A new search for planet transits in NGC 6791
arXiv:0704.1668v1  [astro-ph]  12 Apr 2007
Astronomy & Astrophysics manuscript no. n6791 c© ESO 2021
August 31, 2021
A new search for planet transits in NGC 6791. ⋆
M. Montalto1, G. Piotto1, S. Desidera2, F. De Marchi1, H. Bruntt3,4, P.B. Stetson5
A. Arellano Ferro6, Y. Momany1,2 R.G. Gratton2, E. Poretti7,
A. Aparicio8, M. Barbieri2,9, R.U. Claudi2, F. Grundahl3, A. Rosenberg8.
1 Dipartimento di Astronomia, Università di Padova, Vicolo dell’Osservatorio 2, I-35122, Padova, Italy
2 INAF – Osservatorio Astronomico di Padova, Vicolo dell’ Osservatorio 5, I-35122, Padova, Italy
3 Department of Physics and Astronomy, University of Aarhus, Denmark
4 University of Sydney, School of Physics, 2006 NSW, Australia
5 Herzberg Institute of Astrophysics, Victoria, Canada
6 Instituto de Astronomı́a, Universidad Nacional Autónoma de México
7 INAF – Osservatorio Astronomico di Brera, Via E. Bianchi 46, 23807 Merate (LC), Italy
8 Instituto de Astrofisica de Canarias, 38200 La Laguna, Tenerife, Canary Islands, Spain
9 Dipartimento di Fisica, Università di Padova, Italy
ABSTRACT
Context. Searching for planets in open clusters allows us to study the effects of dynamical environment on planet formation and evolution.
Aims. Considering the strong dependence of planet frequency on stellar metallicity, we studied the metal rich old open cluster NGC 6791 and
searched for close-in planets using the transit technique.
Methods. A ten-night observational campaign was performed using the Canada-France-Hawaii Telescope (3.6m), the San Pedro Mártir tele-
scope (2.1m), and the Loiano telescope (1.5m). To increase the transit detection probability we also made use of the Bruntt et al. (2003)
eight-nights observational campaign. Adequate photometric precision for the detection of planetary transits was achieved.
Results. Should the frequency and properties of close-in planets in NGC 6791 be similar to those orbiting field stars of similar metallicity,
then detailed simulations foresee the presence of 2-3 transiting planets. Instead, we do not confirm the transit candidates proposed by Bruntt et
al. (2003). The probability that the null detection is simply due to chance coincidence is estimated to be 3%-10%, depending on the metallicity
assumed for the cluster.
Conclusions. Possible explanations of the null-detection of transits include: (i) a lower frequency of close-in planets in star clusters; (ii) a
smaller planetary radius for planets orbiting super metal rich stars; or (iii) limitations in the basic assumptions. More extensive photometry with
3–4m class telescopes is required to allow conclusive inferences about the frequency of planets in NGC 6791.
Key words. open cluster: NGC 6791 – planetary systems – Techniques: photometric
1. Introduction
During the last decade more than 200 extra-solar planets have
been discovered. However, our knowledge of the formation
and evolution of planetary systems remains largely incomplete.
One crucial consideration is the role played by environment
where planetary systems may form and evolve.
More than 10% of the extra-solar planets so far discov-
ered are orbiting stars that are members of multiple systems
Send offprint requests to: M. Montalto,
e-mail: marco.montalto@unipd.it
⋆ Based on observation obtained at the Canada-France-Hawaii
Telescope (CFHT) which is operated by the National Research
Council of Canada, the Institut National des Sciences de l’Univers
of the Centre National de la Recherche Scientifique of France, and the
Univesity of Hawaii and on observations obtained at San Pedro Mártir
2.1 m telescope (Mexico), and Loiano 1.5 m telescope (Italy).
(Desidera & Barbieri 2007). Most of these are binaries with
fairly large separations (a few hundred AU). However, in few
cases, the binary separation reaches about 10 AU (Hatzes et
al. 2003; Konacki 2005), indicating that planets can exist even
in the presence of fairly strong dynamical interactions.
Another very interesting dynamical environment is repre-
sented by star clusters, where the presence of nearby stars
or proto-stars may affect the processes of planet formation
and evolution in several ways. Indeed, close stellar encoun-
ters may disperse the proto-planetary disks during the fairly
short (about 10 Myr, e.g., Armitage et al. 2003) epoch of giant
planet formation or disrupt the planetary system after its forma-
tion (Bonnell et al. 2001; Davies & Sigurdsson 2001; Woolfson
2004; Fregeau et al. 2006). Another possible disruptive effect
is the strong UV flux from massive stars, which causes photo-
evaporation of dust grains and thus prevents planet formation
(Armitage 2000; Adams et al. 2004). These effects are expected
http://arxiv.org/abs/0704.1668v1
2 M. Montalto et al.: A new search for planet transits in NGC 6791.
to depend on star density, being much stronger for globular
clusters (typical current stellar density ∼ 103 stars pc−3) than
for the much sparser open clusters (≤ 102 stars pc−3).
The recent discovery of a planet in the tight triple system
HD188753 (Konacki 2005) adds further interest to the search
for planets in star clusters. In fact, the small separation between
the planet host HD188753A and the pair HD188753BC (about
6 AU at periastron) makes it very challenging to understand
how the planet may have been formed (Hatzes & Wüchterl
2005). Portegies, Zwart & McMillan et al. (2005) propose that
the planet formed in a wide triple within an open cluster and
that dynamical evolution successively modified the configura-
tion of the system. Without observational confirmation of the
presence of planets in star clusters, such a scenario is purely
speculative.
On the observational side, the search for planets in star
clusters is a quite challenging task. Only the closest open clus-
ters are within reach of high-precision radial velocity surveys
(the most successful planet search technique). However, the
activity-induced radial velocity jitter limits significantly the
detectability of planets in clusters as young as the Hyades
(Paulson et al. 2004). Hyades red giants have a smaller activity
level, and the first planet in an open cluster has been recently
announced by Sato et al. (2007), around ǫ Tau.
The search for photometric transits appears a more suitable
technique: indeed it is possible to monitor simultaneously a
large number of cluster stars. Moreover, the target stars may
be much fainter. However, the transit technique is mostly sen-
sitive to close-in planets (orbital periods ≤ 5 days).
Space and ground-based wide-field facilities were also used
to search for planets in the globular clusters 47 Tucanae and
ω Centauri. These studies (Gilliland et al. 2000; Weldrake et
al. 2005; Weldrake et al. 2006) reported not a single planet de-
tection. This seemed to indicate that planetary systems are at
least one order of magnitude less common in globular clusters
than in Solar vicinity. The lack of planets in 47 Tuc and ω Cen
may be due either to the low metallicity of the clusters (since
planet frequency around solar type stars appears to be a rather
strong function of the metallicity of the parent star: Fischer &
Valenti 2005; Santos et al. 2004), or to environmental effects
caused by the high stellar density (or both).
One planet has been identified in the globular cluster M4
(Sigurdsson et al. 2003), but this is a rather peculiar case, as
the planet is in a circumbinary orbit around a system including
a pulsar and it may have formed in a different way from the
planets orbiting solar type stars (Beer et al. 2004).
Open clusters are not as dense as globular clusters. The dy-
namical and photo-evaporation effects should therefore be less
extreme than in globular clusters. Furthermore, their metallic-
ity (typically solar) should, in principle, be accompanied by a
higher planet frequency.
In the past few years, some transit searches were specif-
ically dedicated to open clusters: see e.g. von Braun et
al. (2005), Bramich et al. (2005), Street et al. (2003), Burke
et al. (2006), Aigrain et al. (2006) and references therein.
However, in a typical open cluster of Solar metallicity with
∼ 1000 cluster members, less than one star is expected to show
a planetary transit. This depends on the assumption that the
planet frequency in open clusters is similar to that seen for
nearby field stars 1. Considering the unavoidable transits de-
tection loss due to the observing window and photometric er-
rors, it turns out that the probability of success of such efforts
is fairly low unless several clusters are monitored 2.
On the other hand, the planet frequency might be higher for
open clusters with super-solar metallicities. Indeed, for [Fe/H]
between +0.2 and +0.4 the planet frequency around field stars
is 2-6 times larger than at solar metallicity. However, only a
few clusters have been reported to have metallicities above
[Fe/H]= +0.2. The most famous is NGC 6791, a quite massive
cluster that is at least 8 Gyr old (Stetson et al. 2003; King et
al. 2005, and Carraro et al. 2006). As estimated by different au-
thors, its metallicity is likely above [Fe/H]=+0.2 (Taylor 2001)
and possibly as high as [Fe/H]=+0.4 (Peterson et al. 1998). The
most recent high dispersion spectroscopy studies confirmed the
very high metallicity of the cluster ([Fe/H]=+0.39, Carraro et
al. 2006; [Fe/H]=+0.47, Gratton et al. 2006). Its old age im-
plies the absence of significant photometric variability induced
by stellar activity. Furthermore, NGC 6791 is a fairly rich clus-
ter. All these facts make it an almost ideal target.
NGC 6791 has been the target of two photometric cam-
paigns aimed at detecting planets transits. Mochejska et
al. (2002, 2005, hereafter M05) observed the cluster in the R
band with the 1.2 m Fred Lawrence Whipple Telescope dur-
ing 84 nights, over three observing seasons (2001-2003). They
found no planet candidates, while the expected number of de-
tections considering their photometric precision and observing
window was ∼ 1.3. Bruntt et al. (2003, hereafter B03) observed
the cluster for 8 nights using ALFOSC at NOT. They found 10
transit candidates, most of which (7) being likely due to instru-
mental effects.
Nearly continuous, multi-site monitoring lasting several
days could strongly enhance the transit detectability. This idea
inspired our campaigns for multi-site transit planet searches in
the super metal rich open clusters NGC 6791 and NGC 6253.
This paper presents the results of the observations of the cen-
tral field of NGC 6791, observed at CFHT, San Pedro Mártir
(SPM), and Loiano. We also made use of the B03 data-set [ob-
tained at the Nordic Optical Telescope (NOT) in 2001] and re-
duce it as done for our three data-sets. The analysis for the ex-
ternal fields, containing mostly field stars, and of the NGC 6253
campaign, will be presented elsewhere.
The outline of the paper is the following: Sect. 2 presents
the instrumental setup and the observations. We then describe
the reduction procedure in Sect. 3, and the resulting photomet-
ric precision for the four different sites is in Sect. 4. The selec-
tion of cluster members is discussed in Sect. 5. Then, in Sect. 6,
we describe the adopted transit detection algorithm. In Sect. 7
we present the simulations performed to establish the transit
detection efficiency (TDE) and the false alarm rate (FAR) of
1 0.75% of stars with planets with period less than 7 days (Butler et
al. 2000), and a 10% geometric probability to observe a transit.
