Stellar populations and star clusters as galactic building blocks Lecture 3 The IGIMF and implications

Selected Chapters on Charles University, Praha, November & December 2015

Pavel Kroupa Argelander Institute for Astronomy (AIfA) University of Bonn

1 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 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 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 2 The IMF is the key to our understanding of the matter cycle in the Universe.

3 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 3

Counting stars = > LF => PDMF => IMF Remember : dm corrections for Ψ(MV)=− ξ(m) dMV + binaries + main sequence stars

✓ 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 ? - unable to account for IMF shape

4 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 4 Counting stars = > LF => PDMF => IMF Remember : dm corrections for Ψ(MV)=− ξ(m) dMV stellar evolution + binaries + main sequence stars

✓ 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 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 5

Recap IMF = the distribution of stellar masses born together . ξ(m) dm = dN =Nr. of stars in interval [m, m + dm]

α1 ∝ −αi logdN/dlog(m) ξ(m) m

α2

M stars G stars O stars

log(m)

6 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 6 Observations of well-resolved populations show the IMF to be universal !

(except under extreme conditions - see Lecture II)

7 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 7

universal “canonical” two-part power-law IMF :

−α ξ(m) ∝ m i

α1 =1.3 logdN/dlog(m) α2 =2.3

α3,Massey =2.3

M stars G stars O stars 0.5 M ! 0 log(m)

8 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 8 Return to the Scalo / Massey-Salpeter discrepancy :

−α ξ(m) ∝ m i

α1 =1.3 The canonical IMF, logdN/dlog(m) α2 =2.3 equal in each

α3,Massey =2.3 α3,Scalo =2.7 ? M stars G stars O stars 0 log(m)

9 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 9

back to Problem 2: (see Lecture I)

The stellar IMF in the Galactic-field 3 =2.7 and in OB associations/star clusters 3 =2.3 are not equal.

10 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 10 Composite stellar populations

11 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 11

Clustered star formation Megeath et al. 2012 (see also Lada & Lada 2003) and NGC 2071/2068 lack of O stars :

NGC 2024/2023 Many small / low-mass groups or clusters do not yield the same IMF as one massive cluster

ONC

3-4 sigma stochastic IMF L1641 in each group south deficit of massive disfavoured. stars (Hsu, Hartmann et al. 2012, 2013)

12 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 12 Composite Stellar Populations

Stars form in clusters (Lada & Lada 2003). Thus, the Integrated Galactic IMF follows from

Mecl,max(SFR(t)) ξ (m, t)= ξ(m ≤ m (M )) ξ (M ) dM IGIMF ! max ecl ecl ecl ecl Mecl,min

Kroupa & Weidner (2003); Weidner & Kroupa (2005, 2006)

adding-up all IMFs in all clusters ! Vanbeveren (1982)

13 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 13

The universal “canonical” two-part power-law IMF :

−α ξ(m) ∝ m i

α1 =1.3 logdN/dlog(m) α2 =2.3

α3,Massey =2.3

M stars G stars O stars 0.5 M ! 0 log(m) mmax(Mecl)

14 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 14 Composite Stellar Populations

Stars form in clusters (Lada & Lada 2003). Thus, the Integrated Galaxial IMF

Mecl,max(SFR(t)) ξ (m, t)= ξ(m ≤ m (M )) ξ (M ) dM IGIMF ! max ecl ecl ecl ecl Mecl,min

Kroupa & Weidner (2003); Weidner & Kroupa (2005, 2006)

The embedded-cluster MF (ECMF) : −β ξecl ∝ Mecl ; β ≈ 2 − 2.4 solar-neighbourhood few 10 M! − 1000 M! (Lada & Lada 2003) 3 4 LMC & SMC 10 M! − 10 M! (Hunter et al. 2003) 4 6 Antennae 10 M! − 10 M! (Zhang & Fall 1999) 15 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 15

