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Home All issues Volume 565 (May 2014) A&A, 565 (2014) A15 Full HTML
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Issue
A&A
Volume 565, May 2014
Article Number A15
Number of page(s) 14
Section Planets and planetary systems
DOI https://doi.org/10.1051/0004-6361/201323058
Published online 21 April 2014

© ESO, 2014

1. Introduction

Circumstellar debris discs around main-sequence stars are composed of second-generation dust produced by the attrition of larger bodies (Backman & Paresce 1993), which are remnants of primordial protoplanetary discs (Hernández et al. 2007). Debris discs can be detected and analysed based on their thermal infrared emission from the constituent dust particles. Around 16.4+2.8-2.9\hbox{$^{+2.8}_{-2.9}$}% of main-sequence Sun-like stars have evidence of circumstellar dust emission at 70 μm with Spitzer (Trilling et al. 2008). From observations of FGK stars by the Herschel1 DUNES survey an incidence of 20.2 ± 2.0% was measured (Eiroa et al. 2013), whereas the DEBRIS survey measures an incidence of 16.5 ± 2.5% (Sibthorpe et al., in prep.).

Many circumstellar discs around Sun-like stars are seen to have two temperature components, which has been interpreted as arising from two distinct belts at different stellocentric radii (Chen et al. 2009; Morales et al. 2011). The cool discs are more commonly seen and analogous to the Edgeworth-Kuiper belt (EKB) in our own solar system (Greaves & Wyatt 2010; Vitense et al. 2012). The EKB’s existence has been inferred from the detection of over a thousand trans-Neptunian objects2, through ground-based surveys and in situ dust measurement from Voyager 1 and 2 (Gurnett et al. 1997) and New Horizons (Poppe et al. 2010; Han et al. 2011), although direct observation of the dust emission from the EKB is confounded by the bright foreground thermal emission from the zodiacal dust in the inner solar system (Backman et al. 1995). The less commonly seen warm debris disc asteroid-belt analogues, which are more difficult to observe around other stars due to the larger flux density contribution from the stellar photosphere at mid-infrared wavelengths compared with the dust excess, have been detected around ~2% of Sun-like stars (3/7 FGK stars with 24 μm excess and Tdust > 100 K from a sample of 184, Trilling et al. 2008).

Exoplanets3 around Sun-like stars have been identified through radial velocity (e.g. Marcy & Butler 2000; Tinney et al. 2001; Mayor & Queloz 2012) or transit surveys e.g. CoRoT (Auvergne et al. 2009), WASP (Pollacco et al. 2006), HAT (Bakos et al. 2002) and Kepler (Borucki et al. 2011). See Perryman (2011) for a summary of exoplanet detection techniques. The majority of all exoplanet searches have taken place at optical wavelengths, with a sample focus on mature, Sun-like stars as the most suitable candidates for the radial velocity detection technique. A stars are avoided as their atmospheres lack the narrow lines necessary for radial velocity detections through accurate Doppler measurements, but these stars are prime candidates for direct imaging surveys, resulting in the detection of several exoplanet systems around debris disc host stars, e.g. Fomalhaut (Kalas et al. 2008), HR 8799 (Marois et al. 2008), β Pic (Lagrange et al. 2010) and HD 95086 (Rameau et al. 2013). M stars have likewise been avoided because they exhibit high levels of stellar variability and because of their emission peaks in the near-infrared, which render them noisy and faint, although great efforts have been made to overcome these problems because of their sheer number and potential to yield low-mass planets through either transit or radial velocity detections (e.g. Reiners et al. 2010; Rodler et al. 2011; Giacobbe et al. 2012; Anglada-Escudé & Tuomi 2012). This has led to unavoidable bias in the types of stars around which exoplanets have been studied. Comparative analysis or aggregation of results from radial velocity surveys is further complicated by both the differences in sensitivity and the variable baseline of observations for the stellar samples, although broad conclusions, for instance on the absence of Jupiter analogues around most nearby stars, may be drawn (Cumming et al. 1999; Fischer et al. 2014). Recent results from an analysis of microlensing surveys suggest that almost all stars may have one or more exoplanets, with low-mass planets being much more common than Jupiter-mass ones (Cassan et al. 2012). On the other hand, long-term monitoring from the ground has constrained the likelihood of Jovian planets on long orbits (3−6 AU) to <30% of the stellar systems surveyed (Wittenmyer et al. 2011), suggesting that exoplanetary systems very like our own may be rare, a result supported by recent direct imaging searches (Janson et al. 2013).

