White dwarfs: The galactic fossil population

Jordi IsernInstitut de Ciències de l’Espai

IAC, October 3th 2006

Sirius B

Chandra

# White dwarfs were discovered by Alvan Clark in 1862 L ~ 3x10-3 Lo, T, ~ 29500 K R ~ 7.4x10-3 Ro

# Sirius is a binary system and it is possible to obtain the mass, M ~ 1.053 Mo ~ 3x106 g/cm3

40 Eri B 0.48 Mo 0.0124 Ro

Stein 2051 0.50 Mo 0.0115 Ro

Sirius B 1.05 Mo 0.0074 Ro

The Fermi temperature is:Tf ~109 KElectrons are degenerate!

1 3R M

White dwarf structure

/ ( )

th CV WD

WD C

dU dTL c M

dt dtL M f T

tcool ~ 10 Gyr !Energy reservoir

Energy fluxcontrol

The luminosity function

)( () ) (U

l

M

cool MS coolM GalM dt t Mn tL Observations: Stars/pc3/magnitude

Galactic properties

Stellar properties

Good observational properties+

Reliable white dwarf models

Galactic properties can be obtained: , tGal

Sloan sample of WD

Surveys are more and more accurate and signifivcativeNevertheless, the cutoff is still poorly defined

GAIA:~ 300,000 disc WD~ 90,000 halo WD

White Dwarf Cooling

0,WD WD

cV s s c

V xM M

dT P dVL L c dm T dm l e m

dt T dt

To solve this equation it is necessary a L(TC) relationshipthat depends on the properties of the envelope

The cooling process (I)• Neutrino cooling [log(L/Lo) > -1.5]

– Is the must complicated phase because the initial conditions are unknown.

– Neutrinos dominate & thermal structures converge

– Very short epoch ( < 108 yr)

• Fluid cooling [-1.5 > log(L/Lo) > -3]– Gravothermal energy

– Coulomb plasma

– The main uncertainty comes from the C/O abundances that depend on the 12C(,)16O reaction , Z, & the treatment of convection

Salaris et al 1997Domínguez, Höflich & Straniero, 2001

---- Oxygen___ Carbon

The cooling process (II)

• Crystallization [-3 > log(L/Lo) > -4.5]

– Latent heat ( kTs per particle)

– Sedimentation upon crystallization that depends on the chemical profile and the phase diagrams

• Debye cooling [-4.5 > log(L/Lo) ]– At low temperatures, the specific heat follows the Debye law

– Compression of outer layers is the main source of energy & prevents the sudden disappearence of the white dwarf

Ts

X2 0 1

Ts

X2 10

Behavior upon crystallization

Change of the chemical profile because of solidification

Delay in the coolingprocess introduced bysedimentation of oxygenupon crystallization(DA atmosphere)

1.0

0.54

After solidification

White dwarf envelopes• DA: Pure H layers.

– 90,000 K > Te > 6,000 K, below this T Balmer lines are not seen

• DO: spectrum dominated by He II– 100,000 K > Te > 45,000 K. They are the hottest

– C,N,O,Si are present in the photosphere

– The coolest are H-poor

• DB: He dominated armospheres– 30,000 K > Te > 12,000 K

– There is a gap betwee DO and DB!!!

• DQ: He dominated atmospheres – 12,000 K > Te > 6,000 K

– C abundances in the range of 10-7 - 10-2

• DZ: only metallic features (Ca II H-K)– T to small to show the lines of the dominant elements

• DC: So cool that the dominant component is not seen– No lines deeper than 5%

C/O

He

H

Winds

Accretion from ISM(H,He, metals)

Convection

Convection

Light elements float

Heavy elements sink Radiative levitation

Particle diffusion

Two families of white dwarf envelopes

Te

150,000 K

6,000 K

DAs No-DAsThe H layer:•Acts as a source of opacity•If its mass is larger than 2x10-4 Mo, H-burning•Evolution predicts 10-4 Mo

The He layer•Important source of energy at very low Te

•Low opacity (n-Das cool much faster)•Controls the diffusion of H inwards (DA-nDA)•Controle the diffusion of C outwards (DB-DQ)•Evolution predicts 10-2 Mo

Is the origin of the DA, n-DA character:•primordial ?•mixing?•both?

