Subdwarf B stars
from He white dwarf mergers
Haili Hu
Subdwarf B stars
from various formation channels
Haili Hu
subdwarf B stars

Extreme Horizontal Branch
(Heber 86, Dorman et al 93)

 tip
L/L

He-burning core (~0.5 M)
Very thin, inert H-envelope
(<0.02 M)
40-70% found in binaries
L/L

White
sdB
dwarf <-------
(e.g. Allard et al 1994, Maxted et al
2001, Morales-Rueda et al 2006)
Teff
July 28, 2017
(K)
Haili Hu, Stellar Mergers Lorentz Workshop
sdB formation channels

Common-envelope ejection  close binary (Han et al 2002)

Stable Roche lobe overflow  wide binary (Mengel et al 1976)
For single sdB stars:
 Double helium white dwarf merger (Webbink 1984)
 Enhanced mass loss on RGB (d’Cruz 1996)
 CE merger of RGB + low mass companion (Soker 1998,
Politano et al. 2008)
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
sdB formation channels


Common-envelope ejection  close binary (Han et al 2002)
subchannels: Helium flash or non-degenerate ignition
Stable Roche lobe overflow  wide binary (Mengel et al 1976)
subchannels: Helium flash or non-degenerate ignition
For single sdB stars:
 Double helium white dwarf merger (Webbink 1984)
 Enhanced mass loss on RGB (d’Cruz 1996)
 CE merger of RGB + low mass companion (Soker 1998,
Politano et al. 2008)
subchannels: Helium flash or non-degenerate ignition
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
sdB formation channels


Common-envelope ejection  close binary (Han et al 2002)
subchannels: Helium flash or non-degenerate ignition
Stable Roche lobe overflow  wide binary (Mengel et al 1976)
subchannels: Helium flash or non-degenerate ignition
For single sdB stars:
 Double helium white dwarf merger (Webbink 1984)
 Enhanced mass loss on RGB (d’Cruz 1996)
 CE merger of RGB + low mass companion (Soker 1998,
Politano et al. 2008)
subchannels: Helium flash or non-degenerate ignition
0.4-0.5 M
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
sdB formation channels


Common-envelope ejection  close binary (Han et al 2002)
subchannels: Helium flash or non-degenerate ignition
Stable Roche lobe overflow  wide binary (Mengel et al 1976)
subchannels: Helium flash or non-degenerate ignition
For single sdB stars:
 Double helium white dwarf merger (Webbink 1984)
 Enhanced mass loss on RGB (d’Cruz 1996)
 CE merger of RGB + low mass companion (Soker 1998,
Politano et al. 2008)
subchannels: Helium flash or non-degenerate ignition
0.4-0.5 M
July 28, 2017
0.3-0.8 M
Haili Hu, Stellar Mergers Lorentz Workshop
sdB formation channels


Common-envelope ejection  close binary (Han et al 2002)
subchannels: Helium flash or non-degenerate ignition
Stable Roche lobe overflow  wide binary (Mengel et al 1976)
subchannels: Helium flash or non-degenerate ignition
For single sdB stars:
 Double helium white dwarf merger (Webbink 1984)
 Enhanced mass loss on RGB (d’Cruz 1996)
 CE merger of RGB + low mass companion (Soker 1998,
Politano et al. 2008)
subchannels: Helium flash or non-degenerate ignition
0.4-0.5 M
July 28, 2017
0.3-0.8 M
0.4-0.7 M
Haili Hu, Stellar Mergers Lorentz Workshop
Han et al 2003
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
Fontaine et al 2008
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
Asteroseismology

Goal: Better understanding of
stellar structure and evolution
through study of stellar
pulsations

Principle: Use waves (gravity
and sound) to infer what
cannot be seen directly
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
Why do stars pulsate?
Excitation mechanisms:
 opacity/kappa-mechanism (white dwarfs,
massive MS stars, sdB stars)
 convective motions in outer layers (Sun, red
giants)
 dynamic tides (close binaries)
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
How to descibe the oscillations? Easy in 1D
groundtone
first overtone
oscillation modes
July 28, 2017
second overtone
nodes
Haili Hu, Stellar Mergers Lorentz Workshop
But a star has 3d oscillations!




Instead of nodes: node lines on the surface, and
node surfaces in the star
Wave numbers l, m on the surface
Radial wave number n in the star
Each mode (n, l, m) oscillates with
its own eigenfrequency
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
But a star has 3d oscillations!




Instead of nodes: node lines on the surface, and
node surfaces in the star
Wave numbers l, m on the surface
Radial wave number n in the star
Each mode (n, l, m) oscillates with
its own eigenfrequency
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
l=3
m=0
l=3
m=2
l=3
m=3
Blue : moves towards us
Red : moves away from us
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
How to observe pulsations?

photometry
l=m=7

l=m=10
spectroscopy
©C. Schrijvers
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
HR diagram of pulsators

Many classes of
pulsators during
various evolutionary
phases:
•
•
•
•
main sequence stars
red giants
white dwarfs
subdwarf B stars
Figure from Christensen-Dalsgaard (2004)
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
Asteroseismology of sdB stars



