A sensitivity analysis of the WFCAM Transit Survey for short-period giant planets around M dwarfs
Gábor Kovács, S. Hodgkin, B. Sipőcz, D. Pinfield, D. Barrado, J. Birkby, M. Cappetta, P. Cruz, J. Koppenhoefer, E. Martín, F. Murgas, B. Nefs, R. Saglia, J. Zendejas
aa r X i v : . [ a s t r o - ph . E P ] A p r Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 17 August 2018 (MN L A TEX style file v2.2)
A sensitivity analysis of the WFCAM Transit Survey forshort-period giant planets around M dwarfs
Gábor Kovács , S. Hodgkin , B. Sipőcz , D. Pinfield ,D. Barrado , J. Birkby , M. Cappetta , P. Cruz , J. Koppenhoefer , E. Martín ,F. Murgas , B. Nefs , R. Saglia , J. Zendejas Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK Centre for Astrophysics Research, University of Hertfordshire, College Lane, Hatfield, AL10 9AB, UK Centro de Astrobiología, Instituto Nacional de Técnica Aeroespacial, 28850 Torrejón de Ardoz, Madrid, Spain Leiden Observatory, Universiteit Leiden, Niels Bohrweg 2, NL-2333 CA Leiden, The Netherlands Max-Planck-Institut für extraterrestrische Physik, Giessenbachstraße, 85748 Garching, Germany Instituto de Astrofísica de Canarias,C/ Vía Láctea s/n, E38205 La Laguna (Tenerife), Spain
17 August 2018
ABSTRACT
The WFCAM Transit Survey (WTS) is a near-infrared transit survey running on theUnited Kingdom Infrared Telescope (UKIRT), designed to discover planets around Mdwarfs. The WTS acts as a poor-seeing backup programme for the telescope, and rep-resents the first dedicated wide-field near-infrared transit survey. Observations beganin 2007 gathering J-band photometric observations in four (seasonal) fields. In this pa-per we present an analysis of the first of the WTS fields, covering an area of 1.6 squaredegrees. We describe the observing strategy of the WTS and the processing of the datato generate lightcurves. We describe the basic properties of our photometric data, andmeasure our sensitivity based on 950 observations. We show that the photometryreaches a precision of ∼ mmag for the brightest unsaturated stars in lightcurvesspanning almost 3 years. Optical (SDSS griz ) and near-infrared (UKIRT ZY JHK )photometry is used to classify the target sample of 4600 M dwarfs with J magnitudesin the range 11–17. Most have spectral-types in the range M0–M2. We conduct MonteCarlo transit injection and detection simulations for short period ( <
10 day) Jupiter-and Neptune-sized planets to characterize the sensitivity of the survey. We investigatethe recovery rate as a function of period and magnitude for 4 hypothetical star-planetcases: M0–2 + Jupiter, M2–4 + Jupiter, M0–2 + Neptune, M2–4 + Neptune. We find thatthe WTS lightcurves are very sensitive to the presence of Jupiter-sized short-periodtransiting planets around M dwarfs. Hot Neptunes produce a much weaker signal andsuffer a correspondingly smaller recovery fraction. Neptunes can only be reliably re-covered with the correct period around the rather small sample ( ∼ ) of the latestM dwarfs (M4–M9) in the WTS. The non-detection of a hot-Jupiter around an Mdwarf by the WFCAM Transit Survey allows us to place an upper limit of 1.7–2.0 percent (at 95 per cent confidence) on the planet occurrence rate. Key words: stars: planetary systems – stars: late-type – stars: statistics – infrared:stars – techniques: image processing
M dwarfs are the most numerous stars in our Galaxy(Chabrier 2003), and until recently have remained relativelyunexplored as exoplanet hosts. While several hundreds of transiting exoplanets have been discovered around F,G andK dwarfs, only ∼ such planets are known around thelower mass M stars. M dwarfs make interesting targets formany reasons, for example they provide better sensitivity to http://exoplanet.euc (cid:13) G. Kovács et al. smaller (rocky) planets in the habitable zone, and they alsoprovide strong constraints on planetary formation theories.The most successful techniques so far used to discoverexoplanets are the radial velocity (RV) and transit meth-ods. A planet around an early M2 dwarf can have ∼ ∼ : a fraction of 1 per cent oflow mass stars is predicted to have at least one giant planet,assuming that this ratio is 6 per cent for solar mass ones.Due to the failed core outcome, it is not surprising thatNeptunes and rocky planets are predicted to be commonaround low mass stars in core accretion models. Ida & Lin(2005) predict the highest frequency around M dwarfs for afew Earth mass planets in close-in orbits ( < ∼ yr ). They predict that gas giants can form aroundlow mass primaries as efficiently as around more massiveones assuming that the protoplanetary disk is sufficientlymassive to become unstable (Boss 2006).(Wright et al. 2012, and references therein) give a sum-mary of occurrence rates of hot giant planets ( T < days) Planet formation theories usually do not provide absolute num-bers because of free interaction coefficients in their formulae. around solar G type dwarfs. RV studies determined a rateof 0.9–1.5 per cent (Marcy et al. 2005; Cumming et al. 2008;Mayor et al. 2011; Wright et al. 2012), while transit studieshave a systematically lower rate (roughly half of this value)at 0.3–0.5 per cent (Gould et al. 2006; Howard et al. 2012,H12 hereafter).For M dwarfs, recent RV studies support the paucityof giant planets (Cumming et al. 2008; Johnson et al. 2007,2010; Rodler et al. 2012) though there are confirmed detec-tions both with short- and long-period orbits. Johnson et al.(2007) found 3 Jovian planets (with orbital periods of years)in a sample of 169 K and M dwarfs, in the California andCarnegie Planet Search data. The planetary occurrence ratefor stars with M < . M ⊙ in their survey is 1.8 per cent,which is significantly lower than the rate found around moremassive hosts (4.2 per cent for Solar-mass stars, 8.9 percent around higher mass subgiants). The positive correla-tion between planet occurrence and stellar mass remainsafter metallicity is taken into account, although at some-what lower significance. Gravitational microlensing pro-grammes also detected Jupiter-like giants around M dwarfs(e.g. Gould et al. (2010); Batista et al. (2011)) but statisti-cal studies seem to arrive at different conclusions. Microlens-ing surveys are more sensitive to longer period systems thanRV (and particularly transit) surveys. Gould et al. (2010)analyzed 13 high magnification microlensing events with 6planet discoveries around low mass hosts (typically . M ⊕ )and derived planet frequencies from a small but arguablyunbiased sample. They compared their planet frequencies tothe Cumming et al. (2008) RV study. They found that af-ter rescaling with the snow-line distance to account for theirlower stellar masses in the microlensing case, the planet fre-quency at high semi-major axes is consistent with the distri-bution from the RV study extrapolated to their long orbits.They found a planet fraction at semi-major axes beyond thesnow line to be 8 times higher than at 0.3 AU. Consideringthat hot giants in RV discoveries (around solar type stars)are thought to have migrated large distances into their shortorbits, they conclude that giant planets discovered at highsemi-major axes around low mass hosts do not migrate veryfar. Their study suggests that rather than the formationcharacteristics, the migration of gas giants may be differentin the low mass case.Focusing again on giant planets with short orbital pe-riods around M dwarfs, then as of writing, there is onlyone confirmed detection. The Kepler Mission (Borucki et al.1997), includes a sample of 1086 low-mass targets (in Q2)(Borucki et al. 2011, H12) and one confirmed hot Jupiter(P=2.45 days) around an early M dwarf host (KOI-254)(Johnson et al. 2012). Unfortunately, this object was not in-cluded in the statistical analysis of H12 study.For transit surveys, sufficiently bright M dwarfs makegood targets because of their smaller stellar radius. ANeptune-like object in front of a smaller host can producea similar photometric dip ( ∼ per cent) as a Jupiter-radius planet orbiting a Sun-like star. Ground based sur-veys are therefore potentially sensitive to planets around Mdwarfs that could not be detected around earlier type starswith typical ground-based precision. On the other hand, Mdwarfs provide a more demanding technical challenge. Theyare intrinsically faint and their spectral energy distributionpeaks in the near infrared. Their faintness at optical wave- c (cid:13) , 000–000 sensitivity analysis of the WTS lengths also makes spectroscopic follow-up observations diffi-cult. Measuring photometry in the infrared helps, but intro-duces a higher sky background level. It is also worth pointingout that the intrinsic variability of M dwarfs (flaring, spots)could further reduce the ease of discovering transiting sys-tems.One approach is to target a large number of M dwarfs,with a wide-field camera equipped with optical or near-infrared detectors. An alternative approach is to target in-dividual brighter M dwarfs in the optical deploying severalsmall telescopes. Up till now, only 2 transiting planets havebeen discovered around (bright) M stars (Gillon et al. 2007;Charbonneau et al. 2009) by ground based transit surveys.In this paper, we discuss the UKIRT (United King-dom Infra Red Telescope) WFCAM (Wide Field CAMera)Transit Survey (WTS), the first published wide-field near-infrared dedicated programme, searching for short period( <
10 day) transiting systems around M dwarfs. The sur-vey was designed to monitor a large sample ( ∼ , ) oflow-mass stars with precise photometry. In this paper wepresent an analysis of the first completed field in the WTS.We demonstrate that we can already put useful constraintson the hot Jupiter planet occurrence rate around M dwarfstars, and this is currently the strictest constraint available.The survey observing strategy is described in Section2. In Section 3 a summary is given of the data processingpipeline, describing the generation of final clean lightcurvesfrom raw exposures. In Section 4 we describe the M dwarfsample and discuss uncertainties in classification. We eval-uate the sensitivity of the survey in Section 5 using transitinjection and detection Monte Carlo simulations. The lackof giant planets detected by the survey around M dwarfs todate is discussed in Section 6. Finally, in Section 7, we con-sider the H12 sample and use it to place an upper limit onthe frequency of hot Jupiters around M dwarfs based on theKepler Q2 data release. We discuss our WTS results in thecontext of both the Bonfils et al. (2011) and H12 studies. UKIRT is a 3.8m telescope, optimized for near-infrared ob-servations and operated in queue-scheduled mode. The Min-imum Schedulable Blocks are added to the queue to matchthe ambient conditions (seeing, sky-brightness, sky trans-parency etc). The WTS runs as a backup programme whenobserving conditions are not good enough (e.g. seeing > ×
2k pixels eachcovering 13.65 arcmin x 13.65 arcmin at a plate scale of 0.4arcsec/pixel. The detectors are placed in the four cornersof a square with a separation of 12.83 arcmin between thechips. This pattern is called a pawprint .The WTS time series data are obtained in the J band( λ eff = 1220 nm ), the fields were also observed once in allother WFCAM bands (Z,Y,H,K) at the beginning of the sur-vey. This photometric system is described in Hodgkin et al.(2009). Each field, covering 1.6 square degrees, is made up ofan 8 pawprint observation sequence with slightly overlappingregions at the edges of the pawprints (Fig. 1). Observations d3 d4d2 d1 c4c2 c1 b3 b4b2 b1a3 a4a2 a1c3h3 h4h2 h1g2 g1 f3 f4f2 f1e3 e4e2 e1g3 g4 Figure 1.
