Merger Simulations (examining the onset and outcome of various instabilities)
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Transcript of Merger Simulations (examining the onset and outcome of various instabilities)
![Page 1: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/1.jpg)
Merger Simulations(examining the onset and outcome of various instabilities)
Joel E. TohlineLouisiana State University
Collaborators: J. Frank, P. Motl, W. Even, D. Marcello, G. Clayton, C. Fryer, S. Diehl
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LSU: Physics & Astronomy Colloquium
Part I: Broad Context
9/03/2009
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LSU: Physics & Astronomy Colloquium
Double White Dwarfs (DWDs)
9/03/2009
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LSU: Physics & Astronomy Colloquium
Binary System Parameters(circular orbit; point-mass system)
9/03/2009
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LSU: Physics & Astronomy Colloquium
Binary System Parameters(circular orbit; point-mass system)
Sufficient to specify: M, q, Porb
9/03/2009
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LSU: Physics & Astronomy Colloquium
Binary System Parameters(circular orbit; WD mass-radius relationship)
R1
R2 a
M2M1
9/03/2009
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LSU: Physics & Astronomy Colloquium
Binary System Parameters(circular orbit; WD mass-radius relationship)
R1
R2 a
M2M1
9/03/2009
![Page 8: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/8.jpg)
LSU: Physics & Astronomy Colloquium
Binary System Parameters(mass-transfer system)
R1
R2 a
M2M1
donor
9/03/2009
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LSU: Physics & Astronomy Colloquium
Binary System Parameters(circular orbit; point-mass system)
Sufficient to specify: M, q, Porb
9/03/2009
![Page 10: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/10.jpg)
Lorentz Center: Stellar Mergers
(slide stolen from this past Friday’s talk by Nelemans)
9/29/2009
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Lorentz Center: Stellar Mergers
(slide stolen from this past Friday’s talk by Nelemans)
9/29/2009
![Page 12: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/12.jpg)
Lorentz Center: Stellar Mergers
Possible Mtot - q0 Distribution at Birth[borrowing Hurley’s population synthesis code (2002)]
9/29/2009
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LSU: Physics & Astronomy Colloquium
Gravitational-Wave Detectors
9/03/2009
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LSU: Physics & Astronomy Colloquium
Hanford Observatory
LivingstonObservatory
Laser Interferometer Gravitational-wave Observatory (LIGO)
9/03/2009
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Laser Interferometer Gravitational-wave Observatory (LIGO)
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LSU: Physics & Astronomy Colloquium
Gravitational-Wave Signalcharacterized by amplitude “h” and frequency “f”
9/03/2009
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LSU: Physics & Astronomy Colloquium
Gravitational-Wave Signalcharacterized by amplitude “h” and frequency “f”
From GR quadrupole radiation formula (e.g., Peters & Mathews 1963)9/03/2009
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LSU: Physics & Astronomy Colloquium
Classic “chirp” Signaldue to point-mass binary inspiral
From GR quadrupole radiation formula (e.g., Peters & Mathews 1963)9/03/2009
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LSU: Physics & Astronomy Colloquium
Classic “chirp” Signaldue to point-mass binary inspiral
From GR quadrupole radiation formula (e.g., Peters & Mathews 1963)9/03/2009
![Page 20: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/20.jpg)
LSU: Physics & Astronomy Colloquium
Classic “chirp” Signaldue to point-mass binary inspiral
From GR quadrupole radiation formula (e.g., Peters & Mathews 1963)9/03/2009
During inspiral: h ~ f2/3
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LSU: Physics & Astronomy Colloquium
High-Frequency Sources of Gravitational Radiation
Taken from … http://lisa.jpl.nasa.gov/gallery/ligo-lisa.html 9/03/2009
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LSU: Physics & Astronomy Colloquium
Binary Orbital ParametersAM CVn Hulse-Taylor pulsar
9/03/2009
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LSU: Physics & Astronomy Colloquium
Binary Orbital ParametersAM CVn Hulse-Taylor pulsar
9/03/2009
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LSU: Physics & Astronomy Colloquium
Radiation from Hulse-Taylor Pulsar
Taken from … http://lisa.jpl.nasa.gov/gallery/ligo-lisa.html 9/03/2009
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LSU: Physics & Astronomy Colloquium
Binary Orbital ParametersAM CVn Hulse-Taylor pulsar
9/03/2009
