Post on 11-Sep-2019
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
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
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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
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
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.
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
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
⊙
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