANGES THE STABILITY AND STRUCTURE OF ACCRETION DISKS IN ACTIVE GALACTIC NUCLEI

ABSTRACT Accretion disks around supermassive black holes have regions where the Rosseland mean opacity can be larger than the electron scattering opacity due to the large number of bound–bound transitions in iron. We study the effects of this iron opacity “bump” on the thermal stability and vertical structure of radiation-pressure-dominated accretion disks, utilizing three-dimensional radiation magnetohydrodynamic (MHD) simulations in the local shearing box approximation. The simulations self-consistently calculate the heating due to MHD turbulence caused by magneto-rotational instability and radiative cooling by using the radiative transfer module based on a variable Eddington tensor in Athena. For a 5 × 108 solar mass black hole with ∼3% of the Eddington luminosity, a model including the iron opacity bump maintains its structure for more than 10 thermal times without showing significant signs of thermal runaway. In contrast, if only electron scattering and free–free opacity are included as in the standard thin disk model, the disk collapses on the thermal timescale. The difference is caused by a combination of (1) an anti-correlation between the total optical depth and the midplane pressure, and (2) enhanced vertical advective energy transport. These results suggest that the iron opacity bump may have a strong impact on the stability and structure of active galactic nucleus (AGN) accretion disks, and may contribute to a dependence of AGN properties on metallicity. Since this opacity is relevant primarily in UV emitting regions of the flow, it may help to explain discrepancies between observation and theory that are unique to AGNs.

Limit to the radio emission from a putative central compact source in SN1993J

SN1993J in M81 is the best studied young radio-luminous supernova in the Northern Hemisphere. We recently reported results from the analysis of a complete set of VLBI observations of this supernova at 1.7, 2.3, 5.0, and 8.4 GHz, covering a time baseline of more than one decade. Those reported results were focused on the kinematics of the expanding shock, the particulars of its evolving non-thermal emission, the density profile of the circumstellar medium, and the evolving free-free opacity by the supernova ejecta. In the present paper, we complete our analysis by performing a search for any possible signal from a compact source (i.e., a stellar-mass black hole or a young pulsar nebula) at the center of the expanding shell. We have performed a stacking of all our VLBI images at each frequency, after subtraction of our best-fit shell model at each epoch, and measured the peak intensity in the stacked residual image. Given the large amount of available global VLBI observations, the stacking of all the residual images allows us to put upper limits to the eventual emission of a putative compact central source at the level of $\sim102$ $\mu$Jy at 5 GHz (or, more conservatively, $\sim192$ $\mu$Jy, if we make a further correction for the ejecta opacity) and somewhat larger at other wavelengths.

THE IONIZED CIRCUMSTELLAR ENVELOPES OF ORION SOURCE I AND THE BECKLIN-NEUGEBAUER OBJECT

The 229 GHz (lambda 1.3mm) radio emission from Orion-KL was mapped with up to 0.14" angular resolution with CARMA, allowing measurements of the flux densities of Source I ('SrcI') and the Becklin-Neugebauer Object (BN), the 2 most massive stars in this region. We find integrated flux densities of 310 +/- 45 mJy for SrcI and 240 +/- 35 mJy for BN. SrcI is optically thick even at 229 GHz. No trace of the H30alpha recombination line is seen in its spectrum, although the v_2=1, 5(5,0)-6(4,3) transition of H2O, 3450 K above the ground state, is prominent. SrcI is elongated at position angle 140 degrees, as in 43 GHz images. These results are most easily reconciled with models in which the radio emission from SrcI arises via the H- free-free opacity in a T < 4500 K disk, as considered by Reid et al. (2007). By contrast, the radio spectrum of BN is consistent with p+/e- free-free emission from a dense (n_e ~ 5x10^7 cm^{-3}), but otherwise conventional, hypercompact HII region. The source is becoming optically thin at 229 GHz, and the H30alpha recombination line, at VLSR = 23.2 +/- 0.5 km/sec, is prominent in its spectrum. A Lyman continuum flux of 5x10^{45} photons/sec, consistent with that expected from a B star, is required to maintain the ionization. Supplementary 90 GHz observations were made to measure the H41alpha and H42alpha recombination lines toward BN. Published 43 and 86 GHz data suggest that SrcI brightened with respect to BN over the 15 year period from 1994 to 2009.

