the evolution and pulsations of low mass he-core white dwarfs · 134 s) maybe due to p-modes. it...

La Plata Stellar Evolution and Pulsation Research GroupFacultad de Ciencias Astronómicas y Geofísicas

Universidad Nacional de La PlataLa Plata, Argentina

The evolution and pulsations of low mass He-core white dwarfs

Alejandro H. Córsico & Leandro G. Althaus

The evolution and pulsations of low mass He-core white dwarfs, Córsico et al.

What asteroseismology has to offer to astrophysics, 2-4 December 2013, Brussels, Belgium

The classes of pulsating white dwarf starsPulsating low mass (LM) WDs discovered by Hermes et al. (2012, 2013a,b)Up to now, 5 known pulsating objects: a new class of pulsating white dwarfs

MOTIVATION OF THIS WORK: evolutionary and pulsation modeling

Pulsating low mass WDs open the chance of sounding the interiors of these faint stars through asteroseismology, in a similar way than for ZZ Ceti, DBV, GW Vir white dwarfs

BUT …

Detailed theoretical models are needed to accurately assess the pulsation spectrum



Very briefly: the origin of the low-mass (< 0.30 Mo) WD population

They are the result of strong mass-loss episodes during common envelope phase in close binary systems; since this prevents He ignition, these WD stars with M ≤ 0.30 Mo must harbor He cores.

● The evolutionary properties have been thoroughly studied (Nelson et al. 2004; Athaus et al. 2013). An important result is a dichotomy regarding the H envelope thickness and in the cooling timescale (element diffusion is a crucial ingredient; Athaus et al. 2001):

- Stars with M ≥ 0.20-0.18 Msun have very thin H envelopes, because their progenitors experience diffusion-induced CNO flashes. No relevant H burning; short evolutionary timescales (≈107 yr).

- Stars with M < 0.20-0.18 Msun (here arbitrarily referred to as ELM: Extremely Low Mass WDs) have thick H envelopes, because their progenitors do not experience CNO flashes. H burning is the main energy source; long cooling timescales (≈109 yr).



We study the pulsational properties of the low mass He-core WD model sequences of Althaus et al. (2013)

Initial models: the nonconservative evolution of a binary system consisting of an initially 1 Mo ZAMS star and a 1.4 Mo neutron star for various initial orbital periods (Sarna et al. 2000)

Input physics

● Nuclear burning: Network for 16 elements and 34 nuclear reactions for PP chains, CNO bi-cycle, He burning.

● Time-dependent element diffusion due to gravitational settling and chemical and thermal diffusion (Burgers 1969)

● Chemical abundance changes are computed according to element diffusion, nuclear reactions, and convective mixing.





Squares and triangles: post-RGB low-mass stars (Silvotti et al. 2012, Brown et al. 2013)

Filled circles: pulsating low mass WDs (Hermes et al. (2012, 2013ab)



Final cooling tracks and the pulsating stars

Green triangles: stars Not Observed to Vary



Degeneracy of the asymptotic period spacing for masses between 0.19 and 0.17 Mo ∼ ∼(near the critical mass for the development of CNO flashes, 0.18 Mo). ∼

The asymptotic frequency spacing exhibits a clear separation between the sequences that have experienced CNO flashes (> 0.18 Mo) and those that did not (< 0.18 Mo, ELM WDs).

Asymptotic period spacing ∆Πa and frequency spacing ∆νa

Chemical profiles and propagation diagrams

The evolution and pulsations of Extremely Low Mass (ELM) He-core white dwarfs, Córsico et al.


- The ELM WD model and the LM WD model have very different chemical structures. In particular, the ELM model has a H envelope much thicker.- For the ELM model, the Brunt-Väisälä frequency is larger in the core than in the envelope (low degeneracy). g-modes probe mainly the core regions and p-modes the envelope, at variance with what happens in ZZ Ceti stars. For pulsating ELM WDs we have the chance to constrain the core chemical structure with asteroseismology.

ELM WD template model: 0.1554 Mo LM WD template model: 0.2389 Mo

Oscillation kinetic energy density

- Most of the spatial oscillations of g-modes are restricted to the core regions below the He/H interface, even in the case of low-order modes.

- By the contrary, p-modes oscillate mostly in the outer regions

- g-modes oscillate all along the stellar structure, although there is a marked concentration of kinetic energy at the He/H interface. g-modes are very sensitive to this compositional gradient. Potential diagnostic for the H envelope thickness.

- p-modes are rather insensitive to the presence of the He/H composition gradient.



LM WD template model: 0.2389 MoELM WD template model: 0.1554 Mo

Effects of element diffusion

- For the ELM WD model, the H profile changes from a a diffusion-shaped double-layered chemical structure (Teff ≈ 9600 K) to a single-layered chemical one (Teff ≈ 8000 K). The transition occurs at higher effective temperatures (not shown here) for more the massive sequences.- Element diffusion affects all the sequences in the range of Teff of interest (diffusive equilibrium is NOT valid in the He/H transition region), in particular the ELM WD sequences.



LM WD template models: 0.2389 MoELM WD template model: 0.1554 Mo

Interpretation of observations



● The five stars show long-period variations (1184 - 6235 s) presumably due to g-modes with intermediate and high radial orders (12 ≤ k ≤ 50)

● In one star (SDSS J111215.82+111745.0), evidence for short-period pulsations (108 - 134 s) maybe due to p-modes. It could be the first hybrid (g- and p-mode) pulsating white dwarf



- For the temperature and mass (gravity) of SDSS J111215 predicted by spectroscopy, our models are not able to explain the presence of the short periods .

