Issue |
A&A
Volume 509, January 2010
|
|
---|---|---|
Article Number | A103 | |
Number of page(s) | 12 | |
Section | Planets and planetary systems | |
DOI | https://doi.org/10.1051/0004-6361/200912717 | |
Published online | 27 January 2010 |
Hipparcos preliminary astrometric masses for the two close-in companions to HD 131664 and HD 131664
A brown dwarf and a low-mass star
A. Sozzetti1 - S. Desidera2
1 - INAF - Osservatorio Astronomico di Torino, via Osservatorio 20,
10025 Pino Torinese, Italy
2 - INAF - Osservatorio Astronomico di Padova, Vicolo dell'
Osservatorio 5, 35122 Padova, Italy
Received 18 June 2009 / Accepted 23 September 2009
Abstract
Context. Several mechanisms for forming brown dwarfs
have been proposed, which today are not believed to be mutually
exclusive. Among the fundamental characteristics of brown dwarfs that
are intrinsically tied to their origins, multiplicity is particularly
relevant. Any successful determination of the actual mass for such
objects in any systems is thus worthwhile, as it allows one to improve
on the characterization of the multiplicity properties (e.g.,
frequency, separation, mass-ratio distribution) of sub-stellar
companions.
Aims. We attempt to place better constraints on the
masses of two Doppler-detected substellar companions to the nearby G
dwarfs HD 131664 and HD 131664.
Methods. We carried out orbital fits to the
Hipparcos Intermediate Astrometric Data (IAD) for the two stars, taking
advantage of the knowledge of the spectroscopic orbits, and solving for
the inclination angle i and the longitude
of the ascending node ,
the two orbital elements that can be determined in principle solely by
astrometry, A number of checks were carried out to assess the
reliability of the orbital solutions thus obtained.
Results. The best-fit solution for
HD 131664 yields deg and
deg.
The resulting inferred true companion mass is then
.
For HD 131664, we find
deg and
deg,
and a corresponding
.
Based on the statistical evidence from an F-test,
the study of the joint confidence intervals of variation in i
and
and the comparison of the derived orbital semi-major axes with a
distribution of false astrometric orbits obtained for single stars
observed by Hipparcos, the astrometric signal of the two companions to
HD 131664 and HD 131664 is then
considered detected in the Hipparcos IAD, with a level of statistical
confidence not exceeding 95%.
Conclusions. We constrain the true mass of
HD 131664b to that of a brown dwarf to within a
somewhat statistically significant degree of confidence (). For
HD 131664b, a true mass in the brown dwarf regime is
ruled out at the
confidence level. The results are discussed in the context of the
properties of the (few) close substellar and massive planetary
companions to nearby solar-type stars and their implications for
proposed models of formation and structure of massive planets and brown
dwarfs.
Key words: stars: individual: HD 131664, HD 131664 - stars: low-mass - stars: brown dwarfs - planetary systems - astrometry - methods: data analysis
1 Introduction
Similar to the detection of the first Jupiter-mass ()
planet orbiting a star other
than the Sun (Mayor &
Queloz 1995), the first unambiguous discovery of a brown
dwarf
dates back
14 years (e.g.,
Rebolo
et al. 1995; Nakajima et al. 1995).
Several mechanisms for forming brown dwarfs have been proposed:
turbulent fragmentation of molecular clouds, fragmentation of
massive prestellar cores, protoplanetary disk fragmentation, dynamical
ejection of
protostellar embryos, and photoerosion of protostellar
cores (for a review, see Whitworth
et al. 2007).
Such mechanisms are today believed to not be mutually exclusive, and
they all
likely operate in nature. Determining their relative contribution to
the
overall brown dwarf population is a major theoretical challenge. To
date,
agreement must still be reached on fundamental issues such as what the
minimum mass for brown dwarfs is, and
how brown dwarfs might be distinguished from planets. For example, if
brown dwarfs
are identified as objects that form as stars do, on dynamical
timescales by
gravitational instability, regardless of the formation locus (a
molecular cloud or a
marginally unstable protoplanetary disk), and if the minimum mass for
core collapse is a few
(see Whitworth
et al. 2007), then significant overlap between the
mass range of brown dwarfs
and planets would occur and a simple mass cutoff (such as the one
adopted here)
may not apply. Given the significant number of open questions in this
research field,
it is thus essential for theory to accurately reproduce, and for
observations to
carefully determine, the ensemble properties of brown dwarfs,
including the brown dwarfs' initial mass function, the young brown
dwarfs'
kinematics, distribution, and disk frequency, and the binary statistics
of brown
dwarfs across a wide range of primary masses and orbital separations
(for a review
see Luhman et al.
2007; and Burgasser
et al. 2007).
Among the fundamental characteristics of brown dwarfs that are
intrinsically tied to their origin multiplicity properties (e.g,
frequency, separation, mass-ratio distribution) are particularly
relevant, because together with the possibility of determining the
actual internal composition and atmospheric features of individual
objects, they constitute one of the few ways of observationally
distinguishing between planets and brown dwarfs in the possible
overlap region in mass. For example, the frequency of close (a<5AU)
stellar (
)
companions to nearby (d<50pc) solar-type
stars is
% (Duquennoy & Mayor 1991),
while in the
same range of separations the frequency of giant planets (
)
is today known to be about
7% (Marcy et al. 2008).
Brown dwarfs, on the other hand, appear
conspicuously absent in the datasets collected by decade-long,
high-precision radial-velocity surveys of thousands of bright
normal stars, despite how easily their large RV signals would
have been spotted. Initial claims that the frequency of
close brown dwarf companions seemed to be in fair agreement with a
constant distribution of mass ratios (Mayor
et al. 1992) were later
dismissed by studies, based on a combination of radial
velocity measurements and Hipparcos astrometric observations, that
showed how
most of these putative substellar companions where in fact
stars (Halbwachs
et al. 2000). Indeed, among close companions, brown
dwarfs
appear outnumbered by stars and planets by factors of
100
and
50,
respectively, with typical frequency estimates of
0.1% (Marcy & Butler 2000). Only
about half a dozen close
companions with minimum masses in the brown dwarf regime are known
today around bright, nearby solar-type stars It is conceivable
that observational biases might contribute somewhat to a reduction
in the discovery rate of brown dwarfs with respect to planets
(because massive companions are typically assigned lower priorities
than
lower mass planets in Doppler surveys hard-pressed for optimal use
of the precious observing time at 10-m class telescopes). However,
such biases do not seem capable of explaining two orders of
magnitude of difference in the observed frequency of brown dwarf
companions with respect to planets and stellar companions.
