asteroseismology of compact stars
TRANSCRIPT
Asteroseismology of compact stars
Steven Kawaler!Iowa* State University
�1
* Boyhood home of Herbert Hoover & site of his Presidential Library: West Branch, Iowa
Asteroseismology of compact stars
Steven Kawaler!Iowa* State University
�1
* Boyhood home of Herbert Hoover & site of his Presidential Library: West Branch, Iowa
“Hoover, Democratic propaganda to the contrary, did not cause the Great Depression nor was he indifferent to his people's sufferings. A brilliant, decent man, he was absolutely the unluckiest President.”
•Overview of evolution!•White dwarf pulsation classes & selected results of
boutique analyses!•g-mode period spacings and masses!•diffusion and layer thickness!• rotation rates and ‘inversion’!
•white dwarf rotation and prior angular momentum evolution!•Hot subdwarf (sdB) - apologies for tight focus on rotation!!
• “wholesale” rotation rate determinations!•connecting sdB rotation with WD rotation!
•Future prospects (space-based) for verifying asteroseismic rotation measurements
�2
This afternoon’s trajectory
Pulsating stars in the HR diagram
diagram courtesy J. Christensen-Dalsgaard �3
Pulsating stars in the HR diagram
diagram courtesy J. Christensen-Dalsgaard �3
• White Dwarf pulsators!
• DB (He - surface)!
• DA (H - surface)!
• DOZQ (He/C/O surface)
• sdB (horizontal branch) pulsators!
• p-mode pulsators (hotter)!
• g-mode pulsators (cooler)
�4diagram courtesy J. Christensen-Dalsgaard
Post-giant stars in the HR diagram
evolutionary channel to the WD regime �5
3 Mo!(yields 0.75Mo WD)
MS
evolutionary channel to the WD regime �5
3 Mo!(yields 0.75Mo WD)
RGBHB
MS
evolutionary channel to the WD regime �5
3 Mo!(yields 0.75Mo WD)
AGB
RGBHB
MS
evolutionary channel to the WD regime �5
3 Mo!(yields 0.75Mo WD)
AGB
TP-AGB
RGBHB
MS
evolutionary channel to the WD regime �5
3 Mo!(yields 0.75Mo WD)
AGB
TP-AGB
RGBHB
MS
To WD Cooling Track
�6WD Spectral types and chemical evolution
�7mixed modes in giants - a preview to compact pulsators
red clump
secondary clump
Bedding et al. 2011
Bedding et al. 2011
�8mixed modes in giants - a preview to compact pulsators
red clump
secondary clump
shell burning, degenerate He core (WD)
non-degen, He burning core (sdB)
• White Dwarf pulsators!
• DB (He - surface)!
• DA (H - surface)!
• DOZQ (He/C/O surface)
• sdB (horizontal branch) pulsators!
• p-mode pulsators (hotter)!
• g-mode pulsators (cooler)
�9diagram courtesy J. Christensen-Dalsgaard
Post-giant stars in the HR diagram
• spacing depends on l
�10
g-modes: ~ equally spaced in period
n n+1 n+2 n+3 n+4n+5 n+6n-1n-2
......Period
n n+1 n+2 n+3n+4n+5 n+6n-1n-2
...
......
...
Period
l=1
l=2
⇧nl
= n⇧
opl(l + 1)
; ⇧o
= 2⇡2
"Zb
a
N
rdr
#�1
• period of ‘radial fundamental’ ~ tff ~ sound crossing time
�11
Pulsation periods
p-modes g-modes
Periods P < tff P > tff
restoring force pressure buoyancyasymptotic behavior ν ∝ νo × n P ∝ Πo × n
examplesCepheids
solar-like pulsators red giants
white dwarfs sdBs
�12PG 1159-035: a g-mode pulsator
P P-390390 0424 34 ?451 61 3 x 20.3495 105 5 x 21.0516 126 6 x 21.0539 149 7 x 21.3645 255 12 x 21.3832 442 21 x 21.0
�13PG 1159-035: a g-mode pulsator
Corsico et al. 2008 [WET]
�14g-mode period spacing -> mass
Corsico et al. 2007
GW Vir stars DBV stars
Bradley & Winget 1994
Bedding et al. 2011
�15mixed modes in giants - a preview to compact pulsators
red clump
secondary clump
shell burning, degenerate He core (WD)
non-degen, He burning core (sdB)
• multiple triplets!
