Lecture 3 The IGIMF and implications

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1 Stellar populations and star clusters as galactic building blocks Lecture 3 The IGIMF and implications Selected Chapters on Astrophysics Charles University, Praha, November & December 2015 Pavel Kroupa Argelander Institute for Astronomy (AIfA) University of Bonn 1 1 Lecture 1 : The stellar IMF : solar neighbourhood as average IMF theoretical expectations : a variable IMF Lecture 2 : The stellar IMF : constraints from star-forming events : a non-varying IMF? Lecture 3 : The integrated galactic initial mass function (IGIMF) : a new theory How to calculate the stellar population of a galaxy, and implications. Lecture 4 : The stellar binary population: deriving the birth distribution functions Binary dynamical population synthesis: the stellar populations of galaxies 2 2

2 The IMF is the key to our understanding of the matter cycle in the Universe. 3 3 Remember : Counting stars = > LF => PDMF => IMF Ψ(M V )= dm dm V ξ(m) + binaries + main sequence stars corrections for stellar evolution?? peak in LF => m-mv relation nearby LF distant LF MW-field (Scalo) IMF index star-cluster/association (Salpeter/Massey) IMF index star-formation theory (Jeans-mass vs self-regulation) : - expect IMF variation with density and metallicity - unable to account for IMF shape 4 4

3 Remember : Counting stars = > LF => PDMF => IMF Ψ(M V )= dm dm V ξ(m) + binaries + main sequence stars corrections for stellar evolution?? peak in LF => m-mv relation nearby LF distant LF MW-field (Scalo) IMF index star-cluster/association (Salpeter/Massey) IMF index star-formation theory (Jeans-mass vs self-regulation) : - expect IMF variation with density and metallicity - unable to account for IMF shape 5 5 Recap IMF = the distribution of stellar masses born together. ξ(m) dm = dn =Nr. of stars in interval [m, m + dm] logdn/dlog(m) α 1 ξ(m) m α i α 2 M stars G stars log(m) O stars 6 6

4 Observations of well-resolved populations show the IMF to be universal! (except under extreme conditions - see Lecture II) 7 7 universal canonical two-part power-law IMF : ξ(m) m α i logdn/dlog(m) α 1 =1.3 α 2 =2.3 α 3,Massey =2.3 M stars G stars 0.5 M 0 O stars log(m) 8 8

5 Return to the Scalo / Massey-Salpeter discrepancy : logdn/dlog(m) α 1 =1.3 ξ(m) m α i α 2 =2.3 The canonical IMF, equal in each star cluster M stars α 3,Scalo =2.7 G stars 0 α 3,Massey =2.3? O stars log(m) 9 9 back to Problem 2: (see Lecture I) The stellar IMF in the Galactic-field and in OB associations/star clusters are not equal. 3 =2.7 3 =

Composite stellar populations 11 11 Megeath et al.

6 Composite stellar populations Megeath et al Clustered star formation (see also Lada & Lada 2003) and lack of O stars : NGC 2071/2068 Many small / low-mass groups or clusters do not yield the same IMF as one massive cluster NGC 2024/2023 ONC L1641 south 3-4 sigma deficit of massive stars stochastic IMF in each group disfavoured. (Hsu, Hartmann et al. 2012, 2013) 12 12

7 Composite Stellar Populations Stars form in clusters (Lada & Lada 2003). Thus, the Integrated Galactic IMF follows from ξ IGIMF (m, t) = Mecl,max (SFR(t)) M ecl,min ξ(m m max (M ecl )) ξ ecl (M ecl ) dm ecl Kroupa & Weidner (2003); Weidner & Kroupa (2005, 2006) adding-up all IMFs in all clusters! Vanbeveren (1982) The universal canonical two-part power-law IMF : ξ(m) m α i logdn/dlog(m) α 1 =1.3 α 2 =2.3 α 3,Massey =2.3 M stars G stars O stars 0.5 M 0 log(m) m max(m ecl) 14 14

