Rahul Shetty

MAXIMALLY STAR-FORMING GALACTIC DISKS. I. STARBURST REGULATION VIA FEEDBACK-DRIVEN TURBULENCE

Star formation rates in the centers of disk galaxies often vastly exceed those at larger radii, whether measured by the surface density of star formation ΣSFR, by the star formation rate per unit gas mass, ΣSFR/Σ, or even by total output. In this paper, we investigate the idea that central starbursts are self-regulated systems in which the momentum flux injected to the interstellar medium (ISM) by star formation balances the gravitational force confining the ISM gas in the disk. For most starbursts, supernovae are the largest contributor to the momentum flux, and turbulence provides the main pressure support for the predominantly molecular ISM. If the momentum feedback per stellar mass formed is p */m * ~ 3000 km s–1, the predicted star formation rate is ΣSFR ~ 2πGΣ2 m */p * ~ 0.1 M ☉ kpc–2 yr–1(Σ/100 M ☉ pc–2)2 in regions where gas dominates the vertical gravity. We compare this prediction with numerical simulations of vertically resolved disks that model star formation including feedback, finding good agreement for gas surface densities in the range Σ ~ 102-103 M ☉ pc–2. We also compare to a compilation of star formation rates and gas contents from local and high-redshift galaxies (both mergers and normal galaxies), finding good agreement provided that the conversion factor X CO from integrated CO emission to H2 surface density decreases modestly as Σ and ΣSFR increase. Star formation rates in dense, turbulent gas are also expected to depend on the gravitational free-fall time at the corresponding mean ISM density ρ0; if the star formation efficiency per free-fall time is eff(ρ0) ~ 0.01, the turbulent velocity dispersion driven by feedback is expected to be vz = 0.4 eff(ρ0)p */m * ~ 10 km s–1, relatively independent of Σ or ΣSFR. Turbulence-regulated starbursts (controlled by kinetic momentum feedback) are part of the larger scheme of self-regulation; primarily atomic low-Σ outer disks may have star formation regulated by ultraviolet heating feedback, whereas regions at extremely high Σ may be regulated by feedback of stellar radiation that is reprocessed into trapped infrared.

THE EFFECT OF NOISE ON THE DUST TEMPERATURE-SPECTRAL INDEX CORRELATION

We investigate how uncertainties in flux measurements affect the results from modified blackbody spectral energy distribution (SED) fits. We show that an inverse correlation between the dust temperature T and spectral index β naturally arises from least-squares fits due to the uncertainties, even for sources with a single T and β. Fitting SEDs to noisy fluxes solely in the Rayleigh-Jeans regime produces unreliable T and β estimates. Thus, for long wavelength observations (λ 200 μm), or for warm sources (T 60 K), it becomes difficult to distinguish sources with different temperatures. We assess the role of noise in recent observational results that indicate an inverse and continuously varying T-β relation. Though an inverse and continuous T-β correlation may be a physical property of dust in the interstellar medium, we find that the observed inverse correlation may be primarily due to noise.

Global Modeling of Spur Formation in Spiral Galaxies

We investigate the formation of substructure in spiral galaxies using global MHD simulations, including gas self-gravity. Local modeling by Kim & Ostriker previously showed that self-gravity and magnetic fields cause rapid growth of overdensities in spiral arms; differential compression of gas flowing through the arms then results in the formation of sheared structures in the interarms. These sheared structures resemble features described as spurs or feathers in optical and IR observations of many spiral galaxies. Global modeling extends previous local models by including the full effects of curvilinear coordinates, a realistic log-spiral perturbation, self-gravitational contribution from five radial wavelengths of the spiral shock, and variation of density and epicyclic frequency with radius. We show that with realistic Toomre Q-values self-gravity and galactic differential rotation produce filamentary gaseous structures with kiloparsec-scale separations, regardless of the strength—or even presence—of a stellar spiral potential. However, a sufficiently strong spiral potential is required to produce true spurs, consisting of interarm structures emerging from gas concentrations in the main spiral arms. In models where Q is initially constant, filaments due to interarm self-gravity grow mainly in the outer regions, whereas true arm spurs grow only in the inner regions. For models with Q ∝ R, outer regions are intrinsically more stable, so background interarm filaments do not grow, but arm spurs can develop if the spiral potential is strong. Unlike independently growing background filaments, the orientation of arm spurs depends on galactic location. Inside corotation, spurs emanate outward, on the convex side of the arm; outside corotation, spurs grow inward, on the concave side of the arm. Based on orientation and the relation to arm clumps, it is possible to distinguish true spurs that originate as instabilities in the arms from independently growing background filaments. We measure spur spacings of ~3-5 times the Jeans length in the arm and arm clump masses of ≈107 M☉. Finally, we have also studied models without self-gravity, finding that magnetic fields suppress a purely hydrodynamic instability recently proposed by Wada & Koda as a means of growing interarm spurs and feathers. Our models also suggest that magnetic fields are important in preserving grand-design spiral structure when gas in the arms fragments via self-gravity into GMCs.

