Looking into the stars by just counting them · Offner et al., 2014, PPVI The IMF appears largely...

Pavel Kroupa: University of Bonn / Charles University

ING-Mercator Seminar ING-Mercator Mayantigo building Santa Cruz de La Palma

10th September 2019

The systematically varying stellar IMF and

some implications thereof

1

Pavel Kroupa Helmholtz-Institute for Radiation und Nuclear Physics (HISKP)

University of Bonn

Astronomical Institute, Charles University in Prague

c/o Argelander-Institut für Astronomie University of Bonn

Pavel Kroupa: University of Bonn / Charles University 2

Looking into

the stars by

just counting them

follows Ψ(MV) = −

dm

dMV

ξ(m)

We have = # of stars with MV ∈ [MV, MV + dMV]

dN = ξ(m) dm = # of stars with m ∈ [m, m + dm]

dN

dMV

= −

dm

dMV

dN

dmsince

dN = Ψ(MV) dMV

the observablethe obstacle

the target


Strong sharp maximum

near MV ⇡ 11.5

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MI ⇡ 8.5<latexit sha1_base64="ha1CMxoJRh1pB0udKAz7AITFlVs=">AAAB/nicdVBNS8NAEN3Ur1q/ouLJy2IRPIWkVlNvRS96ECrYWmhC2Gy37dLNJuxuxBIK/hUvHhTx6u/w5r9x20ZQ0QcDj/dmmJkXJoxKZdsfRmFufmFxqbhcWlldW98wN7daMk4FJk0cs1i0QyQJo5w0FVWMtBNBUBQychMOzyb+zS0Rksb8Wo0S4keoz2mPYqS0FJg7l0HmiQhejKGHkkTEd7BmHQVm2bZOase260DbsqfQxHFct1qBTq6UQY5GYL573RinEeEKMyRlx7ET5WdIKIoZGZe8VJIE4SHqk46mHEVE+tn0/DHc10oX9mKhiys4Vb9PZCiSchSFujNCaiB/exPxL6+Tql7NzyhPUkU4ni3qpQyqGE6ygF0qCFZspAnCgupbIR4ggbDSiZV0CF+fwv9Jq2I5h1blqlqun+ZxFMEu2AMHwAEuqINz0ABNgEEGHsATeDbujUfjxXidtRaMfGYb/IDx9gnofJTP</latexit>

Kroupa, Tout & Gilmore 1990

Kroupa, Tout & Gilmore 1990; Kroupa, 2002, Science

The mass-luminosity relation of low-mass stars

Ψ(MV) = −

dm

dMV

ξ(m)


Kroupa, Tout & Gilmore 1990; Kroupa, 2002, Science


Ψ(MV) = −

dm

dMV

ξ(m)


Kroupa, Tout & Gilmore 1990;

Kroupa, 2002, Science


1. position 2. width 3. amplitudeall agree !

Ψ(MV) = −

dm

dMV

ξ(m)



1. position 2. width 3. amplitudeall agree !

Ψ(MV) = −

dm

dMV

ξ(m)

fully convective

radiative interrior,

convective shell


Kroupa, Tout & Gilmore 1990;

Kroupa, 2002, Science

7


The Galactic-field IMF

There are two luminosity functions for the solar neighbourhood

I. Count stars nearby to Sun

Obtain and from trigonometric parallaxMV d

−→ Well observed individual stars but small numbers at faint end ( )

II. Deep (100 - 300 pc) pencil-beam photographic/CCD surveys

Formidable data reduction Obtain and from photometric parallaxMV d

−→

(105 images −→ ≈ 100 stars)

Large # of stars but poor resolution (2”-3”) and Malmquist bias ( )Ψphot

Ψnear


The possibility of dark matter in the Galactic disk(Bahcall 1984)

−→ Many surveys of type II (pencil-beams) to constrain the LF :

ground

Reid & Gilmore 1982

Gilmore, Reid & Hewett 1985

Hawkins & Bessell 1988

Leggett & Hawkins 1988

Stobie, Ishida & Peacock 1989

Tinney, Reid & Mould 1993

Kirkpatrick et al. 1994

HSTGould, Bahcall & Flynn 1997

Zheng, Flynn, Gould et al. 2001


Ψ(MV) = −

dm

dMV

ξ(m)

see also Bochanski et al.

(2010, AJ)

Ψphot

- independent of direction

- maximum (peak) at MV ≈ 12{

peak = turnover in the MF ?


Two solar-neighbourhood samples:

I. nearby

II. deep

Ψ(MV) = −

dm

dMV

ξ(m)


?Stellar

samples should be

well-mixed:σ ≈ 25 km/s = 250 pc/10Myr

BUT: two solar-neighbourhood samples:

I. nearby

II. deep

Ψ(MV) = −

dm

dMV

ξ(m)


Problem :

The nearby and deep LFs are not equal.

