EDP Sciences
Free Access
Issue
A&A
Volume 603, July 2017
Article Number A85
Number of page(s) 16
Section Planets and planetary systems
DOI https://doi.org/10.1051/0004-6361/201527562
Published online 11 July 2017

© ESO, 2017

1. Introduction

In recent years, several observational campaigns have been dedicated to search for planets in clusters or stellar associations, where the majority of stars is considered to form. Stars in clusters constitute a homogeneous sample in age and chemical composition that is ideal for investigating the dependence of planet formation on the mass and the properties of the central star (González Hernández et al. 2013, 2010; Baumann et al. 2010; Johnson et al. 2010; Ramírez et al. 2010; Meléndez et al. 2009), for determining the formation timescale and distinguishing different migration processes (Dong et al. 2014; Quinn et al. 2014; Dawson & Murray-Clay 2013), and finally for modeling the effects of stellar encounters on the formation and evolution of planetary systems (Li & Adams 2015; Cai et al. 2016; Shara et al. 2016; Davies et al. 2014; Malmberg et al. 2011; Spurzem et al. 2009). However, the high-precision radial velocity (RV) technique and the transit method have been successful only very recently in discovering planetary-mass companions around stars belonging to open clusters (OC). Of the most recent results in this field, we mention the detection of a hot Jupiter and a multi-planetary system in the Praesepe OC (Quinn et al. 2012; Malavolta et al. 2016), of a hot Jupiter in the Hyades (Quinn et al. 2014), of two sub-Neptune planets in NGC 6811 (Meibom et al. 2013), and the discovery of five Jupiter-mass planets in M 67 (Brucalassi et al. 2014, 2016). Previous RV surveys provided detections of a long-period giant planet around one of the Hyades clump giants (Sato et al. 2007) and a substellar-mass object in NGC 2423 (Lovis & Mayor 2007). No significant exoplanet candidates have been found by either ground- or by space-based transit campaigns in globular clusters (Gilliland et al. 2000; Nascimbeni et al. 2012).

These discoveries confirm that giant planets exist in a dense cluster environment, and suggest that a complete census of planet discoveries may be biased by the detection limit of the instruments and the observations available today. Moreover, results from various simulations show that dense birth environments such as stellar clusters can significantly influence the planet formation process and the resulting orbital properties of the planetary systems. Close encounters between stars or binary companions can modify the structure of any planetary system and also subsequently generate strong interactions between planets over very long timescales (Davies et al. 2014; Malmberg et al. 2011). This leads to the ejection of some planets, but it also seems to favor the conditions for the formation of hot Jupiters (Shara et al. 2016). Studying hot Jupiters in OCs can therefore shed light onto the long-standing problem of identifying their dynamical origin.

For the past seven years we have carried out a search for massive planets around main-sequence (MS) and evolved stars in the OC M 67. The scientific motivations for these studies include determining the impact of a different environment on the frequency and the evolution of planetary systems with respect to field stars. As a long-term goal, we aim to study the connection between giant planet formation and stellar mass and chemical composition. M 67 is the perfect target to search for planets around OC stars. Chemical analysis from several works (Randich et al. 2006; Pace et al. 2008; Önehag et al. 2011, 2014) has shown that M 67 has a chemical composition (not only Fe, but also the other elements) that is extremely similar to solar, as close as allowed by the precision of the measurements. In addition, the age of M 67 (3–5 Gyr), according to numerous determinations, encompasses the accepted value of the Sun, while the age determination for field stars is always rather uncertain. Finally, M 67 is a rich OC, which gives us the opportunity to find many stellar candidates that share similar properties and a large number of stars with different masses, characteristics that are essential to address the questions above.

Through RV measurements obtained with HARPS at La Silla-ESO, SOPHIE at OHP, HRS at HET, HARPS-N at the TNG, and CORALIE at the Euler Swiss Telescope, five new giant planets have been discovered around M 67 stars (Brucalassi et al. 2014, 2016): three hot Jupiters around MS stars, and two long-period planets around evolved stars.

In this paper, we present our RV campaign around stars of the OC M 67 considering data obtained until March 2015, and we provide a complete census of all the stars.

The star sample is described in Sect. 2, RV observations and analyses are reported in Sect. 3. In Sect. 4 we provide more detailed information on individual objects. In Sect. 5 we report a series of simulations based on a Monte Carlo approach that we used to estimate the occurrence rate of giant planets in our radial velocity survey. Finally, we summarize our results in Sect. 6.

2. Sample and observations

Table 1

List of the observations.

A complete description of the sample is reported in our previous works (Pasquini et al. 2012; Brucalassi et al. 2014). We highlight here those characteristics that are most relevant for the aim of this paper.

The original M 67 sample includes a total of 88 stars with V mag between 9 and 15, and a mass range of 0.9–1.4 M.

Main-sequence stars have been selected following Pasquini et al. (2008). In particular, we considered those stars with a membership probability higher than 60% and a proper motion lower than 6 mas/yr with respect to the average according to Yadav et al. (2008). When we considered the selection of the giants, we referred to Sanders (1977) for the membership probability, and the RV membership was derived according to Mermilliod & Mayor (2007) and Mathieu et al. (1986). We are aware that several stars that are particularly close to the turn-off point, although fulfilling our selection criteria, have been not observed because the observation time was too short.

Five different telescopes and instrument combinations have been used to obtain the RV measurements. Table 1 summarizes the number of the observations for each instrument.