• 3.3 µHz splitting!
• rotation period of 1.75 days
�16
a DB pulsator in the Kepler field Østensen et al. 2011
• asymptotic g-mode pulsator !
• 36.3s period spacing!
• M ~ 0.56 Msun
�17
a DB pulsator in the Kepler field Østensen et al. 2011
150
200
250
300
350
400
0 8 16 24 32 40
Perio
d [s
]
Period modulo 36.3 s
•Best fit mass !• 0.570 Msun!
•Best fit Teff!• 29,200K!• much hotter than
spectroscopic value
�18
DB seismic modeling Bischoff-Kim & Østensen 2011
�19WD Spectral types and chemical evolution
Surface Core
diffusive separation of He from C/O (proposed in 1995 by Dehner)
�21
Period Spacing Variations
Modes ‘trapped’ by!composition
transition zone
Manifest as modes that fall below mean
period spacing
• Best fit mass !• 0.570 Msun!
• C/O core size!• 0.36 Msun!
• Central O abund.!• 0.6 - 0.65
�22
DB seismic modeling Bischoff-Kim & Østensen 2011
• Best fit mass !• 0.570 Msun!
• C/O core size!• 0.36 Msun!
• Central O abund.!• 0.6 - 0.65
�23
a DB pulsator in the Kepler field Østensen et al. 2011
150
200
250
300
350
400
0 8 16 24 32 40
Untitled 1
Perio
d [s
]
Period modulo 36.3 s
• Best fit mass !• 0.570 Msun!
• C/O core size!• 0.36 Msun!
• Central O abund.!• 0.6 - 0.65
�23
a DB pulsator in the Kepler field Østensen et al. 2011
150
200
250
300
350
400
0 8 16 24 32 40
Untitled 1
Perio
d [s
]
Period modulo 36.3 s
150
200
250
300
350
400
0 8 16 24 32 40
• Best fit mass !• 0.570 Msun!
• C/O core size!• 0.36 Msun!
• Central O abund.!• 0.6 - 0.65
DB seismic modeling Bischoff-Kim & Østensen 2011
Surface Core
diffusive separation of He from C/O (proposed in 1995 by Dehner)
�26
Rotational Splitting in Kepler DB pulsator
•Δν = 3.3 μHz!• Prot ~ 1.75 days!• implied vrot= 0.4 km/s
�26
Rotational Splitting in Kepler DB pulsator
•Δν = 3.3 μHz!• Prot ~ 1.75 days!• implied vrot= 0.4 km/s
�26
Rotational Splitting in Kepler DB pulsator
•Δν = 3.3 μHz!• Prot ~ 1.75 days!• implied vrot= 0.4 km/s
Star Prot [h] vrot [km/s] Type M/Mo v sin iEC 20058 2 8.73 DBV 0.54 Sullivan
KIC 8626021 41 0.43 DBV 0.56 OstensenGD 358 29 0.60 DBV! 0.61
HL Tau 76 53 0.33 C-ZZ Ceti 0.55R548 37 0.47 H-ZZ Ceti 0.60
HS0507 41 0.43 C-ZZ Ceti 0.6G29-38 32 0.55 C-ZZ Ceti 0.6 45 km/s Koester! GD 165 50 0.35 H-ZZ Ceti 0.63 29 km/s Koester
KUV11370+4222 5.56 3.14 C-ZZ Ceti 0.63 *G185-32 15 1.16 H-ZZ Ceti 0.64GD 154 55 0.32 C-ZZ Ceti 0.70L19-2 13 1.34 H-ZZ Ceti 0.71 38 km/s Koester
G226-29 9 1.94 H-ZZ Ceti 0.78J1612+0830 0.93 18.77 ZZ Ceti 0.8 *J1916+3936 18.8 0.93 ZZ Ceti 0.82 *J1711+6541 16.4 1.06 ZZ Ceti 1.00 *
PG 0122 37 0.66 GW Vir 0.56 Corsico NGC 1501 28 0.87 GW Vir 0.56PG 1707 16 1.53 GW Vir 0.56RX J2117 28 0.87 GW VIr 0.57PG 1159 33 0.74 GW Vir 0.60PG 2131 5 4.89 GW Vir 0.60
some asteroseismic WD rotation
