Matrix-Variate Regressions and Envelope Models

Modern technology often generates data with complex structures in which both response and explanatory variables are matrix-valued. Existing methods in the literature are able to tackle matrix-valued predictors but are rather limited for matrix-valued responses. In this article, we study matrix-variate regressions for such data, where the response Y on each experimental unit is a random matrix and the predictor X can be either a scalar, a vector, or a matrix, treated as non-stochastic in terms of the conditional distribution Y|X. We propose models for matrix-variate regressions and then develop envelope extensions of these models. Under the envelope framework, redundant variation can be eliminated in estimation and the number of parameters can be notably reduced when the matrix-variate dimension is large, possibly resulting in significant gains in efficiency. The proposed methods are applicable to high dimensional settings.Comment: 28 pages, 4 figure

2-D and 3-D Radiation Transfer Models of High-Mass Star Formation

2-D and 3-D radiation transfer models of forming stars generally produce bluer 1-10 micron colors than 1-D models of the same evolutionary state and envelope mass. Therefore, 1-D models of the shortwave radiation will generally estimate a lower envelope mass and later evolutionary state than multidimensional models. 1-D models are probably reasonable for very young sources, or longwave analysis (wavelengths > 100 microns). In our 3-D models of high-mass stars in clumpy molecular clouds, we find no correlation between the depth of the 10 micron silicate feature and the longwave (> 100 micron) SED (which sets the envelope mass), even when the average optical extinction of the envelope is >100 magnitudes. This is in agreement with the observations of Faison et al. (1998) of several UltraCompact HII (UCHII) regions, suggesting that many of these sources are more evolved than embedded protostars. We have calculated a large grid of 2-D models and find substantial overlap between different evolutionary states in the mid-IR color-color diagrams. We have developed a model fitter to work in conjunction with the grid to analyze large datasets. This grid and fitter will be expanded and tested in 2005 and released to the public in 2006.Comment: 10 pages, 8 figures, to appear in the proceedings of IAU Symp 227, Massive Star Birth: A Crossroads of Astrophysics, (Cesaroni R., Churchwell E., Felli M., Walmsley C. editors

Formation of the postmitotic nuclear envelope from extended ER cisternae precedes nuclear pore assembly

During mitosis, the nuclear envelope merges with the endoplasmic reticulum (ER), and nuclear pore complexes are disassembled. In a current model for reassembly after mitosis, the nuclear envelope forms by a reshaping of ER tubules. For the assembly of pores, two major models have been proposed. In the insertion model, nuclear pore complexes are embedded in the nuclear envelope after their formation. In the prepore model, nucleoporins assemble on the chromatin as an intermediate nuclear pore complex before nuclear envelope formation. Using live-cell imaging and electron microscope tomography, we find that the mitotic assembly of the nuclear envelope primarily originates from ER cisternae. Moreover, the nuclear pore complexes assemble only on the already formed nuclear envelope. Indeed, all the chromatin-associated Nup 107–160 complexes are in single units instead of assembled prepores. We therefore propose that the postmitotic nuclear envelope assembles directly from ER cisternae followed by membrane-dependent insertion of nuclear pore complexes

Thermal evolution and structure models of the transiting super-Earth GJ 1214b

The planet GJ 1214b is the second known super-Earth with a measured mass and radius. Orbiting a quiet M-star, it receives considerably less mass-loss driving X-ray and UV radiation than CoRoT-7b, so that the interior may be quite dissimilar in composition, including the possibility of a large fraction of water. We model the interior of GJ 1214b assuming a two-layer (envelope+rock core) structure where the envelope material is either H/He, pure water, or a mixture of H/He and H2O. Within this framework we perform models of the thermal evolution and contraction of the planet. We discuss possible compositions that are consistent with Mp=6.55 ME, Rp=2.678 RE, an age tau=3-10 Gyr, and the irradiation level of the atmosphere. These conditions require that if water exists in the interior, it must remain in a fluid state, with important consequences for magnetic field generation. These conditions also require the atmosphere to have a deep isothermal region extending down to 80-800 bar, depending on composition. Our results bolster the suggestion of a metal-enriched H/He atmosphere for the planet, as we find water-world models that lack an H/He atmosphere to require an implausibly large water-to-rock ratio of more than 6:1. We instead favor a H/He/H2O envelope with high water mass fraction (~0.5-0.85), similar to recent models of the deep envelope of Uranus and Neptune. Even with these high water mass fractions in the H/He envelope, generally the bulk composition of the planet can have subsolar water:rock ratios. Dry, water-enriched, and pure water envelope models differ to an observationally significant level in their tidal Love numbers k2 of respectively ~0.018, 0.15, and 0.7.Comment: 11 pages, 6 figures, 1 table, accepted to Ap

Analytical expressions for the envelope binding energy of giants as a function of basic stellar parameters

