The Independent Discovery of Planet Candidates around Low-mass Stars and Astrophysical False Positives from the First Two TESS Sectors

Our initial stellar sample is retrieved from version 7 of the TESS Input Catalog (TIC-7), which is accessed via the Barbara A. Mikulski Archive for Space Telescope (MAST) Portal.⁴ Among other parameters, the TIC-7 table contains estimates of each star's physical parameters (effective temperatures ${T}_{\mathrm{eff}}$, surface gravities $\mathrm{log}g$, radii R_s, masses M_s, and so on), astrometry (either from the Tycho-Gaia astrometric solution, Gaia Collaboration et al. 2016a, 2016b, or from Hipparcos), G-band magnitude from the Gaia data release 1, and Two Micron All Sky Survey (2MASS) photometry (Cutri et al. 2003). To identify putative low-mass dwarf stars within the TIC-7, we first restrict our sample to sources flagged as dwarf stars based on their 2MASS colors and the reduced proper motion criterion from Stassun et al. (2018), modified from Collier Cameron et al. (2007). We further restrict our sample to stars whose "priority" is ≥10⁻³, where the TIC priority metric is based on the relative probability of detecting small planetary transits. As such, the priority is dependent on R_s, the expected photometric precision, the number of TESS sectors in which the TIC member will be visible, and its contamination ratio, which is the ratio of contamination to source flux where contamination is computed over 10 TESS pixels from the source (∼3.5 arcmin).

Next we establish our initial sample of low-mass stars based on the physical stellar parameters from the TIC-7 and using the following criteria:

• 1.  
  ${T}_{\mathrm{eff}}$ ∈ [2700, 4200] K,
• 2.  
  $\mathrm{log}g$ > 4,
• 3.  
  R_s < 0.75 R_⊙,
• 4.  
  M_s < 0.75 M_⊙.

We note that these criteria are not intended to reflect the exact M dwarf parameter ranges of interest but instead are chosen to be intentionally conservative so as to avoid missing any potential M dwarfs prior to their final classification (for use within this study) based on ${T}_{\mathrm{eff}}$ and near-IR luminosities (${M}_{{K}_{{\rm{S}}}}$ ∈ [4.5, 10]; Delfosse et al. 2000; Benedict et al. 2016) that will be refined in Section 2.2 using Gaia parallaxes. At this stage, we find a total of 93,090 TIC members that obey our criteria. Of these, 2849 TIC members are observed in one or both of TESS sectors 1 and 2 and are depicted in Figure 1.

Zoom In Zoom Out Reset image size

The stellar parameters used to derive our initial stellar sample were obtained from a variety of sources as outlined in Stassun et al. (2018). Effective temperatures within our sample were predominantly obtained from the cool dwarf catalog (Muirhead et al. 2018) or alternatively from spectroscopic catalogs or V–${K}_{{\rm{S}}}$ colors. Most stellar masses and radii also come from the cool dwarf catalog or from the Torres et al. (2010) spectroscopic relations. Stellar surface gravities follow from measurements of R_s and M_s. The TIC-7 stellar radii are typically known at the level of ∼16%, which often dominates the error budget of the measured planetary radii from transit observations. Here we aim to produce a homogeneously derived set of precise stellar parameters by exploiting the exquisite precision of their 2MASS photometry and stellar parallaxes from the Gaia DR2 Gaia Collaboration et al. (2018) available for the majority of stars in our initial sample.

For the accurate and precise characterization of transiting planets, we are principally interested in the measurement of host stellar radii R_s. Additionally, the derivation of other fundamental parameters such as stellar masses and effective temperatures is of importance for a more complete understanding of the effect that stars can have on their host planetary systems. Here, we rederive the stellar parameters of our initial sample by deriving their near-IR absolute magnitudes coupled with empirically derived M dwarf radius–luminosity relations (RLRs; Mann et al. 2015). We begin by querying the Gaia DR2 archive using the star's R.A. and decl. (α, δ) with a search radius of 10–60 arcsec. Cross-matching the TIC-7 with the Gaia DR2 data is necessary to obtain each star's updated parallax from the DR2, additional Gaia photometry (i.e., G_BP and G_RP) that was not included in the TIC-7, and point estimates of their respective measurement uncertainties that we will approximate as Gaussian distributed. Our querying procedure utilizes the astropy.astroquery python package (Ginsburg et al. 2017). Next we identify source matches according to their predicted photometric colors based on the 2MASS-Gaia color–color relations reported in Evans et al. (2018). Explicitly, we use the quadratic polynomial fits from Evans et al. (2018) to predict each of the colors G − K_S, ${G}_{\mathrm{BP}}-{K}_{{\rm{S}}}$, ${G}_{\mathrm{RP}}-{K}_{{\rm{S}}}$, and ${G}_{\mathrm{BP}}-{G}_{\mathrm{RP}}$ and then compare those predictions for potential source matches to the measured TIC member colors. Each of the four color–color relations is accompanied by a characteristic scatter of 0.3692, 0.4839, 0.2744, and 0.2144 mag, respectively. We claim a source match when all of the calculated colors are within 3σ of their predicted values. Based on numerous checks of individual known TIC members, we determined that such a tolerance is required to ensure accurate source matches. This dispersion is also expected given that higher-order effects not taken into account by the polynomial fits can have stark effects on the accuracy of the photometric predictions.

We proceed with identifying bona fide low-mass TIC members within our initial stellar sample by using the Gaia data of matched sources to refine the stellar parameters that were initially used to flag low-mass stars. We will classify low-mass stars within this study based on their absolute ${K}_{{\rm{S}}}$-band magnitudes (Delfosse et al. 2000; Mann et al. 2015; Benedict et al. 2016) and effective temperatures, which are derived in the coming subsections. We focus our analysis on the ${K}_{{\rm{S}}}$ band in this study due to the reduced effects of dust extinction at near-IR wavelengths compared to in the visible. The absolute ${K}_{{\rm{S}}}$-band magnitude is

$$\begin{eqnarray}&&{M}_{{K}_{{\rm{S}}}}={K}_{{\rm{S}}}-\mu -{A}_{{K}_{{\rm{S}}}},\end{eqnarray} \tag{ 1 }$$

where ${K}_{{\rm{S}}}$ is the source's ${K}_{{\rm{S}}}$-band apparent magnitude, $\mu =5{\mathrm{log}}_{10}(d/1\ \mathrm{pc})-5$ is the distance modulus given the distance to the source d, and ${A}_{{K}_{{\rm{S}}}}$ is the source extinction in the ${K}_{{\rm{S}}}$ band. Therefore, in order to compute ${M}_{{K}_{{\rm{S}}}}$ for our stellar sample, we must first obtain the parameters d and ${A}_{{K}_{S}}$.

2.2.1. Stellar Distances from Gaia

2.2.2. Source Extinction Estimates

2.2.3. Deriving the Set of Refined Stellar Radii

Combining the retrieved values of ${K}_{{\rm{S}}}$, μ, and ${A}_{{K}_{{\rm{S}}}}$ into Equation (1) returns the distribution of ${M}_{{K}_{{\rm{S}}}}$ for all of the 2489 stars in our initial sample for which 2MASS photometry and Gaia parallaxes are available.

Calculations of M dwarf stellar radii from their bolometric magnitudes would require ${K}_{{\rm{S}}}$-band bolometric corrections, which for cool stars are known to frequently suffer from comparatively large inaccuracies (${T}_{\mathrm{eff}}$ ≲ 4100 K; Berger et al. 2018). We therefore adopt the alternative approach from Berger et al. (2018), which uses the empirically derived M dwarf RLR from Mann et al. (2015) to update M dwarf stellar radii in the Kepler field using Gaia distances. The fitted RLR employs a quadratic function to map ${M}_{{K}_{{\rm{S}}}}$ to directly measured R_s from the combination of interferometry and parallaxes. Because we are interested in deriving a self-consistent sample of low-mass stellar radii, we restrict our analysis to TIC members with ${M}_{{K}_{{\rm{S}}}}$ values that are applicable to the Mann et al. (2015) RLR, which is valid for M dwarfs with ${M}_{{K}_{{\rm{S}}}}$ ∈ (4.6, 9.8). This condition will be used to establish our final sample of low-mass dwarf stars following the derivation of ${T}_{\mathrm{eff}}$ within our initial sample. The radii inferred from the RLR have a fractional residual dispersion of 0.0289 R_s, which we add in quadrature to the radius uncertainty propagated from ${M}_{{K}_{{\rm{S}}}}$.

Figure 2 compares the TIC-7 stellar radii (compiled from various input sources) with those derived from Gaia distances and the M dwarf RLR from Mann et al. (2015). The relation is largely one-to-one but with a slight translation of the updated R_s distribution to larger radii (∼3.7% median increase). The effect is already known (Berger et al. 2018) and is the result of many sources having their distance measures increased following the release of the Gaia DR2 parallaxes. More notable for the measurement of transit planet radii is the significant reduction in the fractional radius uncertainty, as evidenced in the histogram included in Figure 2. The typical fractional radius uncertainty ${\sigma }_{{R}_{s}}/{R}_{s}$ within our updated sample is ∼4–5 times smaller than in the TIC-7. The median fractional uncertainty on our Gaia-derived stellar radii is ∼3%.

Zoom In Zoom Out Reset image size

2.2.4. Deriving the Set of Refined Stellar Effective Temperatures

2.2.5. Deriving the Set of Refined Stellar Masses

2.2.6. Final Stellar Sample

The execution of ORION on a TIC member begins with downloading the star's publicly available 2 minute TESS extracted light curves and target pixel files for all available sectors. The TESS data are downloaded from the MAST data service.⁵ Only TIC members observed at 2 minute cadence are considered at this time with their extracted light curves made available following their processing by the TESS SPOC. Efforts to extract 30 minute light-curve data from the TESS full-frame images and significantly expand the list of TESS targets accessible to ORION are underway but are reserved for future work. Target pixel files are principally used to quickly assess the data quality and will be used to infer the TIC member's point-spread function (PSF) during the statistical validation of putative PCs in Section 4.2.

For each available sector of data, the chronologically sorted vectors of observing times t, measured fluxes f, and the associated 1σ flux uncertainties ${{\boldsymbol{\sigma }}}_{f}$ are constructed. Fluxes are obtained from the Simple Aperture Photometry Pre-search Data Conditioning extraction, which includes artifact mitigation (Smith et al. 2012). These vectors are attributed to the following fields: TIME [BJD], PDCSAP_FLUX [e⁻/s], and PDCSAP_FLUX_ERR [e⁻/s]. The flux and flux uncertainty vectors are converted into normalized flux units via division by median(f).

Residual systematic effects are clearly visible in many of the extracted light curves. Due to the inherent photometric and pointing precision of the first TESS sectors, these systematic effects are often largely attributable to astrophysical noise sources such as flicker (Bastien et al. 2013) in Sun-like stars but more commonly for low-mass stars from large-scale variability caused by active regions on the rotating stellar surface. As an initial detrending step to correct for temporally correlated noise sources from either systematics or intrinsic stellar phenomena, a semiparametric Gaussian process (GP) regression model is fit to the extracted TESS photometry.