![Page 26: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/26.jpg)
LSU: Physics & Astronomy Colloquium
Binary Orbital ParametersAM CVn Hulse-Taylor pulsar
9/03/2009
![Page 27: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/27.jpg)
LSU: Physics & Astronomy Colloquium
Low-Frequency Sources of Gravitational Radiation
Taken from … http://lisa.jpl.nasa.gov/gallery/ligo-lisa.html 9/03/2009
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LSU: Physics & Astronomy Colloquium
Laser-Interferometer Space Antenna (LISA)
9/03/2009
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LSU: Physics & Astronomy Colloquium
High-Frequency Sources of Gravitational Radiation
Taken from … http://lisa.jpl.nasa.gov/gallery/ligo-lisa.html 9/03/2009
![Page 30: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/30.jpg)
LSU: Physics & Astronomy Colloquium
DWD Orbit Evolutionsin LISA’s Strain-Frequency Domain
9/03/2009
[Kopparapu & Tohline (2007)]
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LSU: Physics & Astronomy Colloquium
DWD Evolutionary Trajectories(for given “q”)
9/03/2009
“detached” inspiral
“mass-transferring” out-spiral
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LSU: Physics & Astronomy Colloquium
DWD Evolutionary Trajectories(for given “q”)
9/03/2009
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LSU: Physics & Astronomy Colloquium
DWD Evolutionary Trajectories(for given “q”)
9/03/2009
“detached” inspiral
“mass-transferring” out-spiral
![Page 34: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/34.jpg)
LSU: Physics & Astronomy Colloquium
DWD Evolutionary Trajectories(for given “q”)
9/03/2009
![Page 35: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/35.jpg)
LSU: Physics & Astronomy Colloquium
DWD Evolutionary Trajectories(for given “q”)
9/03/2009
![Page 36: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/36.jpg)
LSU: Physics & Astronomy Colloquium
Part II: This Work
9/03/2009
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Lorentz Center: Stellar Mergers
General Context of this Work• Onset and nonlinear development of mass-transfer in
Double White Dwarf (DWD) binaries– Initiated by Roche Lobe Overflow (RLOF)– Followed through £ 40 orbits.
• Self-consistent, 3D Newtonian hydrodynamic modeling of mass-transfer (and merger) using a finite-volume “grid” code, not SPH
• The stars have comparable radii, so you’ll see “direct impact” rather than “disk” accretion
9/29/2009
![Page 38: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/38.jpg)
Lorentz Center: Stellar Mergers
General Context of this Work• Onset and nonlinear development of mass-transfer in
Double White Dwarf (DWD) binaries– Initiated by Roche Lobe Overflow (RLOF)– Followed through £ 40 orbits.
• Self-consistent, 3D Newtonian hydrodynamic modeling of mass-transfer (and merger) using a finite-volume “grid” code, not SPH
• The stars have comparable radii, so you’ll see “direct impact” rather than “disk” accretion
9/29/2009
![Page 39: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/39.jpg)
Lorentz Center: Stellar Mergers
General Context of this Work• Onset and nonlinear development of mass-transfer in
Double White Dwarf (DWD) binaries– Initiated by Roche Lobe Overflow (RLOF)– Followed through £ 40 orbits.
• Self-consistent, 3D Newtonian hydrodynamic modeling of mass-transfer (and merger) using a finite-volume “grid” code, not SPH
• The stars have comparable radii, so you’ll see “direct impact” rather than “disk” accretion
9/29/2009
![Page 40: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/40.jpg)
Lorentz Center: Stellar Mergers
General Context of this Work• Onset and nonlinear development of mass-transfer in
Double White Dwarf (DWD) binaries– Initiated by Roche Lobe Overflow (RLOF)– Followed through £ 40 orbits.
• Self-consistent, 3D Newtonian hydrodynamic modeling of mass-transfer (and merger) using a finite-volume “grid” code, not SPH
• The stars have comparable radii, so you’ll see “direct impact” rather than “disk” accretion
9/29/2009
![Page 41: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/41.jpg)
Lorentz Center: Stellar Mergers
General Context of this Work• Onset and nonlinear development of mass-transfer in
Double White Dwarf (DWD) binaries– Initiated by Roche Lobe Overflow (RLOF)– Followed through £ 40 orbits.
• The stars have comparable radii, so you’ll see “direct impact” rather than “disk” accretion
• Self-consistent, 3D Newtonian hydrodynamic modeling of mass-transfer (and merger) using a finite-volume “grid” code, not SPH
9/29/2009
![Page 42: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/42.jpg)
Lorentz Center: Stellar Mergers
General Context of this Work• Onset and nonlinear development of mass-transfer in
Double White Dwarf (DWD) binaries– Initiated by Roche Lobe Overflow (RLOF)– Followed through £ 40 orbits.
