Accretion Induced Collapse of White Dwarfs

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Accretion Induced Collapseof White Dwarfs

• Jordi Isern
• Institute for Space Sciences (CSIC-IEEC)
• In collaboration with
• E.Bravo (UPC-IEEC) I. Domínguez (UGR)

Anacapri, Naples May, 2009
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Explosive sources of energy

Gravitational collapse
Thermonuclear explosion
Neutron star
Electron degenerate core
12C,16O?56Ni q 7x1017 erg/g 1 Mo x q 1051
erg K 1051 erg Eem 1049 erg Lmax 1043 erg/s
M 1.4 Mo R 106 cm
M 1.4 Mo R 108-109 cm
?EG 1053 erg K 1051 erg Eem 1049 erg
Hoyle Fowler (1960)
Zwicky (1938)
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Energy sources
Gamow picture of a core collapse supernovae
Crab Nebula
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Observational constraints. I
SNIa

• H must be absent at the moment of the explosion
• There are some evidences (weak) of H-lines before
  maximum or at late epochs
• Progenitors should be long lived to account for
  their presence in all galaxies, including
  ellipticals
• The explosion should produce at least 0.3 M0 of
  56Ni to account for the light curve and late
  time spectra
• The short risetime indicates that the exploding
  star is a compact object
• No remnant is left

SNIa are caused by the explosion of a C/O
white dwarf in binary systems
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Third Uhuru Catalog (1973)
Highmass Xray binaries O B star
companion Lowmass Xray binaries Low mass
star, 1 Mo
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The question posed by the LMXRs was
-Can the binary system resist the explosion of a
massive star and the subsequent ejection
of matter? If not, two possible solutions
- Capture of a previously formed neutron
star - Non explosive formation of a
neutron star 1

• Non explosive means here without the ejection
• of a huge amount of mass. The 1053 erg are
  always
• present (Schatzman 1974).

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Electron degeneracy
At high densities e- are dominant
If
Even at T0 electrons (and other fermions) are
able to exert pressure!
Zero temperature structures can exist
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Hydrostatic Equilibrium
Characteristic times Hydrodynamic time
?HD? 440 ?-1/2 Thermal time 107 yr
Nuclear time 109 yr
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Non relativistic electrons
If electrons are non relativistic
It is always possible to find an equilibrium
structure The star only needs to contract
Hydrostatic equilibrium
As the WD accretes matter it contracts and
heats up M R-1/3
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Relativistic electrons
If electrons are relativistic
Hydrostatic equilibrium
It is not possible to find an equilibrium
structure
There is not a length scale If ?E lt 0 ?R lt 0
The star contracts If ?E gt 0 ?R gt 0 The star
expands
The ideal scenario for catastrophic events !
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Accretion induced collapse

• Idea Shatzman (1974), Canal Schatzman (1976),
  Ergma Tutukov (1976)
• A white dwarf accretes matter from a companion
• Avoids the thermonuclear explosion and reaches
  the Chandrasekhar limit at a density that ensures
  the collapse
• Small amount of mass is ejected and the binary
  survives
• How to avoid the explosion?
• Cooling the fuel CO white dwarf case (Canal
  Schatzman 1976 Canal Isern 1979)
• Less flamable fuel ONeMg white dwarf case
  (Miyaji et al 1980)

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The energy losses by electron captures depend
on the ignition density The injected energy
depends on the velocity of the burning front
There is not a length scale If ?E lt 0 ?R lt 0
Star contracts If ?E gt 0 ?R gt 0 Star explodes
Nuclear energy release
Electron captures
He cores always experiment a thermonuclear
explosion CO cores can explode or collapse to a
neutron star ONe cores always collapse to a
neutron star Fe cores always collapse to a
neutron star or black hole
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Laminar Flame
Woosley
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Flame acceleration
The laminar flame becomes turbulent
Rayleigh-Taylor instability Kelvin- Helmholtz
Flame surface increases efective velocity
increases
Deflagration subsonic velocity laminar flame v
0.01 cs Turbulent flame v 0.1 - 0.3 cs
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The minimum velocity of the burning front is that
of a laminar flame propagating conductively
Minimum density for obtaining a collapse 5.5 x
109 g/cm3
Bravo GarciaSenz (1999)
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The CO white dwarf case
Bravo et al 1996
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Very high accretion rates 10-5 Mo produce the
off center ignition
The critical issue is the maximum mass of CO
white dwarfs
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He-accreting white dwarfsmerging of COHe white
dwarfs CO WD Helium star (AM CVn stars) If
5x10-8 Mo/y ? dMH/dt ? 10-9 Mo/yr. And MWD lt 1.13
Mo an off center detonation forms

• H-accreting white dwarfs(cataclysmic variables,
  symbiotic stars, supersoft X-ray sources)
• dMH/dt lt 10-9 Mo/yr. Nova explosions. Novae
  reduce the mass or produce a very
• inefficient increase of the total mass, except
  MWD ? 1.2 Mo, but they are made of ONe
• 10-6 Mo/y gt dMH/dt gt 10-9 Mo/yr. Hydrogen burns
  in flasshes, but produces He at a
• rate that can ignite under degenerate
  conditions.
• MEdd gt dMH/dt gt 10-6 Mo/yr. Formation of a red
  giant

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Possible issues rotation?
The lifting effect of rotation allows the
formation of more massive CO cores
Domínguez et al96
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Possible issues A change in the internal
chemical composition?
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---- Oxygen ___ Carbon
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Behavior upon crystallization
Ts
Ts
0
X2
1
X2
1
0
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Change of the chemical profile because of
solidification
Plus a mixture of heavy species
After solidification
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Possible solutions Changes in the 12C12C rate?
Gasques et al (2007)
Reduction of the rate due to saturation Gasques
ety al (2007) Jiang et al (2007)
CO-WD easily colpase Possibility to obtain
more massive CO-WD
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Superbursts Are long, energetic, rare explosions
in LMXRBs, probably triggered by the 12C 12C
burning (Cumming Bildstein 2001 Strohmayer
Brown 2002)
What about an increase of the reaction rate?

