Looking into the stars by just counting them

(1)

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

(2)

follows Ψ(M ^V ) = − dm

dM ^V ξ (m)

We have = # of stars with

M V ∈ [M ^V , M V + dM ^V ]

dN = ξ(m) dm = # of stars with

m ∈ [m, m + dm]

dN

dM _V = − dm dM _V

dN since dm

dN = Ψ(M ^V ) dM ^V

the observable

the obstacle the target

Strong sharp maximum

near

M V ⇡ 11.5

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M I ⇡ 8.5

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Kroupa, Tout & Gilmore 1990

Kroupa, Tout & Gilmore 1990;

Kroupa, 2002, Science

The mass-

luminosity relation of low-mass stars

Ψ(M ^V ) = − dm dM V

ξ (m)

(3)

Kroupa, Tout & Gilmore 1990;

Kroupa, 2002, Science

The mass-

luminosity relation of low-mass stars

Ψ(M ^V ) = − dm dM V

ξ(m)

Kroupa, Tout & Gilmore 1990;

Kroupa, 2002, Science

The mass-

luminosity relation of low-mass stars

1. position 2. width 3. amplitude

all agree !

Ψ(M ^V ) = − dm dM V

ξ (m)

(4)

The mass-

luminosity relation of low-mass stars

1. position 2. width 3. amplitude

all agree !

Ψ(M ^V ) = − dm dM V

ξ(m)

fully convective radiative

interrior, convective

shell

Kroupa, Tout & Gilmore 1990;

Kroupa, 2002, Science

7

The Galactic-field IMF

(5)

There are two luminosity functions

for the solar neighbourhood

I . Count stars nearby to Sun

Obtain and from trigonometric parallax M ^V 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 parallax M ^V d

−→

(10 ⁵ images −→ ≈ 100 stars)

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

Ψ ^near

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

HST Gould, Bahcall & Flynn 1997

Zheng, Flynn, Gould et al. 2001

(6)

Ψ(M

^V

) = − dm dM

V

ξ(m)

(2010, AJ)

Ψ ^phot ^- independent of direction

- maximum (peak) at M ^V ≈ 12

{

peak = turnover in

the MF ?

Two solar-neighbourhood samples:

I. ^nearby

II. ^deep

Ψ(M

V

) = − dm dM

V

ξ(m)

(7)

?

Stellar samples should be well-mixed:

σ ≈ 25 km/s = 250 pc/10Myr

BUT: two solar-neighbourhood samples:

I. ^nearby

II. ^deep

Ψ(M

^V

) = − dm dM

V

ξ(m)

Problem :

The nearby and deep LFs are not equal.

Which LF do we use to calculate the MF ?

ξ (m) = −

! dm dM V

" −1

Ψ(M V )

(8)

Two solar-neighbourhood samples:

I. ^nearby

II. ^deep

Ψ(M

^V

) = − dm dM

V

ξ(m)

Kroupa et al. 2013

unresolved multiples

Kroupa, Tout &

Gilmore 1991

The IMF in star clusters

(9)

Ψ(M

V

) = − dm dM

V

ξ(m)

Kroupa 2002 Science

Ψ(M

^V

) = − dm dM

V

ξ(m)

Kroupa 2002

Science

(10)

Ψ(M

V

) = − dm dM

V

ξ(m)

Kroupa 2002 Science

t = 0

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

N = 1.28 × 10 ⁵ 4 × (N = 8000) (Baumgardt & Makino 2003)

f = 0

low-mass high-mass

P. Kroupa: University of Bonn / Charles University

MF(t) due to cluster evolution

sta nda rd s tel lar IM F

dynamical age

20

(11)

t = 0

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

N = 1.28 × 10 ⁵ 4 × (N = 8000) (Baumgardt & Makino 2003)

f = 0

low-mass high-mass

P. Kroupa: University of Bonn / Charles University

MF(t) due to cluster evolution

sta nda rd s tel lar IM F

dynamical age

21

P. Kroupa: University of Bonn / Charles University

N-body Models of Binary-Rich Clusters

(Kroupa 1995)

20 × (N = 400 stars) f = 1

ξ obs (m) ̸= ξ ^true (m)

(- 2.5 log L)

# The stellar

luminosity function

22

(12)

Massive stars in very young clusters

Pavel Kroupa: AIfA, University of Bonn 23

OB stars in clusters / HII regions

Two competing processes:

Mass segregation

t _msgr ≈ 2

! m

_av

m

_massive

"

t _relax for pre-exposed ONC

e.g. ^t ^relax ≈ 0.6 Myr

t msgr ≈ 0.12 Myr ≪ age of ONC

t

_relax

= 21 ln(0.4N )

! M

_ecl

100 M

⊙

"

¹2

! 1 M

⊙

m

_av

" ! R

₀

.5

1 pc

"

³2

Core decay e.g.

t _decay ≈ N ^m × t ^core,cross

R core ≈ 0.02 pc, M ^core ≈ 150 M ^⊙

t ^core _cross ≈ 1.2 × 10 ⁴ yr

t _decay ≈ 10 ⁴ − 10 ⁵ yr ≪ age of ONC

t

^core_cross

≈ 5

! M

^core

100 M

_⊙

"

−¹₂

! R

^core₀

.5

1 pc

"

³₂

(Pflamm-Altenburg & Kroupa 2006)

(13)

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

Oh & Kroupa 2015, 2016

P. Kroupa: University of Bonn / Charles University

Sverre Aarseth Nbody6 code

25 30000 stars, r 0.5 =0.5pc, mass segr., f=1, uniform q-distr., Sana P-distr.

