NEMESIS: Exoplanet Transit Survey of Nearby M-dwarfs in TESS FFIs. I.

Using the Python package, Astroquery (Ginsburg et al. 2019), to query the TIC from MAST, we obtain the stellar radius and mass, which we can then use to cross-match the quadratic limb-darkening parameters from Claret (2017) for each target star, using the "catalog_info" function from the Transit Least Squares (Hippke & Heller 2019) package. We then perform a radial cone search for each target star, using a radius of 21'', and obtain the R.A. and declination coordinates. Having obtained the celestial coordinates, we then download each target star's FFI square cutout (11× 11 pixels in size) from MAST, using the TESSCut (Brasseur et al. 2019) service.

TESS periodically fires its thrusters in order to unload the angular momentum built up from solar photon pressure at perigee, and throughout its orbit. These periodic firings are commonly referred to as momentum dumps, and are described in more detail in the Data Release Notes (DRN) ¹⁰ produced for each sector. Moreover, the DRN contain brief descriptions of observations containing a high degree of telescope jitter or glare from Earth and/or the Moon in the FFI field of view. For each FFI cutout around the target star, we first refer to the quality flags described by the DRN to remove specific cadences (with non-zero bitmask flag values) where various types of anomaly are detected. We also remove periods of spacecraft adjustments to maintain pointing stability, also discussed in the DRN.

To estimate the pixel masks for the sky background in each image, we find the dimmest pixels in the FFI cutout, using a brightness threshold of 1/1000 standard deviations below the median flux of the images. We then sum the counts in the background mask, and normalize the background flux. To identify the optimal aperture mask around the target star, we perform a centroid analysis around the target's pixel position on the median brightness image, using a bivariate quadratic function to approximate the core of a point-spread function. This centroiding technique was also used in the Eleanor FFI pipeline (Feinstein et al. 2019) and is described in more detail in Vakili & Hogg (2016).

Having established an approximation of the target star's location in the FFI cutouts, we then look for pixels displaying flux above a brightness threshold of 7.5 standard deviations above the median flux of the images. In comparison to the SPOC optimal apertures for TPFs, we found that a brightness threshold of 7.5 standard deviations is typically a close approximation for both FFIs and TPFs. To calculate the background-subtracted flux for our selected pixel masks, we use a simple aperture photometry (SAP) approach, defined as

$$\begin{eqnarray}&&{F}_{\mathrm{BKG}}=\displaystyle \frac{\displaystyle \sum _{i,j}F({{ap}}_{\mathrm{BKG}}(i,j))}{{N}_{\mathrm{pix},{{ap}}_{\mathrm{BKG}}}}\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{F}_{\mathrm{SAP}}=\displaystyle \sum _{i,j}\,\,F({{ap}}_{\mathrm{TGT}}(i,j))-{F}_{\mathrm{BKG}}\times {N}_{\mathrm{pix},{{ap}}_{\mathrm{TGT}}},\end{eqnarray} \tag{ 3 }$$

where F is the image flux, ap denotes the background (BKG) and target (TGT) pixel masks, i and j are the pixel coordinates of each image, and N_pix is the number of pixels in the masks. With the background flux subtracted, we then normalize the SAP flux to have a baseline centered at a value of one. In order to remove sharp changes in flux due to momentum dumps without quality flag values, indicating bad data, we remove data points occurring 30 minutes before and after each thruster firing event.

To account for potential extra light from nearby stars that might contaminate our aperture photometry, we query the TIC for all sources within three TESS pixels of the target star (∼1 arcminute), and record their TESS magnitudes. Typically, our automatically selected apertures spread across 2–3 TESS pixels, so a radial cone search with a width of three TESS pixels is a reasonable general approximation. We calculate the dilution factor as

$$\begin{eqnarray}&&f=1\ -\ \displaystyle \frac{10{}^{-{T}_{\mathrm{mag},\mathrm{target}}}/2.5}{\displaystyle \sum _{1}^{{N}_{\mathrm{starsi}\mathrm{in}\mathrm{aperture}}}{0}^{-{T}_{\mathrm{mag},i}/2.5}}.\end{eqnarray} \tag{ 4 }$$

We then subtract our background-subtracted SAP flux by the dilution factor, and renormalize.

Pixel-level decorrelation (PLD) is an effective technique (Deming et al. 2015; Luger et al. 2016, 2018), used to remove the effects of intrapixel fluctuations attributed to telescope jitter, or short-term variations such as those caused by momentum dumps, which may occur during TESS observations in each sector. By identifying instrumental systematics with methods such as PLD, the rate of false-positive detections can be decreased for period-searching algorithms such as box-fitting least squares (BLS; Kovács et al. 2002). Based on Equations (1)–(4) from Deming et al. (2015), we utilize a third-order PLD to calculate a noise model for the observed time series, so as to model the intrapixel correlations. We then perform a principal component Analysis (PCA) to reduce the number of eigenvectors in our PLD noise model, in order to construct a PCA design matrix and solve for the weights of the PLD model. Having modeled the instrumental systematics, we can then detrend our SAP flux, using the PLD noise model. Based on our testing, we find that using a combination of a third-order PLD with three PCA terms represents the optimal approach to removing short-term intrapixel trends in TESS FFI photometry.

