Star Formation Theory: Connecting the Local to the Extra- Galactic

Transcription

1 Star Formation Theory: Connecting the Local to the Extra- Galactic Mark Krumholz University of California, Santa Cruz Frontiers in Star Formation Conference Yale, October 27, 2012

2 Leroy SF Laws on Galactic Scales

3 SF Laws on Galactic Scales Bigiel Leroy+ 2008

4 SF Laws on Sub- Galactic Scales N(YSOs) Ori A Ori B California Pipe rho Oph Taurus Perseus Lupus 1 Lupus 3 Lupus 4 Corona 10 1 Lada Cloud mass (M ) Wu+ 2005

5 Metallicity- Dependence Bigiel M pc 2 log ΣSFR (M yr 1 kpc 2 ) cz=5 cz=1 cz=0. 2 Bolatto log Σ gas (M pc 2 ) Figure 3. Total gas star formation law in the SMC. The gray scale shows the two-dimensional distribution of the correlation between Σ SFR and Σ gas,where Σ gas is the surface density of atomic plus molecular gas corrected by helium. The white contours indicate the correlation due to atomic gas alone, which dominates the gas mass (and Σ gas ) in the SMC. The contour levels, and the dotted lines indicating constant τ gas dep, are at the same values as in Figure 2. The dash-dotted, dashed, and solid lines indicate the loci of the model by Krumholz et al. (2009c,

6 Phase- Dependence 0.5 Bigiel log ΣSFR (M yr 1 kpc 2 ) log τ dep = log τ dep = 9 normal disks log τ dep = 10 Bolatto log Σ mol (M pc 2 )

7 The Theoretical Challenge Which laws are the fundamental ones, the local or the galactic- scale? Both? Neither? Can we unify the different sets of laws (at different scales, for different phases) within a single theoretical framework?

8 SF Laws: the Top- Down Approach The idea in a nutshell: the SFR is set by galactic- scale regulation, independent of the local SF law. The local law is to be explained separately.

9 STABILITY IN STAR FORMATION Q- Based Models L21 Li Yang Fig. 3. Star formation timescale tsf as a function of initial Qsg(min) for both low-t (open symbols) and high-t (filled symbols) models. The solid line is the least-squares fit. Basic idea: SFR is a function of Toomre Q in galaxy fully resolved models Table 1. in The values ofcloud. Only neutral species are included in this map. The gray-scale runs linearly from 0 to Fig. 1. (a) Total gas surfacelisted densityindistribution the critical Large Magellanic #2 #2. The contour lines show a surface density of 4 M pc Comparison between massive star-forming sites traced by young stellar object candidates (red 100 MQ%sgpcappear to be generally higher than Qg in the%same. (b) galaxy, dots) and and regions where the gas alone is gravitationally unstable. The Toomre both have lower values (!1) in more unstable models. parameter for the gas Qg is shown in gray-scale, running logarithmically from 5.0 to 0.2. which regions are gravitationally unstable. (c) Total stellar surface density distribution. The gray-scale The solid lines delineate the valueas of starbursts Qg ¼ 1 inside Most galaxies notcritical classified have gasthe fractions #2 pc. (d) Same as in (b), but for regions runs linearly from 0 to 200 M % comparable to or less than our most stable models, so where the the gas and stars together are gravitationally unstable, rather than just the gas alone.

10 Feedback Models Hopkins Dobbs Also see Tasker (2011), E. Ostriker s talk Mechanisms that regulate SF rate: supernovae, radiation pressure, ionized gas pressure, FUV heating

11 Characteristics of Top- Down Models Hopkins Figure 8. Cumulative gas mass fraction above a given density n for and feedback efficiency (Fig. 9). Left: density distribution for differ collapse to high densities for the star formation to self-regulate (the h the momentum deposition per unit star formation (η p ; equation 5). Fo for different values of the threshold density for star formation n 0.L formation can self-regulate. Changing the small- scale SF law does not change the SFR in the galaxy, but it does change the gas density distribution

12 Top- Down Model Limitations Krumholz & Thompson 2012 Hopkins Results depend strongly on subgrid feedback model (e.g. radiative trapping, SFE inside unresolved GMCs, UV heating per unit) No independent prediction for local SF laws

