Issue |
A&A
Volume 521, October 2010
|
|
---|---|---|
Article Number | L60 | |
Number of page(s) | 5 | |
Section | Letters | |
DOI | https://doi.org/10.1051/0004-6361/201015472 | |
Published online | 21 October 2010 |
LETTER TO THE EDITOR
Two planets orbiting the recently formed post-common envelope binary NN Serpentis![[*]](/icons/foot_motif.png)
K. Beuermann1 - F. V. Hessman1 - S. Dreizler1 - T. R. Marsh2 - S. G. Parsons2 - D. E. Winget3 - G. F. Miller3 - M. R. Schreiber4 - W. Kley5 - V. S. Dhillon6 - S. P. Littlefair 6 - C. M. Copperwheat2 - J. J. Hermes3
1 - Institut für Astrophysik, Georg-August-Universität, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
2 - Department of Physics, University of Warwick, Coventry, CV4 7AL, UK
3 - Dept. of Astronomy, University of Texas at Austin, RLM 16.236, Austin, TX 78712, USA
4 - Departamento de Fisica y Astronomia, Universidad de Valparaiso, Av. Gran Bretana 1111, Valparaiso, Chile
5 -
Institut für Astronomie & Astrophysik, Universität Tübingen,
Morgenstelle 10, 72076 Tübingen, Germany
6 - Department of Physics & Astronomy, University of Sheffield, S3 7RH, UK
Received 26 July 2010 / Accepted 6 October 2010
Abstract
Planets orbiting post-common envelope binaries provide fundamental
information on planet formation and evolution. We searched for such
planets in NN Ser ab, an eclipsing short-period binary that
shows long-term eclipse time variations. Using published, reanalysed,
and new mid-eclipse times of NN Ser ab obtained between 1988
and 2010, we find excellent agreement with the light-travel-time effect
produced by two additional bodies superposed on the linear ephemeris of
the binary. Our multi-parameter fits accompanied by N-body
simulations yield a best fit for the objects NN Ser (ab)c and
d locked in the 2:1 mean motion resonance, with orbital periods
yrs and
yrs, masses
and
,
and eccentricities
and
.
A secondary
minimum corresponds to an alternative solution with a period ratio of
5:2. We estimate that the progenitor binary consisted of an A star with
and the present M dwarf secondary at an orbital separation of
1.5 AU.
The survival of two planets through the common-envelope phase that
created the present white dwarf requires fine tuning between the
gravitational force and the drag force experienced by them in the
expanding envelope. The alternative is a second-generation origin in a
circumbinary disk created at the end of this phase. In that case, the
planets would be extremely young with ages not exceeding the cooling
age of the white dwarf of 106 yrs.
Key words: binaries: eclipsing - planetary systems - stars: individual: NN Ser - novae - cataclysmic variables -
planets and satellites: formation - stars: evolution
1 Introduction
NN Ser ab is a short-period
(
h) eclipsing binary at a distance of
500 pc. The detached system contains a hot hydrogen-rich white dwarf
NN Ser a of spectral type DAO1 and an M4 dwarf star NN Ser b with
masses of 0.535
and 0.111
,
respectively
(Parsons et al. 2010a). With an effective temperature of 57 000 K
(Haefner et al. 2004), the white dwarf has a cooling age of only
106 yrs (Wood 1995). The present system resulted from a normal
binary with a period of
1 year when the more massive component
evolved to a giant and engulfed the orbit of its companion. The
subsequent common envelope (CE) phase led to the expulsion of the
envelope, laying bare the newly born white dwarf and substantially
shortening the orbital period.
