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AG2014 – Splinter B
24 September 2014
Asteroseismology of evolved stars:
from hot B subdwarfs to white dwarfs
Valerie Van Grootel
Université de Liège, FNRS Research Associate
Main collaborators:
S. Charpinet
(IRAP Toulouse)
G. Fontaine
(U. Montréal)
S.K. Randall
(ESO)
P. Brassard
(U. Montréal)
M.A. Dupret
(U. Liège)
E.M. Green
(U. Arizona)
Evolved stars Asteroseismology
HR Diagram of pulsating stars
•
Hot B subdwarf (sdB) stars
extreme horizontal branch
(EHB) stars
•
White dwarf pulsators:
•
•
•
•
GW Vir (atm. He/C/O)
DBV (atm. He)
DQV (atm. C-rich)
DAV (atm. H) = 80% of WDs
Valerie Van Grootel - AG2014 Splinter B, Bamberg
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Hot B subdwarfs Asteroseismology
Focus: Origin of hot B subdwarfs
Valerie Van Grootel - AG2014 Splinter B, Bamberg
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Hot B subdwarfs
Hot (Teff  20 000 - 40 000 K) and compact stars (log g  5.2 - 6.2)
belonging to the Extreme Horizontal Branch (EHB)
•
•
•
He-burning to C+O (I), radiative He mantle (II) and very thin H-rich envelope (III)
Lifetime of ~ 108 ans (100 Myr) on EHB, then evolve to white dwarfs without AGB phase
~50% of sdBs reside in binary systems, generally in close orbits (Porb  10 d)
2 classes of pulsators:
> Short periods (P ~ 80 - 600 s), A  1%, p-modes (envelope)
> Long periods (P ~ 45 min - 3 h), A  0.1%, g-modes (mantle). Space observations!
> K-mechanism for pulsation driving (Fe accumulation in envelope)
log q
H-rich envelope
He mantle
log (1-M(r)/M*)
M* ~ 0.5 Ms
Menv < 0.005 Ms
He/C/O core
Valerie Van Grootel - AG2014 Splinter B, Bamberg
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The formation of sdB stars
How such stars form is a long standing problem
• For sdB in binaries (~50%)
• For single sdB stars (~50%)
2 main scenarios:
1. Single star evolution:
in the red giant phase: Common
envelope ejection (CEE), stable mass
transfer by Roche lobe overflow (RLOF)
enhanced mass loss at tip of RGB, at
He-burning ignition (He-flash)
mechanism quite unclear (cf later)

The red giant lose its envelope at tip of
RGB, when He-burning ignites (He-flash)

Remains the stripped core of the
former red giant, which is the
sdB star, with a close stellar
companion
Valerie Van Grootel - AG2014 Splinter B, Bamberg
2. The merger scenario:
Two low mass He white dwarfs merge
to form a He core burning sdB star
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Common envelope evolution (close binary sdB systems)
CEE: sdB + MS star or white dwarf
Valerie Van Grootel - AG2014 Splinter B, Bamberg
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Stable Roche lobe overflow (wide binary sdB systems)
RLOF: sdB + MS star (later than F-G)
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Single sdBs: single star evolution or He-white dwarfs mergers
mergers
Envelope ejection at tip of RGB
or
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The formation of sdB stars
• Single star evolution (“almost impossible”): Mass range in 0.40 - 0.43  M*/Ms  0.52
(Dorman et al. 1993)
• Binary star evolution: numerical simulations on binary population synthesis
(Han et al. 2002, 2003)
Figures from Han et al. (2003)
RLOF (Roche Lobe overflow)
Weighted mean distribution
This is the theoretical
mass
distribution
we want to test
CE (common envelope)
for binary evolution:
by eclipsing/reflecting binaries and by asteroseismology
(including selection effects)
mergers
Valerie Van Grootel - AG2014 Splinter B, Bamberg
0.30  M*/Ms  0.70
peak ~ 0.46 Ms (CE, RLOF)
high masses (mergers)
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The method for sdB asteroseismology
Search the stellar model(s) whose theoretical periods best fit all the observed
ones, in order to minimize
•
•
•
Optimization codes (based on Genetic Algorithms) to find the minima of S2
External constraints: Teff, log g from spectroscopy
Results: global parameters (mass, radius), internal structure (envelope & core mass,…)
> Example: PG 1336-018, pulsating sdB + dM eclipsing binary (a unique case!)