2 A planet candidate was recently reported by Mochejska et
al. (2006) in NGC 2158, but the radius of the transiting object is larger
than any planet known up to now (∼ 1.7 RJ). The companion is then
most likely a very low mass star.
M. Montalto et al.: A new search for planet transits in NGC 6791. 3
the algorithm for our data-sets. Sect. 8 illustrates the different
approaches that we followed in the analysis of the data. Sect. 9
gives details about the transit candidates.
In Sect. 10, we estimate the expected planet frequency
around main sequence stars of the cluster, and the expected
number of detectable transiting planets in our data-sets. In
Sect. 11, we compare the results of the observations with those
of the simulations, and discussed their significance. In Sect. 12
we discuss the different implications of our results, and, in
Sect. 13, we make a comparison with other transit searches to-
ward NGC 6791. In Sect. 14 we critically analyze all the ob-
servations dedicated to the search for planets in NGC 6791 so
far, and propose future observations of the cluster, and finally,
in Sect. 15, we summarize our work.
2. Instrumental setup and observations
The observations were acquired during a ten-consecutive-day
observing campaign, from July 4 to July 13, 2002. Ideally, one
should monitor the cluster nearly continuously. For this reason,
we used three telescopes, one in Hawaii, one in Mexico, and
the third one in Italy. In Table 1 we show a brief summary of
our observations.
In Hawaii, we used the CFHT with the CFH12K detector 3,
a mosaic of 12 CCDs of 2048×4096 pixels, for a total field of
view of 42×28 arcmin, and a pixel scale of 0.206 arcsec/pixel.
We acquired 278 images of the cluster in the V filter. The see-
ing conditions ranged between 0.′′6 to 1.′′9, with a median of
1.′′0. Exposure times were between 200 and 900 sec, with a
median value of 600 sec. The observers were H. Bruntt and
P.B. Stetson.
In San Pedro Mártir, we used the 2.1m telescope, equipped
with the Thomson 2k detector. However the data section of the
CCD corresponded to a 1k × 1k pixel array. The pixel scale was
0.35 arcsec/pixel, and therefore the field of view (∼ 6 arcmin2)
contained just the center of the cluster, and was smaller than
the field covered with the other detectors. We made use of 189
images taken between July 6, 2002 and July 13, 2002. During
the first two nights the images were acquired using the focal re-
ducer, which increased crowding and reduced our photometric
accuracy. All the images were taken in the V filter with ex-
posure times of 480 − 1200 sec (median 660 sec), and seeing
between 1.′′1 and 2.′′1 (median 1.′′4). Observations were taken
by A. Arellano Ferro.
In Italy, we used the Loiano 1.5m telescope4 equipped with
BFOSC + the EEV 1300×1348B detector. The pixel scale was
0.52 arcsec/pixel, for a total field coverage of 11.5 arcmin2. We
observed the target during four nights (2002 July 6−9). We ac-
quired and reduced 63 images of the cluster in the V and Gunn
i filters (61 in V , 2 in i). The seeing values were between 1.′′1
3 www.cfht.hawaii.edu/Instruments/Imaging/CFH12K/
4 The observations were originally planned at the Asiago
Observatory using the 1.82 m telescope + AFOSC. However, a ma-
jor failure of instrument electronics made it impossible to perform
these observations. We obtained four nights of observations at the
Loiano Observatory, thanks to the courtesy of the scheduled observer
M. Bellazzini and of the Director of Bologna Observatory F. Fusi
Pecci.
and 4.′′3 arcsec, with a median value of 1.′′4 arcsec. Exposure
times ranged between 120 and 1500 sec (median 1080 sec).
The observer was S. Desidera.
We also make use of the images taken by B03 in 2001.
We obtained these images from the Nordic Optical Telescope
(NOT) archive. As explained in BO3, these data covered
eight nights between July 9 and 17, 2001. The detector was
ALFOSC5 a 2k×2k thinned Loral CCD with a pixel scale of
0.188 arcsec/pixel yielding a total field of view of 6.5 arcmin2.
Images were taken in the I and V filters with a median seeing
of 1 arcsec. We used only the images of the central part of the
cluster (which were the majority) excluding those in the exter-
nal regions. In total we reduced 227 images in the V filter and
389 in the I filter.
It should be noted that ALFOSC and BFOSC are focal re-
ducers, hence light concentration introduced a variable back-
ground. These effects can be important when summed with flat
fielding errors. In order to reduce these un-desired effects, the
images were acquired while trying to maintain the stars in the
same positions on the CCDs. Nevertheless, the precision of
this pointing procedure was different for the four telescopes:
the median values of the telescope shifts are of 0.′′5, 0.′′5, 3.′′4
and 2.′′1, respectively for Hawaii, NOT, SPM, and Loiano. This
means that while for the CFHT and the NOT the median shift
was at a sub-seeing level (half of the median seeing), for the
other two telescopes it was respectively of the order of 2.4
and 1.5 times the median seeing. Hence, it is possible that flat-
fielding errors and possible background variation have affected
the NOT, SPM, and Loiano photometry, but the effects on the
Hawaii photometry are expected to be smaller.
Bad weather conditions and the limited time allocated at
Loiano Observatory caused incomplete coverage of the sched-
uled time interval. Moreover we did not use the images coming
from the last night (eighth night) of observation in La Palma
with the NOT because of bad weather conditions. Our observ-
ing window, defined as the interval of time during which obser-
vations were carried out, is shown in Tab. 2 for Hawaii, SPM
and Loiano observations and in Tab. 3 for La Palma observa-
tions.
3. The reduction process
3.1. The pre-reduction procedure
For the San Pedro, Loiano and La Palma images, the pre-
reduction was done in a standard way, using IRAF routines6.
The images from the Hawaii came already reduced via the
ELIXIR software7.
5 ALFOSC is owned by the Instituto de Astrofisica de Andalucia
(IAA) and operated at the Nordic Optical Telescope under agreement
between IAA and the NBIfAFG of the Astronomical Observatory of
Copenhagen.
6 IRAF is distributed by the National Optical Astronomy
Observatory, which is operated by the Association of Universities for
Research in Astronomy, Inc., under cooperative agreement with the
7 http://www.cfht.hawaii.edu/Instruments/Elixir
4 M. Montalto et al.: A new search for planet transits in NGC 6791.
Table 1. Summary of the observations taken during 4-13 July, 2002 in Hawaii, San Pedro Màrtir, Loiano and from 9-17 July, 2001 in La Palma
(by B03).
Hawaii San Pedro Mártir Loiano NOT
N. of Images 278 189 63 227(V), 389(I)
Nights 8 8 4 8
Scale (arcsec/pix) 0.21 0.35 0.52 0.188
FOV (arcmin) 42 x 28 6 x 6 11.5 x 11.5 6.5 x 6.5
Table 2. The observing window relative to the July 2002 observations.
The number of observing hours is given for each night. The last line
shows the total number of observing hours for each site.
Night Hawaii SPM Loiano
1st 3.58 − −
2nd 3.88 − −
3rd 2.68 6.31 3.58
4th 7.56 6.61 5.21
5th 5.23 6.58 6.08
6th 8.30 6.86 5.45
7th − 3.20 −
8th − 7.03 −
9th 8.34 7.27 −
10th 8.37 4.15 −
Total 47.94 48.01 20.32
Table 3. The observing window relative to the July 2001 observations.
Night La Palma
1st 5.45
2nd 7.06
3rd 8.04
4th 7.61
5th 7.57
6th 7.82
7th 7.72
8th 2.41
Total 53.68
3.2. Reduction strategies
The data-sets described in Sec. 2 were reduced with three dif-
ferent techniques: aperture photometry, PSF fitting photometry
and image subtraction. An accurate description of these tech-
niques is given in the next Sections. Our goal was to compare
their performances to see if one of them performed better than
the others. For what concerned aperture and PSF fitting pho-
tometry we used the DAOPHOT (Stetson 1987) package. In
particular the aperture photometry routine was slightly different
from that one commonly used in DAOPHOT and was provided
by P .B. Stetson. It performed the photometry after subtracting
all the neighbors stars of each target star. Image subtraction was
performed by means of the ISIS2.2 package (Alard & Lupton,
1998) except for what concerned the final photometry on the
subtracted images which was performed with the DAOPHOT
aperture routine for the reasons described in paragraph 3.4.
3.3. DAOPHOT/ALLFRAME reduction: aperture and
PSF fitting photometry
The DAOPHOT/ALLFRAME reduction package has been ex-
tensively used by the astronomical community and is a very
well tested reduction technique. The idea behind this stellar
photometry package consists in modelling the PSF of each im-
age following a semi-analytical approach, and in fitting the
derived model to all the stars in the image by means of least
square method. After some tests, we chose to calculate a vari-
able PSF across the field (quadratic variability). We selected the
first 200 brightest, unsaturated stars in each frame, and calcu-
lated a first approximate PSF from them. We then rejected the
stars to which DAOPHOT assigned anomalously high fitting χ
values. After having cleaned the PSF star list, we re-calculated
the PSF. This procedure was iterated three times in order to
obtain the final PSF for each image.
We then used DAOMATCH and DAOMASTER (Stetson
1992) in order to calculate the coordinate transformations
among the frames, and with MONTAGE2 we created a refer-
ence image by adding up the 50 best seeing images. We used
this high S/N image to create a master list of stars, and applied
ALLFRAME (Stetson 1994) to refine the estimated star posi-
tions and magnitudes in all the frames. We applied a first selec-
tion on the photometric quality of our stars by rejecting all stars
with SHARP and CHI parameters (Stetson 1987) deviating by
more than 1.5 times the RMS of the distribution of these pa-
rameters from their mean values, both calculated in bins of 0.1
magnitudes. About 25% of the stars were eliminated by this se-
lection. This was the PSF fitting photometry we used in further
analysis. The aperture photometry with neighbor subtraction
was obtained with a new version of the PHOT routine (devel-
oped by P. B. Stetson). We used as centroids the same values
used for ALLFRAME. The adopted apertures were equal to the
FWHM of the specific image, and after some tests we set the
annular region for the calculation of the sky level at a distance
< r < 2.5
(both for the ALLFRAME and for the aperture
photometry).
Finally, we used again DAOMASTER for the cross-
correlation of the final star lists, and to prepare the light curves.