Some eclipsing post-CE binaries display long-term eclipse time variations, among them V471 Tau (Kaminski et al. 2007), QS Vir and NN Ser (Parsons et al. 2010b, and references therein). The latter possesses deep and well-defined eclipses, which allow measurements of the mid-eclipse times to an accuracy of 100 ms and better (Brinkworth et al. 2006; Parsons et al. 2010b). The processes advanced to explain them include the long-term angular momentum loss by gravitational radiation and magnetic braking, possible quasi-periodicities caused, e.g., by Applegate's (1992) mechanism, and the strict periodicities produced by apsidal motion or the presence of a third body in the system. Finding the correct interpretation requires measurements of high precision and a coordinated effort over a wide range of time scales. The existence of a third body orbiting NN Ser ab was previously considered by Qian et al. (2009), but the orbital parameters suggested by them are incompatible with more recent data (Parsons et al. 2010b). In this Letter, we present an analysis of the eclipse time variations of NN Ser ab, based on published data, the reanalysis of published data, and new measurements obtained over the first half of 2010.
2 The data
After their 1988 discovery of deep eclipses in NN Ser,
Haefner et al. (2004) acquired a series of accurate mid-eclipse times
in 1989. After a hiatus of ten years, they added a potentially very
accurate trailed CCD imaging observation using the ESO VLT. From 2002
on, the Warwick group systematically secured a total of 22 mid-eclipse
times of high precision (Brinkworth et al. 2006; Parsons et al. 2010b, this
work). Parsons et al. (2010b) list
all published mid-eclipse times by other authors until the end of
2009. These are included in our analysis that weights them by their
statistical errors. Since the individual Warwick mid-eclipse times
between 2002 and 2009 were separated by about one year, information on
eclipse time variations on a shorter time scale is lacking. We,
therefore, organized a collaborative effort of the Göttingen,
McDonald, and Warwick groups to monitor NN Ser over the first half of
2010. We used the remotely controlled MONET/North 1.2-m telescope at
McDonald Observatory via the MONET internet remote-observing
interface, the McDonald 2.1-m telescope, and the ESO 3.5-m NTT. The
MONET data were taken in white light, the McDonald data with a BG40 filter, and the NTT observations were acquired with the ULTRACAM
high-speed CCD camera equipped with Sloan filters. The mid-eclipse
times measured in Sloan u', g', and i' are consistent, and
we used the g' data as the most accurate set for the present purpose.
Table 1 lists the new mid-eclipse times shifted to the solar system
barycenter and corrected for leap seconds. The table also gives the
1-
statistical errors and the residuals relative to our
final fit shown in Fig. 2 and discussed in Sect. 4, below.
Table 1: Revised and new eclipse times of NN Ser ab with residuals for the light-travel-time effect produced by the two planets of Model 2a1.
The mid-eclipse time derived by Haefner et al. (2004) from the trailed
VLT image of 11 June
1999 is the most
variant of the published eclipse time measurements and was assigned a
large error of 17 s, although this should be a very precise
measurement, given the very simple form of the eclipses in NN Ser and
the use of an 8.2 m telescope. We reanalysed the image of 11 June 1999,
which started 04:53:05.537 UT with an exposure of 1125.7462 s and was
taken in good atmospheric conditions. The key issue is the conversion
of the track from pixel space to time. Using two independent methods,
we found that the original analysis by Haefner et al. (2004) was in
error and that the mid-eclipse time can be determined with an accuracy
of 0.20 s (Table 1, cycle E = 30721). We also reanalysed the less
accurate data of Pigulski & Michalska (2002) (cycle E =33233) by
including the effects of the finite integration times.