The dearth of close brown dwarf companions to solar-type
stars, commonly referred to as
the ``brown dwarf desert'' (e.g, Campbell et al. 1988; Marcy &
Butler 2000),
is seen to extend at wider separations. Only recently have Patel et al. (2007)
reported
the first radial velocity detection of a handful of companions with
firmly
established in the brown dwarf mass range at orbital distances of
4 to
18 AU.
These first results do not yet allow an actual number for the brown
dwarf frequency
to be produced in this separation range. At larger separations (
50-1000 AU),
near-IR direct imaging surveys
have confirmed a deficit in substellar companions relative to stellar
companions, but not quite
as extreme as waht is apparent at orbital radii within a
few AUs.
McCarthy &
Zuckerman (2004) find
%,
roughly a
factor of ten lower
than the stellar companion frequency in the same separation range. More
recently
Metchev &
Hillenbrand (2009) have derived
%,
a number
formally compatible with that of McCarthy
& Zuckerman (2004). In any case, the frequency of
wide-separation brown dwarf companions is comparable to that of
free-floating brown dwarfs relative to
stars. The evidence for a not-so-dry desert at wide separations is
usually interpreted as supporting
the view that brown dwarfs form by core fragmentation just like stars.
However, the finer details of the
formation mechanism are not well understood, so a more accurate
characterization of
the multiplicity of brown dwarfs is needed to shed light on the
relative role of the various
proposed scenarios.
The dynamical determination of the mass of a few close brown
dwarfs companions to low-mass stars and
of brown dwarf binaries has been obtained for eclipsing systems for
which both spectra can be observed
(e.g., Stassun
et al. 2006; Zapatero Osorio et al. 2004)
and by a combination of aperture masking interferometry
and astrometry (Ireland
et al. 2008). As for the sample of companions to
nearby dwarfs discovered
by Doppler planet surveys with
values
in the range between high-mass planets and brown dwarfs,
it is conceivable that some of them are in reality stars seen pole-on.
Similar to Halbwachs
et al. (2000),
several authors have attempted to combine the radial-velocity orbits
with Hipparcos astrometry in order
to determine the inclination and true mass of the companions (for a
review see for example Sozzetti
2009).
Recently, Reffert &
Quirrenbach (2006)
presented low-significance detections of the astrometric orbits of the
two outer companions in the
HD 38529 and HD 168443 planetary systems, inferring
masses in the brown dwarf regime
of 37
and 34
for HD 38529c and HD 168443c, respectively.
High-precision astrometry with
HST/FGS allowed Bean
et al. (2007) to determine an actual mass of
0.14
for the companion to
HD 33636, originally published with
.
Any successful attempt to resolve the ambiguity in
the actual companion mass for such objects is thus worthwhile as it
allows improvement of the
characterization of the multiplicity of brown dwarfs. This in turn
permits better understanding of the global
nature of the substellar companions found at larger separations by
means of direct imaging surveys.
In this paper we present a new attempt at combining the information from Doppler measurements with Hipparcos astrometry to place better constraints on the mass of two Doppler-detected low-mass companions to HD 131664 (Moutou et al. 2009) and HD 131664 (Minniti et al. 2009), with published minimum masses in the low-mass brown dwarf regime. A summary of the available data in the literature for the two systems is presented in Sect. 2. We derive improved contraints on the actual companion masses in Sect. 3. Finally, in Sect. 4 we a) put the new results in the context of the properties of the (few) close sub-stellar and massive planetary companions to nearby solar-type stars, collected in a catalogue table for ease of consultation and reference in future works and b) discuss some of the implications of the present-day observational evidence for formation and structural models of massive planets and brown dwarfs.
2 Doppler data and Hipparcos astrometry
Table 1: Stellar characteristics of HD 131664 and HD 131664 and spectroscopic orbital elements for the two Doppler-detected companions.
2.1 HD 131664
Included in the Doppler search for southern extrasolar planets carried
out with the HARPS
(Pepe et al. 2003)
spectrograph on the ESO 3.6-m telescope at La Silla
Observatory,
the bright G-type star HD 131664
(HIP 73408) was recently announced by Moutou et al. (2009) to
be orbited by a companion with a minimum mass of
on an
eccentric
orbit of period
yr
(for convenience, see Table 1
for a summary of the properties
of the primary and of the orbital parameters of detected companion). At
the distance of HD 131664,
the inferred orbital separation ranges between 35 mas and
100 mas (as pointed out by Moutou et al.),
making it a potentially interesting target for future direct-imaging
observations. The viability of
this investigation depends in particular on the true mass of the
companion and the actual contrast ratio.
In the former case, high-precision astrometry with Gaia in space and
VLTI/PRIMA from the ground (e.g., Sozzetti
2009, and references therein)
will allow accurate values to be derived of the actual mass of the
companion. However, it must be noted that
the minimum astrometric signature induced on the primary is just under
1 mas, as opposed to a median
single-measurement error
mas.
Hipparcos observations of this
star could then help place useful mass constraints on the companion
mass. Indeed, the Double and Multiple
Star Annex of the Hipparcos Catalogue reports a G flag, indicating that
a 7-parameter solution
(allowing for acceleration in the proper motion) was found to
significantly improve the standard
5-parameter single-star fit. The reported acceleration solution for
HD 131664 is based on 96 datapoints,
two of which correspond to observations retained only by the NDAC
consortium.
2.2 HD 43848
Doppler measurements taken with the MIKE echelle
spectrograph (Bernstein
et al. 2003) on the 6.5-m Magellan II
(Clay)
telescope have revealed (Minniti
et al. 2009) the nearby solar-type
star HD 131664 (HIP 29804) to be orbited by a
companion
with
on a
high-eccentricity orbit with
yr (for
completeness, Table 1
also
reports the summary of the properties of the primary and of the
orbital parameters of detected companion). This system also
appears to be of potential interest for future direct-imaging
observations, with a separation at apoastron of
0.2 arcsec. Its
minimum astrometric signature, at the distance of HD 43848, is
2.5 mas,
a value comparable to the typical
precision of Hipparcos astrometry for this star (median error
mas).