Light curve modeling (Vuckovic et al. 2007):
M  0.466  0.006 Ms, R  0.15  0.01 Rs,
and log g  5.77  0.06

Seismic analysis (Van Grootel et al. 2013):
M  0.471  0.006 Ms, R  0.1474  0.0009 Rs,
and log g  5.775  0.007
Figure from Vuckovic et al. (2007)
 Our asteroseismic method is sound and free of significant systematic effects
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Available samples of sdBs with known masses
I. The asteroseismic sample
15 sdB stars modeled by asteroseismology
(we took the most recent value in case of several analyses)
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Available samples
II. The extended sample
(sdB + WD or dM star)
Light curve modeling + spectroscopy  mass of the sdB component
Need uncertainties to build a mass distribution
 7 sdB stars retained in this subsample
Extended sample: 15+7  22 sdB stars with accurate mass estimates
• 11 (apparently) single stars
• 11 in binaries (including 4 pulsators)
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Building the mass distributions
Binning the distribution in the form of an histogram (bin width    0.024 Ms)
Extended sample:
Asteroseismic sample:
(white)
Mean mass: 0.470 Ms
Median mass: 0.471 Ms
Range of 68.3% of stars:
0.439-0.501 Ms
(shaded)
Mean mass: 0.470 Ms
Median mass: 0.470 Ms
Range of 68.3% of stars:
0.441-0.499 Ms
No detectable significant differences between distributions
(especially between singles and binaries)
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Comparison with theoretical distributions
 A word of caution: still small number
statistics (need ~30 stars for a
significant sample)
 Distribution strongly peaked near
0.47 Ms
 No differences between subsamples
(eg, binaries vs single sdB stars)
 It seems to have a deficit of high
mass sdB stars, i.e. from the merger
channel. Especially, the single sdBs
distribution ≠ merger distribution.
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Comparison with theoretical distributions
The single sdBs distribution ≠ merger channel distribution
Han et al. 2003
merger channel
Single sdB stars can not be explained
only in terms of binary evolution via
merger channel
Moreover, Geier & Heber (2012): 105 single or in wide binaries sdB stars:
all are slow rotators (Vsin i < 10 km s-1)
(the majority of) sdB stars are post-RGB stars
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sdB stars are (in majority) post-RGB stars, and even
post He-flash stars
MS mass of sdB progenitors:
0.7 – 1.8 Ms
(e.g. Castellani et al. 2000)
So: the red giant has expelled almost all its envelope and
has reached the minimum mass for He-flash
•
At the He-flash: rather unlikely that these 2 events occur simultaneously
•
Alternative: “hot flash”, after having left the RGB (before tip), in the
contraction phase (Castellani&Castellani 1993; D’Cruz et al. 1996)
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Extreme mass loss on RGB
If this scenario holds true, the red giant has experienced extreme mass loss
on RGB (Red Giant Branch)
What could cause extreme mass loss on RGB ?
