1. Molecular Gas, Dense Molecular Gas and the Star Formation Rate in Galaxies (near and far) P. Solomon Molecular Gas Mass as traced by CO emission and the star formation rate in spiral galaxies, LIRGS, ULIRGs and high z molecular galaxies (Early Molecular Galaxies, EMGs) Dense molecular Gas as traced by HCN emission is a star formation rate indicator. The mass of dense molecular gas is the key to understanding the star formation rate HCN observations at low and high z. A new Star Formation Law HCN Observations: Solomon, Downes and Radford; ApJ 1992 Gao and Solomon; ApJ. 2005 Molecular Gas at High z: Solomon and Vanden Bout; ARAA, 2005

2. CO(1-0) luminosity traces the mass of gas at H 2 densities > 300 cm -3 associated with most of the mass in GMCs. HCN(1-0) luminosity traces the mass of gas at H 2 densities > 3 x 10 4 cm -3 associated with star forming GMC Cores. Far IR luminosity traces the star formation rate due to absorption of OB stellar radiation by dust at T ~ 30 –70 K. For a given IMF this yields the total star formation rate. SFR = 1.5 x 10 -10 L FIR [M sun /yr] L FIR /L CO is a measure of the star formation efficiency L HCN /L CO is a measure of the dense gas mass fraction

3. CO luminosity for spirals, ULIRGs and high z EMGs ARAA6

4. Star Formation Efficiency for local Spirals,ULIRGS & high z EMGs ARAA7

5. Slope = 1.7 Star Formation Rate and molecular mass traced by CO in local Spirals, ULIRGS and high z luminous galaxies ARAA 8 Excluding ULIRGS, slope =1.0

6. STAR FORMATION LIFETIME ARAA9

7. Gas Mass of local ULIRGS and Early Molecular Galaxies at z >2 ARAA 10

8. Comparison of molecular gas in ULIRGS and high z EMGs Gas Mass [M o ] CO Diameters ULIRGS 0.5 - 2 x 10 10 0.8 - 2.4 kpc (FWHM) High z EMGs 0.5 - 11 x 10 10 0.8 - 7 kpc one may be larger EMGs are similar to ULIRGS with about 2 or 3 times as much molecular gas and slightly larger Can EMGs form massive ellipticals ? Probably not. They do not have enough gas and the gas is too concentrated in the center.

9. L IR -L HCN for normal spirals, LIRGs and ULIRGs The slope is 1.0

10. Star Formation Efficiency and Dense Gas Fraction L IR --L HCN normalized by L CO. This removes all dependence on distance and total gas mass. The slope is 1.0

11. LIR--LHCN relation for Milky Way GMC cores, spirals, LIRGS and ULIRGS Fit to GMCs Fit to galaxies

12. L IR /L HCN is independent of L IR (Star formation rate/dense gas mass) is the same for spirals and ULIRGs

13. Star formation efficiency, L IR /L CO increases with SFR traced by L IR

14. L HCN --L CO

15. (L HCN /L CO ) A Starburst Indicator All galaxies with a L HCN /L CO > 0.07 are Luminous IR Starbursts

16. Star Formation Law

17. The star formation rate is linearly proportional to the dense gas mass M dense

18. (Luminosity/Dense gas mass) L IR /M dense = 90

19. Status of HCN Observations. at High-z First detection with VLA in lensed Cloverleaf quasar (Solomon, Vanden Bout, Carilli, & Guelin 2003) 5 detections [1@GBT, 3@VLA, 1@PdBI (HCN J=5-4)] + 4 more VLA upper limits (Carilli et al. 2005). Almost all are QSOs--starburst combinations 4 new searches with VLA (Gao,etal) some sub-mm galaxies, >50hrs) difficult with current instruments

20. L IR --L HCN with High z galaxies

21. HCN/CO a starburst indicator at high z ? o o o o o

22. Summary The star formation rate per M sun of dense gas is the same in Milky Way GMC cores, spiral galaxies, ULIRGS and (probably) high z IR starbursts (EMGs). Star formation is very efficient for gas at densities n(H 2 ) > 3x 10 4 cm -3 The strongest starbursts in the universe are characterized by a high fraction of (dense molecular gas/total molecular gas)