GP regression models provide a flexible and probabilistic framework to model the temporal covariances between photometric measurements following the removal of a mean model ${\boldsymbol{\mu }}(\theta )$, which is parameterized by the set of observable parameters θ (e.g., P, T₀, $a/{R}_{s}$). The posterior PDFs of the θ elements can be sampled simultaneously with the GP hyperparameters Θ, which parameterize the residual covariances through the covariance matrix K(Θ) and are fit by optimizing the ln likelihood function

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{ln}{ \mathcal L }(\theta ,{\rm{\Theta }}) & = & -\displaystyle \frac{1}{2}\left[{\left({\boldsymbol{f}}-{\boldsymbol{\mu }}(\theta )\right)}^{{\rm{T}}}\cdot K{\left({\rm{\Theta }}\right)}^{-1}\cdot ({\boldsymbol{f}}-{\boldsymbol{\mu }}(\theta ))\right.\\ & & \left.+\,\mathrm{ln}\,\det K+N\mathrm{ln}2\pi \right]\end{array}\end{eqnarray} \tag{ 2 }$$

along with appropriately chosen priors on the parameters in θ and Θ. Here, N is the number of photometric measurements in the light curve. Similar routines based on GP regression have been adopted for K2 systematic corrections (e.g., Aigrain et al. 2015, 2016; Crossfield et al. 2015) and can also be used to infer accurate photometric stellar rotation periods (Angus et al. 2018). For cases in which the origins of the apparent photometric variations are likely dominated by active regions on rotating spotted stars, the resulting photometric signal will vary nonsinusoidally as the active regions evolve in size, brightness, and location over the observational baseline. This physically motivates the use of a quasi-periodic covariance matrix ${K}_{i,j}={\delta }_{i,j}{\sigma }_{f,i}+{k}_{i,j}$, where ${\delta }_{i,j}$ is the Kronecker delta and ${k}_{i,j}$ is the covariance kernel of the form

$$\begin{eqnarray}&&{k}_{i,j}={a}_{\mathrm{GP}}^{2}\exp \left[-\displaystyle \frac{| {t}_{i}-{t}_{j}{| }^{2}}{2{\lambda }^{2}}-{{\rm{\Gamma }}}^{2}{\sin }^{2}\left(\displaystyle \frac{\pi | {t}_{i}-{t}_{j}| }{{P}_{\mathrm{GP}}}\right)\right].\end{eqnarray} \tag{ 3 }$$

The covariance kernel is parameterized by the four hyperparameters ${\rm{\Theta }}=\{{a}_{\mathrm{GP}},\lambda ,{\rm{\Gamma }},{P}_{\mathrm{GP}}\}$, where a is the correlation amplitude, λ the exponential timescale, Γ the coherence scale, and P_GP the periodic timescale of the correlations. Moreover, a quasi-periodic covariance kernel is favorable for cases in which the origin of apparent photometric variations is dominated by systematics, which need not have a strong periodic component. In this limit, the coherence parameter Γ approaches small values such that the covariance kernel becomes well approximated by a squared exponential kernel with effectively a single timescale λ. Note that because systematic and astrophysical noise sources within the GP noise model are not distinguished, the fitted hyperparameter values are unable to be used to interpret the origin of the photometric variability. Furthermore, during the remainder of this paper, the covariance structures modeled by the GP will be solely referred to as "systematics" despite the possibility that their (partial) origin may be astrophysical.

The logarithmic hyperparameters are initialized and subsequently optimized in an iterative manner and are performed on each TESS sector independently assuming a null mean function (i.e., ${\boldsymbol{\mu }}=0$). The periodic GP timescale P_GP is initialized by peaks in the Lomb–Scargle periodogram (LSP; Scargle 1982) of the extracted light curve whereby, in each of the iterations performed, P_GP is initialized to the ith most significant peak in the LSP where i is the iteration index ∈[1, 10]. Following the use of GP regression modeling for RV activity mitigation in Dittmann et al. (2017b), where the physical source of activity is largely common between the optical RVs and broadband TESS photometry, lnλ is initialized to $\mathrm{ln}3{P}_{\mathrm{GP}}$. In each iteration, lnΓ is initialized to 0 and $\mathrm{ln}{a}_{\mathrm{GP}}=\mathrm{lnmax}(| {{\boldsymbol{f}}}_{\mathrm{bin}}-\mathrm{median}({{\boldsymbol{f}}}_{\mathrm{bin}})| )$ where ${{\boldsymbol{f}}}_{\mathrm{bin}}$ is the vector of binned photometric points whose temporal bin width is set such that a single periodic GP timescale is sampled by at least eight measurements.

Table 2.  Stellar Parameters for the 1599 TICs in Our Sample of Low-mass Stars

TIC	α (J2000)	δ (J2000)	ϖ	d	${M}_{{K}_{{\rm{S}}}}$	Rs	Teff	Ms	$\mathrm{log}g$
	(deg)	(deg)	(mas)	(pc)		(${R}_{\odot })$	(K)	M⊙	(dex)
2733611	356.1299	−15.5194	16.763 ± 0.053	59.654 ± 0.188	5.259 ± 0.024	0.5650 ± 0.0169	3880 ± 49	0.6115 ± 0.0053	4.720 ± 0.026
2758962	356.2124	−15.1250	13.530 ± 0.050	73.911 ± 0.272	5.293 ± 0.022	0.5590 ± 0.0166	3768 ± 49	0.6076 ± 0.0051	4.727 ± 0.026
2761472	356.5801	−11.9453	43.288 ± 0.103	23.101 ± 0.055	7.937 ± 0.021	0.2160 ± 0.0065	3028 ± 49	0.1799 ± 0.0021	5.024 ± 0.027
2761836	356.5473	−14.0693	15.645 ± 0.060	63.920 ± 0.246	6.447 ± 0.026	0.3804 ± 0.0116	3259 ± 49	0.4094 ± 0.0052	4.890 ± 0.027
2762148	356.5982	−15.9872	28.845 ± 0.083	34.668 ± 0.100	7.547 ± 0.020	0.2519 ± 0.0075	3262 ± 49	0.2249 ± 0.0027	4.988 ± 0.027

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image

For each iteration in each TESS sector (if multiple sectors are available), the uniquely initialized GP hyperparameters are optimized using the scipy.optimize.minimize python function to minimize the negative $\mathrm{ln}{ \mathcal L }({\rm{\Theta }})$ from Equation (2) given the Jacobian of $\mathrm{ln}{ \mathcal L }({\rm{\Theta }})$ with respect to the hyperparameters in Θ. During optimization, the ln GP hyperparameters are bounded by broad uninformative priors, which are explicitly reported in Table 4. Broad ln uniform priors enable the generalization of the ORION detrending method across all of the input TESS light curves, which greatly benefit from semiparametric modeling given the wide range of covariance timescales exhibited by TIC members in photometry. Given an optimized set of hyperparameters, the resulting GP posterior PDF is an N-dimensional multivariate Gaussian distribution whose mean function is taken to be a potential systematic correction. The mean function of the GP from the iteration whose optimized hyperparameters maximize $\mathrm{ln}{ \mathcal L }({\rm{\Theta }})$ is assigned as the initial systematic correction and is used to detrend the photometry prior to the search for periodic transit events.

Figure 3 depicts two examples of the results of this iterative detrending procedure over individual TESS sectors for TIC members 235037759 and 262530407. The accuracy of each mean GP regression model is clearly demonstrated. The systematics model for TIC 235037759 is required to be much more aggressive than that for TIC 262530407 given the star's large photometric variability with a peak-to-peak amplitude in the binned light curve of 280,000 ppm and an 85,000 ppm rms. Unlike in the raw light curve, the detrended light curve lacks any low-frequency variations and exhibits a significantly reduced rms of 12,000 ppm.

Zoom In Zoom Out Reset image size

The TIC 262530407 light curve also exhibits photometric variability albeit with a much lower peak-to-peak amplitude and rms of 1700 and 1000 ppm, respectively. After detrending, the rms is slightly reduced to 810 ppm. The most important residual feature of the detrended light curves is that they appear free of the majority of large-scale systematic effects. This fact will facilitate the linear search for transit-like events with minimal contamination from residual systematic features. Indeed, a transiting PC is detected around each of these systems, although the putative PC around TIC 235037759 is ultimately favored by an AFP interpretation, as presented in Section 4.3.

One notable limitation to the systematics correction occurs during a period of a prevalent increase in rms for TIC 235037759 between ∼1347 and 1349 BJD—2,457,000 during a brief period of loss of TESS pointing precision. This is a feature common to the TIC members observed during TESS sector 1. During this time, the extracted light curve is only partially corrected for the pointing precision loss, while the systematic GP model provides only marginal improvements if any at all. To ensure that the GP hyperparameters were not being strongly affected by the anomalous systematics structure during this period, those measurements were masked and the GP hyperparameters reoptimized with the remaining data. The resulting GP systematics only varies marginally from that shown in Figure 3 for TIC 235037759 such that we are confident that the ORION detrending is largely robust to the loss in pointing precision for TIC members observed in TESS sector 1.

Recall that in the initial detrending step discussed in this section that the methodology assumes a null mean function, which implies that any transient events such as flares or transits are still present during the optimization of the detrending model. The principal caveat with this methodology is that one cannot guarantee that the GP model does not (partially) capture any of the in-transit light curve deprecations that ORION is searching for. If partially suppressed by the initial GP model, planets will be more difficult to detect due to the reduced S/N of individual transit events. Furthermore, transit events that remain detectable within the detrended light curve could result in underestimated transit depths and correspondingly smaller planet sizes. To ensure a self-consistent planet+systematics model for putative PCs from ORION, the light model is revisited in Section 3.6 with the inclusion of a transiting planet mean function in place of the null mean function used during the detrending step.

Next, a linear search for individual transit-like events is conducted on the detrended light curves over their full duration. The following methodology is reminiscent of a number of individual transit event search algorithms (e.g., Box Least Squares, BLS; Kovács et al. 2002, Transiting Planet Search, TPS; Jenkins et al. 2010; Christiansen et al. 2013, 2015, 2016, TERRA; Petigura et al. 2013; Foreman-Mackey et al. 2015). The aim here is to identify high-S/N transit-like events along with their associated midtransit times T₀, durations D, and depths Z, which will feed into the search for repeating transit-like events and ultimately the list of putative transiting PCs.

The linear search for transit-like events begins with stepping through a two-dimensional grid of T₀ and D. At each $({T}_{0},D)$ grid point, a simple box model of the form

$$\begin{eqnarray}m(t)=\left\{\begin{array}{ll}1-Z & \mathrm{if}\ {T}_{0}-\displaystyle \frac{D}{2}\leqslant t\leqslant {T}_{0}+\displaystyle \frac{D}{2}\\ 1 & \mathrm{otherwise},\end{array}\right.\end{eqnarray} \tag{ 4 }$$

is constructed with fixed T₀ and D. The box depth Z (or mock transit depth) is fit by ln likelihood maximization and saved along with the value of $\mathrm{ln}{ \mathcal L }$ given the unique set of parameters $\{{T}_{0},D,Z\}$. Computing $\mathrm{ln}{ \mathcal L }$ with Equation (2) implicitly assumes that the flux uncertainties are Gaussian distributed, which allows for the construction of a diagonal covariance matrix K with elements ${K}_{i,j}={\delta }_{i,j}{\sigma }_{f,i}$. The linear search along the T₀ dimension proceeds by stepping through the observation epochs t in 30 minute bins and assigning ${t}_{\mathrm{bin},i}$ to T₀ ∀$i=1,\,\ldots ,\,{N}_{\mathrm{bin}}$. This fixed binning is the first of many ORION free parameters listed in Table 3 along with their default values and brief explanations of their effects. Initial ORION tests on synthetic light curves with injected transit models determined that finer temporal binning did not result in a significant variation in the number of detected high-S/N transit-like events. This is likely due to 30 minute bins being more comparable to typical transit durations of the types of planets that can be detected in 27–54 day baselines, although notably a phase dependence on the sensitivity to short-period planets should persist unless the bin width is reduced (Kovács et al. 2002).