With the instrumental systematics modeled and removed via a PLD noise model, we then remove long-term trends, such as the rotational modulation of starspots, by means of a median-based, time-windowed smoother with an iterative robust location estimator, based on Tukey's biweight (Beyer 1981), using the Wōtan (Hippke et al. 2019) Python package. Removing these trends while keeping the shapes and durations of potential transits intact permits easier detection by period-searching transit-finding algorithms. To determine the optimal window size for the smoothing filter, we calculated the longest transit duration for circular orbits (b = 0, i = 90°, w = 90°, e = 0) of an Earth-sized planet, transiting every 14 days (minimum of about 2 transits per sector):

$$\begin{eqnarray}&&{T}_{\mathrm{dur}}=\displaystyle \frac{P}{\pi }\arcsin \left(({R}_{\mathrm{Star}}+{R}_{\mathrm{Planet}}){\left(\displaystyle \frac{4{\pi }^{2}}{{{GM}}_{\mathrm{Star}}{P}^{2}}\right)}^{1/3}\right).\end{eqnarray} \tag{ 5 }$$

We then use three times this transit duration as our smoothing window, which is calculated for each target star using the stellar radius and mass parameters queried from the TIC.

Once the SAP flux is extracted, known systematics caused by high jitter and momentum dumps are removed, short-term trends at the pixel level and long-term trends in the time series are removed, and we then begin a sliding-window sigma clipping routine, where we remove outliers higher than ± 2 median absolute deviations above and below the median flux in a given window of data spanning the same smoothing window estimated via Equation (5). We are careful to include outliers possessing more than two consecutive data points ("good outliers") in a given window, so as to not remove potential transit events on ∼1 hour timescales. While stellar flares are typically conserved using this approach, for our transit survey, we chose to remove consecutive outliers lying above the local noise thresholds. An example of the full processing of the light curve is displayed in Figure 6.

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To verify the quality of the light curves produced by our pipeline at each step, we calculate the combined differential photometric precision (CDPP; [ppm hr^−1/2]) as shown in Figure 7. We also compare our CDPP values with the preflight theoretical precision of TESS, estimated by Sullivan et al. (2015), and find that the quality of many of our processed light curves exceeds the predicted quality of this model.

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The box least-squares (BLS) algorithm (Kovács et al. 2002, 2016) is a widely used tool in the exoplanet transit search community. BLS approximates the transit light curve as a boxcar function, with a normalized average out-of-transit flux of one, and with a fixed depth during transit. BLS has a high signal detection efficiency (SDE) for Neptune- and Jupiter-sized planet transits; however, for smaller planets, where the transit depths are comparable to instrumental and stellar noise, the SDE is much lower. This is also a challenge in relation to dim stars, such as M-dwarfs, that may have a lot of photometric scatter.

The transit least-squares algorithm (TLS ¹¹ ; Hippke & Heller 2019) was created as an alternative analytical approach to the BLS algorithm, in order to be more sensitive to smaller Earth-sized planetary transits. Unlike BLS, which searches for box-like periodic flux decreases in the light curve, TLS utilizes an analytical transit model, with stellar limb-darkening (Manduca et al. 1977; Mandel & Agol 2002). Hippke & Heller (2019) found that the false-positive rate was suppressed when comparing algorithms for transit-injected light curves, due to the detection of higher signal-to-noise ratio (S/N). A comparison between the two algorithms on a simulated light curve is displayed in Figure 8. In this work, we utilize the Astropy implementation of BLS ¹² alongside TLS.

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While TLS may be the optimal method for detecting smaller planets, it is more computationally expensive than BLS to run. To minimize the computation time of transit searches in this survey, we first perform a BLS search, and look for the strongest peaks in the resulting BLS power spectra. In order to select the grid of trial periods to be searched for each target star, we utilize the TLS "period_grid" function, which estimates optimal frequency sampling as a function of stellar mass and radius, as detailed in Ofir (2014). Based on this period grid, we also use the TLS "duration_grid" function to estimate the trial fractional transit durations (duty cycles) to fit various transit models over. For the period grid, we use an oversampling factor of 9, and for the duration grid, we use a logarithmic step size of 1.05. In order to avoid false-positive detections due to fast stellar rotations of any active M-dwarf stars with residual trends that may have survived our detrending process, we set the minimum period of our period grid to be one day. We also require each transit search have at least three modeled events, which places an upper limit on the maximum period of our period grid of ∼9 days, i.e., ∼1/3 of the duration of a single-sector TESS light curve.

Other studies have found empirical SDE thresholds ranging from 6 to 10 (Siverd et al. 2012; Dressing & Charbonneau 2015; Pope et al. 2016; Aigrain et al. 2016; Livingston et al. 2018; Wells et al. 2018) to be optimal in reducing the overall number of false positives. While higher SDE thresholds typically result in fewer false positives, lower SDE thresholds provide greater completeness. With this in mind, we utilize a minimum TLS SDE threshold of 10 in this work, in order to reduce the number of potential false-positive detections encountered in our search. When running the faster BLS transit searches, for any target stars displaying strong SDEs ≥ 6 in the BLS power spectra, we then run a TLS transit search on the same light curve in order to obtain a better transit fit of the signal causing the initial detection. For TLS transit searches, we use the same period and duration grids used for BLS. For both BLS and TLS transit searches, we record transit parameters corresponding to the strongest peak in their respective power spectra.

One of the many challenges of transit surveys is the weeding-out of false-positive detections by means of a post-detection vetting process. Scenarios that may trigger a false-positive detection include short-term periodic stellar variations, eclipsing binary stars, blended photometry from two stars on one pixel, or periodic movement of the centroid. For our vetting process, we use a one-page validation report (see Appendix A), similar to the validation reports from SPOC, QLP, and DIAmante, containing visual comparisons to other catalogs and archival images (e.g., Gaia, Digitized Sky Survey), as well as several tests to attribute periodic transit-like behavior to planetary transit events. With the metrics produced by these tests, we then visually vet each candidate and refine our TLS searches with finer period and duration grid step sizes. Additionally, we also perform an alternative Lomb–Scargle analysis on each SAP, PLD, and detrended light curve to search for stellar activity that may be triggering transit detections from BLS or TLS. For each TCE, we then vote to determine whether or not it planetary transits is detected, as shown below.