Which LF do we use to calculate the MF ?

ξ(m) = −

!

dm

dMV

"

−1

Ψ(MV )


Two solar-neighbourhood samples:

I. nearby

II. deep

Ψ(MV) = −

dm

dMV

ξ(m)


Kroupa et al. 2013

unresolved multiples

Kroupa, Tout & Gilmore

1991


The IMF in star clusters

Ψ(MV) = −

dm

dMV

ξ(m)

Kroupa 2002 Science


Ψ(MV) = −

dm

dMV

ξ(m)


Kroupa 2002 Science

Ψ(MV) = −

dm

dMV

ξ(m)


Kroupa 2002 Science

t = 0 t = 0.3 Tdiss t = 0.6 Tdiss t = 0.9 Tdiss

N = 1.28 × 105

4 × (N = 8000)

(Baumgardt & Makino 2003)f = 0

low-masshigh-mass

P. Kroupa: University of Bonn / Charles University

MF(t) due to cluster evolution

standard

stella

r IMF

dynamical age

20

t = 0 t = 0.3 Tdiss t = 0.6 Tdiss t = 0.9 Tdiss

N = 1.28 × 105

4 × (N = 8000)

(Baumgardt & Makino 2003)f = 0

low-masshigh-mass


MF(t) due to cluster evolution

standard

stella

r IMF

dynamical age

21


N-body Models of Binary-Rich Clusters

(Kroupa 1995)

20 × (N = 400 stars)f = 1

ξobs(m) ̸= ξtrue(m)

(- 2.5 log L)

#The stellar

luminosity function

22

Massive stars in very young clusters

Pavel Kroupa: AIfA, University of Bonn 23

OB stars in clusters / HII regionsTwo competing processes:

Mass segregation

tmsgr ≈ 2

!

mav

mmassive

"

trelax

for pre-exposed ONCe.g. trelax ≈ 0.6 Myr

tmsgr ≈ 0.12 Myr ≪ age of ONCtrelax =

21

ln(0.4N)

!

Mecl

100 M⊙

"1

2!

1 M⊙

mav

" !

R0.5

1 pc

"3

2

Core decay e.g.tdecay ≈ Nm × tcore,cross

Rcore ≈ 0.02 pc, Mcore ≈ 150 M⊙

tcore

cross ≈ 1.2 × 104 yr

tdecay ≈ 104− 105 yr ≪ age of ONC

tcore

cross ≈ 5

!

M core

100 M⊙

"− 1

2!

Rcore0.5

1 pc

"3

2

(Pflamm-Altenburg & Kroupa 2006)Pavel Kroupa: University of Bonn / Charles University 24


3000 stars, r0.5=0.5pc, mass segr., f=1, uniform q-distr., Sana P-distr.

Oh & Kroupa 2015, 2016


Sverre Aarseth Nbody6 code

25


30000 stars, r0.5=0.5pc, mass segr., f=1, uniform q-distr., Sana P-distr.


Oh & Kroupa 2015, 2016 Sverre Aarseth Nbody6 code

26


Clusters depopulate themselves off low-mass stars and high mass stars.

loss

stellar mass

0.1Msun 150Msun

time-dependent

27

Thus, stellar-dynamical processes are

extremely important when determining the IMF shape!!



Bastian, Covey, Meyer,

2010, ARAA

Offner et al., 2014, PPVI

The IMF appears largely

invariant (in MW CSFEs /

embedded clusters)

Kroupa et al., 2013

Kroupa 2001, 2002

Bastian et al. 2010


The invariant canonical IMF

the canonical IMF :

discontinuity: Thies & Kroupa (2007, 2008), Parker & Goodwin (2010)

log(m)

ξ(m) ∝ m−αi

O starsG starsM stars

α2 = 2.3

α1 = 1.3

α3,Massey = 2.3

0

logdN/dlog(m)

α0 ≈ 0.3

BDs

�0 � 0.3

solivagent Jupiters

1.9 times more

frequent than stars

31 Pavel Kroupa: University of Bonn / Charles University

discontinuity: Thies & Kroupa (2007, 2008), Parker & Goodwin (2010)

log(m)

ξ(m) ∝ m−αi

O starsG starsM stars

α2 = 2.3

α1 = 1.3

α3,Massey = 2.3

0

logdN/dlog(m)

α0 ≈ 0.3

BDs

�0 � 0.3

solivagent Jupiters

1.9 times more

frequent than stars

32 Pavel Kroupa: University of Bonn / Charles University

the canonical IMF :

Rederived later by Chabrier ---

essentially identical result to the

canonical IMF fig.4-24 in Kroupa et al. 2013


Hints towards a variable IMF


Correct star-counts in R136 for ejected starsStar-counts:

