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
LSU: Physics & Astronomy Colloquium
Part I: Broad Context
9/03/2009
LSU: Physics & Astronomy Colloquium
Double White Dwarfs (DWDs)
9/03/2009
LSU: Physics & Astronomy Colloquium
Binary System Parameters(circular orbit; point-mass system)
9/03/2009
LSU: Physics & Astronomy Colloquium
Binary System Parameters(circular orbit; point-mass system)
Sufficient to specify: M, q, Porb
9/03/2009
LSU: Physics & Astronomy Colloquium
Binary System Parameters(circular orbit; WD mass-radius relationship)
R1
R2 a
M2M1
9/03/2009
LSU: Physics & Astronomy Colloquium
Binary System Parameters(circular orbit; WD mass-radius relationship)
R1
R2 a
M2M1
9/03/2009
LSU: Physics & Astronomy Colloquium
Binary System Parameters(mass-transfer system)
R1
R2 a
M2M1
donor
9/03/2009
LSU: Physics & Astronomy Colloquium
Binary System Parameters(circular orbit; point-mass system)
Sufficient to specify: M, q, Porb
9/03/2009
Lorentz Center: Stellar Mergers
(slide stolen from this past Friday’s talk by Nelemans)
9/29/2009
Lorentz Center: Stellar Mergers
(slide stolen from this past Friday’s talk by Nelemans)
9/29/2009
Lorentz Center: Stellar Mergers
Possible Mtot - q0 Distribution at Birth[borrowing Hurley’s population synthesis code (2002)]
9/29/2009
LSU: Physics & Astronomy Colloquium
Gravitational-Wave Detectors
9/03/2009
LSU: Physics & Astronomy Colloquium
Hanford Observatory
LivingstonObservatory
Laser Interferometer Gravitational-wave Observatory (LIGO)
9/03/2009
Laser Interferometer Gravitational-wave Observatory (LIGO)
LSU: Physics & Astronomy Colloquium
Gravitational-Wave Signalcharacterized by amplitude “h” and frequency “f”
9/03/2009
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
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
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
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
LSU: Physics & Astronomy Colloquium
High-Frequency Sources of Gravitational Radiation
Taken from … http://lisa.jpl.nasa.gov/gallery/ligo-lisa.html 9/03/2009
LSU: Physics & Astronomy Colloquium
Binary Orbital ParametersAM CVn Hulse-Taylor pulsar
9/03/2009
LSU: Physics & Astronomy Colloquium
Binary Orbital ParametersAM CVn Hulse-Taylor pulsar
9/03/2009
LSU: Physics & Astronomy Colloquium
Radiation from Hulse-Taylor Pulsar
Taken from … http://lisa.jpl.nasa.gov/gallery/ligo-lisa.html 9/03/2009
LSU: Physics & Astronomy Colloquium
Binary Orbital ParametersAM CVn Hulse-Taylor pulsar
9/03/2009
LSU: Physics & Astronomy Colloquium
Binary Orbital ParametersAM CVn Hulse-Taylor pulsar
9/03/2009
LSU: Physics & Astronomy Colloquium
Low-Frequency Sources of Gravitational Radiation
Taken from … http://lisa.jpl.nasa.gov/gallery/ligo-lisa.html 9/03/2009
LSU: Physics & Astronomy Colloquium
Laser-Interferometer Space Antenna (LISA)
9/03/2009
LSU: Physics & Astronomy Colloquium
High-Frequency Sources of Gravitational Radiation
Taken from … http://lisa.jpl.nasa.gov/gallery/ligo-lisa.html 9/03/2009
LSU: Physics & Astronomy Colloquium
DWD Orbit Evolutionsin LISA’s Strain-Frequency Domain
9/03/2009
[Kopparapu & Tohline (2007)]
LSU: Physics & Astronomy Colloquium
DWD Evolutionary Trajectories(for given “q”)
9/03/2009
“detached” inspiral
“mass-transferring” out-spiral
LSU: Physics & Astronomy Colloquium
DWD Evolutionary Trajectories(for given “q”)
9/03/2009
LSU: Physics & Astronomy Colloquium
DWD Evolutionary Trajectories(for given “q”)
9/03/2009
“detached” inspiral
“mass-transferring” out-spiral
LSU: Physics & Astronomy Colloquium
DWD Evolutionary Trajectories(for given “q”)
9/03/2009
LSU: Physics & Astronomy Colloquium
DWD Evolutionary Trajectories(for given “q”)
9/03/2009
LSU: Physics & Astronomy Colloquium
Part II: This Work
9/03/2009
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
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
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
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
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
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
Lorentz Center: Stellar Mergers
0;
Pure Hydro
0 ;
9/29/2009
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
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
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
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
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
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
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