Weidner & Kroupa 2005, 2006; m M Weidner et al. 2010, 2013; Kroupa et al. 2013; The max ( ecl ) relation Kirk & Myers, 2010, 2012; Hsu, Hartmann et al. 2012, 2013; Megeath et al. 2015

mmax =300M ⇤

mmax =150M physical upper mass limit ? ⇤ (Weidner & Kroupa 2004; Figer 2005; Oey & Clarke 2005, Koen 2006; Maiz Appelaniz et al. 2007)

mmax∗ 1= ξ(m) dm ! Dispersion of data mmax is highly inconsistent mmax with Mecl = m ξ(m) dm random / stochastic !ml sampling from IMF

mmax =fn(Mecl) an mmax -- Mecl relation

16 Pavel Kroupa: University of Bonn Mittwoch, 9. Dezember 15 16 Composite Stellar Populations

Stars form in clusters (Lada & Lada 2003). Thus, the Integrated Galaxial IMF

M SFR t ecl,max( ( )) ✓ ✓ ξ (m, t)= ξ(m ≤ m (M )) ξ (M ) dM IGIMF ! max ecl ecl ecl ecl Mecl,min

Kroupa & Weidner (2003); Weidner & Kroupa (2005)

17 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 17

Correlated star formation events building up a galaxy (i.e. embedded clusters = building blocks; Kroupa, 2005ESASP.576..629K)

The total mass in stars formed in a galaxy over time t is Mtot = SFR t ⇥

Mecl,max But Mtot = ⇠ecl(Mecl) Mecl dMecl ZMecl,min

Mecl,max ⇤ For Mecl,min =5M and with 1= ⇠ecl(Mecl) dMecl ZMecl,max

7 where Mecl,max 10 M ⇤ ⇡

Thus Mecl,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 Pavel Kroupa: Praha Lecture III ⇡ 18

Mittwoch, 9. Dezember 15 18 M = SFR t tot ⇥

Mecl,max Mtot = ⇠ecl(Mecl) Mecl dMecl Weidner et al. 2004 ZMecl,min

Mecl,max ⇤ Mecl,max =fn(SFR) 1= ⇠ecl(Mecl) dMecl ZMecl,max t =10Myr

Mecl,min =5M 7 Mecl,max 10 M { ⇤ ⇡ t =10Myr

19 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 19

M = SFR t tot ⇥

Mecl,max Mtot = ⇠ecl(Mecl) Mecl dMecl Weidner et al. 2004 ZMecl,min

Mecl,max ⇤ 1= ⇠ecl(Mecl) dMecl ZMecl,max t =10Myr

Mecl,min =5M 7 Mecl,max 10 M { ⇤ ⇡ t =100Myr t =1Myr

=2.4 =2.0

20 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 20 Randriamanakoto, Escala, et al. 2013,

"In particular, the scatter in the relation is smaller than expected from pure random sampling strongly suggesting physical constraints."

21 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 21

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 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 22 IGIMF = ∑ of IMFs (in all CSFEs/ embedded clusters) Why is the IGIMF different to the IMF ?

# stars Many low-mass clusters

IGIMF

Rare massive clusters (contribute top-heavy IMF) log stellar mass

23 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 23

M SFR t ecl,max( ( ))✓ ✓ ✓ ξ (m, t)= ξ(m ≤ m (M )) ξ (M ) dM IGIMF ! max ecl ecl ecl ecl Mecl,min

Weidner et al. 2013; Kroupa et al. 2013 The IGIMF for galaxies with different SFRs

24 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 24 Return to the Scalo / Massey-Salpeter discrepancy :

−α ξ(m) ∝ m i

α1 =1.3 logdN/dlog(m) α2 =2.3

α3,Massey =2.3

α3,Scalo =2.7

M stars G stars ✓O stars 0 log(m)

25 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 25

Recall:

Salpeter/Massey : α3 =2.3 for individual clusters and OB associations but

Scalo : α3 =2.7 from Galactic-field star-counts

Independent evidence : based on spectro-photometric Tinsley 1980 Kennicutt 1983 < < and/or 2.5 ∼ α3 ∼ 2.7 Portinari et al. 2000 chemical-evolution modelling Romano et al. 2005} { of the MW disk.

Reid et al. 2002 : α3 =2.5 − 2.8 from Galactic-field star counts.