An astrometric solution with
acceleration terms for this star is also present in the Hipparcos
Catalogue, based on a total of 76 measurements
(with one abscissa
retained only by FAST, one only by
NDAC, and another rejected by NDAC in the solution). For both
HD 131664 and HD 131664 there
appears to be
indication of a long-period trend in the Hipparcos
data, rendering a further investigation of the
available astrometry worthwhile.
3 Combined radial velocity+astrometry solution
When searching for evidence of an orbital signal in the Hipparcos data
of a
given star due to a spectroscopically discovered low-mass companion, a
typical procedure is
applied in which information
from radial velocities is assumed known, and one resorts to probing the
region of the parameter
space not covered by spectroscopy. Orbital fits to the Hipparcos IAD
are then
usually performed (Wittenmyer et al. 2009; Halbwachs
et al. 2000; Mazeh et al. 1999; Han et al.
2001; Reffert
& Quirrenbach 2006; Zucker & Mazeh 2000)
by keeping four orbital elements fixed (P, e,
T0, )
to their spectroscopically
determined values and by solving for inclination angle i
and position angle
of the ascending node
,
with the additional constraint that the astrometric
semi-major axis satisfies the equality (Pourbaix & Jorissen 2000)
where P is in days, the semi-amplitude of the radial velocity curve K is in m s-1, and the orbital parallax


The experience of various authors indicates that one must be careful
not to ask Hipparcos
data to tell more than they actually can. Pourbaix (2001), Pourbaix & Arenou (2001),
and
later Zucker & Mazeh
(2001) have for example shown that the
Hipparcos IAD, while useful to put upper limits on the
size of the astrometric perturbations, must be interpreted with great
caution when attempting
to derive actual astrometric orbits for substellar companions with
semi-major axes close to
or even below the typical single-measurement precision of the
satellite. While the astrometric
orbit does not need to be actually detected in order to derive
constraints on the values of i and ,
reported detections, when not outright refuted (e.g., Pourbaix & Arenou 2001),
usually have relatively low levels of statistical
confidence (e.g., Reffert
& Quirrenbach 2006).
Based on the above considerations, we have adopted a multi-step
approach to the treatment of the Hipparcos IAD for HD 131664
and HD 131664
in an attempt to make a statistically solid case for any conclusions.
![]() |
Figure 1: Periodograms of HD 131664 ( top) and HD 131664 ( bottom)assuming e and T0 from the known spectroscopic orbit. |
Open with DEXTER |
As a first step in the process, we decorrelated and weighted all
available Hipparcos
along-scan measurements for the two stars, following the prescriptions
of Pourbaix &
Jorissen (2000)
and van Leeuwen & Evans
(1998). We then asked whether an orbital model could lead to
an improved
description of the Hipparcos data, and used the Thiele-Innes
representation of a photocentric orbit (Heintz
1978)
to carry out a linear least squares fit over a large grid of periods
bracketing the
ones obtained from the radial velocity measurements, while keeping
fixed eand T0
to their spectroscopic values. We thus seeked to minimize
![]() |
(2) |
where the superscript t indicates transposed,




Table 2:
Orbital fits to the Hipparcos IAD for HD 131664 and
HD 131664,
assuming knowledge of P, e,
T0, and
from the
spectroscopic orbit.




![[*]](/icons/foot_motif.png)


The results of the orbital fit to the Hipparcos IAD of both
HD 131664 and HD 131664 are
summarized in Table 2.
The reported uncertainties on i
and ,
as well as the derived mass values for the
companions, take the 1-
formal errors on the parameters of the
spectroscopic orbits into account. The inferred true masses for
HD 131664b and HD 131664b
are 23-5+26
and
120+167-43
,
respectively. Taken at face value, these numbers would imply that
the companion to HD 131664 has a mass in the brown dwarf
regime at the
confidence level,
while the unseen object around HD 131664 is likely a
low-mass M dwarf (at the
confidence level).
An attempt at using the FAST and NDAC data separately for both stars
resulted in solutions formally compatible with
the ones reported here, albeit with larger uncertainties and looser
constraints on the derived mass estimates.
To assess the statistical soundness of the derived
astrometric orbits, several checks can be performed. First, based
on an F-test of the null hypothesis that there is no companion, we
find that the addition of two parameters to the model describing
the Hipparcos IAD significantly improves the fit in both cases:
P(F)
= 0.0002 and P(F)
= 0.001 for HD 131664 and HD 131664,
respectively. Second, similar to Reffert
& Quirrenbach (2006), we
have further explored the reliability of the orbital solutions by
inspecting the joint confidence regions (corresponding to
iso-
contours) in the
plane, for a given
statistical level of confidence. As shown in
Fig. 2,
the 95% (2-
)
iso-
contours
cover relatively narrow regions in the
plane, ruling
out with confidence very small inclinations in the case of
HD 131664, and close to edge-on configurations in
the
case of HD 131664. Ambiguities in the orbit
orientation
are clearly seen in both cases, highlighted by local minima in
the
surface corresponding to configurations with the opposite
sense of revolution. Nevertheless, one would conclude that
Hipparcos astrometry has successfully detected orbital motion
induced by the two massive companions to HD 131664
and
HD 131664. We consider the 95% confidence
level as the
appropriate measure of the degree of statistical robustness with
which these results can be regarded. Finally, we have applied a
standard bootstrap method (Efron
1982), based on 1000 Monte Carlo resamples
with replacement, to the available data for both
stars in order to derive empirical error estimates on the derived
orbital semi-major axes (constrained by Eq. (1)
during the fits).
Our procedure closely follows the one adopted
by Zucker & Mazeh (2001),
who first realized, from the assigned
correlation between pairs of Hipparcos measurements for which both
FAST and NDAC data are available, the need to preserve the pairing
of the measurements while drawing new random datasets, in order to
make the bootstrap method applicable in the first place. The two
resulting ratios
have then been compared to the
Rayleigh-Rice law distribution of the false
one
can expect to obtain in the case of Hipparcos data of single stars
(see Halbwachs et al.
