Hydrogen in helium white dwarf mergers

Philip D. Hall and C. Simon JefferyArmagh Observatory, Northern Ireland, UK

pdh@arm.ac.uk

Binary Stars in Cambridge 2016Institute of Astronomy, Cambridge, UK

2016-07-27

UK Science and Technology Facilities Council (STFC)Northern Ireland Department of Culture, Arts and Leisure (DCAL)

Hot subdwarfs

• Hot subdwarfs primarily defined by spectra(Heber 2016)

• Modelling of spectra givesTeff , g, He-to-H number ratio y = nHe/nH

• What is the interior structure of stars withthese properties (at the least)?I Naked or nearly naked core He-burning stars:

I He-burning coreI H envelope, low mass (. 0.02M�)

• How do isolated hot subdwarfs form?

Fig: Naslim et al. (2010) with He-poor sdBs (Edelmannet al. 2003), He-rich sdOs (Stroeer et al. 2007) andHe-rich sdBs (Ahmad & Jeffery 2003).

He+He DWD merger channel – Overview

• A close detached HeWD+HeWD systemforms from two main-sequence stars

• If Porb . 6 h then gravitational-waveradiation brings system to semidetachedstate (Porb ≈ 2min) within a Hubble time

• WD2 disrupted to form a hot envelope anddisc around a cold core

• Disc is accreted to make a single He-richstar

• He is ignited to make a hot subdwarf

(Webbink 1984; Iben & Tutukov 1986b; Iben 1990; Saio& Jeffery 2000; Han et al. 2002; Zhang & Jeffery 2012)

He+He DWD merger channel – Hydrogen

• H normally assumed to be burned in the hotenvelope (T & 107K)

• But the H mass is important in dictating theatmospheric parameters of the resultingHe-burning star

• Han et al. (2002) included H with uniformdistribution in envelope mass up to 10−3M�in their populations – is this realistic?

• Key idea:Not all H exposed to high temperatures,mixed throughout the disrupted matter andeventually diffuses to the surface

Fig: Temperature profile in quasi-static remnant of a0.3+0.2M� He+He DWD merger (Dan et al. 2014)

0.0 0.1 0.2 0.3 0.4 0.5m/M�

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

log 1

0(T/K

)

Core Envelope Disc

This project

Plan• Find detailed structure of HeWDs at onsetof merger, particularly the mass of H

• Estimate mass of H that survives the merger• Make core He-burning stars with the rightmass of H

• Model evolution in Teff–log g• Compare to observed isolated hot subdwarfs

Questions• How much H survives a He+He DWDmerger?

• What are the atmospheric properties ofmerger remnants in the core He-burningphase?

• To what extent can isolated hot subdwarfsbe explained as the remnants of He+HeDWD mergers?

Method – Pre-merger evolution

• Close detached HeWD+HeWD systemformed after two mass-loss episodes(Han 1998; Nelemans et al. 2001)

• Our example:0.3+0.2M� system formed through CE+CE

• How much of the envelope remains at theend of the CE phase?I Model with rapid mass-loss in mesa/star,assume star just fills Roche lobe and is inthermal equilibrium at end of CE phase

I Star evolves along plateau to cooling trackand may undergo shell flash(es)

I MH = 1.2 × 10−3 M� when first a WD• 0.2M� WD2 has MH = 2.6 × 10−3M�

(Iben & Tutukov 1986a; Hall et al. 2013)

3.54.04.55.0log10(Teff/K)

−2

−1

0

1

2

3

log 1

0(L/

L�

)

0.3M�

1M�

Z0 = 0.02

Method – Mass transfer and disruption phases

• Dan et al. (2011, 2014) simulated He+HeDWD mergers, included 0.3+0.2M� case

• Mass transfer develops into disruption ofWD2 within tens of P0 ≈ 208 s

• Forms a quasi-static remnant:I Core 0.211M�I Hot envelope 0.181M�I Disc 0.098M�I Tidal tail 0.00965M�

• Becomes a single star byI Eddington-limited accretion for 105 yr (Iben

1990; Saio & Jeffery 2000; Zhang & Jeffery 2012)I MRI-driven viscous evolution for 10−4–1 yr

(Shen et al. 2012; Schwab et al. 2012)

Method – H in the He-burning remnant

• What is MH in the remnant?• Assuming both WDs are young, 0.3+0.2M�has 3.8 × 10−3M� hydrogen, Z = 0.02

• Cold merger:I All H survivesI MH = 3.8 × 10−3 M�

• Hot merger:I H mixed throughoutI Some H burned in hot envelopeI MH = 1.9 × 10−3 M�

Method – Evolution in the Teff–log g plane

0.490 0.492 0.494 0.496 0.498 0.500Enclosed mass, m/M�

0.0

0.2

0.4

0.6

0.8

1.0

Mas

sfr

actio

n,X 1H

4He

Metals

20253035404550Teff/kK

5.2

5.4

5.6

5.8

6.0

6.2

log 1

0(g/

cms−

2 )

