Internal structure of white dwarf probed with asteroseismology

Jianning Fu (付建宁)

(Beijing Normal University)

KIAA — 2016.05.13

Contents

• Introduction about white dwarf stars

• Stellar pulsations and asteroseismology

• Asteroseismology of white dwarf stars

• Case study

– for PG0122+200

– for HS0507+0434B

– for WD0246+326

• Summary and questions

1. Introduction about white dwarf stars

• Basic information

• Formation

• Scientific importance

The Sun and the Earth The white dwarf and the Earth

• White dwarf: a kind of star with low luminosity, high density, high temperature with nuclear reaction stopped

• With the color of Blue/White and small size White dwarf • Composition:

– Carbon-oxygen core – Helium and/or Hydrogen envelope

• Typical size: ~6000 km (the earth size) Typical mass: ~0.6 M⊙ • Characteristics: high gravity, high density

1.1 Basic information

1.2 Formation

• Medium- or low-mass star evolution (M6M⊙):

– Main Sequence (MS) – Subgiant – Red-Giant (RG) – Horizontal Branch (HB) – Asymptotic Giant Branch

(AGB) – Red Super-Giant (RSG) – Planetary Nebula (PN) – White Dwarf: M1.4M⊙ Chandrasekhar mass limit Li & Xiao (2012)

• Inside White Dwarf: – Core: Ionized plasma

with degenerate electron pressure

– Atmosphere: He/H

– Element settling due to high gravity

• H-R diagram of WD L=4R2T4; R=constant

logL=A+4logT

Cooling sequence Li & Xiao (2012)

1.3 Scientific importance

• Physics laboratory under extreme conditions – Plasma neutrino

– Axion

• Clues to the evolution of the medium- and low-mass stars (including the Sun)

• Constraints to the mass loss and angular momentum of the AGB and post-AGB stages

• Limits to the ages of the Galaxy and the Universe

• Open questions – Stellar mass and He/H envelop mass

– Composition of the core

– Rotation and differential rotation

– Cooling and crystallization

– Gravitational settling and turbulent convection

– Element diffusion

– Neutrino radiation in the stellar evolution

– Gravitational wave radiation in the WD binary

– Fate of the planets

……

2. Stellar pulsations and Asteroseismology

• Stellar pulsations

• What is asteroseismology?

• Asteroseismology on H-R diagram

2.1 Stellar pulsations

• Stellar pulsations: luminosity of the star is changing with the time

periodically caused by the pulsations • Pulsation mode： • p-mode: pressure force provides restoring force e.g. pulsations in the sun • g-mode: gravity is the dominant restoring force e.g. pulsations in white dwarfs

ξnlm(r,θ,φ,t)= ξnl(r)Ylm(θ,φ)e-iωnlmt

ξ— radial displacement; r — radial coordinate;

θ— colatitude; φ— longtitude;

n— radial order, the number of nodes;

l — angular degree, horizontal wavenumber;

m— azimuthal degree, projection of l onto equator.

(l,m)=(36,24) (l,m)=(2,1)

(l=2,m=1) (l=5,m=3)

Light curves of θ2 Tauri

Fourier transform of SOHO data of the sun

2.2 What is asteroseismology?

• Definitions:

– the study of normal-mode pulsations of stars that display a large number of simultaneously excited modes (Brown & Gilliland 1994)

– the field probing the internal structure of stars whose pulsations consist of many eigenmodes (Unno et al. 1989)

• Why we need asteroseismology?

To understand the interiors of the stars

• Uncertainty at the Stellar Evolution Theory:

nonlinear hydrodynamics

movement of chemical elements

convective zone and overshooting

amount of material burned in the core

entropy distribution

turbulence

life span

→ Knowledge about stellar interior: poor

• The stellar structure and evolution theory:

not well tested

Reason:

A standard stellar model requires:

mass, age, initial chemical composition,

convection process, MLT α=L/HP

Observables:

Teff and L* (if D known)

taken

• Asteroseismology is a drilling tool of the stellar interiors

Principle: by studying the eigen modes, to understand the inner structures

Methodology: by detecting and interpreting the frequency spectrum, to scan the internal structure

The only way existing to study the stellar interior

2.3 Asteroseismology on H-R diagram

3. Asteroseismology of white dwarf stars

• Pulsations of white dwarf stars

• Seismic diagnostic in white dwarfs

3.1 Pulsations of white dwarfs

• Classification

• PNNV (Planetary Nebulae Nuclei Variables) and DOV pulsators

– PNNV: central stars PG1159 spectral type;

He,C,O; PN, ongoing mass-loss

DOV: no PN , ongoing mass-loss

– Teff: 170 kK – 80 kK; log g:[6 -8]

Periods: ~3000 s - ~400 s, g-modes

Instability: κ-mechanism C,O

Pulsators and non-pulsators mixed

• DBVs: Helium white dwarfs

– Teff: 25kK – 20 kK (depends on H:He)

– Instability: κ-mechanism of He

Diffusion equilibrium not reached

– Layered composition: He/He-C-O in envelope

He-C-O/C-O envelope – core

C/O in the core

– Signature of core chemical composition and profile in the period distribution?

