Effects of clumping on temperature – I. Externally heated clouds

We present a study of radiative transfer in dusty, clumpy star-forming regions. A series of self-consistent, 3D, continuum radiative transfer models are constructed for a grid of models parametrized by central luminosity, filling factor, clump radius and face-averaged optical depth. The temperature distribution within the clouds is studied as a function of this parametrization. Among our results, we find that: (i) the effective optical depth in clumpy regions is less than in equivalent homogeneous regions of the same average optical depth, leading to a deeper penetration of heating radiation in clumpy clouds, and temperatures higher by over 60 per cent; (ii) penetration of radiation is driven by the fraction of open sky (FOS) – which is a measure of the fraction of solid angle along which no clumps exist; (iii) FOS increases as clump radius increases and as filling factor decreases; (iv) for values of   FOS >0.6–0.8  the sky is sufficiently 'open' that the temperature distribution is relatively insensitive to FOS; (v) the physical process by which radiation penetrates is preferentially through streaming of radiation between clumps as opposed to diffusion through clumps; (vi) filling factor always dominates the determination of the temperature distribution for large optical depths, and for small clump radii at smaller optical depths; (vii) at lower face-averaged optical depths, the temperature distribution is most sensitive to filling factors of 1–10 per cent, in accordance with many observations; (viii) direct shadowing by clumps can be important for distances approximately one clump radius behind a clump.     

The effect of mechanical waves on empirical solar models

Empirical solar models contain the effect of heating due to radiative energy loss from acoustic waves. We estimate here the temperature difference between the radiative equilibrium model and the empirical model. At optical depth ₅₀₀₀ = 0.1 this difference is small, but near the temperature minimum (₅₀₀₀ = 10^–4) it reaches between 53 and 83 K. The temperature difference between the equator and the poles caused by a hypothetical difference in the heating is estimated.     

Low-latitude thermal structure of Jupiter in the region 0.1–5 bars

The radiative heat flux from 0.1 to 10 bars is estimated on the basis of a “two-cloud” scattering model that fits available spectral data and Pioneer photometry. Deeper than a few bars, the flux is 4.5 W m^?2, compared with the 18.8 W m^?2 used in an earlier study by Trafton and Stone. A temperature profile is computed, with the H₂ pressure-induced opacity; the temperature at 1 bar is found to be 156°K, rather than the commonly accepted 170°K. An additional optical depth of unity at the 0.67-bar level could restore the conventional value; otherwise a considerably cooler atmosphere is a serious possibility.     

Near-surface winds at the Huygens site on Titan: Interpretation by means of a general circulation model

This study aims at interpreting the zonal and meridional wind in Titan's troposphere measured by the Huygens probe by means of a general circulation model. The numerical simulation elucidates the relative importance of the seasonal variation in the Hadley circulation and Saturn's gravitational tide in affecting the actual wind profile. The observed reversal of the zonal wind at two altitudes in the lower troposphere can be reproduced with this model only if the near-surface temperature profile is asymmetric about the equator and substantial seasonal redistribution of angular momentum by the variable Hadley circulation takes place. The meridional wind near the surface is mainly caused by the meridional pressure gradient and is thus a manifestation of the Hadley circulation. Southward meridional wind in the PBL (planetary boundary layer) is consistent with the near-surface temperature at the equator being lower than at mid southern latitudes. Even small changes in the radiative heating profile in the troposphere can substantially affect the mean zonal and meridional wind including their direction. Saturn's gravitational tide is rather weak at the Huygens site due to the proximity to the equator, and does not clearly manifest itself in the instantaneous vertical profile of wind. Nevertheless, the simulated descent trajectory is more consistent with the observation if the tide is present. Because of a different force balance in Titan's atmosphere from terrestrial conditions, PBL-specific wind systems like on Earth are unlikely to exist on Titan.     

