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Register a new userOn the relation between the Schmidt and Kennicutt-Schmidt star formation laws and its implications for numerical simulations
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When averaged over large scales, star formation in galaxies is observed to follow the empirical Kennicutt-Schmidt (KS) law for surface densities above a constant threshold. While the observed law involves surface densities, theoretical models and simulations generally work with volume density laws (i.e. Schmidt laws). We derive analytic relations between star formation laws expressed in terms of surface densities, volume densities, and pressures and we show how these relations depend on parameters such as the effective equation of state of the multiphase interstellar medium. Our analytic relations enable us to implement observed surface density laws into simulations. Because the parameters of our prescription for star formation are observables, we are not free to tune them to match the observations. We test our theoretical framework using high-resolution simulations of isolated disc galaxies that assume an effective equation of state for the multiphase interstellar medium. We are able to reproduce the star formation threshold and both the slope and the normalisation of arbitrary input KS laws without tuning any parameters and with very little scatter, even for unstable galaxies and even if we use poor numerical resolution. Moreover, we can do so for arbitrary effective equations of state. Our prescription therefore enables simulations of galaxies to bypass our current inability to simulate the formation of stars. On the other hand, the fact that we can reproduce arbitrary input thresholds and KS laws, rather than just the particular ones picked out by nature, indicates that simulations that lack the physics and/or resolution to simulate the multiphase interstellar medium can only provide limited insight into the origin of the observed star formation laws.
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We consider the Schmidt decomposition of a bipartite density operator induced by the Hilbert-Schmidt scalar product, and we study the relation between the Schmidt coefficients and entanglement. First, we define the Schmidt equivalence classes of bipartite states. Each class consists of all the density operators (in a given bipartite Hilbert space) sharing the same set of Schmidt coefficients. Next, we review the role played by the Schmidt coefficients with respect to the separability criterion known as the `realignment or `computable cross norm criterion; in particular, we highlight the fact that this criterion relies only on the Schmidt equivalence class of a state. Then, the relevance -- with regard to the characterization of entanglement -- of the `symmetric polynomials in the Schmidt coefficients and a new family of separability criteria that generalize the realignment criterion are discussed. Various interesting open problems are proposed.
We use a new method to trace backwards the star formation history of the Milky Way disk, using a sample of M dwarfs in the solar neighbourhood which is representative for the entire solar circle. M stars are used because they show H_alpha emission until a particular age which is a well calibrated function of their absolute magnitudes. This allows us to reconstruct the rate at which disk stars have been born over about half the disks lifetime. Our star formation rate agrees well with those obtained by using other, independent, methods and seems to rule out a constant star formation rate. The principal result of this study is to show that a relation of the Schmidt-Kennicut type (which relates the star formation rate to the interstellar gas content of galaxy disks) has pertained in the Milky Way disk during the last 5 Gyr. The star formation rate we derive from the M dwarfs and the interstellar gas content of the disk can be inferred as a function of time from a model of the chemical enrichment of the disk, which is well constrained by the observations indicating that the metallicity of the Galactic disk has remained nearly constant over the timescales involved. We demonstrate that the star formation rate and gas surface densities over the last 5 Gyrs can be accurately described by a Schmidt-Kennicutt law with an index of Gamma = 1.45 (+0.22,-0.09). This is, within statistical uncertainties, the same value found for other galaxies.
The surface densities of molecular gas, $Sigma_{rm H_2}$, and the star formation rate (SFR), $dotSigma_star$, correlate almost linearly on kiloparsec scales in observed star-forming (non-starburst) galaxies. We explore the origin of the linear slope of this correlation using a suite of isolated $L_star$ galaxy simulations. We show that in simulations with efficient feedback, the slope of the $dotSigma_star$-$Sigma_{rm H_2}$ relation on kiloparsec scales is insensitive to the slope of the $dotrho_star$-$rho$ relation assumed at the resolution scale. We also find that the slope on kiloparsec scales depends on the criteria used to identify star-forming gas, with a linear slope arising in simulations that identify star-forming gas using a virial parameter threshold. This behavior can be understood using a simple theoretical model based on conservation of interstellar gas mass as the gas cycles between atomic, molecular, and star-forming states under the influence of feedback and dynamical processes. In particular, we show that the linear slope emerges when feedback efficiently regulates and stirs the evolution of dense, molecular gas. We show that the model also provides insights into the likely origin of the relation between the SFR and molecular gas in real galaxies on different scales.