The HARPS spectrograph (Mayor et al. 2003) at the ESO 3.6 m telescope was used in high-efficiency mode (EGGS mode) since the M 67 stars are quite faint for this instrument. In this configuration the fiber has an aperture on the sky of 1.2 arcsec, corresponding to R = 90 000, and is not equipped with an optical scrambler. The precision is limited to 5–7  m s-1, but the efficiency is 30–40% better than the high-resolution mode (HAM mode), which allows us to obtain the highest resolving power of 115 000 with a fiber aperture of 1 arcsec. The spectral range covered is 378–691 nm. Exposure times ranged from 10 to 45 min, yielding a typical signal-to-noise ratio (S/N) per resolution element of 10 to 15 for the faintest stars. Between January 2008 and March 2015, we gathered 734 observations of 88 stars with HARPS with an associated internal precision of ~10  m s-1. These observations represent the majority of this survey, and we therefore consider HARPS as our reference.

The SOPHIE spectrograph (Bouchy & Sophie Team 2006) at the OHP 1.93 m telescope was used in high-efficiency mode with R = 40 000 and a spectral range of 387–694 nm. We analyzed 168 SOPHIE observations of 70 M 67 stars with an associated internal precision of ~12  m s-1.

For the HRS spectrograph (Tull et al. 1998) at the Hobby Eberly Telescope we opted for a configuration with R = 60 000 and a wavelength range of 407.6–787.5 nm. We obtained 125 observations for 24 stars with a typical error bar associated with the observations of ~25  m s-1. During the period 2013–2015, the HET telescope was not accessible because of a telescope upgrade.

Moreover, we gathered 99 RV data points for 14 giant stars observed between 2003 and 2005 (Lovis & Mayor 2007) with the CORALIE spectrograph at the 1.2 m Euler Swiss telescope.

In addition, 27 h in service mode have been allocated with the TNG on La Palma Canary Island and the HARPS-N spectrograph. The HARPS-N is a fiber-fed echelle spectrograph, similar to HARPS on the 3.6 m ESO telescope and covers the wavelength range between 383 to 693 nm, with a spectral resolution R = 115 000. The two HARPS fibers (object + Sky/ThAr) have an aperture on the sky of 1 arcsec and are equipped with an image scrambler to provide a uniform spectrograph pupil illumination. Unfortunately, the observing campaign during the winter 2013–2014 was not very successful. The run at the TNG was impacted by bad weather and only 10 observing hours could be used, with 23 spectra for 13 stars.

Figure 1 shows a histogram with the number of observations per star updated to March 31, 2015. We have obtained 13 observations per star on average: 10 observations per star for MS stars, and 18 observations per star for giants and turn-off stars. Table A.1 shows the main data for the observed stars. In addition to the basic stellar parameters, the number of observations per star is given for each spectrograph and as a total.

3. RV analysis

thumbnail Fig. 1

Histogram showing the number of observations per star for our total sample. All observations from HARPS, HARPS-N, SOPHIE, CORALIE, and HET HRS are included in the plot and updated to March 31, 2015. The order number of the stars corresponds to Table A.1.

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HARPS, SOPHIE, and HARPS-N are provided with a similar automatic pipeline. The spectra are extracted from the detector images and cross-correlated with a numerical mask. For all of our stars, irrespective of the spectral type and luminosity, we used a G2V mask obtained from Sun spectra. Radial velocities are derived by fitting each resulting cross-correlation function (CCF) with a Gaussian (Baranne et al. 1996; Pepe et al. 2002). This real-time pipeline also provides an associated internal RV error σpn (photon noise error).

For the HRS data, the radial velocities were computed using a series of dedicated routines based on IRAF1. The procedures are described in more detail in Cappetta et al. (2012). The different steps include the wavelength calibration using a Th-Ar lamp exposure acquired before and after each stellar spectrum, the normalization of the spectra, the cleaning of cosmic rays as well as telluric and sky lines, the cross-correlation of the spectrum performed order by order with a G2V star template, and finally, the computation of the heliocentric corrections. The resulting CCFs were fitted with a Gaussian function to determine the RVs. After the orders affected by telluric lines and low S/N are rejected, the final RV value is given by the average value over the retained orders. Finally, the internal RV uncertainties are calculated by , where v is the RV of the individual orders and N is the number of the orders.

We used nightly observations of the RV standard star HD32923 to correct all observations for each star to the zero-point of HARPS (as explained in Pasquini et al. 2012) and to take any instrument instability or any systematic velocity shifts between runs (such as the modification of the SOPHIE fiber link in June 2011 (Perruchot et al. 2011) or technical problems during the calibration phase at HARPS) into account. An additional correction was applied to the SOPHIE data to account for the low S/N of the observations. For this, we corrected our spectra using Eq. (1) in Santerne et al. (2012). Finally, we considered the total error of the RV measurements (σobs) to be the sum in quadrature of all RV error sources described above. After all the observations for each star were corrected to the zero-point of HARPS, they were analyzed together. The combined measurement uncertainties have been compared to the observed velocity dispersions to evaluate the significance of any potential velocity variation and to highlight any possible outliers that would suggest the presence of exoplanets. In Table A.1 the mean stellar RV of each star is given, together with the average associated error (σobs) and the RV dispersion of the observations (σRV). Figure 2 shows (top panel) the histogram of the observed RV scatter (σRV) for the sample stars. Binary candidates were excluded, and the stars with significant RV trend are not shown. The bulk of our observations have an RV scatter represented by a Gaussian distribution centered on ~ 21 ± 7m s-1. Stars with an RV variability at or above 40  m s-1 are considered very good candidates for low-mass companion hosts.

thumbnail Fig. 2

Top: histogram showing the observed velocity dispersions (σRV) for the MS stars (pink) and giants and turn-off stars (blue) of our sample. Binary candidates and stars with high RV trend have been excluded. The black line represents the Gaussian fit centered at ~21  m s-1 of width σ ~ 7m s-1. Bottom: histogram showing the ratio of the RV dispersion (σRV) and the average measurements error (σobs). The symbols are the same as in the top panel.