Luminosity versus time(dotted lines without sedimentation)

DA N-DA

Non-radial g-modes•Long period waves 102 - 103 s•Gravity is the restoring force

dr

d

dr

PdgN

Nf

lnln1

1

2

22

Brunt-Väisälä frequency

dt

Td

dt

d lnln

dt

Td

dt

d lnln

Period increases as the star cools down

The characteristic drift is ~ 10-15 ss-1

G117-B15A

* Discovered by McCraw & Robinson* Main properties

·M 0.53 - 0.59 Mo

·Te 11620 K* Pulsation periods

·0bs = 215.2, 271, 304.4 s & harmonics + linear combinations

115105.30.12 ssData from 1975-90

Data from 1975-00 115104.13.2 ss

Fiducial case & mode identification

e

CHe

HeH

WD

r

WD

H

WD

He

WD

T

q

q

MMq

MM

MM

MM

2.08.0

4.08.0

1log

4log8

2log3

65.0/5.0Parameters range Additional constraints

l=1Te=11620 K

Salaris et al’97 profilelog MHe/MWD =-2qH-He=-0.8qHe-C=-0.4

The most critical parameters are:MWD,MH

Mode identification:M=0.50 Mo k=1,2,3 log MH/MWD=-6.6M=0.55 Mo k=1,2,3 log MH/MWD=-7.0 k=2,3,4 log MH/MWD=-4.0M=0.60 Mo No satisfactory fit

We adopt:M*=0.55 Mo

log(MH/M*) = -4.04

Fiducial model & error budget

PF=210.4 sdP/dt =3.9x10-15ss-1

Error budget____________________________________________Source P(s) dP/dt (ss-1)x1015

_____________________________________________ Mode identification 6 1.0M* 6 1.0

Chemical profile 4 0.1Teff 2 0.2

Input |Δt| Gyr

DA/non-DA < 3

Core composition < 0.5 <

Conductive opacity < 0.3

Radiative opacity < 0.06

Metals in the envelope 0.2

Gravitational settling

C/O 0.8 – 1.256Fe < 1.322Ne < 9; < 0.5

Observational 2 – 3

The luminosity function

)( () ) (U

l

M

cool MS coolM GalM dt t Mn tL If the evolutive models are reliable it is possible to invert the integraland to obtain .

, the initial mass function, is the statistical weight that connects the stellar and the galactic properties and it is assumed constant along thelife of the Galaxy (there is not any example in the contrary) .

The solution is not unique and depends on the shape of the trial function

# The bulk of stars in the galactic plane have been formed during the last 9.5 Gyr# The observed luminosity function is compatible with long tails as long as 20 Gyr# It is necessary to improve the dim part of the luminosity function with deep and large surveys in the red and infrared !

How did the halo form?• By the monolithic collapse of an initial mass of gas?• By accretion of tidally disrupted satellite galaxies?• A mixture of both?

Probably the halo WD population can provide some insight about the problem

WDs may have three origins:•Primitive halo•Capture from the exterior•Expelled from the disc

Identification criteria:•Kinematics•Age

The age depends on the lifetime in the main sequence: tMS(Z)and on the cooling time cool (Z).

halo

disk

The halo luminosity function

*Halo WD cannot be identified by Z*Radial velocities cannot be measured because lines are to shallow* The identification is only based on thetangential component of the velocity*Mixing between the halo and thick disk*Only the bright part is known. Stillincomplete and doubtful

It is clear that if it was possible to detect the halo peakit would be possible to determine the age of the galaxy!

The bright branch of the luminosity function is homologous respect tothe SFR and the information about the temporal properties is lostduring the process of normalization

In order to determine the history of the halo it is necessary to obtain the dim branch

TH = 12 GyrDt: 0.1, 1 & 3 Gyr

DA N-DA

He WD cool much faster!

Discovery functions: Number of white dwarfs per pc3

and interval of magntude (mV < 20)

The chances to detect the dim part is very small for pure He WD

Deep & wide surveys are neededIR colors

He

H

Because of the blocking of the H2, some colors become bluer asthe WD cools down. This offers a good opportunity to detect them!

