white dwarf stars in mass transferring binaries and their

White Dwarf Stars in MassTransferring Binaries and their

OutburstsDean Townsley

Joint Institute for Nuclear Astrophysics

The University of Chicago

Townsley - SUNY Stonybrook 2008 – p.1/22

Binary Evolution

Time

Orbital PeriodIncreasing

WideNo interaction

Ejection

CommonEnvelope

Secondary Mass

Supernova?

MS

WD

CE2

WD

WD

Merger to Supernova?

WD

Giant

Stable hydrogenburning"Supersoft" X−ray sources

WD

MS

Stable mass transfer

Recurrent surface H runaways

Stable H mass transfer

long interval surface H runaways

or collapse?

Post Common Envelope Binaries


Binary Evolution

Time

Orbital PeriodIncreasing

WideNo interaction

Secondary Mass

Supernova?

Merger to Supernova?

WD

Giant

Stable hydrogenburning"Supersoft" X−ray sources

WD

MS

Stable mass transfer

Recurrent surface H runaways

Stable H mass transfer

long interval surface H runaways

or collapse?


CV Angular Momentum LossJ determines evolution of compact binary

Companion B field

WINDWIND

WINDWIND

gravity

waves waves

gravity

Magnetic Brakinghigh J , Porb & 3 hours

Magnetically attached wind from compan-ion star

Jmb = −9.4 × 1038

erg

0

@

M2

M⊙

1

A

0

@

R2

R⊙

1

A

3 Porb

hr

!

−3

Gravitational Radiationlow J

Jgr = −32GQ2ω5

5c5

= −2.7 × 1037

erg

0

@

a

R⊙

1

A

4 0

@

MWDM2

MtM⊙

1

A

2 Porb

hr

!

−5


Interrupted Magnetic (Wind) Braking?

0 1 2 3 4 5 6P

orb (hr)

10-11

10-10

10-9

10-8

<⋅ M

> (

MO· y

r-1)

0 1 2 3 4 5 6

0.65

Mcompanion

=0.22 MO·

0.08

∆t=108 yr10

9 yr3·10

9yr

pre CV

~109yr

MagneticBraking

Grav.Radiation

Evolved fromprescriptions whichreproduced thecompanion contractionnecessary for the periodgap.

Predicts a strongcontrast in both 〈M〉and evolution time – andtherefore space density– of period bins

Difficult to test due toCV variability andcomplexity of disks, butprogress can be madeby other means such asWD Teff . (Townsley & Bildsten 2003,

ApJ, 596, L227)

MWD = 0.7M⊙ , Howell, Nelson, & Rappaport 2001, ApJ 550, 897

Systems evolve from long to short orbital periodsdue to angular momentum losses causing the or-bit to decay.Period gap caused by sudden drop in angularmomentum loss rate.


Available Parameter Space

0.6 0.8 1 1.2M

WD (M

O·)

10-11

10-10

10-9

10-8

10-7

10-6

⋅ M (

MO· y

r-1) M

ign=10

-5M

O·10

-4M

O·

Stable H burning

Contours spaced by ∆ log(Mign/M⊙) = 0.2Townsley & Bildsten 2005, ApJ, 628, 395

Strong contrast in Mign at aroundfew×10−10M⊙ yr−1 created bychange in ignition mode due to dif-ferent Tc as determined by 〈M〉(more on this later).

CVs generally are thought to haveaccretion rates that are low or high,but not much in between.

A system at a given mass canhave a factor of 10 range in Mign

depending on what evolutionarystage it is in.


Heat Sources

COMPRESSION

ADVECTION

HEAT TRANSPORT

5 10 15 20 25log P

104

105

106

107

T (

K)

C-O core

Adi

abat

material moves inwarddue to accretion

H-He Envelope

(very) leaky entropy advection

Heat liberated by compression is transferred out to surfaceand in to core. Often called “compressional heating”.