8 Composite Stellar Populations Stars form in clusters (Lada & Lada 2003). Thus, the Integrated Galaxial IMF ξ IGIMF (m, t) = Mecl,max (SFR(t)) M ecl,min ξ(m m max (M ecl )) ξ ecl (M ecl ) dm ecl Kroupa & Weidner (2003); Weidner & Kroupa (2005, 2006) The embedded-cluster MF (ECMF) : ξ ecl M β ecl ; β solar-neighbourhood (Lada & Lada 2003) LMC & SMC (Hunter et al. 2003) Antennae (Zhang & Fall 1999) 15 few 10 M 1000 M 10 3 M 10 4 M 10 4 M 10 6 M 15 The m max (M ecl ) relation Weidner & Kroupa 2005, 2006; Weidner et al. 2010, 2013; Kroupa et al. 2013; Kirk & Myers, 2010, 2012; Hsu, Hartmann et al. 2012, 2013; Megeath et al m max =300M m max =150M physical upper mass limit? (Weidner & Kroupa 2004; Figer 2005; Oey & Clarke 2005, Koen 2006; Maiz Appelaniz et al. 2007) Dispersion of data is highly inconsistent with random / stochastic sampling from IMF 1= M ecl = mmax m max mmax m l ξ(m) dm m ξ(m) dm m max =fn(m ecl ) an mmax -- Mecl relation 16 Pavel Kroupa: University of Bonn 16

9 Composite Stellar Populations Stars form in clusters (Lada & Lada 2003). Thus, the Integrated Galaxial IMF ξ IGIMF (m, t) = Mecl,max (SFR(t)) M ecl,min ξ(m m max (M ecl )) ξ ecl (M ecl ) dm ecl Kroupa & Weidner (2003); Weidner & Kroupa (2005) Correlated star formation events building up a galaxy (i.e. embedded clusters = building blocks; Kroupa, 2005ESASP K) The total mass in stars formed in a galaxy over time t is M tot = SFR t But M tot = Z Mecl,max M ecl,min ecl (M ecl ) M ecl dm ecl For M ecl,min =5M and with 1= Z Mecl,max M ecl,max ecl (M ecl ) dm ecl where M ecl,max 10 7 M Thus M ecl,max =fn(sfr) What is delta t? The galaxy-wide time-scale of transforming the ISM via molecular clouds into a new stellar population (Egusa et al. 2004; 2009). Disappearance of large molecular clouds around young star clusters (Leisawitz 1989). (see also Schulz et al. 2015) t 10 Myr 18 18

10 Weidner et al M ecl,max =fn(sfr) { M tot = SFR t Z Mecl,max M tot = M ecl,min Z Mecl,max 1= M ecl,max Mecl,max ecl (M ecl ) M ecl dm ecl ecl (M ecl ) dm ecl t =10Myr M ecl,min =5M 107 M t =10Myr Weidner et al t =100Myr t =1Myr { M tot = SFR t Z Mecl,max M tot = M ecl,min Z Mecl,max 1= M ecl,max Mecl,max ecl (M ecl ) M ecl dm ecl ecl (M ecl ) dm ecl t =10Myr M ecl,min =5M 107 M =2.4 =

11 Randriamanakoto, Escala, et al. 2013, "In particular, the scatter in the relation is smaller than expected from pure random sampling strongly suggesting physical constraints." IGIMF = of IMFs (in all CSFEs/ embedded clusters) Why is the IGIMF different to the IMF? # stars Many low-mass clusters log stellar mass 22 22

12 IGIMF = of IMFs (in all CSFEs/ embedded clusters) Why is the IGIMF different to the IMF? # stars Many low-mass clusters IGIMF log stellar mass Rare massive clusters (contribute top-heavy IMF) ξ IGIMF (m, t) = Mecl,max (SFR(t)) M ecl,min ξ(m m max (M ecl )) ξ ecl (M ecl ) dm ecl Weidner et al. 2013; Kroupa et al The IGIMF for galaxies with different SFRs 24 24