3.4. Image Subtraction photometry
In the last years the Image Subtraction technique has been
largely used in photometric reductions. This method firstly im-
plemented in the software ISIS did not assume any specific
functional shape for the PSF of each image. Instead it mod-
eled the kernel that convolved the PSF of the reference image
M. Montalto et al.: A new search for planet transits in NGC 6791. 5
to match the PSF of a target image. The reference image is
convolved by the computed kernel and then subtracted from
the image. The photometry is then done on the resulting differ-
ence image. Isolated stars were not required in order to model
the kernel. This technique had rapidly gained an appreciable
consideration across the astronomical community. Since its ad-
vent, it appeared particularly well suited for the search for vari-
able stars, and it has proved to be very effective in extremely
crowded fields like in the case of globular clusters (e.g. Olech
et al. 1999, Kaluzny et al. 2001, Clementini et al. 2004, Corwin
et al. 2006). An extensive use of this approach has been applied
also in long photometric surveys devoted to the search for ex-
trasolar planet transits (eg. Mochejska et al., 2002, 2004).
We used the standard reduction routines in the ISIS2.2
package. At first, the images were interpolated on the reference
system of the best seeing image. Then we created a reference
image from the 50 images with best seeing. We performed dif-
ferent tests in order to set the best parameters for the subtrac-
tion, and we checked the images to find which combination
with lowest residuals. In the end, we decided to sub-divide the
images in four sub-regions, and to apply a kernel and sky back-
ground variable at the second order.
Using ALLSTAR, we build up a master list of stars from
the reference image. As in Bruntt et al. (2003), we were not
able to obtain a reliable photometry using the standard pho-
tometry routine of ISIS. We used the DAOPHOT aperture pho-
tometry routine and slightly modified it in order to accept the
subtracted images. Aperture, and sky annular region were set
as for the aperture and PSF photometry. Then the magnitude of
the stars in the subtracted images was obtained by means of the
following formula:
mi = mref − 2.5 log
(Nref − Ni
where mi was the magnitude of a generic star in a generic i
subtracted image, mref was the magnitude of the correspondent
star in the reference image, Nref were the counts obtained in the
reference image and Ni is the i
th subtracted image.
3.5. Zero point correction
For what concerns psf fitting photometry and aperture photom-
etry, we corrected the light curves taking into account the zero
points magnitude (the mean difference in stellar magnitude) be-
tween a generic target image, and the best seeing image. This
was done by means of DAOMASTER and can be considered as
a first, crude correction of the light curves. Image subtraction
was able to handle these first order corrections automatically,
and thus the resulting light curves were already free of large
zero points offsets.
Nevertheless, important residual correlations persisted in
the light curves, and it was necessary to apply specific, and
more refined post-reduction corrections, as explained in the
next Section.
3.6. The post reduction procedure
In general, and for long time series photometric studies, it has
been commonly recognized that regardless of the adopted re-
duction technique, important correlations between the derived
magnitudes and various parameters like seeing, airmass, expo-
sure time, etc. persist in the final photometric sequences. As put
into evidence by Pont et al. (2006), the presence of correlated
noise in real light curves, (red noise), can significantly reduce
the photometric precision that can be obtained, and hence re-
duce transit detectability. For example ground-based photomet-
ric measurements are affected by color-dependent atmospheric
extinction. This is a problem since, in general, photometric sur-
veys employ only one filter and no explicit colour information
is available. To take into account these effects, we used the
method developed by Tamuz et al. (2005). The software was
provided by the same authors, and an accurate description of it
can be found in the referred paper.
One of the critical points in this algorithm regarded the
choice of systematic effects to be removed from the data. For
each systematic effect, the algorithm performed an iteration af-
ter which it removed the systematic passing to the next.
To verify the efficiency of this procedure (and establish the
number of systematic effects to be removed) we performed the
following simulations. We started from a set of 4000 artifi-
cial stars with constant magnitudes. These artificial light curves
were created with a realistic modeling of the noise (which ac-
counts for the intrinsic noise of the sources, of the sky back-
ground, and of the detector electronics) but also for the pho-
tometric reduction algorithm itself, as described in Sec. 7.1.
Thus, they are fully representative of the systematics present
in our data-set. At this point we also add 10 light curves in-
cluding transits that were randomly distributed inside the ob-
serving window. These spanned a range of (i) depths from a
few milli-magnitudes to around 5 percents, (ii) durations and
(iii) periods respectively of a few hours to days accordingly to
our assumptionts on the distributions of these parameters for
planetary transits, as accounted in Sec. 7.3.
In a second step, we applied the Tamuz et al. (2005) algo-
rithm to the entire light curves data-set. For a deeper under-
standing of the total noise effects and the transit detection ef-
ficiency, we progressively increased the number of systematic
effects to be removed (eigenvectors in the analysis described
by Tamuz 2005). Typically, we started with 5 eigenvectors and
increased it to 30.
Repeated experiments showed no significant RMS im-
provement after the ten iterations. The final RMS was 15%-
20% lower than the original RMS . Thus, the number of eigen-
vectors was set to 10. In no case the added transits were re-
moved from the light curves and the transit depths remained
unaltered.
We conclude that this procedure, while reducing the RMS
and providing a very effective correction for systematic effects,
did not influence the uncorrelated magnitude variations associ-
ated with transiting planets.
6 M. Montalto et al.: A new search for planet transits in NGC 6791.
4. Definition of the photometric precision
To compare the performances of the different photometric al-
gorithms we calculated the Root Mean Square, (RMS ), of the
photometric measurements obtained for each star, which is de-
fined as:
RMS =
Ii−<I>
N − 1
Where Ii is the brightness measured in the generic i
th image
for a particular target star, < I > is the mean star brightness in
the entire data-set, and N is the number of images in which the
star has been measured. For constant stars, the relative variation
of brightness is mainly due to the photometric measurement
noise. Thus, the RMS (as defined above) is equal to the mean
N/S of the source. In order to allow the detection of transiting
jovian-planets eclipses, whose relative brightness variations are
of the order of 1%, the RMS of the source must be lower than
this level.
4.1. PSF photometry against aperture photometry
The first comparison we performed was that between aper-
ture photometry (having neighboring stars subtracted) and
PSF fitting photometry. We started with aperture photometry.
Figure 1, shows a comparison of the RMS dispersion of the
light curves obtained with the new PHOT software with re-
spect to the RMS of the PSF fitting photometry for the different
sites. We also show the theoretical noise which was estimated
considering the contribute to the noise coming from the pho-
ton noise of the source and of the sky background as well as
the noise coming from the instrumental noise (see Kjeldsen &
Frandsen 1992, formula 31). In Fig. 1- 3, we also separated
the contribution of the source’s Poisson noise from that of the
sky (short dashed line) and of the detector noise (long dashed
line). The total theoretical noise is represented as a solid line.
It is clear that the data-sets from the different telescopes gave
different results. In the case of the CFHT and SPM data-sets,
aperture photometry does not reach the same level of preci-
sion as PSF fitting photometry (for both bright and the faint
sources). Moreover, it appears that the RMS of aperture pho-
tometry reaches a constant value below V ∼ 18.5 for CFHT
data and around V ∼ 17.5 for SPM data, while for PSF fitting
photometry the RMS continues to decrease. For Loiano data,
and with respect to PSF photometry, aperture photometry pro-
vides a smaller RMS in the light curve, in particular for bright
sources. The NOT observations on the other hand show that
the two techniques are almost equivalent. Leaving aside these
differences, it is clear that the CFHT provide the best photo-
metric precision, and this is due to the larger telescope diam-
eter, the smaller telescope pixel scale (0.206 arcsec/pixel, see
Table 1), and the better detector performances at the CFHT. For
this data-set, the photometric error remains smaller than 0.01
mag, from the turn-off of the cluster (∼ 17.5) to around mag-
nitude V = 21, allowing the search for transiting planets over a
magnitude range of about 3.5 magnitudes, (in fact, it is possible
to go one magnitude deeper because of the expected increase
in the transit depth towards the fainter cluster stars, see Sec. 5
for more details). Loiano photometry barely reaches 0.01 mag
photometric precision even for the brightest stars, a photomet-
ric quality too poor for the purposes of our investigation. The
search for planetary transits is limited to almost 2 magnitudes
below the turn-off for SPM data (in particular with the PSF fit-
ting technique) and to 1.5 magnitude below the turn-off for the
NOT data. In any case, the photometric precision for the SPM
and NOT data-sets reaches the 0.004 mag level for the brightest
stars, while, for the CFHT, it reaches the 0.002 mag level.
It is clear that both the PSF fitting photometry and the aper-
ture photometry tend to have larger errors with respect to the
expected error level. This effect is much clearer for Loiano,
SPM and NOT rather than for Hawaii photometry. As explained
by Kjeldsen & Frandsen (1992), and more recently by Hartman
et al. (2005), the PSF fitting approach in general results in
poorer photometry for the brightest sources with respect to the
aperture photometry. But, for our data-sets, this was true only
for the case of Loiano photometry, as demonstrated above. The
aperture photometry routine in DAOPHOT returns for each
star, along with other information, the modal sky value asso-
ciated with that star, and the rms dispersion (σsky) of the sky
values inside the sky annular region. So, we chose to calcu-
late the error associated with the random noise inside the star’s
aperture with the formula:
σAperture =
σ2sky Area (3)
where Area is the area (in pixels2) of the region inside which
we measure the star’s brightness. This error automatically takes
into account the sky Poissonian noise, instrumental effects like
the Read Out Noise, (RON), or detector non-linearities, and
possible contributions of neighbor stars. To calculate this error,
we chose a representative mean-seeing image, and subdivide
the magnitude range in the interval 17.5 < V < 22.0 into
nine bins of 0.5 mag. Inside each of these bins, we took the
minimum value of the stars’ sky variance as representative of
the sky variance of the best stars in that magnitude bin. We
over-plot this contribution in Fig. 4 which is relative to the San
Pedro photometry. This error completely accounts for the ob-
served photometric precision. So, the variance inside the star’s
aperture is much larger than what is expected from simple pho-
ton noise calculations. This can be the effect of neighbor stars
or of instrumental problems. For CFHT photometry, as we have
good seeing conditions and an optimal telescope scale, crowd-
ing plays a less important role. Concerning the other sites, we
noted that for Loiano the crowding is larger than for SPM and
NOT, and this could explain the lower photometric precision of
Loiano observations, along with the smaller telescope diameter.
For NOT photometry, instead, the crowding should be larger
than for San Pedro (since the scale of the telescope is larger)
while the median seeing conditions are comparable for the two
data-sets, as shown in Sect 2. Therefore this effect should be
more evident for NOT rather than for SPM, but this is not the
case, at least for what concerns aperture photometry. For PSF
photometry, as it is seen in Fig. 2, the NOT photometric preci-
sion appears more scattered than the SPM photometry.
