Extragalactic Projects Results and Discussion

TIP Last Modified: JeffMangum - 30 November 2010

Table of Contents:

Merger Systems Notes


  • LIRG (~4x10^(11) Lsolar)
  • D ~ 64 Mpc
  • Late-stage merger
  • Pure SB; No AGN (for whole galaxy)
  • SFR ~ 60 Msolar/yr


  • AGN
  • High HCN/CO
  • H2CO?


  • Clear SN measured in radio
  • No H2CO


  • SFR ~ 10^(-6) Msolar/yr
  • SFR factor of ~100 lower than other galaxies with same HI surface density


Kennicutt-Schmidt Relation

The following summary of the Kennicutt-Schmidt relation is from Heiderman etal. 2010.

The idea that there should be a relation between the density of star formation and gas density was first proposed by Schmidt (1959). Schmidt investigated this relation, now known as the "Schmidt law," assuming that it should be in the form of a power law and suggested that the density of star formation was proportional to gas density squared. Kennicutt (1998b) measured the global or disk-averaged Schmidt law in a sample of spiral and starburst galaxies using the projected star formation and gas surface densities (Σgas) as

\Sigma _{\rm SFR} \propto \Sigma _{\rm gas}^{N},

where N is the power-law index. The global SFR and Σgas measurements for the sample of galaxies in Kennicutt (1998b) were fitted to a power law with N = 1.4, which is known as the "Kennicutt-Schmidt law":

\Sigma _{\rm SFR} = (2.5\pm 0.7) \times 10^{-4} \left(\frac{\Sigma _{\rm gas}}{1 \;M_{\odot } \;{\rm pc}^{-2}} \right)^{1.4\pm 0.15}\times (M_{\odot } \;\rm yr^{-1} \;\rm kpc^{-2}).

Since it is only an assumption that there is only one relation that regulates how gas is forming stars, we refrain from calling this a "law" and instead refer to it as an SFR-gas relation, or as the Kennicutt-Schmidt relation when referring to Equation (2) specifically. Several authors (Larson 1992; Elmegreen 1994; Wong & Blitz 2002; Krumholz & Tan 2007) argue that there is a simple explanation for the Kennicutt-Schmidt relation: if the SFR is proportional to the gas mass divided by the time it takes to convert the gas into stars and if we take this timescale to be the free-fall time, then t_{ff} \propto \rho^{-0.5}_{gas} and \dot{\rho}_{\rm SFR}\propto \rho_{\rm gas}^{1.5}. Taking the scale height to be constant, \rho \propto \Sigma, and this in turn gives the Kennicutt-Schmidt relation (to the extent that 1.4 ± 0.15 = 1.5). A variety of observational methods have been used to investigate this relation in different types of galaxies and on different scales.

Krumholz, McKee, and Tumlinson Star Formation Law

The following is from Krumholz, McKee, and Tumlinson 2009 and describes a very exact yet simple star formation law which fits observations very accurately.

Observational Results Which Must be Explained by Any Star Formation Law

  1. Star formation is a direct product of the molecular gas in a galaxy, not of all the gas.
  2. Giant molecular clouds (GMCs) have remarkably similar properties in all nearby galaxies.

The KMT Star Formation Law

Given that star formation occurs in molecular gas, we formulate our theoretical law for the local SFR surface density \dot{\Sigma }_* in a galaxy as a product of three factors:

\dot{\Sigma }_*= \Sigma _{\rm g}f_{\rm H_2}\frac{\mbox{SFR}_{\rm ff}}{t_{\rm ff}}.

