Transiting Planets with LSST III: Detection Rate per Year of Operation
Savannah R. Jacklin, Michael B. Lund, Joshua Pepper, Keivan G. Stassun
AAccepted to AJ: March 2, 2017
Preprint typeset using L A TEX style emulateapj v. 12/16/11
TRANSITING PLANETS WITH LSST III: DETECTION RATE PER YEAR OF OPERATION
Savannah R. Jacklin , Michael B. Lund , Joshua Pepper , Keivan G. Stassun Accepted to AJ:
March 2, 2017
ABSTRACTThe Large Synoptic Survey Telescope (LSST) will generate light curves for approximately 1 billionstars. Our previous work has demonstrated that, by the end of the LSST 10-yr mission, large numbersof transiting exoplanetary systems could be recovered using the LSST “deep drilling” cadence. Herewe extend our previous work to examine how the recoverability of transiting planets over a range oforbital periods and radii evolves per year of LSST operation. As specific example systems we considerhot Jupiters orbiting solar-type stars and hot Neptunes orbiting K-Dwarfs at distances from Earth ofseveral kpc, as well as super-Earths orbiting nearby low-mass M-dwarfs. The detection of transitingplanets increases steadily with the accumulation of data over time, generally becoming large ( (cid:38) (cid:46) INTRODUCTION
In the era of large all sky survey telescopes suchas LSST, it has become increasingly important for as-tronomers to develop the appropriate tools to analyzethe veritable flood of data that will soon be available.LSST is currently under construction on Cerro Pach´on inChile, and after a scheduled first light in ∼ Kepler (Borucki et al. 2010)and TESS (Ricker et al. 2015), or small, ground-basedsurveys such as KELT (Pepper et al. 2007, 2012), HAT-Net (Bakos et al. 2004), or SuperWASP (Pollacco et al.2006), LSST is not optimized for exoplanet detection.LSST will operate at two primary cadences, hereafterreferred to as “regular” and “deep-drilling”. Regular ca-dence observations will constitute approximately 90% ofthe telescope’s observation time, with target objects re-ceiving approximately 1000 observations over the courseof LSST’s ten year mission. Deep drilling cadence obser-vations will take up the remaining 10% of LSST’s obser-vation time, with target objects receiving ∼ ,
000 ob-servations after ten years (Ivezic et al. 2008). Althoughthese cadences are not ideal for exoplanet detection, weshowed in Lund et al. (2015) and Jacklin et al. (2015)that the sheer number of LSST targets ( ∼ ) makes a Department of Physics, Fisk University, Nashville, TN37208, USA Department of Physics and Astronomy, Vanderbilt Univer-sity, Nashville, TN 37235, USA Department of Physics, Lehigh University, Bethlehem, PA18015, USA large number of hot Jupiter and other short-period exo-planet detections likely, particularly in the deep-drillingmode.Indeed, our previous work has demonstrated thatLSST will have the ability to detect exoplanets in manyinteresting regions of parameter space, and because ofits magnitude depth and sky coverage will include typesof systems that are at present poorly explored. This in-cludes planets orbiting nearby late-type stars and largerplanets orbiting Sun-like stars at very large distances.While Lund et al. (2015) and Jacklin et al. (2015) con-sidered the yield of transiting exoplanets for the full 10-yrLSST dataset, it is worth investigating how quickly LSSTis likely to achieve various types of exoplanet discoveriesover the course of its lifetime. Using the LSST OperationSimulation (OpSim) of deep-drilling fields, in this paperwe predict the rate of transiting exoplanet detection byLSST as a function of year of observation.The paper proceeds as follows: In Section 2 we discussour strategy for generating simulated light curves, thefiducial star-planet systems simulated, the method of re-covering the period of transits, and checking the recoveryresults for false positives in order to determine detectabil-ity. Section 3 presents the results for the detectability ofvarious types of transiting planets, as a function of timethroughout the LSST 10-year mission, for each of thefiducial stellar systems. Our results show that LSST willbe able to detect a wide variety of exoplanets orbitingseveral different types of stars at periods ranging from0.5–20 days, and that it can do so within the first fewyears of data collection in the deep-drilling fields for veryshort-period planets. We conclude with a brief discus-sion, including planned future work, and a summary inSection 4. METHODS