Given that planets are the end state of the agglomeration of smaller bodies from dust to planetesimals (neglecting as a detail the capture of an envelope from the protoplanetary disc for gas giants), and debris discs are the result of collisional grinding of these planetesimals into dust, one might expect the presence of planets and debris discs to be correlated. This expectation is strengthened by the direct imaging of several exoplanet systems around debris disc host stars, as previously noted, and indirectly by the structural features observed in many debris discs (warps, off-sets, asymmetries). These features have generally been thought to arise from the gravitational perturbation of exoplanets (see reviews by Wyatt 2008; Krivov 2010; Moro-Martin 2013), although remnant gas may offer an alternative explantation in some cases (e.g. Lyra & Kuchner 2013). Evidence of disc structures, particularly in the sub-mm, has sometimes weakened upon closer scrutiny, for example the SCUBA detected “blob” in Vega’s disc (Holland et al. 1998; Wyatt 2003; Piétu et al. 2011; Hughes et al. 2012) or the clumps in the disc of HD 107146 (Corder et al. 2009; Hughes et al. 2011), requiring that caution be exercised when attributing these structures to unseen planetary bodies. Until recently, no clear correlation had yet been established between the presence of debris discs and the presence of planets (Greaves et al. 2006; Moro-Martín et al. 2007; Bryden et al. 2009; Kóspál et al. 2009), and larger scale direct imaging surveys have found little evidence of massive planets around debris disc host stars (Wahhaj et al. 2013; Janson et al. 2013). However, new analysis by Maldonado et al. (2012) identified a trend between the presence of a debris disc and cool Jupiter exoplanet around a star, whilst Wyatt et al. (2012) identified a possible trend between cool dust and low-mass planet host stars.

Direct measurement of the spatial distribution of debris in other stellar systems will reveal whether our own EKB is common or unusual. The EKB and its interaction with the outer planets is thought to have played a significant role in the development of life on Earth, having supplied a significant fraction of the impactors thought to have been involved in the Late Heavy Bombardment (Gomes et al. 2005), dictated the development of the terrestrial planets (Walsh et al. 2011), and continues to provide bodies for the short-period comet population through interaction with Jupiter (Horner & Jones 2009). It may also have been involved in the hydration of Earth (Morbidelli et al. 2000), a topic that is still widely debated (Raymond et al. 2004, 2006, 2007; O’Brien et al. 2006; Horner et al. 2009; Bond et al. 2010; Horner & Jones 2010; Izidoro et al. 2013). As such, the nature of exo-EKBs may play a vital role in the determination of the habitability of their host systems (e.g. Horner & Jones 2010), and it is therefore vital that we are able to judge whether the solar system’s architecture and EKB are the norm, or unusual.

The Herschel (Pilbratt et al. 2010) guaranteed time (GT) debris disc programme and the open time key programmes Disc Emission from Bias-free Reconnaissance Infrared Survey (DEBRIS4; Matthews et al. 2010) and DUst around NEarby Stars (DUNES5; Eiroa et al. 2010, 2013) have observed nearby Sun-like stars using the Photodetector Array Camera and Spectrometer instrument (PACS; Poglitsch et al. 2010) at far-infrared wavelengths searching for excess emission caused by circumstellar dust discs analogous to the solar system’s EKB (Vitense et al. 2012). In this work, we have examined all of the stars from the DEBRIS, DUNES and GT programmes that are currently believed to host exoplanets.

In Sect. 2, we present the observations used in this work, the data reduction process, and the stellar physical parameters to be compared with the dust emission. In Sect. 3, a summary of the assumptions used to fit models to the new Herschel photometry are explained and the calculated disc temperatures and masses are shown. In Sect. 4, a comparison of the observed disc fractional luminosities (or 3σ upper limits in the case of non-detections) from Sect. 3 and the stellar properties from Sect. 2 is presented. Finally, in Sect. 5, we present our conclusions and recapitulate our findings.

2. Observations and data reduction

The observations used in this work have been taken from the DEBRIS and DUNES open time key programmes and the debris disc guaranteed time programme. The sample comprises the 14 stars from DEBRIS and 21 stars from DUNES that are main-sequence stars within 25 pc of the Sun with radial-velocity-detected exoplanets. We also added τ Ceti and ϵ Eridani from the guaranteed time key programme. We included both α Centauri B and ϵ Eridani in the sample although there is some doubt about the existence of their respective planets: α Centauri B; Dumusque et al. (2012); Hatzes (2013), and ϵ Eridani; Hatzes et al. (2000); Moran et al. (2004); Zechmeister et al. (2013). There are no A stars that match the criteria for inclusion; although Fomalhaut and β Pictoris both lie within the volume, their planets are directly imaged. Likewise, around G stars, GJ 504 hosts a cold Jovian planet (Kuzuhara et al. 2013) and HN Peg has a borderline brown dwarf/Jovian companion (Faherty et al. 2010). The range of spectral types represented in the sample is therefore F to M. Several exoplanet host stars have not been included, for example HD 136352, HD 147513, and HD 190360 (Wyatt et al. 2012), even though they lie within the volume explored by DEBRIS and DUNES, because they all lie towards regions of bright far-infrared background contamination from Galactic emission and were therefore omitted from observation by the Herschel programmes.