Here \Sigma_g is the total gas surface density at some point in the galaxy. In practice, this will always be an average over some size scale, determined by the resolution of observations (or simulations). This determines the total available "raw material" for star formation. The factor f_{\rm H_2} is the fraction of this mass in molecular form; atomic gas does not participate in star formation. The molecular component of the gas is organized into clouds which have some mean volume density \rho _{\rm H_2}, and t_{\rm ff}=[3\pi /(32 G \rho _{\rm H_2})]^{1/2} is the free-fall time at this mean density. The quantity SFR_{\rm ff} is the dimensionless SFR; it is the fraction of the gas transformed into stars per free-fall time. Alternately, one may think of it as the star formation efficiency over one free-fall time (as opposed to the total star formation efficiency, which might mean the fraction of gas transformed into stars over some other timescale, such as the galactic rotation time or the lifetime of an individual GMC). The third factor, SFR_{\rm ff}/t_{\rm ff}, is simply the SFR per free-fall time divided by the free-fall time, which is the inverse of the time required to convert all of the gas into stars. To make a model for the star formation law, we must estimate f_{\rm H_2}, t_{\rm ff}, and SFR_{\rm ff} in terms of the observable quantities for a galaxy.

The full star formation law is given by KMT as follows:

We have now derived the major components of our star formation law. The molecular fraction f_{\rm H_2} depends only on gas surface density \Sigma_g, metallicity Z', and the clumping of the gas c on scales unresolved in a given observation or simulation. It increases with \Sigma_g, becoming fully molecular at ~10/cZ' M_\odot pc^{-2}. We have also derived an analytic relation for the inverse star formation timescale SFRff/tff in two regimes. Where internal GMC pressure far exceeds the ambient ISM gas pressure and GMCs "forget" their environment—as typically occurs in nearby galaxies with \Sigma_g < 85 M_\odot pc^{-2}—this timescale does not depend on \Sigma_g except indirectly through the molecular cloud mass. Above \Sigma_g = 85 M_\odot pc^{-2}, ambient pressure becomes comparable to the GMC internal pressure and the star formation timescale depends on \Sigma_g. In neither case does the timescale depend on either the metallicity or the clumping, so the SFR in molecular gas does not depend on either of these quantities. Only the SFR in total gas does.

We are now ready to combine these pieces into our single star formation law:

\dot{\Sigma }_* = f_{\rm H_2}(\Sigma _{\rm g}, c, Z^{\prime }) \frac{\Sigma _{\rm g}}{2.6\mbox{ Gyr}} {}\times \left\lbrace \begin{array}{@{}ll} \left(\frac{\Sigma _{\rm g}}{85\,M_{\odot }\,{\rm pc}^{-2}}\right)^{-0.33}, \quad & \frac{\Sigma _{\rm g}}{85\,M_{\odot }\,{\rm pc}^{-2}} < 1 \\ \left(\frac{\Sigma _{\rm g}}{85\,M_{\odot }\,{\rm pc}^{-2}}\right)^{0.33}, \quad & \frac{\Sigma _{\rm g}}{85\,M_{\odot }\,{\rm pc}^{-2}} > 1 \end{array} \right..

Given this three-level power-law relationship between star formation surface density and gas surface density, why then is it possible to fit the data of the Kennicutt (1998) sample with a single power law? The answer comes partly from the fact that the data are averaged over entire galaxies, which introduces significant scatter compared to the more recent data that are resolved to sub-kpc scales. The primary reason for the single power-law Kennicutt fit with an index of n \simeq 1.4, however, is that most of the dynamic range in \Sigma_g that gives rise to the index of 1.4 comes from galaxies with \Sigma_g \geq 100 M_\odot pc^{-2}. The same is true for the observed correlation between CO and IR luminosities in galaxies, where most of the dynamic range in the sample comes from starbursts with large surface densities and SFRs. In this regime our predicted law, Equation (10), also reduces to a simple power law \dot{\Sigma }_*\propto \Sigma _{\rm g}^{1.33}; the index 1.33 is well within the error bars in Kennicutt's fit. Conversely, a fit to only the normal galaxies in Kennicutt's sample produces a much steeper best-fit index of n = 2.47\pm0.39, consistent with the steeper slope we predict for normal galaxies due to the dependence of the H_2 fraction on \Sigma_g. Thus the classic single power-law star formation law is in part an artifact of fitting a single power law between normal galaxies and starbursts, a point also made by Gao & Solomon (2004) and Wyder et al. (2009).

-- JeffMangum - 2010-11-23

Origin of the Observed SFR-Molecule Relations

The following is from Narayanan etal. 2008.