• The stars have comparable radii, so you’ll see “direct impact” rather than “disk” accretion
• Self-consistent, 3D Newtonian hydrodynamic modeling of mass-transfer (and merger) using a finite-volume “grid” code, not SPH
9/29/2009
![Page 43: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/43.jpg)
Lorentz Center: Stellar Mergers
0;
Pure Hydro
0 ;
9/29/2009
![Page 44: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/44.jpg)
Lorentz Center: Stellar Mergers
General Context of this Work• Equation of state: While we have used a zero-
temperature white dwarf (ZTWD) EOS, here I will show only n = 3/2 polytropic (g = 5/3 adiabatic) flows– a reasonably good approximation for low-mass white dwarfs– broadly appealing because polytropes are scale-free
• Effects of photon radiation ignored (until very recently)• Keeping the “micro-physics” simple …
– makes it easier to pinpoint what physics is responsible for the dynamical features that arise in a given simulation
– Makes it easier to ascertain what is physics and what is purely numerical
9/29/2009
![Page 45: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/45.jpg)
Lorentz Center: Stellar Mergers
General Context of this Work• Equation of state: While we have used a zero-
temperature white dwarf (ZTWD) EOS, here I will show only n = 3/2 polytropic (g = 5/3 adiabatic) flows– a reasonably good approximation for low-mass white dwarfs– broadly appealing because polytropes are scale-free
• Effects of photon radiation ignored (until very recently)• Keeping the “micro-physics” simple …
– makes it easier to pinpoint what physics is responsible for the dynamical features that arise in a given simulation
– Makes it easier to ascertain what is physics and what is purely numerical
9/29/2009
![Page 46: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/46.jpg)
Lorentz Center: Stellar Mergers
General Context of this Work• Equation of state: While we have used a zero-
temperature white dwarf (ZTWD) EOS, here I will show only n = 3/2 polytropic (g = 5/3 adiabatic) flows– a reasonably good approximation for low-mass white dwarfs– broadly appealing because polytropes are scale-free
• Effects of photon radiation ignored (until very recently)• Keeping the “micro-physics” simple …
– makes it easier to pinpoint what physics is responsible for the dynamical features that arise in a given simulation
– Makes it easier to ascertain what is physics and what is purely numerical
9/29/2009
![Page 47: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/47.jpg)
Lorentz Center: Stellar Mergers
General Context of this Work• Equation of state: While we have used a zero-
temperature white dwarf (ZTWD) EOS, here I will show only n = 3/2 polytropic (g = 5/3 adiabatic) flows– a reasonably good approximation for low-mass white dwarfs– broadly appealing because polytropes are scale-free
• Effects of photon radiation ignored (until very recently)• Keeping the “micro-physics” simple …
– makes it easier to pinpoint what physics is responsible for the dynamical features that arise in a given simulation
– Makes it easier to ascertain what is physics and what is purely numerical
9/29/2009
![Page 48: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/48.jpg)
Lorentz Center: Stellar Mergers
General Context of this Work• Equation of state: While we have used a zero-
temperature white dwarf (ZTWD) EOS, here I will show only n = 3/2 polytropic (g = 5/3 adiabatic) flows– a reasonably good approximation for low-mass white dwarfs– broadly appealing because polytropes are scale-free
• Effects of photon radiation ignored (until very recently)• Keeping the “micro-physics” simple …
– makes it easier to pinpoint what physics is responsible for the dynamical features that arise in a given simulation
– Makes it easier to ascertain what is physics and what is purely numerical
9/29/2009
![Page 49: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/49.jpg)
Lorentz Center: Stellar Mergers
General Context of this Work• Equation of state: While we have used a zero-
temperature white dwarf (ZTWD) EOS, here I will show only n = 3/2 polytropic (g = 5/3 adiabatic) flows– a reasonably good approximation for low-mass white dwarfs– broadly appealing because polytropes are scale-free
• Effects of photon radiation ignored (until very recently)• Keeping the “micro-physics” simple …
– makes it easier to pinpoint what physics is responsible for the dynamical features that arise in a given simulation
– Makes it easier to ascertain what is physics and what is purely numerical
9/29/2009
![Page 50: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/50.jpg)
Lorentz Center: Stellar Mergers
Some Theoretical Considerations
• “Darwin Instability”– Has been mentioned several different times over the
course of this workshop as relevant to mergers (e.g., DWDs and WUMa systems)
– Point along a (synchronously rotating) binary inspiral sequence at which Jtot and Etot reach a minimum
– Any further loss of angular momentum (inspiral) leads to secular instability loss of synchronous rotation and, perhaps, tidal disruption/merger