Interpretation of the solar continuum from 1680 to 600 Å. Model of the transition region photosphere-chromosphere and of the chromosphere

An interpretation is given of the observations of the continuous solar radiation in the spectral range 600–1700 Å. The model allows for deviations from LTE of H, C, Si and S, and is in hydrostatic equilibrium. The predicted intensity from 1680 to 1520 Å has virtually no dependence on the electron temperature variation in the optical depth range 10^–3–4 × 10^–5, at 5000 Å; the brightness temperature is compatible with a low electronic temperature minimum near the optical depth 10^–4. The model of the low chromosphere is characterized by a steep temperature gradient. The model satisfies observations at millimeter wavelengths.     

Exact solution of a problem in a stellar atmosphere using the Laplace transform and the Wiener-Hopf technique

The general equation for radiative transfer of line scattering intensity — including the effects of scattering, absorption and thermal emission — in the Milne-Eddington model is considered here. The scattering function is assumed to be quadratically anisotropic in the cosine of the scattering angle, and Planck's intensity function is assumed for thermal emission. The exact solutions for emergent intensity from the bounding face and the intensity at any optical depth are obtained by the method of the Laplace transform in combination with the Wiener-Hopf technique.     

Speckle imaging of Titan at 2 microns: surface albedo, haze optical depth, and tropospheric clouds 1996-1998

We present results from 14 nights of observations of Titan in 1996-1998 using near-infrared (centered at 2.1 microns) speckle imaging at the 10-meter W.M. Keck Telescope. The observations have a spatial resolution of 0.06 arcseconds. We detect bright clouds on three days in October 1998, with a brightness about 0.5% of the brightness of Titan. Using a 16-stream radiative transfer model (DISORT) to model the central equatorial longitude of each image, we construct a suite of surface albedo models parameterized by the optical depth of Titan's hydrocarbon haze layer. From this we conclude that Titan's equatorial surface albedo has plausible values in the range of 0-0.20. Titan's minimum haze optical depth cannot be constrained from this modeling, but an upper limit of 0.3 at this wavelength range is found. More accurate determination of Titan's surface albedo and haze optical depth, especially at higher latitudes, will require a model that fully considers the 3-dimensional nature of Titan's atmosphere.     

The Effect of Radiative Efficiency on the Growth of the Black Hole Mass

The effect of variation of radiative efficiency on the growth of the black hole mass is discussed. In the process of accretion, the black hole's angular momentum varies, resulting in a variation of the radiative efficiency, and the growth of the black hole mass is thereby affected. For the exponential growth model of back holes and taking into account the effect of a varying radiative efficiency, the equation for the growth of the black hole mass is solved numerically. Compared to the model that assumes a constant radiative efficiency, the result indicates that variation of radiative efficiency has a marked, retarding effect on the growth of the black hole mass. This model can explain quantitatively some recent observational results.     

An investigation of possible causes of the holes in the condensational Venus cloud using a microphysical cloud model with a radiative-dynamical feedback

Near-infrared observations of the nightside of Venus reveal regions of high brightness temperatures. These regions of high brightness temperatures are caused by the localized evaporation of the middle and lower cloud decks, which are about 50 to 60 km above the surface of the planet. We simulate the Venus condensational middle and lower cloud deck with the University of Colorado/NASA Ames Community Aerosol and Radiation Model for Atmospheres (CARMA). Our simulated clouds have similar characteristics to the observed Venus clouds. Our radiative transfer model reproduces the observed temperature structure and atmospheric stability structure within the middle cloud region. A radiative-dynamical feedback occurs which generates mixing due to increased absorption of upwelling infrared radiation within the lower cloud region, as previously suggested by others. We find that localized variations in temperature structure or in sub-grid scale mixing cannot directly explain the longevity and optical depth of the clouds. However, vertical motions are capable of altering the cloud optical depth by a sufficient magnitude in a short enough timescale to be responsible for the observed clearings.     