• But this scenario has several problems (Cooper et
  al 2009)
• The ocean seems too cold for 12C ignition
• Heavy fusion hindrance (Gasques et al 2007)
  reduces the reaction rate by a factor 2
• Triggering of superbursts demands large amounts
  of 12C. This not seems the case
• Cooper et al (2009) have postulate a resonance
  near the Gamow peak (E 1.5 MeV) similar to that
  found by Spillane et al (2007)
• Secondary effects?

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The onset of the thermonucear runaway
The instability starts when nuclear reactions
overwhelm the thermal netrino emission
(typically T 2x108 K) A grrowing convective
carbon burning core forms (?C 10-100 s lt
?nuc typically T lt 78 x 108 K) At this
temperatures the characteristic time
equilibrates and the thermonuclear runaway
starts Flame propagation is mediated by heat
diffusion (deflagration) or shocks
(detonation).
Both T gt 2 x 109 K)
T
0
radius
The duration of this phase is 1000 yrs
Burning of 0.05 Mo causes en expansion by a
factor 3
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Influence of an additional resonance a la Cooper
et al (E 1.5 MeV strength 0.13 meV)
cm3s-1
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Carbon ignition

• The thermal structure of the white dwarf at
  carbon ignition (?nuc0.1-1 s) sets the initial
  conditions of the explosion ? results of 3D
  simulations of SNIa depend on the initial
  distribution of hot spots (García-Senz Bravo
  2005, Röpke et al 2006, Meakin et al 2009)

Carbon ignition occurs 4.3 x 108 K
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• Implications of the hypothetical resonance at 1.5
  MeV
• The ignition temperature is lowered down to
  T04.5?108 K (the non-resonant value is 8?108 K)
• ?nuc varies more steeply with T
• less hot spots reach ignition conditions before
  the flame is born
• smaller thermal contrast between a hot spot and
  the background temperature ? it is easier for a
  hot bubble to survive dispersion due to
  Rayleigh-Taylor instability (Iapichino et al
  2006)
• multipoint ignition is hampered

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• Implications of the hypothetical resonance at 1.5
  MeV (bis)
• Smaller diference in binding energy from crossing
  the ignition line up to reaching the ignition
  temperature
• less 12C has to be consumed before reaching the
  ignition temperature ? less neutronization during
  simmering (by a factor 0.4) .a fA large ratio
  of ?/p would imply a further reduction of the
  neutronization by a factor 0.5 (at low Z)actor
  0.4)

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The O-Ne case

• Miyaji et al (1980) showed that stars in the
  range 812 Mo could develop ONeMg cores
• Later on Woosley et al (1980), Nomoto (1984)
  reduced the range to 810 Mo S-AGB). The massive
  ones can not avoid the entire burning process.
• Some of these S-AGBs end as O-Ne WDs and some of
  them enter in the process of electron captures
  and collapse to a neutron star (electron-capture
  supernovae)
• The structure of the core of such S-AGBs is very
  different from the one of those arboring an
  Fe-core
• Very steep density gradient in the outer layers
• Surrounded by an extremely extended loosely bound
  H/He envelope
• Kitaura et al (2006) and Burrows et al (2007)
  have found successful explosions without invoking
  any acoustic mechanism

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Electron captures
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Thermal balance of electron captures
Electron captures are endothermic only when
electron comes from well above the thermal tail
This equations need to include the chemical
potentials of the involved nuclei. The threshold
for e-capture increases
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A fundamental ingredient Electron captures
create a thermal gradient that induces
convection and tends to inhibit the ignition but
also a chemical composition gradient that tends
to inhibit convection and favors ignition)!
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Evolution of O-Ne-Mg cores
Gutierrez et al (1996)
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Two critical points 1) The abundance of 24Mg
The off-center ignition is due to the energy
trnsfered and the cntraction induced by
electron captures Mg cannot trigger
the explosion unless 25
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Two critical points 2) The presence of residual
12C
Models suggest incomplete C-burning Xc lt/
1 Domínguez et al93 Ritossa et al96
The C-reaction rate at low temperatures is
critical!
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Spectrum at maximum light

• Peak absorption
• CII OI SiII
• SI CaII MgII
• Incomplete burning

10000 ? 15000 km/s
Near-IR SiII CaII MgII Fe peak
Hatano et al. 1999
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Observational constraints. II

• Intermediate elements must be present in the
  outer layers to account for the spectrum at
  maximum light

• The burning must be subsonic. It can be
  supersonic only if ? lt 107 g/cm3

The abundances of the iron peak elements (54Fe,
58Ni, 54Cr) must be compatible with the Solar
System abundances after mixing with
gravitational supernova products

• Neutron excesses have to be avoided
• Post-burning e- -captures
• Neutrons stored as 22Ne

• Decrease ignition density
• Decrease 22Ne content
• Reduce the SNIa galactic contribution

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Observational constraints. III

• Homogeneity?
• Differences in brightness Overluminous (SN
  1991T), underluminous (SN1991bg)
• Differences in the expansion velocity (vexp
  10,000-15,000 km/s)
• Two points of view
• There is a bulk of homogeneous supernovae plus
  some peculiars
• SNIa display a continuous range of values
• Is there a unique scenario unique mechanism
  able to accommodate the normal behavior plus that
  of dissidents?
• Is there a mechanism able to produce a continuous
  range of situations?
• Can both mechanisms coexist?

Anything able to explode eventually do it !!!