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
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