The common-envelope (CE) phase is an important stage in the evolution of binary stellar populations. The most common way to compute the change in orbital period during a CE is to relate the binding energy of the envelope of the Roche-lobe filling giant to the change in orbital energy. Especially in population-synthesis codes, where the evolution of millions of stars must be computed and detailed evolutionary models are too expensive computationally, simple approximations are made for the envelope binding energy. In this study, we present accurate analytic prescriptions based on detailed stellar-evolution models that provide the envelope binding energy for giants with metallicities between Z = 10-4 and Z = 0.03 and masses between 0.8 Msun and 100 Msun, as a function of the metallicity, mass, radius and evolutionary phase of the star. Our results are also presented in the form of electronic data tables and Fortran routines that use them. We find that the accuracy of our fits is better than 15% for 90% of our model data points in all cases, and better than 10% for 90% of our data points in all cases except the asymptotic giant branches for three of the six metallicities we consider. For very massive stars (M > 50 Msun), when stars lose more than ~20% of their initial mass due to stellar winds, our fits do not describe the models as accurately. Our results are more widely applicable - covering wider ranges of metallicity and mass - and are of higher accuracy than those of previous studies

Distribution and kinematics of the HCN(3-2) emission down to the innermost region in the envelope of the O-rich star W Hya

We report high angular resolution observations of the HCN (3-2) line emission in the circumstellar envelope of the O-rich star W Hya with the Submillimeter Array. The proximity of this star allows us to image its molecular envelope with a spatial resolution of just ~40 AU, corresponding to about 10 times the stellar diameter. We resolve the HCN (3-2) emission and find that it is centrally peaked and has a roughly spherically symmetrical distribution. This shows that HCN is formed in the innermost region of the envelope (within ~10 stellar radii), which is consistent with predictions from pulsation-driven shock chemistry models, and rules out the scenario in which HCN forms through photochemical reactions in the outer envelope. Our model suggests that the envelope decreases steeply in temperature and increases smoothly in velocity with radius, inconsistent with the standard model for mass-loss driven by radiative pressure on dust grains. We detect a velocity gradient of ~5 km/s in the NW--SE direction over the central 40 AU. This velocity gradient is reminescent of that seen in OH maser lines, and could be caused by the rotation of the envelope or by a weak bipolar outflow.Comment: accepted for publication in ApJ

The metallicity dependence of envelope inflation in massive stars

Recently it has been found that models of massive stars reach the Eddington limit in their interior, which leads to dilute extended envelopes. We perform a comparative study of the envelope properties of massive stars at different metallicities, with the aim to establish the impact of the stellar metallicity on the effect of envelope inflation. We analyse published grids of core-hydrogen burning massive star models computed with metallicities appropriate for massive stars in the Milky Way, the LMC and the SMC, the very metal poor dwarf galaxy I Zwicky 18, and for metal-free chemical composition. Stellar models of all the investigated metallicities reach and exceed the Eddington limit in their interior, aided by the opacity peaks of iron, helium and hydrogen, and consequently develop inflated envelopes. Envelope inflation leads to a redward bending of the zero-age main sequence and a broadening of the main sequence band in the upper part of the Hertzsprung-Russell diagram. We derive the limiting L/M-values as function of the stellar surface temperature above which inflation occurs, and find them to be larger for lower metallicity. While Galactic models show inflation above ~29 Msun, the corresponding mass limit for Population III stars is ~150 Msun. While the masses of the inflated envelopes are generally small, we find that they can reach 1-100 Msun in models with effective temperatures below ~8000 K, with higher masses reached by models of lower metallicity. Envelope inflation is expected to occur in sufficiently massive stars at all metallicities, and is expected to lead to rapidly growing pulsations, high macroturbulent velocities, and might well be related to the unexplained variability observed in Luminous Blue Variables like S Doradus and Eta Carina.Comment: 16 pages (with Appendix), accepted in A&

On the alpha formalism for the common envelope interaction

The {\alpha}-formalism is a common way to parametrize the common envelope interaction between a giant star and a more compact companion. The {\alpha} parameter describes the fraction of orbital energy released by the companion that is available to eject the giant star's envelope. By using new, detailed stellar evolutionary calculations we derive a user-friendly prescription for the {\lambda} parameter and an improved approximation for the envelope binding energy, thus revising the {\alpha} equation. We then determine {\alpha} both from simulations and observations in a self consistent manner. By using our own stellar structure models as well as population considerations to reconstruct the primary's parameters at the time of the common envelope interaction, we gain a deeper understanding of the uncertainties. We find that systems with very low values of q (the ratio of the companion's mass to the mass of the primary at the time of the common envelope interaction) have higher values of {\alpha}. A fit to the data suggests that lower mass companions are left at comparable or larger orbital separations to more massive companions. We conjecture that lower mass companions take longer than a stellar dynamical time to spiral in to the giant's core, and that this is key to allowing the giant to use its own thermal energy to help unbind its envelope. As a result, although systems with light companions might not have enough orbital energy to unbind the common envelope, they might stimulate a stellar reaction that results in the common envelope ejection.Comment: 17 pages, 8 figures. Accepted by MNRA