Two-dimensional Radiative Transfer Modeling Research Articles

Temporal Evolution of Titan’s Stratospheric Temperatures and Trace Gases from a Two-dimensional Retrieval of Cassini Composite Infrared Spectrometer Data

We use a two-dimensional (2D) radiative transfer model of Titan, which allows the atmospheric structure to vary in both altitude and latitude, to retrieve the spatial distribution of temperature, haze extinction, and C2H2, C2H6, C3H8, CH3C2H, C4H2, and HCN gases, from Cassini Composite Infrared Spectrometer (CIRS) limb-mapping observations over the duration of the Cassini mission. We compare our results with previous analyses of CIRS limb observations using radiative models that only allow the atmosphere to vary in altitude. The temperature, haze, and gas composition retrieved with the 2D model mostly show the same broad spatial and temporal trends as previously published results from 1D models. However, there are some significant differences in the retrieved structure at the fall and winter poles poleward of 60°. Most noticeably, the HCN abundance in the depleted region near 65°N at 350 km in northern winter is stronger in the 2D retrievals than in previous 1D retrievals, and the 2D retrievals show very different structure from earlier 1D retrievals in the north polar C2H2 structure during early northern spring, with a strong depletion around 70°N at 0.02 mbar.

Flare kernels may be smaller than you think: modelling the radiative response of chromospheric plasma adjacent to a solar flare

ABSTRACT Numerical models of solar flares typically focus on the behaviour of directly heated flare models, adopting magnetic-field-aligned, plane-parallel methodologies. With high spatial- and spectral-resolution ground-based optical observations of flares, it is essential also to understand the response of the plasma surrounding these strongly heated volumes. We investigate the effects of the extreme radiation field produced by a heated column of flare plasma on an adjacent slab of chromospheric plasma, using a two-dimensional radiative transfer model and considering the time-dependent solution to the atomic level populations and electron density throughout this model. The outgoing spectra of H α and Ca ii 854.2 nm synthesized from our slab show significant spatial-, time-, and wavelength-dependent variations (both enhancements and reductions) in the line cores, extending of the order of 1 Mm into the non-flaring slab due to the incident transverse radiation field from the flaring boundary. This may lead to significant overestimates of the sizes of directly heated flare kernels, if line-core observations are used. However, the radiation field alone is insufficient to drive any significant changes in continuum intensity, due to the typical photospheric depths at which they form, so continuum sources will not have an apparent increase in size. We show that the line formation regions near the flaring boundary can be driven upwards in altitude by over 1 Mm despite the primary thermodynamic parameters (other than electron density) being held horizontally uniform. This work shows that in simple models these effects are significant and should be considered further in future flare modelling and interpretation.

Two-dimensional model for the martian exosphere: Applications to hydrogen and deuterium Lyman α observations

The analysis of Lyman α observations in the exosphere of Mars has become limited by the assumption of spherical symmetry in the modeling process, as the models are being used to analyze increasingly detailed measurements. In order to overcome this limitation, a two-dimensional density model is presented, which better emulates the density distribution of deuterium and hydrogen atoms in the exosphere of Mars. A two-dimensional radiative transfer model developed in order to simulate multiple scattering of solar Lyman α photons by an asymmetric, non-isothermal hydrogen exosphere, is also presented here. The models incorporate changes in density and temperature structure of the martian atmosphere with radial distance and solar zenith angle. The 2-D models were applied to the MAVEN-IUVS echelle observations of deuterium and hydrogen Lyman α as well as HST Lyman α observations of hydrogen at Mars. The asymmetric 2-D model provided better fits to the data and smaller thermal escape rates in comparison to the symmetric 1-D model for the exosphere of Mars. However, intensity differences between both models became small above ~2.5 martian radii indicating that the exosphere of Mars approaches spherical symmetry at higher altitudes, in agreement with earlier studies. In addition, a new cross calibration of the absolute sensitivities of two instruments on the Hubble Space Telescope and the MAVEN-IUVS echelle mode is presented based on near-simultaneous observations of the geocorona and Mars.