13 Metallicity in Top- Down Models Hopkins log[σ H2/ΣHI] cz=5 OML10 OML10h cz=1 Bolatto cz= log Σ gas (M pc 2 ) Figure 5. Ratio of molecular-to-atomic gas in the SMC. The blue contours and the gray scale show the two-dimensional distribution of the ratio Σ H2 /Σ H i vs. Σ gas on scales of r 12 pc and r 200 pc, respectively (note that the hard edge present in the blue contours at low ratios and low Σ gas is the result of our adopted 2σ cut in Σ H2 ). The dotted horizontal line indicates Σ H2 /Σ H i = 1, denoting the transition between the regimes dominated by H i and H 2.Thedash-dotted, dashed, and solid lines show the predictions of KMT09 for different values of the cz parameter, as in Figure 3.FortheSMC,cZ = 0.2atr 12 pc, and the KMT09 curve overestimates the molecular-to-atomic ratio by a factor of two to three. At r 200 pc we may expect cz 1 using the standard clumping factor c = 5 adopted by KMT09 for unresolved complexes. Although molecular gas in the SMC is highly clumped, the atomic gas is not, so the cz = 1curve overestimates Σ H2 /Σ H i at 200 pc. The thick gray and black contours indicate the predicted surface density ratio of gas in gravitationally bound complexes to diffuse gas, Σ gbc /Σ diff,inoml10andinthemodelmodifiedtoincorporatethe Top- down models most naturally predict SF laws that do not depend on metallicity or phase, strongly inconsistent with observations to g s h s c in o to ty m a p T ( h p d a d f th c n in s la th p o g d F

14 SF Laws: the Bottom- Up Approach The idea in a nutshell: the SFR is set by a local SF law, plus a galactic- scale distribution of gas.

15 The Dense Gas Model 4 2 normal spirals LIRGs ULIRGs BzKs log(sfr) [M yr -1 ] Heiderman Lada % 10% 1% galactic clouds galaxies log(m) [M ] Basic idea: SFR = M(>ρ dense ) / t dense, with ρ dense, t dense = const Problems: no physical basis for values of ρ dense, t dense ; evidence for threshold mixed

16 Observed Local SF Law Gracilla- Burillo Krumholz Also see Krumholz & Tan (2007) Local SF law: ~1% of gas mass goes into stars per free- fall time, independent of density or presence of massive stars

17 Why is ε ff Low? (Original model: Krumholz & McKee 2005; updates by Padoan & Nordlund 2011, Hopkins 2012, Federrath & Klessen 2012) Properties of GMC turbulence: α vir ~ 1, density PDF lognormal, LWS relation σ v ~ l 1/2 Scaling: M ~ l 3, PE ~ l 5, KE ~ l 4, so PE << KE, typical region unbound Only over- dense regions bound; integrating over lognormal PDF gives ε ff ~ 0.01 KE >> PE L l KE PE

18 Building a Galactic SF Law from a Local One Need to estimate characteristic density In MW- like galaxies, GMCs have Σ GMC ~ 100 M pc 2, M GMC ~ σ 4 / G 2 Σ gal ; this gives In SB / high- z galaxies, Toomre stability gives Ansatz: ρ = max(ρ T, ρ GMC )

19 Combined Local- Galactic Law Krumholz, Dekel, & McKee 2012

20 Metallicity / Phase- Dependence HI, CII H 2, CII Interstellar UV photons H 2, CO T ~ 10 K T ~ 20 K T ~ 300 K

21 Chemical and Thermal Balance H 2 formation H 2 photodissociation Decrease in rad. intensity Line cooling Absorption by dust, H 2 Photoelectric heating Decrease in rad. intensity Absorption by dust Caveat: this is assumes equilibrium, which may not hold

22 Calculating Molecular Fractions To good approximation, solution only depends on two numbers: Krumholz+ 2008, 2009 An approximate analytic solution can be given from Analytic solution for location of HI / H these parameters. 2 transition vs. exact numerical result

