Density Power-law Index Research Articles

Polar alignment of a dusty circumbinary disc–II. Application to 99 Herculis

ABSTRACT We investigate the formation of dust traffic jams in polar-aligning circumbinary discs. In our first paper, we found as the circumbinary disc evolves towards a polar configuration perpendicular to the binary orbital plane, the differential precession between the gas and dust components leads to multiple dust traffic jams. These dust traffic jams evolve to form a coherent dust ring. In part two, we use 3D smoothed particle hydrodynamical simulations of gas and dust to model an initially highly misaligned circumbinary disc around the 99 Herculis (99 Her) binary system. Our results reveal that the formation of these dust rings is observed across various disc parameters, including the disc aspect ratio, viscosity, surface density power-law index, and temperature power-law index. The dust traffic jams are long-lived and persist even when the disc is fully aligned polar. The midplane dust-to-gas ratio within the rings can surpass unity, which may be a favourable environment for planetesimal formation. Using 2D inviscid shearing box calculations with parameters from our 3D simulations, we find streaming instability modes with significant growth rates. The streaming instability growth time-scale is less than the tilt oscillation time-scale during the alignment process. Therefore, the dust ring will survive once the gas disc aligns polar, suggesting that the streaming instability may aid in forming polar planets around 99 Her.

Physical and chemical complexity in high-mass star-forming regions with ALMA

Context. High-mass star formation is a hierarchical process from cloud (>1 pc), to clump (0.1−1 pc), to core scales (<0.1 pc). Modern interferometers that achieve high angular resolutions at millimeter wavelengths allow us to probe the physical and chemical properties of the gas and dust of protostellar cores in the earliest evolutionary formation phases. Aims. In this study we investigate how physical properties, such as the density and temperature profiles, evolve on core scales through the evolutionary sequence during high-mass star formation ranging from protostars in cold infrared-dark clouds to evolved ultracompact HII (UCHII) regions. Methods. We observed 11 high-mass star-forming regions with the Atacama Large Millimeter/submillimeter Array (ALMA) at 3 mm wavelengths. Based on the 3 mm continuum morphology and H(40)α recombination line emission - which trace locations with free-free (ff) emission - the fragmented cores analyzed in this study are classified as either “dust” or “dust+ff” cores. In addition, we resolved three cometary UCHII regions with extended 3 mm emission that is dominated by free-free emission. The temperature structure and radial profiles (T ~ r−q) were determined by modeling the molecular emission of CH3CN and CH313CN with XCLASS and by using the HCN-to-HNC intensity ratio as a probe for the gas kinetic temperature. The density profiles (n ~ r−p) were estimated from the 3 mm continuum visibility profiles. The masses (M) and H2 column densities (N(H2)) were then calculated from the 3 mm dust continuum emission. Results. We find a large spread in mass and peak H2 column density in the detected sources, ranging from 0.1 to 150 M⊙ and 1023 to 1026 cm−2, respectively. Including the results of the CORE and CORE-extension studies to increase the sample size, we find evolutionary trends on core scales for the temperature power-law index (q) increasing from 0.1 to 0.7 from infrared-dark clouds to UCHII regions, while for the density power-law index (p) on core scales, we do not find strong evidence for an evolutionary trend. However, we find that on the larger clump scales the density profile flattens from p ≈ 2.2 to p ≈ 1.2 during these evolutionary phases. Conclusions. By characterizing a large statistical sample of individual fragmented cores, we find that the physical properties, such as the temperature on core scales and the density profile on clump scales, evolve even during the earliest evolutionary phases in high-mass star-forming regions. These findings provide observational constraints for theoretical models that describe the formation of massive stars. In follow-up studies we aim to further characterize the chemical properties of the regions by analyzing the large amount of molecular lines detected with ALMA in order to investigate how the chemical properties of the molecular gas evolve during the formation of massive stars.