The Nitrogen Carrier in Inner Protoplanetary Disks

Abstract The dominant reservoirs of elemental nitrogen in protoplanetary disks have not yet been observationally identified. Likely candidates are HCN, NH3, and N2. The relative abundances of these carriers determine the composition of planetesimals as a function of disk radius due to strong differences in their volatility. A significant sequestration of nitrogen in carriers less volatile than N2 is likely required to deliver even small amounts of nitrogen to the Earth and potentially habitable exoplanets. While HCN has been detected in small amounts in inner disks (<10 au), so far only relatively insensitive upper limits on inner disk NH3 have been obtained. We present new Gemini-TEXES high-resolution spectroscopy of the 10.75 μm band of warm NH3, and use two-dimensional radiative transfer modeling to improve previous upper limits by an order of magnitude to at 1 au. These NH3 abundances are significantly lower than those typical for ices in circumstellar envelopes ( ). We also consistently retrieve the inner disk HCN gas abundances using archival Spitzer spectra, and derive upper limits on the HCN ice abundance in protostellar envelopes using archival ground-based 4.7 μm spectroscopy ([HCNice]/[H2Oice] < 1.5%–9%). We identify the NH3/HCN ratio as an indicator of chemical evolution in the disk, and we use this ratio to suggest that inner disk nitrogen is efficiently converted from NH3 to N2, significantly increasing the volatility of nitrogen in planet-forming regions.

Spectral gradient of the thermal millimetre continuum as a diagnostic for optical thickness in the solar atmosphere (Corrigendum)

Aims. In this Letter we aim to show how the gradient of the thermal millimetre continuum spectrum, as emitted from the quiet solar atmosphere, may be used as a diagnostic for the optical thickness regime at the centre of the observing frequency band. Methods. We show the theoretical derivation of the gradient of the millimetre continuum for both logarithmic- and linear-scale spectra. We compare this expression with the empirical relationship between the slope of the millimetre continuum spectrum and the plasma optical thickness computed from both isothermal and multi-thermal two-dimensional cylindrical radiative transfer models. Results. It is found that the logarithmic-scale spectral gradient provides a clear diagnostic for the optical thickness regime for both isothermal and multi-thermal plasmas, provided that a suitable correction is made for a non-constant gaunt factor over the frequency band. For the use of observers we present values for this correction at all ALMA bands and at a wide range of electron temperatures. Conclusions. We find that the spectral gradient can be used to find (a) whether the source is fully optically thin, (b) the optical thickness of the source if it lies within the transitional regime between optically thin and thick plasma (τ ≈ 10−1−101), or (c) whether the source is fully optically thick for an isothermal plasma. A multi-thermal plasma will act the same as an isothermal plasma for case (a), however, the transitional regime will only extend from τ ≈ 10−1 to τ ≈ 100. Above τ = 1 the slope of the continuum will depend increasingly on the temperature gradient, as well as the optical thickness, reducing the reliability of the diagnostic.

Spectral gradient of the thermal millimetre continuum as a diagnostic for optical thickness in the solar atmosphere

Aims. In this Letter we aim to show how the gradient of the thermal millimetre continuum spectrum, as emitted from the quiet solar atmosphere, may be used as a diagnostic for the optical thickness regime at the centre of the observing frequency band. Methods. We show the theoretical derivation of the gradient of the millimetre continuum for both logarithmic- and linear-scale spectra. We compare this expression with the empirical relationship between the slope of the millimetre continuum spectrum and the plasma optical thickness computed from both isothermal and multi-thermal two-dimensional cylindrical radiative transfer models. Results. It is found that the logarithmic-scale spectral gradient provides a clear diagnostic for the optical thickness regime for both isothermal and multi-thermal plasmas, provided that a suitable correction is made for a non-constant gaunt factor over the frequency band. For the use of observers we present values for this correction at all ALMA bands and at a wide range of electron temperatures. Conclusions. We find that the spectral gradient can be used to find (a) whether the source is fully optically thin, (b) the optical thickness of the source if it lies within the transitional regime between optically thin and thick plasma (τ ≈ 10−1−101), or (c) whether the source is fully optically thick for an isothermal plasma. A multi-thermal plasma will act the same as an isothermal plasma for case (a), however, the transitional regime will only extend from τ ≈ 10−1 to τ ≈ 100. Above τ = 1 the slope of the continuum will depend increasingly on the temperature gradient, as well as the optical thickness, reducing the reliability of the diagnostic.

