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Merger Simulations (examining the onset and outcome of various instabilities) Joel E. Tohline Louisiana State University Collaborators: J. Frank, P. Motl, W. Even, D. Marcello, G. Clayton, C. Fryer, S. Diehl

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Part I: Broad Context 9/03/2009LSU: Physics & Astronomy Colloquium

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Double White Dwarfs (DWDs) 9/03/2009LSU: Physics & Astronomy Colloquium

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Binary System Parameters (circular orbit; point-mass system) 9/03/2009LSU: Physics & Astronomy Colloquium

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Binary System Parameters (circular orbit; point-mass system) Sufficient to specify: M, q, P orb 9/03/2009LSU: Physics & Astronomy Colloquium

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Binary System Parameters (circular orbit; WD mass-radius relationship) R1R1 R2R2 a M2M2 M1M1 9/03/2009LSU: Physics & Astronomy Colloquium

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Binary System Parameters (circular orbit; WD mass-radius relationship) R1R1 R2R2 a M2M2 M1M1 9/03/2009LSU: Physics & Astronomy Colloquium

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Binary System Parameters (mass-transfer system) R1R1 R2R2 a M2M2 M1M1 donor 9/03/2009LSU: Physics & Astronomy Colloquium

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Binary System Parameters (circular orbit; point-mass system) Sufficient to specify: M, q, P orb 9/03/2009LSU: Physics & Astronomy Colloquium

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(slide stolen from this past Friday’s talk by Nelemans) 9/29/2009Lorentz Center: Stellar Mergers

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(slide stolen from this past Friday’s talk by Nelemans) 9/29/2009Lorentz Center: Stellar Mergers

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Possible M tot - q 0 Distribution at Birth [borrowing Hurley’s population synthesis code (2002)] 9/29/2009Lorentz Center: Stellar Mergers

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Gravitational-Wave Detectors 9/03/2009LSU: Physics & Astronomy Colloquium

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Hanford Observatory Livingston Observatory Laser Interferometer Gravitational-wave Observatory (LIGO) 9/03/2009LSU: Physics & Astronomy Colloquium

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Laser Interferometer Gravitational-wave Observatory (LIGO)

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Gravitational-Wave Signal characterized by amplitude “h” and frequency “f” 9/03/2009LSU: Physics & Astronomy Colloquium

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Gravitational-Wave Signal characterized by amplitude “h” and frequency “f” From GR quadrupole radiation formula (e.g., Peters & Mathews 1963) 9/03/2009LSU: Physics & Astronomy Colloquium

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Classic “chirp” Signal due to point-mass binary inspiral From GR quadrupole radiation formula (e.g., Peters & Mathews 1963) 9/03/2009LSU: Physics & Astronomy Colloquium

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Classic “chirp” Signal due to point-mass binary inspiral From GR quadrupole radiation formula (e.g., Peters & Mathews 1963) 9/03/2009LSU: Physics & Astronomy Colloquium

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Classic “chirp” Signal due to point-mass binary inspiral From GR quadrupole radiation formula (e.g., Peters & Mathews 1963) 9/03/2009LSU: Physics & Astronomy Colloquium During inspiral: h ~ f 2/3

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High-Frequency Sources of Gravitational Radiation Taken from … http://lisa.jpl.nasa.gov/gallery/ligo-lisa.htmlhttp://lisa.jpl.nasa.gov/gallery/ligo-lisa.html 9/03/2009LSU: Physics & Astronomy Colloquium

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Binary Orbital Parameters AM CVnHulse-Taylor pulsar 9/03/2009LSU: Physics & Astronomy Colloquium

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Binary Orbital Parameters AM CVnHulse-Taylor pulsar 9/03/2009LSU: Physics & Astronomy Colloquium

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Radiation from Hulse-Taylor Pulsar Taken from … http://lisa.jpl.nasa.gov/gallery/ligo-lisa.htmlhttp://lisa.jpl.nasa.gov/gallery/ligo-lisa.html 9/03/2009LSU: Physics & Astronomy Colloquium