Here we describe the methods by which we generatesimulated LSST light curves, list the fiducial transitingexoplanets that we will analyze throughout this work,describe how we inject simulated transits of these exo-planets into the simulated light curves, and describe theperiod-search methods we use to probe the detection of a r X i v : . [ a s t r o - ph . E P ] M a r the transits in the simulated light curves. Simulated Light Curve Generation
We create simulated light curves using the method de-scribed in Lund et al. (2015); Jacklin et al. (2015) whichwe summarize here. Each light curve depends on fiveparameters: host star mass, radius of transiting planet,distance of the system from Earth, period of transitingplanet, and LSST cadence (i.e. regular or deep-drilling).Each of the systems simulated assumes circular orbitswith equatorial transits (i.e., we do not consider the ef-fects of orbital eccentricity or grazing transits).All host stars in our simulations (see Section 2.2) aredwarfs with spectral types determined via mass inter-polation from Table 15.8 in Cox & Pilachowski (2000),absolute magnitudes per LSST filter from Covey et al.(2007), and radii derived using the mass-radius relation-ship from Beatty & Gaudi (2008). With this informa-tion, we create continuous and noiseless light curves. Wethen inject a simple boxcar transit into each of the lightcurves with a duration based on the planetary orbitalperiod and stellar radius, and a depth dependent on theratio of the stellar to planetary radii. In this analysis weassume circular orbits with equatorial transits, as well asnoiseless stellar hosts.With continuous light curves for a range of stellar radii,spectral types, planet radii, and planet periods (see Sec-tion 2.2), we time-sample them using the LSST oper-ation simulation (OpSim) v2.3.2 run 3.61. The OpSimsimulates ten full years of LSST observations consideringfactors such as weather variations and downtime for tele-scope maintenance. Out of the many parameters avail-able from OpSim, we utilize time of observation, filter,and limiting magnitude. Based on our previous findingsthat the vast majority of transiting exoplanet detectionswill occur in the deep-drilling fields (Lund et al. 2015;Jacklin et al. 2015), we therefore consider only the deep-drilling cadence from the OpSim.Once a light curve has been simulated we sample itand place our planet-star systems at a chosen distanceand calculate the star’s apparent magnitude in LSST’s g, r, and i bands, which exhibit the least random pho-tometric noise as shown in Lund et al. (2015). We thencalculate the expected total per-visit photometric preci-sion per LSST band using the stellar apparent magnitudewith: σ tot = σ sys + σ rand , (1)as described in Ivezic et al. (2008). We take σ sys as thesystem designed noise floor of 0.005 for each band. Therandom photometric noise σ rand varies with respect toa band-specific parameter ( γ ) and the apparent magni-tude, and is calculated by: σ rand = (0 . − γ ) x + γx , (2)in which x = 10 ( m − m ) where m is the 5 σ limiting mag-nitude per LSST filter. The value of m is generated byOPSIM and changes each visit based on sky brightness,seeing, exposure time, airmass, atmospheric extinction,and instrument throughput (Ivezic et al. 2008). We addnoise to the light curves on a per-band basis in order tosimulate observed S/N. After noise is added, the g , r ,and i band light curves are median-subtracted and com-bined in order to form one master light curve. Table 1 TABLE 1Stellar Noise
Mass ( M (cid:12) ) Filter Abs Mag App Mag Total Noise (mag)1.0 g 5.84 20.07 0.011.0 r 4.47 18.70 0.011.0 i 4.31 18.54 0.010.6 g 10.21 24.44 0.020.6 r 7.65 21.87 0.020.6 i 7.10 21.33 0.120.25 g 14.41 28.63 5.540.25 r 11.31 25.53 0.430.25 i 9.72 23.94 0.19Absolute magnitude, total magnitude, and total noise as afunction of LSST filter and band for each of simulated system. lists the absolute magnitude, total magnitude, and totalnoise as a function of LSST filter and band for each ofour simulated systems described in Section 2.2.We note that this treatment of noise in the light curvesdoes not at present include the possible effects of contam-ination by neighboring stars, which could become im-portant for crowded regions such as the Galactic plane,bulge, and possibly also the Magellanic Clouds. We defera treatment of this additional complication to a followuppaper (Lund et al., in preparation), and for our currentpurposes emphasize that the approach laid out here ap-plies, strictly speaking, to non-crowded fields.We also do not attempt to simulate the possible ef-fects of stellar noise (e.g., activity). As described in thefollowing section, we have selected transiting planets tosimulate that would result in relatively large transit sig-nals of (cid:38) Example Exoplanet Systems Simulated