A model for the dust envelope of V1853 Cygni

We computed a model for the dust envelope of the protoplanetary nebula V1853 Cyg by using data on its fluxes from the ultraviolet to the far infrared. The spherically symmetric envelope was assumed to be composed of silicate grains with the standard MRN size distribution; their number per unit volume is inversely proportional to the distance squared. The optical depth of the envelope, whose inner boundary lies at a distance of 7.6×10¹⁶ cm from the central star, is 0.18 at a wavelength of 0.55 μm. The grain temperature at the inner boundary of the envelope is 110 K. The distance to V1853 Cyg is estimated to be 4.1 kpc. The current mass-loss rate of the object was found by solving a self-consistent problem of radiative transfer and dust motion in the envelope to be 2.2 × 10^?5M_⊙ yr^?1.     

A method of analysing the emission lines of solar prominences

A new method of analysing the emission spectrum of solar prominences is presented, in which the source function is allowed to vary with optical depth. Least-squares fitting of the observed profile determines simultaneously the optical depth τ₀, the Doppler width Δλ_D and the factor characterising the variation of the source function. This method is applied to the early Balmer lines in ten prominences of Ref. [1]. The results show that the source function of the self-reversed H line increases towards the centre of the prominence, the value at the centre is 1.2–2.5 times the value at the edge. Neglect of this variation will give too large values of τ₀. The degree of attenuation by selfabsorption also depends on this variation. Discussion of the variation gives support to the view that the main exciting mechanism in solar prominences is the scattering of the incident radiation.     

Suppositions for the Comparison of Infrared Spectra from Terrestrial Silicates with Interstellar Spectra and the Selection of Suitable Silicates (Mitteilungen der Universitäts-Sternwarte zu Jena Nr. 149)

The influence of potassium bromide on the bands near 10 μm, 18 μm and 33 μm was calculated for any silicate. The wavelength shift, the deepening, and the broadening of the bands were calculated for different band's depths of each band. The results were applied on the investigation of an extensive catalogue of silicate spectra, which were got on the basis of the KBr pressing technique too. So it was possible to picle out those silicates from the variety of silicates, which are probable candidates for the interstellar silicate component.     

Dissipation of Titan's north polar cloud at northern spring equinox

Saturn's Moon Titan has a thick atmosphere with a meteorological cycle. We report on the evolution of the giant cloud system covering its north pole using observations acquired by the Visual and Infrared Mapping Spectrometer onboard the Cassini spacecraft. A radiative transfer model in spherical geometry shows that the clouds are found at an altitude between 30 and 65 km. We also show that the polar cloud system vanished progressively as Titan approached equinox in August 2009, revealing at optical wavelengths the underlying sea known as Kraken Mare. This decrease of activity suggests that the north-polar downwelling has begun to shut off. Such a scenario is compared with the Titan global circulation model of Rannou et al. (2006), which predicts a decrease of cloud coverage in northern latitudes at the same period of time.     

Thermal radiation from impact plumes

Plumes produced by the impacts of asteroids and comets consist of rock vapor and heated air. They emit visible light, ultraviolet, and infrared radiation, which can greatly affect the environment. We have carried out numerical simulations of the impacts of stony and cometary bodies with a diameter of 0.3, 1, and 3 km, which enter the atmosphere at various angles, using a hydrodynamic model supplemented by radiation transfer. We assumed that the cosmic object has no strength, and deforms, fragments, and vaporizes in the atmosphere. After the impact on the ground, the formation of craters and plumes was simulated, taking the internal friction of destroyed rocks and the trail formed in the atmosphere into account. The equation of radiative transfer, added to the equations of gas dynamics, was used in the approximation of radiative heat conduction or, if the Rosseland optical depth of a radiating volume of gas and vapor was less than unity, in the volume‐emission approximation. We used temperature and density distributions obtained in these simulations to calculate radiation fluxes on the Earth's surface by integrating the equation of radiative transfer along rays passing through a luminous region. We used tables of the equation of state of dunite and quartz (for stony impactors and a target) and air, as well as tables of absorption coefficients of air, vapor of ordinary chondrite, and vapor of cometary material. We have calculated the radiation impulse on the ground and the impact radiation efficiency (a ratio of thermal radiation energy incident on the ground to the kinetic energy of a body), which ranges from ~0.5% to ~9%, depending on the impactor size and the angle of entry into the atmosphere. Direct thermal radiation from fireballs and impact plumes, poses a great danger to people, animals, plants, and economic objects. After the impacts of asteroids at a speed of 20 km s^?1 at an angle of 45°, a fire can occur at a distance of 250 km if the asteroid has a diameter of 0.3 km, and at a distance of 2000 km if the diameter is 3 km.     