Observation pattern for the WTS. A field of 1.6 squaredegrees consists of 8 pawprints (a-h), each pawprint is built upfrom the simultaneous exposures of the four (numbered) detec-tors. The X-axis is Right Ascension, and increases to the left ofthe figure, while the Y-axis is Declination, and increases to thetop.name coordinates galactic No. of objects stellarRA, DEC l,b epochs (
J < ) objects(h),(d) (d),(d)19 19.58+36.44 70.03+07.83 950 69161 5927017 17.25+03.74 24.94+23.11 340 17103 1534307 07.09+12.94 202.89+08.91 350 24153 2122403 03.65+39.23 154.99-12.99 240 17221 15159 Table 1.
Summary of the WTS fields and their coverage as of27th May 2010. Stellar objects are morphologically identified bythe photometric pipeline (see Sec.3.2). are carried out using 10s exposures in a jitter pattern of 9pointings. A complete field takes 16 min to complete form-ing the minimum cadence of the survey. Observing blockstypically comprise 2 or 4 repeats of the same field.Four distinct WTS survey fields were chosen to be rea-sonably close to the galactic plane to maximize stellar den-sity while keeping giant contamination and reddening atan acceptable level (see Section 4). The four fields are dis-tributed in right ascension at 03, 07, 17 and 19 hours toprovide all year coverage (at least one field is usually visi-ble). At the time of the analysis presented in this paper, the19 hour field has approximately 950 epochs which is close tocompletion (the original proposal requested 1000 exposuresfor each field), the other three are less complete. A summaryof the key properties of the survey regions is shown in Table1. The WTS has a lower priority than most of the mainUKIRT programmes, thus observations are not distributeduniformly over time. For any given field, such as the 19 hourfield (Fig. 2), there are large gaps when the field is not visi-ble, as well as variations between and within seasons.
The WTS uses list-driven aperture photometry on processedimages to construct lightcurves from the stacked data framesat the pawprint level. We describe this procedure briefly inthis section. c (cid:13) , 000–000 G. Kovács et al. -
01 2007 -
07 2008 -
01 2008 -
07 2009 -
01 2009 -
07 2010 - N u m be r o f epo c h s
19 cumulative19 monthly
Figure 2.
Monthly and cumulative distributions of observationalepochs in the 19hr field as of 27th May 2010. There are seasonswhen observations were frequent with a handful of images takenevery night and there are big gaps when the survey was not sched-uled for observation.
All images taken with WFCAM are processed using animage reduction pipeline operated by the Cambridge As-tronomical Survey Unit (CASU) . The WFCAM pipelineloosely evolved from strategies developed for optical pro-cessing (e.g. the Wide Field Survey on the Isaac NewtonTelescope, (Irwin & Lewis 2001)) and implements methodsoriginally presented in Irwin (1985). The 2D processing isa fairly standardized procedure for the majority of projectsusing WFCAM on UKIRT. We give a brief overview of theimage processing steps here.Images are converted into multi extension FITS for-mat, containing the data of the 4 detectors in one pawprintas extensions. Other data products from the pipeline (cat-alogues, lightcurves) are also stored in binary FITS tablefiles. A series of instrumental correction steps is performed,accounting for: nonlinearities, reset-anomalies, dark current,flatfielding (pixel-to-pixel), defringing and sky subtraction.The sky subtraction removes any spatial variation in thesky background but preserves its mean level. The sky back-ground is calculated as a robust kσ clipped median for eachbin in a coarse grid of 64x64 pixels. The sky backgroundmap is filtered by 2D bilinear and median filters to avoidthe sky level shifting in bins dominated by bright objects.The final step is to stack the 9 individual WTS exposures toproduce one 90 second exposure. Note that a simplified ver-sion of the catalogue generation and astrometric calibrationsteps (described below) are run on the individual unstackedexposures to ensure that they can be aligned before combin-ing. http://casu.ast.cam.ac.uk/surveys-projects/wfcam The median absolute deviation (MAD) is used as a robust es-timator of the root mean square (RMS) in most pipeline compo-nents both during processing individual frames and lightcurves.For normal distribution,
RMS = 1 . · MAD . Object detection, astrometry, photometry and classifica-tion are performed for each frame. Object detection followsmethods outlined in Irwin (1985) (see also Lawrence et al.(2007)). Background-subtracted object fluxes are measuredwithin a series of soft-edged apertures (i.e. pro-rata divisionof counts at pixels divided by the aperture edge). In the se-quence of apertures, the area is doubled in each step. Thescale size for these apertures is selected by defining a scaleradius fixed at 1.0 arcsec for WFCAM. A 1.0 arcsec radiusis equivalent to 2.5 pixels for WTS non-interleaved data.In 1 arcsec seeing an rcore-radius aperture contains roughly2/3 of the total flux of stellar images. Morphological objectclassification and derived aperture corrections are based onanalysis of the curve of growth of the object flux in the seriesof apertures (Irwin et al. 2004).Astrometric and photometric calibrations are basedon matching a set of catalogued objects with the 2MASS(Skrutskie et al. 2006) point source catalogue for everystacked pawprint. The astrometry of data frames are de-scribed by a cubic radial distortion factor (zenithal poly-nomial transformation) and a six coefficient linear trans-formation allowing for scale, rotation, shear and coordi-nate offset corrections. Header keywords in FITS files fol-low the system presented in Greisen & Calabretta (2002);Calabretta & Greisen (2002). The photometric calibrationof WFCAM data is described in Hodgkin et al. (2009).These calibrations result in the addition of keywords to thecatalogue and image headers, enabling the preservation ofthe data as counts in original pixels and apertures.
