Oil-on-water: Modelling mass transfer in binaries using SPH Ross Church Department of Astronomy and Theoretical Physics Lund University With Melvyn B. Davies, Christopher Tout, Johann Dischler, Tim Adams & Martin Beer
Friday, November 12, 2010
What is a binary? • A pair of stars orbiting each other • Orbits are circular or elliptical • Most stars are in binaries X
Friday, November 12, 2010
Mass-transfer binaries
• Stars expand as they evolve: mass can be transferred from one star to the other
• Lots of interesting astronomical objects are mass-transfer binaries:
• Cataclysmic variables (CVs) • X-ray binaries • Type IA supernovae • ... (see Rob’s talk) Friday, November 12, 2010
Roche Lobes • The Roche Lobe is the equipotential
surface connecting the two stars in the rotating frame
y/a
0.5
0
−0.5 −1.5
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−1
−0.5
0 x/a
0.5
1
1.5
Roche Lobes
• When a star fills its Roche lobe, mass transfers to its companion
• Steady mass transfer rate keeps the star just inside its Roche Lobe −1.5
0
−0.5 −1.5
−1
−0.5
0 x/a
0.5
1
1.5
Φ/a2 Ω2
y/a
0.5
−2
−2.5
−3
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−2
−1
0 x/a
1
2
Limitations of Roche Lobes • Roche formalism doesn’t apply to eccentric binaries
y/a
0.5
0
−0.5 −1.5
−1
−0.5
0
0.5
1
1.5
x/a
Φ/a2 Ω2
−1.5
−2
about the transfer of momentum
• Doesn’t tell us what fraction of
−2.5
−3
• Have to make assumptions
−2
−1
0 x/a
1
2
the mass is lost from the system
• Can’t study non-equilibrium mass transfer
Friday, November 12, 2010
SPH • SPH (smoothed-particle hydrodynamics) is a Lagrangian hydrodynamic technique
• Represent fluid by particles, each having a mass, internal energy, etc.
• Calculate density, temperature by averaging over particles with an interpolation function W(h), where h is the particle’s smoothing length
• Widely used for astrophysical simulations Friday, November 12, 2010
The problem - numbers Typical mass-transfer rate in CVs M˙ ! 10−9 M" yr−1
with orbital period Porb ! 1 day
giving mass transferred per orbit ∆M ! 10
−12
M" ! 10
−12
M!
This is impractical, even with GPUs! Friday, November 12, 2010
Two-phase system • Body of the star made of heavy “water” particles • Atmosphere made of light “oil” particles • Introduce a Fgrav
fictitious force to stop the oil particles sinking into the water star
• For details see
Fgrav
Fgrav
Fgrav
Fn
Church et al. (2009)
Water particles (heavy)
MNRAS 395 1127
Oil particles (light)
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Fn
Advantages • Water star modelled with full SPH • Includes e.g. tidal deformation of the star • Oil atmosphere modelled with full SPH • Oil particles are not test particles! • Can follow the formation of an accretion disc etc.
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Stellar model
. ... ... . .... . . .... .. ... .. .. . . . . .... .... . . . .... .. .. . . ....... .. . ........ . . ..... . . .. .. .. ........ . .. . . .
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... ...... ....... . . . . . . . . . . ............ ................................................... .. . . . . . . . .. . . . . ................ ............ ...... ........ ........................... .... ................... . . . . .............. . .... ................ ................................................................. ..... ..... ............... . ............. ...................................................................... ...................................... .... ......... ................. .............................. ............................................................................................................................................................................................................. . . . . . .. . .. . . .................. ......................................................................................................................................................................................................................................................................................... ........... ............................................................................................. ......... ...... ........ .... .... ................................................................................. ............. .................................................................................................................................................................................................................................................... ............... .................... ............ .............................. ..................................... ....... .......................... ... ............ .............................................................. ............. .. . .. . . . .. ......................................................................................................................................................................................................................................................................................................... .................... ............................................................................................................................................ ........................ ........... ............. ................ .................. ...... ... ....... ..... ............ ............ ..... ............................... .... ........... .............. ... .......................................................................................... ............... ........ .. .. ............ ............. . .................. ...... .................................... ....................................... ........... . . . .. . . .. .. .... . ... .. . ... . .. ...... . . . ............................. . ................. .................................................................... . . .. .... . ...
• Slice through the centre
• Structure visible in envelope: more particles allow more fine-grained structure
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Next steps • Higher resolution in the envelope • Modelling binaries containing two compact objects (BH/NS/WD)
• Onset of common envelope evolution
Friday, November 12, 2010