MEASUREMENTS OF WATER SURFACE SNOW LINES IN CLASSICAL PROTOPLANETARY DISKS

ABSTRACT We present deep Herschel-PACS spectroscopy of far-infrared water lines from a sample of four protoplanetary disks around solar-mass stars, selected to have strong water emission at mid-infrared wavelengths. By combining the new Herschel spectra with archival Spitzer-IRS spectroscopy, we retrieve a parameterized radial surface water vapor distribution from 0.1 to 100 au using two-dimensional dust and line radiative transfer modeling. The surface water distribution is modeled with a step model composed of a constant inner and outer relative water abundance and a critical radius at which the surface water abundance is allowed to change. We find that the four disks have critical radii of ∼3–11 au, at which the surface water abundance decreases by at least 5 orders of magnitude. The measured values for the critical radius are consistently smaller than the location of the surface snow line, as predicted by the observed spectral energy distribution. This suggests that the sharp drop-off of the surface water abundance is not solely due to the local gas-solid balance, but may also be driven by the deactivation of gas-phase chemical pathways to water below 300 K. Assuming a canonical gas-to-dust ratio of 100, as well as coupled gas and dust temperatures T gas = T dust, the best-fit inner water abundances become implausibly high (0.01–1.0 H 2 − 1 ?> ). Conversely, a model in which the gas and dust temperatures are decoupled leads to canonical inner-disk water abundances of ∼ 10 − 4 H 2 − 1 ?> , while retaining gas-to-dust ratios of 100. That is, the evidence for gas–dust decoupling in disk surfaces is stronger than for enhanced gas-to-dust ratios.

Monte-Carlo radiative transfer simulation of the circumstellar disk of the Herbig Ae star HD 144432

Studies of pre-transitional disks, with a gap region between the inner infrared-emitting region and the outer disk, are important to improving our understanding of disk evolution and planet formation. Previous infrared interferometric observations have shown hints of a gap region in the protoplanetary disk around the Herbig Ae star HD~144432. We study the dust distribution around this star with two-dimensional radiative transfer modeling. We compare the model predictions obtained via the Monte-Carlo radiative transfer code RADMC-3D with infrared interferometric observations and the {\SED} of HD~144432. The best-fit model that we found consists of an inner optically thin component at $0.21\enDash0.32~\AU$ and an optically thick outer disk at $1.4\enDash10~\AU$. We also found an alternative model in which the inner sub-AU region consists of an optically thin and an optically thick component. Our modeling suggests an optically thin component exists in the inner sub-AU region, although an optically thick component may coexist in the same region. Our modeling also suggests a gap-like discontinuity in the disk of HD~144432.