Following the standard 2D image reduction procedures, cat-alogue generation and calibration, we have developed ourown WTS lightcurve generation pipeline. This is largelybased on previous work for the Monitor project described inIrwin et al. (2007) where more technical details are given.As a first step in the lightcurve pipeline, master imagesare created for each pawprint by stacking the 20 best-seeingphotometric frames. The master images play dual roles inour processing: they define the catalogue of objects of thesurvey for each pawprint with fixed coordinates and iden-tifications numbers (IDs). Thus the source-IDs will neverchange for the WTS, however their coordinates could if wewere to include a description of their proper motions. Thishas not yet been done.Source detection and flux measurement is performed foreach master image to create a series of master catalogues,and astrometric and photometric calibration recomputed,again with respect to 2MASS. These object positions arethen fixed for the survey. Each source has significantly bet-ter signal-to-noise on the master image, and thus better as-trometry (from reduced centroiding errors) than could beachieved in a single exposure. As discussed in Irwin et al.(2007), centroiding errors in the placement of apertures canbe a significant source of error in aperture photometry, par-ticularly for undersampled and/or faint sources.This master catalogue is then used as an input list forflux-measurement on all the individual epochs, a techniquewe call list-driven photometry. A WCS transformation is c (cid:13) , 000–000 sensitivity analysis of the WTS computed between the master catalogue and each individualimage using the WCS solutions stored in the FITS headers.Any residual errors in placing the apertures will typically besmall systematic mapping errors that affect all stars in thesame way or vary smoothly across frames. In practice, thiscan be corrected by the normalization procedure (see Section3.4). The same soft-edged apertures are used (as describedabove), except that the position of the source is no longer afree parameter. Thus for each epoch of observation, a seriesof fluxes for the same sources is measured. Although the photometry of each frame is calibrated individ-ually to 2MASS sources (Hodgkin et al. 2009), these valuescan be refined for better photometric accuracy. Lightcurvesconstructed using the default calibrations typically havean
RMS at the few percent level (for bright unsaturatedstars). To improve upon this, an iterative normalization al-gorithm is used to correct for median magnitude offsets be-tween frames, but also allowing for a smooth spatial varia-tion in those offsets. In each iteration, lightcurves are con-structed for all stellar objects and a set of bright stars se-lected ( < J < ) excluding the most variable decile ofthe group based on their (actual iteration) lightcurve RMS.Then for each frame, a polynomial fit is performed on themagnitude differences between the given frame magnitudesand the corresponding median (lightcurve) magnitude forthe selected objects. The polynomial order is kept at 0 (con-stant) until the last iteration. In the last iteration, a secondorder, 2D polynomial is fitted as a function of image coor-dinates. For each frame, the best fit polynomial magnitudecorrection is applied for all objects and the loop starts againuntil there is no further improvement. Multiple iterationsof the constant correction step help to separate inherentlyvariable objects from non-variable ones initially hidden bylightcurve scatter caused by outlier frames. The smooth spa-tial component during the last iteration accounts for the ef-fects of differential extinction, as well as possible residualsfrom variation in the point spread function (PSF) across thefield of view.It is also found that lightcurve variations correlate withseeing. In an additional post-processing step, for each ob-ject, a second order polynomial is fitted to differences frommedian magnitude as a function of measured seeing. Magni-tude values are then corrected by this function on a per-starbasis. Data are taken in a wide range of observing conditions,sometimes with bad seeing ( ∼ arcseconds or worse) or sig-nificant cloud cover. Additionally some frames are affectedby loss and recovery of guiding or tip-tilt correction dur-ing the exposure. We identify and remove bad observationalepochs that add outlier data points for a significant num-ber of objects in any chip of a pawprint. Where a single(corrected) epoch has in excess of 30 per cent of objects de-viating by more than σ from the median flux we flag andremove this epoch from all lightcurves. Fig. 3 shows some ofthe per-epoch parameters (which we store in the lightcurve files) as a function of σ outlier object ratio. The number ofoutlying objects has a strong correlation with the residualRMS of the second order polynomial normalization (panel a)which is a measure of the photometric unevenness of the im-age. The (cumulative) frame magnitude offset applied dur-ing the normalization (panel c) shows two distinct branches,and a large scatter can be seen in the average frame ellip-ticity (panel b). These two panels help to identify the maincauses of bad epochs. High ellipticities arise from frameswith tracking/slewing problems, while high magnitude cor-rections are suggestive of thick (and probably patchy) cloud.Our rejection threshold is a compromise between the num-ber of affected frames and frame quality. At the outlier ratiothreshold of 0.3, 39 frames (out of 950, or 4 per cent) areremoved in the 19hr field. In Fig. 4 and Table 2 we summarize the WTS lightcurvequality at different pipeline steps. In each step we changeor add one pipeline feature. The normalization procedureof the photometric scale by per-frame constant offsets (a),the quadratic spatial correction (b) during the normaliza-tion, the bad epoch filtering (c) and the seeing correction(d) give improvements at the several mmag level for unsat-urated bright stars. In panel (d) a theoretical noise modelcurve consisting of Poisson noise, sky noise and a constantresidual are drawn. A constant systematic error of 3 mmagis applied to the model shown in Fig. 4 to bring the modelroughly into agreement with the data. This should be seenas the minimum systematic error in our lightcurves. Somesaturation appears and makes lightcurve RMS worse for ob-jects brighter than J = 13 while for the faint end, the skynoise dominates. To detect transit signals, we use a variant of the boxcar-fitting (Box Least Squares, or BLS) algorithm developed byAigrain & Irwin (2004). They derive the transit fitting al-gorithm starting from a maximum likelihood approach offitting generalized periodic step functions to the lightcurve.It was demonstrated that for planetary transits a simplebox shaped function is sufficient. The algorithm in this formis equivalent to BLS developed by Kovács, Zucker & Mazeh(2002). The signal to red noise statistic is used to mea-sure transit fitting significance (eq. 4 reproduced fromPont, Zucker & Queloz (2006)): S red = d q σ n + n P i = j C ij (1)where n is the number of in-transit data points in the wholelightcurve, σ is the measurement error of the individualdata points, d is the fitted depth of the BLS algorithm, C ij is the covariance of two in-transit data points. Also following Noise that includes both uncorrelated (white) and correlated(red) components. In some cases, this is called ‘pink’ noise in theliterature.c (cid:13) , 000–000
G. Kovács et al. N o r m a li z a t i o n R M S ( m a g ) a) N E lli p t i c i t y b) M a g n i t u d e s c a l e o ff s e t ( m a g ) c) Figure 3.
Per frame residual normalization RMS (a), average stellar ellipticity (b) and overall magnitude scale correction (c) as afunction of σ outlier object ratio in the 19a pawprint. Epochs above a threshold of 0.3 are removed from the survey’s lightcurve releaseand candidate search. See text for more details. J = Table 2.
Median lightcurve RMS (mmag) as a function of object magnitudes using different pipeline options for the 19a pawprint. Seetext for details, and Fig. 4 for illustration.
Pont, Zucker & Queloz (2006) we adopt a detection thresh-old of S red = 6 . Objects that pass this threshold are consid-ered candidate transiting systems. The high numbers of objects in the WTS and their faintmagnitudes make spectral classification of all WTS objectspotentially resource consuming. Instead, we use homoge-neous broadband optical (from SDSS DR7, Abazajian et al.(2009)) and near-infrared (WFCAM) photometry to esti-mate reliable stellar spectral types. Specifically, effectivetemperatures are measured from fitting NextGen stellarevolution models (Baraffe et al. 1998) to griz (SDSS) and
ZY JHK (WFCAM) magnitudes. For comparison, we alsofit the Dartmouth (Dotter et al. 2008) models, but in thiscase we use 7 passbands (Z and Y are not available). Leastsquares minimization is performed for the available pho-tometry, fitting for temperature and a constant magnitudeoffset (distance modulus) as model parameters. The modelgrid data is smoothed by a cubic interpolation. We fol-low the temperature–spectral-class relation in Table 1 ofBaraffe & Chabrier (1996): i.e. 3800K, 3400K, 2960K and1800K corresponding to spectral types of M0, M2, M4 andM9 respectively.Fig. 5 shows WFCAM and SDSS colour-magnitudeand colour-colour panels of the stellar objects in the 19hrfield. The M dwarf sample identified by the SED fitting onNextGen magnitudes is marked by red ( < J < ) andblue ( < J < ) crosses. A small number (6 per cent)of objects have outlying colour values due to saturation in one or more WFCAM or SDSS filters (typically J < ).These magnitudes are sigma-clipped during the SED fittingprocedure. The panels also show 1 Gyr isochrones from theNextGen and Dartmouth models in the 2000K–6500K and3200K–7700K temperature intervals respectively. The solidand dashed curves correspond to solar metallicity, the dash-dot to a metal-rich ([Fe/H]=+0.5), the dash-double-dot to ametal-poor ([Fe/H]=-0.5) model isochrone of the Dartmouthmodel respectively. Temperatures of 3800K and 3900K aremarked (x) on the isochrones. Comparison between Dart-mouth model isochrones show little significant difference inmodel colours between ages of 250Myr and 5Gyr. For veryyoung stars, we might expect to pick up significant colourvariation, however we expect very few very young (age < Myr) stars in our survey field. In fact Ciardi et al. (2011)analyse the very nearby Kepler field and find that the low-mass dwarf population is dominated by young thin diskstars, thus our selected age of 1Gyr is reasonable.The figure also presents measured colours of K and Mdwarfs and MIII giants of the Pickles photometric standards(dwarfs: (cid:3) , giants: ▽ ) from Covey et al. (2007) and of theBruzual-Persson-Gunn-Stryker atlas (dwarfs: ◦ , giants: △ )from Hewett et al. (2006). All panels show colours in theVega system, AB-Vega offsets are taken from Table 7 inHewett et al. (2006), 2MASS-WFCAM conversions are cal-culated by relations given by Hodgkin et al. (2009). We de-noted by filled green markers the M0 dwarf members (oneand two objects, respectively) of these observations. Ouridentified M dwarfs are separated well from the sample of Mgiants ( ▽ , △ ) in the J-H vs. H-K and g-r vs. r-i panels, so weexpect a low giant contamination level in our sample. Thepanels in Fig. 5 also demonstrate some difficulties in identify-ing M dwarfs. Model predictions do not reproduce observed c (cid:13) , 000–000 sensitivity analysis of the WTS
11 12 13 14 15 16 17 18 19J magnitude10 -3 -2 -1 R M S ( m a g ) a) -3 -2 -1 R M S ( m a g ) b) -3 -2 -1 R M S ( m a g ) c) -3 -2 -1 R M S ( m a g ) d) Figure 4.
RMS of stellar objects in the 19a pawprint with different pipeline optimizations; a) constant normalization b) quadraticnormalization c) outlier frame filtering d) seeing correction. In panel d) a noise model (thick red solid line) consisting of Poisson noise(dashed line), sky noise (dash-dotted line) and systematic noise of 3 mmag (thin blue solid line) is drawn. patterns in all colour combinations. The NextGen isochronehas the best agreement in the infrared (J-H vs. H-K) whilethe Dartmouth models fit the r-i vs. i-z colours rather bet-ter. We note that the Nextgen colour predictions are tooblue in the optical bands for low temperatures, which is aknown model attribute (e.g. by 0.5 mag in V-I, Baraffe et al.1998).We also note that based on the residual χ values duringthe SED fitting procedure the photometric errors from thecatalogues (shown in the colour-colour panels of Fig.5) werefound to be underestimated. We assumed a systematic errorbetween the WFCAM and SDSS catalogues and added a0.03 mag systematic term in quadrature to the individualmagnitude errors (used as weights in the fitting).The Dartmouth data sets cover a narrower tempera-ture range with a lowest temperature of 3200K. This makesthe dataset unsuitable for selecting later (M4 and later) Mdwarfs, although it gives a useful comparison for warmerstars. We conclude that for early M dwarfs (M0-2), the Dart-mouth and Nextgen models give rise to very similar selec-tions assuming solar metallicity. In the metal poor and metal rich cases the Dartmouth isochrones give about 40 per centincrease and 30 per cent decrease in numbers of early Mdwarfs respectively.In the g-r vs. r-i diagram, we note that the scatter ing-r for objects with r-i > is larger (by about 0.2 mags atg=20) than can be explained solely from the SDSS photo-metric errors. This enhanced scatter can be explained byreddening alone (see below), and needs no significant spreadin metallicity.Leggett (1992) analyzed photometry of 322 M dwarfsand found that the effects of metallicity can be seen in Mdwarf infrared colours (I-J, J-K, I-K, J-H, H-K) while notdiscernible in visible colours (U-B, V-I, B-V). They alsonoted that this feature is not reproduced by evolutionarymodels of Mould (1976); Allard (1990). We note that theDartmouth model also shows a much smaller effect than seenin Leggett (1992) in the infrared, but a very large effect ing-r vs r-i.In our paper, we base object classification on theNextGen model. Out of the 59000 morphologically identi-fied stars in the < J < magnitude range, we identified c (cid:13) , 000–000 G. Kovács et al.