26 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 26 Composite stellar populations have a steeper IMF than the stellar IMF : Further observational evidence for steep galaxy-wide massive star IMF

MW disk : α =2.5 − 2.7 (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

27 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 27

Counting stars = > LF => PDMF => IMF Remember : dm corrections for Ψ(MV)=− ξ(m) dMV stellar evolution + binaries + main sequence stars

✓ 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 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 28 Counting stars = > LF => PDMF => IMF Remember : dm corrections for Ψ(MV)=− ξ(m) dMV stellar evolution + binaries + main sequence stars

✓ 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

29 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 29

The IGIMF theory :

Natural explanation of the difference between the Scalo field IMF (α ≈ 2 . 7 ) and the stellar IMF ( α ≈ 2 . 3 ).

30 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 30 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 m< 10 M stars forming.

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) :

31 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 31

Composite stellar populations can have a steeper IMF than the stellar IMF: Further observational verification ?

α = Γ +1

α =2.6 > IGIMF αIGIMF > α3; m ∼ 1.3 M!

theoretical minimal IGIMF 2.4 model Salpeter SMC MW

140 000 SDSS galaxies : Hoversten & Glazebrook (2007)

32 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 32 2011 IGIMF theory Weidner et al. 2013 ↵ top-light top-heavy

log10(SFR) log10(SSFR) log10(⌃SFR) top-heavy Very comparable / consistent results by 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

E galaxies formed with top-heavy IMFs

confirming Matteucci (1994) ! and see recent work by Vazdekis

33 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 33

Some implications

The mass-metallicity relation

34 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 34 The IGIMF theory naturally accounts for the observed mass-metallicity relation of galaxies !

Koeppen, Weidner & Kroupa (2006)

Tremonti et al. 2004

35 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 35

The IGIMF theory naturally accounts for the observed mass-metallicity relation of galaxies !

Koeppen, Weidner & Kroupa (2006)

Tremonti et al. 2004

36 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 36 The IGIMF theory naturally accounts for the observed mass-metallicity relation of galaxies !

Koeppen, Weidner & Kroupa (2006)

IGIMF Tremonti et al. 2004

37 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 37

The IGIMF theory naturally accounts for the observed mass-metallicity relation of galaxies !

Koeppen, Weidner & Kroupa (2006)

IGIMF Fewer Tremonti et al. 2004 massive stars per low-mass star Metal-ejection universal not IMF needed !

Ott, J. et al. (2005, MNRAS)

38 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 38 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]

39 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 39

Recchi et al. 2009 The IGIMF theory naturally IMF accounts for the observed Observations [/Fe] ⇥ IGIMF relation of galaxies ! Fewer massive stars per low-mass star Thomas et al. (2005) Samson & Northeast IMF (2008)

Observations IGIMF Metal-ejection not needed !

Ott, J. et al. (2005, MNRAS)

40 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 40 The IGIMF theory :

Natural explanation of the mass-metallicity relation of galaxies.

41 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 41

Some implications

The Halpha vs UV flux of galaxies

42 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 42 Kennicutt et al. (1994) SFR relation ( for a pure Salpeter power-law IMF betw. 0.1 and 100 Msun )

SFR L always for all galaxies / H↵

(Pflamm-Altenburg et al. 2007)

43 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 43

M SFR t ecl,max( ( ))✓ ✓ ✓ ξ (m, t)= ξ(m ≤ m (M )) ξ (M ) dM IGIMF ! max ecl ecl ecl ecl Mecl,min

Weidner et al. 2013; Kroupa et al. 2013 The IGIMF for galaxies with different SFRs

Expect : IGIMF slope with SFR

44 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 44 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 : SFRUV LUV (Pflamm-Altenburg, Weidner & Kroupa 2009, submitted)

H luminosity is sensitive to massive stars ( m> 10 M ) with life-times of a few Myr.

