EDEN: Sensitivity Analysis and Transiting Planet Detection Limits for Nearby Late Red Dwarfs
Aidan Gibbs, Alex Bixel, Benjamin Rackham, Daniel Apai, Martin Schlecker, Nestor Espinoza, Luigi Mancini, Wen-Ping Chen, Thomas Henning, Paul Gabor, Richard Boyle, Jose Perez Chavez, Allie Mousseau, Jeremy Dietrich, Quentin Jay Socia, Wing Ip, Chow-Choong Ngeow, Anli Tsai, Asmita Bhandare, Victor Marian, Hans Baehr, Samantha Brown, Maximilian Haberle, Miriam Keppler, Karan Molaverdikhani, Paula Sarkis
DDraft version February 25, 2020
Typeset using L A TEX twocolumn style in AASTeX63
EDEN: Sensitivity Analysis and Transiting Planet Detection Limits for Nearby Late Red Dwarfs
Aidan Gibbs,
1, 2
Alex Bixel,
1, 3
Benjamin V. Rackham, D´aniel Apai,
1, 3, 5
Martin Schlecker, N´estor Espinoza, Luigi Mancini,
8, 6, 9, 10
Wen-Ping Chen, Thomas Henning, Paul Gabor, Richard Boyle, Jose Perez Chavez, Allie Mousseau, Jeremy Dietrich, Quentin Jay Socia, Wing Ip, Chow-Choong Ngeow, Anli Tsai, Asmita Bhandare, Victor Marian, Hans Baehr, Samantha Brown, Maximilian H¨aberle, Miriam Keppler, Karan Molaverdikhani, Paula Sarkis, Steward Observatory, The University of Arizona, 933 N. Cherry Avenue, Tucson, AZ 85721, USA Department of Physics & Astronomy, University of California, Los Angeles, Los Angeles, CA 90095, USA NASA Nexus For Exoplanetary System Science: Earths in Other Solar Systems Team Department of Earth, Atmospheric, and Planetary Sciences and Kavli Institute for Astrophysics and Space Research, MassachusettsInstitute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA ∗ Lunar and Planetary Laboratory, The University of Arizona, 1640 E. University Boulevard, Tucson, AZ 85718, USA Max Planck Institute for Astronomy, Konigstuhl 17, D-69117 Heidelberg, Germany Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA † Department of Physics, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Rome, Italy INAF Osservatorio Astrofisico di Torino, via Osservatorio 20, I-10025 Pino Torinese, Italy International Institute for Advanced Scientific Studies (IIASS), Via G. Pellegrino 19, I-84019 Vietri sul Mare (SA), Italy Graduate Institute of Astronomy, National Central University, 300 Jhongda Road, Zhongli, Taoyuan 32001, Taiwan Vatican Observatory Research Group, University of Arizona, 933 N Cherry Ave., Tucson AZ, 85721-0065, USA (Accepted February 20, 2020)
Submitted to AJABSTRACTSmall planets are common around late-M dwarfs and can be detected through highly precise pho-tometry by the transit method. Planets orbiting nearby stars are particularly important as they areoften the best-suited for future follow-up studies. We present observations of three nearby M-dwarfsreferred to as EIC-1, EIC-2, and EIC-3, and use them to search for transits and set limits on the pres-ence of planets. On most nights our observations are sensitive to Earth-sized transiting planets, andphotometric precision is similar to or better than
TESS for faint late-M dwarfs of the same magnitude( I ≈
15 mag). We present our photometry and transit search pipeline, which utilizes simple mediandetrending in combination with transit least squares based transit detection (Hippke & Heller 2019).For these targets, and transiting planets between one and two Earth radii, we achieve an averagetransit detection probability of ∼
60% between periods of 0.5 and 2 days, ∼
30% between 2 and 5 days,and ∼
10% between 5 and 10 days. These sensitivities are conservative compared to visual searches.
Keywords:
Exoplanets, Habitable planets, Transit photometry INTRODUCTIONPlanetary systems around nearby stars are set to playa particularly important role in the future of exoplanetcharacterization studies, yet only a very small fractionof these planets have been identified to date. Recon-naissance spectroscopy of nearby, small (Earth-sized)transiting planets is possible now with the
Hubble Space ∗
51 Pegasi b Postdoctoral Fellow † IAU-Gruber Fellow
Telescope (e.g., as in the TRAPPIST-1 system, see deWit et al. 2016, 2018; Zhang et al. 2018; Wakeford et al.2019) and in-depth spectroscopic studies of these sys-tems will be possible in the near-future with the
JamesWebb Space Telescope (e.g., Greene et al. 2016; Mor-ley et al. 2017; Lustig-Yaeger et al. 2019) and with the
ARIEL mission (e.g., Tinetti et al. 2018). Transiting,habitable-zone, Earth-sized planets around nearby starsare likely to be the only type of habitable planets thatcan be characterized in detail in the next two decades. a r X i v : . [ a s t r o - ph . E P ] F e b Gibbs et al.
