Shaken, Not Stirred: White Dwarf Cocktails

Frank Timmes School of Earth and Space Exploration

Arizona State University

LSU 27sep2018

Why are white dwarfs important?

The Sun will become one Age of the universeProbe of strong equivalence principle Progenitors of supernovaeElement factoriesKinetic energy sources for galaxiesRecords the nuclear physics of a star’s lifeProbes of electron degenerate material

Sirius, only ~8.60 ± 0.04 light-years from Earth, is the fifth closest stellar system.

The Egyptians used Sirius, the brightest star in the sky and which rose with the Sun in early July when the Nile was in flood, to mark the first day of a New Year.

Credit: NASA, ESA, G. Bacon

In 1844 Friedrich Bessel deduced from changes in the orbit that Sirius had an unseen companion. In 1862, Alvan Clark first observed the faint companion during testing of the new 18.5-inch refractor telescope in the Dearborn Observatory at Northwestern University.

A

A

A

A

B

B

B

B

1950

1970

1990

19902010

2010

2000

2000

Period = 50.1 yr

Semi-major axis = 19.8 AU

Eccentricity = 0.59

2020

2020

2030

Tommaso Nicolò, 2016

Strong Equivalence Principlesays accelerations should be the same.

Alternative theories of gravitymostly say the accelerations should be different

The outer white dwarf’sgravity accelerates the pulsarand inner white dwarf.

Microsecond accurate measurementsof the radio pulse arrival times showno difference between the accelerationsto 3 parts per million.

327-day orbit

470 lt-s

118 lt-s

center of mass

Hot, 0.20 M⊙ white dwarf

Cool, 0.41 M⊙white dwarf

MPSR = 1.44 M⊙

radio pulsar

1.6 day orbit

2 lt-s

14 lt-s

Archibald et al 2018

39.3°

4200 lt-yr

Does Strong Gravity Change How Things Fall?

The Triple System PSR J0337+1715

Let’s make a white dwarf.

Modules for Experiments in Stellar Astrophysics

MESA solves the 1D fully coupled structure, mixing, and composition equations governing stellar evolution.

MESA : ~ 300 Registered Users, Sep 2018

South PacificOcean

South AtlanticOcean

North AtlanticOcean

North PacificOcean

IndianOcean

MESA : ~ 900 Registered Users, Sep 2018

Open-Knowledge

Open-Science

Open- Source

2.0 M⊙

L ~ 20 L⊙

1 M⊙

T ~ 2 x 107 K10

1

10-2

ρ(g/cc)

surface T ~ 8000 K

hydrogen

hydrogen burning

P P NP e+ ν+ + +1010 years

P PP

NPP

NPPNNP+ + +

106 years

PNPP

NP+ +6 sec

γ-ray

12C

13N

13C 14N

15O

15N

5.0 Mev

2.0 MeV

7.5 MeV

7.4 MeV1.2 MeV

2.7 MeV

10 min

2 min(p,γ)

(p,γ)

(p,γ)(,e+ν)

(,e+ν)

(p,α)

2.0 M⊙

0.4 M⊙

0.1 M⊙

105 T ~ 2 x 108 K

103

1

10-6

ρ(g/cc)

h-burning

hydrogen

helium burning

helium

L ~ 50 L⊙

surface T ~ 4000 K

0.11010011

10

100M

ass

Frac

tion

(%)

Helium Mass Fraction (%)

12C

12C16O

16O

Yα = −1

2Y3

α R3α − Yα Y12 Rcαγ

Y12 =1

6Y3

α R3α − Yα Y12 Rcαγ

Y16 = Yα Y12 Rcαγ

12C(α, γ)16O3α →12 C

16O(α, γ)20Ne

DeBoer et al 2017

0.8 M⊙

0.61 M⊙

0.62 M⊙

0.6 M⊙

106

1

ρ(g/cc)

carbon-oxygen core

L ~ 5000 L⊙

surface T ~ 3000 K

h-burning

hydrogen

he-burning

T ~ 1 x 108 K

10-6

Credit:Travis Metcalfe and Ruth Bazinet

Surface Temperature (K)

Color

Hot Cool

Blue Red

Dim

Bright

Lum

inos

ity (L

⊙)

106

103

10-1

1

Yellow

Warm50,000 6000 3000

2 M⊙

Main Sequence

Core HDepletion

Core HeDepletion

Lose H and HeLayers

0.6 M⊙ Carbon-OxygenWhite Dwarfin ~1 billion years

2.0 M⊙

L ~ 10 L⊙

1 M⊙

T ~ 2 x 107 K10

1

10-2

ρ(g/cc)

surface T ~ 8000 K

hydrogen

hydrogen burning

2.0 M⊙

0.4 M⊙

0.1 M⊙

105 T ~ 2 x 108 K

103

1

10-6

ρ(g/cc)

h-burning

hydrogen

helium burning

helium

L ~ 50 L⊙

surface T ~ 4000 K

0.8 M⊙

0.61 M⊙

0.62 M⊙

0.6 M⊙

106

1

ρ(g/cc)

carbon-oxygen core

L ~ 5000 L⊙

surface T ~ 3000 K

h-burning

hydrogen

he-burning

T ~ 1 x 108 K

10-6

0

1

2

3

ρ(1

06g

cm−

3)

0

2

4

6

T(1

07K

)

0.00 0.25 0.50 0.75 1.00Mr/M

0.00

0.25

0.50

0.75

1.00

Mas

sFra

ctio

n

0.00 0.25 0.50 0.75 1.00Mr/M

0.00

0.25

0.50

0.75

1.00

Lr/L

Oxygen

Carbon

Helium

An Evolution Model Aiming At KIC 08626021

Timmes et al 2018

M =0.59 M⊙ L = 0.137 L⊙ Teff ~ 29,000 K

KIC 8626021

Constellation: Cygnus

distance~ 1000 ly

Let’s shake a white dwarf.