Heat sources:

Accretion light: only very near surface while activelyaccreting

Compression: throughout star, mostly in light-elementlayer (really gravitational potential energy)

Nuclear “simmering”: fusion near base of accreted layer(eventually becomes fast and triggers classical nova)

Core heat capacityTownsley - SUNY Stonybrook 2008 – p.7/22

Quasi-static Profile

-8 -7 -6 -5 -4 -3log (∆M/M

O·)

1

2

3

4

5

6

7

8

log

(t/y

r)

tacc

tth

Macc

Mign

Local thermal time short compared to

accretion

tth ≡cP T

“

4acT4

3κy2

” < tacc ≡∆M

〈M〉

where y = ∆M/4πR2 is the column depth.

Thermal state set by flux from deeperlayers rather than from fluid element’s

history.

0 staticHeat equation near surface:

−dL

dMr+ǫN = T

„

∂

∂t+vr

∂

∂r

«

s = T∂s

∂t+Tvr

∂s

∂r

where vr = −〈M〉/4πr2ρ. Solve with structure equations. Gives excellentrepresentation of envelope sructure.

L ≃kTc

µmp〈M〉

Energy release related to heat content of compressed material.Townsley - SUNY Stonybrook 2008 – p.8/22

Tc and Classical Nova IgnitionPhysical Conditions at base of H/HeEnvelope determine runaway

102

103

104

ρ (g cm-3

)

0.5

1

2

T (

107 K

)

Tc=?

Stable

Unstable

Evaluating envelope stability:

∂ǫN

∂T=

∂ǫcool

∂T

One-zone approximation,ǫcool ∝ 4acT 4/κy2, only worksin upport portion.

Lower part of curved bettermodeled byǫcool = L(Tc)/Macc, were L(Tc)is given by that of a coolingWD: radiative envelopeoverlying a conductive region.

Thermal state (Tc) has animportant influence on whenthe instability line is crossed.

Composition has significantinfluence on position of upperportion.


Two Kinds of Ignition

m

〈M〉 = 3 × 10−9M⊙ yr−1

Tc = 107

Direct to p + C or 3He +3 He

Most novae by number

〈M〉 = 5 × 10−11M⊙ yr−1

Tc = 5 × 107

p + p (partial chain) envelope heatingeventually leads to p + CLarge accumulated mass


Cooling-Heating Cycle

-1.5

-1

-0.5

0

0.5

Lco

re (

10-3

LO·)

0 0.5 1 1.5 2 2.5 3Accumulated Mass ( 10

-4M

O·)

12

13

14

15

Tef

f

WD Cooling WD Heating

1014

1015

1016

1017

1018

1019

1020

P (erg cm-3

)

106

107

T (

K)

Base of accreted layer

Core will be Reheated until equilibrium is reached.Core thermal time ∼ 108 yr


Cooling-Heating Cycle

-1.5

-1

-0.5

0

0.5

Lco

re (

10-3

LO·)

0 0.5 1 1.5 2 2.5 3Accumulated Mass ( 10

-4M

O·)

12

13

14

15

Tef

f

WD Cooling WD Heating

1014

1015

1016

1017

1018

1019

1020

P (erg cm-3

)

106

107

T (

K)

Base of accreted layer

Core will be Reheated until equilibrium is reached.Core thermal time ∼ 108 yr

〈Lcore〉 =1

tCN

Z tCN

0

Lcore dt


〈Lcore〉 and the equilibrium Tcore

〈Lcore〉 =1

tCN

Z tCN

0

Lcore dt

When Mej = Mign, 〈Lcore〉 = 0 defines anEquilibrium Tcore which is set by M and 〈M〉

Can approximate evolution:

〈Lcore〉(Tc, M) = CWDdTc

dt

where CWD is the total heat capacity of theWD – proportional to mass (have to becareful with latent heat at crystallization) 2 4 6 8 10 12

Tc (10

6 K)

-3

-2

-1

0

Ave

rage

Lco

re (

10-3

LO·)

10-11

10-10

10-9

10-8

10-10.4


WD Thermal State Evolution

10-12

10-11

10-10

10-9

10-8

10-7

<⋅ M

> (

MO· y

r-1)