•
•
For binary stars: ok, thanks to stellar companion
For single stars, it’s more difficult:
-
Internal rotation => mixing of He => enhanced mass loss on RGB
(Sweigart 1997)
-
Dynamical interactions: Substellar companions (Soker 1998)
Indeed, planets and brown dwarfs are discovered around sdB stars:
In short orbits: •
•
5 planets (Charpinet et al. 2011, Silvotti et al. 2014)
At least 2 BDs (Geier et al. 2011, 2012, Schaffenroth et al. 2014)
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A consistent scenario
Figure from Kempton 2011, Nature, 480, 460
 Former close-in giant planets/BDs were deeply engulfed in the red giant envelope
 The planets’ volatile layers were removed and only the dense cores survived and
migrated where they are now seen
 The star probably left RGB when envelope was too thin to sustain H-burning shell
and experienced a delayed He-flash (or, less likely, He-flash at tip of RGB)
 Planets/BDs are responsible of strong mass loss and kinetic energy loss of the
star along the RGB
 As a bonus: this scenario explains why “single” sdB stars are all slow rotators
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Conclusions
 No significant differences between distributions of various samples
(asteroseismic, light curve modeling, single, binaries, etc.)
 Single star evolution scenario does exist; importance of the merger
scenario? (single stars with presumably fast rotation)
 A consistent scenario to form “single” sdB stars: delayed He-
flasher + strong mass loss on RGB due to planets/brown dwarfs?
But:
 Currently only 22 objects: 11 single stars and 11 in binaries
 Among  2000 known sdB, ~100 pulsators are now known
 Both light curve modeling and asteroseismology are a challenge
(accurate spectroscopic and photometric observations, stellar models, etc.)
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White Dwarfs Asteroseismology
Focus: instability strip of DA white dwarf pulsators
(i.e. ZZ Ceti pulsators)
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White dwarfs
Late stages of evolution of ~97% of stars in the Universe
DA (H-rich atmosphere): ~80%; DB (no/little H atmosphere): ~20% of WDs
4 types of g-mode pulsators along
the cooling sequence:
•
GW Vir stars (He/C/O atmospheres)
Teff ~ 120,000 K, discovered in 1979
•
V777 Her stars (He-atmosphere), 1982
Teff ~ 25,000 K
•
Hot DQ stars (C-rich/He atmosphere)
Teff ~ 20,000 K, discovered in 2007
•
ZZ Ceti stars (H-atmosphere, DA)
Teff ~ 12,000 K, discovered in 1968
Most numerous (~200 known including
SDSS+Kepler)
From Saio (2012), LIAC40 proceedings
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Pulsating DA white dwarfs
Excitation mechanism of ZZ Ceti stars
•
Don Winget (1981):
H recombination around Teff~12,000 K
 envelope opacity increase
 strangle the flow of radiation
 modes instabilities
•
Pulsations are destabilized at the
base of the convection zone
(details: e.g. Van Grootel et al. 2012)
“convective driving”
log q
log (1-M(r)/M*)
Pulsations are driven when the convection zone is sufficiently deep and developed
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Pulsating DA white dwarfs
Empirical ZZ Ceti instability strip (classic view)

Observed pulsator ; O non-variable DA white dwarf
Figure from Fontaine & Brassard (2008)
Valerie Van Grootel - AG2014 Splinter B, Bamberg
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Typical mass range: 0.5-1.1 Ms
•
Multiperiodic pulsators, observed
period range: 100-1500 s (g-modes)
•
Reliable atmospheric parameters:
work of Bergeron et al., Gianninas et
al., here with ML2/α=0.6
•
(most probably) a pure strip
•
log g/Teff correlation (with a more
pronounced slope for red edge):
the lower log g, the lower edge Teff
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Pulsating DA white dwarfs
Empirical ZZ Ceti instability strip (2014 view)
non variable (<10mmag);
pulsator
Hermes et al. (2012, 2013a,b):
0.15 Ms
5 Extremely-Low-Mass pulsators
0.20 Ms
Hermes et al. (2013c):
1 ultra-massive pulsator
1.2 Ms
Valerie Van Grootel - AG2014 Splinter B, Bamberg
This is the observed
instability strip we want to
theoretically reproduce
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The theoretical instability strip
•
Evolutionary DA White Dwarf Models
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Evolutionary DA models
•
A standard DA white dwarf structure model (C/O core)
“onion-like” stratification
log q
log (1-M(r)/M*)
-
H envelope
-4.0
He mantle
-2.0
C/O core
0
Base of the atmosphere
•
Evolutionary tracks computed for 0.4Ms to 1.2Ms (0.1Ms step)
• from Teff35,000 K to 2,000 K (~150 models)
• with ML2 version (a1,b2,c16);   1 (ie l  Hp)
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Evolutionary DA models
Base of the atmosphere
Sup
Detailed modeling of the
superficial layers
erficial
convection
zone
Our evolutionary models have the same T stratification
as the complete (1D) model atmospheres
”feedback” of the convection on the global
atmosphere structure
•
•
Valerie Van Grootel - AG2014 Splinter B, Bamberg
Standard grey atmosphere
Detailed atmosphere
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Evolutionary DA models
•
Extremely Low Mass (ELM) DA white dwarf:
H envelope on top of He core
ELM white dwarfs come from stars that never experienced any He-flash, because of extreme
mass loss on RGB (from binary interactions or due to high Z)
• 2 kinds of evolutionary tracks computed here:
I.