4.2.1. Odd–Even Mismatch Test

To search for potential transit detections that may be attributed to eclipsing binaries, we utilize the odd–even mismatch test, which compares primary and secondary transit events in orbital phase. For an unequal size ratio eclipsing binary, the secondary event will be a smaller fraction of the primary event's transit depth, and if the orbit of the transiting star is circular, it will occur at an orbital phase = 0.5. To perform this test, we cut one-day regions around the transit times modeled by TLS, and append these separately into odd- and even-numbered transits. To produce a metric that compares the odd and even transits, we use

$$\begin{eqnarray}&&\mathrm{Odd}\,\mathrm{Even}\,\mathrm{Mismatch}=\displaystyle \frac{| {\delta }_{\mathrm{odd}}-{\delta }_{\mathrm{even}}| }{{\sigma }_{{\delta }_{\mathrm{odd}}}+{\sigma }_{{\delta }_{\mathrm{even}}}},\end{eqnarray} \tag{ 6 }$$

where δ and σ_δ denote the transit depth and transit depth uncertainty of the odd- and even-numbered transits, as measured by TLS. In addition to the odd–even mismatch statistic, we also visually inspect the phase-folded light curves at 0.5, 1, and 2 times the TLS-detected period.

4.2.2. Centroid Motion Test

To help provide an alternative reference analysis for our false-positive tests, we utilize a modified version of the EDI-Vetter Python package (Zink et al. 2020). The EDI-Vetter tool was used to automatically vet planet candidates in campaign 5 of the Kepler K2 mission. The EDI-Vetter Unplugged ¹³ package is a simplified version of the base package, modified to use the output from TLS. The various false-positive tests performed by the EDI-Vetter Unplugged package are described in more detail in Section 3 of Zink et al. (2020), and are briefly summarized here as follows.

• 1.  
  Flux contamination test: a calculation performed to check for significant contributions of flux from stars that might lie on neighboring pixels.
• 2.  
  Outlier detection test: a check for outliers during the transit time that might give rise to a false-positive detection.
• 3.  
  Individual transit test: a comparative check of the S/Ns of individual transits with an SDE threshold >10 used in our transit search.
• 4.  
  Even–odd mismatch test: a check to verify whether the odd–even mismatch metric output by TLS is greater than 5σ.
• 5.  
  Uniqueness test: this test identifies cases where the phase-folded light curve appears to contain several transit-like dips that may appear similar to the candidate transits.
• 6.  
  Secondary eclipse test: a check for statistically significant secondary transit events at 1/2 times the TLS-detected period.
• 7.  
  Phase coverage test: with the removal of all data relating to momentum-dump periods and bad-quality flags, it is possible for the phase-folded data to contain large gaps in its transit signal. This test is designed to determine whether the transit detection lacks sufficient data to detect a statistically significant transit event.
• 8.  
  Transit duration limit test: a check to determine whether the detected transit duration is too long for the detected transit period.
• 9.  
  False-positive flag: if any of the tests listed above listed are flagged as being true, the candidate is flagged as being a potential false positive, requiring closer inspection.

Our transit survey of 33,054 stars observed across TESS sectors 1–5 revealed 183 TCEs with TLS SDEs ≥ 10. Of those 183 TCEs, 29 are planet candidates fulfilling our automated search and vetting criteria, 24 of which are new detections. Of our 29 planet candidates, five are detected transits of TOIs 269.01, 270.03 (sectors four and five), 393.01, 455.01, and 1201.01. For all of our PCs, we refined the orbital parameters describing these transiting systems with an MCMC analysis, as described in Section 5.2. The best-fit TLS and median posterior MCMC transit orbital parameters (P, T0, R_P , and b) for each of our planet candidates are displayed in Table 1.

Table 1. Best-fit and Median Posterior Solutions for Planet Candidate Transit Models from TLS and MCMC