Although only a fraction of planets happen to tran-sit as observed from Earth, fortunately, the high fre-quency of M-dwarfs in the solar neighborhood, the mostfavorable host stars for detecting Earth-sized planets,improves the chances of a positive detection. Based onresults from the RECONS group (Henry et al. 2018),there are 283 currently known M-type stars within 10pc, and that number continues to grow. In addition,small (1–4 R ⊕ ) planets are found to be very commonaround M-dwarfs (Dressing & Charbonneau 2015; Mul-ders et al. 2015a,b; Hardegree-Ullman et al. 2019). How-ever, M-dwarfs in the solar neighborhood are locatedisotropically in the sky, requiring targeted, star-by-starmonitoring (e.g., Nutzman & Charbonneau 2008; Jehinet al. 2011; Delrez et al. 2018). Worldwide networksof ground-based telescopes that can obtain continuoustargeted coverage are therefore well-suited to search forthese planets (Blake et al. 2008).The Exoearth Discovery & Exploration Network(EDEN, PIs: D. Apai, P. Gabor, Th. Henning,W-P. Chen) is a multi-continental research networkthat searches for habitable-zone planets within fiftylightyears . EDEN’s transit survey component beganin Spring 2018 and currently uses eight telescopes tosearch for transiting planets around nearby late M-dwarfstars, which are the easiest stars to find Earth-sizedplanets around. EDEN differs from other ongoing sur-veys in that it uses several large preexisting telescopes( > TESS (Ricker et al. 2015) transitsearch mission.We review here these components of our sensitivityanalysis, and present example results for the first threeEDEN targets searched in depth. We do not detect anyconvincing transit candidates for follow-up, but showthat there is a high probability we would have detectedEarth-sized planets with periods less than 5 days if theirorbital planes were aligned with our line of sight. In Sec- http://project-eden.space tion 2 we briefly describe the EDEN telescopes and ourobservational methods. Section 3 details our data re-duction pipeline before lightcurve detrending and transitsearch described in Section 4. In Section 5, we providebackground on the selected EDEN targets for which weperform a sensitivity analysis in Section 6. Finally, inSection 7 we discuss our planet detection limits in thecontext of M-dwarf planetary occurence rates, knownsystems, and NASA’s TESS mission. OBSERVATIONSWe briefly describe the EDEN telescopes, survey tar-get selection, and photometric data collection proce-dures in order to provide context for our data reduc-tion, transit search, and sensitivity analysis methods.A nuanced discussion of our strategy for selecting andobserving targets, and a comparison with other surveys,will be reserved for a future paper (Apai. et al, in prep.),and only necessary details are included here.2.1.
Observatories
EDEN observations are currently conducted witheight unique telescopes at seven observatories in NorthAmerica, Europe, and Asia. The telescopes are theKuiper 1 .
55 m (Mount Bigelow, Arizona), Bok 2 . . . . .
23 m (Calar Alto, Spain), Cassini1 .
52 m (Mount Orzale, Italy), and Lulin 1 m (MountLulin, Taiwan). Table 1 details the location, design,and CCD imager of each telescope. With the exceptionof the robotic Schulman and Phillips telescopes, eachof them is manually controlled by an observer, who ac-tively monitors weather conditions and instrument per-formance during the course of a night. While the tele-scope designs are varied, each of the telescopes has beencarefully evaluated for photometric performance beforeits inclusion in EDEN and, when necessary, changeshave been made in the telescope’s operation and setup,which will be detailed in Apai et al. (in prep.). System-atic differences between telescopes therefore have veryminor effects on the final lightcurves and transit search.These differences can be compensated for during thedata reduction and detrending steps, discussed in Sec-tion 3 and 4.The majority of the EDEN telescopes are not solelydedicated to EDEN, so observations are scheduled ateach facility individually in blocks usually from two toten days per month, depending on availability. Observ-ing science targets at these sites has been ongoing sinceJune 2018 (following a six-month-long EDEN pilot pro- etection Limits for Nearby Late Red Dwarfs
Target Selection
EDEN’s primary focus is to search for potentially hab-itable planets within 15 pc ( ∼
50 lightyears). Corre-spondingly, for the EDEN Transit Survey, our target se-lection prioritizes M4 and later-spectral-type host stars,which offer favorable planet-to-star projected areal ra-tios, making broadly Earth-sized planets detectable inour data. We eliminate known close binary stars thatmay reduce the stability of putative planets and wouldcomplicate the interpretation of the lightcurve. We thenprioritize sources that are too faint (I >
15 mag) to be ef-ficiently searched by TESS or are outside TESS’s skycoverage. In addition to these high-priority EDEN tar-gets we also include separately targets of particular in-terest in our source catalog. Such targets may be exo-planet candidate host stars (from radial velocity or tran-sit searches), for which EDEN data can prove valuablefor candidate verification. Such follow-up targets (whereprior knowledge about a planets presence exists) will notbe used in future exoplanet occurrence rate studies.2.3.
Science Observations
EDEN targets, including those discussed in this pa-per, are late-M dwarfs scattered throughout the North-ern Hemisphere sky and thus must be observed one at atime. For planets orbiting within or interior to the hab-itable zone of these stars (e.g., Kasting et al. 1993; Kop-parapu et al. 2014), expected transit durations rangefrom 0 . . > ∼
50% successfuldetection of Earth-size transiting planets), which typi-cally translates to some sensitivity ( (cid:38)
Observational Procedures
Although each of our telescopes has somewhat differ-ent capabilities and performance, we adopt the sameobservational procedures at each telescope to minimizesystematic differences.
Filter — For each telescope we use a near-infrared (NIR)(or blue-blocking) filter, such as Harris-I or similar. Thisfilter choice maximizes the collected photons from ourtargets, which are brightest in the NIR, while blockingunwanted sky background from the Moon and skyglow.Since Spring 2019, the filter has been standardized at alltelescopes to an uncoated GG 495 glass long-pass filter(transparent at >
500 nm). Redder filters such as I or z’ have been occasionally used for bright targets if thesky background is very high, for example, during a fullmoon. The z’ is otherwise generally avoided becauseof the low quantum efficiency of most CCD detectorsat those wavelengths and the greater presence of tel-luric absorption bands from water vapor (Bailer-Jones& Lamm 2003; Blake et al. 2008). Exposure Time — The exposure time is chosen to bal-ance competing signal-to-noise and cadence considera-tions. We never allow the peak target flux to go above ∼
60% the detector’s full well, where the detector beginsto exhibit non-linear behavior. In a given period of time,such as a transit duration, the total Poisson-noise-drivensignal-to-noise ratio (SNR) follows the relationship
SN R tot ∝ (cid:114) R R , where R is the ratio of the exposure time to readouttime (Howell & Tavackolimehr 2019). This relationship Gibbs et al.
Table 1.