DUST SPECTRAL ENERGY DISTRIBUTIONS IN THE ERA OF HERSCHEL AND PLANCK: A HIERARCHICAL BAYESIAN-FITTING TECHNIQUE

We present a hierarchical Bayesian method for fitting infrared spectral energy distributions (SEDs) of dust emission to observed fluxes. Under the standard assumption of optically thin single temperature (T) sources, the dust SED as represented by a power-law-modified blackbody is subject to a strong degeneracy between T and the spectral index β. The traditional non-hierarchical approaches, typically based on χ2 minimization, are severely limited by this degeneracy, as it produces an artificial anti-correlation between T and β even with modest levels of observational noise. The hierarchical Bayesian method rigorously and self-consistently treats measurement uncertainties, including calibration and noise, resulting in more precise SED fits. As a result, the Bayesian fits do not produce any spurious anti-correlations between the SED parameters due to measurement uncertainty. We demonstrate that the Bayesian method is substantially more accurate than the χ2 fit in recovering the SED parameters, as well as the correlations between them. As an illustration, we apply our method to Herschel and submillimeter ground-based observations of the star-forming Bok globule CB244. This source is a small, nearby molecular cloud containing a single low-mass protostar and a starless core. We find that T and β are weakly positively correlated—in contradiction with the χ2 fits, which indicate a T-β anti-correlation from the same data set. Additionally, in comparison to the χ2 fits the Bayesian SED parameter estimates exhibit a reduced range in values.

Cloud and Star Formation in Disk Galaxy Models with Feedback

We include feedback in global hydrodynamic simulations in order to study the star formation properties, and gas structure and dynamics, in models of galactic disks. In previous work we studied the growth of clouds and spiral substructureduetogravitationalinstability.Weextendthesemodelsbyimplementingfeedbackingravitationallybound clouds; momentum (due to massive stars) is injected at a rate proportional to the star formation rate. This mechanical energy disperses cloud gas back into the surrounding interstellar medium, truncating star formation in a given cloud andraisingtheoveralllevelof ambientturbulence.Propagatingstarformationcanhoweveroccurasexpandingshells collide, enhancing the density and triggering new cloud and star formation. By controlling the momentum injection per massive star and the specific star formation rate in dense gas, we find that the negative effects of high turbulence outweigh the positive ones, andin net, feedback reduces the fraction of dense gas and, thus,the overallstar formation rate. The properties of the large clouds that form are not, however, very sensitive to feedback, with cutoff masses of a fewmillionM� ,similartoobservations.Wefindarelationshipbetweenthestarformationratesurfacedensityandthe gas surface density with a power-law index � 2 for our models with the largest dynamic range, consistent with theoretical expectations for our model of disk flaring. We point out that the value of the ‘‘Kennicutt-Schmidt’’ index found in numerical simulations (and likely in nature) depends on the thickness of the disk, and therefore, a selfconsistent determination must include turbulence and resolve the vertical structure. With our simple feedback prescription (a single combined star formation event per cloud), we find that global spiral patterns are not sustained; less correlated feedback and smaller scale turbulence appear to be necessary for spiral patterns to persist. Subject headingg galaxies: ISM — ISM: clouds — ISM: kinematics and dynamics — stars: formation — turbulence

Evidence for a non-universal Kennicutt-Schmidt relationship using hierarchical Bayesian linear regression

For investigating the relationship between the star formation rate and gas surface density, we develop a Bayesian linear regression method that rigorously treats measurement uncertainties and accounts for hierarchical data structure. The hierarchical Bayesian method simultaneously estimates the intercept, slope, and scatter about the regression line of each individual subject (e.g. a galaxy) and the population (e.g. an ensemble of galaxies). Using synthetic datasets, we demonstrate that the method accurately recovers the underlying parameters of both the individuals and the population, especially when compared to commonly employed ordinary least squares techniques, such as the bisector fit. We apply the hierarchical Bayesian method to estimate the Kennicutt-Schmidt (KS) parameters of a sample of spiral galaxies compiled by Bigiel et al. (2008). We find significant variation in the KS parameters, indicating that no single KS relationship holds for all galaxies. This suggests that the relationship between molecular gas and star formation differs from galaxy to galaxy, possibly due to the influence of other physical properties within a given galaxy, such as metallicity, molecular gas fraction, stellar mass, and/or magnetic fields. In four of the seven galaxies the slope estimates are sub-linear, especially for M51, where unity is excluded at the 2� level. We estimate the mean index of the KS relationship for the population to be 0.84, with 2� range [0.63, 1.0]. For the galaxies with sub-linear KS relationships, a possible interpretation is that CO emission is tracing some molecular gas that is not directly associated with star formation. Equivalently, a sub-linear KS relationship may be indicative of an increasing gas depletion time at higher surface densities, as traced by CO emission. The hierarchical Bayesian method can account for all sources of uncertainties, including variations in the conversion of observed intensities to star formation rates and gas surface densities (e.g. the XCO factor), and is therefore well suited for a thorough statistical analysis of the KS relationship.

