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Register a new userWhat Sets the Slope of the Molecular Kennicutt-Schmidt Relation?
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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.
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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.
We present an analysis of the global and spatially-resolved Kennicutt-Schmidt (KS) star formation relation in the FIRE (Feedback In Realistic Environments) suite of cosmological simulations, including halos with $z = 0$ masses ranging from $10^{10}$ -- $10^{13}$ M$_{odot}$. We show that the KS relation emerges and is robustly maintained due to the effects of feedback on local scales regulating star-forming gas, independent of the particular small-scale star formation prescriptions employed. We demonstrate that the time-averaged KS relation is relatively independent of redshift and spatial averaging scale, and that the star formation rate surface density is weakly dependent on metallicity and inversely dependent on orbital dynamical time. At constant star formation rate surface density, the `Cold & Dense gas surface density (gas with $T < 300$~K and $n > 10$~cm$^{-3}$, used as a proxy for the molecular gas surface density) of the simulated galaxies is $sim$0.5~dex less than observed at $sim$kpc scales. This discrepancy may arise from underestimates of the local column density at the particle-scale for the purposes of shielding in the simulations. Finally, we show that on scales larger than individual giant molecular clouds, the primary condition that determines whether star formation occurs is whether a patch of the galactic disk is thermally Toomre-unstable (not whether it is self-shielding): once a patch can no longer be thermally stabilized against fragmentation, it collapses, becomes self-shielding, cools, and forms stars, regardless of epoch or environment.
Results from the UV satellite GALEX revealed large extensions of disks in some nearby spiral galaxies, extending out to 3 to 4 times the isophotal radius, r25. M63 is a remarkable example of a spiral galaxy with one of the most extended UV disks, so it offers the opportunity to search for the molecular gas and characterize the star formation in outer disk regions as revealed by the UV emission. We obtained deep CO(1-0) and CO(2-1) observations on the IRAM 30 m telescope along the major axis of the M63 disk from the center out to the galactocentric radius rgal = 1.6 r25 and over a bright UV region at rgal = 1.36 r25. CO(1-0) is detected all along the M63 major axis out to r25, and CO(2-1) is confined to rgal = 0.68 r25, which may betray lower excitation temperatures in the outer disk. CO(1-0) is also detected in the external bright UV region of M63. The radial profiles of the CO emission and of the Halpha, 24 micron, NUV and FUV star formation tracers and HI taken from the literature show a severe drop with the galactocentric radius, such that beyond r25 they are all absent with the exception of a faint UV emission and HI. The CO emission detection in the external UV region, where the UV flux is higher than the UV flux observed beyond r25, highlights a tight correlation between the CO and UV fluxes, namely the amount of molecular gas and the intensity of star formation. This external UV region is dominated by the atomic gas, suggesting that HI is more likely the precursor of H2 rather than the product of UV photodissociation. A broken power law needs to be invoked to describe the Kennicutt-Schmidt (K-S) relation of M63 from the center of the galaxy out to rgal = 1.36 r25. While all along the major axis out to r25 the K-S relation is almost linear, in the external UV region the SFR regime is highly nonlinear and characterized by a steep K-S relation and very low star formation efficiency.
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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