EDEN TelescopesTelescope Location Operation Mount CCD Imager Det. Size FOV Px. Scale Q e at 700 nmPhillips0 . × (cid:48) × (cid:48) . × (cid:48) × (cid:48) . × . (cid:48) × . (cid:48) .
23 m CalarAlto,Spain Remote EQ DLR-MKIIIcamerawith e2vCCD231-84-NIMO-BI-DDsensor 4k ×
4k 21 . (cid:48) × . (cid:48) .
52 m MountOrzale,Italy Classical EQ BolognaFaintObjectSpectro-graph andCamera 1300 × (cid:48) × . (cid:48) .
55 m MountBigelow,Arizona Classical EQ Mont4KSN3088(Weineret al.2018) 4096 × . (cid:48) × . (cid:48) . × . (cid:48) × . (cid:48) . × × . ◦ × . ◦ levels off at R ∼ .
5, and we thus aim for an exposuretime of ∼ . × the readout time. For our telescopes witha diameter larger than one meter and targets with mag-nitude I ∼
14, this gives a cadence <
60 s.
Focus — Previous work (e.g., Southworth et al. 2009)has shown that defocusing can result in more preciselightcurves as the point spread function (PSF) is spreadacross more pixels. We aim for a slight-to-moderate de-focus of 2–3”, so that pixel-to-pixel variations are re- duced, but the PSF maintains a Gaussian shape. Sincedefocusing also reduces the peak of the PSF, it has theadditional benefit of allowing longer exposures.2.4.
Calibration Frames
We follow standard calibration procedures for flat,bias, and dark corrections to reduce systematic effects onour lightcurves. Detailed tests (complete re-reductionand analysis of selected datasets) show that the de- etection Limits for Nearby Late Red Dwarfs ∼
10 twilight flat-fieldswith exposure times chosen to maintain a sky flux ap-proximately at 50% the detector’s full well, the same asour desired peak target flux. In some cases of inclementweather during twilight, we may use dome flats, butthese are not preferred since they have less uniform il-lumination. The minimum flat exposure time is alwayslong enough so that the shutter time has <
1% effect onthe precision of the flat.Generally, at least once per observing run, we collecta set of bias and dark frames. The dark current forour exposure times is nearly zero at all telescopes andis usually not subtracted. At some telescopes darks arenot collected for this reason. There is no evidence forpersistence on any of our detectors. DATA REDUCTIONEDEN data reduction is performed with a customPython-based automatic pipeline, edenAP , which isbased on a precursor pipeline for reducing Las CumbresObservatory Global Telescope (LCOGT) lightcurves(Brown et al. 2013). edenAP is designed to accommo-date the particularities of the individual telescopes inthe EDEN telescope network and reduce the data in aconsistent manner. Differences that must be accountedfor include number and configuration of chip amplifiers,and pixel scale. edenAP is called locally when new rawdata arrive, and produces a comparison-star-detrended(Section 3.4) lightcurve for each observation as its finaloutput, which can be further detrended and used for atransit search. The pipeline is highly automated and,in the event of improvements to the algorithm, edenAP can be re-run on all previous data with minimal effort.All raw data are stored at the University of Arizona, aswell as through a cloud storage provider (Amazon WebServices). 3.1.
Science Calibration
The first step in edenAP is to calibrate the raw sci-ence frames using the calibration frames discussed inSection 2.4. In the event that calibration frames are notavailable or are of poor quality, this step can be skippedwith the rest of the pipeline remaining the same. To cre-ate master calibration frames, we collect all bias frameswithin one month of the observation, and all dark andflat frames within the observation run. Monitoring offlat fields has indicated that these stay mostly constantover the course of a run, with the exception of minor lo-calized dust accumulation and chance occurrences such as insects getting trapped in the optical path. In caseswhere many hundreds of calibration frames are avail-able in the above time periods, we narrow the periodand only collect calibration frames within two to threedays of the observation.3.2.
Astrometry
We then derive the astrometric solution for ev-ery science frame by using a local installation of the astrometry.net software package (Lang et al. 2010).While this solution provides accurate astrometric cal-ibration for most frames, it can fail in case of partialcloud cover or poor seeing. If no astrometric solution canbe found for a particular image, the solution from thepreceding image is used, despite these data typically be-ing very poor. The astrometric solution derived is usedas a first guess for placing photometric apertures, how-ever, we always refine the centroid using the photutils DAOStarFinder method (Bradley et al. 2019), based onthe DAOFIND algorithm (Stetson 1987). Position re-finement is key to getting sub-pixel centroid precision,especially for our high proper motion target stars.3.3.
Photometry
Aperture photometry is performed using the photutils package (Bradley et al. 2019). For everystar in the field of view, we measure the intensity inapertures ranging from 5 to 50 pixels in steps of 1 pixel.The aperture size that minimizes the RMS scatter of thetarget star lightcurve is selected as the best aperture forall sources. The optimal size depends on detector andseeing, but typical size are roughly a few arcseconds.Sky background is calculated as the median of a 60 × Comparison Star Detrending
The final step in edenAP is to detrend the targetlightcurve on the basis of comparison star lightcurves.Trends are long or short term photometric variations inthe lightcurve that decrease transit detection sensitivity,and can arise from instrumental, atmospheric, and stel-lar variability. We select the best comparison stars byfirst filtering out stars that are saturated, are too faint(several magnitudes dimmer than the target) or have too https://photutils.readthedocs.io/en/stable/ Gibbs et al. many failed photometric measurements. Next, we di-vide the flux normalized target lightcurve by the normal-ized lightcurves of every comparison star, and rank thembased on the average standard deviation in windows of20 data points. The six with the lowest average devia-tion (i.e. those with the most similar data trends) aremedian-combined into a “super comparison” lightcurve,which is then divided from the target lightcurve. Forcrowded fields with many available comparison stars, itis conceivable that this selection method could weakenor remove transit signals. We believe this is highly un-likely, however, due to the improbability that compar-ison lightcurves would have the necessary shape to re-move a transit, and because the duration of the windowis shorter than any expected non-grazing transit. Nev-ertheless, we account for this in our sensitivity analysis(Section 6.2) by re-selecting comparison stars after in-jecting transits. TRANSIT SEARCHIn the subsequent steps we identify and remove resid-ual systematic trends (i.e., those not shared fully bycomparison stars) and search for lightcurve features thatare candidate transit events. Our approach is a modular,automatic, step-by-step process that is robust and easilyrepeatable, allowing for detailed test runs and processoptimization. As detailed in the following subsections,we use a simple median-detrending method and base ourvetting methods on instrumental parameters, such asairmass and centroid position, to attempt to explain ob-served trends and transit-like features. The end result iseither a promising candidate, triggering follow-up obser-vations, or sensitivity limits if no convincing candidateis found. A discussion of transit candidate follow-up isreserved for a future paper (Apai et al., in prep.).4.1.