TIC ID	TESS Sector	TLS Period	TLS Planet Radius	TLS Transit Time	MCMC Period	MCMC Planet Radius	MCMC Transit Time	MCMC Impact Parameter
139456051	1	2.8424 ± 0.0019	3.2028 ± 0.3378	1325.3616	${2.8424}_{-0.0056}^{+0.0056}$	${4.1286}_{-0.4470}^{+0.5690}$	${1325.3617}_{-0.0291}^{+0.0296}$	${0.8256}_{-0.0605}^{+0.1036}$
143996634	1	4.9268 ± 0.0110	3.7148 ± 0.6298	1327.406	${4.927}_{-0.0523}^{+0.0536}$	${4.0301}_{-0.1411}^{+0.1455}$	${1327.4058}_{-0.0426}^{+0.0433}$	${0.7067}_{-0.0298}^{+0.0270}$
234299676	1	6.8442 ± 0.0159	2.9942 ± 0.7537	1329.841	${6.8449}_{-0.1073}^{+0.1084}$	${3.4455}_{-0.1686}^{+0.1775}$	${1329.8405}_{-0.0583}^{+0.0584}$	${0.7169}_{-0.0469}^{+0.0380}$
281461138	1	5.2113 ± 0.0131	3.8348 ± 0.6506	1325.5449	${5.2109}_{-0.0677}^{+0.0688}$	${3.8846}_{-0.1309}^{+0.1340}$	${1325.5453}_{-0.0450}^{+0.0445}$	${0.7433}_{-0.0263}^{+0.0225}$
290048573	1	1.4829 ± 0.0030	2.1006 ± 0.1330	1326.6596	${1.4829}_{-0.0045}^{+0.0044}$	${2.8102}_{-0.1799}^{+0.1931}$	${1326.6598}_{-0.0333}^{+0.0334}$	${0.7044}_{-0.0708}^{+0.0535}$
389662862	1	2.9981 ± 0.0044	3.2191 ± 0.3366	1325.9514	${2.998}_{-0.0131}^{+0.0132}$	${3.342}_{-0.1143}^{+0.1122}$	${1325.9516}_{-0.0352}^{+0.0353}$	${0.6259}_{-0.0411}^{+0.0328}$
9632592	2	4.9924 ± 0.0087	3.8078 ± 0.6487	1355.3707	${4.9921}_{-0.0426}^{+0.0431}$	${4.2722}_{-0.1262}^{+0.1250}$	${1355.3707}_{-0.0602}^{+0.0601}$	${0.5511}_{-0.0592}^{+0.0433}$
50270480	2	1.6514 ± 0.0034	1.7106 ± 0.1129	1354.5419	${1.6514}_{-0.0057}^{+0.0056}$	${1.8744}_{-0.2570}^{+0.2909}$	${1354.5419}_{-0.0455}^{+0.0456}$	${0.6734}_{-0.1947}^{+0.1126}$
80315892	2	6.1589 ± 0.0114	2.3433 ± 0.4739	1356.3507	${6.1593}_{-0.0693}^{+0.0702}$	${2.3539}_{-0.1868}^{+0.1900}$	${1356.3505}_{-0.0523}^{+0.0520}$	${0.6948}_{-0.0914}^{+0.0672}$
101991992	2	2.7375 ± 0.0032	1.6507 ± 0.1726	1355.861	${2.7375}_{-0.0088}^{+0.0088}$	${1.7981}_{-0.1439}^{+0.1319}$	${1355.8611}_{-0.0359}^{+0.0358}$	${0.6287}_{-0.1354}^{+0.0872}$
183231138	2	3.5578 ± 0.0036	2.558 ± 0.3320	1355.1669	${3.5578}_{-0.0128}^{+0.0129}$	${2.582}_{-0.1226}^{+0.1198}$	${1355.1668}_{-0.0362}^{+0.0363}$	${0.6665}_{-0.0645}^{+0.0520}$
184111843	2	3.0855 ± 0.0096	2.8029 ± 0.3234	1354.2508	${3.0854}_{-0.0291}^{+0.0293}$	${2.8583}_{-0.1121}^{+0.1117}$	${1354.2509}_{-0.0444}^{+0.0439}$	${0.3814}_{-0.1502}^{+0.0917}$
220570288	2	4.4427 ± 0.0057	1.8601 ± 0.3149	1356.232	${4.4427}_{-0.0247}^{+0.0252}$	${2.3565}_{-0.3356}^{+0.5918}$	${1356.233}_{-0.0670}^{+0.0656}$	${0.8089}_{-0.1072}^{+0.0902}$
281851658	2	6.1993 ± 0.0153	2.2804 ± 0.5746	1359.8757	${6.2007}_{-0.0944}^{+0.0951}$	${2.2441}_{-0.2588}^{+0.2911}$	${1359.8751}_{-0.0685}^{+0.0689}$	${0.632}_{-0.1798}^{+0.1245}$
408038524	3	1.2465 ± 0.0017	2.4323 ± 0.1706	1386.952	${1.2465}_{-0.0021}^{+0.0022}$	${4.565}_{-0.5071}^{+0.6234}$	${1386.952}_{-0.0235}^{+0.0236}$	${0.8776}_{-0.0613}^{+0.0894}$
10934226	4	4.8034 ± 0.0105	2.1807 ± 0.3692	1410.9917	${4.8034}_{-0.0501}^{+0.0508}$	${2.1443}_{-0.2090}^{+0.2219}$	${1410.9919}_{-0.0517}^{+0.0516}$	${0.5252}_{-0.2569}^{+0.1459}$
23138732	4	4.5577 ± 0.0057	3.3202 ± 0.5654	1410.9822	${4.5579}_{-0.0263}^{+0.0260}$	${3.3721}_{-0.1673}^{+0.1727}$	${1410.982}_{-0.0376}^{+0.0380}$	${0.6925}_{-0.0557}^{+0.0431}$
29960109	4	2.4917 ± 0.0077	2.2634 ± 0.2362	1411.6721	${2.4918}_{-0.0192}^{+0.0192}$	${2.2487}_{-0.1479}^{+0.1444}$	${1411.6719}_{-0.0498}^{+0.0504}$	${0.183}_{-0.1278}^{+0.1761}$
29960110	4	2.4918 ± 0.0075	2.1157 ± 0.2212	1411.673	${2.4917}_{-0.0183}^{+0.0185}$	${2.0664}_{-0.1802}^{+0.1790}$	${1411.6728}_{-0.0479}^{+0.0485}$	${0.2366}_{-0.1630}^{+0.2070}$
98796344	4	5.3591 ± 0.0106	1.3391 ± 0.2709	1412.7064	${5.3596}_{-0.0565}^{+0.0558}$	${1.2645}_{-0.1040}^{+0.1300}$	${1412.7064}_{-0.0495}^{+0.0491}$	${0.3311}_{-0.2228}^{+0.2354}$
161478895	4	4.8672 ± 0.0059	3.7196 ± 0.6281	1412.2682	${4.8674}_{-0.0286}^{+0.0285}$	${3.5509}_{-0.1196}^{+0.1247}$	${1412.268}_{-0.0346}^{+0.0346}$	${0.5627}_{-0.0443}^{+0.0485}$
206468250	4	5.5669 ± -0.2128	3.3042 ± 0.6695	1411.4297	${5.5641}_{-0.0772}^{+0.0782}$	${3.2233}_{-0.1408}^{+0.1481}$	${1411.4356}_{-0.0439}^{+0.0445}$	${0.6588}_{-0.0553}^{+0.0476}$
209457622	4	5.0354 ± 0.0079	1.6253 ± 0.3287	1414.9743	${5.0353}_{-0.0395}^{+0.0400}$	${1.5319}_{-0.2419}^{+0.2482}$	${1414.9748}_{-0.0739}^{+0.0734}$	${0.2612}_{-0.1798}^{+0.2482}$
259377017	4	5.6574 ± 0.0139	2.4869 ± 0.5032	1412.1471	${5.6579}_{-0.0774}^{+0.0780}$	${2.3529}_{-0.1629}^{+0.1838}$	${1412.1475}_{-0.0587}^{+0.0590}$	${0.3344}_{-0.2145}^{+0.1915}$
406478079	4	1.57 ± 0.0014	2.5025 ± 0.1749	1412.295	${1.57}_{-0.0022}^{+0.0021}$	${5.3054}_{-0.7614}^{+0.6264}$	${1412.2949}_{-0.0221}^{+0.0222}$	${1.0075}_{-0.0530}^{+0.0343}$
7688647	5	1.9359 ± 0.0035	2.4759 ± 0.2062	1439.1884	${1.9359}_{-0.0067}^{+0.0066}$	${2.7132}_{-0.0835}^{+0.0818}$	${1439.1887}_{-0.0339}^{+0.0332}$	${0.541}_{-0.0463}^{+0.0381}$
44669739	5	2.4111 ± 0.0048	2.7747 ± 0.2673	1438.0304	${2.411}_{-0.0112}^{+0.0116}$	${2.9053}_{-0.1014}^{+0.1039}$	${1438.0305}_{-0.0372}^{+0.0373}$	${0.6064}_{-0.0469}^{+0.0417}$
192833836	5	6.2378 ± 0.0193	3.487 ± 0.8803	1442.9738	${6.2368}_{-0.1190}^{+0.1219}$	${3.6226}_{-0.1609}^{+0.1534}$	${1442.974}_{-0.0677}^{+0.0669}$	${0.6221}_{-0.0663}^{+0.0505}$
220479565	5	3.6944 ± 0.0106	2.0914 ± 0.3052	1441.0207	${3.6946}_{-0.0387}^{+0.0391}$	${2.8577}_{-0.2144}^{+0.2376}$	${1441.0206}_{-0.0546}^{+0.0549}$	${0.7316}_{-0.0697}^{+0.0562}$
259377017	5	5.6605 ± 0.0157	2.5068 ± 0.5077	1440.4501	${5.6604}_{-0.0880}^{+0.0893}$	${2.2633}_{-0.1336}^{+0.1538}$	${1440.4503}_{-0.0708}^{+0.0705}$	${0.2968}_{-0.1941}^{+0.1794}$