In order to explore a representative range of results, wesimulate three fiducial exoplanet systems. We begin withthe same fiducial system as in our previous works (Lundet al. 2015; Jacklin et al. 2015), namely, a hot Jupiterwith a radius of 10 R ⊕ orbiting a 1 M (cid:12) G-dwarf host starat 7 kpc. Second, we simulate a hot Neptune with a ra-dius of 6 R ⊕ orbiting a 0 . M (cid:12) K-dwarf at 2 kpc. Third,we analyze a hot Super-Earth with a radius of 2 R ⊕ or-biting a 0 . M (cid:12) M-dwarf at 200 pc. Each of these caseswas chosen specifically to fit within LSST’s expected pa-rameter space (i.e., within the detection and saturationlimits of all filters; see Fig. 1) (Lund et al. 2016). Theplanet radii were selected to create an approximate 1%drop in total stellar flux as observed from Earth.The quality of light curves generated for exoplanet de-tection primarily depends on the number of points in-cluded, which for LSST is ∼ ∼ Fig. 1.—
This figure displays, for a given stellar mass and dis-tance, how many observations will be of sufficient precision ( < ∼ Recovery of Simulated Planets
Period Search with Box-fitting Least Squares
To detect the planetary transits in the simulated lightcurves, we use the Box-fitting Least Squares (BLS) algo-rithm (Kov´acs et al. 2002) as implemented through theVARTOOLS software package (Hartman & Bakos 2016).Specific details about our usage of BLS as a period finderare described in Lund et al. (2015); Jacklin et al. (2015).For this work, we perform the BLS period search in allcases over the period range 0 . ≤ P ≤
20 d. We imple-ment BLS on each of our simulated light curves for eachsystem architecture (see Section 2.2). To probe the like-lihood of exoplanet detection with the accumulation ofLSST data over time, we apply the BLS detection algo-rithm to each simulated light curve 10 times, once eachfor elapsed time ∆ t = [1 ,
10] yr from the start of LSSTobservations.
Exoplanet Detection
In this work, we deem an exoplanet “recovered” if thetop period returned by BLS is within 0.1% of the inputperiod. An exoplanet is “detected” if the period is recov-ered and the false positive probability is less than 0.1%.The false positive probability varies by the number ofyears of accumulated data.We calculate the false positive probability by creatingan equivalent light curve with no injected transit for eachcadence (i.e. regular or deep-drilling), stellar mass, dis-tance, and year of observation. The resultant light curvesare then run through BLS, which calculates the highestpower peak returned by a non-transiting system. Thisprocess returns ten top values for the BLS powers, onefor each year of observation, for a given stellar mass anddistance combination. These values of the BLS power areused as a comparison template for each transiting systemsharing the same stellar mass and distance: if the periodof a transiting planet is recovered, and the BLS powerof that period is greater than the false alarm probability,the planet is considered detected.
Mitigation of Diurnal Sampling
As a ground-based telescope, exoplanet detection us-ing LSST will necessarily be affected by diurnal observingpatterns. Jacklin et al. (2015) showed that the effects ofdiurnal sampling specifically limit the detection proba-bility at periods of integer and half-integer days. As acheck, we finely sampled the range of periods from 4.9days to 5.1 days with a resolution of 0.01 d for a 12 R ⊕ planet orbiting a 1 M (cid:12) star at 7 kpc over ten years of ob-servation. Figure 2 shows the detection probability, withthe expected drop in detection at a period of exactly fivedays. Based on the sharpness of this probability decreasewe do not consider periods within 0.05d of integer andhalf-integer days for the remainder of this analysis. Asimilar sharp decrease in detection is exhibited at an in-teger sidereal day (at ∼ .
98 solar days); this feature iswithin 0.05d of the integer-day feature and thus is alsoexcluded from the remainder of our analysis.
Fig. 2.—
This figure shows a detection drop at period that is aninteger multiple of 1 day ( ∼ ∼ .