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Binary Orbital Parameters AM CVnHulse-Taylor pulsar 9/03/2009LSU: Physics & Astronomy Colloquium

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Binary Orbital Parameters AM CVnHulse-Taylor pulsar 9/03/2009LSU: Physics & Astronomy Colloquium

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Low-Frequency Sources of Gravitational Radiation Taken from … http://lisa.jpl.nasa.gov/gallery/ligo-lisa.htmlhttp://lisa.jpl.nasa.gov/gallery/ligo-lisa.html 9/03/2009LSU: Physics & Astronomy Colloquium

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Laser-Interferometer Space Antenna (LISA) 9/03/2009LSU: Physics & Astronomy Colloquium

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High-Frequency Sources of Gravitational Radiation Taken from … http://lisa.jpl.nasa.gov/gallery/ligo-lisa.htmlhttp://lisa.jpl.nasa.gov/gallery/ligo-lisa.html 9/03/2009LSU: Physics & Astronomy Colloquium

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DWD Orbit Evolutions in LISA’s Strain-Frequency Domain 9/03/2009LSU: Physics & Astronomy Colloquium [Kopparapu & Tohline (2007)]

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DWD Evolutionary Trajectories (for given “q”) 9/03/2009LSU: Physics & Astronomy Colloquium “detached” inspiral “mass-transferring” out-spiral

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DWD Evolutionary Trajectories (for given “q”) 9/03/2009LSU: Physics & Astronomy Colloquium

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DWD Evolutionary Trajectories (for given “q”) 9/03/2009LSU: Physics & Astronomy Colloquium “detached” inspiral “mass-transferring” out-spiral

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DWD Evolutionary Trajectories (for given “q”) 9/03/2009LSU: Physics & Astronomy Colloquium

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DWD Evolutionary Trajectories (for given “q”) 9/03/2009LSU: Physics & Astronomy Colloquium

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Part II: This Work 9/03/2009LSU: Physics & Astronomy Colloquium

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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 9/29/2009Lorentz Center: Stellar Mergers

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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 9/29/2009Lorentz Center: Stellar Mergers

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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 9/29/2009Lorentz Center: Stellar Mergers

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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 9/29/2009Lorentz Center: Stellar Mergers

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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 9/29/2009Lorentz Center: Stellar Mergers

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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 9/29/2009Lorentz Center: Stellar Mergers

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0; Pure Hydro 0 ; 9/29/2009Lorentz Center: Stellar Mergers

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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 ( = 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 9/29/2009Lorentz Center: Stellar Mergers

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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 ( = 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 9/29/2009Lorentz Center: Stellar Mergers

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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 ( = 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 9/29/2009Lorentz Center: Stellar Mergers

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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 ( = 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 9/29/2009Lorentz Center: Stellar Mergers

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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 ( = 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 9/29/2009Lorentz Center: Stellar Mergers

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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 ( = 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 9/29/2009Lorentz Center: Stellar Mergers

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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 J tot and E tot reach a minimum – Any further loss of angular momentum (inspiral) leads to secular instability loss of synchronous rotation and, perhaps, tidal disruption/merger 9/29/2009Lorentz Center: Stellar Mergers

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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 J tot and E tot reach a minimum – Any further loss of angular momentum (inspiral) leads to secular instability loss of synchronous rotation and, perhaps, tidal disruption/merger 9/29/2009Lorentz Center: Stellar Mergers

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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 J tot and E tot reach a minimum – Any further loss of angular momentum (inspiral) leads to secular instability loss of synchronous rotation and, perhaps, tidal disruption/merger 9/29/2009Lorentz Center: Stellar Mergers

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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 J tot and E tot reach a minimum – Any further loss of angular momentum (inspiral) leads to secular instability loss of synchronous rotation and, perhaps, tidal disruption/merger 9/29/2009Lorentz Center: Stellar Mergers

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Equal-mass DWD Sequences 9/29/2009Lorentz Center: Stellar Mergers New & Tohline 1997

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Equal-mass DWD Sequences 9/29/2009Lorentz Center: Stellar Mergers New & Tohline 1997 Minimum J

