merger simulations (examining the onset and outcome of various instabilities)

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

Double White Dwarfs (DWDs)

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Binary System Parameters(circular orbit; point-mass system)

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Sufficient to specify: M, q, Porb

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Binary System Parameters(circular orbit; WD mass-radius relationship)

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Binary System Parameters(circular orbit; WD mass-radius relationship)

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Binary System Parameters(mass-transfer system)

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Sufficient to specify: M, q, Porb

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Lorentz Center: Stellar Mergers

(slide stolen from this past Friday’s talk by Nelemans)

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(slide stolen from this past Friday’s talk by Nelemans)

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Possible Mtot - q0 Distribution at Birth[borrowing Hurley’s population synthesis code (2002)]

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Gravitational-Wave Detectors

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Hanford Observatory

LivingstonObservatory

Laser Interferometer Gravitational-wave Observatory (LIGO)

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Laser Interferometer Gravitational-wave Observatory (LIGO)

Gravitational-Wave Signalcharacterized by amplitude “h” and frequency “f”

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Gravitational-Wave Signalcharacterized by amplitude “h” and frequency “f”

From GR quadrupole radiation formula (e.g., Peters & Mathews 1963)9/03/2009

Classic “chirp” Signaldue to point-mass binary inspiral

During inspiral: h ~ f2/3

High-Frequency Sources of Gravitational Radiation

Taken from … http://lisa.jpl.nasa.gov/gallery/ligo-lisa.html 9/03/2009

Binary Orbital ParametersAM CVn Hulse-Taylor pulsar

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Radiation from Hulse-Taylor Pulsar

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Low-Frequency Sources of Gravitational Radiation

Laser-Interferometer Space Antenna (LISA)

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High-Frequency Sources of Gravitational Radiation

DWD Orbit Evolutionsin LISA’s Strain-Frequency Domain

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[Kopparapu & Tohline (2007)]

DWD Evolutionary Trajectories(for given “q”)

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“detached” inspiral

“mass-transferring” out-spiral

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“detached” inspiral

“mass-transferring” out-spiral

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Part II: This Work

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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

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Pure Hydro

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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 (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

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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 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

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course of this workshop as relevant to mergers (e.g., DWDs and W UMa systems)

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Equal-mass DWD Sequences

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Minimum J

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Contact

Unequal-mass (q = ½) DWD Sequence

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Evan & Tohline 2009

Unequal-mass (q = ½) DWD Sequence

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Evan & Tohline 2009

Contact

• “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.

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• 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

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• 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

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– 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

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– 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

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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?

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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 …

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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 …

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**NOT**precursors for

Type Ia SNe

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

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q0 < qcrit stable AM CVn (presumably)q0 > qcrit unstable ???

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If qcrit = 2/3 …

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Stable mass-transfer

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If qcrit = 1/5 …

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Stable mass-transferqcrit

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q0 = 0.5 (stable mass-transfer)

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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

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qcrit < qmerge < q0 donor plunges into accretorqcrit < q0 < qmerge tidal disruption of donor

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q0 = 0.7 (tidal disruption of donor)

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What is hydrodynamic outcome of instability?

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Credit: W. Even

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Credit: W. Even

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Credit: W. Even

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If qcrit = 2/3 and qmerge = 0.9 …

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Stable mass-transfer

Tidal disruption of donor

Donor plunges into accretor

qmerge

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.

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Do Results Depend on Choice of Numerical Algorithm?

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LSU grid codeLANL SPH code

106 particles 105 particles

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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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).

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• We have recently modified our code to handle radiation transport in the flux-limited-diffusion approximation, a la Hayes et al. (2006).

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• We have recently modified our code to handle radiation transport in the flux-limited-diffusion approximation, a la ZEUS-MP (Hayes et al. 2006).

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Pure Hydro

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Lorentz Center: Stellar Mergers9/29/2009

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.

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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.

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Very Preliminary Results from this new Radiation-Hydro code

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Very Preliminary Results from this new Radiation-Hydro code (movies not attached)

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Credit: D. Marcello & P. Motl

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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Thanks!

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merger simulations (examining the onset and outcome of various instabilities)

Documents

mass binary inspiral

peters mathews

frequency f

stellar mergers slide

amplitude h

nelemans9292009lorentz

hulsetaylor pulsartaken

past fridays