98 days)for a 1 M (cid:12) , 12 R ⊕ transiting exoplanet system at 7 kpc. Points thatfall within the region of exclusion (gray area) are below the timeresolution of our later simulations. We therefore exclude parameterspace within 0.05 d of integer and half integer multiples of 1 d fromperiod searches for the remainder this study. RESULTS: TRANSITING PLANET DETECTABILITYDURING THE LSST 10-YEAR MISSION
In this section, we present the resulting transitingplanet detection probabilities as a function of time foreach of the three fiducial cases we simulated (Section 2.2),in turn.
Hot Jupiter Detection
The most successful exoplanet detection in the regionof parameter space tested occurred with large planets or-biting a 1 M (cid:12) host star at 7 kpc (see Figure 1). Here wetested a 10 R ⊕ transiting exoplanet (Figure 3), represent-ing the original system analyzed for period recoverabil-ity in Jacklin et al. (2015). As shown by the logarithmicshading in Figure 3, the large size of the transiting exo-planet yields a high probability of detection. Appreciabledetection at very short periods ( < Fig. 3.—
Two-dimensional histogram across orbital period andyear of observation for a G-dwarf located in a deep-drilling field.This figure shows the results of simulating a 10 R ⊕ transiting hotJupiter at 7 kpc. The logarithmic color bar indicates the percentof total cases where the period of the planet is recovered to within0.1% accuracy with an accompanying power that crosses the powerthreshold for a null transit of the same system. Periods at integerand half-integer days are removed in order to mitigate the effectsof diurnal sampling. Hot Neptune Detection
Results for a hot transiting Neptune-sized planet arealso promising. We analyzed a 6 R ⊕ planet and a 4 R ⊕ planet transiting a 0 . M (cid:12) K-dwarf at 2 kpc (Figure 5).Detection of the 6 R ⊕ exoplanet is high out to roughly 8-day periods after seven years of observation, with detec-tion probabilities increasing with further years of obser-vation. Detection of the 4 R ⊕ exoplanet is more difficult,with high detection occurring only at < Hot Super Earth Detection
Fig. 4.—
Detection probability as a function or orbital periodfor a G-dwarf with a 10 R ⊕ transiting exoplanet at 7 kpc, basedon light curves after 4, 6, and 10 years of LSST operations. Thedetection curves have had integer and half-integer periods removed,and are smoothed over a 3-day window. Fig. 5.—
Two-dimensional histograms across orbital period andyear of observation for a K-dwarf located in a deep-drilling field.The top figure simulates a 6 R ⊕ planet, and the bottom figure rep-resents a 4 R ⊕ planet, both utilizing a similar legend to Figure 3.Periods at integer and half-integer days are removed in order tomitigate the negative effects of diurnal sampling. The final system analyzed is a 2 R ⊕ transiting ex-oplanet orbiting a 0 . M ⊕ M-dwarf at a distance of200 pc. This system is the most Earth-like of the ex-amples considered here and could potentially represent
Fig. 6.—
Detection probability as a function or orbital periodfor a K-dwarf at 2 kpc with a transiting exoplanet of 6 R ⊕ (solidlines) and 4 R ⊕ (dashed lines). The data have been processed inthe same manner as Figure 4. Fig. 7.—
M-dwarf deep-drilling field two-dimensional histogramin period and year of observation space. This figure simulates a2 R ⊕ transiting hot Super Earth at 200 pc. This figure was createdusing the same data processing used for Figure 3 and Figure 5. a rocky planet in an optimistic habitable zone as men-tioned by Selsis et al. (2007) and defined by Kasting et al.(1993) at the fringes of our exoplanet detection spaceas defined by number of observations in Figure 1. The0 . M ⊕ system at 200 pc represents an extreme in theLSST parameter space for transiting planet discovery asit is the closest to Earth that an 0 . M ⊕ star can be lo-cated without nominally saturating the LSST detectors.As shown in Figure 7, exoplanet detection in this caseis difficult but not impossible. For the tested system,there is a very high probability that we will be able todetect 2 R ⊕ exoplanets at periods shorter than ∼ ∼ DISCUSSION AND SUMMARY
These results are a continuation of the work of Lundet al. (2015) and Jacklin et al. (2015). We have nowexpanded our parameter space beyond the fiducial hotJupiter orbiting a solar-type star to include more var-ied exoplanetary systems, and to test the boundaries ofLSST’s exoplanetary detection capabilities.Here we focus solely on LSST’s deep-drilling fields, aswe have found that exoplanet detection is significantly
Fig. 8.—
M-dwarf with at 2 R ⊕ transiting exoplanet at 200pc.The data have been processed in the same manner as Figure 4and Figure 6 improved by using deep drilling cadence as opposed toregular cadence. Additionally, since rapid results are ofincreasing importance as first light approaches, we exam-ine not only what LSST will discover after its full tenure,but have also specifically explored exoplanet detectionas LSST steadily accumulates more data. Indeed, thiswork has demonstrated that at least a few percent of theshortest-period ( (cid:46) (cid:38)
10% for periods (cid:46) M (cid:12) ) are the easi-est exoplanets that LSST will be able to detect, howeverthey will be different from the systems explored by mostother current surveys due to their faintness and distancefrom Earth. More generally, our work has shown thatLSST will be capable of detecting a wide variety of exo-planets over a range of parameter space that is previouslyunderexplored, including hot Jupiters at great distancesand super-Earths around red dwarfs. Specifically, LSSTwill have the ability to probe planets orbiting distantand/or intrinsically dim stars ( r ∼ .
