Very Massive Stars

Norbert Langer (Bonn University)

with

Ines Brott (Vienna)

Matteo Cantiello (UCSB)

Selma de Mink (STScI)

Karen Köhler (Bonn)

Debashis Sanyal (Bonn)

Alexandra Kozyreva (Bonn)

Colin Norman (JHU)

Alex Heger (Monash)

Alex de Koter (Amsterdam)

Onno Pols (Nijmegen)

Jorick Vink (Armagh)

Sung-Chul Yoon (Bonn)

St Paul 3-10-12 – p.1/33

The Hunter diagram: early BV stars

Brott, Evans, Hunter et al. 2011St Paul 3-10-12 – p.2/33

The rotation rates: early BV stars

Dufton, Langer, Dunstall et al. 2012St Paul 3-10-12 – p.3/33

The Hunter diagram: OV stars

6.6

6.8

7

7.2

7.4

7.6

7.8

8

8.2

8.4

8.6

8.8

0 50 100 150 200 250 300 350 400

12 +

log

[N/H

]

v sini [km/s]

1

10

100

1000

Rivero Gonzalez, Puls, Najarro & Brott 2012St Paul 3-10-12 – p.4/33

Close binaries: O stars

Sana, de Mink, de Koter, et al. 2012St Paul 3-10-12 – p.5/33

Why mass matters

Langer 2012St Paul 3-10-12 – p.6/33

The Eddington limit

1 = LLEdd

= 14πcG

κeLM

: no upper mass limit

St Paul 3-10-12 – p.7/33

The Eddington limit

1 = LLEdd

= 14πcG

κeLM

: no upper mass limit

1 = 14πcG

κ(Z,X,T,ρ)LM

St Paul 3-10-12 – p.7/33

The Eddington limit

1 = LLEdd

= 14πcG

κeLM

: no upper mass limit

1 = 14πcG

κ(Z,X,T,ρ)LM

1−(

v2rotv2Kepler

)

= 14πcG

κ(Z,X,T,ρ)LM

→ low L; 2D

St Paul 3-10-12 – p.7/33

The Eddington limit

1 = LLEdd

= 14πcG

κeLM

: no upper mass limit

1 = 14πcG

κ(Z,X,T,ρ)LM

1−(

v2rotv2Kepler

)

= 14πcG

κ(Z,X,T,ρ)LM

→ low L; 2D

1−(

v2rotv2Kepler

)

= 14πcG

κ(r)(L(r)−Lconv(r))M(r)

St Paul 3-10-12 – p.7/33

The Eddington limit

1 = LLEdd

= 14πcG

κeLM

: no upper mass limit

1 = 14πcG

κ(Z,X,T,ρ)LM

1−(

v2rotv2Kepler

)

= 14πcG

κ(Z,X,T,ρ)LM

→ low L; 2D

1−(

v2rotv2Kepler

)

= 14πcG

κ(r)(L(r)−Lconv(r))M(r)

inflation!

St Paul 3-10-12 – p.7/33

Inflation: He star models

Petrovic, Pols & Langer 2006 St Paul 3-10-12 – p.8/33

Inflation 6= HD-limit

5.6

5.8

6

6.2

6.4

6.6

6.8

7

7.2

0 10 20 30 40 50 60

log(

L/L ⊙

)

Teff [kK]

60 M⊙

70 M⊙

80 M⊙

100 M⊙

150 M⊙

200 M⊙

300 M⊙

400 M⊙

500 M⊙

HD limit

ZAMS

Köhler et al., in prep.St Paul 3-10-12 – p.9/33

Inflation of main sequence stars

inflation as f(Z):H-ZAMS: Z⊙ →M < 120M⊙ Ishii et al. 1999

ZSMC →M < 200M⊙Z = 0→M < 1000M⊙ Yoon et al. 2012

He-ZAMS: Z⊙ →M < 15M⊙ Petrovic et al. 2006

ZSMC →M < 25M⊙

St Paul 3-10-12 – p.10/33

Inflation of main sequence stars

inflation as f(Z):H-ZAMS: Z⊙ →M < 120M⊙ Ishii et al. 1999

ZSMC →M < 200M⊙Z = 0→M < 1000M⊙ Yoon et al. 2012

He-ZAMS: Z⊙ →M < 15M⊙ Petrovic et al. 2006

ZSMC →M < 25M⊙L

LEdd∼ κL

M:

H→ He⇒ κ ↓ 2, L(M) ↑ 10⇒ He-ZAMS crosses H-ZAMS!

St Paul 3-10-12 – p.10/33

ZAMS crossing

5.6

5.8

6

6.2

6.4

6.6

6.8

7

7.2

0 10 20 30 40 50 60

log(

L/L ⊙

)

Teff [kK]

60 M⊙

70 M⊙

80 M⊙

100 M⊙

150 M⊙

200 M⊙

300 M⊙

400 M⊙

500 M⊙

HD limit

ZAMS

St Paul 3-10-12 – p.11/33

Eddington limit

Langer 2012St Paul 3-10-12 – p.12/33

Eddington limit

Ulmer & Fitzpatrick 1999St Paul 3-10-12 – p.13/33

Eddington-limit

5.6

5.8

6

6.2

6.4

6.6

6.8

7

7.2

0 10 20 30 40 50 60

log(

L/L ⊙

)

Teff [kK]

60 M⊙

70 M⊙

80 M⊙

100 M⊙

150 M⊙

200 M⊙

300 M⊙

400 M⊙

500 M⊙

HD limit

ZAMS

St Paul 3-10-12 – p.14/33

Inflation: f(M )

Petrovic, Pols & Langer 2006St Paul 3-10-12 – p.15/33

Inflation: S Dor Variations?