Interactive Data Viewer
We visually inspect every lightcurve on a single EDENtarget to ensure that lightcurve anomalies are recog-nized and managed correctly. We select high-qualitydata for further analysis without relying on automaticalgorithms. To streamline this process, we have imple-mented an interactive data viewer that displays eachlightcurve along with systematic trends, allowing theuser to flag large sections of problematic data (e.g., stel-lar flares, passing clouds) for removal and points of inter-est (a transit-like feature) for further analysis. Exclud-ing poor-quality data is exceedingly important becausestrong systematic trends can be fit as transits, and theycan throw off the correct period determination if onetransit of an otherwise detectable period happened tooccur within it. Individual outlier data points are ig- nored in this step, but are efficiently removed by ourautomatic filtering in the next step.4.2.
Median Detrending
After visual inspection, lightcurves undergo auto-mated data cleaning and detrending. We fit a long-termtrend with a median filter of two hours and 2 σ -clip up-per outlying data before dividing out the trend. We donot clip below the median because of the risk of clippingdeep transits. Median filtering will reduce the depth ofall transits slightly, though our use of a two-hour filterwindow minimizes this effect for transits with durationsof less than one hour, which comprises most of our dis-covery space. An example of median detrending appliedto a real EDEN lightcurve with an injected transit of ∼
1% depth and TRAPPIST-1 b parameters is shownin Figure 1.While median detrending is a simple method, its ef-fects are predictable and robust. Although the medianfiltering will not remove short-period, transit-like trends,it will not remove real transits either, if they are deeperthan a few tenths of a percent (a danger of more compli-cated detrending techniques). Other trend-fitting meth-ods with which we have experimented when performingtransit injection tests include Savitzky-Golay (Savitzky& Golay 1964), biweight, and multivariate polynomialsconstructed from external parameters such as airmass,and centroid positions. Savitzky-Golay and biweight fil-tering have very similar results to median detrending,and while multivariate polynomials can outperform me-dian filters, they are also more likely to accidentally re-move a real transit feature. Despite their relative sim-plicity, median filters are reliable (Hippke et al. 2019).4.3.
Transit Least Squares
To search for transits in our detrended lightcurves,we utilize the package
Transit Least Squares ( TLS ,Hippke & Heller 2019). The primary improvement overbox least squares (BLS, Kov´acs et al. 2002) is that ratherthan fitting a boxcar model to a time series,
TLS fits amore realistic, fixed transit shape with limb-darkeningincluded, but the same parameters as BLS otherwise.We optimize the
TLS algorithm for our search by settingupper and lower limits on the stellar radius and massto those for M dwarfs (0 . − . (cid:12) , 0 . − . (cid:12) ) andthe maximum period to correspond to the approximateouter edge of the habitable zone ( ∼
10 days). We relyon our previously described data cleaning and detrend-ing steps to remove bad data, and all lightcurves areweighed equally regardless of photometric precision. Foreach search we save a median-smoothed periodogram, aswell as the phase folded model, transit parameters, false etection Limits for Nearby Late Red Dwarfs Figure 1. EIC-2 (LP 412-31) Example Detrending.
Data was taken with the Cassini telescope on 2018-12-11. The redline at bottom shows the injected transit signal (depth ∼ alarm probability (FAP), and signal detection efficiency(SDE) for the highest power period.4.4. Candidate Vetting
Most transit candidates identified by
TLS are falsepositives—and often obvious ones. Currently, vettingis done manually, but it may be automated in the fu-ture. The first check of a candidate is inspection of theviability of the
TLS output: are the transit parametersphysical, does the phase folded lightcurve have obviousflares or systematic trends, what are the SDE and FAPvalues? If these are viable, the interactive data viewer isused to look at systematic trends during transit times,which usually reveal systematic noise sources that in- troduced the feature. We pursue follow-up observationto eliminate astrophysical false positives (such as eclips-ing binaries) only after identifying a promising transitcandidate not explainable by other means. We do notspecifically set SDE or FAP values to eliminate transitcandidates, and consider even those with poor statistics.However, we do perform an analysis of the SDE and FAPvalues that indicate a robust detection in Section 6. THE FIRST EDEN TARGETSEIC-1 ( ), EIC-2 (
LP 412-31 ), and EIC-3 ( ) are all nearby M8/8.5ultracool dwarfs (Table 2). They are near the hydrogenburning limit and thus may be either high-mass brown
Gibbs et al. dwarfs or low-mass stars. In this section we will brieflydescribe their stellar properties and past observationsrelevant to a search for planets.5.1.
EIC-12MASSI J1835379+325954 , hereafter EIC-1, is anM8.5V dwarf located 5.7 parsecs away (Reid et al. 2003).It was discovered and identified as a nearby dwarf byL´epine et al. (2002) as part of the Digitized Sky Survey.Its brown dwarf status is currently unknown due to dif-fering lines of evidence (Saur et al. 2018; Reiners & Basri2009; Berdyugina et al. 2017). It is a known radio pul-sator with a strong magnetic field and a rapid 2 .