Pinpointing the jet apex of 3C 84

Nearby radio galaxies that contain jets are extensively studied with very long baseline interferometry (VLBI), addressing jet launching and the physical mechanisms at play around massive black holes. 3C 84 is unique in this regard because the combination of its proximity and large super massive black hole mass provides a high spatial resolution to resolve the complex structure at the jet base. For 3C 84, an angular scale of 50 μas corresponds to 200−250 Schwarzschild radii (Rs). Recent RadioAstron VLBI imaging at 22 GHz has revealed an east-west elongated feature at the northern end of the VLBI jet, which challenges past interpretations. Here we propose instead that the jet apex is not located within the 22 GHz VLBI core region but more upstream in the jet. We base our arguments on a 2D cross-correlation analysis of quasi-simultaneously obtained VLBI images at 15, 43, and 86 GHz, which measures the opacity shift of the VLBI core in 3C 84. With the assumption of the power-law index (kr) of the core shift being set to 1, we find the jet apex to be located 83 ± 7 μas north (upstream) of the 86 GHz VLBI core. Depending on the assumptions forkrand the particle number density power-law index,n, we find a mixed toroidal-poloidal magnetic field configuration, consistent with a region that is offset from the central engine by about 400–1500Rs. The measured core shift is then used to estimate the magnetic field strength, which amounts toB= 1.80−4.0 G near the 86 GHz VLBI core. We discuss some physical implications of these findings.

Physical and chemical structure of high-mass star-forming regions

Aims. Current star formation research centers the characterization of the physical and chemical properties of massive stars, which are in the process of formation, at the spatial resolution of individual high-mass cores. Methods. We use sub-arcsecond resolution (~0.′′4) observations with the NOrthern Extended Millimeter Array at 1.37 mm to study the dust emission and molecular gas of 18 high-mass star-forming regions. With distances in the range of 0.7−5.5 kpc, this corresponds to spatial scales down to 300−2300 au that are resolved by our observations. We combined the derived physical and chemical properties of individual cores in these regions to estimate their ages. The temperature structures of these regions are determined by fitting the H2CO and CH3CN line emission. The density profiles are inferred from the 1.37 mm continuum visibilities. The column densities of 11 different species are determined by fitting the emission lines with XCLASS. Results. Within the 18 observed regions, we identified 22 individual cores with associated 1.37 mm continuum emission and with a radially decreasing temperature profile. We find an average temperature power-law index of q = 0.4 ± 0.1 and an average density power-law index of p = 2.0 ± 0.2 on scales that are on the order of several 1000 au. Comparing these results with values of p derived from the literature presumes that the density profiles remain unchanged from clump to core scales. The column densities relative to N(C18O) between pairs of dense gas tracers show tight correlations. We applied the physical-chemical model MUlti Stage ChemicaL codE to the derived column densities of each core and find a mean chemical age of ~60 000 yr and an age spread of 20 000−100 000 yr. With this paper, we release all data products of the CORE project. Conclusions. The CORE sample reveals well-constrained density and temperature power-law distributions. Furthermore, we characterized a large variety in molecular richness that can be explained by an age spread that is then confirmed by our physical-chemical modeling. The hot molecular cores show the greatest number of emission lines, but we also find evolved cores at an evolutionary stage in which most molecules are destroyed and, thus, the spectra appear line-poor once again.

Constraining cosmological and galaxy parameters using strong gravitational lensing systems