MAGNETIZED NEUTRON STAR ATMOSPHERES: BEYOND THE COLD PLASMA APPROXIMATION

All the neutron star (NS) atmosphere models published so far have been calculated in the "cold plasma approximation", which neglects the relativistic effects in the radiative processes, such as cyclotron emission/absorption at harmonics of cyclotron frequency. Here we present new NS atmosphere models which include such effects. We calculate a set of models for effective temperatures T_eff =1-3 MK and magnetic fields B \sim 10^{10}-10^{11} G, typical for the so-called central compact objects (CCOs) in supernova remnants, for which the electron cyclotron energy E_{c,e} and its first harmonics are in the observable soft X-ray range. Although the relativistic parameters, such as kT_eff /(m_e c^2) and E_{c,e} /(m_e c^2), are very small for CCOs, the relativistic effects substantially change the emergent spectra at the cyclotron resonances, E \approx sE_{c,e} (s=1, 2,...). Although the cyclotron absorption features can form in a cold plasma due to the quantum oscillations of the free-free opacity, the shape and depth of these features change substantially if the relativistic effects are included. In particular, the features acquire deep Doppler cores, in which the angular distribution of the emergent intensity is quite different from that in the cold plasma approximation. The relative contributions of the Doppler cores to the equivalent widths of the features grow with increasing the quantization parameter b_eff = E_{c,e}/kT_eff and harmonic number s. The total equivalent widths of the features can reach \sim 150-250 eV; they increase with growing b_eff and are smaller for higher harmonics.

Cyclotron harmonics in opacities of isolated neutron star atmospheres

Some of X-ray dim isolated neutron stars (XDINS) and central compact objects in supernova remnants (CCO) show absorption features in their thermal soft X-ray spectra. It has been hypothesized that these features could be due to the periodic peaks in free-free absorption opacities, caused by either Landau quantization of electron motion in magnetic fields B<10^{11} G or analogous quantization of ion motion in magnetic fields B>10^{13} G. Here, I review the physics behind cyclotron quantum harmonics in free-free photoabsorption, discuss different approximations for their calculation, and explain why the ion cyclotron harmonics (beyond the fundamental) cannot be observed.

QUANTUM NATURE OF CYCLOTRON HARMONICS IN THERMAL SPECTRA OF NEUTRON STARS

Some isolated neutron stars show harmonically spaced absorption features in their thermal soft X-ray spectra. The interpretation of the features as a cyclotron line and its harmonics has been suggested, but the usual explanation of the harmonics as caused by relativistic effects fails because the relativistic corrections are extremely small in this case. We suggest that the features correspond to the peaks in the energy dependence of the free-free opacity in a quantizing magnetic field, known as quantum oscillations. The peaks arise when the transitions to new Landau levels become allowed with increasing the photon energy; they are strongly enhanced by the square-root singularities in the phase-space density of quantum states in the case when the free (non-quantized) motion is effectively one-dimensional. To explore observable properties of these quantum oscillations, we calculate models of hydrogen neutron star atmospheres with B \sim 10^{10} - 10^{11} G (i.e., electron cyclotron energy E_{c,e} = 0.1 - 1 keV) and T_{eff} = 1 - 3 MK. Such conditions are thought to be typical for the so-called central compact objects in supernova remnants, such as 1E 1207.4-5209 in PKS 1209-51/52. We show that observable features at the electron cyclotron harmonics form at moderately large values of the quantization parameter, b_{eff} = E_{c,e}/kT_{eff} = 0.5 - 20. The equivalent widths of the features can reach 100 - 200 eV; they grow with increasing b_{eff} and are lower for higher harmonics.

