Issue |
A&A
Volume 513, April 2010
|
|
---|---|---|
Article Number | L7 | |
Number of page(s) | 4 | |
Section | Letters | |
DOI | https://doi.org/10.1051/0004-6361/201013990 | |
Published online | 20 April 2010 |
LETTER TO THE EDITOR
Post common envelope binaries from SDSS
VIII. Evidence for disrupted magnetic braking![[*]](/icons/foot_motif.png)
M. R. Schreiber1 - B. T. Gänsicke2 - A. Rebassa-Mansergas1,2 - A. Nebot Gomez-Moran3 - J. Southworth2,4 - A. D. Schwope3 - M. Müller3 - C. Papadaki5 - S. Pyrzas2,6 - A. Rabitz3 - P. Rodríguez-Gil6,7,8 - L. Schmidtobreick9 - R. Schwarz3 - C. Tappert1 - O. Toloza1 - J. Vogel3 - M. Zorotovic9,10
1 - Departamento de Física y Astronomía, Facultad de
Ciencias,
Universidad de Valparaíso, Valparaíso, Chile
2 -
Department of Physics, University of Warwick, Coventry, CV4 7AL,
UK
3 -
Astrophysikalisches Institut Potsdam, An der Sternwarte 16,
14482 Potsdam, Germany
4 -
Department of Physics and Chemistry, Keele University, Staffordshire, ST5 5BG, UK
5 -
Institute of Astronomy & Astrophysics, National Observatory of Athens,
15236 Athens, Greece
6 -
Isaac Newton Group of Telescopes, Apartado de correos 321,
S/C de la Palma, 38700, Canary Islands, Spain
7 -
Instituto de Astrofísica de Canarias, Vía Láctea, s/n, 38205 La Laguna, Spain
8 -
Departamento de Astrofísica, Universidad de La Laguna, 38206 La Laguna, Tenerife, Spain
9 -
European Southern Observatory, Alonso de Cordova 3107, Santiago, Chile
10 -
Departamento de Física y Astronomía, Facultad de Ciencias, Pont. Universidad Catolica, Santiago, Chile
Received 4 January 2010 / Accepted 15 March 2010
Abstract
Context. The standard prescription of angular momentum loss
in compact binaries assumes magnetic braking to be very efficient as
long as the secondary star has a radiative core, but to be negligible
if the secondary star is fully convective. This prescription has been
developed to explain the orbital period gap observed in the orbital
period distribution of cataclysmic variables but has so far not been
independently tested. Because the evolutionary time-scale of post
common envelope binaries (PCEBs) crucially depends on the rate of
angular momentum loss, a fundamental prediction of the disrupted
magnetic braking theory is that the relative number of PCEBs should
dramatically decrease for companion-star masses exceeding the mass that
corresponds to the fully-convective boundary.
Aims. We present the results of a large survey of PCEBs among
white dwarf/main sequence (WDMS) binaries that allows us to determine
the fraction of PCEBs as a function of secondary star mass and
therewith to ultimately test the disrupted magnetic braking hypothesis.
Methods. We obtained multiple spectroscopic observations spread
over at least two nights for 670 WDMS binaries. Systems showing at
least
radial velocity variations are considered to be strong PCEB candidates.
Taking into account observational selection effects we compare our
results with the predictions of binary population simulations.
Results. Among the 670 WDMS binaries we find 205 strong PCEB candidates. The fraction of PCEBs among WDMS binaries peaks around
and steeply drops towards higher mass secondary stars in the range of
.
Conclusions. The decrease of the number of PCEBs at the fully
convective boundary strongly suggests that the evolutionary time scales
of PCEBs containing fully convective secondaries are significantly
longer than those of PCEBs with secondaries containing a radiative
core. This is consistent with significantly reduced magnetic wind
braking of fully convective stars as predicted by the disrupted
magnetic braking scenario.