2000). As shown in Fig. 3, the
nominal values of
for HD 131664 and
HD 131664 fall in the tail of the Rayleigh-Rice
distribution: the probability that
exceeds the
observed one is found to be 0.03 and
for
HD 131664 and HD 131664,
respectively. This can
again be interpreted as a detection of a significant Hipparcos
astrometric orbit for both stars, at the 97%
and 99.99%
confidence level, respectively. For the purpose of this study, we
adopt the more conservative abovementioned 95% confidence
level
to gauge the actual degree of statistical confidence with which
the orbits of HD 131664b and HD 13664b are
considered
detected.
![]() |
Figure 2:
Iso- |
Open with DEXTER |
4 Summary, discussion, and conclusions
We have inspected the Hipparcos IAD for two stars,
HD 131664 and HD 131664, with
Doppler-detected
companions with minimum masses in the brown dwarf regime. We presented
a body of
supporting evidence that appears to confirm the detection of orbital
motion in the Hipparcos IAD
of HD 131664 and HD 131664, at a
somewhat significant (95%) level of statistical confidence.
The inferred actual masses of HD 131664b and
HD 131664b are found to be
and
,
respectively. The former thus
appears to be a late M dwarf (at the
confidence level),
while the latter appears to be a brown dwarf (at the
confidence level).
Taken at face value, HD 131664 is nominally the
lowest mass brown dwarf confirmed with
a combination of Hipparcos and precision Doppler measurements (the
astrometric orbits of giant
planets obtained with HST/FGS + RV data lie
in a different ballpark).
The larger uncertainties in the spectroscopic orbital elements of
HD 131664, combined with the low
value of i inferred from the orbital fit,
translate into larger uncertainties
in the mass estimate, leaving a margin for this unseen object to also
be a brown dwarf (as well as a higher mass M dwarf).
![]() |
Figure 3:
Distribution of the ratio |
Open with DEXTER |
Based on the mass-luminosity relations of Delfosse
et al. (2000),
HD 131664, with its nominal mass of 120 ,
is expected to have magnitude differences
of about 8.7, 5.7, 5.4, and 5.2 in the V, J,
H, and K bands,
respectively.
With a projected separation of about 0.15 arcsec at apoastron, it
should be detectable with current AO instruments at
8 m class telescopes.
The magnitude difference between HD 131664 and its
parent star depends critically on
the age of the system. Moutou
et al. (2009) give an age of
Gyr for
HD 131664 based on isochrone fitting.
Additional clues can be derived from stellar activity indicators.
Moutou et al. (2009)
measure
.
This corresponds to an age of 3.5 Gyr using
the calibration by Mamajek &
Hillenbrand (2008). We also searched for X-ray emission from
the system.
The ROSAT Faint Source Catalog (Voges
et al. 2000) includes a source (HD 131664)
at 40 arcsec from HD 131664 (with a quoted
positional error of 29 arcsec). The association is then
doubtful. Assuming HD 131664 is the
X-ray counterpart of HD 131664, we
derived (using the flux calibration by Hünsch
et al. 1999)
and
an age of 2.1 Gyr
(using the calibration by Mamajek
& Hillenbrand 2008). Alternatively, a no detection
would imply
an older age. Stellar activity indicators then exclude the youngest
stellar ages compatible with
isochrone fitting. A more plausible lower limit to the stellar age is
about 1.5 Gyr. Given our best-fit mass value and the age of
2.4 Gyr, HD 131664 is expected to have
magnitude differences of about 15.0, 15.2, and 17.2
in J, H, and K bands,
respectively, based on the models of Baraffe
et al. (2003).
The corresponding effective temperature is about 700 K, at the
cool end of the currently known T dwarfs.
Considering the small projected separation
(<0.1 arcsec), such a contrast is not achievable with
current instrumentation, and it would also be challenging for the next
generation of direct-imaging
instruments.
Any successful attempt, such as the one presented here, at deriving true masses of the substellar companion candidates detected from radial velocity surveys is definitely worthwhile, as the results can be seen in the context of the observed paucity of close brown dwarf companions to solar-type stars in the solar neighborhood, the well-known brown dwarf desert, and in particular their binarity properties. For example, taken at face value the rather large eccentricity of HD 131664 (e=0.638) supports the notion that massive planetary companions and brown dwarfs are preferably found on eccentric orbits (Ribas & Miralda-Escudè 2007). On the other hand, the high metallicity of the parent star ([Fe/H = +0.32) does not follow the proposed trend of metallicity vs. mass for substellar companions (Ribas & Miralda-Escudè 2007). While not conclusive, these findings bring new/updated information that can certainly help to deepen our understanding of the formation mechanism of such objects.
Table 3:
Close companions to solar-type stars with (projected) masses between 10
and 80
.
4.1 Properties of massive planets and brown dwarf companions to solar-type stars
To put our discussion into a more general context, we summarize in
Table 3
the main properties of the companions with
projected masses between 10 and 80
and a semimajor axis
smaller than
7 AU,
orbiting main-sequence stars with
masses between 0.7 to 1.5
.
This selection matches the
sample of most high-precision radial velocity surveys and avoids
the additional complications of large variations in the stellar
mass and evolutionary status (very small number statistics being
one of the most relevant). The literature data collected here are
meant to provide ease of consultation and reference for future
works on the many outstanding issues we touch upon thereafter. In
the table, determinations of or constraints on the inclination
and true companion mass derived from astrometry or transit
photometry are included when available. For completeness and
reference, we also include companions with substellar projected
mass and astrometrically derived stellar mass. We have also
included HD 131664, whose companion with
just
below the adopted threshold was shown to be a low-mass star
(Bean et al. 2007).
Orbital elements and projected masses are from
listed discovery papers, Butler
et al. (2006) or Halbwachs
et al. (2000).
Stellar masses and metallicities are from Valenti
& Fischer (2005), discovery
papers, or additional references. Further information, such as
additional stellar or planetary companions, the sources for the
metallicity values, and the specific treatment of some of the mass
and error estimates, can be found in the notes. In the remarks, PL
refers to objects with additional companions of planetary mass,
MULT to multiple systems (additional stellar companions), HIPG to stars
with Hipparcos acceleration solutions.
![]() |
Figure 4:
Period vs. eccentricity ( top panel) and
eccentricity vs. companion mass
( bottom panel). In the lower panel plot, only
objects with periods longer than 20 days are shown.