THE SUB-PARSEC SCALE RADIO PROPERTIES OF SOUTHERN STARBURST GALAXIES. II. SUPERNOVA REMNANTS, THE SUPERNOVA RATE, AND THE IONISED MEDIUM IN THE NGC 4945 STARBURST

Wide-field VLBI observations of the nearby starburst galaxy NGC 4945, obtained with the Australian LBA, have produced 2.3 GHz images over two epochs with a maximum spatial resolution of 0.3 pc. 15 sources were detected, 13 of which correspond to sources identified in higher frequency (3 cm and 12 mm) ATCA images. Four of the sources are resolved into shell-like structures ranging between 1.1 to 2.1 pc in diameter. From these data the spectra of 13 compact radio sources in NGC 4945 were modelled; nine were found to be consistent with free-free absorbed power laws and four with a simple power law spectrum. The free-free opacity is highest toward the nucleus but varies significantly throughout the nuclear region, implying that the overall structure of the ionised medium is clumpy. Of the 13 sources, 10 have steep intrinsic spectra associated with synchrotron emission from supernova remnants, the remaining sources have flat intrinsic spectra which may be associated with thermal radio emission. A non-thermal source with a jet-like morphology is detected ~1" from the assumed location of the AGN. A type II supernova (SN) rate upper limit of 15.3/yr is determined for the inner 250 pc region of the galaxy at the 95% confidence level, based on the lack of detection of new sources in observations spanning 1.9 years and a simple model for the evolution of supernova remnants. A type II SN rate of >0.1(v/1e4)/yr is implied from estimates of supernova remnant source counts, sizes and expansion rates, where v is the radial expansion velocity of the supernova remnant in km/s. A SFR of 2.4(v/1e4)<SFR(M>=5Msun)<370 Msun/yr has been estimated directly from the SN rate limits and is of the same order of magnitude as rates determined from integrated FIR and radio luminosities.

Positional Coincidence of H2O Maser and a Plasma‐Obscuring Torus in Radio Galaxy NGC 1052

We present multifrequency simultaneous VLBA observations at 15, 22, and 43 GHz toward the nucleus of the nearby radio galaxy NGC 1052. These three continuum images reveal a double-sided jet structure whose relative intensity ratios imply that the jet axis is oriented close to the sky plane. The steeply rising spectra at 15-43 GHz at the inner edges of the jets strongly suggest that synchrotron emission is absorbed by foreground thermal plasma. We detected H2O maser emission in the velocity range of 1550-1850 km s−1, which is redshifted by 50-350 km s−1 with respect to the systemic velocity of NGC 1052. The redshifted maser gas appears projected against both sides of the jet, in the same manner as the H I seen in absorption. The H2O maser gas is located where the free-free absorption opacity is large. This probably implies that the masers in NGC 1052 are associated with a circumnuclear torus or disk as in the nucleus of NGC 4258. Such circumnuclear structure could be the source of accretion onto the central engine.

Imaging the Ionized Disk of the High‐Mass Protostar Orion I

We have imaged the enigmatic radio source-I (Orion-I) in the Orion-KL nebula with the VLA at 43 GHz with 34 mas angular resolution. The continuum emission is highly elongated and is consistent with that expected from a nearly edge-on disk. The high brightness and lack of strong molecular lines from Orion-I can be used to argue against emission from dust. Collisional ionization and H-minus free-free opacity, as in Mira variables, require a central star with >10^5 Lsun, which is greater than infrared observations allow. However, if significant local heating associated with accretion occurs, lower total luminosities are possible. Alternatively, photo-ionization from an early B-type star and p+/e- bremsstrahlung can explain our observations, and Orion-I may be an example of ionized accretion disk surrounding a forming massive star. Such accretion disks may not be able to form planets efficiently.

Simultaneous Multi-Wavelength Spectrum of Sgr A* and Long Wavelength Cutoff at λ > 30 cm

We reviewed the multiple-wavelength spectrum of Sgr A*. The recent continuum spectrum was determined using data obtained from the Very Large Array (VLA), the Giant Metrewave Radio Telescope (GMRT), the Submillimeter Array (SMA) and the Keck II 10m telescope on the same date (2003 June 17). The nearly simultaneous spectrum (S∝ λα) covers a broad wavelength (A) range from 90 cm to 3.8 micron. From about 2 cm to 1 mm, the source shows a rising spectrum with a spectral index of α = 0.43 ± 0.04. However, the IR, measurements suggested that the flux density of Sgr A* must drastically drop towards the shorter wavelengths and the turnover likely occurs in the submillimeter regime. The spectrum at wavelengths between 47 and 3.6 cm is flat with α = 0.11 ± 0.03. The flux density of Sgr A* is 0.22±0.06 Jy at 90 cm on this date in 2003. Compared with measurement at 47 cm, the flux density at 90 cm has decreased by a factor of two (or ∼ 4σ), suggesting a cutoff at wavelength longer than 47 cm. The fits using free-free absorption opacity to the spectrum suggest a cutoff wavelength at ∼ 100 cm. The cutoff wavelength appears to be three times longer than that of ∼ 30 cm determined by Davies, Walsh, & Booth [1] three decades ago based on observations in 1974 and 1975. A model interpreting the variation of the long wavelength cutoff using stellar winds (An et al. [2]) is summarized in this paper.