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To provide context for our planet candidates in regard to planet demographics and the radius valley, we display our planet candidates in the planet radius–period space, and compare them with nearby candidates from the TOI and DIAmante catalogs, together with additional confirmed transiting planets observed in sectors 1–5, as shown in Figure 9. Confirmed transiting planets (marked as +s) were queried from the Exoplanet Archive, and the TOI planet candidates (marked as △s) were queried from the TOI catalog. The DIAmante planet candidates (marked as ×s) were queried from the MAST portal (see footnote 3). Planet candidates from this work are marked as ◯s. In addition, we highlight the planet radius–period slopes of the radius valley measured from M19 (for Sun-like stars), VE18 (for FGK stars), and CM20 (for low-mass stars). We also color each confirmed planet and planet candidate based on incident stellar flux (S), defined in Earth units, S_⊕ as

$$\begin{eqnarray}&&\displaystyle \frac{{\rm{S}}}{{{\rm{S}}}_{\oplus }}=\left(\displaystyle \frac{{{\rm{R}}}_{\mathrm{Star}}}{{{\rm{R}}}_{\odot }}\right){\left(\displaystyle \frac{{{\rm{T}}}_{\mathrm{eff}}}{5777{\rm{K}}}\right)}^{4}{\left(\displaystyle \frac{1\mathrm{au}}{{\left(\tfrac{{{\rm{M}}}_{\mathrm{star}}{\rm{G}}{{\rm{P}}}^{2}}{{{\rm{M}}}_{\odot }4{\pi }^{2}}\right)}^{\tfrac{1}{3}}}\right)}^{2}.\end{eqnarray} \tag{ 7 }$$

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In Figure 9, we also display the Kernel density estimate of the planet radius–period space for all planet-hosting M-dwarf stars from the Exoplanet Archive, using the following criteria: T_eff < 4000K, R_Star < 0.5 R_⊙, M_Star < 0.5 M_⊙, and $\mathrm{log}g\gt 3$. In Appendix B, we present a gallery of the phase-folded light curves for our detected planet candidates. Each panel contains the detrended and phase-folded light curve (in black points), and the median transit model obtained via MCMC analysis (red line), as described in Section 5.2. Our planet candidates have orbital periods ranging from 1.25–6.84 days, and planetary radii ranging from 1.26–5.31 R_⊕. In terms of relative incident stellar flux, our candidates range from 3.82–116.18 S_⊕ which is likely to preclude any of our candidates orbiting within the habitable zones of their host stars.

