1. The Prospect of Observing the KS Relation at High-z Desika Narayanan Harvard-Smithsonian CfA Chris HaywardT.J. CoxLars Hernquist Harvard Carnegie

2. Kennicutt-Schmidt SFR Laws Locally: Bigiel 2008; Krumholz et al. 2009

3. Molecular Kennicutt-Schmidt SFR Laws Gao & Solomon 2004 Local: CO J=1-0 SFRSFR Total H 2 Gas Mass z~2: CO (J=3-2) z~2 Bouché et al. 2007

4. Theoretical Approach: SPH simulations of galaxies Springel et al. (2003-2005) Prescriptions for multi-phase ISM (McKee-Ostriker) SF (volumetric Schmidt law) BH growth and associated Feedback Halos scaled to z~2 concentration For z~2 study, isolated galaxies M bar ~ 10 11 M , MMW disks SF follows SFR   1, 1.5, 2

5. Desika Narayanan SFR@50, Spineto Non-LTE Radiative Transfer (Synthetic Molecular Line Emission) 3D Monte Carlo code developed based on improved Bernes (1979) algorithm Considers full statistical equilibrium with collisional and radiative processes Sub-grid algorithm considering mass spectrum GMCs as SIS; M cloud =10 4 -10 6 M , (Blitz et al. 2006, Rosolowsky 2007, Bolatto et al. 2008) Uniform Galactic CO Abundance, no H 2 at N H < 10 21 cm -2 DN+ 2006,2008

6. SUNRISE (dust RT) to ‘Select’ Galaxies GMC Diffuse ISM Physics Included in Monte Carlo IR RT: -IR transfer of stellar and AGN spectrum (starburst 99 for stars and Hopkins+ 07 for AGN) -dust radiative equilibrium -Kroupa IMF, ULIRG/SMG DTG (same as MW DTM) -Stellar Clusters surrounded by HII regions and PDRs (MAPPINGS; Groves et al. 2008) Jonsson, Groves & Cox (2009)

7. Does Differential Excitation Matter?: Local Universe Example CO (J=1-0) Gao & Solomon 2004 CO (J=3-2) Index = 1.0 Narayanan et al. 2005 Iono et al. 2008 SFR ~ CO (1-0) 1.5 SFR ~ CO (3-2) 0.9

8. Molecular Kennicutt-Schmidt SFR Laws HCN J=1-0 Gao & Solomon (2004) CO J=1-0 Index = 1.5 Index = 1.0 SF follows SFR   1.5

9. Molecular Kennicutt-Schmidt SFR Laws CO (J=1-0) Gao & Solomon 2004 CO (J=3-2) Index = 1.0 Narayanan et al. 2005 Iono et al. 2008 SFR ~ CO (1-0) 1.5 SFR ~ CO (3-2) 0.9 SF follows SFR   1.5

10. Differential Excitation; Underlying n=1.5 KS Index Krumholz & Thompson 2007 Narayanan et al. 2008 SF follows SFR   1.5 SFR-CO  indexSFR-HCN  index CO (J=1-0) CO (J=3-2) HCN (J=1-0)

11. HCN (HCN (J=3-2) Observational Survey Bussmann, DN, Shirley, Wu, Juneau, Vanden Bout, Solomon et al. (2008)

12. HCN (HCN (J=3-2) Observational Survey Bussmann, DN, Shirley, Juneau et al. 2008

13. Getting to the KS Relation at z~2 SF follows SFR   1, 1.5, 2

14. Getting to the KS Relation at z~2 SF follows SFR   1, 1.5, 2

15. Getting to the KS Relation at z~2 SFR-LCO index versus Transition for KS = 2 galaxies SF follows SFR   1, 1.5, 2

16. Mapping the CO 3-2 KS relation at z~2 to the underlying volumetric Schmidt Relation Data from Tacconi et al. 2010: SFR ~ L (CO3-2) 0.97 Physical KS index vs. SFR-CO (J=3-2) index

17. Conclusions 1. Excitation Matters

18. Conclusions 1. Excitation Matters 2. Getting the KS relation at high-z is feasible (now!)

19. Desika Narayanan SFR@50, Spineto GADGET SPH Simulations Springel et al. (2003-2005), Prescriptions for multi-phase ISM (McKee-Ostriker), SF, BH growth and associated Feedback (though BH winds turned off) 100 galaxies used: 20 disk Galaxies 80 merger snapshots SF follows SFR   1.5 Assuming the free-fall time argument for SFR ~  1.5 holds

20. Can we Recover the Basic Relations? Narayanan et al. 2008 SF follows SFR   1.5 SFR-CO indexSFR-HCN index CO (J=1-0) CO (J=3-2) HCN (J=1-0) SFR ~  1.5 (assumed Schmidt Law) SFR ~ L mol  (observed) L molecule ~   Then  =1.5/  So we need to understand how line luminosity varies with gas density

21. Fiducial Disk Galaxy V 200 =115 km/s f gas =0.2 SFR ~  1.5 (assumed Schmidt Law) SFR ~ L molecule  (observed) L molecule ~   Then  =1.5/  Narayanan et al. 2008 CO (J=1-0)

22. Fiducial Disk Galaxy V 200 =115 km/s f gas =0.2 SFR ~  1.5 (assumed Schmidt Law) SFR ~ L molecule  (observed) L molecule ~   Then  =1.5/  Then  =1.5/  Narayanan et al. 2008 Increasing density will increase the gas mass, thus increasing the CO (1-0) luminosity proportionally Low n crit

23. Fiducial Disk Galaxy V 200 =115 km/s f gas =0.2 SFR ~  1.5 (assumed Schmidt Law) SFR ~ L molecule  (observed) L molecule ~   Then  =1.5/  Then  =1.5/  Narayanan et al. 2008 High n crit

24. Fiducial Disk Galaxy V 200 =115 km/s f gas =0.2 SFR ~  1.5 (assumed Schmidt Law) SFR ~ L molecule  (observed) L molecule ~   Then  =1.5/  Then  =1.5/  Increasing density will increase the gas mass, thus increasing the CO (1-0) luminosity proportionally >> n crit slope=1.5 << n crit slope < 1.5