Hot Molecular Cores and High-Mass Star Formation

This review covers hot cores in the context of high-mass star formation. After giving an overview of chemical processes and diversity during high-mass star formation, it reviews the `warm envelope' phase which probably precedes the formation of hot cores. Some recent determinations of the cosmic-ray ionization rate are discussed, as well as recent evidence for hot cores around low-mass stars. Routes for future hot core research are outlined.Comment: 8 pages, 1 figure; to appear in the Proceeding of IAU Symposium 221, Star Formation at High Angular Resolution, Editors M. Burton, R. Jayawardhana & T. Bourke, Astronomical Society of the Pacifi

Asymptotic behavior of the finite-size magnetization as a function of the speed of approach to criticality

The main focus of this paper is to determine whether the thermodynamic magnetization is a physically relevant estimator of the finite-size magnetization. This is done by comparing the asymptotic behaviors of these two quantities along parameter sequences converging to either a second-order point or the tricritical point in the mean-field Blume--Capel model. We show that the thermodynamic magnetization and the finite-size magnetization are asymptotic when the parameter $\alpha$ governing the speed at which the sequence approaches criticality is below a certain threshold $\alpha_0$. However, when $\alpha$ exceeds $\alpha_0$, the thermodynamic magnetization converges to 0 much faster than the finite-size magnetization. The asymptotic behavior of the finite-size magnetization is proved via a moderate deviation principle when $0\alpha_0$. To the best of our knowledge, our results are the first rigorous confirmation of the statistical mechanical theory of finite-size scaling for a mean-field model.Comment: Published in at http://dx.doi.org/10.1214/10-AAP679 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Ginzburg-Landau Polynomials and the Asymptotic Behavior of the Magnetization Near Critical and Tricritical Points

For the mean-field version of an important lattice-spin model due to Blume and Capel, we prove unexpected connections among the asymptotic behavior of the magnetization, the structure of the phase transitions, and a class of polynomials that we call the Ginzburg-Landau polynomials. The model depends on the parameters n, beta, and K, which represent, respectively, the number of spins, the inverse temperature, and the interaction strength. Our main focus is on the asymptotic behavior of the magnetization m(beta_n,K_n) for appropriate sequences (beta_n,K_n) that converge to a second-order point or to the tricritical point of the model and that lie inside various subsets of the phase-coexistence region. The main result states that as (beta_n,K_n) converges to one of these points (beta,K), m(beta_n,K_n) ~ c |beta - beta_n|^gamma --> 0. In this formula gamma is a positive constant, and c is the unique positive, global minimum point of a certain polynomial g that we call the Ginzburg-Landau polynomial. This polynomial arises as a limit of appropriately scaled free-energy functionals, the global minimum points of which define the phase-transition structure of the model. For each sequence (beta_n,K_n) under study, the structure of the global minimum points of the associated Ginzburg-Landau polynomial mirrors the structure of the global minimum points of the free-energy functional in the region through which (beta_n,K_n) passes and thus reflects the phase-transition structure of the model in that region. The properties of the Ginzburg-Landau polynomials make rigorous the predictions of the Ginzburg-Landau phenomenology of critical phenomena, and the asymptotic formula for m(beta_n,K_n) makes rigorous the heuristic scaling theory of the tricritical point.Comment: 70 pages, 8 figure

Limits on the cosmic-ray ionization rate toward massive young stars

Recent models of the envelopes of seven massive protostars are used to analyze observations of H3+ infrared absorption and H13CO+ submillimeter emission lines toward these stars, and to constrain the cosmic-ray ionization rate zeta. The H13CO+ gives best-fit values of zeta=(2.6+/- 1.8) x 10^-17 s^-1, in good agreement with diffuse cloud models and with recent Voyager/Pioneer data but factors of up to 7 lower than found from the H3+ data. No relation of zeta with luminosity or total column density is found, so that local (X-ray) ionization and shielding against cosmic rays appear unimportant for these sources. The difference between the H3+ and H13CO+ results and the correlation of N(H3+) with heliocentric distance suggest that intervening clouds contribute significantly to the H3+ absorptions in the more distant regions. The most likely absorbers are low-density (<~10^4 cm^-3) clouds with most carbon in neutral form or in CO.Comment: To be published in A&A 358 (Letters); 4 pages including 3 figure

Detection of extragalactic H3O+

The H3O+ molecule probes the oxygen chemistry and the ionization rate of dense circumnuclear gas in galaxies. In particular, recent H3O+ observations show variations in the cosmic-ray ionization rate by factors of $>$10 within our Galaxy. Using the JCMT, we have observed the 364 GHz line of p-H3O+ in the centers of M82 and Arp 220. In Arp 220, the line profile suggests that the emission originates in the Western nucleus. In M82, both the eastern molecular peak and the circumnuclear region contribute to the emission. The derived column densities, abundances, and H3O+ / H2O ratios indicate ionization rates similar to or even exceeding that in the Galactic Center. Model calculations of the chemistry of irradiated molecular gas indicate a likely origin of this high ionization rate in the extended, evolved starburst of M82. In contrast, irradiation by X-rays from the AGN disk is the most likely model for Arp 220.Comment: Accepted by A&A Letters; 4-5 pages depending on paper format; two b/w figure

Water abundance variations around high-mass protostars: HIFI observations of the DR21 region

