Mass transfer in eccentricWhite Dwarf – Neutron Star binaries

Alexey Bobrick, Melvyn B. Davies, Ross P. Church

Lund UniversityDepartment of Astronomy and Theoretical Physics

2015

Introduction

Image credit: Copyright Mark A. Garlick.

White Dwarf (WD) and a Neutron Star (NS)

Why are WD-NS systems interesting

• May power a special type of GRBs (King et al. 2007)

• Likely source of Ca-rich gap transients (Kasliwal 2012)

• Nuclear burning possibly important (Metzger 2012).

• Main UCXB progenitors (van Haaften et al. 2012).

• Good source for space-based GW missions(Antoniadis 2014).

• High mass loss – possible implications for galacticchemistry.

• Often contain millisecond pulsars (Wijnands 2010).

• Second largest fraction of doubly compact binaries(Nelemans et al. 2001).

Summary on WD-NS systems

• Form at a above ∼ R�

• Inspiral to contact due to GWemission

• Two possibilities after MT starts:• Low mass WD:

• Stable MT on ∼ τGW

• Seen as UCXB• Fade after a few Gyr

• High mass WD:

• Unstable MT on ∼ τdyn• Transient event

WD-NS observations

• Detached systems – binary pulsars (radio):• ∼ 250 known (ATNF catalogue)• 2.2 · 106 expected in the Galaxy (Nelemans et al. 2001)• Merger rate of 1.4 · 10−4 yr−1 per galaxy (Nelemans et al.

2001)

• Transferring systems (low mass WDs) – UCXBs (x-ray):• 13 confirmed (van Haaften et al. 2012)• ∼ 500 expected with P < 70min (Belczynski & Taam 2004)

• Transients (high mass WDs):• ∼ 10 gap transients seen, e.g. Kasliwal (2011)

Our work

• Modified SPH simulations of mass transfer

• Which systems are stable? Mcrit – ?

• How do they look like?• Extract non-conservative mass transfer parameters• Apply binary stellar evolution

log10ρ, g/cm3

5.

4.5

4.

3.5

-1

-2

-3

-4

-5

x, RWD

y,RWD

-6 -4 -2 0 2 4 6-6

-4

-2

0

2

4

6

Eccentricity importance

• Eccentric population with a heavy WD (Davies et al. 2002)• At least ∼ 0.1 of all WD-NS in the field (Nelemans et al.

2001)• Contact e is ∼ 10−2.5 from GWs only• WD atmospheres are thin: hρ ∼ 10−5RWD

• MT turns on and off during the orbit• UCXBs in GCs are often eccentric, e.g. 4U 1820-30, also

Prodan & Murray (2015).

Mass transfers

Mass stays bound

0 π 2 π 3 π 4 π

-4

-2

0

2

4

Orbital phase

Δr/h ρ

Stable mass transfer in SPH

• Hard to model in standard SPH

• Need ∼ 1012 particles

• Typical UCXBs transfer ∼ 10−12MWD per orbit

• Cannot use too different particle masses

• Oil on water approach (Church et al. 2009)

• Treat stellar body and atmosphere separately

OW method scheme

r, RWD

log 10ρ,g/cm

3

ρtheor

ρwat

105ρoil

0.6 0.7 0.8 0.9 1.0 1.1 1.25.5

6.0

6.5

7.0

7.5

log10ρ, g/cm3

8.5

8.

7.5

7.

6.5

6.

2.

1.5

1.

0.5

x, RWD

y,RWD

-1.0 -0.5 0.0 0.5 1.0

-1.0

-0.5

0.0

0.5

1.0

Numerical method 1: Oil layer

• Has to be thick

• Support by artificial T (ideal gas, applies forM < 10−5M�/yr)

• No self-gravity: O(Noil) complexity

• Equations scale-free in moil

log10ρ, g/cm3

8.5

8.

7.5

7.

6.5

6.

2.

1.5

1.

0.5

x, RWD

y,RWD

-1.0 -0.5 0.0 0.5 1.0

-1.0

-0.5

0.0

0.5

1.0

Numerical method 2: The binary

• Quadrupole interactions important

• Keplerian ϕ causes effective e ∼ 0.01

• M swing of ∼ 0.5 dex, e.g. Dan et al. (2011)

MWD,M� 0.15 0.6 1.0 1.3

δequadr 4.0 · 10−3 7.0 · 10−3 6.8 · 10−3 7.0 · 10−3

Numerical method 3: R?(a) dependence

• R? changes with a

• Indirectly observed by Dan et al. (2011)

• Typical change ∼ 5%

• Important for constructing waveforms

He 0.15M⊙

CO 0.6M⊙

ONe 1.0M⊙

ONe 1.3M⊙

1.16 1.18 1.20 1.22 1.24 1.26 1.28 1.300.00

0.05

0.10

0.15

0.20

a/aRLO,Eggl

δR

*/R

*,∞

Simulations: what do we see

Video slide

Mapping SPH to the general model

• Atmosphere:• Artificially thick• Measure everything in hρ

• Timescales:• Real systems evolve over 102 – 106 orbits• SPH: Represents continuum of stages• Scale-free, quasi-steady

• Mass flows:• Split the simulation into regions

Instantaneous Mcirc

• M at given a

• Expect Ritter’s formula (Ritter 1988): M ∼ expR? −RRL

hρ• Observed:

Model ONe 1.0M⊙

0.5 orbit

1 orbit

2 orbits

4 orbits inspiral

Ritter 's slope (correct R*)

Ritter 's slope (constant R*)

1.10 1.15 1.20 1.25 1.30 1.351

2

3

4

5

a/aRLO

log 10N.

orb

Instantaneous Mecc

• Eccentric M : instantaneous response model

• Morb(a, e) = Mcirc(a)f(Re

hρ)

0 1 2 3 4 5 60.00.20.40.60.81.01.21.4

φ

N./N.

c,ref

γ = 0.0

0 1 2 3 4 5 60.00.20.40.60.81.01.21.4

φ

N./N.

c,ref

γ = 0.7

0 1 2 3 4 5 60.00.20.40.60.81.01.21.4

φ

N./N.

c,ref

γ = 1.4

0 1 2 3 4 5 60.00.20.40.60.81.01.21.4

φ

N./N.

c,ref

γ = 2.1

0 1 2 3 4 5 60.00.20.40.60.81.01.21.4

φ

N./N.

c,ref

γ = 2.8

0 1 2 3 4 5 60.00.20.40.60.81.01.21.4

φ

N./N.

c,ref

γ = 3.5

Parameters we extract

• Long term evolution: importance of mass loss

• Measure parameters (Rappaport 1982):• How much mass is lost: β ≡ −M1/M2

• How much of Jz is lost: α ≡ Jlossmloss

/J12µ

• How much does the envelope affect a: αCE ≡ Eorb/Eej

Further results

• Boundary masses ∼ 0.2M� for disc wind model

• Constant e does not affect long-term M

• Varying e may drive M

• Observations affected by: CE, rad. feedback, the jet

Unstable MTStable MT

Model He 0.15M⊙

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

β

α

Unstable MTStable MT

Model CO 0.6M⊙

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

β

α

Conclusions

• WD-NS systems are:• Sources for UCXBs• Likely to produce transients• Often eccentric

• We model them using a modified SPH scheme

• And link the results to a binary evolution model

Thank you!