V361 Hya / EC 14026 stars
(Kilkenny et al 96):
• short-periods (80-600 s)
• p-mode pulsations
V1093 Her / PG 1716 / Betsy
stars (Green et al 03):
• long-periods (30 min-2 hr)
• g-mode pulsations
Both driven by -mechanism
related to the Iron Opacity
Bump(Charpinet et al 97, Fontaine
etal 03)
Figure from Christensen-Dalsgaard (2004)
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
Asteroseismology of sdB stars
Observations:
 42 short-period pulsators
 31 long-period pulsators
 3 hybrid pulsators
Theory:
 Seismic solutions for
12 short-period pulsators
(Fontaine et al 08,
and references therein)
Figure from Fontaine et al (2008)
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
Asteroseismology of sdB stars




Current solutions all based on post-He flash sdB
models
However, structure of a post-non-degenerate
and post-merger sdB model are different
Differing interior structure gives different
oscillation signature (frequencies, mode degree,
excitation)
We focused on differences between post-flash
and post-non-degenerate sdB stars
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
Method
Constructing stellar models with:
 Stellar evolution code STARS (Eggleton 71)
Computing pulsation properties with:
 Adiabatic oscillation code OSC (Scuflaire et al 07)
 Non-adiabatic oscillation code MAD (Dupret 01)
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
Helium flash vs non-degenerate ignition
H-envelope lost when core is
above minimum for He-ignition,
but below the tip of the RGB


Mzams < ~2 M: He-flash
Mzams > ~2 M: Non-degenerate He-ignition
July 28, 2017
Hu et al 2007
Haili Hu, Stellar Mergers Lorentz Workshop
PG 1336-018 / NY Vir:
a post-CE, eclipsing, pulsating sdB binary


ULTRACAM / VLT lightcurves (May 18, 2005)
P = 2.4 hr
Vuckovic et al 2007
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
pre-CE phase of NY Vir
0.49q 2/3 a
R*  RL 
0.6q 2/3  ln(1 q1/3 )
or:
At onset of mass transfer:
I  h /3
Mcore = Mcore,tip
Mcore = Mcore,min

Pi (d)

Model assumptions:
Z = 0.02
Reimer’s mass loss
(η = 0.4)
M2 = 0.12 M
Hu et al 2007
MZAMS (M)
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
Results:
The CE phase

-formalism (Webbink 1984) :
E orb  E bind,env
 GM

GM
M
M
giant
2
remnant
2


 E bind,env



2a f
2ai




0 < < 1
-formalism (Nelemans et al 2000, 2005) :
J f  Ji
Ji

M giant  M 2 (M giant  M remnant )
with J 
Ga
M1 M 2
M1  M 2
 ~1.5
where Mgiant, Rgiant, Mremnant and Ebind,env follow from evolution
calculations, af and M2 from orbital light curve solution
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
Results:
The CE parameter  for NY Vir
Assuming Mremnant = MsdB and M2 = 0.12 M
July 28, 2017
Hu et al 2007
Haili Hu, Stellar Mergers Lorentz Workshop
Results:
The CE parameter  for NY Vir
Assuming Mremnant = MsdB and M2 = 0.12 M
July 28, 2017
Hu et al 2007
Haili Hu, Stellar Mergers Lorentz Workshop
NY Vir

From orbital lightcurve solution (Vuckovic et al 2007) and
asteroseismology (Charpinet et al 2008):
M-dwarf
0.12 M
sdB
0.47 M
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
Helium flash vs non-degenerate ignition
Hu et al 2008
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
Helium flash vs non-degenerate ignition
Comparison between two models with same log g and Teff
Hu et al 2008
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
Helium flash vs non-degenerate ignition
(i) Allow unstable frequencies of
non-degenerate model to be
matched to any frequency of
post-flash model
(ii) Assume mode identification:
allow matching only to modes
with same l - value
(iii) Assume log g & Teff known: i.e.
allow matching only to modes
with ~same log g & Teff
(iv) Allow matching only to unstable
modes
n
1 b i
2
M  ( f a  f bi ) 2
nb i1July 28, 2017
Haili Hu, Stellar Mergers
2 Lorentz Workshop
M
He-flash vs non-degenerate models



Mzams = 1.50 M
At RGB tip:
Mcore = 0.465 M
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
He-flash vs non-degenerate models



Mzams = 3.00 M
At RGB tip:
Mcore = 0.450 M
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
Helium flash vs non-degenerate ignition


Thus seismic difference between post-flash
(Mzams < ~2 M) and post-non-degenerate
(Mzams > ~2 M) sdB stars
Also true for sdB stars from He WD mergers?
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
How to model a He WD merger

Approach so far:
• Accretion of He on a He white dwarf (Iben 1990,
Saio & Jeffery 2000, Han et al 2002)



Maybe ok for following subsequent evolution
NOT ok for comparing seismic properties
Besides global structure parameters (M*, R*,
Teff), we need detailed information on core
composition, chemical stratifications, mass of Henvelope, …
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
Approach (future work)





SPH simulation of WD merger product (or use
entropy sorting algorithm?) (Rosswog)
Import merger product into 1D stellar evolution
code (Glebbeek)
Evolve product further
Compute pulsational properties (frequencies,
excitation, mode degree)
Compare observables: log g, Teff, f, l
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
Approach (future work)





SPH simulation of WD merger product (or use
entropy sorting algorithm?) (Rosswog)
Import merger product into 1D stellar evolution
code (Glebbeek)
Evolve product further
Compute pulsational properties (frequencies,
excitation, mode degree)
Compare observables: log g, Teff, f, l
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop
Difficulties/Problems



How much H is left on merger remnant? i.e. how
much H is burned during merger?
How to deal with He flash? Numerical problem in
the Eggleton code
And many other issues discussed these weeks
July 28, 2017
Haili Hu, Stellar Mergers Lorentz Workshop