Schmidt Law Research Articles

Star formation and feedback in smoothed particle hydrodynamic simulations – I. Isolated galaxies

We present an analysis of star formation and feedback recipes appropriate for galactic smoothed particle hydrodynamics simulations. Using an isolated Milky Way-like galaxy, we constrain these recipes based on well-established observational results. Our star formation recipe is based on that of Katz (1992) with the additional inclusion of physically motivated supernova feedback recipes. We propose a new feedback recipe in which type II supernovae are modelled using an analytical treatment of blastwaves. With this feedback mechanism and a tuning of other star formation parameters, the star formation in our isolated Milky Way-like galaxy is constant and follows the slope and normalisation of the observed Schmidt law. In addition, we reproduce the low density cutoff and filamentary structure of star formation observed in disk galaxies. Our final recipe will enable better comparison of cosmological N-body simulations with observations.

The infrared compactness-temperature relation for quiescent and starburst galaxies

Context. IRAS observations show the existence of a correlation between the infrared luminosity LIR and dust temperature Td in star-forming galaxies, in which larger LIR leads to higher dust temperature. The LIR–Td relation is commonly seen as reflecting the increase in dust temperature in galaxies with higher star formation rate (SFR). Even though the correlation shows a significant amount of dispersion, a unique relation has been commonly used to construct spectral energy distributions (SEDs) of galaxies in distant universe studies, such as source number counting or photometric redshift determination. Aims. In this work, we introduce a new parameter, namely the size of the star-forming region r IR and lay out the empirical and modelled relation between the global parameters LIR, Td and r IR of IR-bright non-AGN galaxies. Methods. IRAS 60-to-100 µm color is used as a proxy for the dust temperature and the 1.4 GHz radio contiuum (RC) emission for the infrared spatial distribution. The analysis has been carried out on two samples. The first one is made of the galaxies from the 60 µm flux-limited IRAS Revised Bright Galaxy Samples (RBGS) which have a reliable RC size estimate from the VLA follow-ups of the IRAS Bright Galaxy Samples. The second is made of the sources from the 170 µm ISOPHOT Serendipity Sky Survey (ISOSSS) which are resolved by the NRAO VLA Sky Survey (NVSS) or by the Faint Images of the Radio Sky at Twenty-cm survey (FIRST). Results. We show that the dispersion in the LIR–Td diagram can be reduced to a relation between the infrared surface brightness and the dust temperature, a relation that spans 5 orders of magnitude in surface brightness. Conclusions. We explored the physical processes giving rise to the ΣIR–Td relation, and show that it can be derived from the Schmidt law, which relates the star formation rate to the gas surface density.

The star-formation efficiency and density of the disks of spiral galaxies

The four well studied spiral galaxies M33, M81, M100, and M101 are used to analyze the dependences of the star-formation rate (SFR) and star-formation efficiency (SFE = SFR/Mgas) on galactocentric distance R and the photometric and some kinematic parameters of galactic disks. The dependences SFR(R) were estimated based on UV and far-infrared data using published extinction-corrected UV brightness profiles of the galaxies. The local SFE values are most closely related to the surface brightness (density) of the galactic disk at a given R, with this dependence being the same for all four galaxies (except for their central regions). In order to explain the observed disk densities in terms of a simple conservative model (“toy model”) for the evolution of the gas density, the local value of the parameter N in the Schmidt law for the disk (SFR ∼ σgasN) must not exceed unity. In this case, the observed dependences σgas(R) and SFE(R) can be matched assuming that accretion is occuring in the central regions of the disks.

Threshold between Spontaneous and Cloud-Collisional Star Formation

Abstract Based on simple physical and geometric assumptions, we have calculated the mean surface molecular density of spiral galaxies at the threshold between star formation induced by cloud-cloud collision and spontaneous gravitational collapse. The calculated threshold is approximately $\log \Sigma_\mathrm{crit} \sim 2.5$, where $\Sigma \;[{{{M}_{\odot}}} \,\mathrm{pc}^{-2}]$ is the observed surface mass density of an assumed flat gas disk. Above this limit, the rate of molecular cloud collisions dominates over spontaneous molecular cloud collapse. This model may explain the apparent discontinuity in the Schmidt law found recently at $2 \lesssim \log \Sigma \lesssim 3$.