The Mass-Size Relation From Clouds to Cores. I. A New Probe of Structure In Molecular Clouds

We use a new contour-based map analysis technique to measure the mass and size of molecular cloud fragments continuously over a wide range of spatial scales (0.05 ≤ r/pc ≤ 10), i.e., from the scale of dense cores to those of entire clouds. The present paper presents the method via a detailed exploration of the Perseus molecular cloud. Dust extinction and emission data are combined to yield reliable scale-dependent measurements of mass. This scale-independent analysis approach is useful for several reasons. First, it provides a more comprehensive characterization of a map (i.e., not biased toward a particular spatial scale). Such a lack of bias is extremely useful for the joint analysis of many data sets taken with different spatial resolution. This includes comparisons between different cloud complexes. Second, the multi-scale mass-size data constitute a unique resource to derive slopes of mass-size laws (via power-law fits). Such slopes provide singular constraints on large-scale density gradients in clouds.

RADIAL DEPENDENCE OF THE PATTERN SPEED OF M51

The grand-design spiral galaxy M51 has long been a crucial target for theories of spiral structure. Studies of this iconic spiral can address the question of whether strong spiral structure is transient (e.g., interaction-driven) or long-lasting. As a clue to the origin of the structure in M51, we investigate evidence for radial variation in the spiral pattern speed using the radial Tremaine-Weinberg (TWR) method. We implement the method on CO observations tracing the ISM-dominant molecular component. Results from the methods numerical implementation—combined with regularization, which smooths intrinsically noisy solutions—indicate two distinct patterns speeds inside 4 kpc at our derived major axis P.A. = 170°, both ending at corotation and both significantly higher than the conventionally adopted global value. Inspection of the rotation curve suggests that the pattern speed interior to 2 kpc lacks an ILR, consistent with the leading structure seen in HST near-IR observations. We also find tentative evidence for a lower pattern speed between 4 and 5.3 kpc measured by extending the regularized zone. As with the original TW method, uncertainty in major axis position angle (P.A.) is the largest source of error in the calculation; in this study, where δP.A. = ± 5° , a ~20% error is introduced to the parameters of the speeds at P.A. = 170°. Accessory to this standard uncertainty, solutions with P.A. = 175° (also admitted by the data) exhibit only one pattern speed inside 4 kpc, and we consider this circumstance under the semblance of a radially varying P.A.

The Dust Emissivity Spectral Index in the Starless Core TMC-1C

In this paper, we present a dust emission map of the starless core TMC-1C taken at 2100 μm. Along with maps at 160, 450, 850, and 1200 μm, we study the dust emissivity spectral index from the (sub)millimeter spectral energy distribution, and find that it is close to the typically assumed value of β = 2. We also map the dust temperature and column density in TMC-1C, and find that at the position of the dust peak (A_V ~ 50) the line-of-sight-averaged temperature is ~7 K. Employing simple Monte Carlo modeling, we show that the data are consistent with a constant value for the emissivity spectral index over the whole map of TMC-1C.

Line Profiles of Cores within Clusters. I. The Anatomy of a Filament

Observations are revealing the ubiquity of filamentary structures in molecular clouds. As cores are often embedded in filaments, it is important to understand how line profiles from such systems differ from those of isolated cores. We perform radiative transfer calculations on a hydrodynamic simulation of a molecular cloud in order to model line emission from collapsing cores embedded in filaments. We model two optically thick lines, CS(2-1) and HCN(1-0), and one optically thin line, N2H+(1-0), from three embedded cores. In the hydrodynamic simulation, gas self-gravity, turbulence, and bulk flows create filamentary regions within which cores form. Though the filaments have large dispersions, the N2H+(1-0) lines indicate subsonic velocities within the cores. We find that the observed optically thick line profiles of CS(2-1) and HCN(1-0) vary drastically with viewing angle. In over 50% of viewing angles, there is no sign of a blue asymmetry, an idealized signature of infall motions in an isolated spherical collapsing core. Profiles that primarily trace the cores, with little contribution from the surrounding filament, are characterized by a systematically higher HCN(1-0) peak intensity. The N2H+(1-0) lines do not follow this trend. We demonstrate that red asymmetric profiles are also feasible in the optically thick lines, due to emission from the filament or one-sided accretion flows onto the core. We conclude that embedded cores may frequently undergo collapse without showing a blue asymmetric profile, and that observational surveys including filamentary regions may underestimate the number of collapsing cores if based solely on profile shapes of optically thick lines.