Table 3.  Descriptions of the Free Parameters Controlling the Performance of ORION

Parameter	Definition	Default Value	Summary of Behavior
Linear search parameters
${\rm{\Delta }}t$	Linear search temporal bin width	30 minutes	Decreasing ${\rm{\Delta }}t$ will improve sensitivity to ultrashort-period planets while increasing the ORION run-time number of signals for confusion in the periodic search stage.
D grid	Grid of transit durations considered during the linear search stage	$\{1.2,2.4,4.8\}$ hr	Decreasing the minimum duration improves sensitivity to ultrashort-period planets but makes ORION more susceptible to stochastic features with short timescales.
S/Nthresh	Minimum linear search S/N of a transit-like event	5	Decreasing S/Nthresh will result in more light curve features being flagged as false positives, thus creating more signals for confusion within the periodic search stage.
Periodic search parameters
${f}_{{\rm{P}}}$	Maximum relative difference between two periods to be flagged as multiple	0.01	Increasing ${f}_{{\rm{P}}}$ makes fewer period pairs consistent with being multiples, thus increasing the sensitivity to resonant planet pairs while simultaneously increasing the number of single planets misidentifed as a resonant pair.
Automated light curve vetting parameters
c1	Minimum transit S/N	8.4	Increasing c1 prevents the detection of some small planets but will also significantly reduce the number false positives due to residual systematics.
c2	Minimum number of MADs from the out-of-transit flux that the difference in median in- and out-of-transit fluxes must exceed	2.4	Behavior similar to c1.
c3	Minimum fraction of in-transit points below $Z+{\sigma }_{Z}$	0.7	Increasing c3 may result in more accurate determinations of correct periods but will also cause some transits to be discarded if residual noise is also present during the transit.
c4	Minimum fraction of in-transit points prior to T0	0.1	Increasing c4 increases sensitivity to asymmetric transit shapes such as those from disintegrating planets.
c5	Minimum number of MADs for a flare above the flux continuum	8	Increasing c5 makes flare detection more robust but at the risk ofmissing some lower-amplitude flares.
c6	Minimum number of successive points within a flare duration	2	Increasing c6 decreases sensitivity to flares of short duration relative to the light curve cadence.
c7	Assumed M dwarf flare duration	30 minutes	Increasing c7 decreases the sensitivity to long-duration flares while increasing the assumed fraction light curve fraction that is contaminated by flares.
c8	Number of transit durations from T0 that cannot be affected by flares	4	Decreasing c8 decreases the probability of a transit being contaminated by flares.
c9	Maximum time from the light curve edges to not be rejected due to possible contamination at the edges	4.8 hr	Increasing c9 decreases the probability of a transit being affected by light-curve systematics at its edges but also narrows the baseline over which transits can be found.
c10	Minimum autocorrelation of flux residuals	0.6	Increasing c10 improves the robustness of transit detections but decreases the detection sensitivity in light curves with imperfect systematics corrections.
Eclipsing binary vetting parameters
${c}_{\mathrm{EB},1}$	Maximum ${r}_{p}/{R}_{s}$ of a transit-like event	0.5	⋯
${c}_{\mathrm{EB},2}$	Maximum planet radius	30 ${R}_{\oplus }$	⋯
${c}_{\mathrm{EB},3}$	Maximum transit duration, $D({r}_{p},P,a/{R}_{s},Z,i)$	$D(30\,{R}_{\oplus },P,a/{R}_{s},Z,i)$	⋯
${c}_{\mathrm{EB},4}$ a	Minimum occultation S/N of an EB (Equation (7))	5	Decreasing ${c}_{\mathrm{EB},4}$ makes a larger fraction of occultations consistent with being due to an EB rather than a transiting planet.
${c}_{\mathrm{EB},5}$ a	Minimum fraction of iterative occultation searches consistent with an EB	0.5	Increasing ${c}_{\mathrm{EB},5}$ makes transit-like events more robust as the probability of being flagged as an EB is reduced.
${c}_{\mathrm{EB},6}$ a	Minimum ingress plus egress time fraction of D for a V-shaped transit	0.9	Increasing ${c}_{\mathrm{EB},6}$ makes fewer transit-like events consistent with having a V-shaped transit.

Note.

^aThese eclipsing binary (EB) parameters are intended to identify favorable EBs rather than transiting planets. Planetary signals of interest are rejected if any of the EB criteria are satisfied.

Download table as:  ASCIITypeset image

The D dimension is sampled on a much coarser grid given that the precision of the box model parameters are not yet required to infer planet properties but only to identify epochs at which transit-like events are likely to have occurred. Explicitly, the adopted linear search D grid contains three possible transit durations of either 1.2, 2.4, or 4.8 hr.

This procedure produces an N_bin × 3 matrix of transit times and durations, with each entry having an associated ln likelihood and optimized depth Z. From the ln likelihoods, an S/N spectrum as a function of transit times is computed for each D value considered. By translating the ln likelihoods by their median value and normalizing by their median absolute deviation (MAD), the aforementioned linear search S/N spectrum versus transit times is calculated. The conversion from ln likelihoods to the ad hoc S/N spectrum centered around zero aids in its interpretation because each TIC member's spectrum can be searched in absolute terms. In adopting the median and MAD ln likelihood values over the mean and standard deviation, the S/N is less sensitive to contamination by stochastic, short-timescale photometric features and results in an S/N spectrum whose baseline is dominated by the light curve's inherent photometric precision. An example linear search S/N spectrum is shown in Figure 4 for a fixed duration of 1.2 hr. We note that referring to the linear search S/N spectra as an S/N is a misnomer given that the spectrum values can be negative either in the presence of noise or due to an apparent brightening of the source. However, we find this language to be a clear descriptor of the spectrum's aim and its interpretability.

Zoom In Zoom Out Reset image size

The S/N spectra are then searched for high-S/N transit-like events similarly to the individual significance events in the primary Kepler transit search, which are combined into a multievent statistic and flagged as a threshold crossing event (Jenkins et al. 2010). Thus, the nature of the linear search is for single-event statistics and occurs prior to the periodic search step (see Section 3.4) for multievent statistics in which the data are folding and repeating events are investigated. High-S/N transit-like events are flagged as peaks in the linear search S/N spectrum when S/N${}_{\mathrm{thresh}}\geqslant 5$. All n_T transit times T₀ with S/N exceeding S/N_thresh for any value of D are compiled into a set of potential transit-like events. Because transit times in the linear search are sampled on a fixed grid (i.e., t binned to Δt), each transit time is refined by Gaussian smoothing the light curve around ±2D of T₀ using scipy.ndimage.filters.Gaussian_filter and updating T₀ to the central time of the box model minimum before proceeding to the search for periodic events that may be indicative of transiting PCs. In the example shown in Figure 4, a PC exists with an ∼1.4 day orbital period. Six out of the 19 transit events that occur within the sector 1 baseline are detected above S/N_thres. This includes two consecutive transits between 1341 and 1343 BJD—2,457,000, which are used in the subsequent section to infer its possible period equal to the time difference between the two events.

The chronologically sorted set of n_T high-S/N transit times in T₀ are used to construct a matrix of differential transit times with elements ${P}_{i,j}={T}_{0,i}-{T}_{0,j}\forall i,j=1,\,\ldots ,\,{n}_{{\rm{T}}}$. A separate matrix is populated for each unique value of D. An example of P is shown in Figure 5 for TIC 234994474 for the fixed duration of 1.2 hr. The n_T × n_T matrix P represents potential transit periods of PCs whose individual transit events may be separated in time by any of the off-diagonal elements of P or some multiple thereof. By its construction, the matrix P is skew-symmetric, implying that only the positive nonzero matrix elements below the main diagonal are valid periods for consideration, for a total of ${\sum }_{i=1}^{{n}_{{\rm{T}}}-1}i$ periods. Because the periodic search is for repeating transit-like events, it is required that n_T > 1. In this way, no more than two transit events are required to detect a repeating putative PC. This fact extends the ORION detection sensitivity to nearly the full observational baseline of ∼27 days for the majority of TIC members.

Zoom In Zoom Out Reset image size

Because each linear search with a unique D is independent of the others, the P matrices of differential transit times are considered together. In this way, a single master set of periods is compiled whose elements are referred to as periods of interest (POIs). Recall that each POI has an associated time of midtransit T₀, duration D, depth Z, and $\mathrm{ln}{ \mathcal L }$ from the linear search. At this stage, the computationally tractable box transit model is substituted in favor of a more physical transit model whose model parameters are initialized using the box model parameters before optimization. The Mandel & Agol (2002) transit model is used through its implementation within the batman python package (Kreidberg 2015) to compute model realizations given the input parameters $\theta =\{P,{T}_{0},a/{R}_{s},{r}_{p}/{R}_{s},i,e,\omega ,{a}_{\mathrm{LDC}},{b}_{\mathrm{LDC}}\}$, where e is orbital eccentricity, ω is the argument of periastron, and $\{{a}_{\mathrm{LDC}},{b}_{\mathrm{LDC}}\}$ are the quadratic limb-darkening coefficients. In practice, only the parameters $\theta =\{P,{T}_{0},a/{R}_{s},{r}_{p}/{R}_{s},i\}$ are optimized by assuming circular orbits and fixing the quadratic limb-darkening coefficients in the TESS bandpass to the values interpolated from the Claret (2017) grid over ${T}_{\mathrm{eff}}$ and $\mathrm{log}g$ and assuming solar metallicity. The θ parameters are optimized using the same routine that was used to optimize the GP hyperparameters during the initial detrending stage (see Section 3.2). With each POI's optimized transit model, the ln likelihood of the data is computed for use during the succeeding steps aimed at identifying repeating transit-like events from the initial set of POIs.

A series of cuts is performed on the set of optimized POIs to identify the most likely independent periods within the data. The first cut is to remove repeated period multiples. If POIs with integer period multiples (i.e., $2{P}_{i},3{P}_{i},...$) are indeed due to a transiting planet, then those POIs are likely to be manifestations of the same object. The exact P value that is retained from a set of apparent period multiples is that with the largest ln likelihood. Any arbitrary pair of POIs (${P}_{i},{P}_{j}$) is flagged as a period multiple if P_i and $n\cdot {P}_{j}$ are within f_P = 1% for any $n=2,\,\ldots ,\,{n}_{\mathrm{transit}}$. One important caveat to the removal of integer multiple periods is that resonant multiplanet systems are undetectable within the periodic transit search because all but one of the POIs will always be rejected in favor of its maximum ln likelihood multiple.

Similarly, because the set of POIs is derived from peaks in the linear search S/N spectrum, rational multiples of each POI must also be sampled (i.e., ${P}_{i}/2,{P}_{i}/3,...$). Consider an S/N spectrum derived from a light curve containing a single transiting planet with ${n}_{\mathrm{transit}}\gt 2$ but whose individual transits are only marginally detectable due to their amplitude relative to the photometric precision. Consider in this case that only a fraction of transit events are detected during the linear search. The detection of only some transit events may result in a misidentified POI that is an integer multiple times greater than the underlying true period if one or more intermediate transit events go undetected due to the effects of random noise. Therefore, fractional multiples of each POI must be considered. These new periods are equal to ${P}_{i}/n$ for all integers n, resulting in a reduced period greater than or equal to the minimum orbital period considered by ORION: 0.5 days. The ln likelihood of the data under the box model with reduced period ${P}_{i}/n$ and remaining parameters $\{{T}_{0,i},{D}_{i},{Z}_{i}\}$ is calculated to be compared with the $\mathrm{ln}{ \mathcal L }$ value for the model with P_i. Here, the latter three parameters are fixed regardless of the input period. The search over period multiples retains the period with the largest ln likelihood. The lower period limit of 0.5 days is imposed to limit the number of rational multiples of each POI that are investigated and because the temporal bin width used during the linear search stage already limits the sensitivity to short-period planets whose transit durations are comparable to the 30 minute bins used therein. Furthermore, consideration of orbital periods <0.5 days in the periodic search stage is unlikely to result in a large number of missed transits, owing to the intrinsically low occurrence rate of ultrashort-period planets (≲1%; Sanchis-Ojeda et al. 2014; Adams et al. 2016).

The result of these cuts to the initial set of POIs is a set of repeating transit-like events with a unique POI that is not deemed to be a multiple of another POI. The inclusion of multiple unique POIs allows ORION to search for multiple planets in a single light curve so long as those planets are not close to a resonant configuration. However, this final set of POIs may or may not correspond to a transiting planet or some other form of periodic astrophysical source such as an eclipsing binary. Therefore, the next steps in ORION are to vet the surviving POIs for systematic false positives given their distinctive light curve features that can be largely vetted in an automated way.

3.5.1. Automated Vetting Based on Light Curve Features

Here, POIs are automatically vetted using a set of eight vetting criteria that investigate the flagged transit-like features in the detrended light curve (see Section 3.4). This automated vetting stage is intended to identify false or insignificant transit-like events and thus provides a preliminary list of putative PCs prior to more selective human vetting and statistical vetting for AFPs.