Herschel PACS 70/160 and/or 100/160 scan map observations were taken of all stars except 51 Peg, which was observed in chop-nod mode with the 100/160 channel combination during the science demonstration phase (SDP). The observation parameters for the DEBRIS and DUNES targets were slightly different: for DEBRIS targets, each scan map consisted of two repetitions of eight scan legs of 3′ length, with a 4′′ separation between legs, taken at the medium slew speed (20′′ per second), whereas DUNES targets had the same parameters, but used ten legs per scan map and the number of repetitions was dictated by the requirement to detect the stellar photosphere at 100 μm with a signal-to-noise ratio (S/N) ≥ 5. The PACS 100/160 scan map observations of q1 Eri were observed as part of the calibration effort during the SDP phase using scans with 16 legs of 3.9′ with 4′′ separation between the legs, also at the medium slew speed. For the GT programme, the targets were observed twice, with each scan map consisting of 11 scan legs of 7.4′ length, with a 38′′ separation between legs, at the medium slew speed. Each of the GT scans was repeated 11 times. In all cases, each target was observed at two array orientation angles (70° and 110° for DEBRIS and DUNES, 45° and 135° for GT), which were combined into a final mosaic to improve noise suppression and assist in the removal of instrumental artefacts and glitches. Several of the targets presented in this work have been observed by Herschel Spectral and Photometric Imaging REceiver (SPIRE; Griffin et al. 2010; Swinyard et al. 2010), but because of the sparse coverage of the sample with that instrument (4/37 targets) we decided to focus here on the PACS photometry to ensure consistency in the data set used for the sample analysis. A summary of all observations is presented in Table 1.

Table 1

Summary of Herschel PACS observations of the target stars.

All observations were reduced interactively using version 8.1.0 of the Herschel Interactive Processing Environment (HIPE, Ott 2010) using PACS calibration version 32 and the standard scripts supplied with HIPE. Individual PACS scans were processed with a high-pass filter to remove background structure, using high-pass filter widths of 15 frames at 70 μm, 20 frames at 100 μm, and 25 frames at 160 μm, equivalent to spatial scales of 62′′, 82′′ , and 102′′. In the case of ϵ Eridani, with its much larger disc (~1′ in diameter), a high-pass filter width of 50 frames, equivalent to 202′′, at both 70 and 160 μm was adopted to avoid removal of disc flux by the filtering. For the filtering process, regions of the map where the pixel brightness exceeded a threshold defined as twice the standard deviation of the non-zero elements in the map were masked from the high-pass filter task. The two individual scans of each target were mosaicked to reduce sky noise and suppress the striping due to detector scanning. Final image scales were 1′′ per pixel at 70 μm and 100 μm and 2′′ per pixel at 160 μm compared with native instrument pixel sizes of 3.2′′ at 70 μm and 100 μm and 6.4′′ at 160 μm.

Point source flux densities were measured with aperture radii of 4′′, 5′′, and 8′′ at 70 μm, 100 μm, and 160 μm to maximize the S/N of the source (Eiroa et al. 2013). The mean full width at half maximum (FWHM) of the PACS instrument is 5.61′′, 6.79′′ and 11.36′′ in the three bands. Extended sources, identified by comparison of a 2D Gaussian fit with the source profile to the PSF FWHM in each band, were measured with varying aperture radii depending on the disc extent. The sky background level and rms noise for each target were estimated from the mean and standard deviation of the total flux density in 25 boxes of dimensions 7 × 7 pixels at 70 μm, 9 × 9 pixels at 100 μm, and 7 × 7 pixels at 160 μm, chosen to match the aperture size of point sources. The boxes were placed randomly around the central area of the mosaic within a region 30′′ to 60′′ from the source position, or 90′′−120′′ in the case of ϵ Eri, to avoid the central source and edges of the maps where the noise increases due to the non-uniform map coverage.

The appropriate aperture corrections were applied to the flux densities based on the PACS aperture photometry calibration (factors of 0.476, 0.513, and 0.521 for point sources, respectively). Correction factors appropriate to the aperture radius based on the point source encircled energy fraction were applied to the extended sources, which, although only an approximation to the true correction, is widely used. A calibration uncertainty of 5% was assumed for all three PACS bands (Balog et al. 2014). The flux densities presented in Table 2 have not been colour corrected.

