Understanding Mass
Transfer in Extremely
Low Mass WD Binaries
David Kaplan (UW-Milwaukee), Lars Bildsten (KITP),
Justin Steinfadt (UCSB➞ATT Govt. Solutions)
Center for Gravitation, Cosmology, & Astrophysics
Tuesday, April 17, 12
composite spectrum of J1056+6536 suffers from flux calibration problems and is not shown in the left panels.
How To Form AM CVn
ere the model using the continuum shape is not a good
h orbital periods. Figure 3 shows the observed radial veloc
tch to the observations. We use the results from the Balmer
ities and the best fit orbits for our targets. We present the
e profile fitting for this star. This model agrees remarkably
l with the spectral energy distribution based on the SDSS
otometry. Or, what happens to double WDs with
Extremely
Mass
(ELM;
M☉) He
Figure 2 compares
the Low
best-fit
Teff and
log <0.2
g measurements
our targets
against the predicted evolutionary sequences
WDs
m Panei et al. (2007). Based on these tracks, our targets
e M = 0.17 − 0.40 M! ; some of them are more massive
SDSS finding many of these (Kilic,
n predicted from the relatively noisy SDSS spectroscopy
Brown,
...) of all seven systems discussed
a. The physical
parameters
his paper are presented in Table 3. The age and distance
mates are somewhat
uncertain
for&Mhot)
≈ 0.17
0.160
! objects,
Stay bright
(large
forMGyr
due to
0.170
ause many ofstably
them fall
in the H
gapshell
between
0.17etand
0.18
0.171
burning
(Panei
al. 2007)
0.180
He-core WD tracks. Panei et al. (2007) and Kilic et al.
0.187
0.203
10a) argue that diffusion-induced
hydrogen-shell flashes
-3
-2
0.225
10 Mto
10
M
of
H
⊙
e place for M > 0.17
,
which
yield
small
hydrogen
en!
0.249
opes. Hence, lower mass objects have massive hydrogen
0.306
elopes, largerMany
radii,found
lower in
surface
andother
longer
tight gravities,
orbits with
0.333
ling times. The
inconsistency
between
the observed
0.384
WDs
(or pulsars),
will reach
contactpa-in <
0.416
meters for Teff ∼ 10,000 K and log g ≤ 6 objects and the
Gyr 2)
(Badenes,
Brown,
Kawka,
nei et al. (2007,10Figure
models makes
accurate
WDKilic,
mass
Mullally,difficult
Steinfadt,
...)
luminosity estimates
for Vennes,
them. Fortunately,
mass
F IG . 2.— Surface gravity versus effective temperature of the observe
luminosity change very little over the range of effective
Known
ELM
WDs
et al.
(2012)
WDs (filled
points)
in the
ELM from
Survey, Kilic
compared
with
predicted track
mperature and surface gravity sampled by these WDs. We
for He WDs with 0.16–0.42 M! (Panei et al. 2007). The dashed and dot
pt M = 0.17 M! and Mg $ 8 mag for these objects.
ted lines show solar metallicity and halo metallicity (Z=0.001) models o
Serenelli et al. (2001, 2002) for 0.17 M! WDs, respectively. The seven new
All seven targets show significant velocity variations with
systems presented in this paper are shown as red points. Triangles show th
k-to-peak velocity amplitudes of 120-640 km s−1 and 1-18
•
•
•
•
•
ELM WD companions to PSR J1012+5307 and J1911−5958A.
Tuesday, April 17, 12
1 Myr
t m e r ge= 10Gyr
100 Myr
Pulsars
1.6
KPD 1930+2752
Total Mass (M ! )
1.4
Single Line
Double Line
sdB
PSR
< 0.20 M !
1.2
1
0.8
First eclipsing
NLTT 11748
SDSS J1840
Extremely short P
SDSS J0651
Pulsations
Second eclipsing
0.6
SDSS J0106
CSS 41177
0.4
0.01
Tuesday, April 17, 12
0.1
Period (days)
1
What Happens at Contact?
•Marsh et al (‘04):
•Detailed mass transfer,
Direct-impact accretion: always unstable
including stability
•But: used cold EOS for both
accretor (CO WD) and donor
(He WD)
•OK for accretor
•But what about for donor?
