Is the IMF a probability density distribution function or is star formation a self-regulated process?

Transcription

1 Is the IMF a probability density distribution function or is star formation a self-regulated process? Observatoire astronomique de Strasbourg 25th of September 2015 Pavel Kroupa Helmholtz-Institut fuer Strahlen und Kernphysik (HISKP) Helmholtz Institute for Radiation and Nuclear Physics c/o Argelander-Institut für Astronomie University of Bonn 1 1 the IMF dn = (m) dm, the number of stars in m, m + dm... as derived from detailed star-count analyses (Kroupa, Tout & Gilmore 1991; 1992, 1993; Kroupa et al 2013) (m) / m i, 1 =1.3 2 =1.3 lm =0.75, A =0.244, k BD =4.46 ( not Chabrier! ) 2 2

2 The IMF as a scale-invariant probability density distribution function 3 The IMF as a scale-invariant probability density distribution function ==> stochastically sampled stellar populations when discretised : Kroupa et al. (2013) stochastic sampling 4 4

3 The IMF as a scale-invariant probability density distribution function ==> stochastically sampled stellar populations when discretised : Kroupa et al. (2013) ==> stochastic variations in the shape of the IMF from case to case. stochastic sampling (for 150 Msun) Elmegreen - many papers Bastian et al. 20 or fractions of stars in low-mass galaxies and low-mass star clusters when analytical description ==> this is unphysical but often employed 5 5 Tests : is the IMF a scale-invariant pdf? Is the standard assumption (invariant probabilistic IMF) consistent with observations? 1. upper mass of stars is limited (to about 150 Msun) ==> i.e physical constraints on the IMF (Weidner & Kroupa 2004; Figer 2005; Oey & Clarke 2005; Koen 2006; Maiz Appelaniz et al. 207) 2. observed variations of IMF shapes much smaller than in theory (m) / m,m>2.5 M 6 6

4 Tests : is the IMF a scale-invariant pdf? Is the standard assumption (invariant probabilistic IMF) consistent with observations? 1. upper mass of stars is limited (to about 150 Msun) ==> i.e physical constraints on the IMF (Weidner & Kroupa 2004; Figer 2005; Oey & Clarke 2005; Koen 2006; Maiz Appelaniz et al. 207) 2. observed variations of IMF shapes much smaller than in theory 1. No assymmetries and sharp Salpeter/Massey peak. (m) / m,m>2.5 M 2. Model worse than data!?... but model has no measurement uncertainties observed systematic change of galaxy-wide IMFs with SFR 8 8

5 (m) / m top-heavy log (SF R) log (SSF R) log ( SF R ) Very comparable 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, M33 - radial distribution of young star clusters stochastic?

6 11 11 Megeath et al Lack of O stars NGC 2071/2068 NGC 2024/2023 Many small / low-mass groups or clusters do not yield the same IMF as one massive cluster ONC 3-4 sigma L1641 deficit south of massive stars (Hsu, Hartmann et al. 2012, 2013) stochastic IMF in each group is ruled out

7 Real young populations are not stochastic ensembles from invariant distr. functions the IMF / star cluster MF an invariant probability density distribution function The IMF as an optimally sampled probability density distribution function 14

8 What is an optimally sampled distribution function? Given the mass reservoir in stellar mass Mecl, starting with the most massive star, select the next most massive such that Mecl is distributed over the distribution function without Poisson scatter. Kroupa et al Schulz, Pflamm-Altenburg & Kroupa Kroupa et al stochastic optimal A correlated starformation event (CSFE) of 150Msun 16 16

9 the IMF as an optimally-sampled distribution function (The Orion case suggests that the most massive star may depend on cluster mass.) Consider : from above in each correlated star-formation event (CSFE embedded cluster) there is one most massive star : 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 m max =300M m max =150M 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 18 18

10 m max =300M Weidner & Kroupa 2005, 2006; Weidner et al. 20, 2013; Kroupa et al. 2013; Kirk & Myers, 20, 2012; Hsu, Hartmann et al. 2012, 2013 m max =150M 1= M ecl = mmax m max mmax m l ξ(m) dm m ξ(m) dm Dispersion of data is highly inconsistent with random / stochastic sampling from IMF m max =fn(m ecl ) an mmax -- Mecl relation A RESULT : the scatter in the data is mostly due to being from measurement uncertainties, i.e. intrinsic scatter may be very small. The IMF can only be a probability distribution function, if sampling from it is close to optimal : 20 20

11 the IMF as an optimally sampled density distribution and by implication, star-formation is largely self-regulated Evidence for a top-heavy IMF 22

12 R Nbody model of R136 Ejection fraction = fn(stellar mass) Corrected IMF Banerjee & Kroupa 2012 input / canonical / Salpeter IMF IMF becomes top heavy with increasing density 24 24

13 IMF becomes top heavy with increasing density : Dib, Kim & Shadmehri (2007) Models of coalescing and collapsing cloud cores in a dense proto cluster Globular clusters : deficit of low-mass stars increases with decreasing concentration disagrees with dynamical evolution correlate energy needed to expell residual gas with number of OB stars required. Marks et al UCDs : higher dynamical M/L ratios UCDs : larger fraction of X-ray sources than expected What this implies : cannot be exotic dark matter => top-heavy IMF Dabringhausen et al no explanation other than many remnants => top-heavy IMF Dabringhausen et al # stars/m BDs stars density m 26