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Figure 2 also includes a second panel (bottom) showing the histogram of the ratio between the observed RV scatter (σRV) and the average associated error (σobs) for each star. Large variations for planet candidates or long-term objects (see Sect. 4) are easy to identify. A clear peak results for most of the stars. Considering only stars with σRV< 4σobs (the small variations) and with no suspected companions, we calculated a peak of ~1.3 (employing a kernel density estimator to smooth the distribution), which is a sign that we may have underestimated the measurement errors. However, halos of excess scatter (RV variability) are present, which are most likely due to a combination of effects. In evolved stars some measurable intrinsic RV variability is present, as shown also in Setiawan et al. (2004) and Hekker et al. (2008), while for the faint MS stars the uncertainty in the measurements increases because of the limited S/N. Finally, some of the stars still have only a few observational points with poorly constrained RV variability, and their scatter is very likely the result of our low data statistics. Pasquini et al. (2012) also investigated whether other instrumental effects such as the observed flux or airmass (not included in the data analysis) could affect the RV measurement precision at low count levels, but no correlation was found. In order to consider these effects during the computation of the giant planet occurrence rate (see Sect. 5), we empirically inflated the estimated errors by adding in quadrature a term () equivalent, on average, to the excess RV scatter. This is calculated by , where and are the mean RV scatter and the mean estimated error, respectively, of stars without a trend and suspected companions. In Table A.1 the corrected associated error for each star is reported as σcor.

We studied the RV variations of our target stars by computing the Lomb-Scargle periodogram (Scargle 1982; Horne & Baliunas 1986). This is a commonly used technique for searching for periodic sinusoidal signals in unevenly sampled data and allows estimates of the detection threshold to be written down for periods shorter than the duration of the observations (Horne & Baliunas 1986). The significance of the sinusoid best fit of our RV values was determined by analytically calculating the false-alarm probability (FAP) level (Horne & Baliunas 1986). Afterward, we applied Levenberg-Marquardt analysis (Wright & Howard 2009, RVLIN) to fit Keplerian orbits to the radial velocity data.

Radial velocity periodic variation can be caused by rotational inhomogeneities related to stellar surface activity, such as plages or spots, including the one that is due to magnetic cycles of several years (Santos et al. 2010). Stellar activity can be diagnosed with spectral indicators or by monitoring the shape of the spectral lines. The low S/N of our observations does not provide sufficient signal in the region of the sensitive Ca II H and K lines. We therefore followed a method similar to the one described in Pasquini & Pallavicini (1991). We investigated the presence and variability of chromospheric active regions in these stars by measuring the variations of the core of Hα with respect to the continuum (see Dollinger 2008, for a more detailed description of how the Hα was measured). For each case we verified the correlation between the RVs and the bisector span of the CCF (calculated following Queloz et al. 2001) or with the FWHM of the CCF.

4. Results

thumbnail Fig. 3

Stars with large RV or significant linear trends (suspected binaries). Black dots: HARPS measurements, red dots: SOPHIE measurements, orange dots: HARPS-N measurements, and green dots: HRS measurements. RV error bars represent σcor.

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In the following, we describe the general results of our survey and discuss our analyses and interpretation of the RV time series for the most relevant targets in more detail. In particular, two further planet candidates are reported in this work. For the other stars, we refer to Table A.1, in which the main data for the observed objects are summarized. Individual RV measurements for all the stars are provided at the CDS in the format listed in Table 2.

Table 2

RV measurements, RV uncertainties, and instrument.

4.1. Binary candidates

Twelve binary candidates were previously published in Pasquini et al. (2012). Here we present two other MS stars in the sample (YBP1051, YBP673) that either show significant linear trends or RV variations that are too large to be produced by an exoplanet or by a non-stellar object. The RV measurements of these stars are shown in Fig. 3. They display a peak-to-peak RV amplitude of ~1.0 km s-1with an RV range spanned over more than six years. All binaries are highlighted in boldface in Table A.1.

4.2. Planets and planetary candidates

Four planets were announced in our previous works (Brucalassi et al. 2014, 2016) for the stars YBP401, YBP1194, YBP1514, and S364. Table 3 reports the main stellar characteristics and the resulting updated orbital parameters of the Keplerian fit for all these stars. Another two stars (S978 and YBP778) show significant indication for the presence of Jovian-mass companions.

YBP778. Twenty-one RV measurements have been obtained for the MS star YBP778 since 2009: 15 with HARPS, the others with SOPHIE and HARPS-N. The typical S/N is 10 and the average measurement uncertainty is ~17 m s-1  for HARPS and HARPS-N, and ~10 m s-1  for SOPHIE. A clear periodic signal can be seen in the periodogram at ~398 days (see Fig. A.3). Thus a single-planet Keplerian model was adjusted to the data, and the best-fit solution corresponds to a signal with a period of 410.4 ± 6.2 days, a semi-amplitude 158.8 ± 21.4 m s-1  (see Fig. 4), and an eccentricity of 0.27 ± 0.11. Although no peak is present in the periodograms of the activity index or the bisector span, nor in the CCF FWHM (see Fig. A.3), we detected an anticorrelation between the RVs and the bisector span with a Pearson correlation coefficient of –0.56, and a slight correlation between the radial velocities and the CCF FWHM (see Fig. A.4). The correlation disappears when we consider the RV residual.

thumbnail Fig. 4

Phased RV measurements and Keplerian best fit, best-fit residuals, and bisector variation for YBP778. Same symbols as in Fig. 3.