P. Kroupa: University of Bonn / Charles University

Oh & Kroupa

2015, 2016 Sverre Aarseth Nbody6 code

26

(14)

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!!

28

(15)

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

(16)

the canonical IMF :

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

& Goodwin (2010)

log(m)

ξ(m) ∝ m ⁻ ^α

ⁱ

O stars G stars

M stars

α 2 = 2.3 α ₁ = 1.3

α _3,Massey = 2.3

0 logdN/dlog(m)

α ₀ ≈ 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 ⁻ ^α

ⁱ

O stars G stars

M stars

α 2 = 2.3 α ₁ = 1.3

α _3,Massey = 2.3

0 logdN/dlog(m)

α ₀ ≈ 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

(17)

Hints towards a variable IMF

Correct star-counts in R136 for ejected stars

Star-counts:

Some subtle hints for a systematically varying IMF

are available at high masses

(18)

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)

(19)

What we know from observation :

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

GCs

(extreme star burst "clusters")

38

(20)

gas expulsion +

mass segregation

!

Cluster reaction to thermal gas removal :

Baumgardt & Kroupa 2007

40

(movie by Baumgardt)

P. Kroupa: University of Bonn / Charles University

(21)

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

42 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 :

stars BDs

# stars /

mass bin

stellar mass

(need gas expulsion from mass-segregated clusters)

(22)

IMF = IMF(Z, SFRD)

Z=metallicity, SFRD=star-formation rate density

Thus

P. Kroupa: University of Bonn / Charles University

Top-heavy IMF in extreme-density environments :

Marks et al. 2012 Kroupa et al. 2013

44

Z

(23)

Top-heavy IMF

"quasars" and a la

Tereza Jerabkova

UCDs ( = Hilker objects)

(extremely extreme star burst "clusters")

46

(24)

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

(25)

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)

Mass [10 Solar masses ] 10

6

1000 100

2.3 1.9 1.5

2.3 small

present-dayUCD

massive

present-day UCD } ³

Initial parameters thereby implied for UCDs

(26)

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

10

⁰

10

¹

10

²

10

³

10

⁴

time [Myr]

10

⁶

10

⁷

10

⁸

10

⁹

10

¹⁰

10

¹¹

10

¹²

10

¹³

L

bol

[L

§

]

M

_{U CD}

= 10

⁸

M

§ LbolÃ MU CD (NOT for MKDP)

10₇ M§

10₈ M§

109M

§

[Fe/H]=≠2 [Fe/H]= 0

MKDP IMF CAN IMF

≠27.5

≠25.0

≠22.5

≠20.0

≠17.5

≠15.0

≠12.5

≠10.0 M

bol

[ma g]

UCDDATA

QUASARS

SUPER NO VAE

Jerabkova et al. 2017

===> Quasar-like objects

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

52

(27)

Looking into the stars by just counting them

ING-Mercator Seminar

ING-Mercator Mayantigo building Santa Cruz de La Palma 10th September 2019

The systematically varying stellar IMF and

some implications thereof

Pavel Kroupa

University of Bonn

Charles University in Prague

Looking into the stars

by

just counting them

follows Ψ(M V ) = − dm

dM V ξ (m)

We have = # of stars with

M V ∈ [M V , M V + dM V ]

dN = ξ(m) dm = # of stars with

m ∈ [m, m + dm]

dN

dM V = − dm dM V

dN since dm

dN = Ψ(M V ) dM V

the observable

the obstacle the target

Strong sharp maximum

near

M V ⇡ 11.5

M I ⇡ 8.5

Kroupa, Tout & Gilmore 1990

Kroupa, Tout & Gilmore 1990;

Kroupa, 2002, Science

The mass-

luminosity relation of low-mass stars

Ψ(M V ) = − dm dM V

ξ (m)

Kroupa, Tout & Gilmore 1990;

Kroupa, 2002, Science

The mass-

luminosity relation of low-mass stars

Ψ(M V ) = − dm dM V

ξ(m)

Kroupa, Tout & Gilmore 1990;

Kroupa, 2002, Science

The mass-

luminosity relation of low-mass stars

1. position 2. width 3. amplitude

all agree !

Ψ(M V ) = − dm dM V

ξ (m)

The mass-

luminosity relation of low-mass stars

1. position 2. width 3. amplitude

all agree !

Ψ(M V ) = − dm dM V

ξ(m)

fully convective radiative

interrior, convective

shell

Kroupa, Tout & Gilmore 1990;

Kroupa, 2002, Science

The Galactic-field IMF

There are two luminosity functions

for the solar neighbourhood

I . Count stars nearby to Sun

Obtain and from trigonometric parallax M V 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 parallax M V d

−→

(10 5 images −→ ≈ 100 stars)

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

Ψ near

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

follows Ψ(M ^V ) = − dm

dM ^V ξ (m)

M V ∈ [M ^V , M V + dM ^V ]

dM _V = − dm dM _V

dN = Ψ(M ^V ) dM ^V

Ψ(M ^V ) = − dm dM V

Ψ(M ^V ) = − dm dM V

Ψ(M ^V ) = − dm dM V

Ψ(M ^V ) = − dm dM V

Obtain and from trigonometric parallax M ^V d

Obtain and from photometric parallax M ^V d

(10 ⁵ images −→ ≈ 100 stars)

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

Ψ ^near

Ψ ^phot ^- independent of direction

- maximum (peak) at M ^V ≈ 12

I. ^nearby

II. ^deep

I. ^nearby

II. ^deep

I. ^nearby

II. ^deep

N = 1.28 × 10 ⁵ 4 × (N = 8000) (Baumgardt & Makino 2003)