Relativistic Accretion Disk Models of High‐State Black Hole X‐Ray Binary Spectra

We present calculations of non-LTE, relativistic accretion disk models applicable to the high/soft state of black hole X-ray binaries. We include the effects of thermal Comptonization and bound-free and free-free opacities of all abundant ion species. We present spectra calculated for a variety of accretion rates, black hole spin parameters, disk inclinations, and stress prescriptions. We also consider nonzero inner torques on the disk, and explore different vertical dissipation profiles, including some which are motivated by recent radiation MHD simulations of magnetorotational turbulence. Bound-free metal opacity generally produces significantly less spectral hardening than previous models which only considered Compton scattering and free-free opacity. It also tends to keep the effective photosphere near the surface, resulting in spectra which are remarkably independent of the stress prescription and vertical dissipation profile, provided little dissipation occurs above the effective photosphere. We provide detailed comparisons between our models and the widely used multicolor disk model. Frequency dependent discrepancies exist that may affect the parameters of other spectral components when this simpler disk model is used to fit modern X-ray data. For a given source, our models predict that the luminosity in the high/soft state should approximately scale with the fourth power of the empirically inferred maximum temperature, but with a slight hardening at high luminosities. This is in good agreement with observations. (abridged)

Mm-wave HCO+, HCN and CO absorption toward NGC 1052

We used the Plateau de Bure Interferometer to observe λ 3 mm $J=1{-}0$ absorption lines of HCO + , HCN and CO toward the core of the nearby elliptical, megamaser-host galaxy NGC 1052. The lines are relatively weak, with peak optical depths 0.03 for HCO + and HCN and 0.1 for CO. Nonetheless the inferred column density of molecular gas 2 N (H 2 ) $\simeq$ 5 $\times$ $10^{21}~{\rm cm}^{-2}$ is consistent with the degree of reddening inferred toward the nucleus from observations of the Balmer series of hydrogen. Mm-wave absorption line profiles are somewhat broader than those of H I and OH, perhaps because lower free-free opacity at mm-wavelengths exposes higher-velocity material nearer the nucleus. Overall, the OH/HCO + ratio in NGC 1052 is as expected from the strong relationship established in local diffuse clouds but the optical depth ratio varies strongly over the line profiles. Similar variations are also seen toward Cen A, which has very different line ratios among H I, OH and HCO + for very nearly the same amount of OH absorption.

Optically thick clumps – not the solution to the Wolf-Rayet wind momentum problem?

The hot star wind momentum problem is revisited, and it is shown that the conventional belief, that it can be solved by a combination of clumping of the wind and multiple scattering of photons, is not self-consistent for optically thick clumps. Clumping does reduce the mass loss rate , and hence the momentum supply, required to generate a specified radio emission measure ε, while multiple scattering increases the delivery of momentum from a specified stellar luminosity L. However, in the case of thick clumps, when combined the two effects act in opposition rather than in unison since clumping reduces multiple scattering. From basic geometric considerations, it is shown that this reduction in momentum delivery by clumping more than offsets the reduction in momentum required, for a specified ε. Thus the ratio of momentum deliverable to momentum required is maximal for a smooth wind and the momentum problem remains for the thick clump case. In the case of thin clumps, all of the benefit of clumping in reducing η lies in reducing for a given ε so that extremely small filling factors are needed. It is also shown that clumping affects the inference of from radio ε not only by changing the emission measure per unit mass but also by changing the radio optical depth unity radius , and hence the observed wind volume, at radio wavelengths. In fact, for free-free opacity , contrary to intuition, increases with increasing clumpiness.