Can pure He WD exist?What about the H accreted from the ISM?

Pre-WD lifetimeHurley et alSalaris et al

Lifetime for 1M and differentmetallicities

Lifetime for Z=0.02 & 0.0005(upper and lower curves respectively)as a function of the mass

The lifetime decreases when the metallicity decreases !

Influence of the metallicity

• Pre-white dwarf lifetime

• Initial-final mass relationship

• C/O profiles: – Larger specific heat

– Lower latent heat

– Higher sedimentation energy

– Energy release at lower temperatures

• Sedimentation of impurities

1

1

v

s

c

Z C

c

l T

L T

Z(t)tMS(Z)

Tcool (WD)

Ages compatible with the error bars as a functionof the metallicity

Possible ages as a function of themetallicity

WD2316-064

Halo location

Straniero et al)

13 Gyr11 Gyr

Salaris et al

log Te M

WD1756+827 3.8615 0.58

WD2316-064 3.6767 0.68

WD0145-174 3.8893 0.6

T=13 Gyrdt=0.001

Z=Z(t)

Z=0.02

T=13 Gyrdt = 13 Gyrm > 0.90

• Metallicity plays an important role at the moment to assign an age, but not in the LF

• The present uncertainties in Mf-Mi do not allow to rule out any suspected halo WD on the basis of the age alone.

• Some relationships predict an excellent agreement• If the IMF is universal, the halo is still producing

bright, low mass WDs

A key problem: is the IMF universal?

Easy to check:

Salpeter’s like IMFs are still producing bright, young WD in the halo!

Biased IMFs will produce anexcess of dim WDs

The initial – final mass function is required for:

• Determination of supernova rates– Core collapse supernovae (Fe & O/Ne cores)

– Thermonuclear supernovae (CO cores)

• Chemical evolution of the Galaxy

• Star formation and feedback processes in galaxies

• Understanding the properties of the galactic population of white dwarfs:– Field white dwarfs (halo & disk)

– Clusters (open & globular)

Despite its importance, this function is poorly known both from the observational and theoretical point of views.First attempt: Weidemann (1977)

MSP

mWD

Initial Final Mass Relationship(Weidemann 2000)

Is it a single valued function? mWD (MSP, Z, , NHe/NH, B, binariety...)

# Magnetic white dwarfs are systematicaly more massive (Ferrario, 1998) (systematic bias in the measurement of the mass?)# Certainly, close binaries can evolve diferently

MSP = 6.5 Mo

# Because of lifting effects, rotation can modify the final size of the core! (Dominguez et al’93)

Hurley et alSalaris et alDomínguez et alWeideman

0.1250.4

MS MWD me

Initial - Final mass

IFMR: WoodSFR = const

IFMR: Wood

SFR = exp

Observational data from the PG survey (LBH’05)

IFMR: DomínguezSFR = const

IFMR: DomínguezSFR = exp

Observational data from the PG survey (LBH’05)

Fraction of white dwarfs with mass larger than m0

(from the PG survey – LBH’05)

• m > 0.6 Mo

• m > 0.7 Mo

IFMR: WoodSFR (unit volume) constSingle stars

IFMR: WoodSFR (unit volume) constSingle stars

IFMR: Domínguez et alSFR (unit volume) constSingle stars

IFMR: Domínguez et alSFR (unit volume) expSingle stars

Wood, expDomínguez, expDominguez, cnst

Mass distribution(single stars)

Normalization from the LF

Mass distribution of DA white dwarfs(Palomar Green survey)Liebert et al (2005)

Helium white dwarfs produced by binary evolution

Excess of WD in the mass range 1.0 – 1.4Defect of WD in the mass range 0.65 – 0.85(Common proper motion pair: REJ0317-853 & LB9802;The most massive is much hotter than the less massive)

Influence of the binary population

1 2

01 2 0 0 1

1

2

2 0

Number of degenerate systems born per unit time and volume with a

separation a at the instant t is:

M , and A are the masses and the inital separation at

( , ) ,

the

( )bM M

dAb a t M M H A t dM dM

M

da

b 1 2 0

1 2 0 0

Z MS

M , , is the time to form a binary degenerate (single or double),

, is the initial mass function of the binary, is the

distribution of initial separations

The DD formed at the insta

M A

M M H A

4

1 2 1 2

nt t will merge after a time:

where 0.6 where masses are in solar units4

separations in solar radii and time in Gyr.