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We therefore cannot completely exclude stellar activity (magnetic cycles) or a binary companion with low sin(i) as the cause of the RV variation at this point, although in the recent study of Geller et al. (2015), YBP778 is also classified as a single member. Interesting, Pace et al. (2012) noted that this star is significantly underabundant in lithium compared to the lithium abundances as a function of stellar mass for MS stars in M 67. This could argue in favor of the possibility that the star might indeed host a planet (see, e.g., Deal et al. 2015). However, Pace et al. (2012) warned that the distance of this star to the isochrone in the color-magnitude diagram (CMD; ~0.06 mag) could also suggest the presence of a stellar or substellar companion.

Table 3

Top: stellar parameters of the M 67 stars that are newly found to host planet candidates. Bottom: orbital parameters of the planetary companions.

S978. The star is a K4 red giant and was observed 40 times over more than five years with HARPS, HRS, SOPHIE, and HARPS-N. The average RV uncertainty is ~3.0 m s-1  for HARPS and SOPHIE, ~26.0 m s-1  for HRS, and ~8.0 m s-1  for HARPS-N. Ten additional RV measurements were obtained with CORALIE between 2003 and 2005, with a mean measurement uncertainty of ~12.0 m s-1. The strongest peak in the periodogram of the RV time series lies at about 510.4 days (see Fig. A.3). Aliases are also present in the periodogram, but at half of the power of the main signal. The bisector inverse slope as well as the activity indicator do not present any significant variation at the period of 510.4 days. We fitted a single-planet Keplerian orbit to this signal (see Fig. 5) and found an orbital solution whose parameters are reported in Table 3. The dispersion of the residuals is σ(O-C) = 12.90 m s-1  and the periodogram of the residuals reveals some structures, but no significant peaks (see Fig. A.3).

thumbnail Fig. 5

Phased RV measurements and Keplerian best fit, best-fit residuals, and bisector variation for S978. Same symbols as in Fig. 4. Green dots: HRS measurements, blue dots: CORALIE measurements.

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Several studies indicate that M 67 stars in general have a low level of chromospheric activity. Pace & Pasquini (2004) computed activity levels for M 67 and other clusters. The paper shows that, for instance, the young Hyades and Presaepe stars on average have a chromospheric emission flux in the CaII K line of erg cm-2 s-1 and erg cm-2 s-1, respectively, while M 67 stars have erg cm-2 s-1, which is not enough to explain the high RV variations we observe. In a survey of the Ca II H and K core strengths of a sample of 60 solar-type stars in M 67, Giampapa et al. (2006) found that the distribution of the HK index (a measure of the strength of the chromospheric H and K cores) is broader than the distribution seen in the contemporary solar cycle. Significant overlap between the HK distribution of the solar cycle and that for the Sun-like stars in M 67 is seen with over 70% of the solar analogs exhibiting Ca II H+K strengths within the range of the modern solar cycle. About ~10% are characterized by high activity in excess of the solar maximum values, while approximately 17% have values of the HK index lower than the solar minimum. Of these, none of the stars showing enhanced activity is present in our final sample. In a following work, the same authors reported the results of the analysis of high-resolution photospheric line spectra obtained with the UVES instrument on the VLT for a subset of 15 solar-type stars in M 67 selected by Giampapa et al. (2006). They found upper limits to the projected rotation velocities that are consistent with solar-like rotation (i.e., vsini ≤ 2–3  km s-1) for objects with Ca II chromospheric activity within the range of the contemporary solar cycle. Two solar-type stars in their sample exhibit chromospheric emission well in excess of even the solar maximum values: Sand747 and Sand1452. In one case, Sand747, the authors found it to be a spectroscopic binary. The other star, Sand1452, was also present in our original sample, but we discovered that the object was also a binary system (Pasquini et al. 2012). Furthermore, of the 15 solar-type stars analyzed in Reiners & Giampapa (2009), seven stars are in common with our sample (in particular our planet-hosts YBP1194 and YBP1514). These objects are slow rotators (vsini ≤ 2km s-1) and have Sun-like HK values.

Melo et al. (2001) used FEROS spectrograph observations to determine accurate projected rotational velocities vsini for a sample of 28 MS, turn-off, and giant stars belonging to M 67. They found that the stars show similar values of vsini depending on their position in the CMD. Early MS G stars have a rotational velocity twice higher than the Sun, and they show a possible trend with (BV) color, with redder colors corresponding to lower vsini. The stars at the turn-off are the fastest rotators, with vsini between 6.3 and 7.6  km s-1, while stars just above the turn-off are already significantly slower, with values between 4.6 and 4.9  km s-1. Along the subgiant branch rotation tends to drop down, and for stars with (BV) > 1 only upper limits can be found, including for the clump stars (vsini ≤ 1.5km s-1). Most of the stars in this last group are in common with our sample.

To rule out activity-related rotational modulation as the cause of the RV variations in our data, we investigated chromospheric activity by measuring the variations of the core of Hα with respect to the continuum. Using public data with known correlations between activity indicators and RVs, we verified that such correlations could be still recorded at low S/N level of the M 67 spectra. Of our targets, S364 and S978 show a variability in Hα of 2%, YBP1514 and YBP1194 of 3% without significant periodicity and YBP401 of 4%, exhibiting all a very low activity level, while for YBP778 Hα variability is slightly higher, with a value of 7%. The fact that these stars are of solar age and that our research is focused on finding giant planets with an expected RV variability of tens of  m s-1 makes the contamination by activity negligible.

4.3. Stars with long-term RV variability

thumbnail Fig. 6

RV time series for S815 (left) and YBP2018 (right). For this latter a tentative Keplerian solution is overplotted in blue. Same symbols as in Fig. 3.