To model the transits of TCEs denoted as planet candidates following the vetting process described in Section 4.2, we employ the use of the exoplanet Python package (Foreman-Mackey et al. 2020), and model various transits in each step of our Markov Chain Monte Carlo (MCMC) simulation. To model transits in general, exoplanet uses an analytical transit model, computed via the STARRY Python package (Luger et al. 2019). Our noise model contains the following free parameters: the orbital period P, time of mid-transit T0, planet-to-star radius ratio R_P /R_S , and impact parameter b. To define our prior distributions for the orbital period, we use a log-normal distribution with a mean value set to the TLS-detected period, and a standard deviation set to the TLS period error. For the prior distributions used for the mid-transit time, we use a normal distribution, with the mean value set to the TLS transit time, and the standard deviation set to the TLS transit duration. For our prior distribution of planet-to-star radius ratio, we use a uniform distribution ranging from 0.01 to R_P /R_S + σ_RP/RS . To calculate the uncertainty for the planet-to-star radius ratio, σ_RP/RS , we query the TIC to obtain the stellar radius and its uncertainty (R_S , σ_RS ), and propagate the errors of the stellar radius, along with the planet radius uncertainty (σ_RP ), as measured by TLS:

$$\begin{eqnarray}&&{\sigma }_{{RP}/{RS}}=\displaystyle \frac{{R}_{{\rm{P}}}}{{R}_{{\rm{S}}}}\sqrt{{\left(\displaystyle \frac{{\sigma }_{\mathrm{RP}}}{{R}_{{\rm{P}}}}\right)}^{2}+{\left(\displaystyle \frac{{\sigma }_{\mathrm{RS}}}{{R}_{{\rm{S}}}}\right)}^{2}}.\end{eqnarray} \tag{ 8 }$$

To define our prior distributions for quadratic limb-darkening coefficients and the impact parameter, we utilize the distributions available within the exoplanet package. To determine the fiducial prior distribution for quadratic limb-darkening coefficients, we use a reparameterization of the two-parameter limb-darkening model to allow for efficient and uninformative sampling, as implemented by Kipping (2013). For the prior distributions of the impact parameter, we utilize a uniform distribution ranging from 0.01 to 1 + R_P/R_S. Our adopted model parameter priors are listed in Table 2. For each transit model produced in the MCMC analysis, we oversample the light curve on a fine time grid, and numerically integrate over the exposure window to avoid smearing of the light curve due to TESS FFI's 30-minute cadence.

Table 2. Example of MCMC Priors Used for Modeling Planet Candidates

Parameter	Units	Prior
Period	Days	${ \mathcal N }$(lnP, σP)
T0	BTJD	${ \mathcal N }$(T0, Dur)
$\tfrac{{{\rm{R}}}_{P}}{{{\rm{R}}}_{S}}$	⋯	${ \mathcal U }$(0.01, RP /RS + σRP )
b	⋯	${ \mathcal U }$(0.01, 1 + RP /RS )

Note: For the input values of our prior distributions, we use the best-fit parameters determined by TLS:pPeriod (P), period error (σ_P ), transit time (T₀), transit duration (Dur), and planet radius (R_P ). We calculate the planet-to-star radius ratio (R_P /R_S , and its propagated error (σ_RP )) via Equation (8).

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An initial maximum a posteriori (MAP) solution was found, and used to initialize the parameters sampled with an MCMC analysis. The MCMC sampling was performed using the No U-Turns step method (Hoffman & Gelman 2014). We ran four chains with 10,000 tuning steps (tuning samples were discarded), and 12,500 draws with a target acceptance of 99%, for a final chain length of 50,000 in each parameter. Once all our runs had been sampled, we then converted our posterior distributions of planet-to-star radius ratio to planet radii in Earth units. An example of the final posterior distributions for our free parameters, together with the median transit model from our MCMC analysis, can be seen in Figures 10 and 11 for TOI 270 c (TIC 259377017).

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5.3.1. Transit Injection Recovery and Sensitivity

To test the detection capability of our pipeline, we used a set of simulated data. In order to select stars that best represented the quality of our data, we looked at our CDPP noise metrics, and divided our light curves into 11 bins of TESS magnitudes, as shown in Figure 12. For each magnitude bin, we then identified light curves with CDPPs closest to the 0.025, 0.5, and 0.975 quantiles as representations of the best, average, and worst quality data, indicated by cyan, red, and orange lines in Figure 12, respectively. For each sector, we selected 30 stars to represent our sample. We randomly sampled uniform distributions of orbital periods ranging from 0.5 to 9 days, and planet radii from 0.5 to 11 Earth radii, and calculated simulated transit models using the BATMAN Python package (Kreidberg 2015).

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Once aperture photometry has been performed on the FFI cutout of a representative star, we inject our simulated transits, starting randomly within the first orbit of TESS in a given sector, and then applying the rest of our pipeline's processes, as described in Section 3. For each of the 30 representative stars, we used 12 randomly selected orbital periods and planet radii, for a total of 21,600 transit injections across TESS sectors 1–5. Our criteria for a successfully recovered transit is based on the orbital period of the transits detected by TLS being within 1% of the injected period. To test the sensitivity of our pipeline, we add an extra criteria to determine whether the injected planet radius falls within the measured error of the TLS-modeled planet radius. We display our 2D injection recovery rate and detection sensitivity maps in Figure 13. Based on our transit injection analysis, we can see that in the 1–9 day regime operated by our transit search, our pipeline is sufficiently sensitive to detect more than 30% of transiting planets with radius >1 R_⊕, and with periods between two and five days. For periods between two and eight days, we maintain a sensitivity of >30%, approximately, for planet radii >4 R_⊕. For injected transits across the full period space explored, and radii >1 R_⊕, the lower limit of our detection sensitivity is ∼14%.