23 Calculating f H2 Qualitative effect: f H2 goes from ~0 to ~1 when ΣZ ~ 10 M pc 2

24 Why Does SF Glover & Clark 2012 Follow H 2? Krumholz, Leroy, & McKee 2011

25 The Local HI H2 Transition KMT09 Figure 12. (Continued) Left: B1; right: NGC Lee+ 2012

26 Extra- Galactic Phase Dependence The Astrophysical Journal, 741:12(19pp),2011November1 map, while the ordinate is chiefly Hα. Thesmallextinction OML10 correction derived OML10h from the 24 µm datahasanegligibleeffect on the correlation. 1 Also note that because we correct for dust log[σ H2/ΣHI] cz=5 cz=1 Bolatto cz=0.2 temperature when deriving the dust surface density, Σ mol should, in principle, also be independent of heating effects. The molecular gas depletion KMT09 time depends on the scale considered (Figure 2). On the smallest scales considered, r 12 pc, 0.5 the depletion time in the molecular gas is log[τdep mol /(1 Gyr)] 0.9 ± 0.6 (τ mol 7.5 Gyrwithafactorof3.5uncertaintyaf- dep 0 ter accounting for observed scatter and systematics involved in producing the H 2 map as well as the geometry of the source). As mentioned in the previous section, τ mol shortens when con- dep sidering 0.5 larger spatial scales due to the fact that the Hα and H 2 distributions differ in detail, but are well correlated on scales of hundreds of parsecs (Figure 1). On size scales of r 200 pc (red squares in Figure 2), corresponding to very good resolu- 1 tion for most studies of galaxies beyond the Local Group, the molecular depletion time is log[τdep mol /(1 Gyr)] 0.2 ± 0.3, or 1.6 Gyr.Thedepletiontimeonr 1kpcscales(black τdep mol circles 1.5 in Figure 2), corresponding to the typical resolution of extragalactic studies, stays log constant Σ gas (Mfor pc the 2 ) central regions of our map (where the smoothing can be accurately performed), log[τ mol scales typically probed by extragalactic studies. This constancy reflects the spatial scales over which Hα and molecular gas are well correlated. Although the precise values differ, a very similar trend for τ mol (Schruba et al. 2010). The further reduction of the depletion time Figure 5. Ratio of molecular-to-atomic gas in the SMC. The blue contours and the gray dep /(1 Gyr)] 0.2±0.2. Thus, our results converge on the scale show the two-dimensional distribution of the ratio Σ H2 /Σ H i vs. Σ gas on scales of r 12 pc and r 200 pc, respectively (note that the hard edge present in the blue contours at low ratios and low Σ gas is the result of our adopted 2σ cut in Σ H2 ). The dotted horizontal line indicates Σ H2 /Σ H i = 1, denoting the transition between the regimes dominated by H i and H 2.Thedash-dotted, dashed, anddep as a function of spatial scale is observed in M 33 solid lines show the predictions of KMT09 for different values of the cz parameter, as in Figure 3.FortheSMC,cZ = 0.2atr 12 pc, and the Bolatto et al. to uncertainty in inclination or other aspects of the SMC s 0.5 geometry. By contrast, the total gas star formation law is offset significantly from that observed in large galaxies. The SMC harbors 1 unusuallykmt09 high Σ H i and low Σ SFR at a fixed total gas surface density (although the Σ SFR versus Σ gas distribution moves closer 1.5 to the loci of large spirals if the star and gas are in a disk inclined by i>40,orifthegalaxyiselongatedalongtheline of site). 2 At a given Σ gas,themoleculargasfractionisalsooffset to values lower than those observed in massive disk galaxies, by typically an order of magnitude. 2.5 Two natural corollaries emerge from these observations. First, molecular clouds in the SMC are not extraordinarily efficient 3 at turning gas into stars; star formation proceeds in them at a pace similar to that in GMCs belonging to normal disk galaxies. 3.5 This suggests that, down to at least the metallicity of the SMC (Z Z /5), the lower abundance of heavy elements does not have 4a dramatic impact on the microphysics of the star formation process, although it does appear to have an important effect at determining 4.5 the fraction of the ISM capable of forming stars. This is not a foregone conclusion. Bolatto+ For example, 2011 it is conceivable 5 that the low abundance of carbon and the consequent low dust-to-gas ratio and low extinction would affect the ionization log Σ fraction in the molecular gas. gas (M pc This may 2 ) result in changes in the coupling with the magnetic field, perhaps slowing the GMC collapse and resulting in lower SFE and longer τdep mol.or,alter- natively, the low abundance of CO (an important gas coolant in dense molecular cores) could make it difficult for cores to shed the energy of gravitational contraction, slowing their collapse and again resulting in longer timescales for dep, are at the same values as in Figure 2. The dash-dotted, consuming log ΣSFR (M yr 1 kpc 2 ) cz=5 cz=1 cz=0. 2 Figure 3. Total gas star formation law in the SMC. The gray scale shows the two-dimensional distribution of the correlation between Σ SFR and Σ gas,where Σ gas is the surface density of atomic plus molecular gas corrected by helium. The white contours indicate the correlation due to atomic gas alone, which dominates the gas mass (and Σ gas ) in the SMC. The contour levels, and the dotted lines indicating constant τ gas dashed, and solid lines indicate the loci of the model by Krumholz et al. (2009c,

27 The Future: Mapping out the Space Between Local and Galactic

28 Extragalactic SF Laws at High Resolution Schruba+ 2010

29 Extragalactic SF Laws at High Resolution Schruba Figure 4. Scale dependence of the location of data in the star formation law

30 Comparison to Model Kim α 2

31 Comparison to Model Kim Σ Σ α 1 2 α 2

32 SF Laws in Many Lines Juneau between infrared luminosity and CO(1 0) (a), HCO + (1 0) (b), HCN(1 0) (c), HCO + (3 2) (d), and HCN(3 2) (e), mole

33 Comparison to Model Juneau Models: Narayanan+ (2008) Bayet+ 2008

34 Summary Can local and extra- galactic laws be unified? Depends on whether SF regulation is top- down or bottom- up Can laws for different phases / metallicities be unified with other laws? Yes, but this only happens naturally in a bottom- up framework. Promising approach: measure and predict SF laws at intermediate scales and densities