9/29/2009
![Page 51: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/51.jpg)
Lorentz Center: Stellar Mergers
Some Theoretical Considerations
• “Darwin Instability”– Has been mentioned several different times over the
course of this workshop as relevant to mergers (e.g., DWDs and W UMa systems)
– Point along a (synchronously rotating) binary inspiral sequence at which Jtot and Etot reach a minimum
– Any further loss of angular momentum (inspiral) leads to secular instability loss of synchronous rotation and, perhaps, tidal disruption/merger
9/29/2009
![Page 52: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/52.jpg)
Lorentz Center: Stellar Mergers
Some Theoretical Considerations
• “Darwin Instability”– Has been mentioned several different times over the
course of this workshop as relevant to mergers (e.g., DWDs and W UMa systems)
– Point along a (synchronously rotating) binary inspiral sequence at which Jtot and Etot reach a minimum
– Any further loss of angular momentum (inspiral) leads to secular instability loss of synchronous rotation and, perhaps, tidal disruption/merger
9/29/2009
![Page 53: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/53.jpg)
Lorentz Center: Stellar Mergers
Some Theoretical Considerations
• “Darwin Instability”– Has been mentioned several different times over the
course of this workshop as relevant to mergers (e.g., DWDs and W UMa systems)
– Point along a (synchronously rotating) binary inspiral sequence at which Jtot and Etot reach a minimum
– Any further loss of angular momentum (inspiral) leads to secular instability loss of synchronous rotation and, perhaps, tidal disruption/merger
9/29/2009
![Page 54: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/54.jpg)
Lorentz Center: Stellar Mergers
Equal-mass DWD Sequences
9/29/2009
New
& To
hlin
e 19
97
![Page 55: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/55.jpg)
Lorentz Center: Stellar Mergers
Equal-mass DWD Sequences
9/29/2009
New
& To
hlin
e 19
97
Minimum J
![Page 56: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/56.jpg)
Lorentz Center: Stellar Mergers
Equal-mass DWD Sequences
9/29/2009
New
& To
hlin
e 19
97
Contact
![Page 57: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/57.jpg)
Lorentz Center: Stellar Mergers
Unequal-mass (q = ½) DWD Sequence
9/29/2009
Evan & Tohline 2009
![Page 58: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/58.jpg)
Lorentz Center: Stellar Mergers
Unequal-mass (q = ½) DWD Sequence
9/29/2009
Evan & Tohline 2009
Contact
![Page 59: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/59.jpg)
Lorentz Center: Stellar Mergers
Some Theoretical Considerations
• “Darwin Instability” (cont.)
– Not relevant to the onset of mass-transfer in DWD binaries because the less massive star fills its Roche Lobe before the binary reaches Jmin along its inspiral sequence.
9/29/2009
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Lorentz Center: Stellar Mergers
Some Theoretical Considerations
• Mass-Transfer Instability– Once the less massive WD (donor) fills its Roche
Lobe and begins to transfer mass to its more massive companion (accretor)… • Donor’s radius expands: zdon = ¶lnRdon/¶lnMdon
• Roche geometry readjusts: zRL = ¶lnRRL/¶lnMdon
– Parameter, D = ½(zdon – zRL), governs stability …• Stable against further mass-transfer if D > 0• Dynamically unstable if D < 0
9/29/2009
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Lorentz Center: Stellar Mergers
Some Theoretical Considerations
• Mass-Transfer Instability– Once the less massive WD (donor) fills its Roche
Lobe and begins to transfer mass to its more massive companion (accretor)… • Donor’s radius expands: zdon = ¶lnRdon/¶lnMdon
• Roche geometry readjusts: zRL = ¶lnRRL/¶lnMdon
– Parameter, D = ½(zdon – zRL), governs stability …• Stable against further mass-transfer if D > 0• Dynamically unstable if D < 0
9/29/2009
![Page 62: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/62.jpg)
Lorentz Center: Stellar Mergers
Some Theoretical Considerations
• Mass-Transfer Instability– Once the less massive WD (donor) fills its Roche
Lobe and begins to transfer mass to its more massive companion (accretor)… • Donor’s radius expands: zdon = ¶lnRdon/¶lnMdon
• Roche geometry readjusts: zRL = ¶lnRRL/¶lnMdon
– Parameter, D = ½(zdon – zRL), governs stability …• Stable against further mass-transfer if D > 0• Dynamically unstable if D < 0
9/29/2009
![Page 63: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/63.jpg)
Lorentz Center: Stellar Mergers
Some Theoretical Considerations
• Mass-Transfer Instability (cont.)
– For n = 3/2 polytropic EOS and assumption of conservative mass transfer (CMT) • zdon = -1/3
• zRL = 2q – 5/3
– Parameter, D = ½(zdon – zRL) = (2/3 – q), • System stable if q < qcrit = 2/3
• Dynamically unstable if q > qcrit 2/3
9/29/2009
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Lorentz Center: Stellar Mergers
Some Theoretical Considerations
• Mass-Transfer Instability (cont.)