The stellar photosphere contribution to the total flux density was calculated from a synthetic stellar atmosphere model interpolated from the PHOENIX/Gaia grid (Brott & Hauschildt 2005). All stars in the sample match the criteria of d< 25 pc and luminosity class V except for HD 217107, which is luminosity class IV. The stellar models were scaled to the combined optical, near-infrared, and WISE data, where the WISE bands were not saturated or showed evidence of excess emission, following Bertone et al. (2004). The stellar physical parameters are given in Table 3. For the DUNES observed targets, the stellar parameters were taken from Eiroa et al. (2013). For the DEBRIS observed targets, the stellar parameters were calculated from archival data using the same procedure as for the DUNES targets, see Eiroa et al. (2013) for details of the method (Maldonado, priv. comm.). Stellar distances were taken from the revised Hipparcos catalogue (van Leeuwen 2007). Stellar ages were computed following Eq. (3) in Mamajek & Hillenbrand (2008) for the Ca ii based values, whilst the X-ray stellar age was calculated through the relation between X-ray emission and stellar age according to Sanz-Forcada et al. (2011), where most of the ages displayed in Table 3 were calculated. Newly calculated X-ray ages are provided for HD 19994, HD 20794, HD 33564, HD 40307, HD 69830, 70 Vir, GJ 581 and HD 192310 according to the method in Sanz-Forcada et al. (2011).

3. Analysis

A determination of the presence of excess emission from each star was made on the basis of the excess significance, or χ value. The significance was calculated using the PACS 100 and 160 μm flux densities and uncertainties in the following manner: χλ=(Fλ,obs−Fλ,pred)σλ,obs2+σλ,pred2+σλ,cal2,\begin{equation} \chi_{\lambda} = \frac{\left(F_{\lambda, \rm obs} - F_{\lambda, \rm pred}\right)}{\sqrt{\sigma^{2}_{\lambda, \rm obs} + \sigma^2_{\lambda, \rm pred} + \sigma^2_{\lambda, \rm cal}}} \label{eqn_chi} , \end{equation}(1)where Fλ,obs and Fλ,pred are the observed and predicted (photosphere) flux densities at the wavelength under consideration and the uncertainty is the quadratic sum of the uncertainties of the observation σλ,obs, the stellar photosphere model σλ,pred, and calibration σλ,cal.

The stars in the sample with χλ > 3 at either (or both) PACS wavelength(s) were classed as having significant excess emission. The disc fractional luminosity was calculated by fitting a black-body emission model parameterised by the dust temperature, Td, and fractional luminosity, LIR/L⋆, to the error-weighted Spitzer MIPS 70 μm and Herschel PACS photometry.

For non-excess sources, the dust temperature was assumed to be 37 K, and a 3σ upper limit for the fractional luminosity was then calculated. Adopting a dust temperature of 37 K for calculation provides a strict minimum for the dust fractional luminosity of the non-excess stars based on the observed 100 μm flux density. The upper limits calculated here (presented in Table 2) are therefore consistent with the typical dust temperature we would expect to observe for debris discs around Sun-like stars.

Although crude, this model allows a consistent and uniform calculation of the dust properties from the observed flux densities, which is necessary for the statistical approach to identify trends in the data without getting distracted by the intricate details of individual sources, such as extended emission or material composition.

We note that for disc radii it is well known that an assumption of black-body emission can underestimate the radial distance of the dust from the star by a factor of 1–2.5 (for A stars, Booth et al. 2013) or a factor of up to 4 around G and M stars, for instance 61 Vir (Wyatt et al. 2012), HD 207129 (Marshall et al. 2011; Löhne et al. 2012), and GJ 581 (Lestrade et al. 2012). We derived radial locations for the dust from the assumption of thermal equilibrium between the dust grains and the incident radiation as a minimum possible orbital distance for the emitting dust in these systems (Backman & Paresce 1993).

We calculated values for the basic physical parameters of the discs, which are presented in Table 2 (dust fractional luminosity, dust temperature, and dust radius) from the black-body fit to the spectral energy distribution and the assumption of black-body absorption and emission for the dust grains. We used the disc fractional luminosity for comparison with the stellar and exoplanet parameters, breaking down the observed sample of exoplanet host stars into three subsamples (low-mass planets, cool Jupiters, and hot Jupiters) to check for evidence of the trends identified in recent articles (e.g. Maldonado et al. 2012; Wyatt et al. 2012).