13 Return to the Scalo / Massey-Salpeter discrepancy : ξ(m) m α i logdn/dlog(m) α 1 =1.3 α 2 =2.3 M stars α 3,Scalo =2.7 G stars 0 α 3,Massey =2.3 O stars log(m) Recall: Salpeter/Massey : α 3 =2.3 for individual clusters and OB associations but Scalo : α 3 =2.7 from Galactic-field star-counts Independent evidence : Tinsley 1980 Kennicutt 1983 < Portinari et al α 3 < 2.7 Romano et al. 2005}2.5 based on spectro-photometric and/or chemical-evolution modelling {of the MW disk. Reid et al : α 3 = from Galactic-field star counts

14 Composite stellar populations have a steeper IMF than the stellar IMF : Further observational evidence for steep galaxy-wide massive star IMF MW disk : α = (Kennicutt 198n; Scalo 1986; Reid et al. 2002) LSBs : bottom heavy IMF (Lee et al. 2005, MNRAS) Dwarf NGC4214 : α > 2.8 (Ubeda et al. 2007, AJ Remember : Counting stars = > LF => PDMF => IMF Ψ(M V )= dm dm V ξ(m) + binaries + main sequence stars corrections for stellar evolution?? peak in LF => m-mv relation nearby LF distant LF MW-field (Scalo) IMF index star-cluster/association (Salpeter/Massey) IMF index star-formation theory (Jeans-mass vs self-regulation) : - expect IMF variation with density and metallicity - unable to account for IMF shape 28 28

15 Remember : Counting stars = > LF => PDMF => IMF Ψ(M V )= dm dm V ξ(m) + binaries + main sequence stars corrections for stellar evolution? peak in LF => m-mv relation nearby LF distant LF MW-field (Scalo) IMF index star-cluster/association (Salpeter/Massey) IMF index star-formation theory (Jeans-mass vs self-regulation) : - expect IMF variation with density and metallicity - unable to account for IMF shape The IGIMF theory : Natural explanation of the difference between the Scalo field IMF ( α 2.7) and the stellar IMF ( α 2.3)

16 Composite stellar populations can have a steeper IMF than the stellar IMF: Further observational verification? Use H flux to measure the number of m>10 M stars forming. (see further below) Use broad-band colours to measure the number of forming. m<10 M stars Observational constraints on the IMF in galaxies. (based on the method by Kennicutt 1983) That is, use the count of ionising photons relative to bulk (optical) photons to estimate the slope of the galaxy-wide IMF (i.e. of the IGIMF) : Composite stellar populations can have a steeper IMF than the stellar IMF: Further observational verification? α = Γ +1 α IGIMF =2.6 α IGIMF > α 3 ; m > 1.3 M SMC MW theoretical minimal IGIMF 2.4 model Salpeter SDSS galaxies : Hoversten & Glazebrook (2007) 32 32

17 2011 IGIMF theory Weidner et al top-light top-heavy Very comparable / consistent results by log 10 (SFR) log 10 (SSFR) log 10 ( SFR ) Hoversten E. A., Glazebrook K., 2008, ApJ, 675, 163 Meurer G. R. et al., 2009, ApJ, 695, 765 Lee, J. C. et al., 2009, ApJ, 706, 599 top-heavy E galaxies formed with top-heavy IMFs confirming Matteucci (1994)! and see recent work by Vazdekis Some implications The mass-metallicity relation 34 34

18 The IGIMF theory naturally accounts for the observed mass-metallicity relation of galaxies! Koeppen, Weidner & Kroupa (2006) Tremonti et al The IGIMF theory naturally accounts for the observed mass-metallicity relation of galaxies! Koeppen, Weidner & Kroupa (2006) Tremonti et al

19 The IGIMF theory naturally accounts for the observed mass-metallicity relation of galaxies! Koeppen, Weidner & Kroupa (2006) IGIMF Tremonti et al The IGIMF theory naturally accounts for the observed mass-metallicity relation of galaxies! Koeppen, Weidner & Kroupa (2006) Fewer massive stars per low-mass star universal IMF IGIMF Tremonti et al Metal-ejection not needed! Ott, J. et al. (2005, MNRAS) 38 38