Tuesday, April 17, 12
:
n
n
o
o
i
i
t
t
e niza
r
c
c
a
ro
t
h
c
c
a syn
p
m
y
-i
t
b
c
e
d
Dir bilize
a
t
s
e
b
can
Disc-fed accretion: always stable
<0.2 M⊙He WDs are Large
0.00
0.02
0.06
0.16 M⊙ w/ 3e-3 M⊙ envelope
0.06
0.07
dP
0.98
0.94
10
10
0.04
1.00
−0.02
0.96
•
•
−0.04
Relative Flux
•
Steinfadt et al.: eclipse observations of
NLTT 11748 show R≈0.04 R☉ for
M≈0.16 M☉
Cold EOS: 0.02 R☉ (e.g., Eggleton)
Outer portions are not degenerate
Phase (cycles)
160
200
240
τP (s)
0.94
−5
10
Envelope (non-degen)
−10
10
Tuesday, April 17, 12
0
0.01
0.02
0.03
Radius (R ! )
0.04
0.05
0.46
0.04
2009-12-22
2010-01-08
2010-02-03
0.48
0.50
0.03
H fraction
dS
0
10
0.96
density
0.98
1.00
5
10
Relative Flux
Dens ity (g/cm 2 ) or X
Core (degenerate)
160
200
240
τS (s)
0.52
0.54
Phase (cycles)
Also see Driebe et al. (’98); Sarna et al. (’00);
Serenelli et al. (’01); Bassa et al. (’03 & ’06); van
Kerkwijk et al. (’05), ...
0.56
•
•
Orbital evolution of ELM He WD
+ CO WD (0.7-1.0 M☉)
He WD follows models of
Steinfadt et al. (2010): used to
determine (dR/dM, X) as mass is
stripped
Follow mass transfer & orbital
evolution
Consider disk/direct impact
Stability of accreted matter to
burning
Do not deal with
synchronizations torques
Range of envelope masses (i.e.,
ages) for each core mass
•
•
•
•
0.15 M⊙ core, with (2-5)x10-3 M⊙ envelope
0.08
0.07
Donor R adius ( R ! )
•
Our Calculation
0.06
0.15/2.12
0.15/2.51
0.15/2.90
0.15/3.30
0.15/3.69
0.15/4.09
0.15/4.50
0.15/4.91
0.15/5.30
M strip=Menv
X=0.01
0.05
0.04
0.03
0.02
0.1
cold EOS
0.11
0.12
0.13
0.14
Donor Mas s ( M ! )
0.15
0.16
Kaplan et al. (2012)
Tuesday, April 17, 12
Response to Mass Loss
•
•
•
•
Normal WD: R~M-⅓
Mdonor
5 ⇣
Mass transfer stable if
< +
Maccrete
6 2
d log R
⇣⌘
is -⅓ for a normal WD, so need mass ratio < ⅔
d log M
ELM He WD:
Outer layers not degenerate, ζ≫1
Disk accretion guaranteed stable; even without disk, more
stable systems (reduce Ṁ, as in D’Antona et al. or Deloye &
Roelofs)
•
•
Tuesday, April 17, 12
P ( min)
5
10
10
| Ṗ | ( s /s)
•
•
10
11
10
Ṗ just set by GR
12
10
2
10
Once on accretor, is H
burning stable? pp only!