Key words: binaries: close - magnetic fields - stars: low mass - white dwarfs
1 Introduction
The formation and evolution of virtually all close compact binaries, including cataclysmic variables (CVs) and low mass X-ray binaries is driven by orbital angular momentum loss due to gravitational radiation and - probably much stronger - magnetic braking. While gravitational radiation has been proven to be correctly described by Einstein's quadrupole formula (Taylor et al. 1979), current prescriptions of magnetic braking differ by up to four orders of magnitude.
The standard theory of angular momentum loss due to magnetic braking
in close compact binaries, known as disrupted magnetic braking (DMB),
was developed in the early eighties. Based on Skumanich's
(1972) analysis of the spin down rates of G-type
stars, Verbunt & Zwaan (1981) derived a prescription for angular
momentum loss due to magnetic braking of the form
.
In order to explain the orbital period
gap observed in the period distribution of CVs, i.e. a statistically
significant deficit of systems with
,
Rappaport et al. (1983)
proposed the DMB scenario by assuming that magnetic braking ceases
when the secondary star becomes fully convective at
- which, for a Roche-lobe filling secondary
star corresponds to
h. In the DMB scenario the donor
stars in CVs above the gap are driven out of thermal equilibrium by
strong mass transfer caused by efficient magnetic braking.
At the upper edge of the gap, the secondary star in a CV becomes fully
convective. Disrupted magnetic braking causes the mass loss rate to
drop and the donor star
to relax to its thermal equilibrium radius, which is smaller than its
Roche-lobe radius. The CV turns into a non-interacting detached white
dwarf plus main sequence (WDMS) binary, and its evolution towards
shorter
is now only driven by angular momentum loss through
gravitational radiation. At
h, the Roche lobe shrinks
sufficiently far to restart mass transfer. Designed to explain the
period gap, additional support for the DMB scenario comes from
(1) the secular mean accretion rates derived from accretion
induced compressional heating that are systematically higher above than
below the gap (Townsley & Gänsicke 2009; Townsley & Bildsten 2003),
and (2) the donor stars in CVs above the gap that appear slightly
expanded with respect to their main-sequence radii, which is
consistent with the donor stars being out of thermal equilibrium
(Knigge 2006).
Nevertheless, the DMB hypothesis remains an ad-hoc assumption. Although there is now some evidence for a discontinuity in the braking of single stars around the fully convective boundary (Reiners & Basri 2008; Bouvier 2007), it is not entirely clear if the DMB scenario correctly describes magnetic braking in single stars. In addition, the DMB idea is not backed-up by a thorough theory describing the interactions between rotation, magnetic field generation, and wind braking for low mass stars. Recent results indicate that the field topology changes at the fully convective boundary (Saunders et al. 2009; Reiners & Basri 2009), but whether this may indeed cause magnetic braking to become inefficient remains an open question. In this letter we present new and strong observational evidence for DMB.
2 Testing magnetic braking with PCEBs
Schreiber & Gänsicke (2003) realised that observational population
studies of the progenitors of CVs, i.e. detached post common envelope
binaries (PCEBs) consisting of a white dwarf primary and an M-dwarf
companion, could lead to new constraints on magnetic braking.
Politano & Weiler (2006) recently proposed a definite and concrete
test of DMB: if magnetic braking is indeed disrupted at the fully
convective boundary (
), the evolutionary
time-scales prior to the onset of accretion should be much longer for
PCEBs with fully convective secondaries compared to those with
secondaries above that boundary. Consequently, one should expect to
find more PCEBs with fully convective secondary stars. More
specifically, Politano & Weiler (2006) predict that the relative
number of PCEBs should abruptly decrease by
at the
fully convective boundary. If in contrast magnetic braking is at work
in secondary stars as proposed by e.g. Andronov et al. (2003), the
relative number of PCEBs should depend little on the mass of the
secondary star, with no abrupt change at the fully convective
boundary.