3 The light-travel-time effect in NN Ser
![]() |
Figure 1: Top: observed - calculated mid eclipse time differences relative to the best-fit linear ephemeris for Model 1 of a single planet orbiting NN Ser ab. Center and bottom: residuals relative to the eccentric-orbit fit for two selected time intervals. |
Open with DEXTER |
![]() |
Figure 2: Same as Fig. 1 for Model 2a of two planets orbiting NN Ser ab. The contributions of components b and c are indicated by the dashed and dot-dashed curves, respectively, the solid curve shows the combined effect. |
Open with DEXTER |
All measurements of mid-eclipse times of NN Ser ab are displayed in Figs. 1 and 2 as O-C values relative to the model-dependent linear ephemerides of the respective fits. Data points with errors <1 s and >1 s are shown as green and yellow dots, respectively. The eclipse time measurements dominating the fit are the 1989 data points of Haefner et al. (2004) near the abscissa value JD' = JD-2 450 000 = -2295, the reevaluated VLT point on JD' = 1340, the 2002-2009 series of Warwick eclipse times since JD' = 2411 (Parsons et al. 2010b), and the data of this work since JD' = 5212. In particular, the revised VLT mid-eclipse time implies a twofold change in the time derivative of O-C and excludes the simple quadratic ephemerides used by Brinkworth et al. (2006) and Parsons et al. (2010b). The available data do not exclude abrupt period changes or an ultimate aperiodicity, but there is no physical process that predicts such behavior. We consider a periodic behavior the most promising assumption and proceed to explore this possibility.
Strictly periodic O-C variations may result from apsidal motion of
the binary orbit or an additional body orbiting the binary. Given the
parameters of NN Ser ab, classical apsidal motion for small
eccentricities
produces a sinusoidally varying time
shift with an amplitude
s
(Todoran 1972). As a result,
would suffice
to produce the observed amplitude. However, the likewise predicted
variation of the FWHM of the eclipse and the time shift of the
secondary eclipse are not observed
(Parsons et al. 2010b, this work). Furthermore, the observed variation is not
sinusoidal and, given an apsidal motion constant for the secondary
star NN Ser b of
,
the period of the apsidal
motion would be as short as
0.4 years. Such periodicity is not
detected (see Fig. 2, bottom panel).
This leaves us with the third-body hypothesis, at least for the major fraction of the observed eclipse time variations. In general, it would be possible that different physical processes combine to produce the observed signal. We find, however, that a perfect fit within the very small statistical errors can be obtained for a signal that consists of the periodicities produced by two objects orbiting NN Ser ab. Guided by Ockham's razor and the history of discoveries in the Solar system, we consider that a fourth body in the presence of a third one is a natural assumption.
4 One-planet and two-planet fits to the data
Including the light-travel-time effect of the objects NN Ser (ab)c
and NN Ser (ab)d, the times of mid-eclipse become
![]() |
(1) |
where time is measured from a fiducial mid-eclipse time T0. A linear binary ephemeris is assumed with












We explored the multi-dimensional
space of the
two-planet model, using the Levenberg-Marquardt routine implemented in
IDL and an independent code. The search showed that compensation
effects render some parameters ill defined. This uncertainty results,
in particular, from the long hiatus between the accurate measurements
of 1989 (Haefner et al. 2004) and 1999 (VLT, this work). We selected the
best model, therefore, by imposing the additional requirement that the
derived orbits be secularly stable. We investigated all
solutions permitted by the data with numerical N-body simulations with
a variable time step Runge-Kutta integrator, following the orbits over
105 yrs, and find that only a narrow range in parameter space
corresponds to stable solutions. In what follows, we consider the
one-planet and the two-planet models in turn.
Model 1 with seven free parameters describes a single planet
with eccentricity e. The fit requires
and is bad for
any value of e, with a reduced
(
for 45 degrees of freedom). The top panel of
Fig. 1 shows the case e = 0.65. The residuals based on the
statistical errors of the data points (center panel) reach 23 standard
deviations and indicate that there is an additional modulation at
about half the orbital period. The residuals of the 2010 data (bottom
panel) demonstrate the lack of O-C fluctuations on a short time
scale.
Model 2 for two planets requires some restriction in
parameters, because the grid search yields good fits for a range of
eccentricities of the outer planet ,
including zero, and for a
period ratio
or
(1-
errors), with the former
slightly preferred. The dichotomy in
arises from the uncertain
phasing of the singular 1989 point relative to the train of the
1999-2010 data. Further minima at still larger
do not
exist. Only a small fraction of the parameter space allowed by the
fits corresponds to secularly stable orbits, however. Near
,
orbits with
tend to
be unstable, while the stability region is broad in the remaining
parameters for
.