10 11 12 13 14 15 16 17 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 J J-K 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 J - H H-KDartmouth[Fe/H]=0.5[Fe/H]=-0.5Nextgen 16 Colour-magnitude and colour-colour plots of the M dwarf sample ( < J < , red crosses; < J < , blue crosses) of thisstudy and other stellar objects ( < J < ) in the 19hr field based on WFCAM and SDSS data. A sequence of spectroscopic K and Mdwarfs are shown from Covey et al. (2007) ( (cid:3) ) and Hewett et al. (2006) ( ◦ ), respectively. Green markers show the M0 dwarf membersof these sequences. Triangles ( ▽ , △ ) are M giants (III) from the same studies. Estimated maximum interstellar extinctions in differentcolours are marked by red arrows. Error crosses are from the corresponding catalogues. ∼ M dwarfs. A more in-depth modelling of the objectsin the WTS is an ongoing effort. During the SED fitting procedure, we cannot fit for theinterstellar reddening and for the distance modulus on aper object basis due to being the fit badly determined.Therefore, we make an upper estimation for the redden-ing in our sample. We estimate a maximum distance fortarget M dwarfs of 1.5 kpc by assuming that one ofour intrinsically brightest objects (an M0, M J = 6 fromNextGen) is observed at the faint limit of the study ( J =17 ). A V extinction values are calculated from the Galac-tic model of Drimmel, Cabrera-Lavers & López-Corredoira(2003). The three dimensional Galactic model consists ofa dust disk, spiral arms mapped by HII regions and a lo-cal Orion-Cygnus arm segment. They use COBE/DIRBEfar infrared observations to constrain the dust parame- ters in the model. We use the code provided to deter-mine A V at 1.5 kpc. To calculate absorption in UKIRTand SDSS bandpasses, we use conversion factors A/A V fromTable 6 of Schlegel, Finkbeiner & Davis (1998) that evalu-ates the reddening law of Cardelli, Clayton & Mathis (1989)and of O’Donnell (1994) for the infrared and the opti-cal bands respectively. The reddening laws assume R V ≡ A V /E B − V = 3 . , an average value for the diffuse inter-stellar medium (Cardelli, Clayton & Mathis 1989). Red ar-rows show our reddening estimates in different colours inFig. 5 ( A V : A J : 0.113, E J − K : 0.067, E J − H : 0.041, E H − K : 0.026, E g − r : 0.130, E r − i : 0.083, E i − z : 0.076). Thetotal Galactic extinction in the 19hr field direction fromSchlegel, Finkbeiner & Davis (1998) is A V = 0 . . Provided by the Nasa Extragalactic Database. http://ned.ipac.caltech.edu/ c (cid:13) , 000–000 sensitivity analysis of the WTS Stellar radius changes significantly between early- and late-type M dwarfs. For our sensitivity simulation purposes, wecan use a linear approximation for the mass-radius relation-ship for M dwarfs: M ∗ /M ⊙ ≈ R ∗ /R ⊙ . This slightly deviatesfrom the NextGen mass-radius prediction (Baraffe et al.1998) but it is in good agreement with observed M dwarfradii in Kraus et al. (2011). It is important in our simula-tions to treat early M dwarfs distinctly from later smallerM dwarfs. Therefore we divided our M dwarf sample intothree coarse spectral bins. In the 19hr field, 2844 stars wereidentified as M0-2 ( > T eff > ), 1679 as M2-4( > T eff > ) and 104 as M4-9 ( > T eff > ). The third, latest (M4-9) type bin is very sparselypopulated (2 per cent of the M dwarf sample) and numberssuffer from high uncertainty, so this bin will be omitted fromthe simulations, leaving us with two subsamples.Considering the ‘colour distance’ along the isochronesbetween the boundary of our identified object groups, thePickles M0 members (green squares) and the dependencyof the isochrones on model parameters, we estimate the bintemperature edges to be uncertain about 250K. M dwarfs are known to be intrinsically more variablethan more massive main sequence stars primarily due tospots (e.g. Chabrier, Gallardo & Baraffe 2007; Ciardi et al.2011). The fraction of active M dwarfs also rises towardslater (M4-9) subtypes (West et al. 2011). We examine thevariability of the M dwarfs compared to the rest of the stel-lar sample in Table 3 and Fig. 6. The photometric precisionis at the 4-5 mmag level for brighter objects ( J < ) andat the percent level for the fainter region ( < J < ,86 per cent of the M dwarfs). We compare the binned me-dian RMS values of the three M subtypes to those of thewarm (T > σ outliers (a proxy forthe most variable objects) for the different subsamples. Wefind that all three M dwarf samples, as well as the warmerstars exhibit a ten per cent outlier fraction.Finally, these findings are also supported by 2DKolmogorov-Smirnov tests (Fasano & Franceschini 1987).The RMS versus magnitude distributions are found to beconsistently different for each of the M dwarf samples ver-sus the warm stars to very high confidence (test p values < − ). These results add support to the argument thatobserving in the J band gives limited sensitivity to spots(Goulding et al. 2012).Typical signal depths for edge-on planetary systems arealso shown in Fig. 6 to give a rough impression of our sensi-tivity. We expect to be able to detect Jupiter size planets inedge-on systems around all of our M dwarfs (in all spectralbins: M0-2, M2-4, M4-9), and Neptunes only in the M2-4and M4-9 bins. As stated above, the latest type bin (M4-9) is sparsely populated, and omitted from the remaininganalysis. J = Table 3. Median RMS (mmag) of M dwarf lightcurves and ofearlier dwarfs for different object magnitudes. The WTS is not the only transit survey specifically aimedat discovering planets around M dwarfs, and it is useful toplace our survey in context. The MEarth survey individuallytargets about 2000 bright M dwarfs in a custom i + z -bandfilter (Berta et al. 2012). The survey was designed to focuson the nearest and brightest mid M dwarfs and has dis-covered one Super Earth size planet at the time of writing(Charbonneau et al. 2009).The Palomar Transient Factory (PTF, Law et al.(2012)) is a project targeting M dwarfs in the R band. Theirgoal is to observe a total of 100,000 M dwarfs during the sur-vey lifetime collecting about 300 epochs in each observingperiod. The PTF operates in roughly the same magnituderange (specifically over R=14–20) as the WTS and has asimilar, seasonal observing schedule.The Pan-Planets project also focuses on late-type stars.Their goal is to target approximately 100,000 M dwarfsin 40 square degrees. The programme collected about 100hours of observations using the Panoramic Survey Tele-scope and Rapid Response System (PanSTARRS) so far(Koppenhoefer et al. 2009).The Next-Generation Transit Survey (NGTS) is alsoan upcoming initiative to target a high number of brightM dwarfs ( V <13) using wide field cameras. The prototypeinstrument observed ∼ 400 early and ∼ 50 late M dwarfsin 8 square degrees FOV at the one per cent photometricprecision level (Chazelas et al. 2012).Regarding space missions, the Kepler Mission in itsQ2 data release has a relatively small (1086) number of Mdwarfs but their data quality is much higher than for groundbased programmes. The mission also samples uniformly intime with no large data gaps. We briefly discuss the planetoccurrence rate in this sample in Section 7 based on H12and compare it with our results.Compared to these other transit surveys, the WTS istargeting a reasonable sample, even using only one of thefour fields (at the time of writing three of the four fieldsare lagging in coverage). The PTF and Pan-Planets samplesare potentially ground-breaking, if they can obtain enoughobservations. In the WTS, the initial candidate selection criterionis currently a well-defined decision based solely on thesignal-to-noise ratio. Exhaustive eyeballing and photomet-ric/spectroscopic follow-up of the small number of candidateplanets around M dwarfs (Sipőcz et al. 2013) has revealedthem all to be grazing eclipsing binary systems, or otherfalse-positives. This search was complete for all ∼ Jupiter- c (cid:13) , 000–000 G. Kovács et al. 13 14 15 16 1710 -3 -2 -1 R M S Jupiter+M0Neptune+M0 M0-2 13 14 15 16 1710 -3 -2 -1 R M S Jupiter+M2Neptune+M2 M2-4 13 14 15 16 17J magnitude10 -3 -2 -1 R M S Super-Earth+M4.5Neptune+M4.5 M4 and later 13 14 15 16 17J magnitude (cid:0) (cid:1) (cid:2) R M S ( mm a g ) Noise models M0-2M2-4M4-908162432404856647280 0816243240485664728008162432404856647280 Figure 6. Comparison of lightcurve RMS in the M dwarf spectral groups. The solid curve shows median values of the RMS per magnitudebin. The bottom right panel shows the differences of the median RMS model curves from the median RMS of the earlier type stars. (M0-2:solid, M2-4: dashed, M4-9: dash dotted). Signal depths of edge-on transiting systems with Neptune, Jupiter or Super-Earth ( . R ⊕ ) sizeplanets are marked. sized candidates down to J=17 in the 19 hour field, althoughavoiding objects with periods very close to one day. Two hotJupiters have however been discovered around more mas-sive hosts (Cappetta et al. 2012; Birkby et al. 2013). Thisconfirms that the WTS is sensitive to transits at the ∼ per cent level (and indeed these two objects are very ob-vious). Zendejas et al. (2013) have independently producedlightcurves (using difference imaging) and searched for can-didate planets in the same data, using stricter automatedclassification, and also find no candidate Jupiters around Mdwarfs in the 19 hour field. This lack of hot Jupiters discov-ered around small stars in the WTS is what motivates therest of this study, to address the question: how significant isthis result. We determine the sensitivity of the WTS for four distinctstar-planet scenarios. For the two M dwarf subsamples, we No. Sp.bin T eff (K) M ∗ /M ⊙ R ∗ /R ⊙ M p /M Jup R p /R Jup Table 4. Simulated planetary systems consider Neptune and Jupiter size planets in short period(0.8–10 days) orbits around early (M0-2) and later type (M2-4) stars. The mass and radius of the star and the radiusof the planet are kept fixed in each scenario (see Table 4).We use conservative assumptions for the stellar parameters:stellar radii are overestimated, using the maximum valuesin each spectral bin (i.e at M0 and M2), and planet radiiare (under)estimated assuming solar system radii even forhot planets. The expected number of recovered planetarysystems can be written as: N det = N stars fP det (2) c (cid:13)000 