4. Results

We have detected far-infrared excess emission with χ> 3 from ten of the 37 systems in this sample. HD 69830 is known to have a warm debris disc (Beichman et al. 2005), bringing the total to 11 systems that have both a debris disc and exoplanet(s). The histogram presented in Fig. 1 illustrates the distribution of the measured (non-)excesses at 100 and 160 μm, with a long tail toward higher significances, as expected. Fitting Gaussian profiles to both distributions reveals that at 100 μm the distribution is peaked at χ100 = −0.5 with σ100 = 1.25, whilst at 160 μm the distribution peaks at χ160 = 0.0 with σ160 = 1.0. The peak position and width of the Gaussian are measures of the goodness of our stellar photosphere and uncertainty estimates, respectively. We expect (assuming normally distributed uncertainties) that both χ distributions would peak at χ = 0 with σ = 1. The discrepancy at 100 μm might be ascribed to a systematic underestimation of the errors, which is hidden at 160 μm by the larger uncertainties, but this same trend is seen in the larger DUNES sample of 133 stars (Eiroa et al. 2013). A physical explanation of the shift of the peak to χ100< 0, implying a deficit in the measured flux density compared with the Rayleigh-Jeans extrapolation of the stellar photosphere model from 50 μm, might be found in the fact that the photosphere models do not take into account the decrease in brightness temperature in the higher layers of the stellar photosphere of Sun-like stars. This decrease in brightness temperature has the effect of reducing the observed flux density below that expected from an extrapolated fit to shorter wavelength measurements, with the greatest effect around 150 μm (Eddy et al. 1969; Avrett 2003; Liseau et al. 2013). The magnitude of the deficit is ~20%, and similar to the magnitude of the measured uncertainty at 100 μm, around 1 to 2 mJy for these stars. If the magnitude of this effect were to be dependent on stellar spectral type, it would also broaden the χ distribution. The negative bias would be statistically significant should the underlying distribution be Gaussian. Because of the many unknowns in this problem, we adopted the conservative approach of noting that the sample standard deviation is larger than the negative absolute value.

thumbnail Fig. 1

Distribution of the significances presented in Table 2 at 100 μm (in blue, hatching top right to bottom left) and 160 μm (in red, hatching top left to bottom right). Debris disc stars with χ values higher than ten have been added to the right-hand side bin.

Examining only the FGK stars (three of the 37 stars, one with an excess, are M dwarfs), we obtain a statistical incidence of circumstellar dust of 29.4 ± 9.3% (10/34), consistent with the general incidence of 20.2 ± 2.0% from the DUNES survey (Eiroa et al. 2013). Previous Spitzer results for 45 FGK exoplanet hosts record an incidence of 20.8+7.0-4.6\hbox{$^{+7.0}_{-4.6}$}% (Trilling et al. 2008) and 14.5 ± 3.5% 117 FGKM stars by Kóspál et al. (2009). It should be noted that the detection frequencies quoted for various disc surveys are strongly dependent on the sensitivities, samples, and observing strategies adopted in each. Comparable incidences between surveys may therefore be coincidental due to survey differences.

From our analysis of the entire sample, we have detected discs with fractional luminosities in the range 2.4 × 10-6 to 4.1 × 10-4 and temperatures from 20 K to 80 K. The 3σ upper limits on the non-detections typically constrain the fractional luminosity to a ~few × 10-6, equivalent to <10-5 M⊕. The range of dust temperatures is broader than might be expected for typical dust temperatures for debris discs, which have the peak of their emission in the far-infrared. In the unusually cold case of HD 210277, the dust temperature can be ascribed to the nature of the source, which is a candidate “cold debris disc” (Eiroa et al. 2011; Krivov et al. 2013). Four of the circumstellar discs are new detections by Herschel: HD 20794, HD 40307, GJ 581, and HD 210277, whilst two more have been confirmed by Herschel DUNES after marginal detection by Spitzer: HD 19994 and HD 117176. Several of the Herschel discovered discs are covered in individual papers; for example HD 210277 has been identified as one of the DUNES “cold debris disc” candidates in Eiroa et al. (2011), HD 20794 in Wyatt et al. (2012) and GJ 581, an M-dwarf debris disc, in Lestrade et al. (2012). The final new detection, HD 40307, was noted in the DUNES survey paper (Eiroa et al. 2013).

thumbnail Fig. 2

Filled circles denote cool debris disc systems, whilst open triangles denote fits to the 3σ upper limits at 100 μm. HD 69830, having a warm debris disc, is denoted as a filled blue triangle to distinguish it from the other far-infrared non-detections. Red data points are cool-giant-planet systems, black data points are hot-giant-planet systems, whilst blue data points are low-mass planet systems.

5. Discussion

5.1. Contamination

A critical problem with the attribution of an infrared excess to circumstellar dust is the chance of contamination by alignment along the line of sight with a background source.

The likelihood that one (or more) of the debris discs in the sample have been spuriously identified as such was calculated from the contamination probabilities within both a radius equivalent to one beam half width at half maximum (HWHM) and the positional offset between the expected and observed source position of all the debris disc stars. The source number counts in DEBRIS survey fields from Sibthorpe et al. (2012) (their equation Eq. (2)) were used to quantify the background source number density at 100 μm and 160 μm for sources with flux densities equal to or brighter than the observed excesses of the debris disc stars presented here. First, the probability of confusion for each individual source, n, was calculated, including the specific S/N and flux density, giving Pn, conf. Second, the probability that none of the sources were confused, Pnone, was calculated by multiplication of the probabilities for the individual sources, that is Pnone = P1,conf × P2,conf × ... × Pn,conf. The probability of confusion for the whole sample is then simply 1 − Pnone.