14 Globular clusters : deficit of low-mass stars increases with decreasing concentration disagrees with dynamical evolution correlate energy needed to expell residual gas with number of OB stars required. Marks et al # stars/m UCDs : higher dynamical M/L ratios UCDs : larger fraction of X-ray sources than expected What this implies : cannot be exotic dark matter => top-heavy IMF Dabringhausen et al no explanation other than many remnants => top-heavy IMF Dabringhausen et al Joerg Dabringhausen BDs stars density m 27 Top-heavy IMF in extreme-density environments : Galactic GCs UCD sim (SFE 1.0,HE 1.00) UCD sim (SFE 0.4,HE 1.00) UCD sim (SFE 0.4,HE 0.03)! 3 =-0.43*log (" cl / 6 M sun pc -3 )+1.86 NGC 3603 Arches Wd1 R136 Marks et al ξ(m) m α(m) slope! 3 2 canonical IMF slope Cloud density [ 6 M sun pc -3 ] 28

15 Top-heavy IMF in extreme-density environments : Galactic GCs UCD sim (SFE 1.0,HE 1.00) UCD sim (SFE 0.4,HE 1.00) UCD sim (SFE 0.4,HE 0.03)! 3 =-0.43*log (" cl / 6 M sun pc -3 )+1.86 NGC 3603 Arches Wd1 R136 Marks et al ξ(m) m α(m) slope! canonical IMF slope 3 =fn(m ecl ) top-heavy SFRD > 0.1 M pc 3 yr 0 00 Cloud density [ 6 M sun pc -3 ] 29 Top-heavy IMF in extreme-density environments : Marks et al ξ(m) m α(m) Galactic GCs! 3 =0.66*[Fe/H]+2.63 NGC 3603 Arches Wd1 R canonical IMF slope top-heavy slope! =fn(fe/h) global cluster metallicity [Fe/H] 30

16 Top-heavy IMF in extreme-density environments : Marks et al Kroupa et al (arxiv: ) Recchi & Kroupa 2014 (arxiv: ) 31 Kroupa et al (arxiv: ) Using for m<1 M 1,2 = 1/2c +0.5 apple Fe H estimated from resolved MW populations (Kroupa 2001) where the canonical solar-abundance values are 1c = <m/m < 0.5 2c = <m/m <

17 Thus there is good and independent quantifiable evidence for the IMF becoming top-heavy with increasing density and decreasing metallicity. Note : extraction of this evidence requires understanding the data and of the dynamical evolution of the CSFEs. IMF = IMF(Z, SFRD) Z=metallicity, SFRD=star-formation rate density From correlated star formation events (CSFEs or embedded clusters) to galaxies 34

18 Correlated star formation events (CSFEs) The stellar population of an individual CSFE is of stellar mass Mecl Assuming star formation takes place in CSFEs, the stellar population from an ensemble of CSFEs can be computed, if the distribution of CSFEs is known. CSFE-mass distribution : ECMF (M ecl )=km ecl ; 2 (Lada & Lada 2003) Correlated star formation events building up a galaxy 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 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). t Myr 36 36

19 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 =Myr M ecl,min =5M 7 M t =Myr Weidner et al t =0Myr t =1Myr { M tot = SFR t Z Mecl,max M tot = ecl (M ecl ) M ecl dm ecl M ecl,min Z Mecl,max 1= ecl (M ecl ) dm ecl M ecl,max t =Myr M ecl,min =5M M ecl,max 7 M =2.4 =

20 Composite Stellar Populations The Integrated Galactic IMF now 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) Vanbeveren (1982) adding-up all IMFs in all SCFEs! The LEGO principle 39 IGIMF = of IMFs (in all CSFEs/ embedded clusters) Natural explanation of the mass-metallicity relation of galaxies and many other problems in understanding galaxies. 40

21 Why is the IGIMF different to the IMF? # stars Many low-mass clusters log stellar mass Pavel Kroupa: AIfA, University of Bonn 41 Why is the IGIMF different to the IMF? # stars Many low-mass clusters IGIMF log stellar mass Rare massive clusters (contribute top-heavy IMF) Pavel Kroupa: AIfA, University of Bonn 42

22 Weidner et al. 2013; Kroupa et al The IGIMF for galaxies with different SFRs The IGIMF for galaxies with different SFRs & [Fe/H] Pflamm-Altenburg & Kroupa, in prep e x e x e x e x e x e x e x e x e x e x -5 1e x e x

23 The IGIMF for galaxies with different SFRs & [Fe/H] Pflamm-Altenburg & Kroupa, in prep e x e x e x e x e x e x e x e x e x e x -5 1e x e x The IGIMF for galaxies with different SFRs & [Fe/H] Pflamm-Altenburg & Kroupa, in prep e x e x e x e x e x e x e x e x e x e x -5 1e x e x

24 2011 IGIMF theory Weidner et al top-light top-heavy Very comparable / consistent results by log (SFR) log (SSFR) log ( 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)! but see recent work by Vazdekis Conclusions The stellar IMF is found to be surprisingly invariant up to a critical star-formation rate density (SFRD) on a <pc scale Above this critical SFRD [GCs + UCDs] ==> evidence for top-heavy IMF in starbursts SFRD > 0.1 M pc 3 yr IMF : not a probabilistic / stochastic distribution function IMF : appears to be closer to an optimally sampled distribution function (i.e. star-formation is feedback regulated) Superposition principle : Sum over all CSFEs (=embedded clusters) : very powerful approach to quantify properties of freshly hatched stellar populations in galaxies : IGIMF, binary properties, thick disks Pioneering application of this concept in self-consistent full-scale hydrodynamic simulations of galaxies by Ploeckinger et al. (2014) 48 48

25 Both, Sverre Aarseth & Chris Tout from Cambridge, have influenced this work profoundly