Strong gravitational lensing along with the distance sum rule method can constrain both cosmological parameters as well as density profiles of galaxies without assuming any fiducial cosmological model. To constrain galaxy parameters and cosmic curvature $(\Omega_{k0})$, we use the distance ratio data from a recently compiled database of $161$ galactic scale strong lensing systems. We use databases of supernovae type-Ia (Pantheon) and Gamma Ray Bursts (GRBs) for calculating the luminosity distance. To study the model of the lens galaxy, we consider a general lens model namely, the Extended Power-Law model. Further, we take into account two different parametrisations of the mass density power-law index $(\gamma)$ to study the dependence of $\gamma$ on redshift. The best value of $\Omega_{k0}$ suggests a closed universe, though a flat universe is accommodated at $68\%$ confidence level. We find that parametrisations of $\gamma$ have a negligible impact on the best fit value of the cosmic curvature parameter. Furthermore, measurement of time delay can be a promising cosmographic probe via "time delay distance" that includes the ratio of distances between the observer, the lens and the source. We again use the distance sum rule method with time-delay distance dataset of H0LiCOW to put constraints on the Cosmic Distance Duality Relation (CDDR) and the cosmic curvature parameter $(\Omega_{k0})$. For this we consider two different redshift-dependent parametrisations of the distance duality parameter $(\eta)$. The best fit value of $\Omega_{k0}$ clearly indicates an open universe. However, a flat universe can be accommodated at $95\%$ confidence level. Further, at $95\%$ confidence level, no violation of CDDR is observed. We believe that a larger sample of strong gravitational lensing systems is needed in order to improve the constraints on the cosmic curvature and distance duality parameter.

Model exploration of near-IR ro-vibrational CO emission as a tracer of inner cavities in protoplanetary disks

Context. Near-IR observations of protoplanetary disks provide information about the properties of the inner disk. High-resolution spectra of abundant molecules such as CO can be used to determine the disk structure in the warm inner parts. The v2∕v1 ro-vibrational ratio of v1−0 and v2−1 transitions has recently been observed to follow distinct trends with the CO emitting radius in a sample of TTauri and Herbig disks; these trends have empirically been interpreted as due to depletion of the inner disk from gas and dust. Aims. We use thermochemical disk models to explore the to interpret the trends of these CO ro-vibrational CO emission. Methods. We used the radiation thermochemical code ProDiMo to explore a set of previously published models with different disk properties and varying one parameter at a time: the inner radius, the dust-to-gas mass ratio, and the gas mass. In addition, we used models in which we changed the surface density power-law index, and employed a larger set of CO ro-vibrational levels that also include fluorescence from the first electronic state. We investigated these models for TTauri and Herbig star disks. Finally, we included a set of DIANA models for individual TTauri and Herbig disks that were constructed to reproduce a large set of multiwavelength observations. Results. This modeling exploration highlights promising parameters that may explain the observed trends in ro-vibrational CO emission. Our models with an increasing inner radius match the observed trend for TTauri disks, in which we were also able to account for the vertical spread in the data by different values for the dust-to-gas mass ratio and for the disk gas mass in different disks. Our models instead match the CO vibrational ratio observed in Herbig disks only in the case of large inner holes and cannot produce the low ratios that are measured in many disks. The models do produce an inversion in the trend, where v2−1∕v1−0 increases and does not decrease for CO radii larger than a few au. The reason for this is that the P(4) v2−1 line becomes optically thin and superthermally excited. In our models, this does not require invoking UV fluorescence pumping. Conclusions. Our modeling explorations suggest that the observed decrease in v2−1∕v1−0 with CO radius in TTauri disks might be a consequence of inside-out disk depletion. For the Herbig disks, a more complex inner disk structure may instead be needed to explain the observed trends in the excitation of CO emission as a function of emitting radius: disk gaps emptied of dust, partially depleted in gas, and/or possibly a disk structure with an inverted surface density profile. These structures need to be further investigated in future work.