84 hr ro-tation period (Berger et al. 2008; Berdyugina et al. 2017;Kuzmychov et al. 2017; Hallinan et al. 2008, 2015). Apossible detection of auroral emission has recently beenreported for this target (Hallinan et al. 2015).EIC-1 has been the target of radial velocity (RV)observations by CARMENES (Tal-Or et al. 2018) andKeck NIRSPEC (Tanner et al. 2012), some photometricmonitoring by MEarth (Dittmann et al. 2016), a wide-orbiting companion search by
Spitzer
IRAC (Carsonet al. 2011), and Subaru adaptive optics (AO) obser-vations (Siegler et al. 2005), as well as numerous spec-troscopic studies from UV to radio wavelengths. Weare unaware of any companion candidates from theseobservations, but note that CARMENES identified itas “active RV-loud”, potentially making the detectionof habitable planets difficult by RV. EIC-1 was not ob-served by K2 and is scheduled to be observed by TESS in Sector 26 in June 2020.5.2.
EIC-2LP 412-31 , hereafter EIC-2, is an M8V dwarf located14.7 parsecs away, identified by Kirkpatrick et al. (1995).It has a rotational period of 0.61 days (Irwin et al. 2011)and is a known flare star with a previously observedgiant flare by XMM-Newton (Stelzer et al. 2006).EIC-2 has been the target of RV observations by theRed-Optical Planet Survey (Barnes et al. 2014) andKeck NIRSPEC (Rodler et al. 2012; Tanner et al. 2012),which have 2 σ sensitivity to M sin i > . M ⊕ through-out the habitable zone. It has also had periodic obser-vations by MEarth (Dittmann et al. 2016). It was notmonitored by K2 or Spitzer and is not scheduled to beobserved by
TESS until after the primary mission dueto its location near the ecliptic.5.3.
EIC-32MUCD 20263 , hereafter EIC-3, is an M8 dwarf lo-cated 15.6 parsecs away, identified by L´epine & Shara(2005). Compared to EIC-1 and EIC-2, it has been the target of relatively few observations. It has been ob-served as part of MEarth and the SDSS-III APOGEERadial Velocity Survey (Deshpande et al. 2013). It wasnot observed by K2 or Spitzer and is scheduled to beobserved by
TESS in Sector 20 in January 2020. PLANET DETECTION LIMITS FOR EIC-1,EIC-2, AND EIC-3In this section we report the results of our previouslydescribed observations, data reduction and detrendingpipelines, and transit search for the first three EDENtargets. Both visual and automatic transit injection andrecovery tests are performed, described in Sections 6.2.2and 6.2.3 respectively. We do not detect any convincingplanet candidates for these stars, but place sensitive up-per limits on the presence of transiting planets aroundthem. 6.1.
Description of Lightcurves
EIC-1, EIC-2, and EIC-3 were observed for 200 to 300hours each from June 2018 to February 2019, with 40to 60 individual observations per target (see Table 3).The observations are highly clustered in time, with a fewperiods of continuous or nearly-continuous observationsat different observatories lasting 24 hours or more.Roughly 60–80% of the cleaned, detrended data areof sufficient quality for a subsequent transit search; therest is affected by bad weather conditions or techni-cal issues. Durations for the individual high-qualitylightcurves range between 2 and 10 hours, depending ontarget priority, observability, and weather. Some gapsless than 2 hours long exist within longer lightcurves be-cause of passing clouds, temporary technical issues, ormanual removal of flares or poor data sections. Cadencesvary by a factor of ∼ ∼ . . etection Limits for Nearby Late Red Dwarfs Table 2.
EDEN TargetsID Name Spec. Type Dist. (pc) I Mag K Mag R.A. (J2000) Decl. (J2000)EIC-1 2MASSIJ1835379+325954 M8.5V 5.7 13.46 9.17 18:35:37.88 +32:59:53.31EIC-2 LP 412-31 M8V 14.7 14.48 10.64 03:20:59.71 +18:54:22.77EIC-3 2MUCD20263 M8 15.6 14.35 10.84 07:14:03.94 +37:02:46.03 of ∼ Sensitivity Analysis
To assess the transit detection capability of our obser-vations, we implement a transit injection and recoveryroutine. We inject realistic transits into our raw tar-get lightcurves using the analytic solutions of Mandel& Agol (2002) as implemented in batman (BAsic Tran-sit Model cAlculatioN, Kreidberg 2015), re-select com-parison stars with the same procedure described in Sec-tion 3.4, and attempt to recover the transit signals usingour detrending and transit search pipeline. We also per-form a limited visual transit recovery test to comparethe sensitivity of the pipeline to a manual search by eye.6.2.1.
Manual Transit Search
Before injecting any simulated transits, we performa
TLS search and manual inspection of the lightcurvesfor each target to attempt to identify real transit candi-dates. Three team members reviewed every lightcurveindividually and marked features of interest (transit can-didates), which were then compared and vetted togetheraccording to Section 4.4, along with the transit candi-dates identified by
TLS . We do not consider any of thetransit candidates to be likely planets worthy of follow-up observation; we instead find them to be consistentwith stellar variability and systematics. These steps donot definitively exclude the presence of transiting plan-ets, but the probability of detecting a transiting planetis low, and will be quantified through our sensitivityanalysis. 6.2.2.
Visual Transit Recovery Tests
As a comparison to the following
TLS sensitivity re-sults in Section 6.2.3, we also performed a limited, visualtransit injection and recovery test. The purpose was toprobe what transits team members could find by eye,without prior knowledge of their existence or location.One team member injected a TRAPPIST-1 b ana-log (1.1 R ⊕ , ∼ .