20 Chemical evolution of the interstellar medium (ISM) of a galaxy from which new stars form : "alpha elements" (e.g. O, Mg) are injected into the inter stellar medium by SNII explosions. Fe is injected into the inter stellar medium by SNII and SNIa explosions. [α/fe] only SNII SNII + SNIa time [Fe/H] Recchi et al IMF Fewer massive stars per low-mass star IMF IGIMF Observations The IGIMF theory naturally accounts for the observed [ /Fe] relation of galaxies! Thomas et al. (2005) Samson & Northeast (2008) Observations IGIMF Metal-ejection not needed! Ott, J. et al. (2005, MNRAS) 40 40

21 The IGIMF theory : Natural explanation of the mass-metallicity relation of galaxies Some implications The Halpha vs UV flux of galaxies 42 42

22 Kennicutt et al. (1994) SFR relation ( for a pure Salpeter power-law IMF betw. 0.1 and 100 Msun ) SFR / L H always for all galaxies (Pflamm-Altenburg et al. 2007) ξ IGIMF (m, t) = Mecl,max (SFR(t)) M ecl,min ξ(m m max (M ecl )) ξ ecl (M ecl ) dm ecl Weidner et al. 2013; Kroupa et al The IGIMF for galaxies with different SFRs Expect : IGIMF slope with SFR 44 44

23 A further observational test UV flux is sensitive to intermediate-mass stars with ages from 0 to 100 Myr. A UV luminosity is therefore proportional to the SFR : (Pflamm-Altenburg, Weidner & Kroupa 2009, submitted) SFR UV L UV H luminosity is sensitive to massive stars (m >10 M ) life-times of a few Myr. with If the IMF=IGIMF and if it is invariant with the SFR (the classical, Kennicutt case), then expect SFR H SFR UV = const with SFR If the IMF=IGIMF and if it varies with the SFR (the IGIMF-theory case), then expect SFR H SFR UV for SFR A further observational test 1 log 10 (SFR H!,IMF /SFR FUV,IMF ) predictions by IGIMF theory (Pflamm- Altenburg, Weidner & Kroupa 2009) Expected for classical, IMF invariant scenario log 10 (SFR tot ) 46 46

24 A further observational test 1 log 10 (SFR H!,IMF /SFR FUV,IMF ) predictions by IGIMF theory (Pflamm- Altenburg, Weidner & Kroupa 2009) measured SFR ratios (Lee, Gil, Tremonti et al., 2009) Expected for classical, IMF invariant scenario log 10 (SFR tot ) α = Γ +1 Composite stellar populations have a steeper IMF than the stellar IMF: Observational verification!! low SFR galaxies SFR α IGIMF high SFR galaxies Salpeter SDSS galaxies : Hoversten & Glazebrook (2007) 48 48

25 The IGIMF theory appears to be affirmed by observation. Todo : compute Halpha / UV flux ratio for galaxies ith high SFRs Some implications The radial cutoff in Halpha/UV ratio in disk galaxies 50 50

The local IGIMF and the radial star-formation cutoff in disk galaxies n = 51 51 Express the IGIMF in terms of local quantities : (Pflamm-Altenburg & Kroupa 2008) ΣSFR (x, y) = A Σngas (x, y),

26 The local IGIMF and the radial star-formation cutoff in disk galaxies n = Express the IGIMF in terms of local quantities : (Pflamm-Altenburg & Kroupa 2008) ΣSFR (x, y) = A Σngas (x, y), (Boissier et al. (local Schmidt law, 2007; Zasov et based on UV GALEX data) al. 2005) n=1 A 1 = 3 Gyr Mecl,max,loc (x, y) = Mecl,max ξlecmf (Mecl, x, y) = ξligimf (m, x, y) =!! Σgas (x, y) Σgas,0 "γ, γ = 3/2 (ansatz - less massive clusters further out) dnecl dmecl dx dy Mecl,max,loc (x,y) ξmecl (m) ξlecmf (Mecl, x, y) dmecl Mecl,min = the local IGIMF = LIGIMF... and study the emission of Hα photons as a function of local gas density and galactocentric radius