Chemical complexity in high-mass star formation

Aims. In order to understand the observed molecular diversity in high-mass star-forming regions, we have to determine the underlying physical and chemical structure of those regions at high angular resolution and over a range of evolutionary stages. Methods. We present a detailed observational and modeling study of the hot core VLA 3 in the high-mass star-forming region AFGL 2591, which is a target region of the NOrthern Extended Millimeter Array (NOEMA) large program CORE. Using NOEMA observations at 1.37 mm with an angular resolution of ~0″. 42 (1400 au at 3.33 kpc), we derived the physical and chemical structure of the source. We modeled the observed molecular abundances with the chemical evolution code MUSCLE (MUlti Stage ChemicaL codE). Results. With the kinetic temperature tracers CH3CN and H2CO we observe a temperature distribution with a power-law index of q = 0.41 ± 0.08. Using the visibilities of the continuum emission we derive a density structure with a power-law index of p = 1.7 ± 0.1. The hot core spectra reveal high molecular abundances and a rich diversity in complex molecules. The majority of the molecules have an asymmetric spatial distribution around the forming protostar(s), which indicates a complex physical structure on scales <1400 au. Using MUSCLE, we are able to explain the observed molecular abundance of 10 out of 14 modeled species at an estimated hot core chemical age of ~21 100 yr. In contrast to the observational analysis, our chemical modeling predicts a lower density power-law index of p < 1.4. Reasons for this discrepancy are discussed. Conclusions. Combining high spatial resolution observations with detailed chemical modeling allows us to derive a concise picture of the physical and chemical structure of the famous AFGL 2591 hot core. The next steps are to conduct a similar analysis for the whole CORE sample, and then use this analysis to constrain the chemical diversity in high-mass star formation to a much greater depth.

An Exo–Kuiper Belt with an Extended Halo around HD 191089 in Scattered Light

Abstract We have obtained Hubble Space Telescope STIS and NICMOS and Gemini/GPI scattered-light images of the HD 191089 debris disk. We identify two spatial components: a ring resembling the Kuiper Belt in radial extent (FWHM ∼ 25 au, centered at ∼46 au) and a halo extending to ∼640 au. We find that the halo is significantly bluer than the ring, consistent with the scenario that the ring serves as the “birth ring” for the smaller dust in the halo. We measure the scattering phase functions in the 30°–150° scattering-angle range and find that the halo dust is more forward- and backward-scattering than the ring dust. We measure a surface density power-law index of −0.68 ± 0.04 for the halo, which indicates the slowdown of the radial outward motion of the dust. Using radiative transfer modeling, we attempt to simultaneously reproduce the (visible) total and (near-infrared) polarized intensity images of the birth ring. Our modeling leads to mutually inconsistent results, indicating that more complex models, such as the inclusion of more realistic aggregate particles, are needed.

Constraints on a possible evolution of mass density power-law index in strong gravitational lensing from cosmological data

In this work, by using strong gravitational lensing (SGL) observations along with Type Ia Supernovae (Union2.1) and gamma ray burst data (GRBs), we propose a new method to study a possible redshift evolution of $\gamma(z)$, the mass density power-law index of strong gravitational lensing systems. In this analysis, we assume the validity of cosmic distance duality relation and the flat universe. In order to explore the $\gamma(z)$ behavior, three different parametrizations are considered, namely: (P1) $\gamma(z_l)=\gamma_0+\gamma_1 z_l$, (P2) $\gamma(z_l)=\gamma_0+\gamma_1 z_l/(1+z_l)$ and (P3) $\gamma(z_l)=\gamma_0+\gamma_1 \ln(1+z_l)$, where $z_l$ corresponds to lens redshift. If $\gamma_0=2$ and $\gamma_1=0$ the singular isothermal sphere model is recovered. Our method is performed on SGL sub-samples defined by different lens redshifts and velocity dispersions. For the former case, the results are in full agreement with each other, while a 1$\sigma$ tension between the sub-samples with low ($\leq 250$ km/s) and high ($>250$ km/s) velocity dispersions was obtained on the ($\gamma_0$-$\gamma_1$) plane. By considering the complete SGL sample, we obtain $\gamma_0 \approx 2$ and $ \gamma_1 \approx 0$ within 1$\sigma$ c.l. for all $\gamma(z)$ parametrizations. However, we find the following best fit values of $\gamma_1$: $-0.085$, $-0.16$ and $-0.12$ for P1, P2 and P3 parametrizations, respectively, suggesting a mild evolution for $\gamma(z)$. By repeating the analysis with Type Ia Supernovae from JLA compilation, GRBs and SGL systems this mild evolution is reinforced.