7% depth, 1.51 day period, Gillon et al. 2017) at a random phase into a fraction of thelightcurves of each target (see Section 6.2.3 for otherparameters). Three other team members each receivedindependent sets of these lightcurves with injections atrandom phase. Nearly half of the lightcurve sets did notcontain any injections so that the team would not becompelled to identify transit candidates if they believednone were convincing.True positives are defined as real injections that arecorrectly identified, false positives are non-injection fea-tures wrongly identified as transits, and false nega-tives are real injections not identified. Collectively, outof 41 observed injected transits in 5 different sets oflightcurves, the team had a 1:1 true to false positive ra-tio, and a 4:1 false negative to true positive ratio. To de-termine our average visual sensitivity to TRAPPIST-1 banalogs, we consider how many sets of target lightcurves(containing multiple observed transit injections) had atleast one true positive, irrespective of false negatives.Four out of five sets of target lightcurves with injectionshad one or more true positive, therefore we consider ouraverage visual sensitivity to TRAPPIST-1 b analogs tobe ∼ Automated Transit Recovery Tests
The purpose of our automatic transit injection andrecovery tests is to provide a scalable and objectivesensitivity analysis method. For these tests, we sim-ulate transits for planets in a logarithmic grid of pe-riod and radius from 0.5 to 10 days and 0.6 to 4 Earthradii, respectively, constituting most of our expecteddiscovery space. The stellar radii of the target stars0
Gibbs et al.
Table 3.
Log of ObservationsID Name Nights Obs. Hours Obs. Median Unbinned Precision (%) % used for
TLS
EIC-1 2MASSIJ1835379+325954 57 205.3 0.163 ∼ ∼ ∼ Note —Appendix A provides a detailed log of the observations.
Figure 2.
EIC-2 (LP 412-31) Sample Lightcurves. The data are unbinned so that the relative cadence and raw precision ofthe instruments can be seen. Telescope and date are shown in the top left for each lightcurve. were determined from available surface gravity measure-ments (Tsuji & Nakajima 2016; Rajpurohit et al. 2018).Within the grid, orbits are assumed to be circular withrandom phases and with impact parameters randomlydrawn from a uniform distribution between 0 . . R p , 1 . R p creates an artificial dependenceon planet radius for transit sensitivity analysis, whichdistracts from more meaningful sensitivity trends.The transit injections have quadratic limb darkeninglaws from Claret (1998) for the I band. While otherlimb darkening laws (e.g., logarithmic or exponential)may be more realistic (Espinoza & Jord´an 2016), thedifferences for the sensitivity analysis are negligible inthe present noise level regime. We further assume that etection Limits for Nearby Late Red Dwarfs Positive Identification of Transits
For us to consider a transit detected by
TLS to be atrue positive result, it must meet one of the followingtwo criteria: (1) the best period is less than 0.5 hoursdifferent from the true period of the injected planet, or(2) at least one identified transit midpoint time is within20 minutes of a real injected transit midpoint (i.e., atransit candidate was correctly identified, but the periodis incorrect). All candidates which meet condition one,naturally meet condition two.We make an additional distinction between true posi-tives recovered by
TLS and “successful recoveries”, whichwe count in our sensitivity analysis. Successful recover-ies are a subset of true positives that also pass a de-tection significance criterion. We make this distinctionbecause it is possible in a real search to detect a shallowtransit only to dismiss it due to low signal. We do notwant to consider these cases as successful in our analysis.Therefore, we limit successful recoveries in this analysisto detections that exceed a minimum signal detectionefficiency (SDE) (Hippke & Heller 2019), correspondingto a detection in a real search that would likely passvetting and trigger follow-up observations. The SDE isthe significance of a period relative to the average sig-nificance of all other periods.We determine the minimum SDE for each target in-dividually based on the global SDE distribution of falsepositives resulting from our injection recoveries. We setthe minimum SDE required for a successful detection asthe SDE that is greater than 95% of false positives (i.e.,only 5% of false positives have a higher SDE). For ourthree targets, the minimum robust SDE value ranges forEIC-1, 2 and 3, are roughly 6, 7, and 11.The true and false positive distributions are shown forEIC-1, EIC-2, and EIC-3 in Figure 3. The differencesresult from the unique structure of each target’s set oflightcurves, which produce higher and lower significance false positives. One noticeable feature of these plots(especially for EIC-3) is that the false positive distribu-tion does not continually increase for lower SDE values,but is instead centered at a specific SDE. This poten-tially counter-intuitive distribution is caused by both thestructure of each target’s set of lightcurves, as well asthe range and step size of the injection grid. Each tar-get has a dominant false positive signal that is returnedwhen there is no transit injection. Our grid range in-cludes two rows of sub-Earth size planets that are ex-tremely shallow in depth, and each injection in theserows will return nearly the same false positive SDE asif there was no injection. This leads to a build-up of ahigh fraction of false positives around the no injectionSDE value, which corresponds roughly to the maximumof the false positive distribution. The higher fraction oftrue positives at lower SDE values is due to the fact thatthere is a certain range of injection depths that will onlybe a marginally higher power than the no injection falsepositive and thus will have a low SDE, but they will stillbe detected successfully at high rates.It is important to note that the SDE cutoff is notused to determine the significance of transit candidatesin the real transit search and is only used in finding thesignificance of injection recoveries after concluding byother means (Section 6.2.1) that the data contains noreal transits. Therefore, it likely provides a conservativesensitivity estimate. Finally, the SDE cutoff cannot beexpected to fully capture the probability that a truepositive candidate would be followed-up and confirmed,but rather is a best attempt at conservatively estimatingthe likelihood given subjective human involvement indeciding what is and what is not a convincing candidate.While it would be more desirable to build a completelyautomatic vetting algorithm, for our observations thealgorithm would need to be prohibitively intelligent andcomplex, and could result in more missed planets.6.2.5.
Pipeline Sensitivity
We illustrate our transit detection sensitivity for EIC-1, EIC-2, and EIC-3 in Figures 4, 5, and 6, respectively.The top plots show the efficiency of our pipeline to de-tect transiting planets, while the bottom plots representtotal detection probability for all planets, both tran-siting and non-transiting, based on our transit detec-tion sensitivity and the geometric transit probability forplanets as a function of semi-major axis ( P tr = R ∗ a ). Tocalculate the overall sensitivity within a specific rangeof periods and radii, we simply average the detectionsensitivity in that range. Mean sensitivities for selectranges are shown in Table 4.2 Gibbs et al.