m

at K m m m m

K

Birthrate calculationIsern et al,

Thermonuclear Supernovae, Ed. Ruiz-Lapuente, Canal, Isern,

Kluwer p. 127 (1997)

• Models obtained with FRANEC. Solar metallicity

• Dmínguez/Straniero IFMR

• Common envelope treatment: Iben & Tutukov (1984)

• Salpeter’s IMF for the primary,

• F(q) q; q = M2/M1

• Distribution of initial separations: H(A0) 1/A0

• During the merging ALL the mass of the secondary is transfered to the primary

Position of the particles Velocities of the particles

0.6+0.8 case Guerrero et al 2004

Mass distribution

Single Binaries, merging allowed, all populationBinaries, merging allowed, hot

Normalization to the tota population independently

Fraction of WD versus luminosity

• m > 0.6 Mo

• m > 0.7 Mo

Binary effects (continuous line)Single WD (dotted line)

• Clusters & non-interacting binaries suggest an IFMR with a large dispersion. A large part of this dispersion may be due to models

• The LF of massive WD can only be reproduced if the IFMR favors the formation of massive WD

• Binary interaction favors the formation of massive WD

• Merging seems to be the responsible of the bumps observed in the mass distribution

White Dwarf Merging&

Emission of Gravitational Waves

Double degenerate binary systems The search of DD systems is difficult because of thecharacter intrinsically dim of white dwarfs.

Several strategies are possible:•Radial motions in spectroscopic binaries (Robinson & Schafter, 1987)•White dwarfs of very low mass (Bergeron et al 1991)•White dwarfs showing peculiar, composite spectra and colors

•(Bergeron et al 1990)•Common proper motion binaries (Sion et al 1991)

Several systems (>15) are known and the search continues:Napiwotzki et al, Marsh et al...

The interest relies on the fact that these systems can mergein less than a Hubble time if roughly a < 3 R

Coalescence of two white dwarfs

• Type Ia supernovae?

• Accretion induced collapse?

• Peculiar WD?

There are several double degenerate binary systems able to merge in a time shorter than the Hubble time because they loose

angular momentum as a consequence of gravitational wave emission

3 2

5 4

1 2

1 2

6.4dJ G M

dt c aM M M

M M

M

Which are the observational consequences?

The outcome depends on:# The chemical composition of both white dwarfs# The effective accretion rate from the disc to the white dwarf# Total mass of the final system (M > MCh ?)

The merging process

The less massive star transfers mass to the most massive( R M-1/3 ) As R2 increases when M2 decreases, transfer accelerates

Since dM1 > 0, da >0 and the separation increases

11 2

1 12

dadM

a M M

Conservative transfer

There is a critical value M2 = 0.3 - 0.4If M2 > Mc dynamic mergingIf M2 < Mc self regulated merging

Method and input physics• SPH (Smoothed Particle Hydrodynamics)

– Artificial viscosity (Balsara 1995)– Binary tree (Barnes & Hut 1986)– Polynomic kernel (Monaghan & Lattanzio 1985)– Predictor corrector (Serna et al 1996)– Energy & angular momentum conserved at 0.01% in 104 steps– 20,000 particle per star

• EOS: Degenerate electrons + Coulomb plasma + photons• Full set of nuclear reactions (α-chain from He to Zn)

plus the C+C and O+O reactions

Simulation 0.6+0.8 0.6+1.0 0.8+1.0Ratio 0.75 0.60 0.80Tmax(K) 1.4x109 1.6x109 2.0x109

Particle mass 3x10-5 3x10-5 4x10-5

Expelled mass (Mo) 2.8x10-3 6.5x10-3 6.5x10-3

Duration (s) 50 65 20

CO + CO mergers

3D density evolutionCase: 0.6+0.8 Mo

Unit mass : 1 Mo

Unit length: 0.1 Ro

G = 1

3D temperature evolutionCase: 0.6+0.8 Mo

Position of the particles0.6+0.8 case

Velocities of the particles

0.6+0.8 case

0.6+0.8 case

Equatorial temperature contours

0.6+0.8 case Density profiles of the disk

R (10-1 Ro)

Z (

10-1 R

o)

0

1000 g/cm3

1

0.6+0.8 case

Evolution of the tangential velocity respect to the center of masses

The critical point is the intrinsic viscosity of the SPH methods

Preliminary resultsThe total mass expelled is very small.Temperature is never high enough to initiate a prompt

explosion.The mass remains roughly confined around the equatorial

beltThe outcome will depend on the evolution of the disk

At which rate the disk transfer mass to the WD?At which rate the WD can accept mass?