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5.3.2. Survey Completeness and Occurrence Rates for M-dwarf stars

The derivation of exoplanet occurrence rates requires the distribution of planet detections to be corrected for imperfect survey completeness. To account for detectable nontransiting planets, we compute the geometric transit probability for each star (n) at each orbital period, and planet radius grid cell (i,j) in our 2D sensitivity maps as

$$\begin{eqnarray}&&{P}_{\mathrm{transit}}(n,i,j)=\displaystyle \frac{{R}_{\mathrm{star},n}+{R}_{\mathrm{Planet},j}}{{\left(\tfrac{G{M}_{\mathrm{star},n}{P}_{i}^{2}}{4{\pi }^{2}}\right)}^{\tfrac{1}{3}}}.\end{eqnarray} \tag{ 9 }$$

The product of our 2D detection sensitivity maps with geometric transit probability yields a 2D completeness map, which can be seen in Figure 13. To estimate the occurrence rate of planets per star for our M-dwarf host stars, we choose to use the TLS 2D completeness map, which is more complete, due to its higher detection sensitivity. For the period–radius parameter space explored in our survey, and the five TESS sectors searched, there are only a few dozen planet candidates, occupying a small region of the period–radius parameter space. Without a more diverse catalog of planet candidates occupying more of the period–radius parameter space, creating a meaningful 2D occurrence rate map is difficult. For this reason, we instead use an integrated occurrence rate to estimate, on average, the number of planets per star for M-dwarf host stars.

By counting the number of times our planet candidates occur within our period and planet radius grid cells, N_detected(P,R_P ), we can calculate the integrated occurrence rate, O(P,R_P ), as a double integral over the period and planet radius space:

$$\begin{eqnarray}&&O(P,{R}_{P})=\displaystyle \int \displaystyle \int \displaystyle \frac{{N}_{\mathrm{detected}}(P,{R}_{{\rm{P}}})}{{N}_{\mathrm{stars}}\times \mathrm{Completeness}(P,{R}_{{\rm{P}}})}\,{{dPdR}}_{{\rm{P}}}.\end{eqnarray} \tag{ 10 }$$

For the full parameter space of P ∈ [1, 9] days, and R_P ∈ [0.5, 11] R_⊕, we calculate the integrated occurrence rates as 1.61 ± 1.27 planets per star. In the same range of periods, but with R_P ∈ [0.5, 4] R_⊕, we calculate the integrated occurrence rates as 1.45 ± 1.2 planets per star. If we also include all other confirmed planets, TOI, and DIA planet candidates in the range of P ∈ [1, 9] days, and R_P ∈ [0.5, 11] R_⊕, we calculate the integrated occurrence rates as 2.49 ± 1.58 planets per star. In the same range of periods, but with R_P ∈ [0.5, 4] R_⊕, we calculate the integrated occurrence rates as 3.62 ± 1.9 planets per star. Previous studies exploring occurrence rates for M-dwarf host stars observed in the Kepler and K2 missions (Morton & Swift 2014; Dressing & Charbonneau 2015; Gaidos et al. 2016; Hardegree-Ullman et al. 2020; Cloutier & Menou 2020; Hsu et al. 2020) found occurrence rates ranging in value from ∼1 to 2.5 planets per star for periods <200 days, which is in agreement with our results. A more detailed comparison can be found in Section 6.3.

One of the primary goals of the TESS mission is to discover at least 50 planets with radii <4 R_⊕, and with measured masses via radial velocity follow-up observations. Many of our planet candidates have radii below 4 R_⊕ (See Figure 9 and Table 1). In an effort to infer the expected radial velocity semi-amplitude of our planet candidates, we utilize the empirical mass–radius relation from Chen & Kipping (2016) to compute the planetary mass of our planet candidates. We assume circular orbits (e = 0, i = 90°) to calculate the expected radial velocity semi-amplitude as

$$\begin{eqnarray}&&K={\left(\displaystyle \frac{2\pi }{G}\mathrm{Period}\right)}^{1/3}\left(\displaystyle \frac{{M}_{\mathrm{Planet}}\sin i}{{{M}_{\mathrm{Star}}}^{2/3}}\right)\left(\displaystyle \frac{1}{\sqrt{1-{e}^{2}}}\right).\end{eqnarray} \tag{ 11 }$$

The expected radial velocity semi-amplitude values are displayed in Table 3 and Figure 14. Some radial velocity spectrometers, such as ESPRESSO, NEID, and EXPRES, are able to remain stable at the level of a few tens of cm s⁻¹. However, due to photon noise and stellar activity, radial velocities can be limited to maintaining an accuracy of a few m s⁻¹ (Fischer et al. 2016). All of our planet candidates have expected radial velocities ranging from 1.8 to 43.9 m s⁻¹, most of which are above this sensitivity limit.

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To further assist in providing an assessment of suitability for follow-up atmospheric characterization, we also calculate the transmission spectroscopy metric (TSM) and emission spectroscopy metric (ESM), as outlined in Equations (1) and (4) of Kempton et al. (2018). The TSM is proportional to the expected transmission spectroscopy S/N, and, together with the inferred planetary mass data, is calculated as

$$\begin{eqnarray}&&\mathrm{TSM}=C\times \ \displaystyle \frac{{R}_{\mathrm{planet}}^{3}{T}_{\mathrm{eq},\mathrm{planet}}}{{M}_{\mathrm{planet}}{R}_{\mathrm{star}}^{2}}\times {10}^{-{\rm{J}}\mathrm{mag}/5},\end{eqnarray} \tag{ 12 }$$

where C is defined as

$$\begin{eqnarray}C=\left\{\begin{array}{ll}0.19, & \mathrm{if}\ {R}_{\mathrm{planet}}\lt 1.5\,{R}_{\oplus }\\ 1.26, & \mathrm{if}\ 1.5\,{R}_{\oplus }\lt {R}_{\mathrm{planet}}\lt 2.75\,{R}_{\oplus }\\ 1.28, & \mathrm{if}\ 2.75\,{R}_{\oplus }\lt {R}_{\mathrm{planet}}\lt 4\,{R}_{\oplus }\\ 1.15, & \mathrm{if}\ 4\,{R}_{\oplus }\lt {R}_{\mathrm{planet}}\lt 10\,{R}_{\oplus }\end{array}\right..\end{eqnarray} \tag{ 13 }$$