No evidence for the evolution of mass density power-law index γ from strong gravitational lensing observation

In this paper, we consider the singular isothermal sphere lensing model that has a spherically symmetric power-law mass distribution $\rho_{tot}(r)\sim r^{-\gamma}$. We investigate whether the mass density power-law index $\gamma$ is cosmologically evolutionary by using the strong gravitational lensing (SGL) observation, in combination with other cosmological observations. We also check whether the constraint result of $\gamma$ is affected by the cosmological model, by considering several simple dynamical dark energy models. We find that the constraint on $\gamma$ is mainly decided by the SGL observation and independent of the cosmological model, and we find no evidence for the evolution of $\gamma$ from the SGL observation.

THE Hα PROFILES OF Be SHELL STARS

A new set of theoretical Hα emission line profiles of Be stars has been computed using the code BERAY, which solves the transfer equation along a series of rays passing through the star+disk system, representing an improved treatment over earlier work done by the authors. The new profiles were compared with the previous work, and general trends (such as line profile shapes and correlations between line equivalent widths as a function of initial density ρ0 and power law index n) were recovered. Additionally, BERAY was employed to model the spectra of eight well-known Be shell stars. Some degeneracy was found in the choice of model parameters, highlighting the need to employ alternate observables to constrain the models. However, the inclination angle of the model seemed relatively insensitive to the choices of other parameters, and we show that, with our models, only a very small range of inclination angles can adequately reproduce the observations. Five of our eight targets were found to have inclination angles of 70° or higher, and two more were found to have inclination angles of 67° and 65°. The observation of one target—4 Aquilae—could only be reproduced by models created at an inclination angle of approximately 45°.

Intrinsic structure of biological layers: Vertical inhomogeneity profiles characterized by label-free optical waveguide biosensors

When various analytes and functional layers are deposited on the surface of optical waveguide based biochips one faces difficulties in correctly interpreting the experimental data. For example, the deposited layer can be highly ordered (lipid bilayers, oriented receptors etc.) or can have significant inhomogeneity both perpendicular and parallel to the sensor surface (adsorbed polymer films, living cells). The generally applied simple optical model, which treats the deposited analyte layers homogeneous, isotropic and usually relatively thin compared to the wavelength of light, therefore, fails in most of the practical cases. In the present contribution, we systematically investigate the limitations of the widely applied optical models, when the analyte layer on the sensing surface has a vertically inhomogeneous refractive index profile. As examples of more realistic density profiles, the step-index, linear, exponential, power law and Gaussian refractive index distributions on various types of waveguide biochips are investigated using analytical and numerical model calculations. The limitations and the possible errors of the homogeneous thin adlayer model are pointed out. It is shown that for all of the vertically inhomogeneous profiles the refractive index obtained from the homogeneous thin layer modeling underestimates the true averaged refractive index of the layer. The calculated thickness can be over or underestimated, even taking up negative values in some cases. This behavior is similar to what was observed for positively birefringent thin adlayers treated with the homogeneous and isotropic model. It is also shown that the surface mass coverages calculated using the thickness and refractive index obtained from the homogeneous and isotropic modeling underestimate the real coverage values. The above errors are smallest when the reverse waveguide sensor design is applied to investigate vertically inhomogeneous analytes.

FRAGMENTATION OF MASSIVE DENSE CORES DOWN TO ≲ 1000 AU: RELATION BETWEEN FRAGMENTATION AND DENSITY STRUCTURE

In order to shed light on the main physical processes controlling fragmentation of massive dense cores, we present a uniform study of the density structure of 19 massive dense cores, selected to be at similar evolutionary stages, for which their relative fragmentation level was assessed in a previous work. We inferred the density structure of the 19 cores through a simultaneous fit of the radial intensity profiles at 450 and 850 micron (or 1.2 mm in two cases) and the Spectral Energy Distribution, assuming spherical symmetry and that the density and temperature of the cores decrease with radius following power-laws. We find a weak (inverse) trend of fragmentation level and density power-law index, with steeper density profiles tending to show lower fragmentation, and vice versa. In addition, we find a trend of fragmentation increasing with density within a given radius, which arises from a combination of flat density profile and high central density and is consistent with Jeans fragmentation. We considered the effects of rotational-to-gravitational energy ratio, non-thermal velocity dispersion, and turbulence mode on the density structure of the cores, and found that compressive turbulence seems to yield higher central densities. Finally, a possible explanation for the origin of cores with concentrated density profiles, which are the cores showing no fragmentation, could be related with a strong magnetic field, consistent with the outcome of radiation magnetohydrodynamic simulations.