Red filled circles: companions with true estimated masses in the range
10-80 |
Open with DEXTER |
![]() |
Figure 5: Orbital period vs. companion mass ( top), metallicity vs. companion mass ( center), stellar mass vs. companion mass ( bottom). Symbols as in the previous figure. |
Open with DEXTER |
As discussed in the introduction, Halbwachs
et al. (2000) have shown how a
significant fraction of Doppler-detected candidate substellar
companions were in fact low-mass stars viewed at low inclination.
Nevertheless, a few candidates have masses firmly in the
substellar regime, partially filling the brown dwarf desert.
Interestingly, in two cases (HD 131664 and
HD 131664), additional companions in the planetary
mass regime were
found We
note that such system configurations are more typical of planetary
systems than of multiple stellar systems. In Figs. 4 and 5 we show a set of
correlation diagrams among the most relevant
quantities of the systems collected in Table 3.
![]() |
Figure 6:
Upper panel: cumulative distribution of the
eccentricity of objects with periods longer than 20 days
orbiting main-sequence stars with mass between 0.7 and
1.5 |
Open with DEXTER |
Ribas & Miralda-Escudè (2007)
note a possible trend in the eccentricity-mass distribution of giant
planets, with more massive
planets (
)
orbiting on average with higher eccentricities. The recent analysis by
Wright et al. (2009), who used 1
as the cut-off value, confirm this trend.
The Ribas &
Miralda-Escudè (2007) analysis also suggests that the
metallicity of stars hosting
massive planets and brown dwarf candidates is compatible with that of
the solar neighborhood (
,
e.g. Nordström
et al. 2004), differing at the 3-
level from the super-solar metallicity distribution of
stars hosting lower mass planets (
,
e.g. Fischer & Valenti 2005).
Hints of such a trend
had already been seen in a more limited dataset by Rice et al. (2003).
We revisit here this statistical analysis, considering all objects
included in Table 3,
as well
as the sample of exoplanets with
reported
in Butler et al.
(2006).
For this purpose, we have divided the full sample into three subsets
according to minimum mass:
,
,
and
,
plus a fourth
subsample formed by those objects in Table 3 with estimated true
masses in the range
.
We then performed on these subsets both a Kolmogorov-Smirnov (K-S)
test, to measure to what extent their e and [Fe/H]
distributions might differ, and a Wilcoxon Rank-Sum (R-S)
test, to measure to what degree the mean e
and [Fe/H] might be considered different. The resulting
values of the probabilities (Pr(D) and Pr(Z),
respectively) of the null hypothesis for both tests on the various
subsamples are
reported in Table 4,
while Fig. 6
shows a comparison between the
resulting cumulative distributions of e and
[Fe/H] for the above-mentioned subsets of systems.
From investigation of Table 4 and Fig. 6,
a few conclusions can be drawn. As for the e distribution,
the
results further corroborate the notion that eccentricities of
not-so-massive planets are clearly less pronounced than those of more
massive planets and brown dwarf companions.
On the other hand,
massive planets appear to have an overall e
distribution that is indistinguishable from that of brown dwarf
candidates.
Similarly, the [Fe/H] distribution of the hosts appears
significantly different for companions with
and for
brown dwarf companions, while other trends are marginal,
and in particular metallicities of massive planet hosts and of
primaries with brown dwarf companions are statistically the
same
.
4.2 Implications for formation and structural models of massive planets and brown dwarfs
The above evidence can be interpreted, keeping in mind the relatively small-number statistics regime we are dealing with here, in the context of the proposed formation scenarios and internal structure models of high-mass planets and brown dwarfs, and as a function of the main properties of the stellar hosts (binarity, mass, metallicity).
Table 4: Results of the K-S and R-S tests on different subsets of systems.
4.2.1 Formation and orbital evolution of massive planets and brown dwarfs
As already pointed out in the introduction, the lower mass limit for
the formation of self-gravitating
objects from fragmentation of molecular cloud cores is today thought to
be a few
(e.g., Whitworth
et al. 2007; Luhman
et al. 2007). Ribas
& Miralda-Escudè (2007) and, more recently,
Font-Ribera et al.
(2009) have proposed direct cloud fragmentation, followed by
inward migration by disk capture,
as a formation mechanism for the high-mass tail of the planetary
population.
The detection of a significant number of free-floating objects down to
6
and the observed continuity of the substellar mass function in young
star-forming regions
(e.g., Caballero
et al. 2007, and references therein; Zuckerman & Song 2009,
and references therein)
are indications that indeed a star-like formation process may form
brown dwarfs, as well as planetary mass objects
.
Indeed, the process outlined by Font-Ribera
et al. (2009) should be effective
independently of the metallicity of the parent cloud, and is expected
to produce an eccentricity distribution similar to that of binary
systems. The results shown in Table 4
and in Fig. 6
can be seen as supporting this scenario.
On the other hand, the disk-capture mechanism proposed by Font-Ribera et al. (2009)
does not naturally
explain the existence of the brown dwarf desert, as increasingly more
massive objects
should actually be easier to capture in their model. Also, Grether & Lineweaver (2006)
have pointed to observable differences in the mass distributions of
isolated objects and companions to solar-type stars,
the latter exhibiting a minimum (the ``driest part of the brown dwarf
desert'')
at
(
).
This evidence does not appear to be readily explained by the mechanism
proposed by Font-Ribera
et al. (2009).
Massive planets and brown dwarfs can also be formed by gravitational fragmentation of extended disks around solar-type primaries. In the models of e.g. Stamatellos & Whitworth (2009), brown dwarfs form by direct gravitational collapse only in the outer regions of the disks, and tend to be scattered farther out, or even into the field. This mechanism can explain the existence of the brown dwarf desert at small separations. The two other conclusions that can be drawn from these models are that 1) no planets formed by disk instability can really be found as close companions, as they can only form in the outer regions of the disks and are scattered with much higher efficiency than brown dwarfs; and b) as a direct consequence short-period Doppler-detected massive planets and brown dwarfs should primarily be low-mass stars. On the one hand, this mechanism can be seen as supported by the data presented here (the properties of massive planets, brown dwarfs, and low-mass stellar companions being very similar). On the other hand, some of the objects in the sample of Table 3 can hardly be explained by this approach (e.g., the transiting objects HD 131664b and HD 131664).