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The turn-off star S815 shows a peak-to-peak RV variation of the order of ~700  m s-1 (see Fig. 6). This star is retained in the single-star sample, although the amplitude of RV values is possibly too high for a planet. Moreover, the RV measurements would indicate a rather high eccentricity.

The MS star YBP2018 presents peak-to-peak RV variations on the order of ~400  m s-1 and appears to have almost completed one orbit. Figure 6 shows the RV measurements with a tentative Keplerian solution, resulting in an orbiting object with a minimum mass of ~11.0 MJup  and a period of ~2487 days. The residuals have an rms of ~30.0 m s-1, but the periodogram of the residuals does not show any clear periodicity. Extensive follow-up over several years is required for this star to understand the nature of the companion candidate.

thumbnail Fig. 7

Left: RV time series with the fitted linear trend of YBP1062 overlaid. Right: periodogram of the residuals after the RV trend has been removed. Same symbols as in Fig. 3.

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The MS stars YBP1062 and YBP1137 exhibit a trend in RV measurements of -28.75 m s-1/yr and 10.57 m s-1/yr. Figures 7 and 8 show the RV time series with the fitted linear trend overlaid. Although the residuals of the linear fit present an RV variability of 33.36 m s-1 for YBP1062 and 18.00 m s-1 for YBP1137, the periodogram of the residuals for the two stars does not reveal any significant peaks.

thumbnail Fig. 8

Left: RV time series with the fitted linear trend of YBP1137 overlaid. Right: periodogram of the residuals after the RV trend has been removed. Same symbols as in Fig. 3.

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The evolved star S488 also shows a high RV variability when compared to the measurement errors but caution is necessary with this star, which is located at the tip on the red giant branch. Dupree et al. (1999) found a strong Ca II emission-line with no visible change in the line asymmetries with time for this star, suggesting the presence of outward mass motions.

When we compute a Lomb-Scargle periodogram, a peak is present at ~2257 days. At this period, the measurements baseline is not yet long enough to constrain any significant orbital solution. A tentative Keplerian curve is given in Fig. 9 and corresponds to an object with a minimum mass of ~14.0 MJup  and a period of ~2332 days. The residuals have an rms amplitude of ~55 m s-1, and when the main signal is removed, the periodogram of the residual shows a peak at ~95.03 days with a lower significance close to a 0.05 FAP level. Additional observations are needed to draw further conclusions.

5. Planet frequency

thumbnail Fig. 9

Phased RV measurements and Keplerian best fit (left), periodogram of the RV data (center), and periodogram of the residuals for S488.

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A series of simulations based on a Monte Carlo approach have been carried out to determine detection limits for the RV data as a function of planet mass and planet period, and to derive a trustworthy estimate of the occurrence rate of giant planets for our RV survey. Understanding the frequency of different types of planets around stars of different mass can provide important clues about the processes of planet formation and evolution. Moreover, the direct comparison with similar analyses on field star samples can reveal important indications about the influence of the stellar birth environment on the evolution of planetary systems.

In general, the determination of the detection efficiency for an RV survey is based on the ability to recover a planetary signal with a given level of statistical significance. This translates into lower limits on the detectable companion mass as a function of orbital period. Several authors (e.g., Cumming et al. 2008; Howard et al. 2011) have presented statistical analyses of their planet surveys and discussed different methods to derive limits on companion detectability and unbiased distributions for a number of RV planet surveys. They used mainly two approaches: one based on χ2 and F-tests to detect excess residuals above an assumed Gaussian noise (Lagrange et al. 2009; Sozzetti et al. 2009), and the other approach is based on a periodogram analysis to identify significant periodicity (Cumming 2004; Narayan et al. 2005; Mortier et al. 2012). For our project, the second approach was selected for all the stars with enough data points for a reliable periodogram analysis. For the stars where the periodogram was not feasible because of the combined effect of poor sampling and the small number of observations per star, we evaluated the detection limit using the variability of the RV values with respect to the measurement errors.

5.1. Method

In order to derive the detectability of planetary signals, we computed synthetic datasets, simulating a series of mass and period data pairs (~106 values) of our “potential planets”, which are uniformly distributed in a logarithmical mass range of 0.2–10.0 MJup  and in a linear period range of 1.0–1000 days. From the real measurements of each star we retain the observation dates (expressed in Baricentric Julian Date) and the corresponding measurement errors, which we inflated as explained in Sect. 3. For random choices of the planet mass-period pairs and assuming eccentric orbits, we calculated the contribution to the radial velocity amplitude K from a giant planet using the relation (1)where M is the mass of the host star that we obtained from isochrone fitting. A random distribution of the orbit inclination was also assumed, and the eccentricity e was allowed to vary randomly between 0.0 <e< 0.5. Then, we derived the synthetic planetary signals following the equation for eccentric Keplerian orbits, (2)where a = Kcosω, b = −Ksinω and c = Kecosω + γ. Here, K is the RV amplitude, e the eccentricity, ω the longitude of periastron, γ the systemic velocity of the system, ν(t) the true anomaly, which is a function of t, P, and e, and t0 is the time of periastron passage. The latter was selected randomly in the time span of the observations, and γ was allowed to vary around the RV value of the M 67 cluster obtained in Pasquini et al. (2012). We then degraded the obtained RVs by adding noise corresponding to the actual measurement error of the real observations.

5.1.1. Stars with at least ten data points

A periodogram-based analysis (Scargle 1982) was applied to each synthetic dataset to verify whether the simulated planet was observable. This approach was chosen for all the stars with enough measurements for a reliable periodogram analysis. We note that this is the same procedure as we applied for the analysis of the RV measurements in Sect. 3.

For a given mass and period values, we considered a planet to be detected if we could obtain a signal from the periodogram analysis that had a power higher than the power associated with a 0.01 FAP. For each star 106 trials were used.