27 According to classical scenario (universal IMF=invariant IGIMF) : H α surface luminosity vs local gas density at different radii in 7 disk galaxies. (Kennicutt 89 [data], 94, 98 [relation]) log 10 (! H" / erg s -1 pc -2 ) ! SFR 1.4! gas H emission scales with number of O stars, and IMF non-varying L H SFR Measure H surface luminosity density and surface gas mass density SF R,H H 1.4 gas The Kennicutt SFR law. log 10 (! gas / M sol pc -2 ) According to classical scenario (universal IMF=invariant IGIMF) : H α surface luminosity vs local gas density at different radii in 7 disk galaxies. (Kennicutt 89 [data], 94, 98 [relation]) log 10 (! H" / erg s -1 pc -2 ) ! SFR 1.4! gas But: new more sensitive data H emission scales with number of O stars, and IMF non-varying L H SFR Measure H surface luminosity density and surface gas mass density. SF R,H H 1.4 gas The Kennicutt SFR law. log 10 (! gas / M sol pc -2 ) 54 54

28 Express the IGIMF in terms of local quantities : (Pflamm-Altenburg & Kroupa 2008) H α surface luminosity vs local gas density at different radii in 7 disk galaxies. (Kennicutt 89 [data], 94, 98 [relation]) log 10 (! H" / erg s -1 pc -2 ) ! SFR 1.4! gas IGIMF theory log 10 (! gas / M sol pc -2 ) 55 True underlying SF density law : Σ SFR = 1 3 Gyr Σ gas converted to H α surface luminosity using standard (but wrong) linear (Kennicutt) H α-sfr relation. Hα Σ gas relation based on standard (but wrong) Kennicutt SFR law Σ SFR = A Σ 1.4 gas ; it is a good (but wrong) fit to the bright data. 55 Express the IGIMF in terms of local quantities : (Pflamm-Altenburg & Kroupa 2008) log 10 (! SFR / M sol pc -2 Gyr -1 ) observed disk galaxies : SFR density from UV flux (Boissier et al. 2007) (UV flux generated by intermediatemass stars with ages Myr, i.e not sensitive to O stars only! ) SFR density from Hα (Martin & Kennicutt 2001) flux LIGIMF-theoretical Hα flux based on true law Σ SFR = A Σ gas r / r threshold 56 56

29 The IGIMF theory : H α cutoff accounted for naturally. True is Σ SFR = 1. 3 Gyr Σ gas (i.e no radial cutoff in SF). Theoretical models : a threshold for star formation a la H α cutoff does not exist! Some implications The stellar-masss buildup times of dwarf galaxies 58 58

30 If dwarf galaxies would have as low SFRs as are implied by the standard theory (Kennicutt), then their blue-band luminosities are too high. Pflamm-Altenburg & Kroupa 2009, ApJ Within the IGIMF theory (fewer massive stars at low SFRs) can the stellar masses of dwarf galaxies be formed within a Hubble time

31 Some implications The gas-consumption time-scales and implications for the matter cycle The traditional view : Dwarf galaxies as modest consumers 62 62

32 SFR vs gas mass : traditional (using linear Kennicutt relation to convert Hα flux to SFR.) log 10 (SFR IMF / M sol yr -1 ) CVnI group M81 group Sculptor group isolated di LG dwarfs LG disks log 10 (M gas / M sol ) 63 Pflamm-Altenburg, Weidner & Kroupa (2007); Pflamm-Altenburg & Kroupa (2008) 63 Pflamm-Altenburg, Weidner & Kroupa (2007); Pflamm-A. & Kroupa (2008) log 10 (! IMF / Gyr) CVnI group M81 group Sculptor group isolated di LG dwarfs LG disks τ = M gas SFR log 10 (M gas / M sol ) Hubble times gas-consumption time scale vs gas mass using Kennicutt relation Dwarf galaxies consume their gas very carefully, very slowly! 64

33 According to the IGIMF theory : Dwarf galaxies as insattiable consumers ξ IGIMF (m, t) = Mecl,max (SFR(t)) M ecl,min Weidner et al. 2013; Kroupa et al ξ(m m max (M ecl )) ξ ecl (M ecl ) dm ecl Back to the integratedgalaxy view. Expect : The IGIMF has fewer ionising photons! IGIMF slope with SFR 66 66