If the IMF=IGIMF and if it is invariant with the SFR (the classical, Kennicutt case) , then expect SFR H = const with SFR SFRUV If the IMF=IGIMF and if it varies with the SFR (the IGIMF-theory case), then expect SFR H for SFR SFRUV

45 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 45

A further observational test

1

) Expected 0 for classical, FUV,IMF -1 IMF invariant /SFR (Pflamm- scenario ,IMF

! predictions by Altenburg,

H -2 Weidner & IGIMF theory Kroupa 2009)

(SFR -3 10 log -4

-5 -4 -3 -2 -1 0 1 2 3

log10(SFRtot)

46 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 46 A further observational test

1

) Expected 0 for classical, FUV,IMF -1 IMF invariant /SFR (Pflamm- scenario ,IMF

! predictions by Altenburg,

H -2 Weidner & IGIMF theory Kroupa 2009)

(SFR -3 10 measured SFR log -4 ratios (Lee, Gil, Tremonti et al., 2009)

-5 -4 -3 -2 -1 0 1 2 3

log10(SFRtot)

47 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 47

Composite stellar populations have a steeper IMF than the stellar IMF: Observational verification !! α = Γ +1

SFR ↓⇒ αIGIMF ↑ low SFR galaxies

high SFR galaxies

Salpeter

140 000 SDSS galaxies : Hoversten & Glazebrook (2007) 48 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 48 The IGIMF theory appears to be affirmed by observation.

Todo : compute Halpha / UV flux ratio for galaxies ith high SFRs.

49 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 49

Some implications

The radial cutoff in Halpha/UV ratio in disk galaxies

50 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 50 The local IGIMF and the radial star-formation cutoff in disk galaxies n× =

51 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 51

Express the IGIMF in terms of local quantities : (Pflamm-Altenburg & Kroupa 2008)

n (local Schmidt law, (Boissier et al. ΣSFR(x, y)=A Σgas(x, y),n=1 2007; Zasov et based on UV GALEX data) al. 2005) A−1 = 3 Gyr

γ Σgas(x, y) (ansatz - less Mecl,max,loc(x, y)=Mecl,max , γ =3/2 ! Σgas,0 " massive clusters further out) dNecl ξLECMF(Mecl, x, y)= dMecl dx dy

Mecl,max,loc(x,y) ξ (m, x, y)= ξ (m) ξ (M , x, y) dM LIGIMF ! Mecl LECMF ecl ecl Mecl,min = the local IGIMF = LIGIMF

. . . and study the emission of Hα photons as a function of local gas density and galactocentric radius . . . 52 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 52 According to classical scenario (universal IMF=invariant IGIMF) : H α surface luminosity vs local 33.5 gas density at different radii in 7 disk galaxies . 33 (Kennicutt ‘89 [data], ‘94, ‘98 [relation])

) 32.5 -2 H emission scales with number pc 32

-1 of O stars, and IMF non-varying

LH SFR 31.5 !SFR / erg s "

H Measure surface luminosity

! H

( 31

10 density and surface gas mass

1.4 density. log 30.5 !gas

30 1.4 SF R,H H gas 29.5 The Kennicutt SFR law. -1 -0.5 0 0.5 1 1.5 2

-2 log (! / M pc ) 10 gas sol 53 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 53

According to classical scenario (universal IMF=invariant IGIMF) : H α surface luminosity vs local 33.5 gas density at different radii in 7 disk galaxies . 33 (Kennicutt ‘89 [data], ‘94, ‘98 [relation])

) 32.5 -2 H emission scales with number pc 32

-1 of O stars, and IMF non-varying

LH SFR 31.5 !SFR / erg s "

H But: Measure surface luminosity

! H

( 31

10 new density and surface gas mass

1.4 more density. log 30.5 ! gas sensitive

30 data 1.4 SF R,H H gas 29.5 The Kennicutt SFR law. -1 -0.5 0 0.5 1 1.5 2

-2 log (! / M pc ) 10 gas sol 54 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 54 Express the IGIMF in terms of local quantities : (Pflamm-Altenburg & Kroupa 2008) H α surface luminosity vs local 33.5 gas density at different radii in 7 disk galaxies . 33 (Kennicutt ‘89 [data], ‘94, ‘98 [relation])

) 32.5

-2 True underlying SF density law :

pc 1 32 -1 Σ = Σ SFR 3 Gyr gas ✓

31.5 !SFR converted to H α surface / erg s " luminosity using standard (but H !