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Equal-mass DWD Sequences 9/29/2009Lorentz Center: Stellar Mergers New & Tohline 1997 Contact

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Unequal-mass (q = ½) DWD Sequence 9/29/2009Lorentz Center: Stellar Mergers Evan & Tohline 2009

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Unequal-mass (q = ½) DWD Sequence 9/29/2009Lorentz Center: Stellar Mergers Evan & Tohline 2009 Contact

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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 J min along its inspiral sequence. 9/29/2009Lorentz Center: Stellar Mergers

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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: don = lnR don / lnM don Roche geometry readjusts: RL = lnR RL / lnM don – Parameter, D = ½( don – RL ), governs stability … Stable against further mass-transfer if D > 0 Dynamically unstable if D < 0 9/29/2009Lorentz Center: Stellar Mergers

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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: don = lnR don / lnM don Roche geometry readjusts: RL = lnR RL / lnM don – Parameter, D = ½( don – RL ), governs stability … Stable against further mass-transfer if D > 0 Dynamically unstable if D < 0 9/29/2009Lorentz Center: Stellar Mergers

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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: don = lnR don / lnM don Roche geometry readjusts: RL = lnR RL / lnM don – Parameter, D = ½( don – RL ), governs stability … Stable against further mass-transfer if D > 0 Dynamically unstable if D < 0 9/29/2009Lorentz Center: Stellar Mergers

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Some Theoretical Considerations Mass-Transfer Instability (cont.) – For n = 3/2 polytropic EOS and assumption of conservative mass transfer (CMT) don = RL = 2q – 5/3 – Parameter, D = ½( don – RL ) = (2/3 – q), System stable if q < q crit = 2/3 Dynamically unstable if q > q crit 2/3 9/29/2009Lorentz Center: Stellar Mergers

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Some Theoretical Considerations Mass-Transfer Instability (cont.) – For n = 3/2 polytropic EOS and assumption of conservative mass transfer (CMT) don = RL = 2q – 5/3 – Parameter, D = ½( don – RL ) = (2/3 – q), System stable if q < q crit = 2/3 Dynamically unstable if q > q crit 2/3 9/29/2009Lorentz Center: Stellar Mergers

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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 9/29/2009Lorentz Center: Stellar Mergers

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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? 9/29/2009Lorentz Center: Stellar Mergers

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1. Is mass-transfer stable or unstable? We’ll discuss this question in the context of an “M tot - q 0 ” parameter-space diagram that contains a hypothetical population of newborn double white dwarf binaries … 9/29/2009Lorentz Center: Stellar Mergers

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1. Is mass-transfer stable or unstable? We’ll discuss this question in the context of an “M tot - q 0 ” parameter-space diagram that contains a hypothetical population of newborn double white dwarf binaries … 9/29/2009Lorentz Center: Stellar Mergers

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Possible M tot - q 0 Distribution at Birth [borrowing Hurley’s population synthesis code (2002)] 9/29/2009Lorentz Center: Stellar Mergers

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Possible M tot - q 0 Distribution at Birth [borrowing Hurley’s population synthesis code (2002)] 9/29/2009Lorentz Center: Stellar Mergers

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Possible M tot - q 0 Distribution at Birth [borrowing Hurley’s population synthesis code (2002)] 9/29/2009Lorentz Center: Stellar Mergers ** NOT ** precursors for Type Ia SNe

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1. Is mass-transfer stable or unstable? Answer depends only weakly on M tot Answer depends principally on initial mass ratio q 0 What is the value of q crit ? – Almost certainly, q crit 2/3 – But maybe, q crit 1/5 (due to direct-impact accretion) Numerical simulations (Motl et al. 2007) indicate that q crit is closer to 2/3 than to 1/5 9/29/2009Lorentz Center: Stellar Mergers q 0 < q crit stable AM CVn (presumably) q 0 > q crit unstable ???

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1. Is mass-transfer stable or unstable? Answer depends only weakly on M tot Answer depends principally on initial mass ratio q 0 What is the value of q crit ? – Almost certainly, q crit 2/3 – But maybe, q crit 1/5 (due to direct-impact accretion) Numerical simulations (Motl et al. 2007) indicate that q crit is closer to 2/3 than to 1/5 9/29/2009Lorentz Center: Stellar Mergers q 0 < q crit stable AM CVn (presumably) q 0 > q crit unstable ???