Volatile snowlines in embedded disks around low-mass protostars

(Abridged*) Models of the young solar nebula assume a hot initial disk with most volatiles are in the gas phase. The question remains whether an actively accreting disk is warm enough to have gas-phase water up to 50 AU radius. No detailed studies have yet been performed on the extent of snowlines in an embedded accreting disk (Stage 0). Quantify the location of gas-phase volatiles in embedded actively accreting disk system. Two-dimensional physical and radiative transfer models have been used to calculate the temperature structure of embedded protostellar systems. Gas and ice abundances of H$_2$O, CO$_2$, and CO are calculated using the density-dependent thermal desorption formulation. The midplane water snowline increases from 3 to 55 AU for accretion rates through the disk onto the star between $10^{-9}$-$10^{-4} \ M_{\odot} \ {\rm yr^{-1}}$. CO$_2$ can remain in the solid phase within the disk for $\dot{M} \leq 10^{-5} \ M_{\odot} \ {\rm yr^{-1}}$ down to $\sim 20$ AU. Most of the CO is in the gas phase within an actively accreting disk independent of disk properties and accretion rate. The predicted optically thin water isotopolog emission is consistent with the detected H$_2^{18}$O emission toward the Stage 0 embedded young stellar objects, originating from both the disk and the warm inner envelope (hot core). An accreting embedded disk can only account for water emission arising from $R < 50$ AU, however, and the extent rapidly decreases for low accretion rates. Thus, the radial extent of the emission can be measured with ALMA observations and compared to this limit. Volatiles sublimate out to 50 AU in young disks and can reset the chemical content inherited from the envelope in periods of high accretion rates. A hot young solar nebula out to 30 AU can only have occurred during the deeply embedded Stage 0, not during the T-Tauri phase of our early solar system.

Multi-Wavelength Eclipse Observations of a Quiescent Prominence

We construct the maps of temperatures, geometrical thicknesses, electron densities and gas pressures in a quiescent prominence. For this we use the RGB signal of the prominence visible-light emission detected during the total solar eclipse of 1 August 2008 in Mongolia and quasi-simultaneous Hα spectra taken at Ondřejov Observatory. The method of disentangling the electron density and geometrical (effective) thickness was described by Jejcic and Heinzel (Solar Phys. 254, 89 – 100, 2009) and is used here for the first time to analyse the spatial variations of prominence parameters. For the studied prominence we obtained the following range of parameters: temperature 6000 – 15 000 K, effective thickness 200 – 15000 km, electron density 5×109 – 1011 cm−3 and gas pressure 0.02 – 0.2 dyn cm−2 (assuming a fixed ionisation degree n p/n H=0.5). The electron density increases towards the bottom of the prominence, which we explain by an enhanced photoionisation due to the incident solar radiation. To confirm this, we construct a two-dimensional radiative-transfer model with realistic prominence illumination.

The chemistry of planet-forming regions is not interstellar.

Advances in infrared and submillimeter technology have allowed for detailed observations of the molecular content of the planet-forming regions of protoplanetary disks. In particular, disks around solar-type stars now have growing molecular inventories that can be directly compared with both prestellar chemistry and that inferred for the early solar nebula. The data directly address the old question of whether the chemistry of planet-forming matter is similar or different and unique relative to the chemistry of dense clouds and protostellar envelopes. The answer to this question may have profound consequences for the structure and composition of planetary systems. The practical challenge is that observations of emission lines from disks do not easily translate into chemical concentrations. Here, we present a two-dimensional radiative transfer model of RNO 90, a classical protoplanetary disk around a solar-mass star, and retrieve the concentrations of dominant molecular carriers of carbon, oxygen and nitrogen in the terrestrial region around 1 AU. We compare our results to the chemical inventory of dense clouds and protostellar envelopes, and argue that inner disk chemistry is, as expected, fundamentally different from prestellar chemistry. We find that the clearest discriminant may be the concentration of CO2, which is extremely low in disks, but one of the most abundant constituents of dense clouds and protostellar envelopes.

RESOLVING THE DUST DISK IN THE PROTOTYPE IONIZED DISK WIND SOURCE S140-IRS1

The dust disk confirming the presence of an ionized disk wind in the massive young stellar object, S140-IRS1, is resolved for the first time. The 1.3 mm continuum observations taken with the CARMA A array configuration achieve a resolution of ~0.''12, probing scales of 100 au. The dust disk is elongated in a direction aligned with a previously discovered ionized disk wind. Both are perpendicular to the large scale molecular outflow and near-infrared reflection nebula. A two-dimensional axis-symmetric radiative transfer model is used to produce synthetic images and visibilities for comparison with the observations. Using a 2D visibility fitting method the position angle of the dusty disk is constrained to 40° ± 5°. This result confirms the disk wind nature of the radio emission from S140-IRS1 and shows that radiation pressure on the gas in the disk is important in the later stages of the massive star formation evolutionary sequence.