The distribution of the ISM in the Milky Way

We use the COBE/DIRBE (1.2, 2.2, 60, 100, 140, and 240 μm) maps and the COBE/FIRAS spectra (for the wavelength range 100-1000 μm) to constrain a model for the spatial distribution of the dust, the stars, and the gas in the Milky Way. By assuming exponential axisymmetric distributions for the dust and the stars and by performing the corresponding radiative transfer calculations we closely (given the simple geometry of the model) reproduce the FIR and NIR maps of the Milky Way. Similar distributions for the atomic and molecular hydrogen in the disk are used (with an inner cut-off radius for the atomic hydrogen) to fit the gas data. The star formation rate as a function of the Galactic radius is derived from the FIR emission and is well in agreement with existing estimates from various star formation tracers. The gas surface density is plotted against the star formation rate density and an “intrinsic” Galactic Schmidt law is derived with excellent agreement with the “external” Schmidt law found for spiral galaxies. The Milky Way is found to consume ~ and ~ of its gas in the outer and inner regions respectively (for a period of 0.1 Gyr) to make stars. The dust-induced color excess observed in various directions and distances (up to ~6.5 kpc) with well-studied Cepheid stars is compared with the model predictions showing a good agreement. The simple assumption of exponential distributions of stars and dust in the Galaxy is found to be quite instructive and adequate in modeling all the available data sets from 0.45 μm (B-band) to 1000 μm.

Radial Variation of Attenuation and Star Formation in the Largest Late‐Type Disks Observed with GALEX

For a sample of 43 nearby, late-type galaxies, we have investigated the radial variation of both the current star formation rate and the dust-induced UV light attenuation. To do this we have cross-correlated IRAS images and GALEX observations for each of these galaxies, and compiled observations of the gas (CO and HI) and metal-abundance gradients found in the literature. We find that attenuation correlates with metallicity. We then use the UV profiles, corrected for attenuation, to study several variants of the Schmidt law and conclude that our results are compatible with a simple law similar to the one of Kennicutt but extending smoothly to lower surface densities, but with considerable scatter. We do not detect an abrupt break in the UV light at the threshold radius derived from H-alpha data (at which the H-alpha profile shows a break and beyond which only a few HII regions are usually found). We interpret the H-alpha sudden break not as a change in the star formation regime (as often suggested) but as the vanishingly small number of ionizing stars corresponding to low levels of star formation.

On the Fueling of Massive Black Holes and the Properties of Their Host Spheroids

We study the relation between nuclear massive black holes and their host spheroid gravitational potential. Using simple models, we analyze how gas is expected to be transported in the nuclear regions of galaxies. When we couple it with the expected gas lifetime given by the Kennicutt-Schmidt Law, this naturally leads to the `M_BH - M_virial' and `M_BH - sigma' relations. We also numerically test, using AMR simulations, our simple models for the mass transport with satisfactory results.

Understanding starbursts through giant molecular clouds in high density environments

AbstractStarburst galaxies are characterized by uncommonly high star formation efficiencies, but it remains unclear what physical conditions in the molecular gas produce this high efficiency. Invariably, high star formation efficiency is associated with high column densities of molecular material (e.g. the Kennicutt-Schmidt law), but what are the conditions in the molecular clouds in starburst galaxies? Direct observations of starburst are difficult or impossible with current instruments, so I present the properties of GMCs in the Local Group as a starting case and then extend the analysis of GMC properties to nearby systems with surface densities of gas intermediate between the Local Group and starbursts. Rather than being constant, molecular cloud properties follow a continuum with significant variation across the Local Group and the intermediate surface density systems. Concomitant with these variations in the macroscopic properties are significant changes in the internal pressure and densities of molecular clouds, which implies significant variability in the initial conditions of the star formation process.