ZAEH

BZAHeMS

Young

OldMid

No hydrogen

Z0 = 0.02

Sample of isolated hot subdwarfs

• Sample of apparently isolated hot subdwarfsto compare against our models

• Best available is sample of sdBs analysed byGeier & Heber (2012), whoI Checked stars from SPY and other surveysfor radial velocity variations

I Found 71 single-lined systems with evidenceagainst radial velocity variability

I Gave atmospheric parameters for 38 of thesesystems (Geier et al. 2013)

1020304050607080Teff/kK

4.5

5.0

5.5

6.0

6.5

log 1

0(g/

cms−

2 )

ZAEH

B

ZAHeMS

Uncertainties

Results – H in He white dwarfs

• 7 white dwarfs MWD = 0.15–0.45M�,∆M = 0.05M�

• Made by removing mass from a Z0 = 0.02,1M� star

Fig: Total H mass in HeWD of given mass

0.15 0.20 0.25 0.30 0.35 0.40 0.45White dwarf mass MWD/M�

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Hyd

roge

nm

ass

MH/1

0−3

M�

Young

Mid

Old

Z0 = 0.02

Results – H in merger remnants

• 28 merger remnants forMWD = 0.15–0.45M�

• Maximum hydrogen mass for each remnantmass

Fig: Maximum hydrogen mass in remnant of given mass

0.3 0.4 0.5 0.6 0.7 0.8 0.9Remnant mass M/M�

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Hyd

roge

nm

ass

MH/1

0−3

M�

Z0 = 0.02

Young

Mid

Old

Results – Evolution in Teff–log g plane

1020304050607080Teff/kK

4.5

5.0

5.5

6.0

6.5

log 1

0(g/

cms−

2 )

ZAEH

B

ZAHeMS

UncertaintiesZ0 = 0.02

Results – Regions in Teff–log g plane

1020304050607080Teff/kK

4.5

5.0

5.5

6.0

6.5

log 1

0(g/

cms−

2 )

ZAEH

B

ZAHeMS

UncertaintiesZ0 = 0.02

Conclusions

• Typical H mass in merger remnants could be up to about 2 × 10−3M�• The sample of observed isolated hot subdwarfs (sdBs and sdOs) is consistent with formationthrough He+He DWD mergers on the basis of their Teff , log g, if H is mixed in the early stagesof the merger and later diffuses to the surfaceI (Except EC 22081−1916 and EC 20229−3716)

• Sample seems to only have stars in a small mass range – is this representative of thepopulation?

• Key questions:I Are the He WD H masses realistic? Asteroseismology of low-mass WDs and pre-WDs couldconstrain

I Is H mixed throughout in the early stages of mergers? Maybe a CE in the early, unresolved phase?I What mixing and burning takes place in the immediate post-merger phase?

References I

Ahmad A., Jeffery C. S., 2003, A&A, 402, 335Dan M., Rosswog S., Brüggen M., Podsiadlowski P., 2014, MNRAS, 438, 14Dan M., Rosswog S., Guillochon J., Ramirez-Ruiz E., 2011, ApJ, 737, 89Edelmann H., Heber U., Hagen H.-J., Lemke M., Dreizler S., Napiwotzki R., Engels D., 2003, A&A, 400,

939Geier S., Heber U., 2012, A&A, 543, A149Geier S., Heber U., Edelmann H., Morales-Rueda L., Kilkenny D., O’Donoghue D., Marsh T. R.,

Copperwheat C., 2013, A&A, 557, A122Grevesse N., Sauval A. J., 1998, Space Sci. Rev., 85, 161Hall P. D., Tout C. A., Izzard R. G., Keller D., 2013, MNRAS, 435, 2048Han Z., 1998, MNRAS, 296, 1019Han Z., Podsiadlowski P., Maxted P. F. L., Marsh T. R., 2003, MNRAS, 341, 669Han Z., Podsiadlowski P., Maxted P. F. L., Marsh T. R., Ivanova N., 2002, MNRAS, 336, 449Han Z., Webbink R. F., 1999, A&A, 349, L17Heber U., 2016, PASP, 128, 082001Herwig F., 2000, A&A, 360, 952