In the still theoretically debated (e.g., Mayer et al. 2002; Rafikov 2005; Stamatellos & Whitworth 2008; Boss 2009; for a review see Durisen et al. 2007) disk instability model of giant planet formation, massive planets with relatively eccentric orbits and moderate-to-large orbital separations are its more likely product (e.g., Rice et al. 2003; Boley 2009). No clear prediction of the expected shapes of the orbital elements and mass distributions of planets formed by disk instability is available yet, because of the numerical complexities of the simulations and to some still open theoretical issues on the input physics (see e.g. Boss 2009, and references therein). However, if high-precision measurements of the actual masses of massive planets, as well as of those of the substellar companions listed in Table 3, were to become available, and were they to prove that these objects are not preferentially low-mass stars, this evidence would argue in favor of a common formation mode for massive planets and brown dwarfs.
In the more widely accepted core-accretion mechanism for the
formation of giant planets (e.g.,
Pollack et al. 1996; Alibert et al. 2005; Ida & Lin 2005; for a review
see Lissauer &
Stevenson 2007)
very massive planets and low-mass brown dwarfs on eccentric orbits are
not a natural outcome
(e.g., Kennedy
& Kenyon 2008; Alibert et al. 2005; Ida & Lin 2005;
Pollack
et al. 1996).
However, recent models have shown that this mechanism might also be
capable of forming such massive objects.
Indeed, in the model of Mordasini
et al. (2009), planets with masses as high as
are
formed in long-lived massive disks
around a solar mass star. Given the increasingly lower probability of
forming very massive planets or
brown dwarfs (``deuterium-burning'' planets in the words of Baraffe et al. 2008),
the brown dwarf desert appears compatible with the
Mordasini et al. (2009)
model (for example, the probability of forming objects with masses
exceeding the deuterium-burning
threshold is found to be
,
in accord with the Marcy
& Butler (2000) estimate).
While the Mordasini et al.
(2009) model does not include multi-planet systems and
planet-planet
interactions, likely to play an important role in shaping the observed
mass, period and eccentricity distributions,
we note that the expected location of such very massive planets is
between 2 to 5 AU, similar to what is observed for
HD 131664, HD 131664 and the
object studied in this paper, HD 131664.
However, no prediction of this model on the eccentricity distribution
is available, which would be a
critical element for distinguishing between this mechanism and the
other aforementioned options.
In addition, super-planets and low-mass brown dwarfs also exist at
small separation, where they are not expected
on the basis of the Mordasini
et al. (2009) model. Noticeable examples are the
transiting systems HD 131664 (Bakos
et al. 2007),
HD 131664 (Joshi
et al. 2009), HD 131664, and
HD 131664, but also other massive objects
such as HD 131664 (Udry
et al. 2002) and
HD 131664 (Zucker
et al. 2004).
Finally, of particular interest are the initial claims of a
possible correlation between massive planets, eccentric orbits,
and high values for the angle between a planetary orbit and the
stellar rotation axis, as determined from spectroscopic
measurements of the Rossiter-McLaughlin (R-M)
effect (McLaughlin
1924; Rossiter
1924) in transiting systems. The
HD 131664, HD 131664, and HD 131664
systems all
have a close-in, massive planet on a very eccentric orbit and with
a significant spin-orbit misalignment (e.g., Johnson et al. 2009,
and references therein).
At first
glance, this might imply that the orbital migration history of
massive, eccentric exoplanets is somehow different for less massive
close-in Jupiters, However, the picture is not likely to be so simple,
not only because of the evidence of other
transiting systems with massive, eccentric planets (HAT-P-2,
HD 17156) showing no signs of spin-orbit misalignment
(e.g., Winn et al. 2007; Barbieri et al. 2009),
but also for the
recent measurements of the R-M effect in transiting systems
with
Jupiter-mass planets on circular orbits, such as CoRot-1, HAT-P-7,
and WASP-17 (Pont et al. 2009,
and references therein) that point toward high values of the projected
spin-orbit angles. Overall,
the evidence collected so far is a likely indication of the
variety of possible outcomes of the complex process of migration
to close-in orbits of companions with a wide range of masses,
which include a host of proposed dynamical mechanisms (e.g.,
interactions between a planet and the gaseous/planetesimal disk,
planet-planet resonant interactions, close encounters between
planets, and secular interactions with a companion star), as well
as different formation scenarios. Statistical studies, such as the
one carried out by Fabrycky
& Winn (2009), who showed the emergency of
a bimodal distribution of spin-orbit angles, on an increasingly
larger sample of transiting systems will ultimately be the optimal
way to compare an ensemble of measurements of the R-M effect
with
the predictions of migration theories.
4.2.2 The impact of binarity
Among the distinctive features of exoplanets discovered around members
of
various types of binary and triple systems (e.g., Eggenberger & Udry 2009,
and references therein),
one of the most intriguing is the evidence that solar-type stars
members of multiple stellar
systems appear to be preferential hosts of the most massive planets on
short-period orbits
(Desidera & Barbieri 2007),
and the fact that the planetary companions with the highest
eccentricities
all have either stellar or brown dwarf companions (Tamuz et al. 2008). These
trends
seem to indicate that planet formation and/or migration in binaries may
proceed differently
than around single stars. Indeed, theoretical studies (Fabrycky
& Tremaine 2007; Wu & Murray 2003; Kley 2000)
within the context of the core accretion model of giant-planet
formation
suggest that the presence of a fairly close companion significantly
enhances the growth rate
and makes the migration timescale of the planet shorter.
On the other hand, the massive super planets or low-mass brown dwarfs
found at separations of
about 2-3 AU orbit stars that are single or with very wide
companions (HD 131664 has a
common
proper motion companion at a projected separation of
12 000 AU), compatible with long-lived, undisturbed
disks required to form such objects according to Mordasini
et al. (2009). Models of giant planet formation by
disk instability,
however, come to opposite conclusions, with giant planet formation
significantly suppressed in binaries with
separations <100 AU (Mayer
et al. 2005). From inspection of Table 3, the above-mentioned
trends
seem to be supported only in part. For example, the short-period
objects HD 131664 and HD 131664
orbit one of the components of wide binaries, but this does not appear
to be the case for HD 131664.
