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Determining Star Formation Thresholds from Observations

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 Added by Shivan Khullar
 Publication date 2019
  fields Physics
and research's language is English




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Most gas in giant molecular clouds is relatively low-density and forms star inefficiently, converting only a small fraction of its mass to stars per dynamical time. However, star formation models generally predict the existence of a threshold density above which the process is efficient and most mass collapses to stars on a dynamical timescale. A number of authors have proposed observational techniques to search for a threshold density above which star formation is efficient, but it is unclear which of these techniques, if any, are reliable. In this paper we use detailed simulations of turbulent, magnetised star-forming clouds, including stellar radiation and outflow feedback, to investigate whether it is possible to recover star formation thresholds using current observational techniques. Using mock observations of the simulations at realistic resolutions, we show that plots of projected star formation efficiency per free-fall time $epsilon_{rm ff}$ can detect the presence of a threshold, but that the resolutions typical of current dust emission or absorption surveys are insufficient to determine its value. In contrast, proposed alternative diagnostics based on a change in the slope of the gas surface density versus star formation rate surface density (Kennicutt-Schmidt relation) or on the correlation between young stellar object counts and gas mass as a function of density are ineffective at detecting thresholds even when they are present. The signatures in these diagnostics sometimes taken as indicative of a threshold in observations, which we generally reproduce in our mock observations, do not prove to correspond to real physical features in the 3D gas distribution.