Hot accretion discs with thermal Comptonization and advection in luminous black hole sources

We solve for the structure of a hot accretion disc with unsaturated thermal Comptonization of soft photons and with advection, generalizing the classical model of Shapiro et al. The upper limit on the accretion rate due to advection constrains the luminosity to ≲ 0.15 y^3/5 α^7/5 of the Eddington limit, where y and α are the Compton and viscosity parameters, respectively. The characteristic electron temperature and Thomson optical depth of the inner flow at accretion rates within an order of magnitude of that upper limit are ∼ 10⁹ K and ∼ 1, respectively. The resulting spectra are then in close agreement with the X-ray and soft γ-ray spectra from black hole binaries in the hard state and Seyferts. At low accretion rates, bremsstrahlung becomes the dominant radiative process.     

Thermal structure of the Martian atmosphere during the dissipation of the dust storm of 1971

The secular variation of the thermal structure of the Martian atmosphere during the dissipation phase of the 1971 dust storm is examined, using temperatures obtained by the infrared spectroscopy investigation on Mariner 9. For the latitude range ?20° to ?30°, the mean temperature at the 2mbar level is found to decrease from approximately 220 K in mid-December 1971 to about 190 K by June 1972 while for the 0.3mbar level a decrease from 203 K to 160 K is observed. Over the same period, the amplitude of the diurnal temperature wave also decreased. Assuming a simplified radiative heating model, the dust optical depth is found to decrease approximately exponentially with an e-folding time of about 60 days at both the 0.3 and 2mbar levels. Stokes-Cunningham settling alone cannot account for this behavior. Sedimentation models which include both gravitational settling and vertical mixing are developed in an effort to explain the time evolution of the dust. Within the framework of a model which assumes an effective vertical diffusivity K independent of height, a mean dust particle diameter of ～2 μm is inferred. To provide the necessary vertical mixing, K ? 10⁷ cm²sec^?1 is required in the lower atmosphere.     

Microlensing of tidal debris on the Magellanic great circle

Increasing evidence suggests that the Galactic halo is lumpy on kpc scales as a result of the accretion of at least a dozen small galaxies [Large and Small Magellanic Clouds (LMC/SMC), Sgr, Fornax, etc.]. Faint stars in such lumpy structures can significantly microlense a background star with an optical depth of 10⁻⁷–10⁻⁶, which is comparable to the observed value to the LMC. The observed microlensing events towards the LMC can be explained by a tidal debris tail from the progenitor of the Magellanic Clouds and Magellanic Stream. The LMC stars can either lense stars in the debris tail a few kpc behind the LMC, or be lensed by stars in the part of the debris tail in front of the LMC. The models are consistent with an elementary particle dominated Galactic halo without massive compact halo objects (MACHOs). They also differ from Sahu's LMC-self-lensing model by predicting a higher optical depth and event rate and lower concentration of events to the LMC centre.     