The automated vetting criteria are controlled by the set of free parameters {c_i} for i = 1, ..., 10, which are described below and are included in the summary Table 3. The adopted values of these parameters control the performance of ORION in terms of its detection sensitivity and false-positive rate and were derived from early ORION executions on both archival Kepler and simulated TESS light curves⁶ prior to the first TESS data release. We do not, however, make any significant claims of their optimality.

The eight automated vetting criteria are defined as follows:

• 1.  
  It is required that each POI's transit depth Z from its optimized transit model be >0.
• 2.  
  The transit S/N is

  $$\begin{eqnarray}&&{{\rm{S}}/{\rm{N}}}_{\mathrm{transit}}=\displaystyle \frac{Z}{{\sigma }_{f,\mathrm{transit}}}\sqrt{{n}_{\mathrm{transit}}(P,{T}_{0},{\boldsymbol{t}})}\end{eqnarray} \tag{ 5 }$$

  where ${\sigma }_{f,\mathrm{transit}}$ is the photometric precision over the transit duration timescale and acts as a proxy for the combined differential photometric precision (CDPP_transit; Christiansen et al. 2012). The number of observed transits is n_transit given the vector of observations t, the POI's orbital period P, and midtransit time T₀. The S/N_transit is required to be >c₁ = 8.4.
• 3.  
  The transit parameters $\{P,{T}_{0},a/{R}_{s},Z,i\}$ are used to phase-fold the light curve and compute the transit duration (Winn 2010) such that the in-transit points, including those in ingress or egress, can be isolated. It is required that the difference in the median in- and out-of-transit fluxes exceed c₂ = 2.4 MADs of the out-of-transit flux.
• 4.  
  If a misidentified POI happens to be less than the true period, then the phase-folded light curve will appear to contain out-of-transit points in transit. This is combated by requiring that the number of in-transit points lying below Z + σ_Z (where σ_Z is the 1σ uncertainty on the transit depth) accounts for at least a c₃ = 0.7 fraction of all in-transit points.
• 5.  
  It is required that the in-transit sampling be approximately symmetric in time by insisting that the number of points between T₁ and T₀ be within 50% ± c₄ of the total number of in-transit points between T₁ and T₄.⁷ Here, c₄ is set to 10%.
• 6.  
  Flare stars such as TIC 25200252 as shown in Figure 6 are found to result in a number of misidentified transit events. Flare events are therefore searched within each light curve by first flagging individual flux measurements that are >c₅ = 8 MADs brighter than the median flux baseline. However, by the aforementioned criterion, individual stochastic flux jumps can also mimic flares. It is therefore required that any window over which a possible flare event occurs must contain >c₆ = 2 successive bright measurements above the c₅ threshold in order to identify a flare. Flux measurements occurring within a flare window are identified from the qth percentile of the light-curve flux distribution, where q is the fraction of the observational baseline that occurs within a flare's duration. The total flare duration over the light curve is calculated from the number of detected flares multiplied by the characteristic M dwarf flare duration c₇ = 30 minutes (Moffett 1974; Walkowicz et al. 2011; Hawley et al. 2014). Transit-like events with an identified flare occurring within c₈ = 4 transit durations from T₀ of a POI are vetted as flares.
• 7.  
  Visual inspection of a number of light curves observed during sector 1 frequently reveals sharp flux losses at the light-curve edges. This signature is often falsely attributed to a transit-like signal but is clearly a systematic effect that is not always well modeled during the detrending stage. Because this edge effect appears to operate over the final ∼4–5 hr of the light curve, POIs with midtransit times within c₉ = 4.8 hr of either the first or final flux measurements around a sampling gap are automatically flagged as probable false positives.
• 8.  
  The optimized transit models of the POIs that satisfy all seven of the aforementioned criteria are removed from the light curve. This produces a maximally clean light curve whose residuals should only arise from random noise in photometry or from inaccuracies in the independent systematic GP and transit models. The numpy.correlate python function is used to compute the autocorrelation of the residual light curve as a function of time delay because light curves demonstrating large autocorrelations due to imperfect systematic models can often mimic transit-like events that satisfy the previous vetting criteria. This criterion is particularly important for the use of ORION on K2 light curves, which often exhibit significant temporal correlations due to the thrusts used for reorientation of the spacecraft and its imperfect correction (Vanderburg & Johnson 2014). It is required that the autocorrelation function for delays greater than zero be ≤c₁₀ = 0.6.

Zoom In Zoom Out Reset image size

3.5.2. Automated Vetting of EBs

The set of transit-like events that satisfy all of the vetting criteria presented in Sections 3.5.1 and 3.5.2 are treated as PCs in this, the final ORION stage. At this point, the modeling of systematic light-curve effects using a one-dimensional GP regression model from Section 3.2 is revisited. The alternative is to simultaneously sample the joint GP plus transit light-curve parameter posterior PDF using Markov chain Monte Carlo (MCMC) simulations. Explicitly, the light-curve model is modified by replacing the previously null mean model ${\boldsymbol{\mu }}({\boldsymbol{t}})$ with a full transit model containing all putative PCs. Overfitting by the systematic model, which can partially fill in planetary transits, is mitigated by simultaneously modeling systematics and PCs. The resulting joint systematic+planet model is therefore derived in a self-consistent manner with more robust solutions for the transiting PC parameters of interest. MCMC sampling of the transit parameter marginalized posterior PDFs allows us to compute point estimates of their MAP values and uncertainties for later use.

For systems containing N_PC PCs, $4+5{N}_{\mathrm{PC}}$ parameter PDFs are sampled by continuing to insist on circular orbits and fixed limb-darkening coefficients. Explicitly, the GP hyperparameters ${\rm{\Theta }}=\{\mathrm{ln}{a}_{\mathrm{GP}},\mathrm{ln}\lambda ,\mathrm{ln}{\rm{\Gamma }},\mathrm{ln}{P}_{\mathrm{GP}}\}$ are fit along with the transiting planet parameters $\theta =\{{P}_{i},{T}_{0,i},{a}_{i}/{R}_{s},{r}_{p,i}/{R}_{s},{i}_{i}\}$ ∀$i=1,\,\ldots ,{N}_{\mathrm{PC}}$. The GP hyperparameters are initialized to their maximum likelihood values from the detrending stage and continue to be bounded by the broad uniform priors listed in Table 4. Transit parameters are initialized by their maximum likelihood values assuming fixed GP hyperparameters from detrending. The adopted prior PDFs on the transit model parameters are also reported in Table 4 for the most common case of fitting transiting PCs with multiple transits over the observational baseline. As we will see in Section 4.1.1, some priors will be modified when sampling transit parameters used to model only a single transit.

Table 4.  Model Parameter Priors

Parameter	Prior
GP hyperparametersa
Covariance amplitude, $\mathrm{ln}{a}_{\mathrm{GP}}$	${ \mathcal U }(-20,0)$
Exponential timescale, $\mathrm{ln}\lambda$/days	${ \mathcal U }(-3,10)$
Coherence, $\mathrm{ln}{\rm{\Gamma }}$	${ \mathcal U }(-5,5)$
Periodic timescale, $\mathrm{ln}{P}_{\mathrm{GP}}$/days	${ \mathcal U }(-3,10)$
Transit model parameters
Orbital period, P [days]	${ \mathcal U }(0.9,1.11)\cdot {P}_{\mathrm{opt}}$ b
Time of midtransit, T0	${ \mathcal U }(-1.11,1.11)\cdot {P}_{\mathrm{opt}}+{T}_{0,\mathrm{opt}}$
[BJD—2,457,000]
Scaled semimajor axis, $a/{R}_{s}$	${ \mathcal U }{(0.58,1.70)\cdot (a/{R}_{s})}_{\mathrm{opt}}$
Planet–star radius ratio, ${r}_{p}/{R}_{s}$	${ \mathcal U }(0,1)$
Orbital inclination, i	${ \mathcal U }{(-1,1)\cdot i((a/{R}_{s})}_{\mathrm{opt}},b\,=\,1)$ c
Single transit model parameters
Orbital period, P [days]	${ \mathcal J }(1,100)\cdot {P}_{\mathrm{inner}}$ d
Time of midtransit, T0	${ \mathcal U }(-3,3)\cdot D$
[BJD—2,457,000]
Scaled semimajor axis, $a/{R}_{s}$	${ \mathcal J }{(1,100)\cdot (a/{R}_{s})}_{\mathrm{inner}}$
Planet–star radius ratio, ${r}_{p}/{R}_{s}$	${ \mathcal U }(0,1)$
Orbital inclination, i	${ \mathcal U }{(-1,1)\cdot i((a/{R}_{s})}_{i},b=1)$

Notes.

^aGP hyperparameter priors used during detrending (i.e., with zero mean model) and during the simultaneous systematics plus transit modeling. ^bThe designation "opt" is indicative of the optimized parameter values from the maximum likelihood model used for parameter initialization. ^cThe function $i(a/{R}_{s},b)=a\cos i/{R}_{s}$ returns the orbital inclination given $a/{R}_{s}$ and the impact parameter b, which is constrained to $| b| \lt 1$ in our transit models. ^dThe designation "inner" is indicative of the innermost orbital period permissible for a single transit event over the TESS baseline.

Download table as:  ASCIITypeset image

MCMC sampling is performed with the emcee ensemble sampler (Foreman-Mackey et al. 2013). One hundred walkers are initialized in small Gaussian balls centered on each parameter's initial value. Throughout the MCMC, each walker's acceptance fraction is monitored and warns the user when its mean value over all walkers fails to fall within the desired range of 20%–60% in either the burn-in or final sampling stages. The desired duration of each MCMC stage is ≳10 autocorrelation times. Warnings are again produced if the MCMC chains fail to reach this length.

The main ORION output is a list of objects of interest (OIs) along with samples from the model parameter marginalized posterior PDFs and point estimates of each parameter's MAP value and uncertainties derived from the 16th and 84th percentiles of their one-dimensional marginalized PDF. The raw light curves and models sampled at observation times t are also saved to produce summary images such as the example shown in Figure 7 for OI 234994474.01, whose PC is a known TESS object of interest: TOI-134.01, a close-in terrestrial planet currently being validated with HARPS and PFS RVs (N. Astudillo-Defru et al. 2019, in preparation).

Zoom In Zoom Out Reset image size

We conduct a visual inspection of each of the raw, detrended, and phase-folded light curves for each OI detected by ORION. In this analysis, we flag 97/121 PCs as being residual systematic effects that are misidentified as transits. Of those, 19 appear to have been directly affected by measurements obtained between ∼1347 and 1349 BJD—24,570,000 during sector 1 at times when TESS briefly lost much of its pointing precision. This effect is not perfectly corrected for in many of the sector 1 extracted light curves nor by ORION's own systematic modeling. Most of the remaining OIs flagged as false positives are attributable to residual systematics mimicking transits. Visual inspection indicates that these OIs are clearly inconsistent with being a planetary transit.

4.1.1. Single Transit Events

We are currently not in a position to distinguish between confirmed planets and various AFP scenarios in an absolute sense. This is because of the lack of follow-up observations in this study, which are ultimately required to validate or disprove the planetary nature of our OIs. Despite the lack of such follow-up observations, it is still advisable to attempt to statistically validate OIs by inferring the relative probabilities of a variety of AFP scenarios, which can be compared to the planetary interpretation. Such considerations are further motivated given that the rate of AFPs in the 2 minute TESS light curves is expected to be significant (∼60%; Sullivan et al. 2015).

We attempt to statistically validate our 24 OIs around 22 TIC members using the PyMultinest (Buchner et al. 2014) implementation of the probabilistic transit validation software vespa (Morton 2012, 2015) for establishing the final dispositions of our OIs by computing the planetary false-positive probabilities (FPP). vespa considers six AFP scenarios as potential explanations for transit-like signals. These include undiluted EBs, hierarchical triple EBs (HEB), and blended background or foreground EBs that are not physically associated with the target (BEB). Each of these scenarios then has two instances, with the first assuming the input orbital period and the second assuming twice the input orbital period (i.e., EB2, HEB2, BEB2). We note, however, that the forthcoming statistical OI interpretations are not treated as absolutely definitive in lieu of the follow-up observations required to distinguish transiting planets from AFPs.