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172 - Joop Schaye 2007
To make predictions for the existence of ``dark galaxies, it is necessary to understand what determines whether a gas cloud will form stars. Star formation thresholds are generally explained in terms of the Toomre criterion for gravitational instability. I contrast this theory with the thermo-gravitational instability hypothesis of Schaye (2004), in which star formation is triggered by the formation of a cold gas phase and which predicts a nearly constant surface density threshold. I argue that although the Toomre analysis is useful for the global stability of disc galaxies, it relies on assumptions that break down in the outer regions, where star formation thresholds are observed. The thermo-gravitational instability hypothesis can account for a number of observed phenomena, some of which were thought to be unrelated to star formation thresholds.
We aim at understanding the massive star formation (MSF) limit $m(r) = 870 M_{odot} (r/pc)^{1.33}$ in the mass-size space of molecular structures recently proposed by Kauffmann & Pillai (2010). As a first step, we build on the hypothesis of a volume density threshold for overall star formation and the model of Parmentier (2011) to establish the mass-radius relations of molecular clumps containing given masses of star-forming gas. Specifically, we relate the mass $m_{clump}$, radius $r_{clump}$ and density profile slope $-p$ of molecular clumps which contain a mass $m_{th}$ of gas denser than a volume density threshold $rho_{th}$. In a second step, we use the relation between the mass of embedded-clusters and the mass of their most-massive star to estimate the minimum mass of star-forming gas needed to form a $10,M_{odot}$ star. Assuming a star formation efficiency of $SFE simeq 0.30$, this gives $m_{th,crit} simeq 150 M_{odot}$. In a third step, we demonstrate that, for sensible choices of the clump density index ($p simeq 1.7$) and of the cluster formation density threshold ($n_{th} simeq 10^4,cm^{-3}$), the line of constant $m_{th,crit} simeq 150 M_{odot}$ in the mass-radius space of molecular structures equates with the MSF limit for spatial scales larger than 0.3,pc. Hence, the observationally inferred MSF limit of Kauffmann & Pillai is consistent with a threshold in star-forming gas mass beyond which the star-forming gas reservoir is large enough to allow the formation of massive stars. For radii smaller than 0.3,pc, the MSF limit is shown to be consistent with the formation of a $10,M_{odot}$ star out of its individual pre-stellar core of density threshold $n_{th} simeq 10^5,cm^{-3}$. The inferred density thresholds for the formation of star clusters and individual stars within star clusters match those previously suggested in the literature.
Through synthetic observations of a hydrodynamical simulation of an evolving star-forming region, we assess how the choice of observational techniques affects the measurements of properties which trace star formation. Testing and calibrating observational measurements requires synthetic observations which are as realistic as possible. In this part of the paper series (Paper I), we explore different techniques for how to map the distributions of densities and temperatures from the particle-based simulations onto a Voronoi mesh suitable for radiative transfer and consequently explore their accuracy. We further test different ways to set up the radiative transfer in order to produce realistic synthetic observations. We give a detailed description of all methods and ultimately recommend techniques. We have found that the flux around 20 microns is strongly overestimated when blindly coupling the dust radiative transfer temperature with the hydrodynamical gas temperature. We find that when instead assuming a constant background dust temperature in addition to the radiative transfer heating, the recovered flux is consistent with actual observations. We present around 5800 realistic synthetic observations for Spitzer and Herschel bands, at different evolutionary time-steps, distances and orientations. In the upcoming papers of this series (Paper II, Paper III and Paper IV), we will test and calibrate measurements of the star-formation rate (SFR), gas mass and the star-formation efficiency (SFE) using our realistic synthetic observations.
Through an extensive set of realistic synthetic observations (produced in Paper I), we assess in this part of the paper series (Paper III) how the choice of observational techniques affects the measurement of star-formation rates (SFRs) in star-forming regions. We test the accuracy of commonly used techniques and construct new methods to extract the SFR, so that these findings can be applied to measure the SFR in real regions throughout the Milky Way. We investigate diffuse infrared SFR tracers such as those using 24 {mu}m, 70 {mu}m and total infrared emission, which have been previously calibrated for global galaxy scales. We set up a toy model of a galaxy and show that the infrared emission is consistent with the intrinsic SFR using extra-galactic calibrated laws (although the consistency does not prove their reliability). For local scales, we show that these techniques produce completely unreliable results for single star-forming regions, which are governed by different characteristic timescales. We show how calibration of these techniques can be improved for single star-forming regions by adjusting the characteristic timescale and the scaling factor and give suggestions of new calibrations of the diffuse star-formation tracers. We show that star-forming regions that are dominated by high-mass stellar feedback experience a rapid drop in infrared emission once high-mass stellar feedback is turned on, which implies different characteristic timescales. Moreover, we explore the measured SFRs calculated directly from the observed young stellar population. We find that the measured point sources follow the evolutionary pace of star formation more directly than diffuse star-formation tracers.
We combine asteroseismology, optical high-resolution spectroscopy, and kinematic analysis for 26 halo red giant branch stars in the textit{Kepler} field in the range of $-2.5<[mathrm{{Fe}/{H}}]<-0.6$. After applying theoretically motivated corrections to the seismic scaling relations, we obtain an average mass of $0.97pm 0.03,mathrm{M_{odot}}$ for our sample of halo stars. Although this maps into an age of $sim 7,mathrm{Gyr}$, significantly younger than independent age estimates of the Milky Way stellar halo, we considerer this apparently young age is due to the overestimation of stellar mass in the scaling relations. There is no significant mass dispersion among lower red giant branch stars ($log g>2$), which constrains a relative age dispersion to $<18%$, corresponding to $<2,mathrm{Gyr}$. The precise chemical abundances allow us to separate the stars with [{Fe}/{H}]$>-1.7$ into two [{Mg}/{Fe}] groups. While [$alpha$/{Fe}] and [{Eu}/{Mg}] ratios are different between the two subsamples, [$s$/Eu], where $s$ stands for Ba, La, Ce, and Nd, does not show a significant difference. These abundance ratios suggest that the chemical evolution of the low-Mg population is contributed by type~Ia supernovae, but not by low-to-intermediate mass asymptotic giant branch stars, providing a constraint on its star formation timescale as $100,mathrm{Myr}<tau<300,mathrm{Myr}$. We also do not detect any significant mass difference between the two [{Mg}/{Fe}] groups, thus suggesting that their formation epochs are not separated by more than 1.5 Gyr.
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