Revealing the inclined circumstellar disk in the UX Orionis system KK Ophiuchi

Aims. We study the inner sub-AU region of the circumstellar environment of the UX Ori-type star KK Oph with near-infrared VLTI/AMBER interferometry. We are particularly interested in the inclination of the star-disk system, and we use this information to test the current standard picture for UX Ori stars. Methods. We recorded spectrally dispersed (R 35) interferograms in the near-infraredH andK bands with the VLTI/AMBER instrument. The derived visibilities, closure phases, and the spectral energy distribution of KK Oph were compared with two-dimensional geometric and radiative transfer models (RADMC). Results. We obtained visibilities at four di erent position angles. Using two-dimensional geometric models, we derive an axis ratio 3:0 corresponding to an inclination of 70 . A fitted inclined ring model leads to a ring radius of 2:8 0:2 mas, corresponding to 0:44 0:03 AU at a distance of 160 pc, which is larger than the dust sublimation radius of 0:1 AU predicted for a dust sublimation temperature of 1500 K. Our derived two-dimensional RADMC model consists of a circumstellar disk with an inclination angle of 70 and an additional dust envelope. Conclusions. The finding of an 70 inclined disk around KK Oph is consistent with the prediction that UX Ori objects are seen under large inclination angles, and orbiting clouds in the line of sight cause the observed variability. Furthermore, our results suggest that the orbit of the companion KK Oph B and the disk plane are coplanar.

A COMPANION AS THE CAUSE OF LATITUDE-DEPENDENT EFFECTS IN THE WIND OF ETA CARINAE

We analyze spatially resolved spectroscopic observations of the Eta Carinae binary system obtained with HST/STIS. Eta Car is enshrouded by the dusty Homunculus nebula, which scatters light emitted by the central binary and provides a unique opportunity to study a massive binary system from different vantage points. We investigate the latitudinal and azimuthal dependence of H$\alpha$ line profiles caused by the presence of a wind-wind collision (WWC) cavity created by the companion star. Using two-dimensional radiative transfer models, we find that the wind cavity can qualitatively explain the observed line profiles around apastron. Regions of the Homunculus which scatter light that propagated through the WWC cavity show weaker or no H alpha absorption. Regions scattering light that propagated through a significant portion of the primary wind show stronger P Cygni absorption. Our models overestimate the H alpha absorption formed in the primary wind, which we attribute to photoionization by the companion, not presently included in the models. We can qualitatively explain the latitudinal changes that occur during periastron, shedding light on the nature of Eta Car's spectroscopic events. Our models support the idea that during the brief period of time around periastron when the primary wind flows unimpeded toward the observer, H alpha absorption occurs in directions toward the central object and Homunculus SE pole, but not toward equatorial regions close to the Weigelt blobs. We suggest that observed latitudinal and azimuthal variations are dominated by the companion star via the WWC cavity, rather than by rapid rotation of the primary star.