A Possible Detection of CO (J = 3–2) Emission From the Host Galaxy of GRB 980425 with Atacama Submillimeter Telescope Experiment

AbstractLong-duration gamma-ray bursts (GRBs) are considered to be due to the death of massive stars. Therefore, GRBs are closely associated with the star formation of host galaxies. Since GRBs can be detected at cosmological distances, they are expected to be probes of the star formation history of the Universe. In order to determine the use of GRBs, it is essential to understand the star formation of their hosts. Multi-wavelength observations have shown that the star formation rates (SFRs) of GRB hosts derived from submillimeter/radio observations are generally higher than those from optical/UV observations (Berger et al. 2003). This implies that GRB hosts have a large amount of molecular gas and massive star formation obscured by dust. In order to solve this problem, it is necessary to derive the SFRs in a method which is independent of existing methods and not affected by dust extinction.We observed 12CO (J = 3–2) line emission from the host galaxy of GRB 980425 using the Atacama Submillimeter Telescope Experiment (ASTE). Five points were observed covering the entire region of the galaxy, and we find possible emission features (S/N ~ 3 σ) at the velocity range corresponding to the redshift of the galaxy. By combining all spectra of five points, we obtain a global spectrum with a ~4 σ emission feature. If the features are real, this is the first detection of CO among GRB hosts. We derive the total gas mass of M(H2)=7 ± 2× 108M⊙ assuming a CO-to-H2 conversion factor of αCO = 8.0M⊙ (K km s−1 pc2)−1, which is deduced using the correlation between the αCO and the metallicity. The dynamical mass is calculated to be Mdyn=2× 1010M⊙, and M(H2)/Mdyn~3% is consistent with those of nearby dwarfs and normal spirals. The derived SFR is 0.5 ± 0.1 M⊙ yr−1 based on the Schmidt law. This SFR agrees with the results of previous Hα observations, suggesting that there is no significant obscured star formation in this host galaxy. This result implies that there is a variety of GRB hosts in terms of the presence of obscured star formation.

Galactic-scale star formation by gravitational instability

AbstractWe present numerical experiments that demonstrate that the nonlinear development of the Toomre instability in disks of isothermal gas, stars, and dark matter reproduces the observed Schmidt Law for star formation. The rate of gas collapse depends exponentially on the (minimum) value of the Toomre parameter in the disk. We demonstrate that spurious fragmentation occurs in the absence of sufficient resolution in our SPH model. Our models also reproduce observed star formation thresholds in disk galaxies. We finally briefly discuss the application of our models to the study of globular cluster formation in merging galaxies.

Star formation on galactic scales

AbstractNew multi-wavelength data on nearby galaxies are providing a much more accurate and complete observational picture of star formation on galactic scales. Here I briefly report on recent results from the Spitzer Infrared Nearby Galaxies Survey (SINGS). These provide new constraints on the frequency and lifetime of deeply obscured star-forming regions in galaxies, the measurement of dust-corrected star formation rates in galaxies, and the form of the spatially-resolved Schmidt law.

Star Formation in Isolated Disk Galaxies. II. Schmidt Laws and Efficiency of Gravitational Collapse

(Abridged). We model gravitational instability in a wide range of isolated disk galaxies, using GADGET, a three-dimensional, smoothed particle hydrodynamics code. The model galaxies include a dark matter halo and a disk of stars and isothermal gas. The global Schmidt law observed in disk galaxies is quantitatively reproduced by our models. We find that the surface density of star formation rate directly correlates with the strength of local gravitational instability. The local Schmidt laws of individual galaxies in our models show clear evidence of star formation thresholds. Our results suggest that the non-linear development of gravitational instability determines the local and global Schmidt laws, and the star formation thresholds.

Where Is the Molecular Hydrogen in Damped Lyα Absorbers?

We show in this paper why molecular millimeter absorption line searches in DLAs have been unsuccessful. We use CO emission-line maps of local galaxies to derive the H2 column density distribution function f(N) at z = 0. We show that it forms a natural extension to f(N): the H2 distribution exceeds f(N) at NH ≈ 1022cm-2 and exhibits a power-law dropoff with slope ~-2.5. Approximately 97% of the H2 mass density ρ is in systems above N = 1021 cm-2. We derive a value ρ = 1.1 × 107 h70 M☉ Mpc-3, which is ≈25% the mass density of atomic hydrogen. Yet the redshift number density of H2 above this N limit is only ≈ 3 × 10-4, a factor 150 lower than that for H I in DLAs at z = 0. Furthermore, we show that the median impact parameter between a N > 1021 cm-2 absorber and the center of the galaxy hosting the H2 gas is only 2.5 kpc. On the basis of arguments related to the Schmidt law, we argue that H2 gas above this column density limit is associated with a large fraction of the integral star formation rate density. Even allowing for an increased molecular mass density at higher redshifts, the derived cross sections indicate that it is very unlikely to identify the bulk of the molecular gas in present quasar absorption lines samples. We discuss the prospects for identifying this molecular mass in future surveys.