M. Montalto et al.: A new search for planet transits in NGC 6791. 7
Fig. 1. Comparison of the photometric precision for aperture photometry with neighbor subtraction (Ap) and for PSF fitting photometry (PSF)
as a function of the apparent visual magnitude for CFHT, SPM, Loiano and NOT images. The short dashed line indicates the N/S considering
only the star photon noise, the long dashed line is the N/S due to the sky photon noise and the detector noise. The continuous line is the total
We are forced to conclude that poor flat fielding, optical
distortions, non-linearity of the detectors and/or presence of
saturated pixels in the brightest stars must have played a sig-
nificant role in setting the aperture and PSF fitting photometric
precisions.
4.2. PSF photometry against image subtraction
photometry
Applying the image subtraction technique we were able to
improve the photometric precision with respect to that ob-
tained by means of the aperture photometry and the PSF fitting
techniques. This appears evident in Fig. 2, in which the im-
age subtraction technique is compared to the PSF fitting tech-
nique. Again, the best overall photometry was obtained for the
CFHT , for the reasons explained in the previous subsection.
For the image subtraction reduction, the photometric precision
overcame the 0.001 mag level for the brightest stars in the
CFHT data-set, and for the other sites it was around 0.002 mag
(for the NOT ) or better (for S PM and Loiano). This clearly al-
lowed the search for planets in all these different data-sets. In
this case, it was possible to include also the Loiano observa-
tions (up to 2 magnitudes below the turn-off), and, for the other
sites, to extend by about 0.5-1 mag, the range of magnitudes
over which the search for transits was possible, (see previous
Section).
The reason for which image subtraction gave better results
could be that it is more suitable for crowded regions (as the
center of the cluster), because it doesn’t need isolated stars in
order to calculte the convolution kernel while the subtraction of
stars by means of PSF fitting can give rise to higher residuals,
8 M. Montalto et al.: A new search for planet transits in NGC 6791.
Fig. 2. Comparison of the photometric precision for image subtraction (ISIS) and for psf fitting photometry (PSF) as function of the apparent
visual magnitude for CFHT, SPM, Loiano, and NOT images.
because it’s much more difficult to obtain a reliable PSF from
crowded stars.
4.3. The best photometric precision
Given the results of the previous comparisons, we decided to
adopt the photometric data set obtained with the image sub-
traction technique. Figure 3, shows the photometric precision
that we obtained for the four different sites. The photometric
precision is very close to the theoretical noise for all the data-
sets. The NOT data-set has a lower photometric precision with
respect to SPM and even to Loiano, in particular for the bright-
est stars. We observed that the mean S/N for the NOT images
is lower than for the other sites because of the larger number of
images taken (and consequently of their lower exposure times
and S/N), see Tab. 1.
5. Selection of cluster members
To detect planetary transits in NGC 6791 we selected the proba-
ble main sequence cluster members as follows. Calibrated mag-
nitudes and colors were obtained by cross-correlating our pho-
tometry with the photometry by Stetson et al. (2003), based on
the same NOT data-set used in the present paper. Then, as done
in M05, we considered 24 bins of 0.2 magnitudes in the interval
17.3 < V < 22.1. For each bin, we calculated a robust mean
of all (B-V) star colors, discarding outliers with colors differing
by more than ∼ 0.06 mag from the mean. Our selected main
sequence members are shown in Fig. 5. Overall, we selected
3311 main-sequence candidates in NGC 6791. These are the
stars present in at least one of the four data-sets (see Sec. 8),
and represent the candidates for our planetary transits search.
Note that our selection criteria excludes stars in the bi-
nary sequence of the cluster. These are blended objects, for
which any transit signature should be diluted by the light
of the unresolved companion(s) and then likely undetectable.
M. Montalto et al.: A new search for planet transits in NGC 6791. 9
Fig. 3. The expected RMS noise for the observations taken at the different sites as a function of the visual apparent magnitude, is compared
with the RMS of the observed light curves obtained with the image subtraction technique.
Furthermore, a narrow selection range helps in reducing the
field-star contamination.
6. Description of the transit detection technique
6.1. The box fitting technique
To detect transits in our light curves we adopted the BLS algo-
rithm by Kovács et al. (2002). This technique is based on the
fitting of a box shaped transit model to the data. It assumes that
the value of the magnitude outside the transit region is constant.
It is applied to the phase folded light curve of each star span-
ning a range of possible orbital periods for the transiting object,
(see Table 4). Chi-squared minimization is used to obtain the
best model solution. The quantity to be maximized in order to
get the best solution is:
)2[ 1
Nin Nout
where mn = Mn − < M >. Mn is the n-th measurement of the
stellar magnitude in the light curve, < M > is the mean mag-
nitude of the star and thus mn is the n-th residual of the stellar
magnitude. The sum at the numerator includes all photometric
measurements that fall inside the transit region. Finally Nin and
Nout are respectively the number of photometric measurements
inside and outside the transit region.
The algorithm, at first, folds the light curve assuming a par-
ticular period. Then, it sub-divides the folded light curve in nb
bins and starting from each one of these bins calculates the T
index shown above spanning a range of transit lengths between
qmi and qma fraction of the assumed period. Then, it provides
the period, the depth of the brightness variation, δ, the transit
length, and the initial and final bins in the folded light curve
at which the maximum value of the index T occurs. We used a
routine called ’eebls’ available on the web8. We applied also the
so called directional correction (Tingley 2003a, 2003b) which
8 http://www.konkoly.hu/staff/kovacs/index.html
10 M. Montalto et al.: A new search for planet transits in NGC 6791.
Fig. 4. RMS noise for the San Pedro Mártir observations with the aper-
ture error (triangles) as estimated by Equation 3.
Fig. 5. The NGC 6791 CMD highlighting the selection region of the
main sequence stars (blue circles).
consists in taking into account the sign of the numerator in the
above formula in order to retain only the brightness variations
which imply a positive increment in apparent magnitude.
6.2. Algorithm parameters
The parameters to be set before running the BLS algorithm
are the following: 1) nf, number of frequency points for which
the spectrum is computed; 2) fmin, minimum frequency; 3) df,
frequency step; 4) nb, number of bins in the folded time se-
ries at any test frequency; 5) qmi, minimum fractional transit
length to be tested; 6) qma, maximum fractional transit length
to be tested; qmi and qma are given as the product of the tran-
Table 4. Adopted parameters for the BLS algorithm: nf is the number
of frequency steps adopted, fmin is the minimum frequency consid-
ered, df is the increasing frequency step, nb is the number of bins in
the folded time series at any test frequency, qmi and qma are the mini-
mum and maximum fractional transit length to be tested, as explained
in the text.
nf fmin(days−1) df(days−1) nb qmi qma
3000 0.1 0.0005 1000 0.01 0.1
sit length to the test frequency. Table 4 displays our adopted
parameters.
6.3. Algorithm transit detection criteria
To characterize the statistical significance of a transit-like
event detected by the BLS algorithm we followed the meth-
ods by Kovács & Bakos (2005): deriving the Dip Significance
Parameter (hereafter DSP) and the significance of the main pe-
riod signal in the Out of Transit Variation (hereafter OOTV,
given by the folded time series with the exclusion of the tran-
sit).
The Dip Significance Parameter is defined as
DSP = δ(σ2/Ntr + A
OOTV)
2 (5)
where δ is the depth of the transit given by the BLS at the point
at which the index T is maximum,σ is the standard deviation of
the Ntr in-transit data points, AOOTV is the peak amplitude in the
Fourier spectrum of the Out of Transit Variation. The threshold
for the DSP set by Kovacs & Bakos (2005) is 6.0 and it was set
on artificial constant light curves with gaussian noise. In real
light curves the noise is not gaussian, as explained in Sec. 3.6,
and, in general, the value of the DSP threshold should be set
case by case. In Sec. 8, we presented the adopted thresholds,
based on our simulations on artificial light curves, described in
Sec. 7.
The significance of the main periodic signal in the OOTV
is defined as:
SNROOTV = σ
A (AOOTV− < A >) (6)
where < A > and σA are the average and the standard deviation
of the Fourier spectrum. This parameter accounts for the Out
Of Transit Variation, and we impose it to be lower than 7.0, as
in Kovacs & Bakos (2005).
For our search we imposed a maximum transit duration of
six hours; we also required that at least ten data points must be
included in the transit region.
7. Simulations
The Transit Detection Efficiency (TDE) of the adopted algo-
rithm and its False Alarm Rate (FAR) were determined by
means of detailed simulations. The TDE is a measure of the
probability that an algorithm correctly identifies a transit in a
light curve. The FAR is a measure of the probability that an
M. Montalto et al.: A new search for planet transits in NGC 6791. 11
algorithm identifies a feature in a light curve that does not rep-
resent a transit, but rather a spurious photometric effect.
In the following discussion, we address the details of the
simulations we performed, considering the case of the CFHT
observations of NGC 6791. Because the CFHT data provided
the best of our photometric sequences, the results on the algo-
rithm performance is shown below, and should be considered
as an upper limit for the other cases.
7.1. Simulations with constant light curves
Artificial stars with constant magnitude were added to each im-
age, according to an equally-spaced grid of 2*PSFRADIUS+1,
(where the PSFRADIUS was the region over which the Point
Spread Function of the stars was calculated, and was around 15
pixels for the CFHT images), as described in Piotto & Zoccali
(1999). We took into account the photometric zero-point dif-
ferences among the images, and the coordinate transformations
from one image to another. 7722 stars were added on the CFHT
images. In order to assure the homogeneity of these simula-
tions, the artificial stars were added exactly in the same posi-
tions, (relative to the real stars in the field), for the other sites.
Because of the different field of views of the detectors, (see
Tab. 1), the number of resulting added stars was 3660 for the
NOT, 5544 for Loiano, and 3938 for SPM. The entire set of
images was then reduced again with the procedure described
in Sec.3. This way we got a set of constant light curves which
is completely representative of many of the spurious artifacts
that could have been introduced by the photometry procedure.
This is certainly a more realistic test than simply considering
Poisson noise on the light curves, as it is usually done. We then
applied the algorithm, with the parameters described in Sec.6,
to the constant light curves. The result is shown in Figure 6,
where the DSP parameter is plotted against the mean magni-
tude of the light curve. For the CFHT data, fixing the DSP
threshold at 4.3 yielded a FAR of 0.1%. This was the FAR
we adopted also when considering the other sites, which corre-
sponded to different levels of the DSP parameter, as explained
in Sec. 8.
Repeating the whole procedure 4 times and slightly shift-
ing the positions of the artificial stars, allowed us to better es-
timate the FAR and its error, FAR=(0.10 ± 0.04)%. Therefore,
running the transit search procedure on the 3311 selected main
sequence stars, we expect (3.3 ± 1.3) false candidates.