Simulated planetary systems consider Neptune and Jupiter size planets in short period(0.8–10 days) orbits around early (M0-2) and later type (M2-4) stars. The mass and radius of the star and the radiusof the planet are kept fixed in each scenario (see Table 4).We use conservative assumptions for the stellar parameters:stellar radii are overestimated, using the maximum valuesin each spectral bin (i.e at M0 and M2), and planet radiiare (under)estimated assuming solar system radii even forhot planets. The expected number of recovered planetarysystems can be written as: N det = N stars fP det (2) c (cid:13)000 , 000–000 sensitivity analysis of the WTS where N stars denotes the number of stars in the actual starsubtype group, f is the (unknown) fraction of the stars thatharbour a planetary system, P det is the (average) probabil-ity of discovering a system by the survey around one of itstargets if we assume that the star harbours a (not neces-sarily transiting) planetary system. P det is expressed as afunction of planetary radius ( R p ) and orbital period ( T ). Ingeneral, we can write (Hartman et al. 2009): P det = Z Z P r P T p ( R p , T ) dR p dT (3)where P r is the average recovery ratio, i.e. the average (con-ditional) probability of recovering a transit from a lightcurveif the lightcurve belongs to a transiting system, P T is thegeometric probability of having a transit in a randomly ori-ented planetary system, and p ( R p , T ) is the joint probabilitydensity function of R p and T for planetary systems. We de-termine these terms in Eq. 3 separately in each scenario. Seealso Burke et al. (2006); Hartman et al. (2009).We consider circular orbits only ( e =0). P T can begiven analytically, for a random system orientation, P T =( R ∗ + R p ) /a where a denotes the semi-major axis of the sys-tem, R ∗ is the stellar radius. The joint probability density, p ( R p , T ) , must be treated as a prior. We consider planetaryconfigurations at discrete R P values only, so the R P depen-dence of the density function simplifies to a δ -function. Asthe period dependence is ill-constrained, we will discuss uni-form and power-law functions as a prior distributions. In theH12 study, a power law model with an exponential cutoff atshort periods was fitted (Table 5 in H12) to Kepler giantplanet detections around mostly GK dwarfs (see sample cri-teria in Section 7). We use their model function normalizedto our studied period range as prior distribution. P r is determined numerically by the Monte Carlo iter-ation loop. P r We identify a set of 4700 quiet lightcurves in the 19hrfield that serve as input for the simulations. This simula-tion sample consists of mostly M dwarfs (and slightly hot-ter stars) covering the magnitude range 11–17. The sam-ple preserves the observed distribution of M dwarf apparentmagnitudes in the WTS. By quiet we mean that the un-perturbed lightcurves show no signature of a transit (BLS S red < = 6 ). By adding noise free signals to these lightcurvesand recovering them from the noisy data, we can quan-tify the effect of noise on P r . As shown in Section 4.4, wefound little difference between the noise properties of thelightcurves for the M0-2 and M2-4 subclasses. We simulatelarge numbers of transiting exoplanet systems to determinethe recovery ratios for the four scenarios under investigation.In each iteration, a transiting planetary system is createdwith parameters randomly drawn from fixed prior distribu-tions as detailed below (assuming a circular orbit). A simu-lated transit signal is then added to the randomly selected(real) lightcurve. We try to recover the artificial system us-ing the transit detection algorithm discussed in Section 3.7(Aigrain & Irwin (2004)). P r is estimated as the ratio be-tween successful transit recoveries and the total number of it-erations. We make a distinction between two different cases.In the threshold case we consider the signal successfully re- covered if the detection passes the same signal to red noiselevel as used for WTS candidate selection ( S red >6). In the periodmatch case, we additionally require that the recoveredperiod value matches the simulated one. This is discussed inmore detail in Sec. 6.3.The period value ( T ) is drawn from a uniform distribu-tion in the range of . to days. The period determinesthe semi-major axis ( a ) of the system, given the massesof the star (assumed to be 0.6 or 0.4 M ⊙ ) and the planet(assumed to be 1.0 or 0.054 M Jup ). A randomly orientedsystem is uniformly distributed in cos i where i is its or-bital inclination. The random inclination is chosen to satisfy cos i < ( R ∗ + R p ) /a to yield a transiting system. Thisalso allows for grazing orientations. The phase of the transitis also randomly chosen from within the orbital period.Observed dates in the target lightcurve are now com-pared with predicted transit events. If there would be noaffected observational epochs, then the iteration ends andthe generated parameters recorded. Otherwise, a realis-tic, quadratic limb darkening model is used with coeffi-cients from Claret (2000) to calculate brightness decreaseat in-transit observational epochs (Mandel & Agol 2002; Pál2008). This artificial signal is added to the lightcurve magni-tude values, and BLS is run on the modified lightcurve. Bothgenerated and detected transit parameters are recorded forthe iteration. We note that the transit detection algorithmis the most computationally intensive step in the loop. Atotal of 75,000 iterations were performed. The flexible observing mode of WTS has an inherent limi-tation on our sensitivity to short-period transiting systems,and it takes multiple seasons to build up enough epochs toreliably detect them. In Fig. 7 a simple sensitivity diagram isshown which considers only the actual distribution of obser-vational epochs for the 19 hour field. We use the simulatedtransiting systems from the Neptune-size planets around anM0 dwarf scenario and compare the simulated transit timeswith our real observational epochs. A system is considereddetectable here if at least 5, 10 or 15 in-transit observationalepochs occur calculated from the simulated parameters. Thefraction of detectable systems has an obvious strong depen-dence on the period of the transiting system and the re-quired number of in-transit observational epochs as well. Ofcourse, it depends on the noise properties of our data howmany in-transit observations are necessary for detecting atransit event. We show the (signal to red-noise) detection statistic distri-butions in Fig. 8. The black curve belongs to the survey Mdwarfs (unmodified data) in the 19hr field (selection criteriadescribed in 4.3) . The coloured curves are for the simulatedtransiting systems for the four scenarios. For comparison,they are normalized to the total number of M dwarfs in thesurvey, i.e as if every WTS M dwarf target were either an M0 c (cid:13) , 000–000 G. Kovács et al. R e c o v e r y r a t i o Figure 7. The effect of the observation strategy on the WTSsensitivity to short period transiting systems in the 19 hour field.We use the actual epochs of our 19 hour field observations com-bined with a large sample of simulated planets. The fraction ofsimulated transiting systems is shown where at least 5, 10 or 15 actual WTS observational epochs coincide with the simulated in-transit times. This illustration does not use the noise-propertiesof the WTS, thus does not consider the case as to whether theevents are actually detected or not. or an M2 with a transiting Jupiter or a Neptune (which may,or may not, have transited during the WTS observations).The original (unperturbed) WTS M dwarf S red distribu-tions shows a marked tail above the detection threshold (25per cent of all objects, see Sec.6.4). This could be caused byeffects such as: correlated noise, intrinsic variability (spots),eclipsing binaries or possibly transiting planets. The simula-tions show that for initially “quiet” lightcurves ( S red < ) theinjection of a planet signal (transiting, but could be graz-ing) can perturb the measured signal-to-noise value abovethe detection threshold. (M2+J:50, M0+J:39, M2+N: 5.1,M0+N: 4.1 per cent of all iterations) In other words, theWTS is sensitive to Jupiters, and rather less sensitive toNeptunes. Given the other possible causes for a perturbed S red , the shape of this distribution does not in itself presenta direct measurement of the planet population. It is worthnoting that for the Jupiters (M0+J,M2+J), the recovered S red values can be rather higher than the largest values weactually see in the WTS.The Neptune cases have much smaller residual tailswhich sit only a little above the detection threshold. Thesesignal injections cause detection statistic increases above thedetection threshold only in a small number of cases. There isalso little dependence on the size of the host star (the greenand red curves are similar). Our simulations, with the samestellar magnitude distribution as the survey, are dominatedby fainter objects. The similarity of the detection statisticdistributions in the figure indicates that for Neptune sizedplanets, the survey sensitivity depends on the stellar radiusonly for the brightest stars. For fainter objects, the sensitiv-ities are the same and as we see later, they are equally low(Figures 10 and 11). While passing the signal-to-noise statistic threshold in thesimulation is caused by the injected signal, the detected (re-covered) parameters, particularly the period, may not becorrect. Indeed, it is common in ground based surveys to findmultiple peaks in the BLS periodogram containing aliases ofthe observing window function.The detected period is perhaps the most important ofthe model parameters: At the eyeballing stage of candidates,this period has the most influence in judging a transit detec-tion real or false. In a lightcurve folded on the correct period(or a harmonic thereof), the transit signals are visually eas-ily recognized. When folded on a random period, in-transitpoints are hardly distinguishable from random outliers. Agood initial period value is also important for the timingof follow-up observations. With this in mind, we try to ac-count for the importance of this effect in our simulations.We consider two recovery rates: • threshold — S red exceeds 6.0, and • periodmatch — we additionally require that the de-tected period value matches (or be a harmonic of) the gen-erated period. We allow factors of 1, 5/4, 4/3, 3/2, 5/3, 2,5/2, 3, 4, 5 between the two values.This step uses external information and obviously wecannot know the true period in the actual survey. However,in the simulations, it does allow us to place more strict cri-teria on detected simulated planets, and mimic the effectsof differentiating between high priority candidates, whichare likely to receive follow-up time, and low-priority candi-dates for which follow-up may be too expensive. This effectis much more significant for the Neptunes, where individualevents are shallow.We note that the number of in-transit data points iscorrelated with recovering the correct period. In the M2+Jcase, we find that if a simulated system has 10 in-transit datapoints we detect the correct period 80 per cent of the time,reaching almost 100 per cent with 20 in-transit data points.For larger stars (shallower transits), more in-transit datapoints are needed (M0+J: 12 and 30 points for 80 and 100per cent respectively). For Neptunes even more transits arerequired to secure the period. For the M2+N case, we find 20in-transit points recovers 50 per cent of the detected systemswith the correct period. For the M0+N case the situation iseven worse, and we almost always detect an alias (see Fig. 9).This confirms that the BLS algorithm is “lost” at these lowsignal levels. Comparing the necessary number of in-transitdata points for reliable transit detections, according to Fig.7, we can see an inherent limitation of the transit searchingefficiency of the WTS and possibly other ground based lowcadence surveys (e.g. PTF).In this study we determine P r for the threshold and pe-riodmatch cases. The real value of P r that characterizes theWTS probably lies between these two extremes and dependson all the (sometimes subjective) steps of the candidate se-lection and follow-up strategy. Having fewer quality criteriain the survey increase the number of candidates at the costof higher false alarm ratio and more follow-up resource con-sumption.We note that surveys with close to real time data pro-cessing and instant access to follow-up observation facilities c (cid:13) , 000–000 sensitivity analysis of the WTS red N o . o f o b j e c t s surveyM2+JM0+J 0 5 10 15 20S red N o . o f o b j e c t s surveyM2+NM0+N Figure 8. Detected signal to red noise histograms (bin size is 0.2) of the transit injected quiet lightcurve iterations (coloured) for Jupiter(left) and Neptune (right) size planets in the four simulated scenarios. For comparison, the unmodified (black) M dwarf lightcurves ofthe survey is shown and curves of the iteration loops are normalized to the number of M dwarf objects in the survey (black curve). Thevertical line indicates our candidate selection threshold of 6. could use a different approach and need not necessarily bal-ance between quality of recovered transits and false positiverates. They can maximize the probability of detecting ac-tual transit events by selecting follow-up times optimizedto their current data and iteratively revise predictions asdata accumulates. A Bayesian approach to such a strategyis described in Dzigan & Zucker (2011).In Fig. 9 scatter diagrams and histograms of simu-lated and detected periods are shown for recovered simu-lated planets. We compare our most sensitive case in termsof injected signal depth (M2+J), to the least sensitive case(M0+N). They show a clear contrast in the quality of de-tected (signal to noise selected) transit signals.For Jupiters, about 70 per cent of the detections also re-cover the injected period or its harmonic value (middle rowin Fig. 9). Strong harmonic lines can be seen in the scatterpanel (top left). For M0 stars (not shown), the ratio of recov-ered period values is even better. The shallower transits arelonger in duration for a given period. The detected periods(bottom row, filled histogram) are biased towards shortervalues peaking around 3 days, with aliases appearing at 1and 2 days. In these iterations the injected signal changesthe lightcurve in a way that aliased periods give the mostsignificant box-fit signals. We see a gently decreasing trendfor the periods of simulated systems that were recovered(bottom row, empty histogram), i.e. we are less sensitiveto longer period planets, and more likely to underestimatetheir periods. We can conclude that signals of Jupiter sizedplanets can firmly be detected around all of the M dwarfsin the survey with good initial period values.The Neptunes are shown in the right-hand column ofFig. 9. In accordance with our qualitative assessment basedon the lightcurve RMS, signals of Neptune sized planets areat the boundary of being lost in the lightcurve noise in theWTS. In the M2+N case, only 12 per cent of the detec-tions have also matching periods, in the M0+N case thecorrect period is almost never recovered by the box fittingalgorithm (middle row). Recovered period values are heavily dominated by alias values. We conclude that Neptune sizedplanets can be detected in the survey only in favorable casesaround smaller (later) M dwarfs. In a transiting planet survey, we have to deal with two typesof false positives at the initial transit candidate discoverystep. The detection statistic may pass where the transit boxmodel is fitted just on (i) random fluctuations or systemat-ics. In this case, the transit signal does not exist at all. (ii)Physical signals in the lightcurve may also belong to variouseclipsing binary configurations or to variable stars (e.g. fromspots) which can mimic transit events for the algorithm.The amount of additional analysis to rule out false posi-tive candidates can vary from little additional manual check-ing, through refinement of transit parameters, up-to obtain-ing additional observational data with better cadence. Graz-ing binary stellar systems can mimic planetary transits be-yond the survey’s photometric precision and require addi-tional spectroscopy measurements to be ruled out with highconfidence.The false positive ratio of the candidate selection pro-cedure of the survey cannot be quantified by the simula-tion alone. A lightcurve passing the detection threshold withknown injected simulated transit signal cannot be a falsepositive per se.So far, all the actually selected, eyeballed and laterfollowed-up (by additional photometry and/or spectroscopy)candidates around M dwarfs turned out not to be a plan-etary system (Sipőcz et al. 2013). Following Miller et al.(2008), this can be used to estimate the false positive ra-tio of the survey. This encompasses both false positive casesabove. We assume that all S red > detections in our original(unmodified) lightcurves are false positives. At 25 per cent(black curve above the marker in Fig. 8), this is a ratherlarge fraction. This number gives a simple (worst-case) de- c (cid:13) , 000–000 G. Kovács et al. D e t e c t e d p e r i o d ( d a y ) M2+J D e t e c t e d p e r i o d ( d a y ) M0+N F r a c t i o n M2+J F r a c t i o n M0+N F r a c t i on M2+ J F r a c t i o n M0+N Figure 9. Properties of period values of iterations that pass the signal-to-noise threshold in the most (M2+Jupiter, left) and least(M0+Neptune, right) sensitive scenarios. Best fit detected period values as a function of simulated period values (top row) and normalizedhistograms of simulated/detected period ratios (middle row; bin size is 0.05). Bottom row: Normalized histograms (bin size 0.1) of detected(filled) and simulated periods (empty) i.e. projections to axes of top row scatter panels. c (cid:13)000 Properties of period values of iterations that pass the signal-to-noise threshold in the most (M2+Jupiter, left) and least(M0+Neptune, right) sensitive scenarios. Best fit detected period values as a function of simulated period values (top row) and normalizedhistograms of simulated/detected period ratios (middle row; bin size is 0.05). Bottom row: Normalized histograms (bin size 0.1) of detected(filled) and simulated periods (empty) i.e. projections to axes of top row scatter panels. c (cid:13)000 , 000–000 sensitivity analysis of the WTS scription of our false positive ratio, and cannot be usefullyapplied to the simulations. We show results of P r as a function of stellar magnitude forranges of simulated period in Figs. 10 and 11. We adopt 0.8–3.0, 3.0–5.0, 5.0–10.0 day ranges following Hartman et al.(2009) for extremely hot Jupiters (EHJ), very hot Jupiters(VHJ), and hot Jupiters (HJ) respectively. Filled red circles( • ) and green crosses (+) represent the threshold and period-match cases respectively. Integrated detection probabilities( P det ) weighted by different prior assumptions including thegeometric probabilities of transiting orientations are shownin Table 5.For the Jupiter cases (upper rows in both figures),the WTS sensitivity has a maximum around J=13.5 anddrops towards fainter (J>15-16) objects. This is in accor-dance with our expectations, we have higher noise levelstowards fainter objects but there is occasional saturation atthe bright end ( J < ). There is little dependence on stel-lar radius, appearing only for the fainter stars. The threshold curves are less affected by simulated period than the peri-odmatch recovery rate. In the shortest period window the threshold and periodmatch values are practically the same.In the longest period panels the threshold ratio is about twicethat of the periodmatch ratio showing that while the signal-to-noise detection statistic can recover signals, many of thesesystems may be missed due to poor initial period guesses.The survey has a much lower sensitivity for Neptunes (bot-tom rows in Figs. 10 and 11). The threshold curves showroughly 25 per cent of the recovery rate seen for Jupitersaround bright stars. The difference between the threshold and periodmatch case is also more significant. The period-match recovery rates are close to zero for all M0 cases andvery low for the M2 cases as well. The only exception is thebest signal-to-noise case around M2 stars, in the short periodwindow for bright objects where threshold rates reach half ofthe Jupiter value and the periodmatch rates are not close tozero. It looks like the WTS survey only really has a chanceof discovering extremely hot