Dust shell model of the water fountain source IRAS 16342–3814

We investigate the circumstellar dust shell of the water fountain source IRAS 16342-3814. We performed two-dimensional radiative transfer modeling of the dust shell, taking into account previously observed spectral energy distributions (SEDs) and our new $J$-band imaging and $H$- and $K_S$-band imaging polarimetry obtained using the VLT/NACO instrument. Previous observations expect an optically thick torus in the equatorial plane because of a striking bipolar appearance and a large viewing angle of 30 - 40$\degr$. However, models with such a torus as well as a bipolar lobe and an AGB shell cannot fit the SED and the images simultaneously. We find that an additional optically and geometrically thick disk located inside a massive torus solves this problem. The masses of the disk and the torus are estimated to be 0.01 $M_{\sun}$ at the $a_\mathrm{max}=100 \mu$m dust and 1 $M_{\sun}$ at $a_\mathrm{max}=10 \mu$m dust, respectively. We discuss a possible formation scenario for the disk and torus based on a similar mechanism to the equatorial back flow. IRAS 16342-3814 is expected to undergo mass loss at a high rate. The radiation from the central star is shielded by the dust that was ejected in the subsequent mass loss event. As a result, the radiation pressure on dust particles cannot govern the motion of the particles anymore. The mass loss flow can be concentrated in the equatorial plane by help of an interaction, which might be the gravitational attraction by the companion, if it exists in IRAS 16342-3814. A fraction of the ejecta is captured in a circum-companion or circum-binary disk and the remains are escaping from the central star(s) and form the massive torus.

Identifying the Low‐Luminosity Population of Embedded Protostars in the c2d Observations of Clouds and Cores

We present the results of a search for all embedded protostars with internal luminosities ≤1.0 L☉ in the full sample of nearby, low-mass star-forming regions surveyed by the Spitzer Space Telescope Legacy Project "From Molecular Cores to Planet Forming Disks" (c2d). The internal luminosity of a source, Lint, is the luminosity of the central source and excludes luminosity arising from external heating. On average, the Spitzer c2d data are sensitive to embedded protostars with Lint ⩾ 4 × 10−3(d/140 pc)2 L☉, a factor of 25 better than the sensitivity of the Infrared Astronomical Satellite (IRAS) to such objects. We present a set of selection criteria used to identify candidates from the Spitzer data and examine complementary data to decide whether each candidate is truly an embedded protostar. We find a tight correlation between the 70 μm flux and internal luminosity of a protostar, an empirical result based on both observations and detailed two-dimensional radiative transfer models of protostars. We identify 50 embedded protostars with Lint ⩽ 1.0 L☉; 15 have Lint ⩽ 0.1 L☉. The intrinsic distribution of source luminosities increases to lower luminosities. While we find sources down to the above sensitivity limit, indicating that the distribution may extend to luminosities lower than probed by these observations, we are able to rule out a continued rise in the distribution below Lint = 0.1 L☉. Between 75% and 85% of cores classified as starless prior to being observed by Spitzer remain starless to our luminosity sensitivity; the remaining 15%-25% harbor low-luminosity, embedded protostars. We compile complete spectral energy distributions for all 50 objects and calculate standard evolutionary signatures (Lbol, Tbol, and Lbol/Lsmm) and argue that these objects are inconsistent with the simplest picture of star formation, wherein mass accretes from the core onto the protostar at a constant rate.

Radiative transfer model for aerosols at infrared wavelengths for passive remote sensing applications: revisited

We introduced a two-dimensional radiative transfer model for aerosols in the thermal infrared [Appl. Opt.45, 6860-6875 (2006)APOPAI0003-693510.1364/AO.45.006860]. In that paper we superimposed two orthogonal plane-parallel layers to compute the radiance due to a two-dimensional (2D) rectangular aerosol cloud. In this paper we revisit the model and correct an error in the interaction of the two layers. We derive new expressions relating to the signal content of the radiance from an aerosol cloud based on the concept of five directional thermal contrasts: four for the 2D diffuse radiance and one for direct radiance along the line of sight. The new expressions give additional insight on the radiative transfer processes within the cloud. Simulations for Bacillus subtilis var. niger (BG) bioaerosol and dustlike kaolin aerosol clouds are compared and contrasted for two geometries: an airborne sensor looking down and a ground-based sensor looking up. Simulation results suggest that aerosol cloud detection from an airborne platform may be more challenging than for a ground-based sensor and that the detection of an aerosol cloud in emission mode (negative direct thermal contrast) is not the same as the detection of an aerosol cloud in absorption mode (positive direct thermal contrast).