7.2. Masking bad regions and temporal intervals
We verified that, when stars were located near detector defects,
like bad columns, saturate stars, etc., or, in correspondence of
some instants of a particular night, (associated with sudden cli-
matic variations, or telescope shifts), it was possible to have an
over-production of spurious transit candidates. To avoid these
effects, we chose to mask those regions of the detectors and
the epochs which caused sudden changes in the photometric
quality. This was done also for the simulations with the con-
stant added stars, that were not inserted in detector defected
regions, and in the excluded images that generating bad pho-
Fig. 6. False Alarm Probability (FAR) in %, against the DSP parame-
ter given by the algorithm. The points indicate the results of our sim-
ulations on constant light curves, the solid line is our assumed best
tometry. In particular, we observed these spurious effects for
the NOT and SPM images. We further observed, when dis-
cussing the candidates coming from the analysis of the whole
data-set (as described in Sec.10.3) that the photometric varia-
tions were concentrated on the first night of the NOT. This fact,
which appeared from the simulations with the constant stars
too, meant that this night was probably subject to bad weather
conditions. had not we applied the Because we didn’t recog-
nize it at the beginning, we retained that night, as long as those
candidates, which were all recognized of spurious nature. Had
not we applied any masking the number of false alarms would
have almost quadruplicated. This fact probably can explain at
least some of the candidates found by B03 (see Sec. 13) that
were identified on the NOT observations. Even if some kind of
masking procedure was applied by B03, many candidates ap-
peared concentrated on the same dates, and were considered
rather suspicious by the same authors.
7.3. Artificially added transits
The transit detection efficiency (TDE) was determined by ana-
lyzing light curves modified with the inclusion of random tran-
sits. To properly measure the TDE and to estimate the number
of transits we expect to detect it is mandatory to consider real-
istic planetary transits. We proceeded as follows:
7.3.1. Stellar parameters
The basic cluster parameters were determined by fitting the-
oretical isochrones from Girardi et al. (2002) to the observed
color-magnitude diagram (Stetson et al. 2003). Our best fit pa-
rameters are (see Fig. 7): age = 10.0 Gyr, (m − M) = 13.30,
E(B−V) = 0.12 for Z = 0.030 (corresponding to [Fe/H]=
12 M. Montalto et al.: A new search for planet transits in NGC 6791.
Fig. 7. CMD diagram of NGC6791 with the best fit Z=0.030 isochrone
(dashed line), and the best fit Z=0.046 isochrone (from Carraro et
al. 2006, solid line). Photometry: Stetson et al. (2003)
Fig. 8. Left: Mi/M⊙ vs visual apparent magnitude Right: Ri/R⊙ vs vi-
sual apparent magnitude, from our best fit isochrone (dashed line)
and from the Z=0.046 isochrone (solid line) applied to the stars
of NGC 6791.
+0.18), and age = 8.9 Gyr, (m−M) = 13.35 and E(B−V) = 0.09
for Z=0.046 (corresponding to [Fe/H]= +0.39).
From the best-fit isochrones we then obtained the values of
stellar mass and radius as a function of the visual magnitude
(Fig. 8).
7.3.2. Planetary parameters
The actual distribution of planetary radii has a very strong im-
pact on the transit depth and therefore on the number of plan-
etary transits we expect to be able to detect. The radius of
the fourteen transiting planets discovered to date ranges from
R=1.35 ± 0.07 RJ (HD209458b; Wittenmyrer et al. 2005) to
R=0.725 ± 0.03 RJ (HD149026b; Sato et al. 2005), where
J refers to the value for Jupiter. The observed distribution is
likely biased towards larger radii. Gaudi (2005a) suggests for
the close-in giant planets a mean radius Rp = 1.03 RJ. To eval-
uate the efficiency of the algorithm we have considered three
cases:
Fig. 9. Continuous line: adopted distribution for planet peri-
ods. Histogram: RV surveys data (from the Extrasolar Planets
Encyclopaedia).
– Rp = (0.7 ± 0.1) RJ
– Rp = (1.0 ± 0.2) RJ
– Rp = (1.4 ± 0.1) RJ
assuming a Gaussian distribution for Rp. We fixed the planetary
mass at Mp = 1 MJ , because the effect of planet mass on transit
depth or duration is negligible.
The period distribution was taken from the data for plan-
ets discovered by radial velocity surveys, from the Extra-solar
Planets Encyclopaedia9. We selected the planets discovered by
radial velocity surveys with mass 0.3MJ ≤ Mpl sin i ≤ 10MJ
(the upper limit was fixed to exclude brown dwarfs; the lower
limit to ensure reasonable completeness of RV surveys and to
exclude Hot Neptunes that might have radii much smaller than
giant planets, Baraffe et al. 2005) and periods 1 ≤ P ≤ 9 days.
We assumed that the period distribution of RV planets is un-
biased in this period range. We then fitted the observed period
distribution with a positive power law for the Very Hot Jupiters
(VHJ, 1 ≤ P ≤ 3) and a negative power law for the Hot Jupiters
(HJ, 3 < P ≤ 9, see Gaudi et al. 2005b for details) as shown in
Fig. 9.
7.3.3. Limb-darkening
To obtain realistic transit curves it is important to include the
limb darkening effect. We adopted a non-linear law for the spe-
cific intensity of a star:
= 1 −
ak (1 − µ
k/2) (7)
from Claret (2000).
9 http://exoplanet.eu/index.php
M. Montalto et al.: A new search for planet transits in NGC 6791. 13
In this relation µ = cosγ is the cosine of the angle between
the normal to the stellar surface and the line of sight of the
observer, and ak are numerical coefficients that depend upon
vturb (micro-turbulent velocity), [M/H], Te f f , and the spectral
band. The coefficients are available from the ATLAS calcula-
tions (available at CDS).
We adopted the metallicity of the cluster for [M/H] and
vturb=2 km s
−1 for all the stars. For each star we adopted the
appropriate V-band ak coefficients as a function of the values
of log g and Te f f derived from the best fit isochrone.
7.3.4. Modified light curves
In order to establish the TDE of the algorithm, we considered
the whole sample of constant stars with 17.3 ≤ V ≤ 22.1, and
each star was assigned a planet with mass, radius and period
randomly selected from the distributions described above. The
orbital semi-major axis a was derived from the 3rd Kepler’s
law, assuming circular orbits.
To each planet, we also assigned an orbit with a random
inclination angle i, with 0 < cos i < 0.1, with a uniform dis-
tribution in cos i. We infer that ∼ 85% of the planets result in
potentially detectable transits. We also assigned a phase 2φ0
randomly chosen from 0 to 2π rad and a random direction of
revolution s = ±1 (clockwise or counter-clockwise).
Having fixed the planet’s parameters (P, i, φ0, Mp, Rp, a),
the star’s parameters (M⋆, R⋆) and a constant light curve (ti ,
Vi) it is now possible to derive the position of the planet with
respect to the star at every instant from the relation:
φ = φ0 +
where φ is the angle between the star-planet radius and the
line of sight. The positions were calculated at all times ti
corresponding to the Vi values of the light curve of the star.
When the planet was transiting the star, the light curve was
modified, calculating the brightness variation ∆V(ti) and
adding this value to the Vi (see Fig. 10).
7.4. Calculating the TDE
We then selected only the light curves for which there was
at least a half transit inside an observing night and applied
our transit detection algorithm. We considered not only central
transits but also grazing ones. We considered the number of
light curves that exceeded the thresholds, and also determined
for how many of these the transit instants were correctly iden-
tified on the unfolded light curves.
We isolated three different outputs:
1. Missed candidates: the light curves for which the algorithm
did not get the values of the parameters that exceeded the
thresholds (DSP, OOTV, transit duration and number of in
transit points, see Sec 6.3), or if it did, the epochs of the
transits were not correctly recovered;
2. Partially recovered transit candidates: the parameters ex-
ceeded the thresholds and at least one of the transits that
fell in the observing window was correctly identified;
Fig. 10. Top: constant light curve Bottom: the same light curve after
inserting the simulated transit with limb-darkening (black points). The
solid line shows the theoretical light curve of the transit.
3. Totally recovered transit candidates: the parameters ex-
ceeded the thresholds and all the transits that were present
were correctly recovered.
The TDE was calculated as the sum of the totally and partially
recovered transit candidates relative to the whole number of
stars with transiting planets. We derive the TDE as a function
of magnitude in Fig. 11. The TDE decreases with increasing
magnitude because the lower photometric precision at fainter
magnitudes is not fully compensated by the larger transit depth.
The TDE depends strongly also on the assumptions concerning
the planetary radii, and on the inclusion of the limb darkening
effect. Fig. 11 is relative to a threshold equal to 4.3 for the DSP
(cf. Fig. 6).
The resulting TDE is about 11.5% around V = 18 and 1%
around V = 21 for the case with R = (1.0 ± 0.2)RJ.
Figure 12–14 show the histograms relative to the input tran-
sit parameters and the recovered values of the BLS algorithm
normalized to the whole number of transiting planets. For com-
parison we also show in the upper left panel of each figure
the recovered values of the BLS for the constant simulated
light curves (normalized to the total number of constant light
curves). We found that on average the BLS algorithm has un-
derestimated the depth and duration of the transit by about 15-
20%. This is likely due to the deviation of the transit curves
from the box shape assumed by the algorithm. For the periods,
(Fig. 13), the recovered transit period distribution shown in the
upper right panel of Fig. 13, had two clear peaks at 1.5 and 3
days, with the first one much more evident meaning that the
algorithm tends to estimate half of the input transit period, as
shown in the lower panels of the same Figure. The constant
light curve period distribution of the upper left panel, instead,
showed that the vast majority of constant stars were recovered
with periods between 0.5 and 1 day, but residual peaks at 2.5
and 5 days were present.
14 M. Montalto et al.: A new search for planet transits in NGC 6791.
Fig. 11. TDE as a function of the stellar magnitude for various as-
sumptions on planetary radii distribution. From the top to the bottom:
1) Dashed line, R = (1.4 ± 0.1) RJ ; 2) Solid line, R = (1.0 ± 0.2) RJ ;
3) Dotted line, R = (0.7 ± 0.1) RJ . The adopted threshold for the DSP
in this figure is 4.3. The normalization is respect to the whole number
of transiting planets.
