asteroseismology of evolved stars: from hot b subdwarfs to white dwarfs

Asteroseismology of evolved stars:

from hot B subdwarfs to white dwarfs

Valerie Van GrootelUniversité de Liège, FNRS Research Associate

Main collaborators:

AG2014 – Splinter B24 September 2014

S. Charpinet(IRAP Toulouse)

G. Fontaine(U. Montréal)

S.K. Randall(ESO)

M.A. Dupret(U. Liège)

E.M. Green(U. Arizona)

P. Brassard(U. Montréal)

Valerie Van Grootel - AG2014 Splinter B, Bamberg 2

Evolved stars Asteroseismology

• 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

HR Diagram of pulsating stars


Hot B subdwarfs Asteroseismology

Focus: Origin of hot B subdwarfs


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)

> 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)

2 classes of pulsators:

Core

Env

elop

eHe/C/O core

He mantle

H-rich envelope

log q log (1-M(r)/M*)

M* ~ 0.5 Ms

Menv < 0.005 Ms


The red giant lose its envelope at tip of RGB, when He-burning ignites (He-flash)

The formation of sdB stars

1. Single star evolution: enhanced mass loss at tip of RGB, at

He-burning ignition (He-flash)mechanism quite unclear (cf later)

2. The merger scenario:Two low mass He white dwarfs merge

to form a He core burning sdB star

• For sdB in binaries (~50%)

How such stars form is a long standing problem

in the red giant phase: Common envelope ejection (CEE), stable mass transfer by Roche lobe overflow (RLOF)

• For single sdB stars (~50%)

Remains the stripped core of the former red giant, which is the sdB star, with a close stellar companion

2 main scenarios:

Valerie Van Grootel - AG2014 Splinter B, Bamberg

Common envelope evolution (close binary sdB systems)

6

CEE: sdB + MS star or white dwarf


Stable Roche lobe overflow (wide binary sdB systems)

7

RLOF: sdB + MS star (later than F-G)


Single sdBs: single star evolution or He-white dwarfs mergers

8

Envelope ejection at tip of RGB

mergers

or


The formation of sdB stars

CE (common envelope)

RLOF (Roche Lobe overflow)

mergers

Weighted mean distributionfor binary evolution:

(including selection effects)

0.30 M*/Ms 0.70peak ~ 0.46 Ms (CE, RLOF)

high masses (mergers)

Figures from Han et al. (2003)

• 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)

This is the theoretical mass distribution we want to test by eclipsing/reflecting binaries and by 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,…)

The method for sdB asteroseismology

> 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

Our asteroseismic method is sound and free of significant systematic effects

Figure from Vuckovic et al. (2007)


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)


Available samples

II. The extended sample (sdB + WD or dM star)

Need uncertainties to build a mass distribution 7 sdB stars retained in this subsample

Light curve modeling + spectroscopy mass of the sdB component

Extended sample: 15+7 22 sdB stars with accurate mass estimates• 11 (apparently) single stars• 11 in binaries (including 4 pulsators)


Building the mass distributions

Extended sample: (white)Mean mass: 0.470 MsMedian mass: 0.471 MsRange of 68.3% of stars:0.439-0.501 Ms

Binning the distribution in the form of an histogram (bin width 0.024 Ms)

Asteroseismic sample: (shaded)Mean mass: 0.470 MsMedian mass: 0.470 MsRange of 68.3% of stars:0.441-0.499 Ms

No detectable significant differences between distributions(especially between singles and binaries)


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 sub samples (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.


Comparison with theoretical distributions

(the majority of) sdB stars are post-RGB stars

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)


sdB stars are (in majority) post-RGB stars, and even post He-flash stars

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

MS mass of sdB progenitors:

0.7 – 1.8 Ms

(e.g. Castellani et al. 2000)

• Alternative: “hot flash”, after having left the RGB (before tip), in the contraction phase (Castellani&Castellani 1993; D’Cruz et al. 1996)


Extreme mass loss on RGB

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• 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)

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 ?

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)


A consistent scenario

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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

Figure from Kempton 2011, Nature, 480, 460


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.)


