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Register a new userThe Star Formation Rate - Dense Gas Relation in Galaxies as Measured by HCN (3-2) Emission
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We present observations made with the 10m Heinrich Hertz Sub-Millimeter Telescope of HCN (3-2) emission from a sample of 30 nearby galaxies ranging in infrared luminosity from 10^10 - 10^12.5 L_sun and HCN (3-2) luminosity from 10^6 - 10^9 K km s^-1 pc^2. We examine the correlation between the infrared luminosity and HCN (3-2) luminosity and find that the best fit linear regression has a slope (in log-log space) of 0.74+/-0.12. Including recently published data from Gracia-Carpio et al. tightens the constraints on the best-fit slope to 0.79+/-0.09. This slope below unity suggests that the HCN (3-2) molecular line luminosity is not linearly tracing the amount of dense gas. Our results are consistent with predictions from recent theoretical models that find slopes below unity when the line luminosity depends upon the average gas density with a power-law index greater than a Kennicutt-Schmidt index of 1.5.
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We investigate the relationship between the star formation rate (SFR) and dense molecular gas mass in the nuclei of galaxies. To do this, we utilize the observed 850 micron luminosity as a proxy for the infrared luminosity and SFR, and correlate this with the observed CO (J=3-2) luminosity. We find tentative evidence that the LIR-CO (J=3-2) index is similar to the Kennicutt-Schmidt (KS) index (N ~ 1.5) in the central ~1.7 kpc of galaxies, and flattens to a roughly linear index when including emission from the entire galaxy. This result may imply that the volumetric Schmidt relation is the underlying driver behind the observed SFR-dense gas correlations, and provides tentative confirmation for recent numerical models. While the data exclude the possibility of a constant LIR-CO (J=3-2) index for both galaxy nuclei and global measurements at the ~80% confidence level, the considerable error bars cannot preclude alternative interpretations.
We model the star formation relation of molecular clumps in dependence of their dense-gas mass when their volume density profile is that of an isothermal sphere, i.e. $rho_{clump}(r) propto r^{-2}$. Dense gas is defined as gas whose volume density is higher than a threshold $rho_{th}=700,M_{odot}.pc^{-3}$, i.e. HCN(1-0)-mapped gas. We divide the clump into two regions: a dense inner region (where $rho_{clump}(r) geq rho_{th}$), and low-density outskirts (where $rho_{clump}(r) < rho_{th}$). We find that the total star formation rate of clumps scales linearly with the mass of their dense inner region, even when more than half of the clump star formation activity takes place in the low-density outskirts. We therefore emphasize that a linear star formation relation does not necessarily imply that star formation takes place exclusively in the gas whose mass is given by the star formation relation. The linearity of the star formation relation is strengthened when we account for the mass of dense fragments (e.g. cores, fibers) seeding star formation in the low-density outskirts, and which our adopted clump density profile $rho_{clump}(r)$ does not resolve. We also find that the star formation relation is significantly tighter when considering the dense gas than when considering all the clump gas, as observed for molecular clouds of the Galactic plane. When the clumps have no low-density outskirts (i.e. they consist of dense gas only), the star formation relation becomes superlinear and progressively wider.
It is well-established that a gas density gradient inside molecular clouds and clumps raises their star formation rate compared to what they would experience from a gas reservoir of uniform density. This effect should be observed in the relation between dense-gas mass $M_{dg}$ and star formation rate $SFR$ of molecular clouds and clumps, with steeper gas density gradients yielding higher $SFR/M_{dg}$ ratios. The content of this paper is two-fold. Firstly, we build on the notion of magnification factor introduced by Parmentier (2019) to redefine the dense-gas relation (i.e. the relation between $M_{dg}$ and $SFR$). Not only does the $SFR/M_{dg}$ ratio depend on the mean free-fall time of the gas and on its (intrinsic) star formation efficiency per free-fall time, it also depends on the logarithmic slope $-p$ of the gas density profile and on the relative extent of the constant-density region at the clump center. Secondly, we show that nearby molecular clouds follow the newly-defined dense-gas relation, provided that their dense-gas mass is defined based on a volume density criterion. We also find the same trend for the dense molecular clouds of the Central Molecular Zone (CMZ) of the Galaxy, although this one is scaled down by a factor of $10$ compared to nearby clouds. The respective locii of both nearby and CMZ clouds in the $(p, SFR/M_{dg})$ parameter space is discussed.