II.
Standard C core models, but for 0.125Ms and 0.15-0.4Ms (steps 0.05Ms)
Pure He core/H envelope models, for the same masses, thick envelopes
log q
log (1-M(r)/M*)
log q
log (1-M(r)/M*)
-
H envelope
-
H envelope
-4.0
He mantle
-2.0
He core
-2.0
C core
0
0
Instability strip location in Teff-log g plane insensitive to detailed core
composition and envelope thickness
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The theoretical instability strip
•
•
Evolutionary DA White Dwarf Models
Time-Dependent Convection (TDC) Approach
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The Time-Dependent Convection approach
For a standard 0.6Ms DA model:
•Teff ~ 12,000 K: convective turnover timescale conv   (pulsation periods)
 convection adapts quasi-instantaneously to the pulsations
•Teff ~ 11,000 K: conv ≈   NEED full Time-Dependent Convection (TDC)
• Frozen convection (FC), i.e. conv  : NEVER justified in the ZZ Ceti Teff regime
(FC is the usual assumption to study the theoretical instability strip)
  1500 s
  100 s
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The Time-Dependent Convection theory
• Full development in Grigahcène et al.(2005), following the theory of M. Gabriel (1974,1996),
based on ideas of Unno et al. (1967)
• The Liege nonadiabatic pulsation code MAD (Dupret 2002) is the only one to implement
convenient TDC treatment
• The timescales of pulsations and convection are both taken into account
• Perturbation of the convective flux taken into account here:
• Built within the mixing-length theory (MLT), with the adopted perturbation of the mixing-
length:
if   conv (instantaneous adaption):
if   conv (frozen convection):
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The theoretical instability strip
•
•
•
Evolutionary DA White Dwarf Models
Time-Dependent Convection (TDC) Approach
Results
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Results: computing the theoretical instability strip
•
We applied the MAD code to all evolutionary sequences
•“normal” CO-core DA models, 0.4 – 1.2Ms, log q(H)=-4.0
• ELM, C-core models: 0.125-0.4 Ms, log q(H)=-4.0
• ELM, He-core models: 0.125-0.4 Ms, log q(H)=-2.0
• 0.17Ms, He-core models, “thin” envelope log q(H)=-3.7
with ML2/  1, detailed atmospheric modeling, and TDC treatment
•
We computed the degree l1 in the range 10-7000 s (p- and g-modes)
•
For the red edge (long-standing problem):
based on the idea of Hansen, Winget & Kawaler (1985): red edge arises when
th ~ Pcrit α (l(l+1))-0.5
(th : thermal timescale at the base of the convection zone),
which means the mode is no longer reflected back by star’s atmosphere
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Empirical ZZ Ceti instability strip (2014 view)
non variable (<10mmag);
pulsator
Spectroscopic estimates:
0.15 Ms
• ELM white dwarfs: D.
