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White dwarfs : The galactic fossil population

White dwarfs : The galactic fossil population. Jordi Isern Institut de Ciències de l’Espai. IAC , October 3 th 200 6. Sirius B. # White dwarfs were discovered by Alvan Clark in 1862 L ~ 3x10 -3 L o, T , ~ 29500 K  R ~ 7.4x10 -3 R o

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White dwarfs : The galactic fossil population

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  1. White dwarfs: The galactic fossil population Jordi Isern Institut de Ciències de l’Espai IAC, October3th 2006

  2. Sirius B # 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 Chandra The Fermi temperature is: Tf ~109 K Electrons are degenerate!

  3. White dwarf structure Energy flux control Energy reservoir tcool ~ 10 Gyr !

  4. The luminosity function Observations: Stars/pc3/magnitude Galactic properties Stellar properties Good observational properties + Reliable white dwarf models Galactic properties can be obtained: , tGal

  5. Surveys are more and more accurate and signifivcative Nevertheless, the cutoff is still poorly defined Sloan sample of WD GAIA: ~ 300,000 disc WD ~ 90,000 halo WD

  6. White Dwarf Cooling To solve this equation it is necessary a L(TC) relationship that depends on the properties of the envelope

  7. 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

  8. ---- Oxygen ___ Carbon Salaris et al 1997 Domínguez, Höflich & Straniero, 2001

  9. 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

  10. Behavior upon crystallization Ts Ts 0 X2 1 0 X2 1

  11. Change of the chemical profile because of solidification Delay in the cooling process introduced by sedimentation of oxygen upon crystallization (DA atmosphere) 1.0 After solidification 0.54

  12. 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%

  13. Winds Accretion from ISM (H,He, metals) Light elements float H Convection He Particle diffusion Convection C/O Radiative levitation Heavy elements sink

  14. Two families of white dwarf envelopes • The H layer: • Acts as a source of opacity • If its mass is larger than 2x10-4 Mo, H-burning • Evolution predicts 10-4 Mo Te DAs No-DAs 150,000 K • 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? 6,000 K

  15. Luminosity versus time (dotted lines without sedimentation) DA N-DA

  16. Long period waves  102 - 103 s • Gravity is the restoring force Non-radial g-modes Brunt-Väisälä frequency Period increases as the star cools down The characteristic drift is ~ 10-15 ss-1

  17. 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 Data from 1975-90  Data from 1975-00 

  18. Fiducial case & mode identification Parameters range Additional constraints l=1 Te=11620 K Salaris et al’97 profile log MHe/MWD =-2 qH-He=-0.8 qHe-C=-0.4 The most critical parameters are: MWD,MH

  19. Mode identification: M=0.50 Mo k=1,2,3 log MH/MWD=-6.6 M=0.55 Mo k=1,2,3 log MH/MWD=-7.0 k=2,3,4 log MH/MWD=-4.0 M=0.60 Mo No satisfactory fit We adopt: M*=0.55 Mo log(MH/M*) = -4.04

  20. Fiducial model & error budget PF=210.4 s dP/dt =3.9x10-15ss-1 Error budget ____________________________________________ Source P(s) dP/dt (ss-1)x1015 _____________________________________________ Mode identification 6 1.0 M* 6 1.0 Chemical profile 4 0.1 Teff 2 0.2

  21. The luminosity function If the evolutive models are reliable it is possible to invert the integral and to obtain . , the initial mass function, is the statistical weight that connects the stellar and the galactic properties and it is assumed constant along the life 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

  22. # 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 !

  23. 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).

  24. 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 the tangential component of the velocity *Mixing between the halo and thick disk *Only the bright part is known. Still incomplete and doubtful disk halo

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

  26. The bright branch of the luminosity function is homologous respect to the SFR and the information about the temporal properties is lost during the process of normalization In order to determine the history of the halo it is necessary to obtain the dim branch

  27. TH = 12 Gyr Dt: 0.1, 1 & 3 Gyr He WD cool much faster! N-DA DA

  28. 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 needed IR colors H He

  29. Because of the blocking of the H2, some colors become bluer as the WD cools down. This offers a good opportunity to detect them! Can pure He WD exist? What about the H accreted from the ISM?

  30. Pre-WD lifetime Hurley et al Salaris et al Lifetime for 1M and different metallicities 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 !

  31. 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

  32. Z(t) WD2316-064 tMS(Z) Tcool (WD) Straniero et al) Ages compatible with the error bars as a functionof the metallicity Possible ages as a function of the metallicity Halo location

  33. Salaris et al 13 Gyr 11 Gyr

  34. T=13 Gyr dt=0.001 Z=Z(t) Z=0.02

  35. T=13 Gyr dt = 13 Gyr m > 0.90

  36. 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

  37. 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 an excess of dim WDs

  38. 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)

  39. mWD Initial Final Mass Relationship (Weidemann 2000) MSP 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

  40. MSP = 6.5 Mo # Because of lifting effects, rotation can modify the final size of the core! (Dominguez et al’93)

  41. Initial - Final mass Hurley et al Salaris et al Domínguez et al Weideman

  42. IFMR: Wood SFR = exp IFMR: Wood SFR = const Observational data from the PG survey (LBH’05)

  43. IFMR: Domínguez SFR = const IFMR: Domínguez SFR = exp Observational data from the PG survey (LBH’05)

  44. Fraction of white dwarfs with mass larger than m0 (from the PG survey – LBH’05) • m > 0.6 Mo • m > 0.7 Mo

  45. IFMR: Wood SFR (unit volume) const Single stars IFMR: Wood SFR (unit volume) const Single stars

  46. IFMR: Domínguez et al SFR (unit volume) const Single stars IFMR: Domínguez et al SFR (unit volume) exp Single stars

  47. Mass distribution (single stars) Normalization from the LF Wood, exp Domínguez, exp Dominguez, cnst

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