In the two-dimensional space of orbital period and planet mass, we consider a grid of period and log-spaced mass cells within which the planet detectability (or detection efficiency, Eij) is individually computed as the number of the potentially detected planets with respect to the total simulated planets in each bin of mass and period. On the base of this analysis, the detection efficiency was carried out for 14 MS stars and 10 evolved stars. Figures A.1 and A.2 show the detection efficiencies for the 24 stars as color contours from 0.0 to 1.0. The red regions have a 100% detectability of planets, and blue regions have low detectability. This means that in red regions (high detectability) all potential planets at the given period and mass would be detected. In the blue regions (low detectability) the detection efficiency decreases, and we are not able to discover their presence at high confidence. In Figs. A.1 and A.2, the resulting distribution of the planet detection efficiency clearly reduced with decreasing planet mass and with increasing period. This is due to the insufficient number of measurements, to the distribution of the observations, and to the weak RV signal. Moreover, windows of poor detectability in the period-mass grid occur for two main reasons: the data structure (number of observations and phase coverage), and the one-year seasonal period that affects any ground-based observing program.

5.1.2. Stars with poor sampling and few observations

In order to take into account the contribution of stars with poor sampling and few observations, we derived the number of detectable planets using the measurements rms. We considered the same grid of period and log-spaced mass cells as described in Sect. 5.1. In each cell of the mass-period grid, we evaluated the average rms of the synthetic radial velocities for the simulated planets (RMSsim). We set our detection threshold by identifying for each star the mass-period cells with synthetic average RV variation more than three times higher than the estimated errors (RMSsim > 3σcorr) of our real measurements. Inflated measurements errors were used in the analysis.

All potential planets with RMSsim smaller than 3σcorr were instead considered undetectable.

Finally, we folded the results of all the stars by obtaining the mass-period cell-matrix M. The value for each Mij cell represents the total number of poorly sampled stars for which planets in that cell would be detected.

As an example, the detection regions for a star of the sample derived using the RV rms analysis is shown in Fig. 10. In the red area the rms of the simulated RV values (RMSsim) is more than three times higher than the real measurements error (σcorr): all hypothetical planets in this mass-period range would be detected. In the blue ruled area the rms of the simulated RV values (RMSsim) is lower than 3σcorr: potential planets in this mass-period range cannot be detected with our observations.

thumbnail Fig. 10

Planet detection regions for a star of the sample derived using the RV rms analysis. Red area: the rms of the simulated RV values is more than three times higher than the real measurement error, thus all potential planets can be detected. Blue ruled area: the rms of the simulated RV values is lower than three times the real measurement errors. Potential planets in this mass-period range cannot be detected with our observations.

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5.1.3. Planetary occurrence

We computed the planet occurrence rate γ(P,M), that is, the fraction of stars of our survey that are orbited by giant planets in the selected period-mass ranges, using the following formalism. Considering the 24 stars analyzed with the Lomb-Scargle method, we derived the completeness, expressed as detectable planetary number, R,k, for each k star. First we weighted the calculated detection efficiency with the mass-period distribution of planets derived from the relation of Cumming et al. (2008): dfM− 0.31 ± 0.2P0.26 ± 0.1dlog Mdlog P. Therefore we defined (3)where the sum is evaluated over the entire mass-period bins. Eij corresponds to the detection efficiency for each period-mass cell, Dij represents the mass-period distribution of planets within each bin and is calculated by (4)The normalization constant c is defined conveniently inside our mass-period domain by the relation (5)Finally, we summed the values obtained from the analysis of all the MS and giant stars (G) as (6)RMStot and RGtot can be interpreted as the number of planets that would be detected if every star in the sample were hosting a planet. We imposed the result to be proportional to the number of real detected planets in the seven-year-long RV survey (three MS and two giant stars): (7)Therefore, the proportional constants γMS and γG represent an estimate of the planet occurrence rate of our survey for the MS and G stars respectively. In the analysis, turn-off stars with 12.5 ≤ MV ≤ 13.5 and 0.540 ≤ (BV) ≤ 0.640 were considered part of the MS sample, and the others were considere part of the G sample.

Subsequently, we decided to include a correction for the total detection efficiency to take the contribution of the stars with few observations and poor sampling into account in computing the planet occurrence rate.

Two cases were evaluated.

In the first, the planet occurrence among the MS stars (NMS = 14) and the evolved stars (NG = 10) was rescaled with the ratio of NMS or NG over the total number of stars considered in the analysis: 14 of 56 for the MS and 10 of 20 for the giant stars. This corresponds to the more conservative approach, where all the stars with few observations do not have a companion.

In the second case, we instead decided to rescale the detection efficiency for each cell Eij as (8)where Mij is the number of stars with potentially detectable planets for each mass-period cell calculated using the method based on the RV value rms. In this case, only stars with few observations and poor sampling were considered. Nstars is the number of the stars with potentially detectable planets obtained with the periodogram-based analysis.

5.2. Discussion

When we consider only the 14 MS and the 10 evolved stars described in the previous section, the planet occurrence in our survey results in the values of % for the MS and % for giants. The errors on the number of found planets are calculated following the prescription of Gehrels (1986). Combining the values for MS and giants gives a total occurrence rate of %. These 24 objects represent the fraction of the stars with a detection efficiency high enough for the number of observations to observe giant planets in the selected range of mass and period (see Figs. A.1 and A.2).

Applying then the correction for the detectability based on those stars that have fewer observations, we obtained the following values for the two considered approaches. In the more conservative case, without further detections, the planet occurrence becomes ~14.6% for the MS stars, ~21.9% for the giant stars, and ~16.3% for the whole sample.