Table 4.
EDEN SensitivityTransit Sensitivity (%) Total Detectability (%)ID 0.5 to 2 days 2 to 5 days 5+ days 0.5 to 2 days 2 to 5 days 5+ daysEIC-1 60 ±
10 35 ± ± ± ± ± ±
10 22 ± ± ± ± ± ±
10 40 ± ± ± ± ± Note —Reported transit sensitivity and total detectability values are averages for planets between one and two Earth radii.Listed errors are the standard error of the mean.7.
DISCUSSION7.1.
EDEN Sensitivity
The sensitivity maps for EIC-1, EIC-2, and EIC-3show that we have the potential to successfully detecttransiting Earth-sized planets in the habitable zones ofnearby, ultracool dwarfs. Furthermore, they show thatin a few cases we can detect sub-Earth-sized planets oncloser orbits provided two or more transits occur dur-ing high-quality observations. To compare these resultswith
TESS , the estimated photometric precisions forEIC-1, EIC-2, and EIC-3 are 0.136, 0.299, and 0.343 %respectively in one hour periods of observation (
TESS
Mag. 13.28, 14.35, and 14.52) (Stassun et al. 2018).These are very similar to the median achieved precisionsof unbinned EDEN lightcurves typically at a one minute cadence (0.163, 0.315, and 0.380 % respectively). Thus,with long-term targeted observations it is possible wecould achieve better sensitivities than
TESS for singletargets, in cases where the benefit of our increased pho-tometric precision can outweigh the benefit of
TESS ’scontinuous 28 day coverage.7.2.
Sensitivity Analysis and Detection Biases
The primary goal of our sensitivity analysis is settingplanetary limits around the target stars that will be use-ful for future observations. These limits can potentiallyimprove the efficiency of similar transit surveys, andin the case of any future radial velocity (RV) compan-ion candidates, help to constrain the inclination. Thesecondary goal is to help to identify strengths, weak-nesses, and biases of our observations and routines. Us-ing this information we can improve our future observa-tions, data reduction, detrending, and search methods.That being stated, we believe our methods are nearlyoptimized, and only minor improvements can still beexpected, which would not significantly change our sen-sitivity results.The sensitivity maps in Figures 4, 5 and 6 show twodistinct gradients of decreasing sensitivity. As one would expect, these gradients are for smaller planets ( < R ⊕ ,i.e., lower transit signal-to-noise), and longer periods( > ∼ ∼ Kepler , it is possible that by misfortune ashort-period planet never transits during an observation.Some columns may also have lower or higher sensitivitycompared to their surroundings depending on whetheror not the period is close to a harmonic of the period ofobservations, and therefore are more or less sensitive tophase. 7.3.
Inner Planets and Outer Planets
Our detection limits for inner, shorter period plan-ets can place significant constraints on the probabil-ity of outer, longer period planets, where observational etection Limits for Nearby Late Red Dwarfs Figure 3. Signal Detection Efficiency (SDE) Distribution for EICs.
SDE is calculated as the signal to noise of thehighest power in the recovery periodogram (Hippke & Heller 2019). The number of false positives does not continue increasingfor lower SDE values because of the characteristic false positive unique to each set of lightcurves. Further discussion can befound in Section 6.2.4. coverage is lacking, in light of the occurrence rates ofsmall planets around M-dwarfs (Mulders et al. 2015a).The strongest example of this is the TRAPPIST-1 sys-tem. TRAPPIST-1b and c were detected by groundbased observations that motivated space-based follow-up, which discovered longer-period planets. For our tar-gets, the approximate probability to detect transitingplanets analogous to TRAPPIST-1b and c with one ormore transits is ∼ Constraints on Planet Formation Theory
The sample of planets around very cool stars is stillsmall, since late M-dwarfs are too faint for wide-fieldtransit surveys. In addition, higher stellar activity canfurther complicate the analyses of their lightcurves (e.g.,Perger et al. 2017). EDEN has unique capabilities totarget these stars and any planet our survey may detectwill serve as a valuable addition to this small sample.The examples of TRAPPIST-1 (Gillon et al. 2017) andGJ 3512b (Morales et al. 2019) showed how individualdiscoveries can challenge our current understanding ofplanet formation and inform tests of competing forma-tion theories. To assess such discoveries in terms of theactual underlying population of exoplanets, it is crucialto be aware of and able to quantify the relevant selection4
Gibbs et al.
Figure 4. EIC-1 (2MASSI J1835379+325954) sensitivity maps.
Top: Pipeline sensitivity to transiting planets. Eachgrid block represents the fraction of transiting planets recovered out of all injected planets (both recoverable and non-recoverable)for a period and radius centered within the block. Bottom: Total detectability considering the geometric transit probability( p tr × p det ). etection Limits for Nearby Late Red Dwarfs Figure 5. EIC-2 (LP 412-31) sensitivity maps.
Top: Pipeline sensitivity to transiting planets. Each grid block representsthe fraction of transiting planets recovered out of all injected planets (both recoverable and non-recoverable) for a period andradius centered within the block. Bottom: Total detectability considering the geometric transit probability ( p tr × p det ). Gibbs et al.
Figure 6. EIC-3 (2MUCD 20263) sensitivity maps.