- However, these periodscould be attributed to low order p-modes if the stellar mass is lower (≈ 0.16 Mo).

- Alternatively, they could be low order g-modes if the stellar mass is substantially larger (≈ 0.43 Mo)

- Another possibility: higher degree (l= 2, 3) low order g-modes at the spectroscopic mass (gravity) and Teff.

The case of SDSS J111215 (M= 0.18 Mo)

Some conclusions

● ELM WDs and LM WDs have very different chemical structures, and so different pulsation properties.

● Pulsating ELM WDs (M < 0.18 Mo) have asteroseismological potential for constrain the chemical structure of the core.

● Pulsating LM WDs (M > 0.18 Mo) have asteroseismological potential for constrain the H envelope thickness.

● Differences in the period spacings could allow discriminate ELM WDs from LM WDs (NOT SHOWN IN THIS TALK)

● Pulsations could help to distinguish a ELM WD from a more massive He-WD going through a CNO flash episode (NOT SHOWN IN THIS TALK)



BUT a lot of modelling work and observations are required before we can apply asteroseismology to

pulsating low mass WDs

Thank you!

Search for pulsations in low mass DA white dwarfs (WD) (M< 0.5 Mo)

● Steinfadt et al. (2010) proposed that low mass WDs should pulsate (semi-analytic criterion) like the more massive DA (H-rich) WDs (DAV or ZZ Ceti stars). Steinfadt et al. (2012) searched for luminosity variations in low-mass DA WDs, but with null results.

● JJ Hermes et al. (McDonald Observatory) started an intensive observing program, with targets from the “ELM Survey” (Brown et al. 2010, 2012, Kilic et al. 2011, 2012)

● Hermes et al. (2012): SDSS J184037.78+642312.3 (companion: probably a WD), the first pulsating object of this kind

● Hermes et al. (2013a): SDSS J111215.82+111745.0 (companion: probably another He-core WD), SDSS J151826.68+065813.2 (companion: probably another He-core WD)

● Hermes et al. (2013b): SDSS J161431.28+191219.4 (companion: undetected), SDSS J222859.93+362359.6 (companion: undetected)

● Up to now, 5 known pulsating objects: a new class of pulsating white dwarfs





Age dichotomy (Althaus et al. 2013)

ELM WD sequences with M= 0.15540, 0.16115, 0.16499, 0.17064, 0.17624 Mo (thick lines), together with the lowest mass He-core WD sequence that undergoes CNO flashes (M= 0.18213 Mo, thin line).The 0.18213 Mo sequence evolves much faster as compared with ELM WDs.

Pulsation properties of low mass and ELM WD stars (final cooling tracks)

- adiabatic pulsation periods of dipole (l= 1) g- and p-modes

- periods from 10 to 7000 s

- LP-PUL adiabatic pulsation code (Córsico & Althaus 2006)

- effective temperatures from 11000 K to 7000 K

- It is planned to compute pulsation periods of radial (l= 0) and nonradial p- and g-modes with l= 2, 3 also.



Adiabatic pulsation properties of g- and p-modes(WORK IN PROGRESS)

LP-PUL adiabatic pulsation code (Córsico & Althaus 2006)



Asymptotic period spacing of g-modes:

- Larger for smaller stellar masses

- Larger for lower effective temperatures

Asymptotic frequency spacing of p-modes:

- Larger for higher stellar masses

- Larger for lower effective temperatures

Dependence with effective temperature



- The periods of g-modes (except g

1) increase for

decreasing effective temperature, and the opposite happens for the periods of p-modes.

- The “gap” between p- and g-modes increases for decreasing effective temperature

Dependence with stellar mass



- The periods of both p-and g-modes increase with decreasing stellar mass.

- The “gap” between p- and g-modes strongly decreases for ELM WD models (below 0.18 Mo).

- The step in the periods corresponds to the limit stellar mass value.

Period spacing ∆Π and frequency spacing ∆νELM

- g-modes show strong departures from uniform period spacing: mode trapping. “Trapping cycle” of about 1800 s.

- Frequency separations of p-modes very close to the asymptotic predictions

- Mode trapping signatures are evident, but the trapping cycle is much shorter, of about 200 s.

- Frequency separation of p-modes shows some signatures of mode trapping for low order modes.



Differences in the period and frequency spacing distributions could be exploited to distinguish ELM and LM WDs .

M= 0.2389 Mo

An interesting example: the most massive ELM model (0.1762 Mo) and the lowest mass CNO flashing model (M =

0.1805 Mo)ELM WD: M= 0.1762 Mo M= 0.1805 Mo



- Differences in the period spacing distribution of g-modes, mode trapping is stronger for the LM WD model, for periods shorter than ≈ 2000 s (Althaus et al. 2013).

- The asympotic frequency spacing of p-modes for the LM WD model is about twice than for the ELM model. This, in spite that the difference in stellar mass is of only 0.0043 Mo!

Pulsating low mass white dwarfs

● The five stars show long-period variations (1184 - 6235 s) presumably due to g-modes with intermediate and high radial orders (12 ≤ k ≤ 50)

● In one star (SDSS J111215.82+111745.0), evidence for short-period pulsations (108 - 134 s) attributable to p-modes. The first hybrid (g- and p-mode) pulsating white dwarf?

Hermes et al. (2013b)





Theory and observations: the case of SDSS J111215 (M= 0.18 Mo)

the evolution and pulsations of low mass he-core white dwarfs · 134 s) maybe due to p-modes. it...

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