In the more general case, the procedure previously described instead gives a giant planet occurrence of ~15.8% for the MS stars and ~23.0% for the evolved stars. When referring to the whole sample, the occurrence is ~18.0%.

The values from the latter more general analysis are finally considered as the final results of our study. Interestingly, they are similar to the results of RV surveys around FGK field stars that show exoplanet rates of ~13% for Jupiter-mass stars in approximately the same range of periods (Mayor et al. 2011; Cumming et al. 2008).

Moreover, when we investigated only the frequency of hot Jupiters around MS stars of our survey and exactly repeated the procedure described in the previous sections, but focusing on objects with periods shorter than 10 days, we found a hot Jupiter occurrence rate of ~5.1% for the conservative approach and of ~5.7% for the more general case. These values appear to be higher than what is observed in field stars (Wright et al. 2012; Howard et al. 2011). About this argument in particular, we refer to the discussion presented in our parallel work (Brucalassi et al. 2016). We pointed out in that paper that the high rate of hot Jupiters could be favored by a formation scenario dominated by strong encounters with other stars or binary companions and subsequent planet-planet scattering, as predicted by N-body simulations. In this context, we should consider that rescaling the actual M 67 detectability with the mass-period distribution derived by Cumming et al. (2008) for the field stars as done in the previous section could produce a biased result. However, future investigations and a larger number of planet detections in stars cluster are required to assess this hypothesis.

Finally, it is worth to point out that we did not find any clear detection of long-period giant planets around MS stars, possibly because the sensitivity of our survey decreases heavily for long-period planets. However, the recent discovery in the Praesepe cluster of a second massive outer planet around Pr0211 that hosts a close hot Jupiter on a slightly eccentric orbit (Malavolta et al. 2016) suggests that further long-term monitoring could yield indications of interesting discoveries in OCs.

6. Summary and conclusion

We have presented the results of a long-term search program for giant planets in the solar-age, solar-metallicity open cluster M 67.

Five different instruments were used, and after finding proper zero-point corrections to HARPS, 1145 observations for 88 stars were analyzed.

The problem of combining long-term precision RV data from different instruments complicates the analysis. Zero-points offsets were derived with a limited precision, which leads to a loss of sensitivity for trends and long periods. However, this problem quite frequently occurs in long-term surveys because spectrographs receive upgrades or survey projects are transferred to new instruments. Long-term access to the same telescope or instrument configuration is therefore quite important for this type of studies.

Five stars of our sample are found to host planets. One of them (YBP401) has recently been presented in Brucalassi et al. (2016), and in that work we have refined the parameters, based on new measurements, of other two planets announced previously around YBP1194 and YBP1514 (Brucalassi et al. 2014). The other planet-host candidate S978 was discussed in this paper. We have no clear additional planet detection in our sample, but some promising or controversial cases such as YBP778 and YBP2018 call for follow-up observations. Fourteen new binaries were identified and added to the catalog of known M 67 binaries that has been created in Paper I (Pasquini et al. 2012). Moreover, we see trends in S1062 and S1137, and large RV scattering is exhibited by S815 and S488, which might be explained by stellar companions or substellar objects. However, stellar chromospherical activity and magnetic cycles may cause RV variations that might be mistaken as companions. Activity indicators such as the Ca II H&K lines, Hα, and the bisector span are fundamental to verify claimed planets from RV variability.

We provided an estimate of the planet occurrence rate γ(P,M), that is, the fraction of stars of our survey that is orbited by Jupiter planets in the ranges of period between 1.0 day and 1000 days and has a planet mass between 0.2 MJ and 10.0 MJ. Although one of the main problems of this survey was the poor and sparse sampling and the small number of observations per star, which complicates the statistical analysis and increases the uncertainty on the frequency of Jupiters in our survey, we find a total occurrence rate of Jupiter-mass planets in the M 67 sample of ~18.0% (precisely ~15.8% for the MS stars and ~23.0% for the evolved stars). It is worth noting that on average we need a minimum number of 20 observations per star to exclude Jupiter-mass planets at high confidence when a periodogram analysis is applied.

The Jupiter-mass planets in our sample imply that our results are consistent with the planet frequency of much larger surveys carried out for field star samples. For example, from the ELODIE survey, Naef et al. (2005) estimated that a fraction of 7.5 ± 1.5% stars host giant planets with periods shorter than 10 yr, while Cumming et al. (2008) derived a frequency of 12 ± 1.6% from the Keck survey and Mayor et al. (2011) 13.9 ± 1.7% from the HARPS/CORALIE survey.

As a general conclusion, our simulation study seems to confirm the recent finding (Meibom et al. 2013) that the frequency of massive planets around stars of open clusters agrees with the frequency of these planets around field stars.

However, we note that when we only investigate the frequency of hot Jupiters around MS stars of our survey, we find a hot Jupiter occurrence rate (~5.7%) that is substantially higher than what is observed in field stars (see also Brucalassi et al. 2016).

We have shown that the search for planets in open clusters is a powerful test benchmark for the theory of planet formation and stellar evolution. The new generation of spectrographs such as ESPRESSO (Pasquini et al. 2009) will extend this search more effectively. It is clear, however, that to efficiently perform a planet search survey in star clusters, a multi-object capability, even with relatively low multiplex (10–50), is desirable. Unfortunately, no such facility is currently planned.


Acknowledgments

L.P. acknowledges the Visiting Researcher program of the CNPq Brazilian Agency, at the Fed. Univ. of Rio Grande do Norte, Brazil. RPS thanks ESO DGDF, the whole GAPS-TNG community, the Hobby Eberly Telescope (HET) project, the PNPS and PNP of INSU – CNRS for allocating the observations and the technical support. M.T.R. received support from PFB06 CATA (CONICYT). We are grateful to Gaspare Lo Curto and Michele Cappetta for the support in data reduction analysis and helpful discussions.