The generality of the following results occurs because the origin of the SFR-molecular line relations arise from the nature of the molecular emission from the individual galaxies themselves. To see this, consider a galaxy that is forming stars at rate

SFR \propto \rho^N,

where /rho is the mean molecular gas mass density. The relationship between the SFR and the luminosity of a molecular line from a cell of clouds

SFR \propto L^\alpha_{molecule}

is dependent on the relationship between the molecular line luminosity and the mean gas density in a cell of clouds

L_{molecule} \propto \rho^\beta

where \beta = N/\alpha. Therefore, for a given Schmidt law index, N, the root issue in determining how the SFR relates to molecular line luminosity is understanding how the molecular line traces molecular gas of different densities (\beta).

The global relationship between molecular line luminosity and mean gas density traced (\beta) is driven by how the critical density of the molecular line compares with the density of the bulk of the clouds across the galaxy. In short, lines that have critical density below the mean density of most of the emitting gas cells will be thermalized and rise linearly with increasing cloud density. These lines will consequently have SFR-line luminosity relations (\alpha) similar to the Schmidt index controlling the SFR.

Lines that have critical density well above the mean density of most of the emitting gas cells will be thermalized in only a small fraction of the gas. In the case of high critical density tracers such as, for example, CO (3-2 ), a small fraction of the gas is thermalized. As the mean density increases, the fraction of thermalized gas (and consequently photon production) increases superlinearly, driving, for example, an SFR-CO (3-2) relation with index less than that of the Schmidt index. This is similar to the physical mechanism driving the SFR-{\mathrm L}_{\mathrm mol} relation in star-forming GMCs by Krumholz & Thompson (2007).

This all results in the following conclusions regarding the processes which drive the observed molecular line-SFR relations:

  1. For lines with critical densities well below the mean density of the clouds in the galaxy, the emission line will trace the total molecular content of the galaxy. In these cases, we find an SFR-molecular line luminosity index equivalent to the Schmidt-law index. This results in an SFR-CO (1-0) slope of ~1.5 when the SFR is constrained by SFR \propto \rho^{1.5} . Observationally, the SFR-CO (1-0) index is found to lie between 1.4 and 1.6.
  2. For lines with high critical densities, a superlinear relation exists in {\mathrm L}_{\mathrm{mol}\,} and \overline{n} in the gas owing to thermalized gas lying only on the high-density tail of the density distribution. The light from the thermalized cores is redistributed such that the final surface of emission is diffuse, subthermally excited gas along the line of sight. When the line is a ground-state transition (e.g., HCN 1-0), the intensity from gas cells rises monotonically with mean cloud density, although superlinearly owing to heavy contribution to the excitation from line trapping. When the line is a transition above the ground state (e.g., CO 3-2), emission from the subthermally excited cells is roughly constant with increasing mean gas density until the level populations involved in the transition begin to approach LTE, at which point the intensity is roughly linear with mean cloud density. In either case, for high critical density lines, a superlinear increase in thermalized gas and high critical density photon production with mean gas density results in an SFR-line luminosity index (\alpha) lower than the Schmidt-law index. In the example of CO (3-2) and HCN (1-0) presented here, this results in SFR-line luminosity indices of ~1, consistent with the measurements of Narayanan et al. (2005) and Gao & Solomon (2004a) and Gao & Solomon (2004b).

Finally, we note that a general consequence of these models is that at the highest SFRs, the SFR-L_{\mathrm{mol}\,} slope will naturally turn toward the underlying Schmidt index. This is because at these SFRs, the mean density of the galaxies is typically high enough that the mean density is of order the critical density of the molecular transition. In these cases, the molecular line emission will be essentially counting clouds in a manner similar to the CO (1-0) emission described earlier, and an SFR-L_{\mathrm{mol}\,} index of ~1.5 will result. This is similar to the interpretation advocated by Krumholz & Thompson (2007).

-- JeffMangum - 2010-11-30
Topic revision: r4 - 2013-12-05, JeffMangum
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