Lum

ino

sity

Frequency

Like a sound wave resonating in an organ pipe, sound waves can resonate inside a star. By measuring these wave frequencies, we learn about the star’s internal structure.

We see these oscillations as subtle, rythmic changes in the star’s luminosity.

Vibrations are generated by ionization and turbulence near the star’s surface.

The vibrations penetrate into the interior, setting up resonances at frequencies dependent on density, temperature, and abundance profiles.

Resonant frequencies can vary from one every few minutes in Sun-like stars to one every few hundred days in red giants.

GYRE solves the system of equations governing small periodic perturbations to an equilibrium stellar state.

ξr(r, θ, ϕ, t) = Re [ 4π ξr(r) Ymℓ (θ, ϕ) exp(−iωt)]

ξh(r, θ, ϕ, t) = Re [ 4π ξh(r)r∇h Ymℓ (θ, ϕ) exp(−iωt)]

f′�(r, θ, ϕ, t) = Re [ 4π f′�(r) Ymℓ (θ, ϕ) exp(−iωt)]

Solutions take the form

Solutions which satisfy the boundary conditions only occur for discrete values of the frequency ω - these are the eigenfrequencies of the star.

Credit: Stéphane Charpinet

Cocktails to fit a white dwarf model’s eigenfrequencies to those derived from the Kepler mission’s photometric data:

1) Evolve a model from the main sequence to a white dwarf with the observed surface properties

2) Evolve a hot white dwarf to the observed surface properties

3) Flexible templates of the interior profiles

Core Oxygen

Mass

Ab

un

dan

ce

t1 Oxygen

t1

2 ∆t1

2 ∆t2

t2

t2 Oxygen

Envelope Oxygen

Oxy

gen

Mas

s Fr

acti

on

1

0.8

0.6

0.4

0.2

00 1 2

log ( 1 - M(r)/M )3

Template models

Giammichelle et al 2017

Template model for KIC 08626021

Giammichelle et al 2018

0 0.15

16O

Wow!

12C

0.30 0.45

Mass (M⊙)

0

0.2

0.4

0.6

0.8

1.0M

ass

Frac

tio

n

0

1

2

3

ρ(1

06g

cm−

3)

0

2

4

6

T(1

07K

)

original

relaxed

0.00 0.25 0.50 0.75 1.00Mr/M

0.00

0.25

0.50

0.75

1.00

Mas

sFra

ctio

n

XHe

XC

XO

0.00 0.25 0.50 0.75 1.00Mr/M

0.00

0.25

0.50

0.75

1.00

Lr/L Template model assumption

Evolutionary model

L = 0.137 L⊙ Teff ~ 29,000 K

Timmes et al 2018

2000 4000 6000 8000νorig (µHz)

−40

−20

0

20

40

60

80

ν rel

ax−

ν ori

g(µ

Hz)

-8

-5

-2

-16

-13

-10

-7

-4ℓ = 1

ℓ = 2

Range of Kepler observations

g-modes:

Timmes et al 2018

We find the low order g-mode frequencies differ by up to ≃ 70 μHz over the range of Kepler observations for KIC 08626021.

By neglecting the proper thermal structure of the star (e.g., accounting for plasmon 𝜈 losses), model frequencies calculated by assuming an Lr∝Mr profile may have

uncorrected, effectively random errors at ≃ tens of μHz.

Extrapolating known uncertainties, a 30 μHz error causes a ~12% error in the white dwarf mass, a ~9% error in its radius, and a ~3% error in its central oxygen abundance.

0.0

0.2

0.4

0.6

0.8ϵ ν

[erg

g−1s−

1]

0.0 0.2 0.4 0.6 0.8 1.0Mr/M

0.00

0.25

0.50

0.75

1.00

Lr/L

Teff = 29765K

Teff = 25000K

Teff = 20000K

Teff = 12000K

Evolution of the luminosity profiles show Lr∝Mr does

not occur until Teff ≲ 20, 000 K

Timmes et al 2018

Questions and Discussion

SPIDER

Starlib

THE ASTROPHYSICAL JOURNAL

isotopesproject100

S I M O N S F O U N D A T I O N

SCORPION

O

PVSG

Ceph

Mira

SR

RG

1 M⊙

2 M⊙

3 M⊙

4 M⊙

7 M⊙

12 M⊙

20 M⊙

Solar-like

DAV

DBV

p-mode

g-mode

DOV

sdBV

SPB

RR Lyr

δ Sct + roApγ Dor

β Cep

Spectral typeB A F G K M6

5

4

3

2

1

log

[lu

min

osi

ty (L

⊙)]

0

5.0 4.8 4.6 4.4log [effective temperature (K)]

4.2 4.0 3.8 3.6 3.4

-1

-2

⊙

Critical community-driven software and data for new science.

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Stars:

Pulsations:

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Support:

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Nuclear:

WeakLib

Cyberhub:

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Nuclear:

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Support:

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GCE:

Support:

JINABaseMESA-

Test

3D hydro:PhantomIsochrones:

GYRE

N-Body:

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Spectra:CMFGENSpectra:

CLOUDY

N-body:

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3D hydro:

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Education:

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