• DAVs (ZZ Ceti): Discovery in 1968 by A.U. Landolt – H envelope, 143 pulsators (>70 from SLOAN)

– Periods: 70 s – 1500 s

– Diffusion equilibrium almost achieved:

C/O core, He layer, H envelope

– Instability: κ-mechanism H in hot DAV +

convective driving in cool DAV

– Teff: ~12500 K ~11000 K; pure?

– Core composition, M, H mass fraction, rotation

– DA models, cosmochronology

3.2 Seismic diagnostic in white dwarfs

• If a star is rotating, rotation will lead to the frequency splitting

• In the asymptotic approximation, the frequency splitting due to rotation is (Brickhill 1975)

where l,n,m is the frequency with indices l, n, m

is the rotation frequency of white dwarf

• A frequency with l = 1 will be splitted as 3 ones and called a triplet

• A frequency with l = 2 will be splitted as 5 ones and called a quintuplet

• According to the asymptotic theory of g-mode, an expression of periods of a mode with l and n (Unno et al. 1979; Tassoul 1980) is,

in which N is the Brunt-Väisälä frequency, and R is the stellar radius

• For a white dwarf, the right integral is approximately invariable in the restricted temperature range covered by the ZZ Ceti instability strip

• Pulsation periods of different modes with the same l and two adjacent n should have an uniform period spacing

• △P(1)/ △P(2) ∼ √3 between the period spacing of different modes with l = 1 and with l = 2

• Stratification: deviation from uniform period

spacing, mode trapping

reflexion of waves with nodes at transition zones → fractional mass above transition zones

For the PG1159 star RXJ 2117+3412 (Vauclair et al. 2002)

4. Case study

4.1 For PG0122+2000

• Introduction:

—A pulsating star between the central star of planetary nebulae and white dwarfs

—Teff=80 000±4000K, logg=7.5±0.5

—Lneutrino/Lphoton=2.5, if M=0.66M⊙;

Lneutrino/Lphoton=0.1, if M=0.586M⊙ (PG1159-035)

—Scattering processes: plasmaneutrino, Bremsstrahlung neutrino, photonneutrino emission

(I) Asteroseismology

• Mass determination: period spacing;

Mode identification l (non-radial g-mode)

• Observation history:

—Discovery in 1986;

—reobserved in 1986;

—single-site, in 1990;

—WET, in 1996;

—campaign, in 1999

• Problem: ΔP=16/21 s ? → M=0.75/0.68 M⊙

Reason: too few modes detected

• China-France-USA-Korea network for WD

• Born: in 1994

• Telescopes: 2-meter class

• Photometry: CCD camera;

4-channel photoelectric photometer

• Frequency: ~once a year

• Objects: >10

• PG0122+200: 2001, 2002 target

• Observations in 2001

• Observations in October of 2002

• Light curves in October of 2001

• Light curves in December of 2001

• Light curves in 2002

• FT in 2001, 2002

7 triplets + 2 single modes

Frequency triplets

—Rotation rate: P=1.55 days

—Magnetic field:

≤a few 103 G

—ΔP=22.9 s

→ M=0.59 ± 0.02 M⊙

As Teff=80 000±4000 K

log g=7.5±0.5

→ log(L/L⊙)=1.3±0.5;

→ D≈0.7 (+1.0,-0.4) kpc

→ Lneutrino/Lphoton=1.6 ± 0.2

Mode trapping → Helium mass：-6.0 ≤ log(qy) ≤ -5.3

(Fu et al.2007,A&A,467,237-248)

Cited by “Pulsating white dwarfs and precision asteroseismology” (2008, Annual review A&A)

ΔP

(II) Numerical models

• Paper: Córsico et al. 2007,A&A,475,619

• New generation evolutionary models:

M=1-3.75M⊙ at ZAMS

post-AGB phase followed through the very late thermal pulse and the resulting born-again episode

Remnant mass: 0.530-0.741 M⊙

• Compute l=1 g-mode adiabatic pulsation periods

• 3000 models calculated

Best-fit model:

χ2=Σmin(Π0-Πk)2/n

Teff [kK]

• Comparison with the observed periods: δ∏=0.88 s

Results:

(III) Period and Amplitude Changes

Light curves in 2005

Light curves in 2008

FT of light curves in 2005

FT of light curves in 2008: a new f= 938.767 µHz

Period changes:

the triplets of 2224 µHz

Amplitude changes:

the triplets of 2224 µHz

Period changes:

the triplets of 2493 µHz

Amplitude changes:

the triplets of 2493 µHz

Period and amplitude changes： 2973 µHz，m=+1

Polynomial fit to 2497 µHz：τ=[(1/f)(df/dt)]-1=5.4×104 yr Sine function fit to the residuals：195 days, 0.14 µHz