Within one beam HWHM, the probability of contamination of at least one source amongst the 37 is 1.4% at 100 μm and 8.2% at 160 μm. Within the maximum position offset (6.7′′), the probability of confusion increases to 4.8% at 100 μm and 11.0% at 160 μm. In the worst case, based on the maximum offset radius, two stars at 100 μm and four stars at 160 μm out of the 37 could be the result of contamination.

5.2. Correlations

We have plotted the calculated dust fractional luminosities (or upper limits) of the exoplanet stars against several physical parameters of the host stars and exoplanets to search for trends in the sample. For Figs. 2d−f we adopted the same exoplanet parameters to characterise each system as used in Maldonado et al. (2012), so a comparison between our findings and theirs can be made more easily. We categorised the type of exoplanet system (low-mass, hot Jupiter, or cold Jupiter) according to the planet mass where MPlanet > 30 M⊕ is a giant planet and a system with a planet of RPlanet < 0.1 AU and MPlanet > 30 M⊕ defines a hot-Jupiter system. Within the sample there are 11 low-mass planet systems, five hot-Jupiter systems, and 21 cold-Jupiter systems. Although no cold dust emission from HD 69830’s circumstellar disc has been detected, it is included as a debris disc star in the statistics but is not marked as an excess source in the plots in Fig. 2, which were based on far-infrared emission alone. To quantify the significance of any trend observed in the figures we used the Fisher exact probability test, which has the virtue (compared with a χ2 test) of producing meaningful results even for small sample sizes (N< 5), but the test only gives a probability in support of the null hypothesis (i.e. that both samples are from the same underlying distribution). For example, comparing the number of debris disc stars around the FGK exoplanet host stars in this sample (34 stars, 10 discs) with the Spitzer and Herschel DUNES frequencies (Trilling et al. 2008; Eiroa et al. 2013), we find that the resulting p-values are 0.19 and 0.34, respectively. The exoplanet host sample is not significantly different from these larger samples and can be presumed to have been drawn from the same underlying population, despite the inherent biases of being composed solely of exoplanet host stars and the difference in sensitivity of the Spitzer MIPS and Herschel PACS based surveys.

The relationship between stellar age and fractional luminosity for circumstellar discs, presented in Fig. 2a, has been explored for a broad range of ages for example by Decin et al. (2003), Hernández et al. (2007), and Wyatt et al. (2007). In this work we have used stellar ages derived from Ca ii H and K activity and X-ray luminosity taken from Eiroa et al. (2013) for the DUNES observed sources or calculated in the same manner as the DUNES sources, but based on publicly available data (Maldonado & Sanz Forcada, priv. comm.). From binning the sample into three broad age ranges, we find that the incidence of dust weakly decreases with age, albeit with error bars large enough that the incidence could be constant across the bins considered here, from 50 ± 29% (t < 3.5 Gyr) to 28 ± 12% (t = 3.5−7.0 Gyr) to 25 ± 14% (t > 7.0 Gyr). The decay of debris discs around Sun-like stars is examined in greater detail in Kains et al. (2011).

The sample of exoplanet host stars is almost evenly divided between sub- and supra-Solar metallicity, with 18 and 19 stars in each subsample, which is shown in Fig. 2b. Of the stars with higher metallicities than the Sun, five host a hot-Jupiter planet, whilst none of the 18 low metallicity stars have hot Jupiters, giving a p-value of 0.04, that is the hot Jupiters and other planets do not come from the same underlying distribution, therefore we are able to identify the well-known correlation between increased stellar metallicity and hot Jupiters from our data set (Fischer & Valenti 2005; Greaves et al. 2006; Maldonado et al. 2012). From comparing the distribution of hot and cold Jupiters versus metallicity, we find a p-value of 0.58, which means that we cannot differentiate between the stars with wide and close orbiting Jovian exoplanets from this sample.