For vespa input, we use the TIC member's celestial coordinates (α, δ), stellar parameters ${T}_{\mathrm{eff}}$, $\mathrm{log}g$, and ϖ, along with the star's ${{JHK}}_{{\rm{S}}}$ photometry. vespa also requires the photometric band in which the putative transit is detected, but the code cannot properly handle the TESS bandpass in its current version. Fortunately, the central wavelengths of the TESS bandpass and the Cousins I_C band are similar, but with the TESS band being much wider (Sullivan et al. 2015). Given the similarity of the I_C and SDSS i bands, and the compatibility of the latter passband within vespa, we use T and ${K}_{{\rm{S}}}$ to derive i using the color relation from Muirhead et al. (2018). We also pass to vespa the OI's MAP P and ${r}_{p}/{R}_{s}$ along with its detrended light curve following the removal of all candidate transit models that are not associated with the OI being statistically validated. The light curves are phase-folded and restricted to ±3D around T₀ for comparison to light-curve models generated under the transiting planet and all AFP scenarios.

vespa also requires constraints on the maximum angular separation (maxrad) from the target star that should be searched for potential blending sources. We limit this separation to be less than the median FWHM of the target's approximate PSF. The FWHM of the PSF is derived by fitting a two-dimensional Gaussian profile to the target image in each target pixel file over time and adopting the median FWHM as vespa input. The median FWHM value among the 22 TIC members is ∼37 arcsec or nearly two TESS pixels across. Over such a large field, it is reasonable to expect that many of the OIs may be favored by either the BEB or BEB2 models.

Lastly, vespa requires the maximum permissible depth of a secondary eclipse of an EB (secthresh) to be specified. Recall that attempts within ORION were made to automatically vet EBs among our OIs in Section 3.5.2. We therefore expect that vespa is unlikely to detect any probable EBs. Nevertheless, the input secthresh value for each TIC member is derived from the box model depths fitted to each transit time in T₀ during the linear search stage (see Section 3.3). After masking measurements that occur within the PC's transit window and extrapolating the fitted depths to the PC's transit duration, we adopt the 95th percentile of the depth distribution depths as the value of secthresh (Crossfield et al. 2018). The median secthresh is ∼2100 ppm. The input maxrad and secthresh for each OI are reported in Table 5 along with the results of our vespa calculations.

Table 5.  vespa Input Parameters and Inferred Probabilities of Transiting Planets and Astrophysical False-positive Models for Our 24 Objects of Interest

IDs		vespa Input		vespa Results
OI	TOI	maxrad	secthresh	PEB	${P}_{\mathrm{EB}2}$	${P}_{\mathrm{HEB}}$	${P}_{\mathrm{HEB}2}$	PBEB	${P}_{\mathrm{BEB}2}$	FPPa	Dispositionb
12421862.01	198.01	34.755	9.9 × 10−4	2.0 × 10−9	4.9 × 10−5	1.1 × 10−14	9.8 × 10−8	5.8 × 10−2	3.7 × 10−2	9.6 × 10−2	PC
47484268.01	226.01	34.147	4.8 × 10−3	1.3 × 10−7	3.8 × 10−3	1.4 × 10−9	1.6 × 10−4	3.9 × 10−1	2.8 × 10−1	6.8 × 10−1	pPC
49678165.01	⋯	75.094	7.7 × 10−3	9.4 × 10−27	1.4 × 10−14	2.4 × 10−26	3.5 × 10−14	9.1 × 10−3	7.1 × 10−3	1.6 × 10−2	ST
92444219.01	⋯	35.723	3.8 × 10−3	4.1 × 10−15	6.7 × 10−8	4.4 × 10−15	1.6 × 10−8	2.6 × 10−1	1.6 × 10−1	4.1 × 10−1	pST
100103200.01	⋯	47.832	7.0 × 10−4	5.1 × 10−19	4.3 × 10−12	5.0 × 10−33	2.9 × 10−20	3.8 × 10−3	2.0 × 10−3	5.7 × 10−3	BEBc
100103201.01	⋯	47.941	8.1 × 10−4	2.2 × 10−73	1.7 × 10−67	5.1 × 10−132	3.7 × 10−91	6.2 × 10−1	3.5 × 10−1	9.7 × 10−1	BEB
100103201.02	⋯	47.941	8.1 × 10−4	2.2 × 10−73	1.7 × 10−67	5.1 × 10−132	3.7 × 10−91	6.2 × 10−1	3.5 × 10−1	9.7 × 10−1	BEB
141708335.01	⋯	33.606	3.6 × 10−3	6.7 × 10−39	2.9 × 10−31	3.4 × 10−35	8.6 × 10−26	6.3 × 10−1	3.3 × 10−1	9.5 × 10−1	BEB
206660104.01	⋯	38.276	8.4 × 10−4	1.7 × 10−65	8.6 × 10−39	2.5 × 10−87	1.2 × 10−40	1.3 × 10−2	9.3 × 10−3	2.2 × 10−2	PC
231279823.01	⋯	36.346	5.3 × 10−4	7.7 × 10−43	7.9 × 10−47	7.5 × 10−55	4.0 × 10−78	5.1 × 10−1	4.9 × 10−1	1.0 × 100	BEB
231702397.01	122.01	36.485	6.9 × 10−3	7.5 × 10−18	8.7 × 10−6	1.8 × 10−23	5.1 × 10−9	2.3 × 10−3	2.7 × 10−3	5.0 × 10−3	PC
234994474.01	134.01	37.794	7.1 × 10−4	1.2 × 10−51	8.5 × 10−34	3.9 × 10−107	4.2 × 10−61	9.6 × 10−4	1.9 × 10−4	1.2 × 10−3	PC
235037759.01	⋯	39.567	1.9 × 10−2	⋯	⋯	⋯	⋯	⋯	⋯	⋯	AFPd
238027971.01	⋯	37.085	1.4 × 10−3	2.5 × 10−67	7.5 × 10−92	5.6 × 10−76	4.1 × 10−79	3.4 × 10−1	6.6 × 10−1	1.0 × 100	BEB2
260004324.01	⋯	35.803	1.1 × 10−3	3.3 × 10−44	4.1 × 10−17	1.4 × 10−61	8.8 × 10−20	5.3 × 10−2	2.8 × 10−2	8.1 × 10−2	PC
262530407.01	177.01	40.509	8.0 × 10−4	6.5 × 10−38	3.2 × 10−41	7.6 × 10−45	5.5 × 10−44	1.8 × 10−7	5.7 × 10−7	7.5 × 10−7	PC
278661431.01	⋯	48.894	5.1 × 10−3	2.4 × 10−31	1.4 × 10−37	3.6 × 10−48	6.9 × 10−55	3.8 × 10−1	4.8 × 10−1	8.6 × 10−1	pPC
279574462.01	⋯	146.950	1.3 × 10−2	⋯	1.7 × 10−86	1.0 × 10−304	1.9 × 10−77	3.0 × 10−1	7.0 × 10−1	1.0 × 100	BEB2
303586421.01	⋯	32.084	6.2 × 10−3	7.8 × 10−53	6.2 × 10−47	3.1 × 10−67	1.5 × 10−31	3.3 × 10−1	5.6 × 10−1	9.0 × 10−1	BEB2
305048087.01	237.01	34.445	8.7 × 10−3	2.6 × 10−30	1.4 × 10−8	4.8 × 10−27	8.0 × 10−8	1.8 × 10−2	1.4 × 10−2	3.2 × 10−2	PC
307210830.01	175.01	38.817	7.7 × 10−4	1.7 × 10−5	8.0 × 10−3	9.0 × 10−10	7.5 × 10−5	9.2 × 10−3	4.3 × 10−3	2.2 × 10−2	PC
415969908.01	233.01	32.000	2.3 × 10−3	1.5 × 10−11	1.1 × 10−5	1.4 × 10−18	2.0 × 10−8	6.0 × 10−3	5.5 × 10−3	1.2 × 10−2	PC
415969908.02	⋯	32.000	2.3 × 10−3	2.5 × 10−19	2.4 × 10−10	4.9 × 10−28	2.7 × 10−13	2.6 × 10−3	2.0 × 10−3	4.7 × 10−3	ST
441056702.01	⋯	35.795	1.9 × 10−3	5.5 × 10−19	5.3 × 10−9	1.8 × 10−37	6.0 × 10−17	2.5 × 10−2	1.7 × 10−2	4.2 × 10−2	PC

Notes. P_i represents the relative probability (i.e., the product of the model's prior and likelihood relative to the probabilities of all other models) of the ith astrophysical false-positive scenario, where i is one of six possible scenarios: blended eclipsing binaries (BEB), undiluted eclipsing binaries (EB), and hierarchical eclipsing binaries (HEB), each with either one or twice its input orbital period.

^aTransiting planet false-positive probability. ^bPossible dispositions of objects of interest are a planet candidate (PC), a putative planet candidate (pPC), a single transit event (ST), a putative single transit event (pST), an unclassified astrophysical false positive (AFP), or any of the scenarios i. The putative dispositions have FPP ∈ [0.1, 0.9], whereas remaining candidates and astrophysical false positives have FPP < 0.1 and >0.9, respectively. ^cOI 100103200.01 is assigned the BEB disposition despite having an FPP < 0.1 because of its proximity to and contamination from the comparably bright TIC 100103201 (see Figure 8). ^dThe MCMC for OI 235037759.01 failed to converge, so we broadly classify it as an astrophysical false positive (AFP) based on the prevalence of nearby bright sources from Gaia (see panel "v" in Figure 8). We are unable to classify the object as a particular type of astrophysical false positive.

Download table as:  ASCIITypeset image

The true power of vespa is realized when additional follow-up observations such as contrast curves from AO-assisted imaging or photometric follow-up are used to inform the interpretation of transiting PCs. Given the lack of such data in this study, we adopt conservative limits on the interpretation of the resulting vespa probabilities. Similarly, we also do not claim to validate planets with ultralow FPP (<0.01; e.g., Montet et al. 2015; Crossfield et al. 2018; Livingston et al. 2018) because we will caution in Section 4.3 that vespa results should not be taken absolutely in the absence of follow-up observations. Our limiting values on interpreting FPPs are as follows. OIs with FPP < 0.1 are classified as PCs. Similarly, OIs are classified as AFPs when FPP ≥ 0.9 and have their dispositions assigned to the specific AFP model with the highest probability. OIs with intermediate FPPs are classified as putative planet candidates (pPC).

The statistical validation calculations with vespa result in 13/24 of our OIs being classified as PCs, plus 3/24 as pPCs. The OIs 49678165.01, 415969908.02, and 92444219.01 correspond to the three ST events detected during the manual vetting stage. We reclassify these objects as STs and a pST, respectively. Seven of the remaining eight OIs are favored by either BEB model with 4/7 BEBs and 3/7 BEB2s. The MCMC during the vespa calculation of the lone remaining OI 235037759.01 failed to converge, leaving its disposition as of yet undefined. We will show in the following subsection that despite the failure of the FPP calculation, the nature of OI 235037759.01 is likely to be an AFP, although we are unable to distinguish between the different AFP scenarios. The derived rate of AFPs from this small sample of OIs is ∼33 ± 12%, which is somewhat lower than the expected AFP rate of 60% from the TESS simulations by Sullivan et al. (2015), a discrepancy that is likely explained by incompleteness in our vetting (see Section 5.1).

vespa calculations are based on synthetic stellar populations from the TRILEGAL galaxy model (Girardi et al. 2005). These synthetic results can be supplemented by querying the Gaia DR2 in the vicinity of each TIC member to empirically investigate the number density and brightness distribution of nearby sources on the sky. In this way, we hope to find supporting empirical evidence for any of the BEB interpretations of OIs with high FPPs as those inferences should be expected if nearby bright sources fall within or near the TESS PSF of the targeted TIC member. The resulting maps of Gaia sources around the 22 TIC members with OIs in our sample are shown in Figure 8. Querying the Gaia DR2 is performed identically to the method used in Section 2.2 to match TIC members with the Gaia DR2 catalog, although here we conduct our searches with a fixed radius of 105 arcsec or ∼5 TESS pixels.