Investigations are encouraged that would aim at verifying the possible
existence of binary companions to
HD 131664 and HD 131664. Furthermore, the brown-dwarf
candidates with the highest eccentricities do not
seem to be found primarily in multiple systems.
4.2.3 The role of the primary mass and metallicity
In the core-accretion model of giant-planet formation, the upper
limit on the mass of the planetary companion and the final orbital
arrangement are expected to depend on stellar mass and
metallicity. Based on arguments of protoplanetary disk size and
lifetime as a function of ,
one would expect massive
planets to be found with higher probabilities around more massive
primaries (Kennedy &
Kenyon 2008) and at typically moderate-to-large
separations (Burkert
& Ida 2007; Currie 2009). Indeed, the
observational
evidence indicates that, for higher stellar masses, massive
companions with
are significantly more
numerous
than around solar type stars (e.g., Johnson 2008; Lovis &
Mayor 2007.
For a review see Hatzes 2008,
and references therein). On
the opposite end, M dwarfs are expected to show a paucity of
giant
planets (Ida
& Lin 2005; Laughlin et al. 2004),
which is also
observed (Endl
et al. 2006; Johnson et al. 2007; Bailey
et al. 2009). The core-accretion
mechanism also naturally predicts that super-massive planets
should not be found at all around metal-poor stars, given the lack
of material for accumulation (e.g., Ida
& Lin 2005). The
alternative disk instability mechanism is instead rather
insensitive to the values of
and [Fe/H] of the stellar
host (e.g., Boss 2002, 2006). As a
consequence, a qualitative prediction of this model
(e.g., Rice et al. 2003)
is that massive planets found on moderate-to-large separations around
massive and/or metal-deficient hosts
would be likely to have been formed by gravitational instability.
In this respect, the data collected here and the results of the
statistical analysis, which corroborate the findings
of Ribas &
Miralda-Escudè (2007), can be read as partly supporting the
latter
view. Interestingly, the frequency of (massive) planets (
)
around intermediate-mass (mostly giant) stars appears to be rather
independent of [Fe/H] (Hatzes
2008). However, the four known
planet - brown dwarf systems (HD 131664,
HD 131664, HD 131664,
HD 131664) all have
super-solar mass, very metal-rich (main-sequence) primaries. This last
piece of evidence might be seen as supporting the core accretion
formation mode, while the former dataset might point to a
significant role for the disk instability mechanism. However, the
global picture is likely to rather complex. For example, Doppler
surveys for giant planets around intermediate-mass stars typically
include targets that have evolved to some degree, given that
massive main sequence stars are unsuitable for high-precision
radial-velocity measurements (too few spectral lines, often
broadened by high rotation rates). The very different dependence
of
on [Fe/H] for intermediate-mass stars with respect to
their solar-mass counter-parts might then reflect a non-primordial
origin to the metallicity enhancement in solar-type planet
hosts (Pasquini
et al. 2007) rather than point to different
formation
modes.
As for the possible dependence of brown dwarf frequency on
stellar
mass and metallicity, this is still a poorly understood issue. A
quick look at literature data allows us to speculate on the
possibility that the brown dwarf desert may not be very ``dry'' when
it comes to close substellar companions to intermediate-mass
stars, in light of a handful of systems containing at least one
companion with minimum mass in the brown dwarf regime
(e.g., Omiya et al.
2009, and references therein). In particular,
the recently announced system of brown dwarfs around HD 131664 (Niedzielski et al.
2009) has an architecture very similar to that of
HD 131664, with a solar-type primary. It is
reminiscent
of an origin in a massive circumstellar disk, further suggesting a
scenario in which more massive substellar companions are found
around more massive stellar hosts (and their frequency also
increases with increasing primary mass). Such systems would be
more likely to have been formed by local gravitational instabilities in
protoplanetary disks (e.g., Rice
et al. 2003) rather than
protostellar cloud fragmentation, given the difficulties in
forming extreme mass-ratio binaries by the latter mechanism
(e.g., Bate 2000).
However, the combination of small-number
statistics, the different priority given to observations of stars
with very massive companions in Doppler surveys, the variable
detection thresholds as a function of companion mass and
separation due to the decreasing radial-velocity precision in
increasingly higher mass stars, and the uncertainty on the actual
mass values for most of the objects included in Table 3
(as well as those noted above) prevents one, as of today,
from drawing any serious conclusions on the possibility that the
brown dwarf desert may move in mass and/or separation range
depending on
and [Fe/H].
4.2.4 Structural and atmospheric models
Finally, one of the most effective ways of distinguishing between massive planets and brown dwarfs is through a comparison of their internal structure properties and of the composition of their atmospheres (e.g., Chabrier et al. 2009; Burgasser 2009). Studies at this level are still in their infancy, particularly for what concerns the possibility of determining their actual nature based on their condensate cloud formation properties, non-equilibrium chemistry, and atmospheric dynamics (Burgasser 2009).
However, the class of transiting systems
is already providing relevant data. For example, Mordasini
et al. (2009)
have proposed that massive planets might contain a large amount of
heavy elements (about
for the individual case shown in
their Fig. 12). In the case of the transiting massive planet
HD 131664 (HAT-P-2b), with a mass of
(Bakos et al. 2007),
just below the threshold of
adopted here for inclusion in Table 3,
Baraffe et al. (2008)
and Leconte et al. (2009)
argue from the measured
radius (
, Bakos et al. 2007) for a
total amount of heavy elements of about
,
excluding a gaseous H/He object with solar composition. This
indicates that indeed
planets might be formed by the
core accretion mechanism, unless such a high mass is the result
of planetary collision, as speculated by Baraffe
et al. (2008). In the
case of the super-massive transiting planet HD 131664,
despite its rather uncertain radius (due to discrepancies in the
stellar radius estimates from photometry and spectroscopy), there
seems to be no need for a large content of heavy elements in the
core (Winn et al. 2008).
Similarly, the 22-
transiting object
CoRoT-3b fits the Baraffe
et al. (2008) models for solar composition,
with no need for large metal enrichment (Leconte et al. 2009).