All the low-mass planetary systems (i.e. those where the most massive planet is <30 M⊕) except α Cen B have host stars with sub-Solar metallicity (10/18), consistent with Jenkins et al. (2013). Stars hosting low-mass planets have not been found to be preferentially metal rich, unlike stars hosting high-mass planets (Santos et al. 2001; Ghezzi et al. 2010; Buchhave et al. 2011; Mayor et al. 2011). By comparing the incidence of low-mass and high-mass planets around stars with sub- or supra-Solar metallicity, we obtain a probability p-value of 0.001, suggesting that the low-mass and high-mass planet stars are not drawn from the same underlying population. This correlation between low-mass planets and low-metallicity stars could be the product of two phenomena: in a low-metallicity disc there will be fewer solids from which to form massive planetary cores that go on to become gas giant planets, making such planets rarer around those stars (Greaves et al. 2007; Wyatt et al. 2007); additionally, protoplanetary discs with lower metallicity are thought to be dispersed more easily and quickly because of the lower optical depth, so UV and X-rays penetrate farther into the disc and cause the gas loss through winds to be stronger, such that any nascent giant planet must capture its gaseous envelope more quickly because the disc dispersal occurs more rapidly in such systems, thereby limiting the number of gas giants that will form (Yasui et al. 2009; Ercolano & Clarke 2010).

We find an incidence of debris around 10/18 stars in the low-metallicity group and 2/19 in the high-metallicity group. This implies an anti-correlation between the presence of debris and metallicity, with a p-value of 0.005. The presence of brighter debris discs around low-metallicity stars could be inferred to represent the inability of the low-mass planets to scatter the dust producing planetesimals near their formation region, or via migration from a larger initial semi-major axis, as effectively as a gas giant, as proposed in Wyatt et al. (2012). The observed anticorrelation may therefore not be directly related to the properties of the debris disc and stellar metallicity, but could be a consequence of the type of planets that form around low-metallicity stars as stated above and can be explained within the context of a model in which planets form through core accretion.

The effect of the stellar temperature on the determination of the upper limit to the dust fractional luminosity can be seen in Fig. 2c. For the coolest stars in the sample, we are limited to disc brightnesses of ≥2 × 10-5, whilst at the hotter end we can put better constraints of ≥2 × 10-6 on the dust present around these stars. For most stars in our sample we obtained 3σ upper limits on the fractional luminosity of a few ×10-6, that is several ten times higher than that expected of the EKB (Vitense et al. 2012). There is no visible correlation between the stellar photosphere temperature and the presence of dust around the star. Dividing the sample by spectral type, we find debris discs around 33.3 ± 23.6% of F stars (2/6), 27.3 ± 11.1% of G stars (6/22), 33.3 ± 23.6% of K stars (2/6), and 33.3 ± 33.3% of M stars (1/3). These values are consistent with the measurements from surveys with much larger samples, e.g. Trilling et al. (2008), Kóspál et al. (2009) and Eiroa et al. (2013) for FGK stars, and Lestrade et al. (2006, 2009), Gautier et al. (2007) for M stars.

As seen in Fig. 2d, the exoplanets around the Herschel discovered debris disc stars all have masses MPlanet < 30 M⊕. Comparing the most massive exoplanet in each system with the dust fractional luminosity reveals that the stars with brighter discs generally have a low-mass planet (MPlanet < 30 M⊕), being 6/11 stars for the low-mass subset or 5/26 for the remainder of the sample. The p-value for the comparison of these two sub-samples is 0.05. Stars with only low-mass planets are more likely to harbour debris discs than stars with Jovian planet(s), consistent with the prediction of (Raymond et al. 2012) and the findings of Maldonado et al. (2012), thereby confirming the trend suggested in Wyatt et al. (2012) (based on a smaller sample of G stars).

The relationship between eccentricity, characterised by the orbital eccentricity of the innermost exoplanet, and fractional luminosity illustrated in Fig. 2e appears to favour the presence of debris discs around stars with low-eccentricity planetary systems (e < 0.2). Splitting the sample at e = 0.2, we find a higher incidence of dust in low-eccentricity systems (7/20) over high-eccentricity systems (4/17), agreeing with the predictions (for giant planets) in Raymond et al. (2011, 2012) – see Figs. 13 and 18 in Raymond et al. (2011), and similarly consistent with the results of Maldonado et al. (2012). However, putting these subsamples to the test, we find that the p-value is 0.49, which is an inconclusive result, but suggests that the two groups are more similar than not, which may be interpreted as illustrating that the known exoplanets in these systems have little dynamical influence on the visible debris.

Similarly, a comparison of the fractional luminosities of systems with hot Jupiters and those with cold Jupiters in Fig. 2f is suggestive that cold Jupiter systems have a stronger tendency to host debris discs. We see that none of the five subsets of hot Jupiter planet host stars are observed to have excess emission, whilst five of the 21 cold Jupiter planet host stars do have a detectable debris disc. In this case the Fischer test again returns an intermediate result, whose p-value is 0.54. We therefore cannot confirm the trend identified in Maldonado et al. (2012) between cool giant planets and fainter debris discs based on the observations analysed here.