Carrying out this test of the DMB model, i.e. measuring the relative
number of PCEBs among WDMS binaries as a function of the secondary
mass, requires a large sample of PCEBs, which is only now becoming
available because of the efficiency of the Sloan Digital Sky Survey
spectroscopy (SDSS, Abazajian et al. 2009; Yanny et al. 2009; Adelman-McCarthy et al. 2008) in discovering WDMS binaries
(e.g. Smolcic et al. 2004; Silvestri et al. 2007; Schreiber et al. 2007; Rebassa-Mansergas et al. 2010,2007). The population of SDSS WDMS binaries
contains wide systems whose stellar components did not interact and
thus evolved like single stars, and close binaries that suffered from
dynamically unstable mass transfer, i.e. PCEBs. We are carrying out a
dedicated follow-up observing program with the aim to identify the
PCEBs among the SDSS WDMS binaries, and to determine their binary
parameters. First results on individual systems have been published
by Nebot Gómez-Morán et al. (2009); Pyrzas et al. (2009); Schreiber et al. (2008); Rebassa-Mansergas et al. (2008); Schwope et al. (2009). Here
we present radial velocity studies of 670 SDSS WDMS binaries, identify
205 strong PCEB candidates and determine the fraction of PCEBs among
WDMS binaries, henceforth
,
as a function of secondary
mass.
3 Observations
We carried out extensive follow-up observations of the most
complete published sample of WDMS binaries (based on SDSS Data Release 6, Rebassa-Mansergas et al. 2010),
obtaining at least two
spectra per system, spread over at least two nights. At the time of
writing (January 2010) we obtained a total of 3308 spectra
for 670 SDSS WDMS binaries. The design of the observations and
data reduction as well
as the radial velocity measurements of the secondary stars, primarily
based on the
Na I
8183.27,8194.81 absorption doublet,
are described in detail in Gänsicke et al. (2010, MNRAS, in prep.)
and Nebot Gomez-Moran et al. (2010, A&A, in prep.)
![]() |
Figure 1:
Distributions of WDMS binaries that have at least two radial
velocity measurements separated by at least one day. The left bottom
panel shows the distributions of systems with at least |
Open with DEXTER |
The observational results are summarized in Table 1
which is electronically available at the
Centre de Donnees astronomiques de Strasbourg (CDS).
We tested the 670 systems for radial velocity variations using a
test, i.e. the measured radial velocities were tested against
the hypothesis of a constant radial velocity. Systems showing
radial velocity variations with a confidence level of at least 0.9973
(henceforth
)
are identified as strong PCEB
candidates, systems with less significant variations are considered as
wide WDMS candidates, i.e. systems where the two stars did not undergo
any interaction during their evolution. Stellar parameters of the
670 systems (masses and spectral types for the white dwarf and
secondary
star and the distance to the binary) were taken from
Rebassa-Mansergas et al. (2010) and Nebot Gomez-Moran (2010, A&A,
in prep.) and are provided in Table 2 available at the CDS.
The peak-to-peak radial velocity variations of the PCEB
candidates range from
25-450 km s-1, corresponding to maximum
binary separations of
and maximum orbital
periods of
2 h-160 days.
In a parallel effort we
measured the orbital periods of a representative sub-sample consisting
of 60 PCEBs that have been identified through our
radial velocity criterion and find that all these systems have orbital
periods shorter than four days, the vast majority (
)
even shorter than one day (Gänsicke et al. 2010,
MNRAS, in prep.). We therefore here assume that all the PCEB
candidates are synchronised and circularised short period close binary
systems.
4 PCEB fraction among SDSS WDMS binaries
Our large set of strong PCEB candidates and WDMS binaries that are
most likely wide systems provides the potential to test the DMB
hypothesis. The distributions of the PCEB candidates and the entire
WDMS binary sample are shown as a function of secondary spectral type
in the bottom left panel of Fig. 1. Performing a
test of the PCEB candidate against the wide candidate
distribution we find that the null-hypothesis can be rejected
with
confidence. Thus the secondary spectral type
distributions of wide WDMS binary candidates and PCEB candidates are
intrinsically different.
as a function of secondary
spectral type is shown in the top left panel of
Fig. 1. Apparently, the fraction of PCEBs is very low
(<20%) for M 0-M 2 secondary stars, significantly increases around
spectral types M 3-M 4, and finally exceeds
for M 5-M 7
secondary stars. At M 7
of the observed systems are strong
PCEB candidates. For the latest M dwarf secondaries (M 8-M 9) our data
are subject to low number statistics, but it seems that the PCEB
fraction again drops below
.