5) over the en-tire southern sky. Finally, because the specific cadencesand deep-drilling fields for LSST have not yet been fullydefined, the work presented here may further help to de-velop optimal choices for the telescope.Our simulations can be enhanced in a number of waysto more fully and realistically assess the range of condi-tions under which these types of transiting planets maybe discovered by LSST. Our treatment of noise in theLSST light curves currently neglects both the effects ofcontamination (e.g., crowding) and of stellar variability(e.g., activity). Future simulations could attempt to es-timate likely contamination ratios for different positionson sky, as has been done for the TESS Input Catalog(Stassun et al. 2014), and could also include a randomsampling of typical activity levels as a function of stel-lar spectral type. This could be especially important forvery late-type stars. We have also not attempted here toestimate the absolute number of transiting planets thatmay be discovered by LSST. To do this will require acomprehensive assessment of various types of false pos-itives, which the additional capabilities described abovewould enable. Lastly, we have also not yet grappled withthe probability that most, if not all, LSST transit de-tections may not be possible to confirm using traditionaldynamical techniques (e.g., radial-velocity followup) dueto the host star faintness, so statistical methods will be required to translate such detections into more useful re-sults.Most importantly, as we have demonstrated with anumber of exemplar cases here, LSST should be capableof discovering a variety of exotic exoplanetary systems.A more complete exoplanetary census will contribute todeeper understanding of the frequency, structure, andformation of these systems in our galaxy and beyond.S.J. and K.G.S. gratefully acknowledge partial supportfrom NSF PAARE grant AST-1358862. S.J. also ac-knowledges considerable academic insight from NatalieHinkel.5) over the en-tire southern sky. Finally, because the specific cadencesand deep-drilling fields for LSST have not yet been fullydefined, the work presented here may further help to de-velop optimal choices for the telescope.Our simulations can be enhanced in a number of waysto more fully and realistically assess the range of condi-tions under which these types of transiting planets maybe discovered by LSST. Our treatment of noise in theLSST light curves currently neglects both the effects ofcontamination (e.g., crowding) and of stellar variability(e.g., activity). Future simulations could attempt to es-timate likely contamination ratios for different positionson sky, as has been done for the TESS Input Catalog(Stassun et al. 2014), and could also include a randomsampling of typical activity levels as a function of stel-lar spectral type. This could be especially important forvery late-type stars. We have also not attempted here toestimate the absolute number of transiting planets thatmay be discovered by LSST. To do this will require acomprehensive assessment of various types of false pos-itives, which the additional capabilities described abovewould enable. Lastly, we have also not yet grappled withthe probability that most, if not all, LSST transit de-tections may not be possible to confirm using traditionaldynamical techniques (e.g., radial-velocity followup) dueto the host star faintness, so statistical methods will be required to translate such detections into more useful re-sults.Most importantly, as we have demonstrated with anumber of exemplar cases here, LSST should be capableof discovering a variety of exotic exoplanetary systems.A more complete exoplanetary census will contribute todeeper understanding of the frequency, structure, andformation of these systems in our galaxy and beyond.S.J. and K.G.S. gratefully acknowledge partial supportfrom NSF PAARE grant AST-1358862. S.J. also ac-knowledges considerable academic insight from NatalieHinkel.