rates
�27
Mean = 26 +/- 20 hours
These values represent decades of ground-based effort
Star Prot [h] vrot [km/s] Type M/Mo v sin iEC 20058 2 8.73 DBV 0.54 Sullivan
KIC 8626021 41 0.43 DBV 0.56 OstensenGD 358 29 0.60 DBV! 0.61
HL Tau 76 53 0.33 C-ZZ Ceti 0.55R548 37 0.47 H-ZZ Ceti 0.60
HS0507 41 0.43 C-ZZ Ceti 0.6G29-38 32 0.55 C-ZZ Ceti 0.6 45 km/s Koester! GD 165 50 0.35 H-ZZ Ceti 0.63 29 km/s Koester
KUV11370+4222 5.56 3.14 C-ZZ Ceti 0.63 *G185-32 15 1.16 H-ZZ Ceti 0.64GD 154 55 0.32 C-ZZ Ceti 0.70L19-2 13 1.34 H-ZZ Ceti 0.71 38 km/s Koester
G226-29 9 1.94 H-ZZ Ceti 0.78J1612+0830 0.93 18.77 ZZ Ceti 0.8 *J1916+3936 18.8 0.93 ZZ Ceti 0.82 *J1711+6541 16.4 1.06 ZZ Ceti 1.00 *
PG 0122 37 0.66 GW Vir 0.56 Corsico NGC 1501 28 0.87 GW Vir 0.56PG 1707 16 1.53 GW Vir 0.56RX J2117 28 0.87 GW VIr 0.57PG 1159 33 0.74 GW Vir 0.60PG 2131 5 4.89 GW Vir 0.60
some asteroseismic WD rotation
rates
�28
Mean = 26 +/- 18 hours
These values represent decades of ground-based effort
�29
IAU Symp. 215: Stellar Rotation page 12
Trouble enroute to paradise?
Koester et al. (‘98) Seismology Star v sin i (km/s) vrot (km/s)
L19-2 38 +/- 3 0.55 +/- 0.05
GD165 29 +/- 7 0.50 +/- 0.05
G29-38 45 +/- 5 0.55 +/- 0.05
0.35
1.34
Koester & Kompe (2007): ! Broadening caused by ! velocity fields of the pulsations
Star Prot [h] vrot [km/s] Type M/Mo v sin iEC 20058 2 8.73 DBV 0.54 Sullivan
KIC 8626021 41 0.43 DBV 0.56 OstensenGD 358 29 0.60 DBV! 0.61
HL Tau 76 53 0.33 C-ZZ Ceti 0.55R548 37 0.47 H-ZZ Ceti 0.60
HS0507 41 0.43 C-ZZ Ceti 0.6G29-38 32 0.55 C-ZZ Ceti 0.6 45 km/s Koester! GD 165 50 0.35 H-ZZ Ceti 0.63 29 km/s Koester
KUV11370+4222 5.56 3.14 C-ZZ Ceti 0.63 *G185-32 15 1.16 H-ZZ Ceti 0.64GD 154 55 0.32 C-ZZ Ceti 0.70L19-2 13 1.34 H-ZZ Ceti 0.71 38 km/s Koester
G226-29 9 1.94 H-ZZ Ceti 0.78J1612+0830 0.93 18.77 ZZ Ceti 0.8 *J1916+3936 18.8 0.93 ZZ Ceti 0.82 *J1711+6541 16.4 1.06 ZZ Ceti 1.00 *
PG 0122 37 0.66 GW Vir 0.56 Corsico NGC 1501 28 0.87 GW Vir 0.56PG 1707 16 1.53 GW Vir 0.56RX J2117 28 0.87 GW VIr 0.57PG 1159 33 0.74 GW Vir 0.60PG 2131 5 4.89 GW Vir 0.60
some asteroseismic WD rotation
rates
�30
These values represent decades of ground-based effort
Mean = 26 +/- 18 hours
Star Prot [h] vrot [km/s] Type M/Mo v sin iEC 20058 2 8.73 DBV 0.54 Sullivan
KIC 8626021 41 0.43 DBV 0.56 OstensenGD 358 29 0.60 DBV! 0.61
HL Tau 76 53 0.33 C-ZZ Ceti 0.55R548 37 0.47 H-ZZ Ceti 0.60
HS0507 41 0.43 C-ZZ Ceti 0.6G29-38 32 0.55 C-ZZ Ceti 0.6 45 km/s Koester! GD 165 50 0.35 H-ZZ Ceti 0.63 29 km/s Koester
KUV11370+4222 5.56 3.14 C-ZZ Ceti 0.63 *G185-32 15 1.16 H-ZZ Ceti 0.64GD 154 55 0.32 C-ZZ Ceti 0.70L19-2 13 1.34 H-ZZ Ceti 0.71 38 km/s Koester