Furthermore, all
solutions with
are unstable, with only
some solutions stable at
.
The solutions near
are more generally stable. We consider
Models 2a and 2b, representing the cases of
and 2.5, respectively, both with
.
Model 2a provides the slightly better fit
and is shown in Fig. 2. It yields
s,
s,
yrs,
yrs, and
with
for 42 d.o.f.). Periastron
passage of NN Ser (ab)d occurred last on JD
.
At
that time NN Ser (ab)c was at longitude
.
For the low
value of
,
a shallow minimum of
is
attained for aligned apses. From the present data, we cannot infer the
true value of
with certainty, but it is intriguing that objects c
and d may be locked in either the 2:1 resonance, found also in
other planetary systems, or the 5:2 resonance. The parameters
for Models 2a and 2b are listed in Table 2, together with their
1-
errors. A simpler model with two circular orbits reaches
only
for 44 d.o.f.) at
and can be excluded.
Table 2:
Parameters of the models fitted to the measured mid-eclipse
time variations of NN Ser, where
indicates a fixed
parameter.
Using Model 2a as input to our N-body simulations, we find that
and
oscillate around 0.02 and 0.22 with amplitudes of 0.02
and 0.05, respectively. The difference
of the
periastron longitudes circulates on a time scale of 400 yrs. The
periods perform small-amplitude anti-phased oscillations, which cause
to oscillate between 1.9 and 2.2. Even if the two planets are
secularly locked in the 2:1 mean motion resonance, therefore, the
observed period ratio at any given time may deviate slightly from its
nominal value.
For Model 2a, the best-fit binary ephemeris is T = BJED
2 447 344.524425(40) + 0.1300801419(10) E, where the errors refer
to the last digits. Adding a quadratic term BE2 to the ephemeris
does not improve the two-planet fit and yields a 1-
limit of
days, leaving room for a period
change by gravitational radiation or a long-term activity-related
effect (Brinkworth et al. 2006; Parsons et al. 2010b).
5 Discussion
The large amplitude of the O-C eclipse time variations in NN Ser can only be explained by a third body in the system, while the still substantial residuals from a single-planet fit could, in principle, have a different origin from that of a fourth body. The two-planet model, however, possesses the beauty of simplicity, and the fact that the residuals for the entire data set vanish simultaneously imposes tight restrictions on any other mechanism. In particular, the lack of short-term variability of the residuals in the first half of 2010 argues against any process that acts on a short time scale or leads to erratic eclipse time variations. Hence, there is strong evidence for two planets orbiting NN Ser ab.
With masses
and
,
NN Ser (ab)c
and NN Ser (ab)d both qualify as giant planets for all inclinations
28
and
,
respectively. The probable detection of resonant motion with a period
ratio of either 2:1 or 5:2 is a major bonus, which adds to the
credence of the two-planet model. It is the second planetary
system found by eclipse timing, after HW Vir (Lee et al. 2009).
Given a pair of planets orbiting a post-CE binary, two formation
scenarios are possible. They could either be old first-generation
planets that formed in a circumbinary protoplanetary disk or they
could be young second-generation planets formed 106 yrs ago in
a disk that resulted from the CE (Perets 2010). To
evaluate both scenarios, we have reconstructed the CE evolution of
NN Ser ab using the improved algorithm by Zorotovic et al. (2010),
who constrain the CE efficiency to a range
.
