1. The Global Star Formation Laws in Galaxies: Recent Updates Yu Gao Purple Mountain Observatory Chinese Academy of Sciences May 15, 2012 @5 th sino-french

2. Outline of this talk What are the star formation (SF) recipes? SFR-gas (HI, CO) scaling laws: Kennicutt - Schmidt law, SF laws in other forms Why do we need a SFR-dense gas law A linear FIR(SFR)--HCN (dense gas tracer) relation for all star-forming systems (GMCs-->high-z): SF law in dense gas Major issues and debates (CS surveys) Conclusions

3. Star formation laws Schmidt (1959): SFR~density(HI)^n, n=1-3, mostly 2-3 in ISM of our Galaxy. Kennicutt (1989): Disk-average [SFR~ density(HI+H2)^n] n is not well constrained. ~1-3, wide spread. Kennicutt (1998): n=1.4 ? Total gas (HI + H2) vs. Dense gas Better SF law in dense gas? (Hubble law and H 0 analogy)

4. Hubble law

5. Kennicutt 1998 n=1.4

6. Normal disk spirals IR circumnuclear starbursts

7. SFR vs. M(H2): No Unique Slope:1, 1.4, 1.7? HI-dominated LSB galaxies HI ~ H2 H2-dominatedLIRGs/ULIRGs Gao & Solomon 2004b ApJExtragalactic SF=CO until 90’s

8. Bigiel’s talk @SFR50 SF thresholds may simply reflect the change of the dominant cold gas phase in galaxies from HI ->H2 & from H2->denseH2 Schruba+2011 ~linear in H2!

9. GMCs enbed in diffuse a tomic gas （ HI ）, the gas reservoir for molecular clouds, and the supply for future star formation. PDRs

10. Stars are forming in giant molecular clouds (GMCs)

11. High Density Tracers Merging/interactions trigger gas infall to nuclear regions Nuclei of Galaxies should possess denser gas as GMCs have to survive to tidal forces (must be denser) Critical density: the radiating molecule (eg, CO) suffers collisions at the rate: n(H2) sigma v = A ( Einstein coefficient A ~ nu^3 mu^2 ) * High-J (>~3) levels of CO (nu ~ J) higher critical density to be excited (>10 5 cm -3 ) * & High dipole moment molecules HCN, HNC, HCO+, CS (mu ~ 30x > CO), etc.. * X factor ? CO-to-H2, HCN-to-DenseH2 conversions

12. Dense gas is the essential fuel for high mass star formation in galaxies HCN Surveys in 53 Galaxies: Gao & Solomon 2004a ApJS Far-IR, HCN, CO Correlations : Gao & Solomon 2004b ApJ

13. SFR Dense Molecular Gas

14. Baan, Henkel, Loenen + 2008 Baan et al. (2008) Kohno 2007, et al. (2003) Imanishi (2006) Aalto et al. 2007, 2002, 1995 Solomon et al. 1992 Nguyen et al. 1992 Henkel et al. 1990 Henkel, Baan, Mauersberger 1991 HCN,CS,HNC etc. in SF gals. Best case studies: Arp 220 & NGC 6240 (Greve + 2009)

15. 13 HCN @high-zHCN @high-z Gao, Carilli, Solomon & Vanden Bout 2007 ApJ, 660, L93

16. Wu, Evans, Gao et al. 2005 ApJL Fit to GMCs Fit to Galaxies Fit to both GMCs & Gals.. Wu+2010

17. CARMA+45m CO (Koda + 09) HST

18. Total useful on-source integration time >~110 hours. HCN spectra with S/N>3 (a channel width dV ~7 km/s). Typical rms ~1-2 mK at dV~20 km/s.

19. HCN contours are overlaid on the CO image

20. Correlations between 8um-HCN & 24um- HCN. The solid lines: fixed slope of 1. SFR HCN

21. Chen & Gao in prep. M33GMCs (Rosolowsky, Pineda & Gao 2011)

22. ∑M dense vs. ∑ SFR Dense H2 show the best correlation with SFR (linear Liu & Gao 2011). Liu & Gao arXiv:1106.2813

23. K-S SF Law in high-redshift galaxies K-S SF Law in high-redshift galaxies Daddi et al. 2010; Genzel+2010 CO->H2 conversion factor ?? α co (Msun (K km/s pc 2 ) -1 : 4.6 for local spirals 3.6 ± 0.8 for BzKs 0.8 for LIRGs/SMGs/QSOs Two major SF modes: 1. a long-lasting mode for disks (local spirals and BzKs) 2. a rapid starburst for LIRGs ULIRGs & SMGs/QSOs

24. Bi-modal SF laws in high-z gals (Daddi+2010; Genzel+2010) also exist in local gals

25. Juneau+2009; Narayanan+2008; Krumholz & Thompson 2007; Iono+2008; Mao+2010 SFR – CO & SFR -- HCN indexes

30. Dense gas over a range of 10^4-8 /cm^3

31. Concluding Remarks SF: quiescent (few Dense Cores=DCs), normal, active/burst modes (starbursts: active formation of DCs) DCs in Dense Molecular Gas Complexes  High Mass Stars/Clusters (SF in different environments: SMGs/hi-z QSOs; ULIRGs/Starbursts; Spirals; LSBs; DCs) SF thresholds: change of the dominant cold gas phase in galaxies from HI ->H2 & from H2->denseH2 (FIR-HCN, CS Linear Correlations) SFR ~ M(DenseH2): the total mass of dense molecular gas in galaxies & all star-forming systems (spanning 10 orders of mag.)? SFR-DenseGas: Counting DCs(=SF units) in Galaxies? Gao & Solomon: Dense H 2  DCs/StarsClusters

32. New Star Formation Law Dense Molecular Gas  High Mass Stars SFR ~ M(DENSE) ~ density of dense gas (e.g. gas density >~10^5 cc), linear HI  H 2  DENSE H 2  Stars Schmidt law : HI  Stars Kennicutt : HI + H 2  Stars Gao & Solomon: Dense H 2  Stars From Cores to High-z: Dense Gas  Massive SF