G226-29 9 1.94 H-ZZ Ceti 0.78J1612+0830 0.93 18.77 ZZ Ceti 0.8 *J1916+3936 18.8 0.93 ZZ Ceti 0.82 *J1711+6541 16.4 1.06 ZZ Ceti 1.00 *
PG 0122 37 0.66 GW Vir 0.56 Corsico NGC 1501 28 0.87 GW Vir 0.56PG 1707 16 1.53 GW Vir 0.56RX J2117 28 0.87 GW VIr 0.57PG 1159 33 0.74 GW Vir 0.60PG 2131 5 4.89 GW Vir 0.60
some asteroseismic WD rotation
rates
�31
Mean = 26 +/- 17 hours
These values represent decades of ground-based effort
�32
Rota
tion
Perio
d [h
ours
]
0
15
30
45
60
0.50 0.60 0.70 0.80 0.90 1.00
Period vs. mass
•A: rotation kernels suggest that it’s a ‘global average’ weighted (heavily) by the envelope:
�33
Q: what parts of the DA white dwarf are rotational splittings sampling?
•A: rotation kernels suggest that it’s a ‘global average’ weighted (heavily) by the envelope:
�34
Q: what parts of the DB white dwarf are rotational splittings sampling?
•A: rotation kernels suggest that it’s a true ‘global average’ with mode trapping effects playing a role
�35
Q: what parts of the GW Vir star are rotational splittings sampling?
•handful of splittings available!•difficult to optimize kernels!•‘regularized’ inversion necessary!•also parametric approach - test classes of rotation curves
and minimize forward-computed splitting differences!•Kawaler, Sekii & Gough (1999): inconclusive results for!
•GD 358 (DBV)!•PG 1159-035 (GW Vir)!
•Charpinet et al (2009): PG 1159!•solid body rotation!
•Corsico et al. (2011): PG 0122!•some differential rotation
�36
rotational inversions?
•pattern of period spacing matches pattern of splitting variation (mode trapping effects both)!
•suggests slightly faster core rotation than envelope
�37
Kawaler, Sekii & Gough (1999): PG 1159
•pattern of period spacing matches pattern of splitting variation (mode trapping effects both)!
•suggests slightly faster core rotation than envelope!•‘regularized’ inversion agrees - small slope
�38
Kawaler, Sekii & Gough (1999): PG 1159
�39
Charpinet et al (2009): PG 1159 (GW Vir)
�40
Charpinet et al (2009): PG 1159 (GW Vir)
�40
Charpinet et al (2009): PG 1159 (GW Vir)
�40
Charpinet et al (2009): PG 1159 (GW Vir)
�40
Charpinet et al (2009): PG 1159 (GW Vir)
�41
Corsico et al. (2011): PG0122•Regularized inversion - core faster than envelope!•Linear rotation curve - similar χ2 as inversion
what to expect for WD rotation
�42
Angular momentum channels to the WD regime �43
3 Mo!(yields 0.75Mo WD)
AGB
TP-AGB
RGBHB
MS
To WD Cooling Track
•Low mass case!•post-MS coupling: Prot ~ 5 hr!•max. coupling: Prot ~ infinity
�44
MS to RGB core rotation to HB/Clump!(Tayer & Pinsonneault 2013)
2.5 Mo
~0.9 Mo
•High mass case!•post-MS coupling: Prot ~ 0.7 hr!•max. coupling: Prot ~ >1000 d
Angular momentum channels to the WD regime!Tayar & Pinsonneault (2013) “style”
�45
M < 1.3 MoM > 1.2 Mo!