Zoom In Zoom Out Reset image size

From Figure 8 it is clear that many of the statistically favored interpretations as either some form of PC or a BEB are consistent with the lack or prevalence of nearby bright sources to the targeted TIC member, respectively. All panels with PC OIs in Figure 8 show no or minor sources of comparable brightness within or very close to the target PSF edges to significantly contaminate the measured TIC member photometry and consequently result in a probable FP. Similarly, all AFP panels other than "q" and "s" do have at least one neighboring source of comparable brightness that may be responsible for the favorability of an AFP scenario by vespa. This includes the TIC 235037759, whose vespa calculation failed. Two bright sources are clearly seen to contribute to the flux within the target's PSF, thus supporting the probable interpretation of the OI 235037759.01 transit-like event as being caused by an AFP.

We note, however, that some discrepancies between the distributions of Gaia sources and our vespa interpretations still persist, particularly with regard to TIC 100103200.01 and TIC 100103201.01 (panels "l" and "p" in Figure 8), which strongly favor the PC and BEB models, respectively, despite being located within 1 TESS pixel of one another on the sky, having very similar brightnesses (i.e., J = 7.50, 7.66), and being located at effectively identical distances (i.e., d = 16.745 pc). Perhaps naively, we might expect this architecture to favor an AFP scenario for both stars including blends, an EB, or an HEB. Indeed, the apparent flux dips, which appear qualitatively consistent with a transiting planet around either one of the TIC members, are also seen to have a clear manifestation in the light curve of the other, as evidenced in Figure 9. This is almost certainly caused by the overlap of each target's PSF. However, vespa results indicate FPPs that differ by over two orders of magnitude between the two TIC members. Perhaps it is feasible, although seemingly unlikely, for TIC 100103200 to host a detectable transiting PC while being blended with the nearby TIC 100103201, whose transit-like events are strongly favored by the BEB scenario. Indeed, the transit times of each TIC member's transit-like events flagged by ORION appear out of phase as they do not align nor do they overlap in Figure 9, implying that transit-like events detected around each TIC member by ORION do not affect the transit-like events in the light curve of the other, even if there are regions of the out-of-transit light curve that are mutually affected. We are therefore left with the questionable interpretation of these OIs based on the vespa dispositions alone and note that additional vetting criteria should be used in upcoming versions of ORION to flag other instances of probable blends. Here we opt to override the vespa dispositions and assign a BEB to each of these OIs (see Table 5).

Zoom In Zoom Out Reset image size

After manual vetting and statistical validation, we are left with 15 candidate planets. These include 10 PCs, two STs, two pPCs, and one pST. Half of our candidates are "new," having not yet been released as TOIs.⁸ Point estimates of observable and derived planetary parameters for these candidates are reported in Table 6. Figure 10 also depicts their phase-folded light curves along with the transit models computed using the MAP parameter values from Table 6.

Zoom In Zoom Out Reset image size

Table 6.  Planetary Parameters for Our 16 Vetted Candidates

OI	TOI	P	T0	$a/{R}_{s}$	${r}_{p}/{R}_{s}$	i	rp	S	Dispositiona
		(days)	[BJD—2,457,000]			(deg)	(R⊕)	(S⊕)
12421862.01	198.01	20.4282 ± 0.0042	1376.8028 ± 0.0023	${68.05}_{-9.86}^{+6.21}$	${0.033}_{-0.002}^{+0.001}$	${90.24}_{-0.40}^{+0.44}$	${1.59}_{-0.10}^{+0.09}$	2.7 ± 0.2	PC
47484268.01	226.01	20.2833 ± 0.0048	1378.7855 ± 0.0042	${56.34}_{-8.28}^{+9.13}$	${0.090}_{-0.006}^{+0.004}$	${90.62}_{-0.19}^{+0.32}$	${3.82}_{-0.25}^{+0.20}$	1.4 ± 0.1	pPC
49678165.01	⋯	${35.64}_{-14.61}^{+49.78}$	1371.1945 ± 0.0038	${74.13}_{-26.55}^{+102.92}$	${0.10}_{-0.00}^{+0.01}$	${90.00}_{-0.36}^{+0.36}$	${3.02}_{-0.19}^{+0.21}$	${0.3}_{-0.2}^{+0.3}$	ST
92444219.01	⋯	${39.52}_{-16.90}^{+45.64}$	1342.4729 ± 0.0037	${49.71}_{-19.54}^{+55.87}$	${0.07}_{-0.00}^{+0.00}$	${89.99}_{-0.41}^{+0.40}$	${3.07}_{-0.14}^{+0.13}$	${0.5}_{-0.3}^{+0.6}$	pST
206660104.01	⋯	13.4507 ± 0.0081	1379.7842 ± 0.0079	${27.84}_{-1.05}^{+1.82}$	${0.021}_{-0.001}^{+0.001}$	${90.00}_{-0.49}^{+0.44}$	${1.21}_{-0.07}^{+0.08}$	5.2 ± 0.4	PC
231702397.01	122.01	5.0789 ± 0.0010	1349.4338 ± 0.0031	${31.23}_{-4.64}^{+3.05}$	${0.077}_{-0.005}^{+0.004}$	${90.55}_{-1.12}^{+0.96}$	${2.80}_{-0.19}^{+0.18}$	7.5 ± 0.7	PC
234994474.01	134.01	1.4013 ± 0.0001	1345.6507 ± 0.0010	${8.68}_{-1.10}^{+0.73}$	${0.021}_{-0.001}^{+0.001}$	${88.84}_{-3.67}^{+2.67}$	${1.39}_{-0.06}^{+0.07}$	145.1 ± 11.0	PC
260004324.01	⋯	3.8157 ± 0.0007	1357.9369 ± 0.0036	${17.89}_{-2.73}^{+1.98}$	${0.021}_{-0.002}^{+0.001}$	${91.12}_{-2.14}^{+1.23}$	${1.15}_{-0.09}^{+0.07}$	24.6 ± 1.9	PC
262530407.01	177.01	2.8540 ± 0.0001	1364.7070 ± 0.0004	${16.69}_{-2.17}^{+1.86}$	${0.033}_{-0.001}^{+0.001}$	${90.95}_{-1.11}^{+1.45}$	${1.87}_{-0.08}^{+0.08}$	39.7 ± 3.3	PC
278661431.01	⋯	17.6317 ± 0.0048	1343.9299 ± 0.0025	${46.41}_{-0.38}^{+0.26}$	${0.094}_{-0.002}^{+0.002}$	${89.98}_{-0.08}^{+0.12}$	${2.82}_{-0.10}^{+0.11}$	1.1 ± 0.1	pPC
305048087.01	237.01	5.4310 ± 0.0014	1376.9753 ± 0.0037	${35.04}_{-5.12}^{+3.47}$	${0.073}_{-0.006}^{+0.004}$	${90.33}_{-1.14}^{+0.80}$	${1.67}_{-0.14}^{+0.12}$	3.6 ± 0.4	PC
307210830.01	175.01	3.6893 ± 0.0001	1374.6508 ± 0.0005	${22.34}_{-2.52}^{+1.64}$	${0.039}_{-0.001}^{+0.001}$	${90.35}_{-0.58}^{+0.88}$	${1.34}_{-0.04}^{+0.05}$	12.0 ± 0.9	PC
415969908.01	233.01	11.6658 ± 0.0056	1376.9247 ± 0.0040	${45.23}_{-7.04}^{+4.77}$	${0.046}_{-0.003}^{+0.003}$	${90.11}_{-0.73}^{+0.67}$	${1.90}_{-0.13}^{+0.13}$	3.8 ± 0.3	PC
415969908.02	⋯	${52.74}_{-20.31}^{+56.33}$	1381.0703 ± 0.0042	${98.07}_{-33.09}^{+90.89}$	${0.05}_{-0.00}^{+0.00}$	${90.01}_{-0.37}^{+0.36}$	${2.02}_{-0.20}^{+0.22}$	${0.5}_{-0.3}^{+0.5}$	ST
441056702.01	⋯	6.3424 ± 0.0093	1371.8111 ± 0.0055	${20.88}_{-3.40}^{+3.80}$	${0.031}_{-0.003}^{+0.003}$	${89.81}_{-1.24}^{+1.67}$	${1.97}_{-0.19}^{+0.19}$	25.0 ± 2.2	PC

Note.

^aPossible dispositions of objects of interest are a planet candidate (PC), a putative planet candidate (pPC), a single transit event (ST), or a putative single transit event (pST). The putative dispositions have FPP $\in [0.1,0.9]$, whereas the remaining candidates have FPP < 0.1.

Download table as:  ASCIITypeset image

Figure 11 depicts our candidate population and compares it to the 12 TOIs whose TIC hosts are included in our stellar sample. Our candidates have orbital periods from 1.4 to 20 days for PCs and MAP orbital periods from 35 to 50 days for ST events, although ST periods exhibit large uncertainties of order of the MAP period value. Our candidates have radii between 1.1 and 3.8 R_⊕, potentially making them targets of interest for the completion of the TESS level one science requirement of delivering 50 planets with r_p < 4 R_⊕ with measured masses. In Section 5.4.1 we will discuss the prospects that our candidates have for contributing to the realization of the TESS level one science requirement. We do not detect any hot sub-Neptunes in the photoevaporation desert (Lundkvist et al. 2016) nor any small planets (≲1.5 R_⊕) on orbits longer than ∼20 days. This is largely attributable to our poor detection sensitivity in that regime, due to the limited TESS baselines of just 27 days.

Zoom In Zoom Out Reset image size

Figure 11 also depicts our candidates as a function of insolation. The majority of candidates (10/15) experience incident insolation levels S in excess of twice that of the Earth. However, five candidates, including all three ST events and two pPCs, are likely more temperate and experience insolations ≲1.5 S_⊕. This S limit marks the "recent Venus" inner edge of the low-mass star habitable zone (HZ; Kopparapu et al. 2013). Our STs also lie within the more conservative HZ definition bounded by the "water loss" inner edge, where an increase in insolation results in the photolysis of stratospheric water vapor, causing the atmosphere to experience rapid hydrogen escape, and the "maximum greenhouse" outer edge, where an increase in CO₂ no longer results in a net surface heating due to the increased albedo. Our five temperate candidates may represent attractive targets for the characterization of HZ exoplanets around nearby low-mass stars. We will address the prospect of atmospheric characterization of these planets in Section 5.4.2.

The distribution of our candidates versus stellar parameters of interest is shown in Figure 12. All candidates are detected around stars hotter than 3000 K, which approximately corresponds to stars earlier than M5.5V (Pecaut & Mamajek 2013). Most candidates are detected around stars with ${T}_{\mathrm{eff}}$ ∈ [3200, 3900] K, which is largely consistent with the population of confirmed transiting planets recovered from the NASA Exoplanet Archive on 2018 December 13 (Akeson et al. 2013), modulo the TRAPPIST-1 planets (Gillon et al. 2017), GJ 1214b (Charbonneau et al. 2009), and the Kepler-42 planets (Muirhead et al. 2012). The median effective temperature of the candidate-hosting TIC members in our sample is 3560 K. A notable dearth of PCs with r_p ≳ 2 R_⊕ exists around stars hotter than ∼3500 K. The cause of this is unlikely to be due to sensitivity losses around these relatively hot (and correspondingly bright) stars and is instead likely attributable to the sharp decrease in the number of stars within our sample at ${T}_{\mathrm{eff}}$ ∼ 3550 K (see Figure 1).