2

3

4

5

Tc/1

06 K

5

10

50

Tef

f/103 K

0 2 4 6 8 10t (Gyr)

0

1

2

3

4

5

P orb (

hour

s)

Phases of accretion

1. Magnetic Braking 〈M〉 ∼ 5 × 10−9M⊙ yr−1

2. Period gap 〈M〉 = 0

3. Gravitational radiation 〈M〉 ≃ 5 × 10−11M⊙ yr−1

4. Post-period minimum 〈M〉 < 10−11M⊙ yr−1

Phases of WD evolution

1. Reheating – Teff set by 〈M〉

2. Equilibrium – Teff set by 〈M〉

3. Cooling – Teff set by core cooling

Accretion resets the clock for WD cooling


Tc EvolutionEpelstain, Yaron, Kovetz, Prialnik 2007, MNRAS, 374, 1449Full, multi-cycle nova simulations

M = 1.0M⊙, 〈M〉 = 10−11M⊙/yr M = 0.65M⊙, 〈M〉 = 10−9M⊙/yr

time (100 Myr)time (Gyr)

core

T (

10 K

)7

cooling WD

nova WD

Demonstrates equilibrium and evolution times. Unlikely to come fully into equilibriumabove gap, but plenty of time below gap, especially with the “boost” from above-gapevolution.

Also demonstrates that nova WDs in CVs generally will not stay very hot (& 2× 107) formore than a few 100 Myr. (Note being "caught" in this state would be exceedingly rarein any case due to post-CE cooling.)


Teff vs. PorbTownsley & Bildsten 2003, ApJ, 596, L227Townsley & Gänsicke, submitted

1 2 3 4 5Orbital Period (hours)

10

20

30

40

50

Tef

f/103 K

0.6-1.0 MO·

Low disk state systems (DN, SW Sex)⋄ Magnetics

Theory range shown: 0.6-1.0M⊙

Factor of ∼ 10 〈M〉 contrast across

period gap confirmed

Current Mag. Braking prescription

matches well with DN at 4-5 hours

Separate population of high 〈M〉 at

3 hours?

Magnetic CVs above gap nearGrav. Radiation prediction

– WD magnetic field preventingmagnetic braking?!(Li, Wu, & Wickramasinghe 1994, MNRAS, 268, 61)


Classical NovaPorb Distribution

0 1 2 3 4 5 6P

orb (hr)

0

2

4

6

8

10

Num

ber

of N

ovae

0 1 2 3 4 5 60

2

4

6

8

10

Relative number of CVs

Theory curve uses Interrupted MagneticBraking for Porb(〈M〉) and population nP

(Howell, Nelson, Rappaport 2001, ApJ 550, 897)

νCNP = nP〈M〉

Mign

But since nP ∝ M2/〈M〉 this gives

νCNP ∝1

Mign

Thus the dominant contribution is fromthe variation in the ignition mass acrossthe period gap (2-3 hours)

(Townsley & Bildsten 2005, ApJ, 628, 395)

Supports a factor of > 10 drop in 〈M〉 across gap

Consistent with idea that CVs evolve across the gap

Possible population of magnetic systems filling in gap

Ignores selection effects – hard to quantify


Classical Nova〈M〉 Distribution

0

0.5

1

Rel

ativ

e N

ova

rate

0

0.5

1

-11 -10 -9 -8log (< ⋅M>/ (M

O· yr

-1) )

0

1

2

3

Eje

ctio

n ra

te p

er N

ova

(10-5

MO·)

Φ(〈M〉)

Most observed Novae have “high”

〈M〉 ∼ 10−9M⊙ yr−1

Similar amount of matter is ejected fromNovae with 〈M〉 ∼ 10−9M⊙ yr−1 and

∼ 10−10M⊙ yr−1.

Character of ignition very different for

these two

direct Carbon or 3He trigger

p-p heated deep envelope trigger

Features of Novae which depend on 〈M〉

are expected to have a bimodal character.