Fig. 12. (Upper left) Distributions of transit depths measured by
the BLS algorithm on the artificial constant-light-curves (lc); (upper
right) transit depths measured on artificial light curves with transits
added;(lower left) input transit depths used to generate artificial light
curves with transits;(lower right) relative difference between the tran-
sit depth recovered by BLS and its input value. Empty histograms refer
to distributions relative to all light curves, filled ones to light curves
with totally and partially recovered transits. Histograms are normal-
ized to all light curves with transiting planets, or, for the upper left
panel to all constant light curves. This Figure is relative to CFHT data,
and the assumed planetary radii distribution is R = (1.0 ± 0.2).
Fig. 13. The same as Fig.12 for the transit periods.
Fig. 14. The same as Fig.12 for the transit durations.
8. Different approaches in the transit search
The data we have acquired on NGC 6791 came from four dif-
ferent sites and involved telescopes with different diameters
and instrumentations. Moreover, the observing window of each
site was clearly different with respect to the others as well as
observing conditions like seeing, exposure times, etc.
The first approach we tried consisted in putting together
the observations coming from all the different telescopes. The
most important complication we had to face regarded the dif-
M. Montalto et al.: A new search for planet transits in NGC 6791. 15
Table 5. The different cases in which the data-sets analysis was split-
ted into. The notation in the first column is explained in the text,
the second column shows the number of stars in each case and the
third column refers to the DSP values assumed, correspondent to a
FAR= 0.1%.
Case N.stars DSP threshold
11111 1093 7.5
10000 771 4.3
10100 870 5.5
11011 162 7.1
10001 112 7.1
11001 108 7.5
10111 99 7.2
10011 96 6.5
ferent field of views of the detectors. This had the consequence
that some stars were measured only in a subset of the sites,
and therefore these stars had in general different observing win-
dows. Considering only the stars in common would reduce the
number of candidates from 3311 to 1093 which means a re-
duction of about 60% of the targets. We decided to distinguish
eight different cases, which are shown in Tab. 5. In the first col-
umn a simple binary notation identifies the different sites: each
digit represents one site in the following order: CFHT, SPM,
Loiano, NOT(V) and NOT(I). If the number correspondent to a
generic site is 1, it indicates that the stars contained in that case
have been observed, otherwise the value is set to 0. For exam-
ple, the notation 11111 was used for the stars in common to all
4 sites. The notation 10000 indicates the number of stars which
were present only on the CFHT field, and so on. Each one of
these cases was treated as independent, and the resulting FAR
and expected number of transiting planets were added together
in order to obtain the final values.
The second approach we followed was to consider only the
CFHT data. As demonstrated in Section 3, overall we obtained
the best photometric precision for this data-set. We considered
the 3311 candidates which were recovered in the CFHT data-
For the CFHT data-set, as shown in Tab. 5, the DSP value
correspondent to a FAR= 0.1% is equal to 4.3, lower than the
other cases reported in that Table. Thus, despite the reduced
observing window of the CFHT data, it is possible to take ad-
vantage of its increased photometric precision in the search for
planets.
In Section 9, and in Section 10, we presented the candidates
and the different expected number of transiting planets for these
two different approaches.
9. Presentation of the candidates
Table 6 shows the characteristics of the candidates found by the
algorithm, distinguishing those coming from the entire data-set
analysis from those coming from the CFHT analysis.
Fig. 15. Composite light curve of candidate 6598. In ordinate is re-
ported the calibrated V magnitude and in abscissa the observing
epoch, (in days), where 0 corresponds to JD = 52099. Filled circles
indicate CFHT data, crosses SPM data, open triangles Loiano data,
open circles NOT data in the V filter and open squares NOT data in
the I filter. Light blue symbols highlight regions which were flagged
by the BLS.
9.1. Candidates from the whole data-sets
Applying the algorithm with the DSP thresholds shown
in Tab. 5 on the real light curves we obtained four can-
didates. Hereafter we adopt the S03 notation reported in
Tab. 6. For what concerns candidates 6598, 4304, and 4699
(Fig. 15, 16, 17) we noted (see also Sec. 7.2) that the points
contributing to the detected signal came from the first observ-
ing night at the NOT, meaning that bad weather conditions
deeply affected the photometry during that night. In particu-
lar candidate 6598, was also found in the B03 transit search
survey, (see Sec. 13), and flagged as a probable spurious can-
didate. In none of the other observing nights we were able to
confirm the photometric variations which are visible in the first
night at the NOT. We concluded that these three candidates are
of spurious nature.
The fourth candidate corresponds to star 1239, that is lo-
cated in the external regions of the cluster. For this reason we
presented in Fig. 18 only the data coming from the CFHT. In
this case, the data points appear irregularly scattered underly-
ing a particular pattern of variability or simply a spurious pho-
tometric effect.
9.2. Candidates from the CFHT data-set
Considering only the data coming from the CFHT observing
run we obtained three candidates. The star 1239 is in common
with the list of candidates coming from the whole data-sets be-
cause, as explained above, it is located in the external regions
for which we had only the CFHT data. For candidate 4300,
the algorithm identified two slight (∼ 0.004 mag) magnitude
variations with duration of around one hour during the sixth
and the tenth night, with a period of around 4.1 days. A jovian
16 M. Montalto et al.: A new search for planet transits in NGC 6791.
Table 6. The candidates found in the two cases discussed in Sec. 8. The case of the whole data-sets put together is indicated with ALL (1st
column), that one for the only CFHT data-set is indicated with CFHT (2nd column). A cross (x) indicates that the candidate was found in that
case, a trait (-) that it is absent. In the 3rd column, the ID of the stars taken from S03 is shown. Follow the V calibrated magnitude, the (B − V)
color, the right ascension, (α), and the declination, (δ), of the stars.
ALL CFHT ID(S tetson) V (B − V) α(2000) δ(2000)
x - 6598 18.176 0.921 19h 20m 48s.65 +37◦ 47
x - 4304 17.795 0.874 19h 20m 41s.39 +37◦ 43
x - 4699 17.955 0.846 19h 20m 42s.67 +37◦ 43
x x 1239 19.241 1.058 19h 20m 25s.42 +37◦ 47
- x 4300 18.665 0.697 19h 20m 41s.38 +37◦ 45
- x 7591 18.553 0.959 19h 20m 51s.51 +37◦ 48
Fig. 16. Composite light curve of candidate 4304.
Fig. 17. Composite light curve of candidate 4699.
planet around a main sequence star of magnitude V=18.665,
(with R = 0.9 R⊙, see Fig. 8), should determine a transit with
a maximum depth of around 1.2%, and maximum duration of
2.6 hours. Although compatible with a grazing transit, we ob-
served that the two suspected eclipses are not identical, and, in
Fig. 18. CFHT light curve for candidate 1239.
Fig. 19. CFHT light curve for candidate 4300.
Fig. 20. CFHT light curve for candidate 7591.
any case, outside these regions, the photometry appears quite
scattered. Star 7591, instead, does not show any significant fea-
ture.
From the analysis of these candidates we concluded that
no transit features are detected for both the entire data-sets and
the CFHT data. Moreover, we can say to have recovered the
expected number of false alarm candidates which was (3.3 ±
1.3) as explained in Sec. 10.3.
10. Expected number of transiting planets
10.1. Expected frequency of close-in planets in
NGC 6791
The frequency of short-period planets in NGC 6791 was es-
timated considering the enhanced occurrence of giant planets
M. Montalto et al.: A new search for planet transits in NGC 6791. 17
around metal rich stars and the fraction of hot Jupiters among
known extrasolar planets.
Fischer & Valenti (2005) derived the probability P of for-
mation of giant planets with orbital period shorter than 4 yr and
radial velocity semi-amplitude K > 30 ms−1 as a function of
[Fe/H]:
P = 0.03 · 10 2.0 [Fe/H] − 0.5 < [Fe/H] < 0.5 (8)
The number of stars with a giant planet with P < 9 d was
estimated considering the ratio between the number of the plan-
ets with P < 9 days and the total number of planets from Table
3 of Fischer & Valenti 2005 (850 stars with uniform planet de-
tectability). The result is 0.22+0.12
−0.09.
Assuming for NGC 6791 [Fe/H]= +0.17 dex, a conserva-
tive lower limit to the cluster metallicity, from Equation 8 we
determined that the probability that a cluster star has a giant
planet with P < 9 is 1.4%. Assuming [Fe/H]= +0.47, the
metallicity resulting from the spectral analysis by Gratton et
al. (2006), the probability rises to 5.7%.
Our estimate assumes that the planet period and the metal-
licity of the parent star are independent, as found by Fischer
& Valenti (2005). If the hosts of hot Jupiters are even more
metal rich than the hosts of planets with longer periods, as pro-
posed by Society (2004), then the expected frequency of close-
in planets at the metallicity of NGC 6791 should be slightly
higher than our estimate.
10.2. Expected number of transiting planets
In order to evaluate the expected number of transiting planets
in our survey we followed this procedure:
– From the constant stars of our simulations (see Sec. 7), tak-
ing into account the luminosity function of main sequence
stars of the cluster, we randomly selected a sample cor-
responding to the probability that a star has a planet with
P ≤ 9 d.
– From the V magnitude of the star we calculated the mass
and radius.
– To each star in this sample we assigned a planet with mass,
radius, period randomly chosen from the distributions de-
scribed in Sec. 7.3.2, and cos i randomly chosen inside
the range 0 - 1. The range spanned for the periods was
1 < P < 9 days, with a step size of 0.006 days. For plane-
tary radii we considered the three distributions described in
Sec. 7.3.2, sampled with a step size of 0.001 RJ, and incli-
nations were varied of 0.005 degrees.
– We selected only the stars with planets that can make tran-
sits thanks to their inclination angle given by the relation:
cos i ≤
Rpl + R⋆
– Finally, as described above, we assigned to each planet the
initial phase φ0 and the revolution orbital direction s and
modified the constant light curves inserting the transits. The
initial phase was chosen randomly inside the range 0-360
degrees, with a step size of 0.3 degrees.
– We applied the BLS algorithm to the modified light curves
with the adopted thresholds.
We performed 7000 different simulations and we calculated
the mean values of these quantities:
– The number of MS stars with a planet: Npl
– The number of planets that make transits (thanks to
their inclination angles): Ngeom
– The number of planets that make one or more transits
in the observing window: N+1
– The number of planets that make one single transit in
the observing window: N1
– The number of transiting planets detected by the algo-
rithm for the three different planetary radii distributions
adopted, (as described in Sect. 7), R1 = (0.7 ± 0.1) RJ,
R2 = (1.0 ± 0.2) RJ, and R
3 = (1.4 ± 0.1) RJ.