Ingredients:

R(inflated layer) = f(M) Petrovic et al. 2006

M = f(R) e.g. Vink: bistability

St Paul 3-10-12 – p.16/33

Inflation: S Dor Variations?

Ingredients:

R(inflated layer) = f(M) Petrovic et al. 2006

M = f(R) e.g. Vink: bistability

1) star compact: M small→ 2) inflation→ 3) M large→ 1) star compact

St Paul 3-10-12 – p.16/33

The role of stellar evolution

Langer 1998

St Paul 3-10-12 – p.17/33

MS evolution & the Ω-limit

Langer 1998

St Paul 3-10-12 – p.18/33

MS evolution: M

Langer 1998

St Paul 3-10-12 – p.19/33

Mass loss rate at the Edd.-limit

nuclear timescale evolution: M ≃ Mτnuc

M = 100M⊙: τnuc = 3106 yr → M ≃

3 10−5 M⊙ yr−1

St Paul 3-10-12 – p.20/33

Mass loss rate at the Edd.-limit

nuclear timescale evolution: M ≃ Mτnuc

M = 100M⊙: τnuc = 3106 yr → M ≃

3 10−5 M⊙ yr−1

thermal timescale evolution: M ≃ Mτth

M = 100M⊙: τth = 104 yr→ M ≃ 10−2 M⊙ yr−1

St Paul 3-10-12 – p.20/33

Mass loss rate at the Edd.-limit

nuclear timescale evolution: M ≃ Mτnuc

M = 100M⊙: τnuc = 3106 yr → M ≃

3 10−5 M⊙ yr−1

thermal timescale evolution: M ≃ Mτth

M = 100M⊙: τth = 104 yr→ M ≃ 10−2 M⊙ yr−1

⇒ LBV eruptions need thermal timescale evolution

St Paul 3-10-12 – p.20/33

Post-LBV evolution

Langer 1987

St Paul 3-10-12 – p.21/33

Evolutionary scheme

Langer 2012

St Paul 3-10-12 – p.22/33

Evolutionary scheme

St Paul 3-10-12 – p.23/33

Galactic Wolf-Rayet stars

4.5

5.0

5.5

6.0

6.5

5.5 5.0 4.5 4.0log (T*/K)

log

(L/L

)

WNL (XH > 5%)WNE (XH < 5%)

T*/kK10204060100150200

WC 4

WC 5

WC 6

WO

known distance

unsure distance

WC 7

WC 8

WC 9

WN/WC

ZAMSHe-ZAMS

Sander, Hamann & Todt 2012 St Paul 3-10-12 – p.24/33

Galactic Wolf-Rayet stars

25 M

40 M

60 M

85 M

120 M

4.5

5.0

5.5

6.0

6.5

5.5 5.0 4.5 4.0log (T*/K)

log

(L/L

)

Evo

l. m

odel

s pre WR phase

WNL phase

WNE phase

WC phase

WC 4

WC 5

WC 6

WO

known distance

unsure distance

WC 7

WC 8

WC 9

WN/WC

T*/kK10204060100150200

ZAMSHe-ZAMS

Sander, Hamann & Todt 2012 St Paul 3-10-12 – p.25/33

Local low-Z VMS

Langer, Norman, de Koter et al. 2007 St Paul 3-10-12 – p.26/33

Local Pair-Instability SNe

Kozyreva et al., in prep.St Paul 3-10-12 – p.27/33

Local Pair-Instability SNe

Herzig, El Eid, Fricke & Langer 1990St Paul 3-10-12 – p.28/33

Local Pair-Instability SNe: Yields

0 20 40 60 80 100 120 140 1600

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Iso

top

e M

ass

frac

tio

n

250 Msun PISN

H

He

C

O

NeMg

Si

Fe+Ni

He

Mass, Solar massesKozyreva al., in prep.

St Paul 3-10-12 – p.29/33

Summary

Complex physics at the Ω-limit

Inflation: ZAMS crowing, S Dor variability?

Eruptions← τth-evolution⇒ erupting LBVs: after core-H, core-Heburning

PISNe in the local universe

St Paul 3-10-12 – p.30/33

VMS binary evolution

-12

-10

-8

-6

-4

-2

0

2

0 20 40 60 80 100 120

log

(mas

s de

nsity

[gm

/cc]

)

Radius [R⊙

]

100M⊙

+50M⊙

binary; Porb=30 days

Yc=0.8254

Primary star at the onset of RLOF

Density inversion

Mass=87M⊙

Sanyal et al., in prep.

St Paul 3-10-12 – p.31/33

VMS binary evolution

5.5

5.6

5.7

5.8

5.9

6

6.1

6.2

6.3

6.4

4.3 4.35 4.4 4.45 4.5 4.55 4.6 4.65 4.7

Lum

inos

ity (

log[

L/L ⊙

])

log Teff (K)

100M⊙

+50M⊙

binary; Porb=30 days; H-R diagrams

Yc=0.8254 for primary end of evolution

Yc=0.5846 for secondary end of evolution

PrimarySecondary

Sanyal et al., in prep.

St Paul 3-10-12 – p.32/33

VMS binary evolution

10-6

10-5

10-4

10-3

5x10-3

10-2

0 5 10 15 20 25 30

Max

imum

mas

s tr

ansf

er r

ate

[M⊙

/yr]

Porb (days)

100M⊙

+ 50M⊙

binary

Sanyal et al., in prep.

St Paul 3-10-12 – p.33/33