( 31 wrong) linear (Kennicutt) 10 Hα -SFR relation. 1.4 log 30.5 ✗!gas H α − Σ relation based on 30 gas IGIMF theory standard (but wrong) Kennicutt SFR law Σ = A Σ 1 . 4 ; 29.5 SFR gas ✗ -1 -0.5 0 0.5 1 1.5 2 it is a good (but wrong) fit to the bright data. -2 log (! / M pc ) 10 gas sol 55 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 55

Express the IGIMF in terms of local quantities : (Pflamm-Altenburg & Kroupa 2008)

9 observed disk galaxies : 2 ) -1 1 Gyr -2 SFR density from UV flux pc 0 (Boissier et al. 2007)

sol (UV flux generated by intermediate- mass stars with ages 0-100 Myr, i.e / M -1 not sensitive to O stars only ! )

SFR SFR density from H α flux ! ( -2 (Martin & Kennicutt 2001) 10 LIGIMF-theoretical log Hα -3 flux based on true law 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 ΣSFR = A Σgas r / r threshold 56 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 56 The IGIMF theory :

Hα cutoff accounted for naturally. 1 True is Σ = Σ . SFR 3 Gyr gas (i.e no radial cutoff in SF).

Theoretical models : a threshold for star formation a la Hα cutoff does not exist !

57 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 57

Some implications

The stellar-masss buildup times of dwarf galaxies

58 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 58 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

59 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 59

Within the IGIMF theory (fewer massive stars at low SFRs) can the stellar masses of dwarf galaxies be formed within a Hubble time.

60 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 60 Some implications

The gas-consumption time-scales and implications for the matter cycle

61 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 61

The traditional view :

Dwarf galaxies as modest consumers

62 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 62 SFR vs gas mass : traditional (using linear Kennicutt relation to convert H α flux to SFR.)

1 CVnI group M81 group ) Sculptor group isolated dI -1 LG dwarfs 0 LG disks yr

sol -1

/ M -2 IMF -3

(SFR -4 Pflamm-Altenburg, 10 Weidner & -5 Kroupa (2007); log Pflamm-Altenburg & Kroupa (2008) -6 4 5 6 7 8 9 10 11 log (M / M ) 10 g63as sol Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 63

Pflamm-Altenburg, Weidner & Kroupa (2007); Pflamm-A. & Kroupa (2008) 4 gas-consumption

CVnI group M81 group time scale Sculptor group 3 isolated dI LG dwarfs LG disks vs 10 Hubble 2 gas mass times / Gyr) 1 IMF ! (

10 0 using Kennicutt

log relation -1 M τ = gas Dwarf galaxies SFR consume their gas -2 4 5 6 7 8 9 10 11 very carefully, very slowly ! log10(Mgas / Msol) 64 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 64 According to the IGIMF theory :

Dwarf galaxies as insattiable consumers

65 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 65

M SFR t ecl,max( ( ))✓ ✓ ✓ ξIGIMF(m, t)= ξ(m ≤ mmax(Mecl)) ξecl(Mecl) dMecl Back to !M ecl,min the Weidner et al. 2013; Kroupa et al. 2013 integrated- galaxy view. The IGIMF has fewer ionising photons ! Expect : IGIMF slope with SFR

66 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 66 The variable IGIMF notion revision of the L H α − SFR relation (the Kennicutt relation) !

Pflamm-Altenburg, Weidner & Kroupa (2007)

Kennicutt LH SFR ( for invariant IMF )

67 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 67

The variable IGIMF notion revision of the L H α − SFR relation (the Kennicutt relation) !

Pflamm-Altenburg, Weidner & Kroupa (2007)

IGIMF

Kennicutt Deficit of massive stars in the IGIMF increased SFR

68 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 68 SFR vs gas mass : new (using IGIMF theory) ) 1 CVnI group -1 M81 group Sculptor group isolated dI yr LG dwarfs 0 LG disks sol

-1 / M

-2

-3 IGIMF,std

-4 Pflamm-Altenburg, (SFR 1.02 Weidner & 10 -5 Mgas Kroupa (2007); Pflamm-Altenburg log -6 & Kroupa (2008) 4 5 6 7 8 9 10 11

log10(Mgas / Msol) 69 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 69

SFR vs gas mass : traditional (again) (using linear Kennicutt relation to convert H α flux to SFR.)