Comment regarding the functional form of the Schmidt law

Star formation rates on the galactic scale are described phenomenologically by two distinct relationships, as emphasized recently by Elmegreen [Elmegreen, B.G., 2002. ApJ, 577, 206. astro-ph/0207114.]. The first of these is the Schmidt law, which is a power-law relation between the star formation rate SFR and the column density Σ. The other relationship is that there is a cutoff in the gas density below which star formation shuts off. The purpose of this paper is to argue that: (1) these two relationships can be accommodated by a single functional form of the Schmidt law, (2) this functional form is motivated by the hypothesis that star formation is a critical phenomenon, and that as a corollary, (3) the existence of a sharp cutoff may thus be an emergent property of galaxies, as was argued by Seiden [Seiden, P.E.,1983. ApJ, 266, 555.], as opposed to the classical view that this cutoff is due to an instability criterion.

Molecular Gas, Kinematics, and OB Star Formation in the Spiral Arms of the Southern Milky Way

The rotation curve for the IV galactic quadrant, within the solar circle, is derived from the Columbia University - U. de Chile CO(J=1-0) survey of molecular gas. A new sampling, four times denser in longitude than in our previous analysis, is used to compute kinematical parameters that require derivatives w/r to galactocentric radius; the angular velocity Omega(R), the epicyclic frequency kappa(R), and the parameters A(R) and B(R) describing, respectively, gas shear and vorticity. The face-on surface density of molecular gas is computed from the CO data in galactocentric radial bins for the subcentral vicinity, the same spectral region used to derive the rotation curve, where the two-fold ambiguity in kinematical distances is minimum. The rate of massive star formation per unit area is derived, for the same radial bins, from the luminosity of IRAS point-like sources with FIR colors of UC HII regions detected in the CS(J=2-1) line. Massive star formation occurs preferentially in three regions of high molecular gas density, coincident with lines of sight tangent to spiral arms. The molecular gas motion in these arms resembles that of a solid body, characterized by constant angular velocity and by low shear and vorticity. The formation of massive stars in the arms follows the Schmidt law, Sigma_{MSFR} is proportional to [Sigma_{gas}]^n, with an index of n = 1.2 +- 0.2 Our results suggest that the large scale kinematics, through shear, regulate global star formation in the Galactic disk.

The Schmidt Law at High Molecular Densities

Abstract We combined $\mathrm{H}\alpha$ and recent high-resolution ${{12\atop} \mathrm{CO}}$ ($J = 1 \hbox{--} 0$) data to consider the quantitative relation between the gas mass and the star-formation rate, or the so-called Schmidt law in nearby spiral galaxies at regions of high molecular density. The relation between the gas quantity and the star-formation rate has not been previously studied for high-density regions, but using high-resolution CO data obtained at the Nobeyama Millimeter Array, we found that the Schmidt law is valid at densities as high as $10^3 \,{{{M}_{\odot}}} \,\mathrm{pc}^{-2}$ for sample spiral galaxies, which is an order of magnitude denser than what has been known to be the maximum density at which the empirical law holds for non-starburst galaxies. Furthermore, we obtained a Schmidt law index of $N = 1.33 \pm 0.09$ and a roughly constant star-formation efficiency over the entire disk, even within several hundred parsecs of the nucleus. These results imply that the physics of star formation does not change in the central regions of spiral galaxies. Comparisons with starburst galaxies are also given. We find a possible discontinuity in the Schmidt law between normal and starburst galaxies.