Koester models (Brown et
al. 2012)
•UHM white dwarf:
Gianninas et al. (2011)
•Standard ZZ Ceti: P.
Bergeron et al.
0.20 Ms
But all ML2/α=0.6
(must be consistent)
1.2 Ms
Valerie Van Grootel - AG2014 Splinter B, Bamberg
+ standard ZZCeti: spectroscopic
observations gathered during
several cycles of pulsations
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Theoretical instability strip (g-modes l=1)
non variable (<10mmag);
pulsator
TDC blue edge
Red edge
0.15 Ms
• Narrower strip at low masses
(larger slope for the red edge)
0.20 Ms
•
Structure models:
ML2/  1
Model atmospheres:
ML2/  0.6

1.2 Ms
Convective efficiency
increases with depth?
(consistent with hydrodynamical
simulations; Ludwig et al. 1994,
Tremblay & Ludwig 2011)
NB: evolutionary and atmospheric MLT calibrations are dependent
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Theoretical instability strip (g-modes l=1)
Is the whole ZZ Ceti instability strip pure?
YES
•
0.15 Ms
Need only small fine-tuning
J2228 is a little bit tricky
Consistency between ML
calibrations atmospheres 
structure models
Spectra must cover a few
pulsational cycles !
•
•
0.20 Ms
•
BUT
1.2 Ms
Valerie Van Grootel - AG2014 Splinter B, Bamberg
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Are all ELM pure H (DA)
white dwarfs or with traces of
He ?
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Qualitative fit to the observed periods of the ELM pulsators
SDSS J1840+6423
Teff~ 9140±170 K, logg ~ 6.16±0.06
He-core model, log q(H)=-2.0
SDSS J1518+0658
Teff~ 9810±320 K, logg ~ 6.66±0.06
He-core model, log q(H)=4.0 and -2.0
SDSS J1112+1117
Teff~ 9400±490 K, logg ~ 5.99±0.12
He-core model, log q(H)=-2.0
Adiabatic properties are sensitive to exact interior structure
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Conclusion and prospects
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Conclusion and Prospects
Conclusions:
• Excellent agreement between theoretical and observed instability strip:
-Blue edge, TDC approach
-Red edge, by energy leakage through the atmosphere
•ELM pulsators are low mass equivalent to standard ZZ Ceti pulsators
excited by convective driving
 such pulsators exist from 0.15 to 1.2 Ms (log g = 5 – 9 !)
•Is ML2/α=1.0 the good flavor for convection inside white dwarfs?
Related to spectroscopic calibration (here ML2/α=0.6) and 3D hydrodynamical
simulations (Tremblay et al. 2011,2012, 2014)
Prospects:
• Is the ZZ Ceti instability strip pure? Traces of He in ELM white dwarfs?
• Instability strip with structure models including 3D atmospheres?
• Asteroseismology of ELM/standard/massive ZZ Ceti pulsators
1.
2.
3.
internal structure & fundamental parameters
age
understanding of matter under extreme conditions
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Supp slides
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(the majority of) sdB stars are post-RGB stars,
and even post He-flash stars
What does it imply ?
The star has removed all but a small fraction of its envelope
and has reached the minimum mass to trigger He-flash
•
at tip of RGB, as a classic RGB-tip flasher ? (classic way for HB stars)
-> It’s rather unlikely that the 2 events occur at the same time !
•
an alternative (old and somewhat forgotten) idea:
Hot He-flashers (Castellani&Castellani 1993; D’Cruz et al. 1996)
i.e., stars that experience a delayed He-flash during contraction, at
higher Teff, after leaving the RGB before tip
(H-burning shell stops due to strong mass loss on RGB)
D’Cruz et al. (1996) showed that such stars populate the EHB, with similar
(core) masses
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Another hint: Horizontal branch/EHB morphology
There is a gap between EHB and classic blue HB (BHB)
Green et
al. (2008)
Size of dots related
to He abundance
This suggests something “different” for the formation of
EHB and classic HB stars
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