Both
HAT-P-2b and CoRoT-3b have surface gravities similar to those of
young, very low-mass brown dwarfs such as AB Pic (see Fig. 2
of Burgasser 2009),
suggesting an overlap in the parameter
space of some physical properties (e.g., gas pressure,
temperature). Interestingly, as discussed by Deleuil et al. (2008),
all transiting massive planets orbit stars more massive than the
Sun, as predicted by the core accretion model of planet formation.
On the other hand, their actual existence on such short periods
and relatively eccentric orbits (except for CoRoT-3b) and the
fact that the metallicities of their parent stars are not skewed
towards super-solar values calls for the possibility of
differences in their origin.
In conclusion, the present-day evidence on the orbital and
structural properties of massive
planets and brown dwarfs as close companions to nearby solar-type stars
can be interpreted
as supporting a picture in which different mechanisms for the formation
of such objects
are at work. The above discussion also indicates how the lack of a
clean, statistically significant
sample of high-mass planets and brown dwarf companions to solar-type
stars with well-determined
mass estimates hampers the possibility of conclusively distinguishing
among the various competing
modes of formation of such objects. From an observational viewpoint,
improvements in determining the multiplicity properties of substellar
companions are very much needed, and will be obtained in the near
future through the combined contribution of a variety of
techniques. For example, some of the massive planets and brown dwarfs
objects in
Table 3
are within reach of next-generation direct-imaging instruments
such as SPHERE (Beuzit et al.
2008) and for many of them true masses will be measured with
high precision by ground-based and space-borne astrometric
observatories, such as VLTI/PRIMA
and Gaia (e.g., Launhardt
et al. 2008; Casertano
et al. 2008; Sozzetti
2009,
and references therein). The possibility that objects with similar
masses formed in a different way and
exhibit different chemical composition depending on the formation
mechanism open exciting perspectives
for such instruments. Therefore, they will represent key benchmarks for
the calibration of the masses of substellar
objects, for furthering our understanding of the dependence of the
brown dwarf desert on the properties
of the stellar hosts, and even for reaching a final agreement on the
actual definition of planets and
brown dwarfs themselves that is based not simply on semantics but
rather on robust physical grounds.
This research has been partially supported by INAF through PRIN 2009 ``Environmental effects in the formation and evolution of extrasolar planetary system''. A.S. gratefully acknowledges support from the Italian Space Agency (Contract ASI-Gaia I/037/08/0). We thank J.-L. Halbwachs for stimulating discussions and the referee for a timely and useful report that helped improve the presentation of the results. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, and of NASA’s Astrophysics Data System Bibliographic Services.
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Footnotes
- ...
dwarf
- We operationally adopt the commonly used definition of
brown dwarf
as a deuterium-burning substellar object with mass in the approximate
range 15-80
.
- ... 76 measurements
- Minniti et al. (2009) looked for, and failed to find, hints of higher dispersion in the Hipparcos measurements for HD 43848 with respect to those of stars of similar magnitude and distance.
- ... parameters
- We used both
and its transformed value
in the fitting process, a trick utilized by Pourbaix & Jorissen (2000) to prevent parallaxes from becoming negative, and converting back to
at the end of the minimization procedure. No significant differences in the final results were found.
- ...
found
- Two additional probable cases of a system with a brown dwarf and a planet in close orbits are those of HD 43848 (Bakos et al. 2009) and HD 43848 (Correia et al. 2005). In the first case, the planetary nature of the inner companion is confirmed by the occurrence of the transit. The true masses of the more massive companions are not available, but there are perspectives for deriving them thanks to the strong dynamical interactions in the case of HD 43848 and the transit timing variations in the case of HD 43848.
- ... companions
- The statistical analysis presented here does not take into account the eccentricity bias in Keplerian fits to Doppler data collected by radial-velocity planet search programs, which a) underestimates the abundance of low-amplitude, low-eccentricity planets, and b) makes low-amplitude, high-eccentricity planets hard to unveil (Shen & Turner 2008; O'Toole et al. 2009; Valenti et al. 2009).
- ...
same
- It also appears that the brown dwarfs with the highest actual mass estimates seem to be found more frequently as close companions to stars belonging to the thick disk population of the Milky Way (see Table 3), but this can only be regarded as a tentative speculation, given the very limited statistics, large mass uncertainties, and the heterogeneity of the datasets.
- ... objects
- However, see e.g. Boss (2000) and Bate et al. (2002) for alternative scenarios in which isolated planetary mass objects are the result of ejections through dynamical interactions in protoplanetary disks.
- ... therein)
- While the results are not conclusive due to the presence of systematics in the dataset, it is worth noting that the CoRot-3 system also exhibits a formally non-zero spin-orbit angle (Triaud et al. 2009); however, the large uncertainties reported make the detection of spin-orbit misalignment in the CoRoT-3 system only marginal.
All Tables
Table 1: Stellar characteristics of HD 131664 and HD 131664 and spectroscopic orbital elements for the two Doppler-detected companions.
Table 2:
Orbital fits to the Hipparcos IAD for HD 131664 and
HD 131664,
assuming knowledge of P, e,
T0, and
from the
spectroscopic orbit.
Table 3:
Close companions to solar-type stars with (projected) masses between 10
and 80
.
Table 4: Results of the K-S and R-S tests on different subsets of systems.
All Figures
![]() |
Figure 1: Periodograms of HD 131664 ( top) and HD 131664 ( bottom)assuming e and T0 from the known spectroscopic orbit. |
Open with DEXTER | |
In the text |
![]() |
Figure 2:
Iso- |
Open with DEXTER | |
In the text |
![]() |
Figure 3:
Distribution of the ratio |
Open with DEXTER | |
In the text |
![]() |
Figure 4:
Period vs. eccentricity ( top panel) and
eccentricity vs. companion mass
( bottom panel). In the lower panel plot, only
objects with periods longer than 20 days are shown.
Red filled circles: companions with true estimated masses in the range
10-80 |
Open with DEXTER | |
In the text |
![]() |
Figure 5: Orbital period vs. companion mass ( top), metallicity vs. companion mass ( center), stellar mass vs. companion mass ( bottom). Symbols as in the previous figure. |
Open with DEXTER | |
In the text |
![]() |
Figure 6:
Upper panel: cumulative distribution of the
eccentricity of objects with periods longer than 20 days
orbiting main-sequence stars with mass between 0.7 and
1.5 |
Open with DEXTER | |
In the text |
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