| Ṁ | ( M ! /y r) ∆M ( M ! )
•
Early evolution:
prolonged period of
hydrogen accretion
3
10
4
10
6
10
7
10
8
10
0
X
10
1
10
2
10
0.20 M☉
ζHe
1
10
0.15 M☉
0
10
10
1
1
0.1
0.01
0.001
T ime Be f or e Pe r iod Minimum ( My r )
Kaplan et al. (2012)
Tuesday, April 17, 12
5
Mass Transfer Rate (M ! /yr)
10 donor:
High-mass (small)
accretion starts late, enters
direct-impact, but stays
dynamically stable 6
0.1
10
10
10
10
10
10
0.125/3.00
0.200/1.80
Higher Ṁ: only Ṁ<Ṁedd stays on
S ta b l e H e
High Ṁ: stable H or He
burning: accreted matter
stays on
0.3 S ta b l e H
7
1
8
3
Low-mass (large) donor:
accretion starts early,
remains disk-fed & stable
3
1
9
0.30.1
10
11
4
5
0.8 M⊙ accretor
d N e u n stab l e
20
Kaplan et al. (2012)
Stable burning calculations still preliminary (based on Nomoto et al. 2007 & Iben & Tutukov 1989)
Tuesday, April 17, 12
3
X=0.99
X=0.9
X=0.5
X=0.1
X=0.01
X=0.001
Late evolution: ζ
determines Ṁ, follows
classical result
6
7 8 9 10
Orbital Period (min)
Vary accretor mass:
10
10
10
10
M a = 0. 7 M !
6
S ta b l e H e
7
S ta b l e H
8
9
Mass Transfer Rate (M ! /yr)
10
10
10
10
Tuesday, April 17, 12
10
10
10
11
10
10
10
X=0.99
X=0.9
X=0.5
X=0.1
X=0.01
X=0.001
10
5 3
4
5
10
M a = 0. 9 M !
10
0.125/3.00
0.125/6.00
0.150/2.12
0.150/5.30
0.175/1.90
0.175/5.10
0.200/1.80
0.200/4.90
10
Mass Transfer Rate (M ! /yr)
Mass Transfer Rate (M ! /yr)
10
5
10
6
6
7 8 9 10
Orbital Period (min)
S ta b l e H
7
20
0.125/3.00
0.125/6.00
0.150/2.12
0.150/5.30
0.175/1.90
0.175/5.10
0.200/1.80
0.200/4.90
8
9
X=0.99
X=0.9
X=0.5
X=0.1
X=0.01
X=0.001
4
5
S ta b l e H e
7
S ta b l e H
10
10
10
8
9
10
7 8 9 10
Orbital Period (min)
20
X=0.99
X=0.9
X=0.5
X=0.1
X=0.01
X=0.001
d N e u n stab l e
6
7 8 9 10
Orbital Period (min)
20
0.125/3.00
0.125/6.00
0.150/2.12
0.150/5.30
0.175/1.90
0.175/5.10
0.200/1.80
0.200/4.90
6
S ta b l e H
7
8
9
10
d N e u n stab l e
6
0.125/3.00
0.125/6.00
0.150/2.12
0.150/5.30
0.175/1.90
0.175/5.10
0.200/1.80
0.200/4.90
S ta b l e H e
10
3
6
10
5 3
4
5
10
M a = 1. 0 M !
10
11
M a = 0. 8 M !
11
S ta b l e H e
10
5
d N e u n stab l e
Mass Transfer Rate (M ! /yr)
10
10
11
3
X=0.99
X=0.9
X=0.5
X=0.1
X=0.01
X=0.001
4
5
d N e u n stab l e
6
7 8 9 10
Orbital Period (min)
20
Kaplan et al. (2012)
Changing H fraction reduces luminosity
53
10
4
5
6
7
8
9
10
4
5
Nuclear Burning Luminosity (L ! )
7
9
S tab l e H
S tab l e H
10
8
3
10
time
10
10
2
10
5
10
10
M a = 0. 7 M !
M a = 0. 8 M !
L Ed d
4
10
10
L Ed d
S tab l e H
S tab l e H
10
0.125/3.00
0.125/6.00
0.150/2.12
0.150/5.30
0.175/1.90
0.175/5.10
0.200/1.80
0.200/4.90
3
10
2
10
1
10
3
10 5
10
L Ed d
L Ed d
4
6
M a = 0. 9 M !
4
5
M a = 1. 0 M !