M < 2.3 MoM > 2.3 Mo
Main Sequencemagnetic braking, !
slow start!20 days
no dJ/dt,!fast start!20 hours
no dJ/dt,!fast start!20 hours
RGB / He ignition
mass, J loss at RGB tip!5 hours
mass, J loss at RGB tip!
~0.7 hours
no mass loss, !no J loss!0.7 hours
Helium core burning
post-flash!horizontal branch!
50 hours
post-flash!HB / Clump!~ 7 hours
non-degen!ignition, clump!
~0.7 hours
AGB / post-AGB
sudden!dM/dt and dJ/dt at
termination!5 hours
sudden!dM/dt and dJ/dt at
termination!~0.7 hours
sudden!dM/dt and dJ/dt at
termination!~0.07 hours
MS
RGB
HB
�46
M < 1.3 MoM > 1.2 Mo!
M < 2.3 MoM > 2.3 Mo
Main Sequencemagnetic braking, !
slow start!20 days
no dJ/dt,!fast start!20 hours
no dJ/dt,!fast start!20 hours
RGB / He ignition
mass, J loss at RGB tip!5 hours
mass, J loss at RGB tip!
~0.7 hours
no mass loss, !no J loss!0.7 hours
Helium core burning
post-flash!horizontal branch!
50 hours
post-flash!HB / Clump!~ 7 hours
non-degen!ignition, clump!
~0.7 hours
AGB / post-AGB
sudden!dM/dt and dJ/dt at
termination!5 hours
sudden!dM/dt and dJ/dt at
termination!~0.7 hours
sudden!dM/dt and dJ/dt at
termination!~0.07 hours
MS
RGB
HB
AGBTP-
AGB
These are ‘fast’ limits for core rotation - no coupling (aside convection) with envelope
Angular momentum channels to the WD regime!Tayar & Pinsonneault (2013) “style”
WD initial-final mass relation
• from Kalirai (2008, 2013)!
•MOST isolated white dwarfs are in the intermediate case regime
• 2.25 Mo > Minitial > 1.3 Mo
�47
WD initial-final mass relation
• from Kalirai (2008, 2013)!
•MOST isolated white dwarfs are in the intermediate case regime
• 2.25 Mo > Minitial > 1.3 Mo
�47
•conclusion from limiting cases, accounting for MS angular momentum redistribution (and loss) as initial conditions for RGB (to AGB & beyond):!
•core @RGB Tip: !•M < 1.3 Mo - ‘slow’ core (> 5 h)!•M > 1.3 Mo - ‘fast’ core ( > 0.7 h)!
•core @ HB / clump / sdB:!•M < 1.3 Mo - ‘slow’ core (> 50 h)!•M > 1.3 Mo - ‘medium’ core ( 0.7h - 7h lower limit)!
•Core as a White Dwarf!•Mwd < 0.56, P > 5 h!•0.65 > Mwd > 0.56, P > 0.7 h!•Mwd > 0.65 , P > 0.07h
�48
so…what is ‘fast’ for a WD?
�49
Rota
tion
Perio
d [h
ours
]
0
15
30
45
60
0.50 0.60 0.70 0.80 0.90 1.00
Minitial > 2.25Minitial < 1.3
Period vs. mass
•“SLOW ROTATION” (> several hours) means! more / faster coupling on RGB/AGB ! ! ! ! ! ! ! BUT
•any rotation = imperfect coupling on RGB/AGB
�50
what is ‘fast’ for a WD?
• White Dwarf pulsators!
• DB (He - surface)!
• DA (H - surface)!
• DOZQ (He/C/O surface)
• sdB (horizontal branch) pulsators!
• p-mode pulsators (hotter)!
• g-mode pulsators (cooler)
�51diagram courtesy J. Christensen-Dalsgaard
Post-giant stars in the HR diagram
• White Dwarf pulsators!
• DB (He - surface)!
• DA (H - surface)!