10.3. FAR and expected number of detectable
transiting planets for the whole data-sets
We followed the procedure reported in Sec. 7 to perform simu-
lations with the artificial stars. It is important to note that artifi-
cial stars were added exactly in the same positions in the fields
of the different detectors. This is important because it assured
the homogeneity of the artificial star tests. We decided to accept
a FAR equal to 0.1%, which meant that we expected to obtain
(3.3 ± 1.3) false alarms from the total number of 3311 clus-
ter candidates. The DSP thresholds correspondent to this FAR
value are different for each case, and is reported in Table 5.
Table 7 displays the results for the simulations performed
in order to obtain the expected numbers of detectable transit-
ing candidates for three values of [Fe/H] (the values found by
Carraro et al. 2006 and Gratton et al. 2006 and a conservative
lower limit to the cluster metallicity).
The columns listed as Ngeom, N1+ and N1 indicate respec-
tively the number of planets which have a favorable geometric
inclination for the transit, the number of expected planets that
transit at least one time within the observing window and the
number of expected planets that transit exactly one time in the
observing window.
The numbers of expected transiting planets in our observ-
ing window detectable by the algorithm were calculated for
the three different planetary radii distributions (see Sec. 7, and
previous paragraph). On the basis of the current knowledge
on giant planets the most likely case corresponds to R2 =
(1.0 ± 0.2) RJ.
Table 7 shows that, assuming the most likely planetary radii
distribution R = (1.0 ± 0.2) RJ and the high metallicity result-
ing from recent high dispersion studies (Carraro et al. 2006;
Gratton et al. 2006), we expected to be able to detect 2 − 3
planets that exhibit at least one detectable transit in our observ-
ing window.
10.4. FAR and expected number of detectable
transiting planets for the CFHT data-set
Table 8 shows the expected number of detectable planets in
our observing window for the case of the CFHT data. A
18 M. Montalto et al.: A new search for planet transits in NGC 6791.
Table 7. The Table shows the results of our simulations on the expected number of detectable transiting planets for the whole data-set (all
the cases of Tab. 5) as explained in Sect. 10.3. Ngeom indicates planets with favorable inclination for transits, N1+, and N1, planets that transit
respectively at least one time and only one time inside the observing window. R1, R2, R3, indicate the expected number of detectable transiting
planets inside our observing window, for the three assumed planetary radii distributions, (see Sec. 7.3.2).
[Fe/H] Ngeom N1+ N1 R
1 R2 R3
+0.17 5.39 3.08 1.68 0.0 ± 0.0 0.0 ± 0.0 1.8 ± 0.9
+0.39 15.13 8.32 4.60 0.1 ± 0.1 1.9 ± 0.8 3.6 ± 1.8
+0.47 21.92 11.95 6.62 0.2 ± 0.3 3.2 ± 1.9 5.4 ± 1.8
comparison with Table 7 revealed that, in general, except for
the largest planetary radii distribution, R3, the number of ex-
pected detections is not increasing considering all the sites to-
gether instead of the CFH only. Moreover, for the cases of
[Fe/H]= (+0.39,+0.47)dex, and the R = (0.7 ± 0.1)RJ radii
distribution, we obtained significantly better results consider-
ing only the CFHT data than putting together all the data-sets.
We interpreted this result as the evidence that the transit signal
is, in general, lower than the total scatter in the composite light
curves and this didn’t allow the algorithm to take advantage of
the increased observing window giving, for the cases of ma-
jor interest, R = (1 ± 0.2)RJ and [Fe/H]= (+0.39,+0.47)dex,
comparable results.
11. Significance of the results
As explained in Sec. 9, on real data we obtained 4 candidates,
considering the data coming from the entire data-sets, (all the
cases of Tab. 5), and 3 candidates considering only the best
photometry coming from the CFHT . None of these candidates
shows clear transit features, and their number agrees with the
expected number of false candidates coming from the simula-
tions (3.3 ± 1.3) as explained in Sec. 7.1.
Considering the case relative to the metallicity of Carraro
et al. 2006 ([Fe/H]= +0.39) and the one relative to the metallic-
ity of Gratton et al. 2006, ([Fe/H]= +0.47), and given the most
probable planetary radii distribution with R = (1.0 ± 0.2)RJ,
from Table 7 and Table 8 we expected between 2 and 3 planets
with at least one detectable transit inside our observing win-
Therefore, this study reveals a lack of transit detections.
What is the probability that our survey resulted in no tran-
siting planets just by chance? To answer this question we went
back to the simulations described in Sect. 10.2 and calculated
the ratio of the number of simulations for which we were not
able to detect any planet relative to the total number of simula-
tions performed. The resulting probabilities to obtain no tran-
siting planets were respectively around 10% and 3% for the
metallicities of Carraro et al. 2006 and Gratton et al. 2006 con-
sidered above.
12. Implication of the results
Beside the rather small, but not negligible probability of a
chance result, (3-10%, see Sec. 11), different hypothesis can
be invoked to explain the lack of observed transits. We have
discussed them here.
12.1. Lower frequency of close-in planets in cluster
environments
The lack of observed transits might be due to a lower frequency
of close-in planets in clusters compared to the field stars of sim-
ilar metallicity. In general, two possible factors could prevent
planet formation especially in clustered environments:
– in the first million years of the cluster life, UV-flux can
evaporate fragile embryonic dust disks from which planets
are expected to form. Circumstellar disks associated with
solar-type stars can be readily evaporated in sufficiently
large clusters, whereas disks around smaller (M-type) stars
can be evaporated in more common, smaller groups. In ad-
dition, even though giant planets could still form in the disk
region r = 5-15 AU, little disk mass (outside that region)
would be available to drive planet migration.;
– on the other hand, gravitational forces could strip nascent
planets from their parent stars or, taking in mind that tran-
sit planet searches are biased toward ’hot jupiter’ plan-
ets, tidal effects could prevent the planetary migration pro-
cesses which are essential for the formation of this kind of
planets.
These factors depend critically on the cluster size. Adams
et al. (2006), show that for clusters with 100-1000 members
modest effects are expected on forming planetary systems. The
interaction rates are low, so that the typical solar system ex-
periences a single encounter with closest approach distance of
1000 AU. The radiation exposure is also low, so that photo-
evaporation of circumstellar disks is only important beyond 30
AU. For more massive clusters like NGC6791, these factors
are expected to be increasingly important and could drastically
affect planetary formation (Adams et al. 2004).
12.2. Smaller planetary radii for planets around very
metal rich host stars
Guillot et al. (2006) suggested that the masses of heavy ele-
ments in planets was proportional to the metallicities of their
parent star. This correlation remains to be confirmed, being
still consistent with a no-correlation hypothesis at the 1/3 level
in the least favorable case. A consequence of this would be
a smaller radius for close-in planets orbiting super-metal rich
stars. Since the transit depth scales with the square of the ra-
dius, this would have important implications for ground-based
transit detectability, (see Tables 8- 7).
M. Montalto et al.: A new search for planet transits in NGC 6791. 19
Table 8. The same as 7, but for the case of the only CFHT data as explained in Sect. 10.2.
[Fe/H] Ngeom N1+ N1 R
1 R2 R3
+0.17 5.39 2.49 1.98 0.2 ± 0.5 0.4 ± 0.7 0.6 ± 0.8
+0.39 15.13 7.01 5.39 1.6 ± 1.3 2.3 ± 1.6 2.6 ± 1.7
+0.47 21.92 10.12 7.94 2.5 ± 1.7 3.4 ± 2.0 4.0 ± 2.1
12.3. Limitations on the assumed hypothesis
While we exploited the best available results to estimate the ex-
pected number of transiting planets, it is possible that some of
our assumptions are not completely realistic, or applicable to
our sample. One possibility is that the planetary frequency no
longer increases above a given metallicity. The small number of
stars in the high metallicity range in the Fischer & Valenti sam-
ple makes the estimate of the expected planetary frequency for
the most metallic stars quite uncertain. Furthermore, the con-
sistency of the metallicity scales of Fischer & Valenti (2005),
Carraro et al. (2006) and Gratton et al. (2006) should be
checked.
Another possibility concerns systematic differences be-
tween the stellar sample studied by Fischer & Valenti, and the
present one. One relevant point is represented by binary sys-
tems. The sample of Fischer & Valenti has some biases against
binaries, in particular close binaries. As the frequency of plan-
ets in close binaries appears to be lower than that of planets
orbiting single stars and wide binaries (Bonavita & Desidera
2007, A&A, submitted), the frequency of planets in the Fischer
& Valenti sample should be larger than that resulting in an un-
biased sample. On the other hand, our selection of cluster stars
excludes the stars in the binary sequence, partially compensat-
ing this effect.
Another possible effect is that of stellar mass. As shown in
Fig. 8, the cluster’s stars searched for transits have mass be-
tween 1.1 to 0.5 M⊙. On the other hand, the stars in the FV
sample have masses between 1.6 to 0.8 M⊙. If the frequency of
giant planets depends on stellar mass, the results by Fischer &
Valenti (2005) might not be directly applicable to our sample.
Furthermore, some non-member contamination is certainly
present. As discussed in Section 5, the selection of cluster
members was done photometrically around a fiducial main se-
quence line.
12.4. Possibility of a null result being due to chance
As shown in Sec. 11, the probability that our null result was
simply due to chance was comprised between 3% and 10%,
depending on the metallicity assumed for the cluster. This is
a rather small, but not negligible probability, and other efforts
must be undertaken to reach a firmer conclusion.
13. Comparison of the transit search surveys on
NGC 6791
It is important to compare our results on the presence of planets
with those of other photometric campaigns performed in past
years. We consider in this comparison B03 and M05.
13.1. The Nordic Optical Telescope (NOT) transit
search
As already described in this paper, (e.g. see Sect. 2), in July
2001, at NOT, B03 undertook a transit search on NGC 6791
that lasted eight nights. Only seven of these nights were good
enough to search for planetary transits. Their time coverage
was thus comparable to the CFHT data presented here. The
expected number of transits was obtained considering as can-
didates all the stars with photometric precision lower than 2%,
(they did not isolate cluster main sequence stars, as we did,
but they then multiplied their resulting expected numbers for a
factor equal to 85% in order to account for binarity), and as-
suming that the probability that a local G or F-type field star
harbors a close-in giant planet is around 0.7%. With these and
other obvious assumptions B03 expected 0.8 transits from their
survey. However, they made also the hypothesis that for metal-
rich stars the fraction of stars harboring planets is ∼ 10 times
greater than for general field stars, following Laughlin (2000).
In this way, they would have expected to find “at least a few
candidates with single transits”. In Section 3 we showed how
the photometric precision for the NOT was in general of lower
quality for the brightest stars with respect to that one of SPM
and Loiano. This fact can be recognized also in Table 5 where
the value of the threshold for the DSP was always bigger than
6.5 when the NOT observations were included. This demon-
strates the higher noise level of this data-set. We did not per-
form the accurate analysis of the expected number of transit-
ing planets considering only the NOT data, but, on the basis of
our assumptions, and on the photometric precision of the NOT
data, the numbers showed in Table 8 for the CFHT should be
considered as an upper limit for the expected transit from the
NOT survey.