In a second step we used the spectral type-mass relation of
Rebassa-Mansergas et al. (2007) to derive
as a
function of secondary mass (solid line in the top right panel of
Fig. 1). Because
the masses of M 0-M 1 respectively M 7-M 9
secondary stars are very similar, this
distribution contains just seven
bins. The measured fraction of PCEBs is steeply decreasing towards
higher mass secondaries in the range of
,
but stays at about
for lower
mass secondaries.
5 Selection effects
A first general note is that the SDSS sample of WDMS binaries is not
complete and probably subject to selection effects
in various stellar
parameters like white dwarf
temperature or secondary mass. Given
that these effects will affect PCEBs and wide WDMS binaries in the
same way our choice of investigating
as a function of
is independent of these selection effects. However, there
are two possible observational biases which may skew
,
i.e. selection effects within the target algorithm of the SDSS
spectroscopy that is used to identify WDMS binaries in the first
place, and selection effects that might be introduced through the
design of our follow-up programme that affect PCEBs and wide WDMS
binaries in a different way. These will be discussed below.
The algorithm selecting objects for SDSS fibre spectroscopy may
introduce a subtle bias affecting
as a function
of apparent magnitude and hence of secondary mass that needs to be
evaluated. The majority of the WDMS binaries are serendipitously
picked up by fibres allocated to objects that have non-stellar
colours, i.e. colours that differ from single main sequence stars and
white dwarfs. Because of their composite spectral energy
distributions, WDMS binaries appear as objects with non-stellar
colours within SDSS as long as they are not spatially resolved by the
typical seeing of
.
Those WDMS binaries
that are spatially
resolved will have star-like colours for each component, and are
unlikely to obtain an SDSS fibre spectrum. The
magnitude limit of SDSS spectroscopy and of our follow-up programme
implies that the average distance to SDSS WDMS binaries increases with
absolute magnitude - and hence with the mass of the secondary star.
Figure 1 (bottom right) illustrates this effect, the
average distance of the WDMS binaries in the sample discussed here
increases from
220 pc for
to
820 pc
for
.
Hence, intrinsically faint WDMS
binaries have on average a higher chance to be spatially resolved than
bright ones, and would consequently not be targeted for SDSS follow-up
spectroscopy, introducing a bias towards low-mass secondaries
in
. Assuming an average spatial resolution of
and the average distances from above
(Fig. 1, bottom right) translate into minimum
projected separations of resolved WDMS binaries ranging from
220 AU for the lowest mass bin to
820 AU for the highest
mass bin. Assuming binary separations of
(e.g Willems & Kolb 2004), and
taking into account that the initial distribution of binary
separations a is supposed to decrease with increasing a, i.e.
(Popova et al. 1982), we estimate that the
fraction of wide WDMS binaries that are spatially resolved by SDSS is
decreasing from
at
to
at
.
The finite spectral resolution and the details of the temporal
sampling of our follow-up radial velocity studies will prevent us from
identifying some genuine PCEBs within the observed sample of WDMS
binaries. To evaluate this selection effect, we calculated
the average
PCEB detection probability p for each secondary mass bin. Taking
into account the times of observations and the stellar masses, we
performed Monte-Carlo simulations similar to those presented in
Gänsicke et al. (2010, MNRAS in prep.), i.e. for typical PCEB
orbital periods (2 h-2 days) we randomly selected
10 000 times
the phases and an inclination for each system and calculated the
corresponding radial velocities. Averaging over the orbital period the
fraction of >
radial velocity variations gives the average
PCEB detection probability for each system. The PCEB detection
probabilities averaged over all systems that fall in a certain mass
bin are given as black dots in the bottom right panel of
Fig. 1. Because the avererage detection
probabilities are nearly constant as a function of
,
,
the number of genuine PCEBs missed by our follow-up
programme are simply proportional to the number of PCEBs that we did
identify, leading to a bias against PCEBs with low mass
companions in
. We used the calculated PCEB detection
probabilities to find the most likely fraction of PCEBs for each mass
bin using Bayes' theorem according to Maxted et al. (2000) and
indeed found an even steeper decline in the range of secondary masses
corresponding to the fully convective boundary.