References

Appendix A: Accompanying plots and table

Table A.1

Observed targets in M 67.

thumbnail Fig. A.1

Contours of the planet detection efficiency for the MS stars in the domains of 1–1000 days for planet period and 0.2–10 MJ for planet mass. A 0.01 FAP level has been used as detection planet threshold in the periodogram analysis. A filled circle indicates the planet position.

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thumbnail Fig. A.2

Contours of the planet detection efficiency for the evolved stars in the domains of 1–1000 days for planet period and 0.2–10 MJ for planet mass. A 0.01 FAP level has been used as detection planet threshold in the periodogram analysis. A filled circle indicates the planet position.

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thumbnail Fig. A.3

Top: Lomb-Scargle periodogram of the RV measurements, residuals, bisector span, and FWHM for YBP778. Bottom: same plots for S978. The dashed lines correspond to 5% and 1% FAPs, calculated according to Horne & Baliunas (1986) and white noise simulations.

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thumbnail Fig. A.4

Top: RV measurements versus bisector span, residuals versus bisector span, RV measurements versus CCF FWHM, and RV measurements versus Hα activity indicator for YBP778. The Hα activity indicator is computed as the area below the core of Hα line with respect to the continuum. CCF FWHM values are calculated by subtracting in quadrature the respective instrumental FWHM. The same symbols as in Fig. 4. Bottom: same plots for S978.

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All Tables

Table 1

List of the observations.

Table 2

RV measurements, RV uncertainties, and instrument.

Table 3

Top: stellar parameters of the M 67 stars that are newly found to host planet candidates. Bottom: orbital parameters of the planetary companions.

Table A.1

Observed targets in M 67.

All Figures

thumbnail Fig. 1

Histogram showing the number of observations per star for our total sample. All observations from HARPS, HARPS-N, SOPHIE, CORALIE, and HET HRS are included in the plot and updated to March 31, 2015. The order number of the stars corresponds to Table A.1.

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In the text
thumbnail Fig. 2

Top: histogram showing the observed velocity dispersions (σRV) for the MS stars (pink) and giants and turn-off stars (blue) of our sample. Binary candidates and stars with high RV trend have been excluded. The black line represents the Gaussian fit centered at ~21  m s-1 of width σ ~ 7m s-1. Bottom: histogram showing the ratio of the RV dispersion (σRV) and the average measurements error (σobs). The symbols are the same as in the top panel.

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In the text
thumbnail Fig. 3

Stars with large RV or significant linear trends (suspected binaries). Black dots: HARPS measurements, red dots: SOPHIE measurements, orange dots: HARPS-N measurements, and green dots: HRS measurements. RV error bars represent σcor.

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In the text
thumbnail Fig. 4

Phased RV measurements and Keplerian best fit, best-fit residuals, and bisector variation for YBP778. Same symbols as in Fig. 3.

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In the text
thumbnail Fig. 5

Phased RV measurements and Keplerian best fit, best-fit residuals, and bisector variation for S978. Same symbols as in Fig. 4. Green dots: HRS measurements, blue dots: CORALIE measurements.

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In the text
thumbnail Fig. 6

RV time series for S815 (left) and YBP2018 (right). For this latter a tentative Keplerian solution is overplotted in blue. Same symbols as in Fig. 3.

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In the text
thumbnail Fig. 7

Left: RV time series with the fitted linear trend of YBP1062 overlaid. Right: periodogram of the residuals after the RV trend has been removed. Same symbols as in Fig. 3.

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In the text
thumbnail Fig. 8

Left: RV time series with the fitted linear trend of YBP1137 overlaid. Right: periodogram of the residuals after the RV trend has been removed. Same symbols as in Fig. 3.

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In the text
thumbnail Fig. 9

Phased RV measurements and Keplerian best fit (left), periodogram of the RV data (center), and periodogram of the residuals for S488.

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In the text
thumbnail Fig. 10

Planet detection regions for a star of the sample derived using the RV rms analysis. Red area: the rms of the simulated RV values is more than three times higher than the real measurement error, thus all potential planets can be detected. Blue ruled area: the rms of the simulated RV values is lower than three times the real measurement errors. Potential planets in this mass-period range cannot be detected with our observations.

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In the text
thumbnail Fig. A.1

Contours of the planet detection efficiency for the MS stars in the domains of 1–1000 days for planet period and 0.2–10 MJ for planet mass. A 0.01 FAP level has been used as detection planet threshold in the periodogram analysis. A filled circle indicates the planet position.

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In the text
thumbnail Fig. A.2

Contours of the planet detection efficiency for the evolved stars in the domains of 1–1000 days for planet period and 0.2–10 MJ for planet mass. A 0.01 FAP level has been used as detection planet threshold in the periodogram analysis. A filled circle indicates the planet position.

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In the text
thumbnail Fig. A.3

Top: Lomb-Scargle periodogram of the RV measurements, residuals, bisector span, and FWHM for YBP778. Bottom: same plots for S978. The dashed lines correspond to 5% and 1% FAPs, calculated according to Horne & Baliunas (1986) and white noise simulations.

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In the text
thumbnail Fig. A.4

Top: RV measurements versus bisector span, residuals versus bisector span, RV measurements versus CCF FWHM, and RV measurements versus Hα activity indicator for YBP778. The Hα activity indicator is computed as the area below the core of Hα line with respect to the continuum. CCF FWHM values are calculated by subtracting in quadrature the respective instrumental FWHM. The same symbols as in Fig. 4. Bottom: same plots for S978.

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In the text

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