B03 reported ten transit events, two of which, (identified in
B03 as T6 and T10), showed double transit features, and the
others were single transits. Except for candidate T2, which was
recovered also in our analysis (see Sec. 9.1) our algorithm did
not identify any other of the candidates reported by B03.
B03 recognized that most of the candidates were likely spu-
rious, while three cases, referred as T5, T7 and T8, were con-
sidered the most promising ones. We noted that T8 lies off the
cluster main sequence. Therefore, it can not be considered as a
planet candidate for NGC 6791. Furthermore, from our CFHT
images we noted that this candidate is likely a blended star. The
other two candidates were on the main sequence of NGC 6791.
Visual inspection of the light curves in Fig. 21 and Fig. 22 also
show no sign of eclipse.
Finally, candidate T9, (Fig. 23) lies off the cluster main
sequence and it was recognized by B03 to be a long-period
low-amplitude variable (V80). In our photometry, it shows
clear signs of variability, and a ∼ 0.05 mag eclipse during the
20 M. Montalto et al.: A new search for planet transits in NGC 6791.
Fig. 21. Composite light curve for candidate 3671 correspondent to T5
of BO3. Different symbols have the same meaning of Fig. 15.
Fig. 22. Composite light curve for candidate 3723 correspondent to T7
of BO3.
second night of the CFHT campaign at t = 361.8, and probably
a partial eclipse at the end of the seventh night of the NOT
data-set, at t = 6.4, ruling out the possibility of a planetary
transit, because the magnitude depth of the eclipse is much
larger than what is expected for a planetary transit.
It is not surprising that almost all of the candidates reported
by B03 were not confirmed in our work, even for the NOT pho-
tometry itself. Even if the photometry reduction algorithm was
the same, (image subtraction, see Sec. 3), all the other steps
that followed, and the selection criteria of the candidates were
in general different. This, in turn, reinforces the idea that they
are due to spurious photometric effects.
Fig. 23. Composite light curve for candidate 12390 correspondent to
T9 of BO3.
13.2. The PISCES group extra-Solar planets search
The PISCES group collected 84 nights of observations on
NGC 6791, for a total of ∼ 300 hours of data collection from
July 2001 to July 2003, at the 1.2m Fred Lawrence Whipple
Observatory (M05). Starting from their 3178 cluster mem-
bers (selected considering all the main sequence stars with
RMS≤ 5%), assuming a distribution of planetary radii between
0.95 RJ and 1.5 RJ, and a planet frequency of 4.2%, M05 ex-
pected to detect 1.34 transiting planets in the cluster. They
didn’t identify any transiting candidate. Their planet frequency
is within the range that we assumed (1.4%–5.7%). Our number
of candidate main-sequence stars is slightly in excess relative
to that of M05, even if their field of view is larger than our own
(∼ 23 arcmin2 against ∼ 19 arcmin2 of S03 catalog), since we
were able to reach ∼ 2 mag deeper with the same photomet-
ric precision level. Their number of expected transiting plan-
ets is of the same order of magnitude as our own because of
their huge temporal coverage. In any case, looking at figure
7 of M05, one should recognize that their detection efficiency
greatly favors planetary radii larger than 1 RJ. A more realistic
planetary radius distribution, for example (1.0± 0.2) RJ, should
significantly decrease their expectations, as recognized by the
same authors.
14. Future investigations
NGC 6791 has been recognized as one of the most promising
targets for studying the planet formation mechanism in clus-
tered environments, and for investigating the planet frequency
as a function of the host star metallicity. Our estimate of the ex-
pected number of transiting planets, (about 15–20 assuming the
metallicity recently derived by means of high-dispersion spec-
troscopy by Carraro et al. 2006, and Gratton et al. 2006, and the
planet frequency derived by Fischer & Valenti 2005), confirms
that this is the best open cluster for a planet search.
M. Montalto et al.: A new search for planet transits in NGC 6791. 21
However, in spite of fairly ambitious observational efforts
by different groups, no firm conclusions about the presence or
lack of planets in the cluster can be reached.
With the goal of understanding the implications of this re-
sult and to try to optimize future observational efforts, we show,
in Table 9, that the number of hours collected on this cluster
with > 3 m telescopes is much lower than the time dedicated
with 1 − 2 m class telescopes. Despite the fact that we were
able to get adequate photometric precisions even with 1 − 2 m
class telescopes, (see Sec. 3), in general smaller aperture tele-
scopes are typically located on sites with poorer observing con-
ditions, which limits the temporal sampling and their photom-
etry is characterized by larger systematic effects. As a result,
the number of cluster stars with adequate photometric precision
for planet transit detections is quite limited. Our study suggests
that more extensive photometry with wide field imagers at 3 to
4-m class telescopes (e.g. CFHT) is required to reach conclu-
sive results on the frequency of planets in NGC 6791.
We calculated that, extending the observing window to two
transit campaigns of ten days each, providing that the same
photometric precision we had at the CFHT could be reached,
we could reduce the probability of null detection to 0.5%.
15. Conclusions
The main purpose of this work was to investigate the problem
of planet formation in stellar open clusters. We focused our at-
tention on the very metal rich open cluster NGC 6791. The idea
that inspired this work was that looking at more metal rich stars
one should expect a higher frequency of planets, as it has been
observed in the solar neighborhood (Santos et al. 2004, Fisher
& Valenti, 2005). Clustered environments can be regarded as
astrophysical laboratories in which to explore planetary fre-
quency and formation processes starting from a well defined
and homogeneous sample of stars with the advantage that clus-
ter stars have common age, distance, and metallicity. As shown
in Section 2, a huge observational effort has been dedicated
to the study of our target cluster using four different ground
based telescopes, (CFHT, SPM, Loiano, and NOT), and trying
to take advantage from multi-site simultaneous observations.
In Section 3, we showed how we were able to obtain adequate
photometric precisions for the transit search for all the differ-
ent data-sets (though in different magnitude intervals). From
the detailed simulations described in Section 10, it was demon-
strated that, with our best photometric sequence, and with the
most realistic assumption that the planetary radii distribution is
R = (1.0 ± 0.2)RJ, the expected number of detectable transiting
planets with at least one transit inside our observing window
was around 2, assuming as cluster metallicity [Fe/H]=+0.39,
and around 3 for [Fe/H]= +0.47. Despite the number of ex-
pected positive detections, no significant transiting planetary
candidates were found in our investigation. There was a rather
small, though not negligible probability that our null result can
be simply due to chance, as explained in Sect. 11: we esti-
mated that this probability is 10% for [Fe/H]= +0.39, and 3%
for [Fe/H]= +0.47. Possible interpretations for the lack of ob-
served transits (Sect. 12) are a lower frequency of close-in plan-
ets around solar-type stars in cluster environments with respect
to field stars, smaller planetary radii for planets around super
metal rich stars, or some limitations in the assumptions adopted
in our simulations. Future investigations with 3-4m class tele-
scopes are required (Sect 14) to further constrain the planetary
frequency in NGC 6791. Another twenty nights with this kind
of instrumentation are necessary to reach a firm conclusion on
this problem. The uniqueness of NGC 6791, which is the only
galactic open cluster for which we expect more than 10 giant
planets transiting main sequence stars if the planet frequency
is the same as for field stars of similar metallicity, makes such
an effort crucial for exploring the effects of cluster environment
on planet formation.
22 M. Montalto et al.: A new search for planet transits in NGC 6791.
Table 9. Number of nights and hours which have been devoted to the study of NGC 6791 as a function of the diameter of the telescope used
for the survey. We adopted a mean of 5 hours of observations per night.
Telescope Diameter(m) Nnights Hours Ref.
FLWO 1.2 84 ∼300 M05
Loiano 1.5 4 20 This paper
SPM 2.2 8 48 This paper
NOT 2.54 7 35 B03 and this paper
CFHT 3.6 8 48 This paper
MMT 6.5 3 15 Hartmann et al. (2005)
Acknowledgements. We warmly thank M. Bellazzini and F. Fusi Pecci
for having made possible the run at Loiano Observatory.
This work was partially funded by COFIN 2004 “From stars to plan-
ets: accretion, disk evolution and planet formation” by Ministero
Universitá e Ricerca Scientifica Italy.
We thanks the referee, Dr. Mochejska, for useful comments and sug-
gestions allowing the improvement of the paper.
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M. Montalto et al.: A new search for planet transits in NGC 6791. 23
List of Objects
‘NGC 6791’ on page 1
‘NGC 6791’ on page 1
‘NGC 6791’ on page 1
‘NGC 6791’ on page 1
‘NGC 6791’ on page 1
‘HD188753’ on page 2
‘HD188753A’ on page 2
‘HD188753BC’ on page 2
‘Hyades’ on page 2
‘47 Tucanae’ on page 2
‘ω Centauri. These studies (Gilliland et al. 2000; Weldrake et
al. 2005; Weldrake et al. 2006) reported not a single planet de-
tection. This seemed to indicate that planetary systems are at
least one order of magnitude less common in globular clusters
than in Solar vicinity.’ on page 2
‘47 Tuc’ on page 2
‘ω Cen’ on page 2
‘M4’ on page 2
‘NGC 6791’ on page 2
‘NGC 6791’ on page 2
‘NGC 6791’ on page 2
‘NGC 6791’ on page 2
‘NGC 6253’ on page 2
‘NGC 6791’ on page 2
‘NGC 6253’ on page 2
‘NGC 2158’ on page 2
‘NGC 6791’ on page 3
‘NGC 6791’ on page 3
‘NGC 6791’ on page 8
‘NGC 6791’ on page 8
‘NGC 6791’ on page 10
‘NGC 6791’ on page 11
‘NGC6791’ on page 12
‘NGC 6791’ on page 12
‘HD209458b’ on page 12
‘HD149026b’ on page 12
‘NGC 6791’ on page 14
‘NGC 6791’ on page 16
‘NGC 6791’ on page 16
‘NGC 6791’ on page 17
‘NGC 6791’ on page 17
‘NGC6791’ on page 18
‘NGC 6791’ on page 19
‘NGC 6791’ on page 19
‘NGC 6791’ on page 19
‘NGC 6791’ on page 19
‘NGC 6791’ on page 20
‘NGC 6791’ on page 20
‘NGC 6791’ on page 21
‘NGC 6791’ on page 21
‘NGC 6791’ on page 21
‘NGC 6791’ on page 21
‘NGC 6791’ on page 22