Neptunes around late (M2 orlater) and bright M stars ( J < ). The lack of an accurateperiod determination would make follow-up of Neptune sizecandidates difficult in all other cases. We use the seeing corrected lightcurves as a source for oursimulation. While it could be more accurate to modify mea-sured raw flux values and to run all the pipeline componentsto create the modified lightcurves, it would be unreasonablyresource consuming, nor assumed to have an impact on oursensitivity results. Burke et al. (2006) decrease the sensitiv-ity with a constant estimation of . to deal with their trendfilterings’ flattening effect. In our case it is assumed to havea negligible difference only as we do not use trend filters thatuses solely lightcurve data. As it is described in the pipelineoverview, images are transformed into lightcurves simultane-ously, calculating magnitude scale offsets using non-variable,bright objects on each frame. Compared to the several thou-sand objects per frame, only a small fraction of objects may 12 13 14 15 16 170.00.20.40.60.81.0 R a t i o 12 13 14 15 16 170.00.20.40.60.81.0 12 13 14 15 16 170.00.20.40.60.81.0 12 13 14 15 16 17J magnitude0.00.20.40.60.81.0 R a t i o 12 13 14 15 16 17J magnitude0.00.20.40.60.81.0 12 13 14 15 16 17J magnitude0.00.20.40.60.81.0 Figure 10. Recovery ratios ( P r ) of simulated transiting systemfor M0+Jupiter (upper row) and M0+Neptune (lower row) sce-narios in three period ranges as a function of stellar brightness.Filled circles ( • ) and crosses (+) represent the threshold and pe-riodmatch ratio respectively. 12 13 14 15 16 170.00.20.40.60.81.0 R a t i o 12 13 14 15 16 170.00.20.40.60.81.0 12 13 14 15 16 170.00.20.40.60.81.0 12 13 14 15 16 17J magnitude0.00.20.40.60.81.0 R a t i o 12 13 14 15 16 17J magnitude0.00.20.40.60.81.0 12 13 14 15 16 17J magnitude0.00.20.40.60.81.0 Figure 11. Recovery ratios ( P r ) for M2+Jupiter (upper row)and M2+Neptune (lower row) simulated scenarios. have a transit on a given frame thus the determined magni-tude offset value would be independent of an injected signal.Being a bad weather fallback project, the survey typicallyhas a few (2-3) observational epochs per observing night.Thus we do not expect significant correlation between theseeing and the timing of transit signals. Assuming that the survey planetary candidates are all falsepositives, as our follow-up suggests (see Sec. 4.6), we canplace upper limits on the planetary fraction ( f ) for our fourtest cases. The assumption of complete follow-up is muchless secure for Neptune-sized planets, nevertheless the upperlimits remain valid for the survey until a signal is detected.While Eq. 2 gives the expected number of detections, the c (cid:13) , 000–000 G. Kovács et al. System type prior N stars P det f P det f sn sn pm pmM0+Jupiter Kep. 2844 0.0363 2.9% 0.0311 3.4%M2+Jupiter Kep. 1679 0.0414 4.3% 0.0346 5.2%M0-4+Jupiter Kep. 4523 0.0382 1.7% 0.0324 2.0%M0+Jupiter uni. 2844 0.0360 2.9% 0.0305 3.5%M2+Jupiter uni. 1679 0.0405 4.4% 0.0332 5.4%M0-4+Jupiter uni. 4523 0.0377 1.8% 0.0315 2.1%M0+Neptune Kep. 2844 0.0027 39% 0.0001 100%M2+Neptune Kep. 1679 0.0025 71% 0.0003 100% Table 5. Planet detection probability and upper limit results onplanetary fractions in the WTS in the signal-to-noise threshold (sn) and periodmatch (pm) interpretation. The upper part showslimits for the simulated Jupiter scenarios (M0,M2) and its inter-pretation for the whole M0-4 dwarf sample. Values are shown forpriors based on the H12 study (Kep.) and uniform (uni.). Thelower part shows representative values for the Neptune cases. actual number of detections follows a Poisson distribution.If the expected number of planets is N det , the probability ofdetecting k planets is: P k = N k det k ! exp( − N det ) (4)We use this expression at k = 0 as a likelihood function for N det . We require that N det be within our N det < N max confidence interval with 95 per cent confidence . Solving P ( N det < N max ) = N max Z exp( − N ) dN = 0 . (5)for N max , we get N max = 3 . . From the requirement of N det < . , using Eq. 2, we get: f . N stars P det (6)Assuming zero detections and applying the above tech-nique, we can compute robust upper limits on the fractionof planet host stars in our sample. We show the threshold and periodmatch P det values along with the planetary frac-tions in Table 5. We show results for the two different as-sumptions for the period distribution: best fit exponentialcut power law from Kepler (H12) (Kep.), uniform (uni.).For the hot Jupiters as a whole (periods 0.8–10 days), wecan place an upper limit of f = threshold and periodmatch detection probabil-ities are essentially the same, and the chosen prior perioddistribution has also little impact.We can combine the M0–M4 stars into one bin by calcu-lating the average sensitivity for the whole sample weighted This is actually a Bayesian interpretation for the 95 per centprobability credible interval for the parameter of the Poisson dis-tribution, assuming a sufficiently wide, uniform prior for the pa-rameter. For nonzero cases in Sec.7, intervals with equal posteriorprobability values at the endpoints are chosen. by the number of M dwarfs in the corresponding groups.The WTS can put an upper limit of f = threshold / periodmatch interpretations.As seen, the recovery of Neptunes in the WTS is a difficultand unreliable task. The probability of recovering a Neptunewith the correct period ( periodmatch P det ) is so low becausedetected signals are dominated by aliased periods. Thus itis very difficult to distinguish genuine Neptunes from falsedetections. The main way to improve on the WTS sensitivityto Neptunes would be to improve on the noise properties inthe data. This is beyond the scope of this paper. Although Kepler is not a specialized survey for M dwarfs,due to its exceptional quality data and large number of tar-gets, it is probably the highest impact exoplanetary transitsurvey to date. In this section we compare our results to theplanet occurrence study of the Kepler data in paper H12.In the second part of the H12 study, the planet oc-currence rate is determined in three planet radius bins (2-4 R ⊕ , 4-8 R ⊕ , 8-32 R ⊕ ) as a function of stellar type (effectivetemperature; in 500K wide temperature bins from 3600K to7100K; see figure 8 in H12). They use the Q2 Kepler data re-lease (Borucki et al. 2011). In each stellar temperature bin,the total planet occurrence rate is calculated by adding thecontribution of each discovered (high quality) Kepler planet(candidate). eq.2 from H12 is reproduced here: f = N pl X j =1 /P T n ∗ ,j (7) f is evaluated for each studied stellar bin. Each planet’s con-tribution is augmented by its geometric transit probability( /P T ) to include planetary systems with non-transiting ori-entations as well (i.e. a detected planet with low geometrictransit probability give a high contribution). Each planet’sfractional contribution is calculated over the number of highphotometric quality stars only ( n ∗ ,j ). Only those stars areselected from the Kepler Input Catalog (KIC) that belongto the analyzed stellar bin and have a high enough qualitylightcurve where the actual planetary transit can be cer-tainly detected (Table 6). A SNR value is derived from theedge-on planetary transit depth signal and from the mea-sured scatter ( σ CDPP ; see eq.1 in H12) of the lightcurve. Alightcurve counts in the total number of stars if SNR>10 isfulfilled.For transiting planets, a SNR>10 transit detection (cal-culated from the actual transit signal depth) and orbitalperiod T < days are required. These planets are notall confirmed yet but part of the released Kepler planetarycandidates passing an automated vetting procedure of theKepler data processing pipeline. They are counted as planetsboth in H12 and in the present paper as they are assumed c (cid:13) , 000–000 sensitivity analysis of the WTS Stellar effective temperature bins 3600–4100, ...,6600–7100KStellar surface gravity, log g 4.0–4.9Kepler magnitude, K p < Lightcurve quality, SNR > Planetary radius bins, R ⊕ T < daysDetection threshold, SNR > Table 6. Properties of stellar and planetary samples consideredin the H12 Kepler study. to be actual planets with high probability (Borucki et al.2011).To obtain stellar parameters, the Kepler project usesmodel atmospheres from Castelli & Kurucz (2004). Theyperform a Bayesian model fitting on seven colours ofthe KIC objects determining effective temperature ( T eff ),surface gravity ( log g ) and metallicity ( log Z ) amongother non-independent model parameters simultaneously(Brown et al. 2011). Restrictive priors also ensure that pa-rameters remain within realistic value ranges. Temperaturesare considered to be most reliable for Sun-like stars with dif-ferences from other models below 50K and up to 200K forstars further away from the Sun on the CMD. Brown et al.