The Porb distribution below 6 hours shows

initial indications of this.Townsley - SUNY Stonybrook 2008 – p.17/22

Luminosity Function of Old CVs

10-12

10-11

10-10

<⋅ M

> (

MO· y

r-1)

M = 0.6 MO·

0 2 4 6 8 10 12t (Gyr)

5

10

Tef

f/103 K

WD Cooling

11.5 12 12.5 13 13.5 14 14.5WD M

V

Rel

ativ

e N

11.5 12 12.5 13 13.5 14 14.5

M = 0.6 MO·

Gra

v. R

ad.

Near Porb

min.WD Cooling

< ⋅M> dropping

Low 〈M〉 leads to infrequent disk outbursts

CV V magnitude dominated by WD

Most old CVs appear as cooling WDs until inspected carefully


Broadband CV Spectral EvolutionTownsley & Bildsten 2002, ApJ, 565, L35

0 1 2 3 4V-I

20

21

22

23

24

25

26

I

0.2 MO·

0.3 MO·

0.15 MO·

Predict

ed C

V Evolution

MWD

=0.6 MO·

MWD

=0.4 MO·

= 1 Gyr

M4 Predicted CV Color Evolution0.6 M

O· WD No accretion disk included

Proper-motion selectedmembers of M4 at 4 coreradii (Richer et al. 2002, ApJ, 574L, 151)

Color selection criteria forold CVs

CVs Mixed with WDpopulation used to datecluster


Evolution of He Accretors (AM CVns)Bildsten, Townsley, Deloye, & Nelemans 2006, ApJ, 640, 466

10-12

10-11

10-10

10-9

10-8

10-7

10-6

<⋅ M

> (

MO· y

r-1)

M=0.65 MO·

M=1.05 MO·

104

105

Tef

f (K

)

DBV strip

0 10 20 30 40 50 60 70P

orb (hr)

6

8

10

12

14

16

18

MV

WDs which accrete helium from a

companion lower mass heilum WD

〈M〉 monotonically decreases with time as

Porb increases

Curves show 2 WD masses and 2 possible

donor thermal states(Deloye & Bildsten 2003, ApJ, 598, 1217)

Similar evolution: reheating, equilibrium(short!), WD cooling

Accretion disk phenomenology not wellunderstood, two-state (DN) accretion

expected with increasing time spent inquiescence

Both measured MV agree well with theory!


Accreting WD SeismologyCan greatly change characterof mode spectrum

Naturally gives sets of manyclosely spaced modes

Surface eigenfunctions havedistinctive shape (squeezed toequator) that can be confirmedby multi-band observations

Can give modes at frequenciesmuch higher and much lowerthan the driving frequency inthe rest rest frame

0 0.001 0.002 0.003 0.004 0.005observer frame mode frequency |ω-mΩ| (Hz)

0

0.002

0.004

0.006

0.008

0.01

spin

fre

quen

cy Ω

(H

z)0 0.001 0.002 0.003 0.004 0.005

0

0.002

0.004

0.006

0.008

0.01

Shown are the first ∼ 20 modes from the same physical model of GW Lib.The horizontal line represents a moderate spin hypothesis, in which Ω ∼ ω for the lowradial order modes.Heavy blue indicates a single mode triplet (m = −1, 0, +1).Plotted are frequencies in the observer’s frame |ω − mΩ|.Modes that "bounce" off of zero are modes travelling opposite to the rotational sense


SummaryGaining understanding about the accreting WD binary population constrains the

properties of outbursts

Accreting WDs are reheated by “compressional heating” and Hydrogen “simmering”

Equilibrium Tcore allows relation of observables to M, 〈M〉

Consistent with quiescent Teff , indicating variation in 〈M〉 across period gap

Reproduces classical nova Porb distribution

Evolution of broadband colors in quiescence

Late time magnitudes and Teff for both CVs and Helium accretors

Seismology can determine spin, M , Macc


white dwarf stars in mass transferring binaries and their

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