MID-INFRARED EXTINCTION MAPPING OF INFRARED DARK CLOUDS. II. THE STRUCTURE OF MASSIVE STARLESS CORES AND CLUMPS

(abridged) We develop the mid-infrared extinction (MIREX) mapping technique of Butler & Tan (2009, Paper I), presenting a new method to correct for the Galactic foreground emission based on observed saturation in independent cores. Using Spitzer GLIMPSE 8 micron images, this allows us to accurately probe mass surface densities, Sigma, up to ~0.5g/cm^2 with 2" resolution. We then characterize the structure of 42 massive starless and early-stage IRDC cores and their surrounding clumps, measuring Sigma_cl(r) from the core/clump centers. We first assess the properties of the core/clump at a scale where the total enclosed mass as projected on the sky is M_cl=60Msun. We find these objects have a mean radius of R_cl~0.1pc, mean Sigma_cl=0.3g/cm^2 and, if fit by a power law density profile rho_cl ~ r^{-k_{rho,cl}}, a mean value of k_{rho,cl}=1.1. If we assume a core is embedded in each clump and subtract the surrounding clump envelope to derive the core properties, we find a mean core density power law index of k_{rho,c} = 1.6. We repeat this analysis as a function of radius and derive the best-fitting power law plus uniform clump envelope model for each of the 42 core/clumps. The cores have typical masses of M_c~100Msun and mean Sigma_c~0.1g/cm^2, and are embedded in clumps with comparable mass surface densities. We conclude massive starless cores exist and are well-described by singular polytropic spheres. Their relatively low values of Sigma and the fact that they are IR dark may imply that their fragmentation is inhibited by magnetic fields rather than radiative heating. Comparing to massive star-forming cores, there is tentative evidence for an evolution towards higher densities and steeper density profiles as star formation proceeds.

NON-RELATIVISTIC RADIATION-MEDIATED SHOCK BREAKOUTS. I. EXACT BOLOMETRIC PLANAR BREAKOUT SOLUTIONS

The problem of a non-steady planar radiation-mediated shock (RMS) breaking out from a surface with a power-law density profile, ρ∝xn, is numerically solved in the approximation of diffusion with constant opacity. For an appropriate choice of time, length, and energy scales, determined by the breakout opacity, velocity, and density, the solution is universal, i.e., depends only on the density power-law index n. The resulting luminosity depends weakly on the value of n. An approximate analytic solution, based on the self-similar hydrodynamic solutions and on the steady RMS solutions, is constructed and shown to agree with the numerical solutions as long as the shock is far from the surface, τ ≫ c/vsh. Approximate analytic expressions, calibrated based on the exact solutions, are provided, which describe the escaping luminosity as a function of time. These results can be used to calculate the bolometric properties of the bursts of radiation produced during supernova shock breakouts. For completeness, we also use the exact breakout solutions to provide an analytic approximation for the maximum surface temperature for fast (vsh ≳ 0.1) non-thermal breakouts and show that it is a few times smaller than inferred based on steady state RMS solutions.

Physical structure and water line spectrum predictions of the intermediate mass protostar OMC2-FIR4