• Theoretical prediction：(Córsico et al. 2007)

Time scale of period changes:

τ=8.0×106 yr

• From observations：

τ=5.4×104 yr

• Conclusion：

can not be caused by the cooling due to the neutrino loss

• Possible mechanism：

resonant coupling induced by the rotation

(Vauclair, G., Fu, J.N., et al. 2011, A&A, 528, A5)

(IV) Differential rotation of PG 0122+200

• Paper: Corsico et al. 2011, MNRAS, 418, 2519

• Subject: Probing the internal rotation of

PG 0122+200 with asteroseismology

• Employing a state-of-the-art model and assessing the expected frequency splittings induced by rotation

• Comparing the theoretical frequency separations with the observed ones assuming different types of internal rotation profiles

• Conclusion: the frequency splittings of the rotational

multiplets are compatible with a rotation profile

the central regions are spinning about 2.4 times faster than the stellar surface

• The first detection of differential rotation of white dwarf stars

• Providing hints of the angular-momentum loss problem during stellar evolution to the white dwarf stage!

4.2 For HS 0507+0434B

Paper: Fu et al. 2013, MNRAS, 429, 1585-1595 Introduction: —HS 0507+0434B: Teff=12 290±186 K, logg=8.24±0.05 in the middle of the DAV Instability Strip —HS 0507+0434A: a 21 550 ±318 K DA white dwarf —Both members of the pair must have been

formed at the same time. One additional constraint is provided on the modeling of

their evolution

Observation history:

—discovered to be a DAV in 1996

(Jordan et al. 1998)

—single-site observations in 1997 (Kotak et al. 2002)

—single-site observations in 2000

(Handler et al. 2002)

—bi-site (XL+BOAO) in 2007

(Fu et al. 2013)

—observations in Dec. 2009-Jan. 2010

(Fu et al. 2013)

Fourier spectra of the 5 seasons 1996→

1997→

2000→

2007→

2009-2010→

• Observations in 2009-2010:

– Single site (XL), Dec. 13-18, 2009;

– Single site (LJ), Dec. 25-31, 2009;

– Bi-site (XL+SPM), Jan. 12-17, 2010;

– Single site (LJ), Jan. 24-31, 2010.

• FT in 2009-2010

From the triplets: —Rotation rate: P=1.61±0.26 days Then: —ΔP=49.63 s —M=0.675 M⊙, L/L⊙=3.5×10-3

—MH=10-8.5 M*

— The amplitudes of the

modes vary on week

time scale

— The “Pulsation power”

is time dependent

4.3 For WD0246+326

—WD 0246+326: a ZZ Ceti Star —Teff: 11940 ±180 K Log g: 8.21±0.05 (Gianninas et al. 2011)

—Teff: 11290 ±200 K Log g: 8.08±0.05 (Bergeron et al. 1995b)

—locates close to the red edge of the instability strip —Discovered by Fontaine et al. 2001

Fourier Spectrum

• 11 periods extracted • 2 triplets and 1 doublelet were found • mode identification: l=1,2 • triplets: average δf=1.54 ±0.19 μHz →rotational period: 3.75 ±0.42 days • Average period spacing: ΔP=30.28 s

Linear least-square fit of l=1 modes with ΔP=30.28s

825,794, 767s of l=1 mode 887.2, 847.8 of l=2 mode 953.0,618.8 of l=? mode were used in fitting

Using the standard deviation to indentify the best modes

Constraints from the Theoretical Models

WDEC program

Parameters of the Large Grid

Parameters of the Detailed Grid

The Best fit model

Mode identification from the best fit mode

Results

• Time-series light curves in 2014

11 independent pulsation modes

• Triplets: ℓ=1 & 2 g-modes split by rotation with an

average period spacing of 30.28 s

• An average rotational splitting of δf=1.54±0.19 μHz

an average rotation rate of 3.75 ±0.42 days.

• Theoretical periods vs observed periods: standard deviation

One best fit model with 0.95 M⊙ & 11700 K

An ultramassive DAV

• Paper: submitted to MNRAS

• BPM 37093: a white dwarf with core crystallization

M=1.1M⊙

(Kanaan, et al, 2005, A&A, 432, 219)

A diamond star

5. Summary

• Asteroseismology : a powerful tool to probe the interior of the stars • White dwarfs: simple structure • Pulsating white dwarfs: ideal laboratories with asteroseismology

– Derive stellar parameters precisely – Study the stellar evolution of late stages – Study the Period/Amplitude changes – Rotation & Angular momentum evolution – Magnetic field of white dwarfs – Constrain mass loss during stellar evolution……

Questions

1. How to make good enough observations for asteroseismology of White dwarfs?

2. What can multiplets of frequency tell us? How to get the multiplets well observed?