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1. Is mass-transfer stable or unstable? Answer depends only weakly on M tot Answer depends principally on initial mass ratio q 0 What is the value of q crit ? – Almost certainly, q crit 2/3 – But maybe, q crit 1/5 (due to direct-impact accretion) Numerical simulations (Motl et al. 2007) indicate that q crit is closer to 2/3 than to 1/5 9/29/2009Lorentz Center: Stellar Mergers q 0 < q crit stable AM CVn (presumably) q 0 > q crit unstable ???

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1. Is mass-transfer stable or unstable? Answer depends only weakly on M tot Answer depends principally on initial mass ratio q 0 What is the value of q crit ? – Almost certainly, q crit 2/3 – But maybe, q crit 1/5 (due to direct-impact accretion) Numerical simulations (Motl et al. 2007) indicate that q crit is closer to 2/3 than to 1/5 9/29/2009Lorentz Center: Stellar Mergers q 0 < q crit stable AM CVn (presumably) q 0 > q crit unstable ???

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1. Is mass-transfer stable or unstable? Answer depends only weakly on M tot Answer depends principally on initial mass ratio q 0 What is the value of q crit ? – Almost certainly, q crit 2/3 – But maybe, q crit 1/5 (due to direct-impact accretion) Numerical simulations (Motl et al. 2007) indicate that q crit is closer to 2/3 than to 1/5 9/29/2009Lorentz Center: Stellar Mergers q 0 < q crit stable AM CVn (presumably) q 0 > q crit unstable ???

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If q crit = 2/3 … 9/29/2009Lorentz Center: Stellar Mergers Stable mass-transfer q crit

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1. Is mass-transfer stable or unstable? Answer depends only weakly on M tot Answer depends principally on initial mass ratio q 0 What is the value of q crit ? – Almost certainly, q crit 2/3 – But maybe, q crit 1/5 (due to direct-impact accretion) Numerical simulations (Motl et al. 2007) indicate that q crit is closer to 2/3 than to 1/5 9/29/2009Lorentz Center: Stellar Mergers q 0 < q crit stable AM CVn (presumably) q 0 > q crit unstable ???

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If q crit = 1/5 … 9/29/2009Lorentz Center: Stellar Mergers Stable mass-transfer q crit

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1. Is mass-transfer stable or unstable? Answer depends only weakly on M tot Answer depends principally on initial mass ratio q 0 What is the value of q crit ? – Almost certainly, q crit 2/3 – But maybe, q crit 1/5 (due to direct-impact accretion) Numerical simulations (Motl et al. 2007) indicate that q crit is closer to 2/3 than to 1/5 9/29/2009Lorentz Center: Stellar Mergers q 0 < q crit stable AM CVn (presumably) q 0 > q crit unstable ???

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q 0 = 0.5 (stable mass-transfer) 9/29/2009Lorentz Center: Stellar Mergers

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2. What is hydrodynamic outcome of instability? Answer depends on q 0 Numerical simulations have not yet pinned down the value of q merge, but it is certainly > 0.7 9/29/2009Lorentz Center: Stellar Mergers q crit < q merge < q 0 donor plunges into accretor q crit < q 0 < q merge tidal disruption of donor

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2. What is hydrodynamic outcome of instability? Answer depends on q 0 Numerical simulations have not yet pinned down the value of q merge, but it is certainly > 0.7 9/29/2009Lorentz Center: Stellar Mergers q crit < q merge < q 0 donor plunges into accretor q crit < q 0 < q merge tidal disruption of donor

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2. What is hydrodynamic outcome of instability? Answer depends on q 0 Numerical simulations have not yet pinned down the value of q merge, but it is certainly > 0.7 9/29/2009Lorentz Center: Stellar Mergers q crit < q merge < q 0 donor plunges into accretor q crit < q 0 < q merge tidal disruption of donor

