Asteroseismology of compact stars

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