White Dwarfs Asteroseismology

Focus: instability strip of DA white dwarf pulsators(i.e. ZZ Ceti pulsators)


White dwarfs

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)

Late stages of evolution of ~97% of stars in the Universe

From Saio (2012), LIAC40 proceedings

DA (H-rich atmosphere): ~80%; DB (no/little H atmosphere): ~20% of WDs


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”


Pulsations are driven when the convection zone is sufficiently deep and developed

Pulsating DA white dwarfs



Empirical ZZ Ceti instability strip (classic view)

• 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

Observed pulsator ; O non-variable DA white dwarfFigure from Fontaine & Brassard (2008)



Empirical ZZ Ceti instability strip (2014 view)

Hermes et al. (2012, 2013a,b):

5 Extremely-Low-Mass pulsators

non variable (<10mmag); pulsator

Hermes et al. (2013c):

1 ultra-massive pulsator

1.2 Ms

0.20 Ms

0.15 Ms

This is the observed instability strip we want to

theoretically reproduce


• Evolutionary DA White Dwarf Models

The theoretical instability strip


Evolutionary DA models

Core

Env

elop

e

C/O core

He mantle

H envelope


-

0

-4.0

-2.0

“onion-like” stratification

Base of the atmosphere

• A standard DA white dwarf structure model (C/O core)

• Evolutionary tracks computed for 0.4Ms to 1.2Ms (0.1Ms step)

• from Teff35,000 K to 2,000 K (~150 models)• with ML2 version (a1,b2,c16); 1 (ie l Hp)


Superficial convection zone

Detailed modeling of the superficial layers

Our evolutionary models have the same T stratification as the complete (1D) model atmospheres

”feedback” of the convection on the global atmosphere structure

Base of the atmosphere

• Standard grey atmosphere• Detailed atmosphere



• 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. Standard C core models, but for 0.125Ms and 0.15-0.4Ms (steps 0.05Ms)

II. Pure He core/H envelope models, for the same masses, thick envelopes

Core

Env

elop

e

C core

He mantle

H envelope


-

0

-4.0

-2.0

Core

Env

elop

e

He core

H envelope


-

0

-2.0

Instability strip location in Teff-log g plane insensitive to detailed core composition and envelope thickness



• Evolutionary DA White Dwarf Models• Time-Dependent Convection (TDC) Approach



The Time-Dependent Convection approach

•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

For a standard 0.6Ms DA model:

(FC is the usual assumption to study the theoretical instability strip)

1500 s

100 s


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):


• Evolutionary DA White Dwarf Models• Time-Dependent Convection (TDC) Approach• Results



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

• We computed the degree l1 in the range 10-7000 s (p- and g-modes)

with ML2/ 1, detailed atmospheric modeling, and TDC treatment

• 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



Empirical ZZ Ceti instability strip (2014 view)

Spectroscopic estimates:• ELM white dwarfs: D. Koester models (Brown et al. 2012)•UHM white dwarf: Gianninas et al. (2011) •Standard ZZ Ceti: P. Bergeron et al.

But all ML2/α=0.6(must be consistent)

+ standard ZZCeti: spectroscopic observations gathered during several cycles of pulsations

1.2 Ms

0.20 Ms

0.15 Ms


Theoretical instability strip (g-modes l=1)

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•Structure models: ML2/ 1

TDC blue edge

Red edge


Model atmospheres:ML2/ 0.6

• Narrower strip at low masses (larger slope for the red edge)

Convective efficiency increases with depth?

(consistent with hydrodynamical simulations; Ludwig et al. 1994, Tremblay & Ludwig 2011)

NB: evolutionary and atmospheric MLT calibrations are dependent

1.2 Ms

0.20 Ms

0.15 Ms


Is the whole ZZ Ceti instability strip pure?

Theoretical instability strip (g-modes l=1)

• 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 !

YES

BUT• Are all ELM pure H (DA)

white dwarfs or with traces of He ?

1.2 Ms

0.20 Ms

0.15 Ms


SDSS J1112+1117Teff~ 9400±490 K, logg ~ 5.99±0.12

He-core model, log q(H)=-2.0

Qualitative fit to the observed periods of the ELM pulsators

SDSS J1840+6423Teff~ 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

Adiabatic properties are sensitive to exact interior structure


Conclusion and prospects


Conclusion and 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. internal structure & fundamental parameters2. age3. understanding of matter under extreme conditions

Conclusions:

Prospects:

• 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)


Supp slides


What does it imply ?

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(the majority of) sdB stars are post-RGB stars, and even post He-flash stars

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)

• 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

-> It’s rather unlikely that the 2 events occur at the same time !


Another hint: Horizontal branch/EHB morphology

There is a gap between EHB and classic blue HB (BHB)

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This suggests something “different” for the formation of EHB and classic HB stars

Green et al. (2008)

Size of dots related to He abundance

asteroseismology of evolved stars: from hot b subdwarfs to white dwarfs

Documents

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hot b subdwarfshot teff

wide binary sdb systems

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