– For n = 3/2 polytropic EOS and assumption of conservative mass transfer (CMT) • zdon = -1/3
• zRL = 2q – 5/3
– Parameter, D = ½(zdon – zRL) = (2/3 – q), • System stable if q < qcrit = 2/3
• Dynamically unstable if q > qcrit 2/3
9/29/2009
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Lorentz Center: Stellar Mergers
Some Theoretical Considerations
• Mass-Transfer Instability (cont.)
– For much more complete discussion, including important considerations of non-CMT• Paczyński (1967)• King & Kolb (1995)• Marsh, Nelemans & Steeghs (2004)• Gokhale, Peng & Frank (2007)• Belczynski et al. (2008) -- StarTracks
9/29/2009
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Lorentz Center: Stellar Mergers
Key Questions[that we may be able to answer with numerical simulations]
1. At onset, is mass-transfer stable or unstable?2. If unstable, what is the hydrodynamic
outcome of instability?3. Do results depend on choice of numerical
algorithm?4. How does outcome depend on the system’s
ability to cool (via photon radiation)?5. What about super-Eddington accretion?
9/29/2009
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Lorentz Center: Stellar Mergers
1. Is mass-transfer stable or unstable?
• We’ll discuss this question in the context of an “Mtot - q0” parameter-space diagram that contains a hypothetical population of newborn double white dwarf binaries …
9/29/2009
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Lorentz Center: Stellar Mergers
1. Is mass-transfer stable or unstable?
We’ll discuss this question in the context of an “Mtot - q0” parameter-space diagram that contains a hypothetical population of newborn double white dwarf binaries …
9/29/2009
![Page 69: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/69.jpg)
Lorentz Center: Stellar Mergers
Possible Mtot - q0 Distribution at Birth[borrowing Hurley’s population synthesis code (2002)]
9/29/2009
![Page 70: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/70.jpg)
Lorentz Center: Stellar Mergers
Possible Mtot - q0 Distribution at Birth[borrowing Hurley’s population synthesis code (2002)]
9/29/2009
![Page 71: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/71.jpg)
Lorentz Center: Stellar Mergers
Possible Mtot - q0 Distribution at Birth[borrowing Hurley’s population synthesis code (2002)]
9/29/2009
**NOT**precursors for
Type Ia SNe
![Page 72: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/72.jpg)
Lorentz Center: Stellar Mergers
1. Is mass-transfer stable or unstable?• Answer depends only weakly on Mtot
• Answer depends principally on initial mass ratio q0
• What is the value of qcrit?– Almost certainly, qcrit £ 2/3– But maybe, qcrit » 1/5 (due to direct-impact accretion)
• Numerical simulations (Motl et al. 2007) indicate that qcrit is closer to 2/3 than to 1/5
9/29/2009
q0 < qcrit stable AM CVn (presumably)q0 > qcrit unstable ???
![Page 73: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/73.jpg)
Lorentz Center: Stellar Mergers
1. Is mass-transfer stable or unstable?• Answer depends only weakly on Mtot
• Answer depends principally on initial mass ratio q0
• What is the value of qcrit?– Almost certainly, qcrit £ 2/3– But maybe, qcrit » 1/5 (due to direct-impact accretion)
• Numerical simulations (Motl et al. 2007) indicate that qcrit is closer to 2/3 than to 1/5
9/29/2009
q0 < qcrit stable AM CVn (presumably)q0 > qcrit unstable ???
![Page 74: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/74.jpg)
Lorentz Center: Stellar Mergers
1. Is mass-transfer stable or unstable?• Answer depends only weakly on Mtot
• Answer depends principally on initial mass ratio q0
• What is the value of qcrit?– Almost certainly, qcrit £ 2/3– But maybe, qcrit » 1/5 (due to direct-impact accretion)
• Numerical simulations (Motl et al. 2007) indicate that qcrit is closer to 2/3 than to 1/5
9/29/2009
q0 < qcrit stable AM CVn (presumably)q0 > qcrit unstable ???
![Page 75: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/75.jpg)
Lorentz Center: Stellar Mergers
1. Is mass-transfer stable or unstable?• Answer depends only weakly on Mtot
• Answer depends principally on initial mass ratio q0
• What is the value of qcrit?– Almost certainly, qcrit £ 2/3– But maybe, qcrit » 1/5 (due to direct-impact accretion)
• Numerical simulations (Motl et al. 2007) indicate that qcrit is closer to 2/3 than to 1/5
9/29/2009
q0 < qcrit stable AM CVn (presumably)q0 > qcrit unstable ???
![Page 76: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/76.jpg)
Lorentz Center: Stellar Mergers
1. Is mass-transfer stable or unstable?• Answer depends only weakly on Mtot
• Answer depends principally on initial mass ratio q0
• What is the value of qcrit?– Almost certainly, qcrit £ 2/3– But maybe, qcrit » 1/5 (due to direct-impact accretion)
• Numerical simulations (Motl et al. 2007) indicate that qcrit is closer to 2/3 than to 1/5
9/29/2009
q0 < qcrit stable AM CVn (presumably)q0 > qcrit unstable ???