References IIIben Jr. I., 1990, ApJ, 353, 215Iben Jr. I., Tutukov A. V., 1986a, ApJ, 311, 742Iben Jr. I., Tutukov A. V., 1986b, ApJ, 311, 753Iglesias C. A., Rogers F. J., 1996, ApJ, 464, 943Ivanova N., 2011, ApJ, 730, 76Naslim N., Jeffery C. S., Ahmad A., Behara N. T., Şahìn T., 2010, MNRAS, 409, 582Nelemans G., Yungelson L. R., Portegies Zwart S. F., Verbunt F., 2001, A&A, 365, 491Paxton B., Bildsten L., Dotter A., Herwig F., Lesaffre P., Timmes F., 2011, ApJS, 192, 3Paxton B. et al., 2013, ApJS, 208, 4Paxton B. et al., 2015, ApJS, 220, 15Saio H., Jeffery C. S., 2000, MNRAS, 313, 671Schwab J., Shen K. J., Quataert E., Dan M., Rosswog S., 2012, MNRAS, 427, 190Shen K. J., Bildsten L., Kasen D., Quataert E., 2012, ApJ, 748, 35Stroeer A., Heber U., Lisker T., Napiwotzki R., Dreizler S., Christlieb N., Reimers D., 2007, A&A, 462, 269Webbink R. F., 1984, ApJ, 277, 355Zhang X., Jeffery C. S., 2012, MNRAS, 419, 452

Other channels I

• Seems like some isolated hot subdwarfs are difficult to explain as He+He DWD mergerremnants

• Might the other proposed channels give a better explanation? Can they explain all isolated hotsubdwarfs?

• Channels:I Enhanced single-star mass-lossI Interaction with substellar/planetary companionI Merger: HeWD + HeWDI Merger: COWD + HeWDI Merger: HeWD + MSI Merger: RGB core + MS (in a common envelope)I Envelope stripped by a supernova

Method – mesa/star stellar evolution code

• Open-source 1D stellar-evolution codemesa/star r7624, 2015-06-03 (Paxton et al.2011, 2013, 2015)

• Physics choices:I o18_and_ne22.net for He burningI GS98 metals mixture (Grevesse & Sauval 1998)I OPAL Type 2 opacity tables

(Iglesias & Rogers 1996)I Exponential overshooting, fov = 0.016

(Herwig 2000)I Core boundary at hydrogen mass fraction

X(1H) = 0.1I Eddington grey atmosphere

Method – Mass-transfer stability

• What is the response to mass transfer ofI the orbit and Roche lobes?I WD2 and WD1?

• Simple treatment: dynamically unstablemass transfer if q = MWD2/MWD1 & 2/3

• Complicated by details ofI Super-Eddington mass-transfer ratesI Spin–orbit coupling for direct impactaccretion

I Possibility of novae leading to CE• 0.3+0.2M� merger?

Fig: Stability for He+He DWD mergers. Based on workof Dan et al. (2011), lines from Han & Webbink (1999) 0.15 0.20 0.25 0.30 0.35 0.40 0.45

MWD1/M�

0.15

0.20

0.25

0.30

0.35

0.40

0.45

MW

D2/

M�

q> 2/3

Sub-EddingtonSuper-Eddington

HeWD+HeWDDirect impact accretion

Method – Post-disruption and post-merger phases

• 1. Disc accretionI Central remnant accretes from disc at criticalEddington rate for about 104 yr (Iben 1990;Saio & Jeffery 2000; Zhang & Jeffery 2012)

• 2. Viscous evolutionI Disc subject to magnetic instabilities suchthat there is rapid redistribution of angularmomentum and disc becomes near-sphericalenvelope in 10−4–1 yr (Shen et al. 2012; Schwabet al. 2012)

• Burning as star approaches core He-burningphase?

Method – General method

• Find detailed structure of HeWDs at onsetof merger, particularly the mass of H

• Estimate mass of H remaining after mergerusing the Dan et al. (2014) simulations

• Find the maximum hydrogen mass for eachremnant mass

• Find region in Teff–log g where coreHe-burning merger remnants are found

• Compare to observed isolated hot subdwarfs

0.15 0.20 0.25 0.30 0.35 0.40 0.45MWD1/M�

0.15

0.20

0.25

0.30

0.35

0.40

0.45

MW

D2/

M�

Conclusions

• Many observed isolated hot subdwarfs (sdBs and sdOs) consistent with formation throughHe+He DWD mergers on the basis of their Teff , log gI Mixing of H throughout in early stages of mergerI Diffusion of H to surface before core He-burning

• Some seem to have too much H to be explained as merger remnants• Upper limit for envelope mass of 1 × 10−3M� used by Han et al. (2002, 2003) is reasonablealthough there is a mass dependence

• Sample seems to only have stars in a small mass range• What could change these conclusions?

Uncertainties

• Knee instead of old WDs would make it easier to explain the full sample – is this realistic?• Alternative treatment of post-CE structure, e.g., that of Ivanova (2011) could give much lowerenvelope masses for HeWDs, reduce H mass in remnants

• Diffusion in the pre-HeWD evolution can increase the range that undergo shell flashes, reduceH mass in remnants

• Mass-loss in post-merger phase could reduce H mass in remnants, may be necessary to removeangular momentum

• Burning of H in the post-merger phase