Possible solutions for the progenitor binary of NN Ser ab are
not very sensitive to
:
for
,
the progenitor was a giant of 2.08
and radius
194
with the present secondary star at a separation of
1.44 AU. When the CE engulfed the secondary star, dynamic friction
caused the latter to spiral in rapidly, thereby dramatically decreasing the
binary separation to the current
0.0043 AU.
Stability arguments imply that any planet from the pre-CE phase must
have formed with semi-major axes exceeding 3.5 AU
(Holman & Wiegert 1999). With three quarters of the central mass
expelled in the CE event, pre-existing planets would move outward or
may even be lost from the system. However, given a sufficiently dense
and slowly expanding CE,
the dynamical force experienced by them may
have ultimately moved them inward (Alexander et al. 1976). Since the
dragprimarily affects the more massive and more slowly moving outer
planet, such a scenario could lead to resonant orbits, so a
first-generation origin appears possible.
The alternative post-CE origin in a second-generation of planet formation is also possible, since the formation of circumbinary disks is a common phenomenon among post-AGB binary stars and the concentration of a slow, dusty wind to the orbital plane of the binary is thought to favor the formation of planets (e.g. Perets 2010; van Winckel et al. 2009). In particular the tiny separation of the present binary poses no problem for stable orbits of second-generation planets even at significantly shorter distances than the inner planet that we have detected (Holman & Wiegert 1999). A particularly intriguing aspect of a second-generation origin of the planets in NN Ser would be their extreme youth, equal to or less than the 106 yrs cooling age of the white dwarf (Wood 1995). This feature would distinguish them from all known exoplanets and may ultimately lead to their direct detection. While we cannot presently prove a second-generation origin for these planets, modeling the CE event may allow us to distinguish between the two scenarios.
AcknowledgementsWe would like to thank Dr. Reinhold Haefner for information concerning the original VLT observations and analyses and Dr. Andrzej Pigulski for sending us his original photometry. This work is based on data obtained with the MONET telescopes funded by the ``Astronomie & Internet'' program of the Alfried Krupp von Bohlen und Halbach Foundation, Essen, on observations with the ESO NTT under ESO programme 085.D-0541, and on data obtained from the ESO/ST-ECF Science Archive Facility. T.R.M., V.S.D., C.M.C., and S.P.L. acknowledge grant support from the UK's STFC. M.R.S. acknowledges support from FONDECYT under grant number 1061199 (MRS) and the Centre of Astrophysics Valparaíso. D.E.W. acknowledges the support of the Norman Hackerman Advanced Research Program under grant 003658-0255-2007.
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Online Material
Table 3: Previously published, reanalysed, and new mid-eclipse times of the white dwarf in NN Ser with residuals for the light-travel-time effect produced by the two planets of Model 2a.
Footnotes
- ... Serpentis
- Table 3 is only available in electronic form at http://www.aanda.org
- ...NN Ser ab
- On recommendation by the Editor of A&A, we refer to the system as NN Ser, to the binary explicitly as NN Ser ab, and to the objects orbiting the binary as NN Ser (ab)c and NN Ser (ab)d.
- ...
1999
- http://www.eso.org/public/images/eso9936b/
All Tables
Table 1: Revised and new eclipse times of NN Ser ab with residuals for the light-travel-time effect produced by the two planets of Model 2a1.
Table 2:
Parameters of the models fitted to the measured mid-eclipse
time variations of NN Ser, where
indicates a fixed
parameter.
Table 3: Previously published, reanalysed, and new mid-eclipse times of the white dwarf in NN Ser with residuals for the light-travel-time effect produced by the two planets of Model 2a.
All Figures
![]() |
Figure 1: Top: observed - calculated mid eclipse time differences relative to the best-fit linear ephemeris for Model 1 of a single planet orbiting NN Ser ab. Center and bottom: residuals relative to the eccentric-orbit fit for two selected time intervals. |
Open with DEXTER | |
In the text |
![]() |
Figure 2: Same as Fig. 1 for Model 2a of two planets orbiting NN Ser ab. The contributions of components b and c are indicated by the dashed and dot-dashed curves, respectively, the solid curve shows the combined effect. |
Open with DEXTER | |
In the text |
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