![Page 77: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/77.jpg)
Lorentz Center: Stellar Mergers
If qcrit = 2/3 …
9/29/2009
Stable mass-transfer
qcrit
![Page 78: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/78.jpg)
Lorentz Center: Stellar Mergers
1. Is mass-transfer stable or unstable?• Answer depends only weakly on Mtot
• Answer depends principally on initial mass ratio q0
• What is the value of qcrit?– Almost certainly, qcrit £ 2/3– But maybe, qcrit » 1/5 (due to direct-impact accretion)
• Numerical simulations (Motl et al. 2007) indicate that qcrit is closer to 2/3 than to 1/5
9/29/2009
q0 < qcrit stable AM CVn (presumably)q0 > qcrit unstable ???
![Page 79: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/79.jpg)
Lorentz Center: Stellar Mergers
If qcrit = 1/5 …
9/29/2009
Stable mass-transferqcrit
![Page 80: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/80.jpg)
Lorentz Center: Stellar Mergers
1. Is mass-transfer stable or unstable?• Answer depends only weakly on Mtot
• Answer depends principally on initial mass ratio q0
• What is the value of qcrit?– Almost certainly, qcrit £ 2/3– But maybe, qcrit » 1/5 (due to direct-impact accretion)
• Numerical simulations (Motl et al. 2007) indicate that qcrit is closer to 2/3 than to 1/5
9/29/2009
q0 < qcrit stable AM CVn (presumably)q0 > qcrit unstable ???
![Page 81: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/81.jpg)
Lorentz Center: Stellar Mergers
q0 = 0.5 (stable mass-transfer)
9/29/2009
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Lorentz Center: Stellar Mergers
2. What is hydrodynamic outcome of instability?
• Answer depends on q0
• Numerical simulations have not yet pinned down the value of qmerge, but it is certainly > 0.7
9/29/2009
qcrit < qmerge < q0 donor plunges into accretorqcrit < q0 < qmerge tidal disruption of donor
![Page 83: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/83.jpg)
Lorentz Center: Stellar Mergers
2. What is hydrodynamic outcome of instability?
• Answer depends on q0
• Numerical simulations have not yet pinned down the value of qmerge, but it is certainly > 0.7
9/29/2009
qcrit < qmerge < q0 donor plunges into accretorqcrit < q0 < qmerge tidal disruption of donor
![Page 84: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/84.jpg)
Lorentz Center: Stellar Mergers
2. What is hydrodynamic outcome of instability?
• Answer depends on q0
• Numerical simulations have not yet pinned down the value of qmerge, but it is certainly > 0.7
9/29/2009
qcrit < qmerge < q0 donor plunges into accretorqcrit < q0 < qmerge tidal disruption of donor
![Page 85: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/85.jpg)
Lorentz Center: Stellar Mergers
2. What is hydrodynamic outcome of instability?
• Answer depends on q0
• Numerical simulations have not yet pinned down the value of qmerge, but it is certainly > 0.7
9/29/2009
qcrit < qmerge < q0 donor plunges into accretorqcrit < q0 < qmerge tidal disruption of donor
![Page 86: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/86.jpg)
Lorentz Center: Stellar Mergers
2. What is hydrodynamic outcome of instability?
• Answer depends on q0
• Numerical simulations have not yet pinned down the value of qmerge, but it is certainly > 0.7
9/29/2009
qcrit < qmerge < q0 donor plunges into accretorqcrit < q0 < qmerge tidal disruption of donor
![Page 87: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/87.jpg)
Lorentz Center: Stellar Mergers
q0 = 0.7 (tidal disruption of donor)
9/29/2009
![Page 88: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/88.jpg)
Lorentz Center: Stellar Mergers
What is hydrodynamic outcome of instability?
9/29/2009
Credit: W. Even
![Page 89: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/89.jpg)
Lorentz Center: Stellar Mergers
What is hydrodynamic outcome of instability?
9/29/2009
Credit: W. Even
![Page 90: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/90.jpg)
Lorentz Center: Stellar Mergers
What is hydrodynamic outcome of instability?
9/29/2009
Credit: W. Even
W0
![Page 91: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/91.jpg)
Lorentz Center: Stellar Mergers
2. What is hydrodynamic outcome of instability?
• Answer depends on q0
• Numerical simulations have not yet pinned down the value of qmerge, but it is certainly > 0.7
9/29/2009
qcrit < qmerge < q0 donor plunges into accretorqcrit < q0 < qmerge tidal disruption of donor
![Page 92: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/92.jpg)
Lorentz Center: Stellar Mergers
If qcrit = 2/3 and qmerge = 0.9 …
9/29/2009
Stable mass-transfer
Tidal disruption of donor
Donor plunges into accretor
qcrit
qmerge
![Page 93: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/93.jpg)
Lorentz Center: Stellar Mergers
3. Do Results Depend on Choice of Numerical Algorithm?
• We are in the middle of a collaborative project in which an extensive set of binary simulations is being carried out to compare results from two very different numerical algorithms:– Our grid-based, finite-volume hydrocode [P. Motl, W. Even, J.E.