It has been recently argued that the HCN J=1--0 line emission may not be an unbiased tracer of dense molecular gas ($rm nga 10^4 cm^{-3}$) in Luminous Infrared Galaxies (LIRGs: $rm L_{FIR}> 10^{11} L_{odot}$) and HCO$^+$ J=1--0 may constitute a better tracer instead (Gracia-Carpio et al. 2006), casting doubt into earlier claims supporting the former as a good tracer of such gas (Gao & Solomon 2004; Wu et al. 2006). In this paper new sensitive HCN J=4--3 observations of four such galaxies are presented, revealing a surprisingly wide excitation range for their dense gas phase that may render the J=1--0 transition from either species a poor proxy of its mass. Moreover the well-known sensitivity of the HCO$^+$ abundance on the ionization degree of the molecular gas (an important issue omitted from the ongoing discussion about the relative merits of HCN and HCO$^+$ as dense gas tracers) may severely reduce the HCO$^+$ abundance in the star-forming and highly turbulent molecular gas found in LIRGs, while HCN remains abundant. This may result to the decreasing HCO$^+$/HCN J=1--0 line ratio with increasing IR luminosity found in LIRGs, and casts doubts on the HCO$^+$ rather than the HCN as a good dense molecular gas tracer. Multi-transition observations of both molecules are needed to identify the best such tracer, its relation to ongoing star formation, and constrain what may be a considerable range of dense gas properties in such galaxies.
We study the spatially resolved Radio Continuum-Star Formation Rate (RC-SFR) relation using state-of-the-art star-formation (SF) tracers in a sample of 17 THINGS galaxies. We use hybrid Sigma_SFR maps (GALEX FUV plus Spitzer 24 mu), RC maps at 22/18 cm from the WSRT SINGS survey, and H-alpha maps to correct for thermal RC emission. We compare azimuthally averaged radial profiles of the RC and FUV/MIR-based Sigma_SFR maps and study pixel-by-pixel correlations at fixed linear scales of 1.2 and 0.7 kpc. The ratio of the integrated SFRs from the RC emission to that of the FUV/MIR-based SF tracers is R_int = 0.78 +/- 0.38, consistent with Condons relation. We find a tight correlation between the radial profiles of the radio and FUV/MIR-based Sigma_SFR for the entire extent of the disk. The ratio R of the azimuthally averaged radio to FUV/MIR-based Sigma_SFR agrees with the integrated ratio with only small quasi-random fluctuations as function of radius. Pixel-by-pixel plots show a tight correlation in log-log diagrams of radio to FUV/MIR-based Sigma_SFR, with a typical standard deviation of a factor of two. Averaged over our sample we find (Sigma_SFR)_RC ~ (Sigma_SFR)_hyb^{0.63+/-0.25} implying that data points with high Sigma_SFR are relatively radio dim, whereas the reverse is true for low Sigma_SFR. We interpret this as a result of spectral ageing of CRe, which is supported by the radio spectral index: data points dominated by young CRe are relatively radio dim, those dominated by old CRe are relatively radio bright. The ratio of radio to FUV/MIR-based integrated SFR is independent of global galaxy parameters, suggesting that we can use RC emission as a universal SF tracer for galaxies, if we restrict ourselves to global or azimuthally averaged measurements. A magnetic field-SFR relation, B ~ SFR_hyb^{0.30+/-0.02}, holding both globally and locally, can explain our results. (abridged)
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