Gravitational waves

•Accelerated masses produce GW•GW stretch & squeeze objects because of their quadrupolar nature•Two polarization states: “+” and “x”•If ldetector << λGW both polarizations act as:

+ polarization x polarizationx

y

z

From LIGO pages

Chirping binaries

Inspiral merger

ringdown

Isolated, spherically symmetric star

GW from a binary as compared with the analytical result

Merging of a 0.8 and a 1.0 MΘ white dwarfs

LISA

Comparison of Sensitivity Estimates

Maximum distances of detectability S/N = 5

Detection probabilityrmer ~ 0.03 - 0.008 yr-1

Vaccs ~ 1.2x1014 pc3

Vgal ~ 3x1011 pc3

rdiscovery ~ rmer

• During merging the major part of the mass of the system remains bounded to it (at least for the adopted initial conditions.

• There is not a prompt explosion.

• A significant part of the gravitational signal is out from the expected confusion limit.

• However, the signal is to weak to have any chance to be detected during the lifetime of LISA

White dwarfsas

Astroparticle PhysicsLaboratories

tLn )(

nn

n

L

Ls

0

Influence of extra sources & sinks

Non-radial g-modes•Long period waves 102 - 103 s•Gravity is the restoring force

dr

d

dr

PdgN

Nf

lnln1

1

2

22

Brunt-Väisälä frequency

dt

Td

dt

d lnln

dt

Td

dt

d lnln

Period increases as the star cools down

If the characteristic drift , ~ 10-15 ss-1, is known for a bunch of starsanomalous cooling or heating could be detected

m

obsa

L

LL

EXEMPLES

•Axions •(Isern et al 1993, Althaus et al 2001)

•Gravity constant •(Garcia-Berro et al 1996, Isern et al 2001)

•Compactification scales of extra dimensions •(Biesiada & Malec 2001)

•Neutrino magnetic momentum •(Blinnikov & Dunina-Barkovskaya 1994)

Axion case

• Axions were proposed as a solution to the strong CP problem– KVSZ model -> Axions coulple to hadrons & photons

– DFSZ model -> Axions also couple to charged electrons

• Coupling is determined by the Peccei-Quinn scale f which is related to the mass of the axion

• Experiments have failed to detect axions• Constraints from astrophysical arguments

– Solar properties

– Red giants (HB & AGB stars)

– Gravitational supernovae

– Cosmological considerations

10-2 - 10-5 eV

Asteroseismological propertiesof white dwarfs ?

White dwarf cooling

Bremsstrahlung is dominantL T7

La T4

Lph T2.5

3

cos

110·5.8

4

)(10·08.1

2

11

2

47

223

e

aeze

ae

a

c

eVmcg

g

FTA

Z

Mode identification:M=0.50 Mo k=1,2,3 log MH/MWD=-6.6M=0.55 Mo k=1,2,3 log MH/MWD=-7.0 k=2,3,4 log MH/MWD=-4.0M=0.60 Mo No satisfactory fit

We adopt:M*=0.55 Mo

log(MH/M*) = -4.04

G117-B15A

Axions influence

Axions do not change the thermalstructure

Fiducial model + axions

Rate of change of Pk=3 is trapped

• Models are able to reproduce the evolution and seismological properties of DAVs

• It is not necessary to invoke additional cooling to account for the behavior of G117-B15A

• This allows to set a strong limit the mass of axions (DFSZ) macos2<4 meV

• The interaction axion-electron cannot be ruled out• We need:

– A set of DAVs with well defined fundamental parameters– Precise measurements of dP/dt– A good theory of the evolution of the outer layers