1 CVnI group M81 group ) Sculptor group isolated dI -1 LG dwarfs 0 LG disks yr

sol -1

/ M -2 IMF -3

(SFR -4 Pflamm-Altenburg, 10 Weidner & -5 Kroupa (2007); log Pflamm-Altenburg & Kroupa (2008) -6 4 5 6 7 8 9 10 11 log (M / M ) 10 g70as sol Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 70 SFR vs gas mass : new (again) (using IGIMF theory) ) 1 CVnI group -1 M81 group Sculptor group isolated dI yr LG dwarfs 0 LG disks sol

-1 / M

-2

-3 IGIMF,std ✓ -4 Pflamm-Altenburg, (SFR 1.02 Weidner & 10 -5 Mgas Kroupa (2007); Pflamm-Altenburg log -6 & Kroupa (2008) 4 5 6 7 8 9 10 11

log10(Mgas / Msol) 71 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 71

SFR vs gas mass : (traditional: invariant IMF) (using IGIMF theory) Pflamm-Altenburg, Weidner & Kroupa (2007); Pflamm-Altenburg & Kroupa (2009) 1 10 A B 100 )

-1 10-1 yr -2

sol 10

10-3

-4 SFR (M 10 10-5 IMF ✓IGIMF 10-6 104 105 106 107 108 109 1010 105 106 107 108 109 1010 1011 Mgas (Msol) Mgas (Msol) 72 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 72 Pflamm-Altenburg, Weidner & Kroupa (2007); Pflamm-A. & Kroupa (2008) 4 gas-consumption Mgas CVnI group τ = M81 group time scale Sculptor group SFR 3 isolated dI LG dwarfs LG disks vs 10 Hubble gas mass

/ Gyr) 2 times

1 IGIMF,std !

( 0 10

log -1

-2 4 5 6 7 8 9 10 11

log10(Mgas / Msol) 73 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 73

Pflamm-Altenburg, Weidner & Kroupa (2007); Pflamm-A. & Kroupa (2008) 4 gas-consumption

CVnI group M81 group time scale Sculptor group 3 isolated dI LG dwarfs LG disks vs 10 Hubble 2 gas mass times / Gyr) 1 IMF ! (

10 0 using Kennicutt

log relation -1 M τ = gas Dwarf galaxies SFR consume their gas -2 4 5 6 7 8 9 10 11 very carefully, very slowly ! log10(Mgas / Msol) 74 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 74 Pflamm-Altenburg, Weidner & Kroupa (2007); Pflamm-A. & Kroupa (2008) 4 gas-consumption Mgas CVnI group τ = M81 group time scale Sculptor group SFR 3 isolated dI LG dwarfs LG disks vs 10 Hubble gas mass

/ Gyr) 2 times

1 using IGIMF IGIMF,std

! theory

( 0 10

log -1 IGIMF theory -2 4 5 6 7 8 9 10 11 constant gas depletion time-scale ! log10(Mgas / Msol) 75 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 75

constant for galaxies with IGIMF theory gas depletion M 105 ∼< gas ∼< 1011 time-scale ! M! 70

60 2.9 Gyr IGIMF 50 traditional Pflamm- Altenburg, log-norm 40 Weidner & Kroupa (2007); 30 Pflamm-A. &

# Galaxies Kroupa 20 (2008)

10

0 6 7 8 9 10 11 12 13 14

log(!gas / Gyr) M for all late-type galaxies 10 6 ∼< gas ∼< 10 11 2.9 Gyr 76 M! ? Pavel Kroupa: Praha Lecture III

Mittwoch, 9. Dezember 15 76 Pflamm- 1 Altenburg, SFR = Mneutral gas Weidner & 3 Gyr Kroupa (2007); Pflamm-A. & Kroupa (2008)

i.e. every 10 Myr a galaxy transforms 0.3 % of its neutral gas mass into stellar mass.

77 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 77

But where is all the star-forming gas coming from at just the right rate ?

78 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 78 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) :

79 Pavel Kroupa: Praha Lecture III

Mittwoch, 9. Dezember 15 79

END of Lecture 3

80 Pavel Kroupa: Praha Lecture III Mittwoch, 9. Dezember 15 80