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2. What is hydrodynamic outcome of instability? Answer depends on q 0 Numerical simulations have not yet pinned down the value of q merge, but it is certainly > 0.7 9/29/2009Lorentz Center: Stellar Mergers q crit < q merge < q 0 donor plunges into accretor q crit < q 0 < q merge tidal disruption of donor

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2. What is hydrodynamic outcome of instability? Answer depends on q 0 Numerical simulations have not yet pinned down the value of q merge, but it is certainly > 0.7 9/29/2009Lorentz Center: Stellar Mergers q crit < q merge < q 0 donor plunges into accretor q crit < q 0 < q merge tidal disruption of donor

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q 0 = 0.7 (tidal disruption of donor) 9/29/2009Lorentz Center: Stellar Mergers

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What is hydrodynamic outcome of instability? 9/29/2009Lorentz Center: Stellar Mergers Credit: W. Even

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What is hydrodynamic outcome of instability? 9/29/2009Lorentz Center: Stellar Mergers Credit: W. Even

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What is hydrodynamic outcome of instability? 9/29/2009Lorentz Center: Stellar Mergers Credit: W. Even 00

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2. What is hydrodynamic outcome of instability? Answer depends on q 0 Numerical simulations have not yet pinned down the value of q merge, but it is certainly > 0.7 9/29/2009Lorentz Center: Stellar Mergers q crit < q merge < q 0 donor plunges into accretor q crit < q 0 < q merge tidal disruption of donor

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If q crit = 2/3 and q merge = 0.9 … 9/29/2009Lorentz Center: Stellar Mergers Stable mass-transfer Tidal disruption of donor Donor plunges into accretor q crit q merge

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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. 9/29/2009Lorentz Center: Stellar Mergers

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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. 9/29/2009Lorentz Center: Stellar Mergers

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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. 9/29/2009Lorentz Center: Stellar Mergers

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Do Results Depend on Choice of Numerical Algorithm? 9/29/2009Lorentz Center: Stellar Mergers LSU grid code LANL SPH code 10 6 particles10 5 particles

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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.) 9/29/2009Lorentz Center: Stellar Mergers

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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.) 9/29/2009Lorentz Center: Stellar Mergers

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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.) 9/29/2009Lorentz Center: Stellar Mergers

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4. How Does Outcome Depend on System’s Ability to Cool? 9/29/2009Lorentz Center: Stellar Mergers

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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). 9/29/2009Lorentz Center: Stellar Mergers

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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). 9/29/2009Lorentz Center: Stellar Mergers

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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). 9/29/2009Lorentz Center: Stellar Mergers

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0; Pure Hydro 0 ; 9/29/2009Lorentz Center: Stellar Mergers

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9/29/2009Lorentz Center: Stellar Mergers

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5. What About Super-Eddington Accretion? For an opacity of the form … we can write … so we can define, where, Then, f Edd > 1 means super-Eddington accretion. 9/29/2009Lorentz Center: Stellar Mergers

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5. What About Super-Eddington Accretion? 9/29/2009 If we actually set … then, f Edd 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 K 1 by a factor of 10 10. Then, f Edd will climb above unity when climbs above 10 -2. Lorentz Center: Stellar Mergers

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5. What About Super-Eddington Accretion? 9/29/2009 If we actually set … then, f Edd 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 K 1 by a factor of 10 10. Then, f Edd will climb above unity when climbs above 10 -2. Lorentz Center: Stellar Mergers

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5. What About Super-Eddington Accretion? 9/29/2009 If we actually set … then, f Edd 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 K 1 by a factor of 10 10. Then, f Edd will climb above unity when climbs above 10 -2. Lorentz Center: Stellar Mergers

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Very Preliminary Results from this new Radiation-Hydro code 9/29/2009Lorentz Center: Stellar Mergers

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Very Preliminary Results from this new Radiation-Hydro code (movies not attached) 9/29/2009Lorentz Center: Stellar Mergers Credit: D. Marcello & P. Motl

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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 9/29/2009Lorentz Center: Stellar Mergers

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Thanks! 9/29/2009Lorentz Center: Stellar Mergers

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