Some subtle hints for a systematically varying IMF are available at high masses

R136

35 P. Kroupa: University of Bonn / Charles University

2 Myr old


Correct star-counts in R136 for ejected stars

Excess of massive stars in whole 30Dor region(Schneider et al. 2018)

IMF in R136 top-heavy (Banerjee & Kroupa 2012)

Top-heavy IMF in Magellanic Bridge cluster NGC796(Kalari et al. 2018)

Star-counts:

Some subtle hints for a systematically varying IMF are available at high masses

GCs in M31: more top-heavy IMF at lower metallicity(Zonoozi et sl. 2016; Haghi et al. 2017)

What we know from observation :


Globular clusters : deficit of low-mass stars increases with decreasing concentrationdisagrees with dynamical evolution (Marks et al. 2012)

GCs (extreme star burst "clusters")


gas expulsion +

mass segregation !


Cluster reaction to thermal gas removal :

40Baumgardt & Kroupa 2007

(movie by Baumgardt)


Nbody models of binary rich initially mass segregated clusters with redisual gas expulsion after birth

(Marks, Kroupa & Baumgardt 2008)

gas expulsion

stellar loss independent of mass

loose mostly low-mass stars

41 P. Kroupa: University of Bonn / Charles University

What we know from observation :

density


UCDs : higher dynamical M/L ratios (Dabringhausen et al. 2009)

mutual consistency !!

cannot be exotic dark matter

no explanation other than many remnants

Globular clusters : deficit of low-mass stars increases with decreasing concentration

UCDs : larger fraction of X-ray sources than expected (Dabringhausen et al. 2012)

disagrees with dynamical evolution (Marks et al. 2012)

What this implies :

starsBDs

# stars / mass bin

stellar mass

(need gas expulsion from mass-segregated clusters)


IMF = IMF(Z, SFRD) Z=metallicity, SFRD=star-formation rate density

Thus


Top-heavy IMF in extreme-density environments :

Marks et al. 2012 Kroupa et al. 2013

44

Z


Top-heavy IMF and

"quasars" a la

Tereza Jerabkova

UCDs ( = Hilker objects) (extremely extreme star burst "clusters")


Properties of ultra compact dwarf galaxies (UCDs)

Image by M. Hilker

UCD

dE

UCDs occur mostly in

galaxy clusters


From close distance, a UCD probably looks similar to this:

Image from ESO

� Cen 48

Would UCDs with a top-heavy IMF survive their early evolution?

Perform N-Body simulations of UCDs with mass-loss through gas expulsion and stellar evolution

UCDs can also form with top-heavy IMFs, but this implies extreme initial conditions for them.

(Dabringhausen, Fellhauer & Kroupa 2010)


(Dabringhausen, Fellhauer & Kroupa 2010)

Mass [10 Solar masses ]

106

1000100

2.31.91.5

2.3

small present-dayUCD

massive present-day UCD

}�3

Initial parameters thereby implied for UCDs


scouting work by Tereza Jerabkova


Can this IMF variation be confirmed?

---> probe conditions at high redshift

51

ESO student of the year with ESO staff of the year

(Chris Harrison and Michael Hilker) ESO Annual Report 2018


100 101 102 103 104

time [Myr]

106

107

108

109

1010

1011

1012

1013

Lbol[L§]

MUCD = 108 M§

Lbol ÃMUCD (NOT for MKDP)

10 7M§

10 8M§

10 9M§

[Fe/H]=≠2

[Fe/H]= 0

MKDP IMFCAN IMF

≠27.5

≠25.0

≠22.5

≠20.0

≠17.5

≠15.0

≠12.5

≠10.0

Mbol[m

ag]

UC

DD

ATA

QUASARS

SUPE

RN

OVA

EJerabkova et al. 2017===> Quasar-like objects

The redshift dependent photometric properties are calculated as predictions for James Webb Space Telescope (JWST) observations.

52


10 20 30 40 50time [Myr]

10≠4

10≠3

10≠2

10≠1

100

SNeI

Irat

e[y

r≠1 ]

MUCD = 109 M§

ÃMUCD (NOT for MKDP)

[Fe/H]=≠2[Fe/H]= 0

107 M§

108 M§

shorter SF historyMKDP IMFCAN IMF

Jerabkova et al. 2017

53


Conclusions

Significant evidence that the IMF varies with Z and rho.

The galaxy-wide IMF (the gwIMF) changes with SFR, as expected.

Testbed: extremely star-bursting clusters (UCDs) at high-z.

Are some/most quasars at very high z merely young UCDs ?

54

Jerabkova et al. 2017

The IMF is not observable (it is a mathematical "hilfsconstruct")

This hilfsconstruct is not a probability distribution function.

Looking into the stars by just counting them · Offner et al., 2014, PPVI The IMF appears largely...

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