6
7
8
9
10
4
5
6
7
8
9
10
10
10
10
4
3
2
5
4
3
2
1
Orbital Period (min)
Kaplan et al. (2012)
Tuesday, April 17, 12
Stability: many more systems avoid merger
Disc fed
Direct Impact
Donor Mass (M ! )
0.25
We see no dynamically unstable systems
0.2
range in Menv
0.15
t
e
sh
r
a
M
c
e
r
i
d
/
k
s
i
d
.
al
0.1
t
i
m
t li
More disk-fed
0.05
0
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
Accretor Mass (M ! )
1
1.05
1.1
Kaplan et al. (2012)
Tuesday, April 17, 12
Stability: many more systems avoid merger
Disc fed
Direct Impact
Donor Mass (M ! )
0.25
We see no dynamically unstable systems
0.2
range in Menv
0.15
t
e
sh
r
a
M
c
e
r
i
d
/
k
s
i
d
.
al
0.1
t
i
m
t li
More disk-fed
0.05
0
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
Accretor Mass (M ! )
1
1.05
1.1
Kaplan et al. (2012)
Tuesday, April 17, 12
Direct-Impact of H-Rich Material
•
•
•
HM Cancri (5.4 min binary): 0.27
M☉& 0.55 M☉ (Roelofs et al.;
Israel et al., Cropper et al.;
Strohmayer et al.)
Ṗ<0 but Lx (Ṁ) puzzlingly low
D’Antona et al. (2006): mass
transfer will start from nondegenerate H envelope
Changes orbital evolution, since
dR/dM<0
Largely can explain orbital
evolution, luminosity of HM
Cnc
All metals sedimented out of H
layer, somewhat out of He
(Hebert et al.)
•
1432
D’ANTO
V407 Vul
HM Cnc
•
•
Tuesday, April 17, 12
Fig. 1.— Evolution of radius, mass, and mass-loss rate along sequences: 1 (dashdotted line), 2 (dashed line), and 3 (dotted line). The periods of RX J0806+15 and
RX J1914+24 are indicated as vertical segments. [See the electronic edition of the
Journal for a color version of this figure.]
mass transfer from the now pure helium WD.4 The mass-transfer
rate Ṁ is much smaller, up to a factor 10, when the period is decreasing. The period derivative is shown in Figure 2, where we see
that the value of Ṗorb for RX J0806+15 is in the range provided by
our models. The Ṗorb of RX J1914+24 (V407 Vul) is much smaller
Direct-Impact of H-Rich Material
•
•
•
1432
HM Cancri (5.4 min binary): 0.27
M☉& 0.55 M☉ (Roelofs et al.;
Israel et al., Cropper et al.;
Strohmayer et al.)
Ṗ<0 but Lx (Ṁ) puzzlingly low
D’Antona et al. (2006): mass
transfer will start from nondegenerate H envelope
Changes orbital evolution, since
dR/dM<0
Largely can explain orbital
evolution, luminosity of HM
Cnc
All metals sedimented out of H
layer, somewhat out of He
(Hebert et al.)
1432
D’ANTO
D’ANTONA ET AL.
•
Vol. 653
V407 Vul
HM Cnc
•
•
Fig. 1.— Evolution of radius, mass, and mass-loss rate along sequences: 1 (dashTuesday,
April
17, 12 line), and 3 (dotted line). The periods of RX J0806+15 and
dotted
line),
2 (dashed
Fig. 1.— Evolution of radius, mass, and mass-loss rate along sequences: 1 (dashdotted line), 2 (dashed line), and 3 (dotted line). The periods of RX J0806+15 and
RX J1914+24 are indicated as vertical segments. [See the electronic edition of the
Journal for a color version of this figure.]
mass transfer from the now pure helium WD.4 The mass-transfer
rate Ṁ is much smaller, up to a factor 10, when the period is decreasing. The period derivative is shown in Figure 2, where we see
that the value of Ṗorb for RX J0806+15 is in the range provided by
our models. The Ṗorb of RX J1914+24 (V407 Vul) is much smaller
Conclusions
•
•
•
•
Detailed calculation of mass transfer for ELM He WD and CO WD
Hot, non-degenerate envelope prolongs period of stable mass
transfer, significantly expands systems that will avoid merger
•
•
Nout/Nin~4 just based on Ṗ; weight by Ṁ increases outgoing bias
If stable burning, that could change luminosity
Long period of stable H burning kept He WD hot, explains highentropy AM CVn donors?
Still need to do fully self-consistent calculation of ζ and burning
stability for these accretion rates and compositions (MESA)
Tuesday, April 17, 12