Top: Pipeline sensitivity to transiting planets. Each grid blockrepresents the fraction of transiting planets recovered out of all injected planets (both recoverable and non-recoverable) fora period and radius centered within the block. Bottom: Total detectability considering the geometric transit probability( p tr × p det ). etection Limits for Nearby Late Red Dwarfs observable synthetic population enables statistical com-parisons between theory and observations (e.g., Mor-dasini et al. 2009). Detailed forward models of well-characterized exoplanet surveys can directly test planetformation models and even optimize free parameters(Mulders et al. 2018, 2019). Such dedicated M-dwarfpopulation syntheses are powerful tools to constrainplanet formation in a parameter space different fromthat around solar-type stars. The predictive power of ex-oplanet surveys depends on the survey’s sensitivity andthe number of targets observed: as the number of tar-gets observed by EDEN increases, the emerging planetstatistics will increase in significance. Currently, we aresurveying targets at an increasing rate. CONCLUSIONSWe present the first lightcurves and sensitivity anal-ysis from the EDEN transiting exoplanet survey. Thekey results of our studies are as follows:1) EDEN’s 0.6–2.3 m diameter telescopes provide veryhigh-quality (median 0.28% precision) red-visual (500–900 nm) lightcurves for late-M-dwarf stars in the solarneighborhood.2) We present data on three nearby late-M dwarfs,obtained in the context of a multi-continental transitsearch campaign. Our observations include 57, 56, and43 nights of data on the three targets (EIC-1, EIC-2,EIC-3), respectively.3) We reviewed the EDEN data reduction and pho-tometry pipeline and our de-trending and transit searchprocedure. Our procedure has been tested, optimized,and validated through transit injection-and-recoverytests.4) Our lightcurves reach the sensitivity to detect tran-sits of Earth-sized planets. In the total of 156 obser-vations on the three targets, no convincing candidatetransit events have been identified.5) We describe our transit injection-and-recovery-based approach to assess sensitivity to planetary tran-sits as a function of planet radius and orbital period. Weprovide a detailed assessment of the sensitivity to tran-sits around our three targets. We show these estimates are conservative compared to manual transit searches byeye.6) Our data can confidently exclude the presenceof Earth-sized transiting planets with orbital periodsshorter than 1 day around each of the targets. Earth-sized planets with 1–2 day periods would have been de-tected in our data in two transits with ∼
60% probabil-ity.7) EDEN reaches a sensitivity to Earth-sized plan-ets around faint red dwarf stars ( I ≈
15 mag), whichare challenging targets even for NASA’s
TESS mission.Thus, EDEN data on such systems can provide comple-mentary information to
TESS lightcurves.8) Our study demonstrates the potential of the EDENsurvey to robustly probe the presence of transiting,Earth-sized planets within and inside of the habitablezones of nearby late red dwarfs and, in case of non-detection, to set stringent upper limits on the presenceof such planets.ACKNOWLEDGMENTSThe results reported herein benefited from collabora-tions and/or information exchange within NASAs Nexusfor Exoplanet System Science (NExSS) research coordi-nation network sponsored by NASAs Science MissionDirectorate. This study used results from the RECONSproject (recons.org). T. Henning acknowledges supportfrom the European Research Council under the Horizon2020 Framework Program via the ERC Advanced GrantOrigins 83 24 28. B.V. Rackham acknowledges supportfrom the Heising-Simons Foundation.This research made use of Photutils, an Astropypackage for detection and photometry of astronomicalsources (Bradley et al. 2019).The principal investigators of EDEN are D. Apai, P.Gabor, T. Henning, and W-P. Chen. Initial target se-lection was performed by A. Mousseau, A. Bixel, and D.Apai. Telescope allocation is organized by D. Apai, L.Mancini, W-P. Chen, C.C. Ngeow, and P. Gabor. Ob-servations have been performed by H. Baehr, A. Bhan-dare. A. Bixel, R. Boyle (pilot studies as VATT’s Tele-scope Scientist), S. Brown, J. Dietrich, A. Gibbs, M.H¨aberle, W. Ip, M. Keppler, L. Mancini, V. Marian,K. Molaverdikhani, A. Mousseau, J. Perez Chavez, B.Rackham, P. Sarkis, M. Schlecker, Q.J. Socia, A. Tsaiand others. Software has been developed by A. Bixel, N.Espinoza, A. Gibbs, J. Perez Chavez, and B. Rackham.The EDEN automatic pipeline ( edenAP ) was developedby N. Espinoza (precursor pipeline), B. Rackham (bulkdevelopment), A. Bixel, J. Perez Chavez (calibrationsteps), and A. Gibbs. Data organization and collec-8
Gibbs et al. tion, and the interactive data viewer were developed byA. Bixel. Detrending, transit search, sensitivity analy-sis steps have been implemented and developed by A.Gibbs.This research has made use of the Cassini 1.52 m tele-scope, which is operated by INAF-OAS “Osservatorio diAstrofisica e Scienza dello Spazio” of Bologna in Loiano(Italy).We thank the mountain operations staff at the Univer-sity of Arizona, Mount Lemmon Sky Center, Lulin Ob-servatory, Calar Alto Observatory, Loaino Telescopes,Mount Graham International Observatory, Vatican Ad- vanced Technology Telescope, and Kitt Peak NationalObservatory.
Facilities:
Mount Lemmon Sky Center, Lulin Obser-vatory, Calar Alto Observatory, Loiano 152cm CassiniTelescope, Kuiper 61-inch Telescope, Vatican AdvancedTechnology Telescope (VATT), Bok 2.3m Telescope
Software:
Numpy (van der Walt et al. 2011), Pan-das(McKinney 2010), Scipy (Virtanen et al. 2019), As-tropy (Price-Whelan et al. 2018), Photutils (Bradleyet al. 2019), astronomy.net (Lang et al. 2010),
TLS (Hippke & Heller 2019), batman (Kreidberg 2015), edenAP
APPENDIX A. OBSERVATION LOGIn case of future research or discoveries where EDEN data may be useful, we list all periods of observations forEIC-1, EIC-2, and EIC-3 in Tables 5, 6, and 7. REFERENCES
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EIC-1 (2MASSI J1835379+325954) List of Observations
Telescope Local Date BJD Start ( − − Gibbs et al.
Table 6.
EIC-2 (LP 412-31) List of Observations
Telescope Local Date BJD Start ( − − etection Limits for Nearby Late Red Dwarfs Table 7.
EIC-3 (2MUCD 20263) List of Observations
Telescope Local Date BJD Start ( − −−