(2011) call temperatures below 3750K untrustworthy . Thereare 1086 M dwarfs identified in Q2 (Table 7).Using the Q2 Kepler data release, we calculate Keplerplanetary fractions for the 0.8–10 days period range to com-pare with our present WTS study. We follow the steps ofH12 by selecting KIC objects and Kepler planets (candi-dates) from the Q2 data release using most criteria listed inTable 6 but selecting planets with T < 10 days (Fig. 12).We cannot filter for high quality lightcurves however as noisedata is not readily available from H12. It is beyond the scopeof this paper to process each released Kepler lightcurve andcheck its noise properties. Rather, we determine a correctionfactor for each stellar type bin. We reproduce the calculationfor the planetary fraction in the T < day case omittingthe lightcurve SNR>10 quality criterion and compare it tothe published values in fig. 8 in H12. This reveals a correc-tion factor that is applied to the T < 10 day case in eachstellar bin (Table 7).For stellar bins with nonzero planets 95 per cent confi-dence intervals (red error bars in Fig. 13) are calculated fol-lowing the logic of ‘effective stars’ from H12; using a Poissondistribution for having the actual number of planet detec-tions ( N pl ) from N pl /f ‘effective stars’. Most stellar binshave only a few detections, so errors are heavily dominatedby small number statistics. For bins with zero candidates (95per cent confidence) statistical upper limits are calculatedin the same way as for the WTS earlier in this study. Inthis case the number of ‘effective stars’ are calculated as theintegrated overall detection probability in the 0.8–10 daysperiod range. In Fig. 13 and Table 7 Kepler planetary fractions ( f )are shown for short period (0.8–10 days) hot Jupiters (8-32 R ⊕ ). E.g. in the coolest stellar bin, there are 9 planets(2-32 R ⊕ ) with period T < days, counting as 320.5 occur- For a Jupiter size planet, using the Kepler prior this factor is P det = 0 . . N Figure 12. Cumulative number of discovered Jupiter size (8-32 R ⊕ ) planets in Kepler Q2 as a function of orbital period (T)in different stellar temperature bins. There are no planets in thetwo coolest stellar bins (3600–4100K, 4100K–4600K). Planet oc-currence fractions in Fig. 13 are calculated for the 0.8–10 daysregion, augmenting the contribution of each discovery by its geo-metric transit probability.Temp (K) N stars corr. N pl N aug f f Table 7. Total number of stars ( N stars ) in Kepler Q2 tempera-ture bins, their corresponding correction (corr.) factors (see text),number of Jupiter size short period planets ( N pl ), their aug-mented contribution ( N aug ) and the occurrence ratio ( f ) or up-per limit ( f ). rences around 1086 M dwarfs. This yields a fraction of 0.295which is the same rate published in H12. This means thatthe correction factor for the M dwarf bin (3600-4100K) is 1i.e. all 1086 M dwarf lightcurves are good enough to detectplanets down to super-Earth sizes. As there is no Jupitersize planet (8-32 R ⊕ ) in the 0.8–10 day period interval, wecalculate an upper limit of the planet occurrence rate as / (1086 · . . .We recall that in this study 2844 early (M0-2, 3400K–3800K) and 1679 later type (M2-4, 2960K–3400K) M dwarfswere identified in the 19hr field of the WTS while thereare 1086 early M dwarfs (3600K–4100K) in the Kepler Q2dataset. Due to the factor of 2 higher number of early Mdwarfs, the statistical upper limit set up by present studyfor the WTS M0-2 bin is a stricter constraint both in the threshold (2.9 per cent) and periodmatch approaches (3.4per cent) than the one that can be derived for the (early)Kepler M dwarfs (4 per cent, Fig. 13). Though the WTSis more sensitive for Jupiters around later type M dwarfs,the upper limit for the M2-4 bin is slightly worse due to thesmaller sample size: f = c (cid:13) , 000–000 G. Kovács et al. Figure 13. Short period (0.8–10 day) hot Jupiter planetary oc-currence fractions (x) and upper limits ( ↓ ) in case of null detec-tions in the WTS (green), Kepler Q2 (H12) (red) and from theHARPS planet search (Bonfils et al. 2011) (blue). WTS upperlimits are shown for the M0-2, M2-4 bins and also for the wholeM0-4 sample (green arrows). Vertical error bars on WTS upperlimit markers cover the uncertainty from the threshold and pe-riodmatch interpretations (Table 5). Horizontal bars ( ⊢⊣ ) showtemperature bin widths, horizontal arrows ( ↔ ) mark estimateduncertainty of bin edges where available. All upper limits anderror bars of nonzero fractions are for 95 per cent confidence. the period prior), while for the overall M0-4 sample, it is1.7–2.0 per cent.The WTS upper limits sit above the measured HotJupiter fractions found for hotter stars by Kepler which havemuch less uncertainty from much larger samples (bins withhigher than 4600K in Fig. 13). With our analysis of theWTS, we cannot rule out a similar Hot Jupiter occurrencerate around M dwarfs (M0-4). Our main conclusion is thatthere is currently no evidence to support the argument thatHot Jupiters are less common around M dwarfs than aroundsolar-type stars.To push our constraints to lower levels we will need tocomplete the remaining three fields of the WTS, or waitfor the completion of other surveys such as Pan-Planets(Koppenhoefer et al. 2009) or PTF (Law et al. 2012).The completed WTS survey contains a total of almost15,000 M0-4 dwarfs. A confirmed null detection for hotJupiters in the larger sample would push our upper limiton the HJ fraction down by a factor 3.2, i.e. to f = were part of the H12 sample, this sole detectionwould mean a . +4 . − . per cent occurrence rate which is lowerthan the upper limits but still compatible with the findingsof the present and the Bonfils et al. (2011) RV study. Wenote that this is an overestimation of the real weight of this planet detection as there are more cool hosts in KIC downto K p = ∼ K p < )which is different from the magnitude range of WTS objectsstudied here ( J < ). It is possible that the Kepler early Mdwarf sample is from a different population than the samplein the present study (Mann et al. 2012). (iii) The sensitivityfor Jupiters in the WTS was determined for a conservative R ⊕ radius while hot Jupiters may have larger radii. TheKepler study uses the 8–32 R ⊕ radius range for hot Jupiters. Bonfils et al. (2011) analyze RV data observed by theESO/HARPS spectrograph for planet signatures in their Mdwarf (M0-6) sample of 102 nearby (<11pc, V < ) starsand find no Hot Jupiters. According to their sensitivity con-siderations, this sample is equivalent to 96.83 effective stars.Using our 95 per cent confidence level, their null detectionof hot Jupiters (1-10 days) implies a 3.1 per cent upper limiton the planetary occurrence rate around M dwarfs, in goodagreement with our WTS results.Wright et al. (2012) find that 1.2 ± . per cent ofnearby Solar-type stars host hot Jupiters. Their results arein good agreement with previous RV works (Marcy et al.2005; Cumming et al. 2008; Mayor et al. 2011). Occurrencerates found by transit studies are systematically lower(Gould et al. (2006), H12), around 0.5 per cent.As the rates around G dwarfs are about the same (RV)or lower (transit) than the upper limits reached by the WTSaround M dwarfs in present study, we cannot rule out planetformation scenarios in this paper. We admit that this is avery brief comparison only, avoiding the discussion of themethods and error levels used by the studies cited above. The WFCAM Transit Survey has observed 950 epochs forone of its four target fields. These data were collected overmore than three years and will provide a valuable resourcefor general studies of the photometric and astrometric prop-erties of large numbers of objects in the near-infrared. In thispaper we determined the sensitivity of this dataset to shortperiod ( < 10 day) Jupiter and Neptune sized planets aroundhost stars of spectral type M0-M4. We identify and classifytwo subsamples of M dwarfs: M0-M2 comprising 2844 stars,and M2-M4 comprising 1679 stars. We compare Dartmouthand NextGen models to derive estimates of T eff for the sam-ple, and demonstrate that reddening effects are small forthe 19-hour field. This forms one of the largest samples ofM dwarfs targeted by any dedicated transit survey, and cur-rently the only one working in the near-infrared. c (cid:13) , 000–000 sensitivity analysis of the WTS We have described how our multi epoch WFCAM dataare filtered and processed to produce lightcurves with me-dian RMS ∼ mmag down to J = 14 and RMS ∼ . mmag at J = 17 . We found the RMS for the brightest starssuffers a significant contribution from systematic noise atthe > mmag level. The origin of this is not determined,but we note that we see similar (albeit smaller) effects in theoptical (e.g. Irwin et al. 2007). We leave for future work aninvestigation of the flatfield and near-infrared backgroundas two potential contributors to the systematics.We performed Monte-Carlo simulations on the WTSlightcurves, injecting and recovering fake transit events. Wegeneralise each of the stellar and planet populations intotwo distinct radius regimes, giving us 4 scenarios for tran-sit depths: Jupiters and Neptunes, around M0-M2 stars andM2-M4 stars. We investigate the resultant signal-to-noise ofthe recovered events and compare this to the survey detec-tion thresholds. We also investigate our sensitivity to these4 scenarios as a function of orbital period and stellar mag-nitude. Our analysis of the simulations enables us to placeconstraints on the incidence of hot Jupiters.With 95 per cent confidence and for periods < 10 days,we showed that fewer than 4.3–5.2 per cent of M2-M4 dwarfshost hot Jupiters. Constraints are even stronger for earlierspectral types, and fewer than 2.9–3.4 per cent of M0-M2dwarfs host hot Jupiters, while for the overall M0-4 sample,it is 1.7–2.0 per cent. An analysis of the Kepler Q2 datashows that the WTS provides more rigorous upper limitsaround cooler objects, thanks to the larger size of our sample(2844 M dwarfs in the WTS compared to 1086 in the Keplersample under consideration). We compare these upper limitsto the measured hot Jupiter fraction around more massivehost stars, and find that they are consistent, i.e. we cannotrule out similar planet formation scenarios around at leastthe earlier M dwarfs (M0-4) at the moment.We used our simulations to demonstrate that the WTSlightcurves are sensitive to transits induced by hot Neptunesin favorable cases, but that the ability to distinguish themfrom false alarms (astrophysical or systematic) is limited bya number of factors. Firstly the transit events have signifi-cantly lower to signal-to-noise than events arising from hotJupiters, and thus the contamination by false alarms (fromsystematic noise) is higher at the required detection thresh-olds. Secondly, the recovered periods for the simulated hotNeptunes are dominated by spikes at multiples of 1 day, notseen so strongly for the larger planets. Without reliable peri-ods, any attempts at follow-up photometry and spectroscopyfor detected candidates will be hardly viable, especially forsuch faint target stars.The data presented in this paper represent one quarterof the planned WFCAM Transit Survey (the other 3 fieldscurrently lack sufficient coverage to include in the analysis).If the WTS is completed then we expect our statistical con-straints to improve by a factor of 3–4 (dependent on theactual numbers of M dwarfs in the remaining three fields).If no hot Jupiters are found, our upper limits get to the 0.5per cent level for M0-M4 dwarfs, and may ultimately reacha significantly lower level for hot Jupiter occurrence than ismeasured around G dwarfs by other surveys. 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