34 The variable IGIMF notion revision of the L Hα SFR relation (the Kennicutt relation)! Pflamm-Altenburg, Weidner & Kroupa (2007) Kennicutt L H SFR ( for invariant IMF ) The variable IGIMF notion revision of the L Hα SFR relation (the Kennicutt relation)! Pflamm-Altenburg, Weidner & Kroupa (2007) IGIMF Kennicutt 68 Deficit of massive stars in the IGIMF increased SFR 68

35 SFR vs gas mass : new (using IGIMF theory) log 10 (SFR IGIMF,std / M sol yr -1 ) CVnI group M81 group Sculptor group isolated di LG dwarfs LG disks 1.02 M gas log 10 (M gas / M sol ) 69 Pflamm-Altenburg, Weidner & Kroupa (2007); Pflamm-Altenburg & Kroupa (2008) 69 SFR vs gas mass : traditional (again) (using linear Kennicutt relation to convert Hα flux to SFR.) log 10 (SFR IMF / M sol yr -1 ) CVnI group M81 group Sculptor group isolated di LG dwarfs LG disks log 10 (M gas / M sol ) 70 Pflamm-Altenburg, Weidner & Kroupa (2007); Pflamm-Altenburg & Kroupa (2008) 70

36 SFR vs gas mass : new (again) (using IGIMF theory) log 10 (SFR IGIMF,std / M sol yr -1 ) CVnI group M81 group Sculptor group isolated di LG dwarfs LG disks 1.02 M gas log 10 (M gas / M sol ) 71 Pflamm-Altenburg, Weidner & Kroupa (2007); Pflamm-Altenburg & Kroupa (2008) 71 SFR vs gas mass : (traditional: invariant IMF) (using IGIMF theory) Pflamm-Altenburg, Weidner & Kroupa (2007); Pflamm-Altenburg & Kroupa (2009) A B SFR (M sol yr -1 ) IMF IGIMF M gas (M sol ) M gas (M sol ) 72

37 Pflamm-Altenburg, Weidner & Kroupa (2007); Pflamm-A. & Kroupa (2008) log 10 (! IGIMF,std / Gyr) CVnI group M81 group Sculptor group isolated di LG dwarfs LG disks τ = M gas SFR 10 Hubble times gas-consumption time scale vs gas mass log 10 (M gas / M sol ) Pflamm-Altenburg, Weidner & Kroupa (2007); Pflamm-A. & Kroupa (2008) log 10 (! IMF / Gyr) CVnI group M81 group Sculptor group isolated di LG dwarfs LG disks τ = M gas SFR log 10 (M gas / M sol ) Hubble times gas-consumption time scale vs gas mass using Kennicutt relation Dwarf galaxies consume their gas very carefully, very slowly! 74

38 Pflamm-Altenburg, Weidner & Kroupa (2007); Pflamm-A. & Kroupa (2008) log 10 (! IGIMF,std / Gyr) CVnI group M81 group Sculptor group isolated di LG dwarfs LG disks τ = M gas SFR 10 Hubble times gas-consumption time scale vs gas mass using IGIMF theory log 10 (M gas / M sol ) 75 IGIMF theory constant gas depletion time-scale! 75 IGIMF theory 70 constant gas depletion time-scale! for galaxies with 10 5 < M gas M < # Galaxies Gyr IGIMF traditional log-norm Pflamm- Altenburg, Weidner & Kroupa (2007); Pflamm-A. & Kroupa (2008) log(! gas / Gyr) for all late-type galaxies 10 6 < M gas < 2.9 Gyr M 10 11? 76 76

39 SFR = 1 3 Gyr M neutral gas Pflamm- Altenburg, Weidner & Kroupa (2007); Pflamm-A. & Kroupa (2008) i.e. every 10 Myr a galaxy transforms 0.3 % of its neutral gas mass into stellar mass But where is all the star-forming gas coming from at just the right rate? 78 78

40 Further work is required These are possible research projects. - Unify the local and the galaxy-wide / global IGIMFs (theoretical). - Compute Halpha/UV flux ratios, photometric properties and M/L ratios of galaxies with different SFRs and SFHs (theoretical) - Test IGIMF theory via diret counts of O stars in nearby dwarf galaxies with low SFRs (see predictions in Weidner et al. 2013) : END of Lecture

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