Circumstellar dust shells around very young and massive stars

In this paper we investigate the properties of dust in circumstellar shells around very young massive compact IR sources (Becklin-Neugebauer objects).We found no correlation between the optical depth in the centre of the 10-m band and the 3.1-m ice band. An inverse correlation between the strength of the silicate feature and the colour temperature for the 8–13 m interval was detected. Our sample of BN objects extends this kind of relation already known for Mira stars and OH/IR stars to higher optical depths.We present a radiative transfer model for BN objects and discuss its main properties. Using this model, the interpretation of the observations led to the conclusion that the type of silicates present in the dust shells of very young stellar objects is different from that type around oxygen-rich giants and supergiants. These different silicates may be tentatively identified with pyroxenes and olivines, respectively.We studied the influence of the adopted dust model in deriving source parameters of BN objects. The object W3-IRS5 was discussed in some detail.Paper presented at a Workshop on The Role of Dust in Dense Regions of Interstellar Matter, held at Georgenthal, G.D.R., in March 1986.     

The optical depth sensor (ODS) for column dust opacity measurements and cloud detection on martian atmosphere

A lightweight and sophisticated optical depth sensor (ODS) able to measure alternatively scattered flux at zenith and the sum of the direct flux and the scattered flux in blue and red has been developed to work in martian environment. The principal goals of ODS are to perform measurements of the daily mean dust opacity and to retrieve the altitude and optical depth of high altitude clouds at twilight, crucial parameters in the understanding of martian meteorology. The retrieval procedure of dust opacity is based on the use of radiative transfer simulations reproducing observed changes in the solar flux during the day as a function of 4 free parameters: dust opacity in blue and red, and effective radius and effective width of dust size distribution. The detection of clouds is undertaken by looking at the time variation of the color index (CI), defined as the ratio between red and blue ODS channels, at twilight. The retrieval of altitude and optical depth of clouds is carried out using a radiative transfer model in spherical geometry to simulate the CI time variation at twilight. Here the different retrieval procedures to analyze ODS signals, as well as the results obtained in different sensitivity analysis are presented and discussed.     

Self-gravity wakes and radial structure of Saturn's B ring

We analyze stellar occultations by Saturn's rings observed with the Cassini Ultraviolet Imaging Spectrograph and find large variations in the apparent normal optical depth of the B ring with viewing angle. The line-of-sight optical depth is roughly independent of the viewing angle out of the ring plane so that optical depth is independent of the path length of the line-of-sight. This suggests the ring is composed of virtually opaque clumps separated by nearly transparent gaps, with the relative abundance of clumps and gaps controlling the observed optical depth. The observations can be explained with a model of self-gravity wakes like those observed in the A ring. These trailing spiral density enhancements are due to the competing processes of self-gravitational accretion of ring particles and Kepler shear. The B ring wakes are flatter and more closely packed than their neighbors in the A ring, with height-to-width ratios <0.1 for most of the ring. The self-gravity wakes are seen in all regions of the B ring that are not opaque. The observed variation in total B ring optical depth is explained by the amount of relatively empty space between the self-gravity wakes. Wakes are more tightly packed in regions where the apparent normal optical depth is high, and the wakes are more widely spaced in lower optical depth regions. The normal optical depth of the gaps between the wakes is typically less than 0.5 and shows no correlation with position or overall optical depth in the ring. The wake height-to-width ratio varies with the overall optical depth, with flatter, more tightly packed wakes as the overall optical depth increases. The highly flattened profile of the wakes suggests that the self-gravity wakes in Saturn's B ring correspond to a monolayer of the largest particles in the ring. The wakes are canted to the orbital direction in the trailing sense, with a trend of decreasing cant angle with increasing orbital radius in the B ring. We present self-gravity wake properties across the B ring that can be used in radiative transfer modeling of the ring. A high radial resolution (∼10 m) scan of one part of the B ring during a grazing occultation shows a dominant wavelength of 160 m due to structures that have zero cant angle. These structures are seen at the same radial wavelength on both ingress and egress, but the individual peaks and troughs in optical depth do not match between ingress and egress. The structures are therefore not continuous ringlets and may be a manifestation of viscous overstability.