Zoom In Zoom Out Reset image size

The distributions of previously confirmed planets and our candidates versus J-band magnitude reveal that many (∼9/15) of our candidates orbit systematically brighter stars than the majority of confirmed transiting planets with J < 10. This directly demonstrates the power of a survey mission like TESS to discover transiting planets orbiting nearby bright stars that are amenable to forthcoming detailed characterization efforts. The remaining six candidates still orbit moderately bright stars with J ∈ [10, 12]. The median J of our candidate-hosting TIC members is 9.9. From the number of ORION candidates as a function of J, it is clear that the ORION sensitivity to planets orbiting low-mass TIC members starts to drop off around J ≳ 12. The large photometric uncertainties in this regime are largely dominated by photon noise from the target star, zodiacal light, and unresolved background stars (Ricker et al. 2015).

The distance distribution of our candidates is also included in Figure 12. All of our candidates are found between 10 and 65 pc with a median distance of 34 pc. Our sample includes five candidates within ∼25 pc as well as the closest transiting PC around a low-mass star to date: TIC 307210830.01 (TOI-175.01) at 10.6 pc, which also contains two additional TOIs (Cloutier et al. 2019; Kostov et al. 2019) not detected by ORION (see Section 5.3). Among our seven new candidates not released as TOIs, we detect one candidate within 25 pc: the PC 206660104.01. Barring the rejection of this candidate and the TOIs around TIC 307210830, these two systems of four PCs represent 2/7 of the closest transiting planetary systems around low-mass stars along with GJ 1132 (Berta-Thompson et al. 2015; Bonfils et al. 2018), TRAPPIST-1 (Gillon et al. 2017; Luger et al. 2017), LHS 1140 (Dittmann et al. 2017b; Ment et al. 2019), GJ 1214 (Charbonneau et al. 2009), and GJ 3470 (Bonfils et al. 2012).

A number of potentially useful diagnostics of the validity of transit-like events should be implemented to improve the sensitivity and systematic false-positive rate of future ORION versions. These include the characterization of internal scattered light from centroid offsets between the average in- and out-of-transit pixel response functions, consideration of each epoch's quality flag from the SPOC (Jenkins et al. 2016), and other stochastic effects on photometry such as imperfect systematics corrections at the edges of the light curves. These and other vetting criteria are expected to be realized through the analysis of additional TESS data from its many upcoming observing sectors and will help to make the ORION pipeline more robust.

OI 12421862.01. This PC has already been reported as TOI-198.01. The ORION planet parameters are consistent with those of TOI-198.01 with a 20.4 day orbital period and measured radius of 1.6 R_⊕, making it an interesting target for probing the photoevaporation valley around M dwarfs.

OI 47484268.01. This pPC, based on its moderate FPP, has already been reported as TOI-226.01. The ORION orbital period is consistent with that of TOI-226.01, but we derive a 10% smaller planet radius of 3.8 R_⊕ despite the star's refined radius being 15% larger. At 1.4 S_⊕, this pPC orbits within the "recent Venus" habitable zone but remains an attractive target for rapid RV characterization owing to its expected large mass compared to most of the smaller candidate planets (see Section 5.4.1).

OI 49678165.01. This is a new candidate ST event with an estimated period between 21 and 85 days and a radius of 3 R_⊕. This candidate is likely the coldest object in our sample with an MAP S = 0.3 S_⊕ and a corresponding equilibrium temperature of T_eq = 212 K assuming zero albedo and perfect heat redistribution.

OI 92444219.01. This is a pST based on its moderate FPP. This cool 3 R_⊕ candidate has an estimated period between 22 and 95 days, placing it at S = 0.5 S_⊕ with an equilibrium temperature T_eq = 238 K.

OI 206660104.01. This is a new terrestrial-sized (1.2 R_⊕) PC at 13.4 days. This PC is the second smallest candidate recovered by ORION and is smaller than most (3/4) of the TOIs missed by ORION (see Section 5.3).

OI 231702397.01. This PC has already been reported as TOI-122.01. The ORION orbital period is consistent with that of TOI-122.01, although we derive a 15% larger radius (2.8 R_⊕), corresponding to the 13% larger stellar radius in our sample. Given its large size, the expected mass from the Chen & Kipping (2017) mass–radius relation is 8.26 M_⊕, making it an attractive target for rapid RV follow-up despite being relatively dim with J = 11.5.

OI 234994474.01: This PC has been reported as TOI-134.01 and is being validated with RVs from HARPS and PFS (N. Astudillo-Defru et al. 2019, in preparation). The ORION parameters are largely consistent with the TOI-134.01 parameters, albeit with a slightly smaller radius of 1.38 R_⊕ (12% reduction) for an unchanged stellar radius. Being by far the hottest target in the candidate sample (T_eq = 965 K) and orbiting an early-M dwarf with J = 7.9, this PC is one of the best targets for any further RV characterization to search for longer period companions, transmission spectroscopy, and even thermal emission spectroscopy. Regarding the latter, TOI-134.01 is even more favorable than the previously most attractive terrestrial-sized planet for such observations: GJ 1132b (Morley et al. 2017).

OI 260004324.01. This is a new terrestrial-sized PC that is the smallest in our sample at 1.15 R_⊕ with a 3.8 day period. Its small size and small expected mass of 1.6 M_⊕ around a 0.56 M_⊕ early-M dwarf (J = 8.8) will make this a slightly more challenging target for RV follow-up but may still be of interest for probing the low-mass end of the 50 planets smaller than 4 R_⊕ targeted for completion of the TESS level one science requirement.

OI 262530407.01. This PC has already been reported as TOI-177.01. The ORION orbital period is consistent with that of TOI-177.01, although we find a 12% smaller radius of 1.87 R_⊕ for an unchanged stellar radius. The short period and host star brightness (J = 8.17) make this PC an exceptional candidate for transmission spectroscopy observations and is one that is less affected by the NIRISS bright limit of its Single Object Slitless Spectroscopy (SOSS) mode compared to other close-in super-Earth-sized planets in this catalog.

OI 278661431.01. This is a new pPC based on its moderate FFP. If validated, the candidate would have an orbital period of 17 days and a radius of 2.8 R_⊕. This pPC is temperate at S = 1.1 S_⊕ and near the "water loss" HZ inner edge. This pPC orbits one of the cooler TIC members in our candidate-hosting sample (${T}_{\mathrm{eff}}$ = 3300 K) with a correspondingly small radius of 0.28 R_⊙, thus making it an attractive target for transmission spectroscopy observations.

OI 305048087.01. This PC has already been reported as TOI-237.01. The ORION orbital period is consistent with the 5.4 day period and 1.7 R_⊕ radius of TOI-177.01.

OI 307210830.01. This PC is one of the three reported TOIs around TIC 307210830 (i.e., 175-01, 02, 03). Only TOI-175.01 is detected by ORION, for the reasons discussed in Section 5.3. The ORION planet parameters for this, the middle planet in this candidate three-planet system, are all consistent with those for TOI-175.01. This PC is in the closest planetary system in our sample and is correspondingly an attractive target for RV characterization of individual masses and the RV analysis of the possible resonant pair 175.01/175.02 for comparisons to transit timing variation analyses from follow-up photometry. This PC is also a viable target for the atmospheric characterization of a terrestrial-sized planet (1.3 R_⊕).

OI 415969908.01. This PC has already been reported as TOI-233.01. The ORION orbital period is consistent with that of TOI-233.01 but finds a 26% smaller radius (1.9 R_⊕) in part because of the refined stellar radius being reduced by 21% in our sample.

OI 415969908.02. This ST event is detected in the light of TIC 415969908, which already hosts the aforementioned candidate TOI-233.01 at 11.7 days. The estimated period of OI 415969908.02 is 32–108 days, which effectively spans the conservative HZ limits from Kopparapu et al. (2013) and whose MAP value is 53 days or S = 0.5 S_⊕. The measured radius is 2 R_⊕ (${r}_{p}/{Rs}=0.05$), making this ST event the most difficult to follow up from the ground among the three ST events in our candidate catalog.

OI 441056702.01. This is a new PC with an orbital period of 6.3 days and radius of 2 R_⊕, thus potentially being located within the photoevaporation valley around M dwarfs. Orbiting a moderately bright early-M to late-K dwarf (${T}_{\mathrm{eff}}$ = 4030 K) and with an expected mass of 4.5 M_⊕, this PC represents another attractive target for RV characterization aimed at addressing the TESS level one science requirement.

Our stellar sample, using refined stellar parameters based on Gaia distances, contains 10 TIC members with TOIs listed as part of the TESS alerts (see footnote 8). These 10 systems host a total of 12 TOIs in nine single PC systems plus TIC 307210830, which hosts three TOIs. The ORION results presented in this paper include the independent detection of 8/12 TOIs with an additional ST event around TIC 415969908, which already hosts TOI-233.01. The discrepancies between the TESS alerts and our ORION results are described in what follows.

TIC 259962054. This star was observed in the consecutive TESS sectors 1 and 2. The TOI-203.01 has an orbital period of 52 days, longer than any repeating candidate in our catalog. A signal at ∼52.1 days is found in the ORION linear and periodic search stages with an orbital phase that is consistent with that reported for TOI-203.01. This suggests that the TOI-203.01 transit-like signal at 52 days does exist in the light curve. The phase-folded light curve satisfies all but the second criterion from the automated vetting stage (see Section 3.5.1) with S/N_transit = 5.6 < c₁ = 8.4. This is principally because the fitted transit depth within ORION is Z = 1839 ppm, which is just ∼73% of the TOI's reported depth, thus making it difficult to confirm the nature of the repeating signal as being due to a transiting planet with just two transits observed.

TIC 307210830. This system contains three TOIs (175.01, 175.02, 175.03) at 3.69, 7.45, and 2.25 days, respectively. The innermost PC is not found during the linear and periodic search stages. This is likely caused by the candidate's depth of 571 ppm (as reported by the SPOC) being less than the median photometric uncertainty of its light curve (i.e., median (σ_f) ∼770 ppm). The two remaining PCs were each seen to be detected in the ORION linear search stage owing to their ∼3 times larger transit depths. However, this candidate pair has an orbital period ratio that is within 1% of a 2:1 resonant configuration. Recall that pairs of periods of interest which are that close to an integer period ratio will have one of those periods automatically discarded in the periodic search stage because the detected periodic signals are likely aliases of each other rather than being due to two separate planetary candidates.

TIC 316937670. TOI-221.01 has an orbital period of 0.624 days and a low transit depth of 954 ppm. By adopting the reported TOI-221.01 transit depth and duration, we estimate CDPP_transit and find that Z/CDPP_transit ∼ 1.1. Because of this, the results of the ORION linear search only detect a single transit event above the S/N threshold such that no periodic events can be found. If the linear search S/N threshold is lowered such that multiple transits from TOI-221.01 are detected in the linear and periodic search stages, then the expected S/N_transit is ∼7.2 < c₁ = 8.4, which would still be insufficient to detect the PC in a single TESS sector. We are further discouraged by the prospect of lowering the linear search S/N threshold as this would drastically increase the number of FPs purely from the noise.

5.4.1. Mass Characterization via Precision RVs

The TESS level one science requirement is to deliver at least 50 planets smaller than 4 R_⊕ with measured masses via precision RV follow-up. All 15 of our candidates have a measured radius consistent with being <4 R_⊕ (see Table 6). Using the empirical mass–radius relation for small planets <14.26 R_⊕ from Chen & Kipping (2017), we compute the maximum likelihood masses m_p of our PCs and single transit events to then infer their expected RV semiamplitudes using

$$\begin{eqnarray}&&{K}_{\mathrm{RV}}=2.4\ {\rm{m}}\,{{\rm{s}}}^{-1}\left(\displaystyle \frac{{m}_{p}}{5\ {M}_{\oplus }}\right){\left(\displaystyle \frac{{M}_{s}}{0.5{M}_{\odot }}\right)}^{-2/3}{\left(\displaystyle \frac{P}{10\mathrm{days}}\right)}^{-1/3}.\end{eqnarray} \tag{ 8 }$$

These values are shown in the first panel of Figure 13 versus J-band magnitude and are accompanied by the simulated TESS yield from Barclay et al. (2018) and the set of confirmed transiting planets from the NASA Exoplanet Archive. Both of the latter samples are restricted to cool host stars (i.e., ${T}_{\mathrm{eff}}$ < 4200 K). Many existing high-performance RV spectrographs are stable at the level of a few cm s⁻¹, but RV observations are often limited by photon noise and intrinsic stellar activity at the level of one to a few m s⁻¹, even for relatively inactive stars (Fischer et al. 2016). The majority of our objects of interest have expected K_RV values in excess of this typical RV sensitivity limit and are reported in Table 7.