6. Conclusions

We have presented Herschel PACS observations of 37 nearby exoplanet systems from the DUNES and DEBRIS samples aimed at searching for exo-EKB analogues. Excess emission attributable to the presence of a circumstellar debris disc was observed around ten of these stars; for the remaining stars we found no evidence of significant excess emission, including the non-measurement of cold emission around HD 69830, providing a tighter upper limit to any possible cold dust in that system. We improved on the upper limits for dust detection for the stars in this sample by a factor of two over previous Spitzer observations, constraining the possible flux from cold dust in all observed systems to at worst two orders of magnitude higher than that of the EKB and in several cases at levels similar to that of the EKB.

We found incidences of ~30% for cool debris discs around exoplanet host stars from the sample examined here, irrespective of the spectral type. Due to the large uncertainties in this measurement (from the small sample sizes), these values are in fact consistent with the incidence of debris discs measured by DUNES 20.2 ± 2.0% (Eiroa et al. 2013). The incidence of debris is seen to decrease around older stars, again with large uncertainties.

We identified several trends between the stellar metallicity, the presence of a debris disc, and the mass of the most massive exoplanet around the star. We found that low-metallicity stars are more likely to host low-mass planets, low-metallicity stars are also more likely to have a detectable debris disc, and that low-mass planets are more likely to be associated with a detectable debris disc. This is consistent with what would be expected from the core-accretion planet formation model. We combined these trends and developed a picture for these systems in which the gas is stripped from the protoplanetary disc too quickly for Jovian-mass planets to form and the resulting low-mass planets cannot scatter planetesimals as strongly as more massive planets if they form in situ, or as they migrate through a disc from a larger initial semi-major axis (Maldonado et al. 2012; Wyatt et al. 2012).

Furthermore, we found no significant evidence for a trend relating the eccentricity of the innermost planet with the fractional luminosity, suggesting that the known exoplanets in these systems have little influence on the visible presence of dust, which is expected because the two components are well separated. We also found no evidence to support the proposed trend between cold Jupiters and lower dust luminosities proposed in Maldonado et al. (2012), though this is expected because the sample analysed here is only a subset of those from Maldonado et al.’s work, and the newly discovered Herschel debris discs have been found exclusively around low-mass planet host stars.

As an extension to this analysis, a companion paper is in preparation, which will compare the exoplanet samples presented here with unbiased control samples of stars with exoplanets or a debris disc, or without either. This future paper will search for differences in the incidence of dusty debris between these different subsamples. In future work, observations from the Herschel open time programme “Search for Kuiper Belts Around Radial-Velocity Planet Stars” (SKARPS; Bryden et al. 2013; Kennedy et al. 2013) will be used to increase the number of radial velocity planet host stars for which far-infrared fluxes are available, which will clarify, and hopefully support, the trends seen between dust, planet, and stellar properties in this, and earlier, works.

Online material

Table 2

Spitzer MIPS70 and Herschel PACS photometry along with photospheric estimates for the exoplanet host stars.

Table 3

Stellar and planetary parameters of the exoplanet host star sample.

Table 4

Summary table of all exoplanets in each system.

1

Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA.

2

1258 as of 29th October 2013, see: http://www.minorplanetcenter.net/iau/lists/TNOs.html

3

Databases of exoplanet properties are maintained at http://exoplanet.eu and http://exoplanets.org

Acknowledgments

This research has made use of NASA’s Astrophysics Data System Bibliographic Services. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This research has made use of the Exoplanet Orbit Database and the Exoplanet Data Explorer at exoplanets.org, and the Extrasolar Planets Encyclopedia at exoplanets.eu. J.P.M., C.E., J.M. and B.M. are partially supported by Spanish grant AYA 2011-26202. This work was supported by the European Union through ERC grant number no. 279973 (GMK and MCW) and has been partially supported by Spitzer grant OT1_amoromar_1 (AMM).

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All Tables

Table 1

Summary of Herschel PACS observations of the target stars.

In the text
Table 2

Spitzer MIPS70 and Herschel PACS photometry along with photospheric estimates for the exoplanet host stars.

In the text
Table 3

Stellar and planetary parameters of the exoplanet host star sample.

In the text
Table 4

Summary table of all exoplanets in each system.

In the text

All Figures

thumbnail Fig. 1

Distribution of the significances presented in Table 2 at 100 μm (in blue, hatching top right to bottom left) and 160 μm (in red, hatching top left to bottom right). Debris disc stars with χ values higher than ten have been added to the right-hand side bin.
In the text
thumbnail Fig. 2

Filled circles denote cool debris disc systems, whilst open triangles denote fits to the 3σ upper limits at 100 μm. HD 69830, having a warm debris disc, is denoted as a filled blue triangle to distinguish it from the other far-infrared non-detections. Red data points are cool-giant-planet systems, black data points are hot-giant-planet systems, whilst blue data points are low-mass planet systems.
In the text

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