Interestingly, the two selection effects related to the spatial
resolution of SDSS and to our spectral resolution and temporal
sampling nearly cancel each other out:
the dotted histogram in the top
right panel of Fig. 1 shows the bias-corrected fraction
of PCEBs among WDMS binaries, which is
very similar to the measured one
(solid line histogram in the same panel). We therefore conclude that
the intrinsic fraction of PCEBs among WDMS binaries does indeed
decrease significantly in the range of
.
6 Discussion
Overall, our result agrees well with the main prediction of
Politano & Weiler (2006) for DMB. We find the fraction of PCEBs
steeply decreasing by
in the secondary mass range that
corresponds to the fully convective boundary, and only the DMB
prescription predicts this decrease.
While this is an important
finding, it is worth to keep in mind that Politano & Weiler (2006)
calculated the relative number of PCEBs as a function of
,
which
is not identical to
measured here. To derive the
predicted
,
one needs to divide the relative number of
PCEBs by the assumed secondary mass function. As the pairing algorithm
used by Politano & Weiler (2006) predicts the number of
WDMS binaries
to smoothly increase with secondary mass (Kouwenhoven et al. 2009),
the decrease of
predicted by their simulations is
>
in agreement with the
measured here.
Comparing the predictions of Politano & Weiler (2006) and our
observational result in more detail, we find that the measured
decrease in
is slightly broader than the predicted
one. This can easily be understood as resulting from uncertainties in
the spectral type determination and the spectral type mass relation.
Both uncertainties contribute to the uncertainty of the secondary mass
determination,
which naturally causes any steep gradient to be smeared
out.
7 Conclusion
We have measured the fraction of PCEBs among white dwarf/main sequence binaries identified by the SDSS and found a steep decrease at the secondary star mass corresponding to the fully convective boundary, i.e. there are substantially less PCEBs with secondaries that have a radiative core. This result agrees excellently with the disrupted magnetic braking scenario thatpredicts significantly longer evolutionary timescales for PCEBs containing fully convective secondary stars. We therefore conclude that magnetic braking is disrupted, or is at least significantly reduced at the fully convective boundary. According to recent magnetic field measurements of M-dwarfs, this might be caused by changes of the magnetic field topology at the fully convective boundary.
AcknowledgementsWe acknowledge support from FONDECYT (grant 1061199, MRS), ESO/Comite Mixto, Gemini/Conicyt (grant 32080023, ARM) and DLR (FKZ 50OR0404, ANGM). This paper includes data collected at (1) ESO Paranal and La Silla, Chile under programme IDs 083.D-0862, 082.D-0507, 080.D-0407,079.D-0531, 078.D-0719,(2) the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the NSF (United States), the STFC (United Kingdom), the NRC (Canada), CONICYT (Chile), the ARC (Australia), MCT (Brazil) and MINCYT (Argentina), (3) Las Campanas Observatory, Chile with the 6.5 m Magellan Telescopes, (4) the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias with the WHT, which is operated on the island of La Palma by the Isaac Newton Group, and (5) at the Centro Astronómico Hispano Alemán (CAHA) at Calar Alto, operated jointly by the Max-Planck Institut für Astronomie and the Instituto de Astrofísica de Andalucía (CSIC).
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Footnotes
- ... braking
- RV tables are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/513/L7
All Figures
![]() |
Figure 1:
Distributions of WDMS binaries that have at least two radial
velocity measurements separated by at least one day. The left bottom
panel shows the distributions of systems with at least |
Open with DEXTER | |
In the text |
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