Zoom In Zoom Out Reset image size

Table 7.  Metric Values Indicating the Feasibility of a Variety of Follow-up Programs for Our 16 Vetted Candidates

OI	TOI	J	P	rp	mpa	K	Ωb	${T}_{\mathrm{eq}}$ c	TSMd	ESMe
			(days)	(R⊕)	(M⊕)	(m s−1)		(K)
12421862.01	198.01	8.65	20.43	1.59	3.16	1.19	0.58	358	53.4	0.6
47484268.01	226.01	10.85	20.28	3.82	14.03	5.93	1.40	302	69.0	0.9
49678165.01	⋯	11.14	35.64	3.02	9.40	4.40	0.92	212	57.7	0.1
92444219.01	⋯	10.49	39.52	3.07	9.68	3.35	0.90	238	51.1	0.1
206660104.01	⋯	8.36	13.45	1.21	1.92	0.76	0.51	419	5.9	0.7
231702397.01	122.01	11.53	5.08	2.80	8.26	6.35	1.63	461	69.3	3.2
234994474.01	134.01	7.94	1.40	1.39	2.52	1.98	1.24	965	14.2	9.8
260004324.01	⋯	8.80	3.82	1.15	1.62	0.98	0.74	619	7.6	2.1
262530407.01	177.01	8.17	2.85	1.87	4.16	2.74	1.32	698	119.8	10.1
278661431.01	⋯	10.89	17.63	2.82	8.36	5.14	1.08	288	86.2	0.7
305048087.01	237.01	11.74	5.43	1.67	3.44	4.06	0.95	384	66.2	1.3
307210830.01	175.01	7.93	3.69	1.34	2.37	2.15	0.87	517	26.4	6.7
415969908.01	233.01	9.94	11.67	1.90	4.26	2.21	0.84	387	55.5	1.1
415969908.02	⋯	9.94	52.74	2.02	4.74	1.48	0.54	234	36.4	0.1
441056702.01	⋯	9.89	6.34	1.97	4.53	2.17	1.06	622	39.8	2.4

Notes. Bolded values are indicative of candidates that exceed threshold values of that parameter (see Cloutier et al. 2018 for Ω and Kempton et al. 2018 for the TSM and ESM) and should be strongly considered for rapid confirmation and follow-up.

^aPlanet masses are estimated from the planet radius using the deterministic version of the mass–radius relation from Chen & Kipping (2017). ^bΩ is a diagnostic metric that is indicative of the observing time required to characterize a planet's RV mass (Cloutier et al. 2018); ${\rm{\Omega }}={r}_{p}/{P}^{1/3}$ where r_p is given in Earth radii and P in days. ^cPlanetary equilibrium temperature is calculated assuming zero albedo and full heat redistribution via ${T}_{\mathrm{eq}}={T}_{\mathrm{eff}}\sqrt{{R}_{s}/2a}$. ^dTransmission spectroscopy metric from Kempton et al. (2018). See Section 5.4.2 for the definition. ^eEmission spectroscopy metric from Kempton et al. (2018). See Section 5.4.2 for the definition.

Download table as:  ASCIITypeset image

Cloutier et al. (2018) calculated the observing time required to complete the TESS level one science requirement based on the expected TESS yield from Sullivan et al. (2015). The 50 TOIs requiring the shortest time commitment to characterize their planet masses at 5σ with RVs satisfy the following empirically derived conditions:

$$\begin{eqnarray}&&J\lt 11.7\ \mathrm{and}\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&{\rm{\Omega }}\gt 0.14J-0.35,\end{eqnarray} \tag{ 10 }$$

where

$$\begin{eqnarray}&&{\rm{\Omega }}=\left(\displaystyle \frac{{r}_{p}}{\ {R}_{\oplus }}\right){\left(\displaystyle \frac{P}{\mathrm{day}}\right)}^{-1/3}\end{eqnarray} \tag{ 11 }$$

is a proxy for K_RV that can be computed from transit-derived parameters. Six out of 15 of our candidates satisfy Equations (9) and (10) and are highlighted in Table 7 and in Figure 13. If AFP scenarios can be ruled out, then these OIs represent highly favorable targets for RV follow-up observations and the rapid completion of the TESS level one science requirement. This assumes that the host stars themselves are not active, which is an important characteristic to consider for RV follow-up (Moutou et al. 2017) and is one that is not taken into account in Equations (9) and (10).

5.4.2. Atmospheric Characterization

TESS will provide many of the best transiting exoplanets for atmospheric characterization in the near future. Kempton et al. (2018) presented a framework to prioritize transiting planets for either transmission spectroscopy or emission spectroscopy observations with dedicated missions like JWST and ARIEL. This framework consists of analytical metrics that quantify the expected S/N of transmission and emission signals from planetary atmospheres.

The transmission spectroscopy metric (TSM) from Kempton et al. (2018) is

$$\begin{eqnarray}&&\mathrm{TSM}=f\cdot {10}^{-0.2J}\cdot \left(\displaystyle \frac{{r}_{p}^{3}{T}_{\mathrm{eq}}}{{m}_{p}{R}_{s}^{2}}\right).\end{eqnarray} \tag{ 12 }$$

The TSM represents the expected S/N of 10 hr observing programs with JWST/NIRISS assuming fixed atmospheric compositions for different planet types, cloud-free atmospheres, and a deterministic planet mass–radius relation. The planetary equilibrium temperature in Equation (12) is ${T}_{\mathrm{eq}}={T}_{\mathrm{eff}}\sqrt{{R}_{s}/2a}$, where a is the planet's semimajor axis and is calculated assuming zero albedo and full heat redistribution over the planetary surface. The scale factor f is used to make the TSM nondimensional and is used to correct discrepancies between the analytical TSM and the detailed simulations from Louie et al. (2018) using the NIRISS simulator for SOSS observations. Values of f are reported in Kempton et al. (2018) for each of four planet types separately: terrestrials (r_p < 1.5 R_⊕), super-Earths (1.5 < r_p/R_⊕ < 2.75), sub-Neptunes (2.75 < r_p/R_⊕ < 4), and giants (4 < r_p/R_⊕ < 10). We calculate the TSM for our 15 candidates and report those values in Table 7 and in Figure 13. Kempton et al. (2018) highly recommend planets for atmospheric characterization (and therefore a priori RV characterization) based on their TSM values relative to their derived cutoffs (see their Table 1). Four out of 15 candidates exceed the threshold TSM cutoff as highlighted in Table 7 and should be considered for confirmation as they represent highly attractive targets for transmission spectroscopy observations. We note, however, that host stars with J ≲ 8.1 begin to approach the NIRISS bright limit (depending on its spectral type) and will require specialized fast readout modes or the use of detector subarrays to be observed with NIRISS in its SOSS mode (Beichman et al. 2014).

Similarly to the TSM, Kempton et al. (2018) defined the thermal emission spectroscopy metric as

$$\begin{eqnarray}&&\mathrm{ESM}=c\cdot {10}^{-0.2{K}_{{\rm{S}}}}\cdot \displaystyle \frac{{B}_{7.5}({T}_{\mathrm{day}})}{{B}_{7.5}({T}_{\mathrm{eff}})}\cdot {\left(\displaystyle \frac{{r}_{p}}{{R}_{s}}\right)}^{2},\end{eqnarray} \tag{ 13 }$$

where B_7.5(T) is the Planck function of spectral irradiance evaluated for a given temperature T at 7.5 μm, and T_day is the planet's day-side temperature assumed to be $1.1{T}_{\mathrm{eq}}$. The constant c = 4.29 × 10⁶ is used to scale the ESM to yield the S/N of the reference planet GJ 1132b (Berta-Thompson et al. 2015; Dittmann et al. 2017a) in the center of the MIRI low-resolution spectroscopy bandpass at 7.5 μm. We calculate the ESM for our 15 candidates and report those values in Table 7 and in Figure 13. Kempton et al. (2018) advocate that planets with ESM > ESM${}_{\mathrm{GJ}1132}=7.5$ should be considered favorable targets for thermal emission spectroscopy observations with MIRI. Within our candidate sample, 2/15 candidates exceed this threshold ESM and represent some of the best targets to date for the characterization of terrestrial and super-Earth atmospheres with emission spectroscopy for the first time.

Ballard (2019) performed a set of yield simulations focusing on M dwarfs not unlike the stellar population considered in this study. Ballard (2019) derive an ensemble completeness function for M dwarfs observed by TESS based on the simulated TESS yield from Sullivan et al. (2015), which includes details of the TESS footprint, systematics, the photometric error budget, and FP likelihoods. The expected TESS yield around M dwarfs is then derived by applying the completeness as a function of P and r_p to M dwarf planet occurrence rates. Said occurrence rates are derived from Dressing & Charbonneau (2015) and corrected for the eccentricity distribution (Limbach & Turner 2015), dynamical stability (Fabrycky et al. 2012), and multiplicity effects according to the "Kepler dichotomy" (Ballard & Johnson 2016) of M dwarf planet populations: either high-multiplicity systems (N > 5) with low mutual inclinations, or systems with lower multiplicity (N ∼ 1–2) and high mutual inclinations. The resulting TESS yield around M1–M4 dwarfs is predicted to be ∼1100 ± 220 planets.

The following back-of-the-envelope calculation reveals how the expected M dwarf planet population to be discovered with TESS compares to our ORION results from the first two TESS sectors. First we note that the Sullivan et al. (2015) stellar population is a synthetic one derived from the TRILEGAL galaxy model (Girardi et al. 2005). It contains 200,000 stars targeted by TESS, which is effectively the size of the TIC (Stassun et al. 2018). Using the stellar parameters from the TIC-7, we find 53,204 M1–M4 dwarfs in the TIC (${T}_{\mathrm{eff}}$ ∈ [3200–3700] K; Pecaut & Mamajek 2013). Of these, 1624 and 1869 are targeted in sectors 1 and 2, respectively, with 2849 being unique TIC members. However, unlike in the TIC-7, our stellar sample is derived using parallaxes from the Gaia DR2, which results in a distinct population of just 1149 M1–M4 dwarfs observed in either or both of TESS sectors 1 and 2. We use a simple correction factor to the expected TESS yield to account for the fractionally fewer M1–M4 stars that we target for transit searches compared to the TIC-7. This factor is f = 1149/2849 = 0.40 ± 0.01, where the f uncertainty is propagated from Poisson statistics.

The predicted number of M dwarf TESS planets discovered in sectors 1 and 2 is 1100 · w ∼ 59 ± 12, where w = 2849/53,204 is the fraction of all M1–M4 dwarfs targeted in those sectors. Correcting this expected number of planets from the first two TESS sectors by the f times fewer M1–M4 dwarfs in our stellar sample compared to in the TIC-7, we find that we are expected to detect ∼23 ± 5 planets in the first two TESS sectors. Note that this calculation inherently assumes that the detection completeness of ORION is equivalent to the ensemble completeness derived in Ballard (2019), which cannot be confirmed without performing a detailed characterization of the ORION completeness.

The ORION yield of 15 planets is somewhat on the lower end of what is expected based on the TESS yield predictions. If the TESS alert TOIs around M1–M4 dwarfs that remain undetected by ORION in this study are also included in the cumulative number of planet detections, then TESS has discovered ∼19 M1–M4 PCs in its first two sectors. The consistency between the ORION yield and the expected TESS yield speaks highly to TESS's overall performance compared to its expected completeness from Sullivan et al. (2015) and Ballard (2019), as well as to the outstanding performance that the TESS mission has already achieved so early on in its lifetime.