HK-band imaging polarimetry and radiative transfer modeling of the massive young stellar object CRL 2136

Aims. We investigate the physical properties of the dust environment of the massive proto-stellar object CRL 2136 by means of two-dimensional radiative transfer modeling, which combines fitting of the spectral energy distribution, the intensity images, and the polarization images. Methods. We obtained polarimetric images of CRL 2136 in the H and K bands using the CIAO instrument on the 8 m Subaru telescope. We developed a new Monte Carlo code which can deal with multiple-grain models and computes the SED, the dust temperature, and the Stokes IQUV images. With this code, we performed two-dimensional modeling of CRL 2136’s circumstellar disk and envelope. Results. Our images show a compact infrared source, two bright lobes extending towards the south and east, and two faint lobes extending towards the northwest and west. The polarization images show a polarization disk near the central star with a position angle of ∼−135 ◦ , a polarization vector alignment approximately parallel to the polarization disk, and a region with low polarization between the eastern and the southern lobes. In our modeling, we assume three grain models: bare grains, warm grains with a crystalline water ice mantle, and cold grains with an amorphous water ice mantle. We obtained a maximum grain core size of 0.45 μm. We found that the CRL 2136 disk has a low disk mass of 0.007 M� , a large radius of 2000 AU, a scale height of 1.0, and a low accretion rate of ✭

Near-IR bispectrum speckle interferometry, AO imaging polarimetry, and radiative transfer modeling of the proto-planetary nebula Frosty Leonis

Aims. We combined bispectrum speckle interferometry, adaptive optics (AO) imaging polarimetry, and radiative transfer modeling of polarized light to derive various physical properties of the proto-planetary nebula Frosty Leo. Methods. We performed bispectrum K � -band speckle interferometry and H -a ndK-band imaging polarimetry of Frosty Leo using the ESO 3.6 m telescope and the AO-equipped CIAO instrument of the 8 m Subaru telescope, respectively. Two-dimensional radiative transfer modeling was carried out in order to obtain a quantitative interpretation of our observations. Results. Our diffraction-limited speckle image shows distinct hourglass-shaped, point-symmetric bipolar lobes, an equatorial dust lane, and complex clumpy structures in the lobes. Our polarimetric data display a centro-symmetric polarization vector pattern with P ∼ 30–50% in the bipolar lobes and a polarization disk between them. The polarization images also reveal an elongated region with low polarization along a position angle of −45 ◦ . The observations suggest that this region has a low dust density and was carved out by a jet-like outflow. Our radiative transfer modeling can simultaneously explain the observed spectral energy distribution, the intensity distribution of the hourglass-shaped lobes, and our polarization images if we use two grain species with sizes of 0.005 ≤ a ≤ 2.0 μm at latitudes between −2 ◦ and +2 ◦ ,a nd 0.005 ≤ a ≤ 0.7 μm in the bipolar lobes. Assuming a distance of 3 kpc, an expansion velocity of 25 km s −1 , and a gas-to-dust mass ratio of 160, we derive a dust mass of the disk of 2.85 × 10 −3 M� , a gas mass-loss rate of ) ( ) ( *

2-D Radiation Transfer Model of Non-Spherically Symmetric Dust Shell in Proto-Planetary Nebulae

Resent high-resolution optical imaging has directly revealed reflection nebulosity around proto-planetary nebulae (PPNs), the transition objects between asymptotic giant branch (AGB) stars and planetary nebulae (Sahai et al. 1998, Su et al. 1998, Ueta et al. 2000, Su et al. 2001). The existence of bipolar nebulae observed in the PPN phase suggests the presence of asymmetry in the AGB circumstellar dust shell. In order to model these objects, a self-consistent radiation transfer model is necessary. As a first attempt, we construct an approximate two-dimensional dust radiative transfer model to simultaneously fit the spectral energy distribution (SED) and images of a centrally-heated dust envelope.