Aims. Intermediate Mass (IM) stars are an important component of our Galaxy, as they significantly contribute to the interstellar FUV field and, consequently, play an important role in the energy balance of the ISM. Despite their importance, very little is known about their formation process and only a few studies have been devoted to characterize the first phases in the evolution of intermediate mass protostars. Here we consider in great detail the case of the brightest and closest known young IM protostar: FIR4 in the OMC2 component of the Orion molecular cloud complex. Methods. We analyzed the available continuum emission (maps and SED) through one-dimensional dust radiative transfer calculations. We ran large grids of models to find the envelope model that best fits the data. The derived dust density and temperature profiles have been then used to compute the gas temperature profile, equating gas cooling and heating terms across the envelope. Last, we computed the water line spectrum for various possible values of water abundance. Results. The luminosity of FIR4 has been reevaluated to 1000 Lo, making FIR4 definitively an Intermediate Mass protostar. The envelope surrounding FIR4 has a relatively shallow density power law index, ~ 0.6. The most surprising result is that the gas and dust are thermally decoupled in the interior of the envelope, where the dust ices sublimate at 100 K. This has important consequences in the interpretation of the line data. We provide the predictions for the water spectrum, and discuss in detail the lines which will be observed by the Herschel Space Observatory .

A Flattened Protostellar Envelope in Absorption around L1157

Deep Spitzer IRAC images of L1157 reveal many of the details of the outflow and the circumstellar environment of this Class 0 protostar. In IRAC channel 4 (8 μm), there is a flattened structure seen in absorption against the background emission. The structure is perpendicular to the outflow and is extended to a diameter of ~2'. This structure is the first clear detection of a flattened circumstellar envelope or pseudodisk around a Class 0 protostar. Such a flattened morphology is an expected outcome for many collapse theories that include magnetic fields or rotation. We construct an extinction model for a power-law density profile, but we do not constrain the density power-law index.

Resolving and Probing the Circumstellar Disk of the Herbig Ae Star MWC 480 at λ = 1.4 mm: Evolved Dust?

We present high-resolution 045 × 032 observations from the BIMA array toward the Herbig Ae system MWC 480 in the λ = 1.4 mm dust continuum. We resolve a circumstellar disk of radius ~170 AU and constrain the disk parameters by comparing the observations to flat-disk models. These results show that the typical fit parameters of the disk, such as the mass, MD ~ 0.04-0.18 M☉, and the surface density power-law index, p = 0.5 or 1, are comparable to those of the lower mass T Tauri stars. The dust in the MWC 480 disk can be modeled as processed dust material (β ≈ 0.8), similar to the Herbig Ae star CQ Tau disk; the fitted disk parameters are also consistent with less evolved dust (β ≈ 1.2). The possibility of grain growth in the MWC 480 circumstellar disk is supported by the acceptable fits with β ≈ 0.8. The surface density power-law profiles of p = 0.5 and p = 1 can be easily fitted to the MWC 480 disk; however, a surface density power-law profile similar to the minimum mass solar nebula model p = 1.5 is ruled out at an 80% confidence level.

Distribution function of dark matter

There is good evidence from N-body simulations that the velocity distribution in the outer parts of halos is radially anisotropic, with the kinetic energy in the radial direction roughly equal to the sum of that in the two tangential directions. We provide a simple algorithm to generate such cosmologically important distribution functions. Introducing r_E(E), the radius of the largest orbit of a particle with energy E, we show how to write down almost trivially a distribution function of the form f(E,L)=g(r_E)/L for any spherical model -- including the NFW profile. We in addition give the generic form of the distribution function for any model with a local density power-law index and anisotropy parameter, and provide limiting forms appropriate for the central parts and envelopes of dark matter halos. From those, we argue that, regardless of the anisotropy, the density fall-off at large radii must evolve to 1/r^4 or steeper ultimately.

The physical structure of high-mass star-forming cores

We present models of the temperature and density structure of the envelopes of ten deeply embedded massive stars associated with ultracompact H regions. Constraints come from 60-1300 µm photometry including ISO-LWS spectra, maps at 450 and 850 µm, and CS emission line data. Radial profiles extracted from the maps after removing neighbouring sources were modelled taking the chopping process into account. The line data are modelled with a Monte Carlo program and the continuum data with a dust radiative transfer code. For an assumed n(r) ∝ r −p density structure, the index p is found to be uniformly distributed between 1.25 and 2.25 for this sample. The density power law index from radial profiles and emission lines agree well (by ±0.25), while the continuum spectrum sometimes deviates (by ±0.5). Reliable models thus require all three kinds of data.