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
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
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
Lorentz Center: Stellar Mergers
Equal-mass DWD Sequences
9/29/2009
New
& To
hlin
e 19
97
Lorentz Center: Stellar Mergers
Equal-mass DWD Sequences
9/29/2009
New
& To
hlin
e 19
97
Minimum J
Lorentz Center: Stellar Mergers
Equal-mass DWD Sequences
9/29/2009
New
& To
hlin
e 19
97
Contact
Lorentz Center: Stellar Mergers
Unequal-mass (q = ½) DWD Sequence
9/29/2009
Evan & Tohline 2009
Lorentz Center: Stellar Mergers
Unequal-mass (q = ½) DWD Sequence
9/29/2009
Evan & Tohline 2009
Contact
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
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
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
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
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
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
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
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
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
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
Lorentz Center: Stellar Mergers
Possible Mtot - q0 Distribution at Birth[borrowing Hurley’s population synthesis code (2002)]
9/29/2009
Lorentz Center: Stellar Mergers
Possible Mtot - q0 Distribution at Birth[borrowing Hurley’s population synthesis code (2002)]
9/29/2009
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
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 ???
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 ???
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 ???
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 ???
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 ???
Lorentz Center: Stellar Mergers
If qcrit = 2/3 …
9/29/2009
Stable mass-transfer
qcrit
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 ???
Lorentz Center: Stellar Mergers
If qcrit = 1/5 …
9/29/2009
Stable mass-transferqcrit
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 ???
Lorentz Center: Stellar Mergers
q0 = 0.5 (stable mass-transfer)
9/29/2009
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
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
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
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
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
Lorentz Center: Stellar Mergers
q0 = 0.7 (tidal disruption of donor)
9/29/2009
Lorentz Center: Stellar Mergers
What is hydrodynamic outcome of instability?
9/29/2009
Credit: W. Even
Lorentz Center: Stellar Mergers
What is hydrodynamic outcome of instability?
9/29/2009
Credit: W. Even
Lorentz Center: Stellar Mergers
What is hydrodynamic outcome of instability?
9/29/2009
Credit: W. Even
W0
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
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
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
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
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
Lorentz Center: Stellar Mergers
Do Results Depend on Choice of Numerical Algorithm?
9/29/2009
LSU grid codeLANL SPH code
106 particles 105 particles
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
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
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.)
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Lorentz Center: Stellar Mergers
4. How Does Outcome Depend on System’s Ability to Cool?
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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
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
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
Lorentz Center: Stellar Mergers
0;
Pure Hydro
0 ;
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Lorentz Center: Stellar Mergers9/29/2009
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
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.
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.
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.
Lorentz Center: Stellar Mergers
Very Preliminary Results from this new Radiation-Hydro code
9/29/2009
Lorentz Center: Stellar Mergers
Very Preliminary Results from this new Radiation-Hydro code (movies not attached)
9/29/2009
Credit: D. Marcello & P. Motl
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
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Lorentz Center: Stellar Mergers
Thanks!
9/29/2009