The structure and fate of white dwarf

merger remnants

Marius Dan

Hamburger Sternwarte, Universitat Hamburg

In collaboration with:

M. Bruggen (Universitat Hamburg) E. Ramirez-Ruiz (UC Santa Cruz)S. Rosswog (Stockholm University) J. Guillochon (Harvard, CfA)P. Podsiadlowski (University of Oxford)

March 25th, 2014

White dwarfs (WDs) in binaries

I ∼ 1010 WDs in Galaxy (Napiwotzki 2009)

I ∼ 108 Galactic double WDs (DWDs) (Nelemans+2001)

I 50% DWDs evolve into contact within Hubble time

Mass transfer phase

Roche model

I In a non-inertial frame, gravitational andcentrifugal forces are described by apotential

I Roche lobes: a critical equipotentialintersects itself at L1

I When WD fills its Roche lobe masstransfer sets in through L1

I Two regimes of mass transfer: disk anddirect impact

Mass transfer is...

I stable if donor has same size as itsRoche lobe −→ DWDs become AMCVn stars

I unstable if donor overflows its Rochelobe −→ binary merger

-10 -5 0 5 10

-10

-5

0

5

10

A large parameter space study

Numerical methods:(Benz+ 1990, Hix+ 1998, Timmes & Sweesty 2000, Rosswog+ 2008)

I Smoothed Particle HydrodynamicsI Helmholtz equation of stateI Quasi-equilibrium reduced α-networkI self-gravity via a binary tree

Initial conditions (Dan et al. 2011):

I binary carefully relaxed in corotating frame

I synchronized, cold and isothermal stars

-1 10-2

-8

-6

-4

-2

0

x [109 cm]

-p

m (

x, y, z)

| %

(x, y, z)

% t = 0

-pm

Parameter space:

I mass range between 0.2 and 1.2 M�

I different chemical compositions

I 225 systems

CO - CO

CO - He+CO

CO - HeHe+CO He - He

HeONe - He

ONe - CO

ONe

He+CO He+CO

-

-

He+CO-

CO-donors

He-donors

(Dan et al., 2012)

Mass transfer phase

I Marsh, Nelemans & Steeghs (2004):

I unstable for q & 2/3, (q = Mdon/Macc)

I stable for q . 1/5

I uncertain for 1/5 < q < 2/3, requires strong

spin-orbit coupling

I Mass transfer is long-lived

I Norbs increases with decreasing mass ratio

I Systems with CO donors are in unstable,direct impact regime of mass transfer:16− 28 orbits

I System within uncertain region merge after30− 60 orbits −→ consistent with a weakaccretor–orbit coupling

I Systems with q . 1/5 do not merge after75 – 90 orbits

I Norbs is an increasing function of resolution−→ conservative lower limit

NorbsCO donors

(Dan et al., 2012)

Structure of merger remnants at tmerger + 3P0

I cold core: fraction of former accretor

I hot envelope: mixed material Macc/Mdon

core

Keplerian disk

envelope

I Keplerian disk: mixed material Macc/Mdon, mainly Mdon

I tidal tail: fraction of former donor

(Dan et al, 2014)

Remnants’ morphology as a function of stars’ spins

I Corotating systems lead to hot spots incore’s outer layers while non-rotatingdeep inside core

I ρmax(corot.) at core’s centreρmax(non-rot.) off core’s centre

I ρmax(corot.) > ρmax(non-rot.)

I corotating systems lead to faster rotators

0 0.2 0.4 0.6 0.8 1

(Dan et al, 2014)

Dynamical burning and possible detonations

I τnuc = u/εnuc

I τdyn = (Gρ)−1/2

I τnuc/τdyn . 1 expansion tooslow to quench burning

−→ hydrodynamical burningand possibly a detonation

2.5 3 3.5 4 4.5 5 5.5 6 6.57.6

7.8

8

8.2

8.4

8.6

8.8

9

9.2

9.4

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

I Tmax − ρmax increase with Mtot and with numerical resolution

I He – detonations possible for Mtot & 1M�

I CO – detonations possible for Mtot & 2M�

I Schwab et al. (2012): τnuc/τdyn decreases by a factor of 10 duringviscous evolution

Ejected mass

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

4

8

12

16

20

× 10−3

0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

−1.5

−1

−0.5

0

0.5

1

I Mesc increases with decreasing q from ∼10−4 to 3.4× 10−2 M� (filled circles for

τnuc/τdyn ≤ 10)

I Lesc up to 12% of Ltot (larger symbols for τnuc/τdyn ≤ 10)

−→ Systems with substantial burning unbind more mass and angular momentum

Possible outcomes of white dwarf mergers

I He – He: extreme He stars (He-sdO andHe-sdB)

I He – CO: R Coronae Borealis (RCB) andextreme He stars; some sub-luminous TypeIa Supernovae (SN)

I CO – CO:• Mtot ∼ MCh, SN Ia or Accretion

Induced Collapse (AIC) to a Neutron Star(NS)

• Mtot < MCh, massive CO or ONeWDs; some sub-luminous SNe Ia

• Mtot > MCh, AIC to NS;super-Chandra SN Ia

I ONe – He: RCB and eHe stars; some donot merge (AM CVn stars)

I ONe – CO: AIC to a NS

I ONe – ONe: small mass black hole or willthey explode (Oxygen detonation)?

e.g., Webbink 1984, Iben & Tutukov 1984, Iben 1990,Saio & Nomoto 1985, Segretain+ 1997, Saio & Jeffery 2000,Yoon+ 2007, Han+ 2002, Justham+ 2010, Sim+ 2010Fryer+ 2010, Shen+ 2010,Pakmor+ 2010, Solheim 2010,Waldman+ 2011, Clayton 2012

CO-detonationssingle-det.

(1991bg-like SN)

SN Ia~10 yr5

He-rich sdO HeCO~10 yr7

sdB HeCO~10 yr8

7

R Coronae Borealis~10 yr CO

single-det.interm. phase RCB

(non-standard Ia later?)

M =1.4tot

double-det.(SN Ia)

double-det. supra-Ch. SN

AIC~10 yr

4

(interm. phase RCB)

(Dan et al., 2014)

Summary

I Mass transfer is long lived, duration increases with decreasing mass ratio:

I Systems in direct impact regime merge within ∼ 60 orbits;

I Disk accreting systems do not merger after 75− 90 orbits (AM CVn?).

I WD-WD mergers leave behind remnants consisting of a cold core, a hotenvelope, a Keplerian disk and a tidal tail

I Large fraction of systems can explode (i.e., τnuc/τdyn . 10)

I He mass transferring systems with Mtot & 1M�

I CO mass transferring systems with Mtot & 2M�

I WDs’ spin state could be decisive for the question where the ignition is

triggered:

I tidally locked stars produce hot spots in core’s outer layers

I irrotational systems produce hot spots deep inside core

I For most systems, Mesc and Lesc tend to increase with decreasing mass ratio.

Profiles of all 225 merger remnants are available at

http://tinyurl.com/nb83zev

poz. x−directionneg. x−directionpoz. y−directionneg. y−directionpoz. z−directionneg. z−direction

poz. x−directionneg. x−directionpoz. y−directionneg. y−directionpoz. z−directionneg. z−direction

poz. x−directionneg. x−directionpoz. y−directionneg. y−directionpoz. z−directionneg. z−direction

Stars’ mixing

Mixing between binary components increases with mass ratio q

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Chemical mixing between binary components

0

0.2

0.4

0.6

0.8

1

0

0

0.2

0.4

0.6

0

0.2

0.4

0.6

0

0.2

0.4

0.6

(Dan et al, 2014)