A General Theory of Turbulence‐regulated Star Formation, from Spirals to Ultraluminous Infrared Galaxies

We derive an analytic prediction for the star formation rate in environments ranging from normal galactic disks to starbursts and ULIRGs in terms of the observables of those systems. Our calculation is based on three premises: (1) star formation occurs in virialized molecular clouds that are supersonically turbulent; (2) the density distribution within these clouds is lognormal, as expected for supersonic isothermal turbulence; and (3) stars form in any subregion of a cloud that is so overdense that its gravitational potential energy exceeds the energy in turbulent motions. We show that a theory based on this model is consistent with simulations and with the observed star formation rate in the Milky Way. We use our theory to derive the Kennicutt-Schmidt law from first principles and make other predictions that can be tested by future observations. We also provide an algorithm for estimating the star formation rate that is suitable for inclusion in numerical simulations.

The Molecular Interstellar Medium of Dwarf Galaxies on Kiloparsec Scales: A New Survey for CO in Northern,IRAS‐detected Dwarf Galaxies

We present a new survey for CO in dwarf galaxies using the ARO Kitt Peak 12 m telescope. This survey consists of observations of the central regions of 121 northern dwarfs with IRAS detections and no known CO emission. We detect CO in 28 of these galaxies and marginally detect another 16, increasing by about 50% the number of such galaxies known to have significant CO emission. The galaxies we detect are comparable in stellar and dynamical mass to the Large Magellanic Cloud, although somewhat brighter in CO and fainter in the far-IR. Within dwarfs, we find that the CO luminosity LCO is most strongly correlated with the K-band and the far-infrared luminosities. There are also strong correlations with the radio continuum (RC) and B-band luminosities and linear diameter. Conversely, we find that far-IR dust temperature is a poor predictor of CO emission within the dwarfs alone, although a good predictor of normalized CO content among a larger sample of galaxies. We suggest that LCO and LK correlate well because the stellar component of a galaxy dominates the midplane gravitational field and thus sets the pressure and density of the atomic gas, which control the formation of H2 from H I. We compare our sample with more massive galaxies and find that dwarfs and large galaxies obey the same relationship between CO and the 1.4 GHz RC surface brightness. This relationship is well described by a Schmidt law with ΣRC ∝ Σ. Therefore, dwarf galaxies and large spirals exhibit the same relationship between molecular gas and star formation rate (SFR). We find that this result is robust to moderate changes in the RC-to-SFR and CO-to-H2 conversion factors. Our data appear to be inconsistent with large (order of magnitude) variations in the CO-to-H2 conversion factor in the star-forming molecular gas.

Control of Star Formation in Galaxies by Gravitational Instability

We study gravitational instability and consequent star formation in a wide range of isolated disk galaxies, using three-dimensional smoothed particle hydrodynamics simulations at a resolution sufficient to fully resolve gravitational collapse. Stellar feedback is represented by an isothermal equation of state. Absorbing sink particles are inserted in dynamically bound, converging regions with number density n > 103 cm-3 to directly measure the mass of gravitationally collapsing gas available for star formation. Our models quantitatively reproduce not only the observed Schmidt law, but also the observed star formation threshold in disk galaxies. Our results suggest that the dominant physical mechanism determining the star formation rate is just the strength of gravitational instability, with feedback primarily functioning to maintain a roughly constant effective sound speed.

The Molecular Gas Distribution and Schmidt Law in M33

The relationship between the star formation rate and surface density of neutral gas within the disk of M33 is examined with new imaging observations of CO J=1-0 emission gathered with the FCRAO 14m telescope and IRAS HiRes images of the 60 micron and 100 micron emission. The Schmidt law, Sigma_SFR ~ Sigma_gas^n, is constructed using radial profiles of the HI 21cm, CO, and far infrared emission. A strong correlation is identified between the star formation rate and molecular gas surface density. This suggests that the condensation of giant molecular clouds is the limiting step to star formation within the M33 disk. The corresponding molecular Schmidt index, n_{mol}, is 1.36 +/- 0.08. The star formation rate has a steep dependence on total mass gas surface density, (Sigma_{HI}+Sigma_{H_2}), owing to the shallow radial profile of the atomic gas which dominates the total gas surface density for most radii. The disk pressure of the gas is shown to play a prominent role in regulating the molecular gas fraction in M33.