Tohline]– A smoothed-particle hydrocode (SPH) used by Fryer’s group at LANL
[S. Diehl, C. Fryer]• Preliminary report: Amazingly good agreement for unstable
(i.e., merger or tidal disruption) evolutions if …– Simulations start from identical “quiet” starts;– The number of SPH particles is comparable to number of grid cells.
9/29/2009
![Page 94: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/94.jpg)
Lorentz Center: Stellar Mergers
3. Do Results Depend on Choice of Numerical Algorithm?
• We are in the middle of a collaborative project in which an extensive set of binary simulations is being carried out to compare results from two very different numerical algorithms:– Our grid-based, finite-volume hydrocode [P. Motl, W. Even, J.E.
Tohline]– A smoothed-particle hydrocode (SPH) used by Fryer’s group at LANL
[S. Diehl, C. Fryer]• Preliminary report: Amazingly good agreement for unstable
(i.e., merger or tidal disruption) evolutions if …– Simulations start from identical “quiet” starts;– The number of SPH particles is comparable to number of grid cells.
9/29/2009
![Page 95: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/95.jpg)
Lorentz Center: Stellar Mergers
3. Do Results Depend on Choice of Numerical Algorithm?
• We are in the middle of a collaborative project in which an extensive set of binary simulations is being carried out to compare results from two very different numerical algorithms:– Our grid-based, finite-volume hydrocode [P. Motl, W. Even, J.E.
Tohline]– A smoothed-particle hydrocode (SPH) used by Fryer’s group at LANL
[S. Diehl, C. Fryer]• Preliminary report: Amazingly good agreement for unstable
(i.e., merger or tidal disruption) evolutions if …– Simulations start from identical “quiet” starts;– The number of SPH particles is comparable to number of grid cells.
9/29/2009
![Page 96: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/96.jpg)
Lorentz Center: Stellar Mergers
Do Results Depend on Choice of Numerical Algorithm?
9/29/2009
LSU grid codeLANL SPH code
106 particles 105 particles
![Page 97: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/97.jpg)
Lorentz Center: Stellar Mergers
4. How Does Outcome Depend on System’s Ability to Cool?
• In our collaboration with the LANL group, we are also examining two extremes:– Using an “ideal-gas” equation of state, the accreted layers trap all of
the heat that is generated through the accretion shock (no cooling)– Using a “polytropic” equation of state, the accreted layers are allowed
to cool back down to the specific entropy of the donor material• Preliminary report: Unstable (i.e., merger or tidal disruption)
evolutions change only in relatively subtle ways when the “ideal-gas” EOS is used in place of the “polytropic” EOS. (On this point, as well, there is good agreement between the SPH and grid-code simulations.)
9/29/2009
![Page 98: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/98.jpg)
Lorentz Center: Stellar Mergers
4. How Does Outcome Depend on System’s Ability to Cool?
• In our collaboration with the LANL group, we are also examining two extremes:– Using an “ideal-gas” equation of state, the accreted layers trap all of
the heat that is generated through the accretion shock (no cooling)– Using a “polytropic” equation of state, the accreted layers are allowed
to cool back down to the specific entropy of the donor material• Preliminary report: Unstable (i.e., merger or tidal disruption)
evolutions change only in relatively subtle ways when the “ideal-gas” EOS is used in place of the “polytropic” EOS. (On this point, as well, there is good agreement between the SPH and grid-code simulations.)
9/29/2009
![Page 99: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/99.jpg)
Lorentz Center: Stellar Mergers
4. How Does Outcome Depend on System’s Ability to Cool?
• In our collaboration with the LANL group, we are also examining two extremes:– Using an “ideal-gas” equation of state, the accreted layers trap all of
the heat that is generated through the accretion shock (no cooling)– Using a “polytropic” equation of state, the accreted layers are allowed
to cool back down to the specific entropy of the donor material• Preliminary report: Unstable (i.e., merger or tidal disruption)
evolutions change only in relatively subtle ways when the “ideal-gas” EOS is used in place of the “polytropic” EOS. (On this point, as well, there is good agreement between the SPH and grid-code simulations.)