Using N-body/gasdynamic simulations of a Milky Way-like galaxy we analyse a Kennicutt-Schmidt relation, $Sigma_{SFR} propto Sigma_{gas}^N$, at different spatial scales. We simulate synthetic observations in CO lines and UV band. We adopt the star formation rate defined in two ways: based on free fall collapse of a molecular cloud - $Sigma_{SFR, cl}$, and calculated by using a UV flux calibration - $Sigma_{SFR, UV}$. We study a KS relation for spatially smoothed maps with effective spatial resolution from molecular cloud scales to several hundred parsecs. We find that for spatially and kinematically resolved molecular clouds the $Sigma_{SFR, cl} propto Sigma_{rm gas}^N$ relation follows the power-law with index $N approx 1.4$. Using UV flux as SFR calibrator we confirm a systematic offset between the $Sigma_{rm UV}$ and $Sigma_{rm gas}$ distributions on scales compared to molecular cloud sizes. Degrading resolution of our simulated maps for surface densities of gas and star formation rates we establish that there is no relation $Sigma_{rm SFR, UV} - Sigma_{rm gas}$ below the resolution $sim 50$ pc. We find a transition range around scales $sim 50-120$ pc, where the power-law index $N$ increases from 0 to 1-1.8 and saturates for scales larger $sim 120$ pc. A value of the index saturated depends on a surface gas density threshold and it becomes steeper for higher $Sigma_{gas}$ threshold. Averaging over scales with size of $>150$ pc the power-law index $N$ equals 1.3-1.4 for surface gas density threshold $sim 5 M_odot$pc$^{-2}$. At scales $>120$ pc surface SFR densities determined by using CO data and UV flux, $Sigma_{rm SFR, UV}/Sigma_{rm SFR, cl}$, demonstrate a discrepancy about a factor of 3. We argue that this may be originated from overestimating (constant) values of conversion factor, star formation efficiency or UV calibration used in our analysis.
The Kennicutt-Schmidt (KS) relation between the gas mass and star formation rate (SFR) describes the star formation regulation in disk galaxies. It is a function of gas metallicity, but the low metallicity regime of the KS diagram is poorly sampled. We have analyzed data for a representative set of extremely metal-poor galaxies (XMPs), as well as auxiliary data, and compared these to empirical and theoretical predictions. The majority of the XMPs possess high specific SFRs, similar to high redshift star-forming galaxies. On the KS plot, the XMP HI data occupy the same region as dwarfs, and extend the relation for low surface brightness galaxies. Considering the HI gas alone, a considerable fraction of the XMPs already fall off the KS law. Significant quantities of dark H$_2$ mass (i.e., not traced by CO) would imply that XMPs possess low star formation efficiencies (SFE$_{rm gas}$). Low SFE$_{rm gas}$ in XMPs may be the result of the metal-poor nature of the HI gas. Alternatively, the HI reservoir may be largely inert, the star formation being dominated by cosmological accretion. Time lags between gas accretion and star formation may also reduce the apparent SFE$_{rm gas}$, as may galaxy winds, which can expel most of the gas into the intergalactic medium. Hence, on global scales, XMPs could be HI-dominated, high specific SFR ($gtrsim $ 10$^{-10}$ yr$^{-1}$), low SFE$_{rm gas}$ ($lesssim$ 10$^{-9}$ yr$^{-1}$) systems, in which the total HI mass is likely not a good predictor of the total H$_2$ mass nor of the SFR.
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