• DOZQ (He/C/O surface)
• sdB (horizontal branch) pulsators!
• p-mode pulsators (hotter)!
• g-mode pulsators (cooler)
�51diagram courtesy J. Christensen-Dalsgaard
Post-giant stars in the HR diagram
• White Dwarf pulsators!
• DB (He - surface)!
• DA (H - surface)!
• DOZQ (He/C/O surface)
• sdB (horizontal branch) pulsators!
• p-mode pulsators (hotter)!
• g-mode pulsators (cooler)
�51diagram courtesy J. Christensen-Dalsgaard
Post-giant stars in the HR diagram
• White Dwarf pulsators!
• DB (He - surface)!
• DA (H - surface)!
• DOZQ (He/C/O surface)
• sdB (horizontal branch) pulsators!
• p-mode pulsators (hotter)!
• g-mode pulsators (cooler)
�51diagram courtesy J. Christensen-Dalsgaard
Post-giant stars in the HR diagram
Østensen 2008
red/green = short period purple = long-period
Horizontal Branch Basics
Post helium core flash structure...!our Sun in ~ 5 billion years
HHe
H burning shell (if MH big enough)
convective core
�54
HHe
H burning shell (if MH big enough)
convective core
Charpinet et al. 2002, 2013
Period spacing pattern depends on
layer thickness
�55
what we see
period spacings in sdB stars via KeplerStar ∆P1 ∆P2 ∏o
10670103 251 s 146 s 355 / 3582697388 241 s - 3413527751 - 154 s 3777664467 262 s - 3702991403 247 s 136 s 349 / 33311179657 252 s 136 s 356 / 33311558725 249 s 143 s 352 / 350KPD 1943 243 s - 344
Van Grootel (model) 240 s 139 s 339 / 340
Bedding et al. 2011
�57mixed modes in giants - a preview to compact pulsators
red clump
secondary clump
shell burning, degenerate He core (WD)
non-degen, He burning core (sdB)
sdB / EHB rotation• Kepler pulsating sdB stars show clear signs of rotational splitting!
• Isolated sdB periods range from 23-88 days; median of ~30 d!
• This suggests rather strong coupling.
�58
KIC
�59
Q: what parts of the sdB are rotational splittings sampling?
•A: ‘global average’ weighted (heavily) by area between the convective core & H/He shell
�60
sdB rotation via KeplerKIC Teff log g
Rotation Period![days]
vrot![km/s]
Binary Period ref
11179657 26000 5.14 7.4 1.38 0.40 d Pablo et al. 2012
B4 = 2438324 27100 5.69 9.6 1.06 0.40 d Pablo et al. 2011
2991403 27300 5.43 10.3 0.99 0.44 d Pablo et al. 2012
10139564 31859 5.67 25.6 0.40 - Baran et al. 2012
3527751 27900 5.37 25 0.41 - Reed et al. 2013
11558725 27910 5.41 45 0.23 10.05 d Telting et al. 2012
2697388 23900 5.32 45 0.23 - Baran 2012
10670103 20900 5.11 88 0.12 - Reed et al. 2013
Median = 25.3 days!Mean = 32 +/- 16 days
•reverse this process to project WD rotation velocity from HB!
•factor of 10 decrease in moment of inertia!
•sdB median = 25.3 d!• projected WD period
~ 3.2 d (2 x observed)!•suggests minimal
residual coupling post-HB (i.e. AGB)
�61
post-He flash core slowing!(Kawaler & Hostler 2005)
pre core flash (degenerate)
He core burning
�62
if I have any time (probably not…)
•‘traditional’ asteroseismic analysis of white dwarfs is a mature field - tests of equation of state, internal structure, and diffusion!
•asteroseismic rotation measurements of WDs (and sdBs) as a final ‘boundary condition’ for angular momentum evolution!• (single) sdB rotation periods are ~ 26 days!
• (single) white dwarf rotation periods are ~ 1 day!•much (most?) core-envelope coupling is prior to AGB!
•independent tests of asteroseismic rotation measurements are needed - precise photometry to the rescue?!
•Kepler transformed sdBs from “boutique” modeling to class properties!
•K2 promises to do the same for white dwarfs
�67
summary
�68
a local Puls(at)ion boutique