9/29/2009
![Page 100: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/100.jpg)
Lorentz Center: Stellar Mergers
4. How Does Outcome Depend on System’s Ability to Cool?
9/29/2009
![Page 101: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/101.jpg)
Lorentz Center: Stellar Mergers
5. What About Super-Eddington Accretion?
• Up to now, our simulations have not included forcing due to a radiative flux. Hence, we have not been in a position to examine how the dynamics is altered when the accretion flow resulting from unstable mass-transfer becomes “super-Eddington”.– Does mass (and angular momentum) get ejected from the system?– Does a significant “common envelope” form as a result?
• We have recently modified our code to handle radiation transport in the flux-limited-diffusion approximation, a la Hayes et al. (2006).
9/29/2009
![Page 102: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/102.jpg)
Lorentz Center: Stellar Mergers
5. What About Super-Eddington Accretion?
• Up to now, our simulations have not included forcing due to a radiative flux. Hence, we have not been in a position to examine how the dynamics is altered when the accretion flow resulting from unstable mass-transfer becomes “super-Eddington”.– Does mass (and angular momentum) get ejected from the system?– Does a significant “common envelope” form as a result?
• We have recently modified our code to handle radiation transport in the flux-limited-diffusion approximation, a la Hayes et al. (2006).
9/29/2009
![Page 103: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/103.jpg)
Lorentz Center: Stellar Mergers
5. What About Super-Eddington Accretion?
• Up to now, our simulations have not included forcing due to a radiative flux. Hence, we have not been in a position to examine how the dynamics is altered when the accretion flow resulting from unstable mass-transfer becomes “super-Eddington”.– Does mass (and angular momentum) get ejected from the system?– Does a significant “common envelope” form as a result?
• We have recently modified our code to handle radiation transport in the flux-limited-diffusion approximation, a la ZEUS-MP (Hayes et al. 2006).
9/29/2009
![Page 104: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/104.jpg)
Lorentz Center: Stellar Mergers
0;
Pure Hydro
0 ;
9/29/2009
![Page 105: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/105.jpg)
Lorentz Center: Stellar Mergers9/29/2009
![Page 106: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/106.jpg)
Lorentz Center: Stellar Mergers
5. What About Super-Eddington Accretion?For an opacity of the form …
we can write …
so we can define,
where,
Then, fEdd > 1 means super-Eddington accretion.
9/29/2009
![Page 107: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/107.jpg)
Lorentz Center: Stellar Mergers
5. What About Super-Eddington Accretion?
9/29/2009
If we actually set …
then, fEdd climbs above unity (i.e., the flow becomes super-Eddington) when climbs above 10-12.
This is not good because, with present numerical techniques, we cannot resolve mass-transfer rates ( ) substantially smaller than 10-4.
Solution: Artificially lower K1 by a factor of 1010. Then, fEdd will climb above unity when climbs above 10-2.
![Page 108: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/108.jpg)
Lorentz Center: Stellar Mergers
5. What About Super-Eddington Accretion?
9/29/2009
If we actually set …
then, fEdd climbs above unity (i.e., the flow becomes super-Eddington) when climbs above 10-12.
This is not good because, with present numerical techniques, we cannot resolve mass-transfer rates ( ) substantially smaller than 10-4.
Solution: Artificially lower K1 by a factor of 1010. Then, fEdd will climb above unity when climbs above 10-2.
![Page 109: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/109.jpg)
Lorentz Center: Stellar Mergers
5. What About Super-Eddington Accretion?
9/29/2009
If we actually set …
then, fEdd climbs above unity (i.e., the flow becomes super-Eddington) when climbs above 10-12.
This is not good because, with present numerical techniques, we cannot resolve mass-transfer rates ( ) substantially smaller than 10-4.
Solution: Artificially lower K1 by a factor of 1010. Then, fEdd will climb above unity when climbs above 10-2.
![Page 110: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/110.jpg)
Lorentz Center: Stellar Mergers
Very Preliminary Results from this new Radiation-Hydro code
9/29/2009
![Page 111: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/111.jpg)
Lorentz Center: Stellar Mergers
Very Preliminary Results from this new Radiation-Hydro code (movies not attached)
9/29/2009
Credit: D. Marcello & P. Motl
![Page 112: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/112.jpg)
Lorentz Center: Stellar Mergers
Summary
• Hopefully, answers to the set of questions we are probing with hydrodynamic simulations …– Will advance our fundamental understanding of a
variety of issues related stellar mergers;– Will help determine what branching ratios are
appropriate to use at key points along the decision trees of stellar-population synthesis codes
9/29/2009
![Page 113: Merger Simulations (examining the onset and outcome of various instabilities)](https://reader035.fdocuments.in/reader035/viewer/2022062814/568166ec550346895ddb37a6/html5/thumbnails/113.jpg)
Lorentz Center: Stellar Mergers
Thanks!
9/29/2009