Context. Water is a key molecule in the star formation process, but its spatial distribution in star-forming regions is not well known. Aims. We study the distribution of dust continuum and H_(2)O and ^(13)CO line emission in DR21, a luminous star-forming region with a powerful outflow and a compact H ii region. Methods. Herschel-HIFI spectra near 1100 GHz show narrow ^(13)CO 10–9 emission and H_(2)O 1_(11)–0_(00) absorption from the dense core and broad emission from the outflow in both lines. The H_(2)O line also shows absorption by a foreground cloud known from ground-based observations of low-J CO lines. Results. The dust continuum emission is extended over 36” FWHM, while the ^(13)CO and H_(2)O lines are confined to ≈24” or less. The foreground absorption appears to peak further North than the other components. Radiative transfer models indicate very low abundances of ~2×10^(-10) for H_(2)O and ~8×10^(-7) for ^(13)CO in the dense core, and higher H_(2)O abundances of ~4×10^(-9) in the foreground cloud and ~7×10^(-7) in the outflow. Conclusions. The high H_(2)O abundance in the warm outflow is probably due to the evaporation of water-rich icy grain mantles, while the H_(2)O abundance is kept down by freeze-out in the dense core and by photodissociation in the foreground cloud

The Evolution of Altruism in Spatially Structured Populations

The evolution of altruism in humans is still an unresolved puzzle. Helping other individuals is often kinship-based or reciprocal. Several examples show, however, that altruism goes beyond kinship and reciprocity and people are willing to support unrelated others even when this is at a cost and they receive nothing in exchange. Here we examine the evolution of this "pure" altruism with a focus on altruistic teaching. Teaching is modeled as a knowledge transfer which enhances the survival chances of the recipient, but reduces the reproductive efficiency of the provider. In an agent-based simulation we compare evolutionary success of genotypes that have willingness to teach with those who do not in two different scenarios: random matching of individuals and spatially structured populations. We show that if teaching ability is combined with an ability to learn and individuals encounter each other on a spatial proximity basis, altruistic teaching will attain evolutionary success in the population. Settlement of the population and accumulation of knowledge are emerging side-products of the evolution of altruism. In addition, in large populations our simple model also produces a counterintuitive result that increasing the value of knowledge keeps fewer altruists alive.Altruism, Teaching, Knowledge Transfer, Spatially Structured Social Dilemmas

Energetic radiation and the sulfur chemistry of protostellar envelopes: Submillimeter interferometry of AFGL 2591

CONTEXT: The chemistry in the inner few thousand AU of accreting envelopes around young stellar objects is predicted to vary greatly with far-UV and X-ray irradiation by the central star. Aim We search for molecular tracers of high-energy irradiation by the protostar in the hot inner envelope. METHODS: The Submillimeter Array (SMA) has observed the high-mass star forming region AFGL 2591 in lines of CS, SO, HCN, HCN(v2=1), and HC15N with 0.6" resolution at 350 GHz probing radial scales of 600-3500 AU for an assumed distance of 1 kpc. The SMA observations are compared with the predictions of a chemical model fitted to previous single-dish observations. RESULTS: The CS and SO main peaks are extended in space at the FWHM level, as predicted in the model assuming protostellar X-rays. However, the main peak sizes are found smaller than modeled by nearly a factor of 2. On the other hand, the lines of CS, HCN, and HC15N, but not SO and HCN(v2=1), show pedestal emissions at radii of about 3500 AU that are not predicted. All lines except SO show a secondary peak within the approaching outflow cone. A dip or null in the visibilities caused by a sharp decrease in abundance with increasing radius is not observed in CS and only tentatively in SO. CONCLUSIONS: The emission of protostellar X-rays is supported by the good fit of the modeled SO and CS amplitude visibilities including an extended main peak in CS. The broad pedestals can be interpreted by far-UV irradiation in a spherically non-symmetric geometry, possibly comprising outflow walls on scales of 3500 -- 7000 AU. The extended CS and SO main peaks suggest sulfur evaporation near the 100 K temperature radius.Comment: Astronomy and Astrophysics, in pres

Chemical Modelling of Young Stellar Objects, I. Method and Benchmarks

Upcoming facilities such as the Herschel Space Observatory or ALMA will deliver a wealth of molecular line observations of young stellar objects (YSOs). Based on line fluxes, chemical abundances can then be estimated by radiative transfer calculations. To derive physical properties from abundances, the chemical network needs to be modeled and fitted to the observations. This modeling process is however computationally exceedingly demanding, particularly if in addition to density and temperature, far UV (FUV) irradiation, X-rays, and multi-dimensional geometry have to be considered. We develop a fast tool, suitable for various applications of chemical modeling in YSOs. A grid of the chemical composition of the gas having a density, temperature, FUV irradiation and X-ray flux is pre-calculated as a function of time. A specific interpolation approach is developed to reduce the database to a feasible size. Published models of AFGL 2591 are used to verify the accuracy of the method. A second benchmark test is carried out for FUV sensitive molecules. The novel method for chemical modeling is more than 250,000 times faster than direct modeling and agrees within a mean factor of 1.35. The tool is distributed for public use. In the course of devloping the method, the chemical evolution is explored: We find that X-ray chemistry in envelopes of YSOs can be reproduced by means of an enhanced cosmic-ray ionization rate. We further find that the abundance of CH+ in low-density gas with high ionization can be enhanced by the recombination of doubly ionized carbon (C++) and suggest a new value for the initial abundance of the main sulphur carrier in the hot-core.Comment: Accepted by ApJS. 24 pages, 15 figures. A version with higher resolution images is available from http://www.astro.phys.ethz.ch/staff/simonbr/papgridI.pdf . Online data available at http://www.astro.phys.ethz.ch/chemgrid.html . Second paper of this series of papers available at arXiv:0906.058