ESM is proportional to the expected S/N of a James Webb Space Telescope secondary eclipse detection at mid-infrared wavelengths, and is calculated as

$$\begin{eqnarray}\begin{array}{rcl}\mathrm{ESM} & = & 4.29\times {10}^{6}\times {\displaystyle \frac{{B}_{7.5({T}_{\mathrm{day}})}}{B}}_{7.5({T}_{\mathrm{eff},\mathrm{star}})}\times {\displaystyle \frac{{R}_{\mathrm{planet}}}{{R}_{\mathrm{star}}}}^{2}\\ & & \times {10}^{-{\rm{K}}\mathrm{mag}/5},\end{array}\end{eqnarray} \tag{ 14 }$$

where B is Planck's function, evaluated for a given temperature, at a representative wavelength of 7.5 μm, and T_day is the dayside temperature in Kelvin, which we calculate to be 1.1 times the equilibrium temperature of the planet (T_eq,planet). Assuming albedo (A = 0), and heat redistribution factor (f = 1), we calculate T_eq,planet as

$$\begin{eqnarray}&&{T}_{\mathrm{eq},\mathrm{planet}}={T}_{\mathrm{eff}}\sqrt{\displaystyle \frac{{R}_{\mathrm{star}}}{a}}{\left(\displaystyle \frac{1-A}{4f}\right)}^{1/4}.\end{eqnarray} \tag{ 15 }$$

Moreover, we also calculate the S/N of our detected transit events as a function of transit depth, photometric precision, number of transits, transit duration, and cadence:

$$\begin{eqnarray}&&\mathrm{SNR}=\displaystyle \frac{{\delta }_{\mathrm{transit}}}{{\sigma }_{\mathrm{CDPP}}}\sqrt{\displaystyle \frac{{N}_{\mathrm{transits}}\,{T}_{\mathrm{duration}}}{\mathrm{cadence}}}.\end{eqnarray} \tag{ 16 }$$

The TSM, ESM, and S/N values are displayed in Table 3 and Figure 14. For planet candidates with S/Ns >7, 23 of our new candidates have TSMs >38, and ESMs >10, making them promising targets for follow-up characterization.

Previous studies by Sullivan et al. (2015), Barclay et al. (2018), and Ballard (2019) have predicted that the TESS mission will discover thousands of planets over the course of its two-year mission. In terms of M-dwarf stars, Sullivan et al. (2015) predict the detection of roughly 1,700 transiting planets from about 200,000 stars observed in a two-minute cadence, with about 419 planets with radii > 2 R_⊕ orbiting M-dwarfs. Barclay et al. (2018) predict that TESS will find 496 planets orbiting M-dwarfs, of which 371 orbit stars observed in a two-minute cadence. Ballard (2019) performed yield estimations focused on M-dwarfs with effective temperatures ranging from 3200–4000 K, and postulated that TESS would find approximately 1274 planets, orbiting 1026 M-dwarf stars.

In this study, we found 33,054 nearby M-dwarf stars meeting our selection criteria, as outlined in Section 2. Applying selection cuts of 2300 K < T_eff < 4000 K, R_Star < 0.5 R_⊙, M_Star < 0.5 M_⊙, and $\mathrm{log}g\gt 3$ to the TESS Candidate Target List ¹⁴ (CTL Version 8), we find 138,962 M-dwarf stars within 100 pc, and 1,562,038 M-dwarf stars in total. Using the predicted number of M-dwarf TESS planets from Ballard (2019), the expected planet yield from sectors 1–5 is 1,274 planets × 33,054 stars/1,562,038 stars ∼27 ± 5 planets, where the uncertainty is $\sqrt{N}$. Our yield of 29 planet candidates in TESS sectors 1–5 matches very well with this predicted yield estimate. Propagating our rates of detection to the M-dwarf stars in the CTL, we expect to detect (29 planets/33,054 stars) × 138,962 stars ∼122 ± 11 planets of nearby stars from FFI data over the two-year TESS mission. If we extend our search to more distant stars (>100 pc), and assume similar rates of detection, we can expect to detect (29 planets/33,054 stars) × 1,562,038 stars ∼1370 ± 37 planets total from the FFI data for the two-year TESS mission.

Various studies over the past few years have focused on occurrence rates for M-dwarfs, using confirmed planets and planet candidates from the NASA Kepler and K2 missions. Morton & Swift (2014) found an occurrence rate of Kepler M-dwarf planet hosts to be 2 ± 0.45 planets per star for P < 150 days, and R_P ∈ [0.5, 4] R_⊕. Gaidos et al. (2016) found an occurrence rate of 2.2 ± 0.3 planets per star for P ∈ [0.5, 180] days, and R_P ∈ [1, 4] R_⊕. Dressing & Charbonneau (2015) found Kepler M-dwarf planet hosts to have an occurrence rate of 2.5 ± 0.2 planets per star for P < 200 days, and R_P ∈ [1, 4] R_⊕; for Earth-sized planets (R_P ∈ [1, 1.5] R_⊕) and super-Earths (R_P ∈ [1.5, 2] R_⊕) in the ranges P < 50 days, the occurrence rate is 0.56 ± 0.06, and ${0.46}_{-0.05}^{+0.07}$ planets per star, respectively. Hardegree-Ullman et al. (2020) explored occurrence rates of Kepler M-dwarfs by spectral type and computed an occurrence rate of ${1.19}_{-0.49}^{+0.70}$ planets per star in the parameter space of P ∈ [0.5, 10] days and R_P ∈ [0.5, 2.5] R_⊕. Cloutier & Menou (2020) explored the parameter space in the ranges of P ∈ [0.5, 100] days and R_P ∈ [0.5, 4] R_⊕ and found occurrence rates for the Kepler and K2 missions in the ranges of 2.485 ± 0.32 and 2.26 ± 0.38 planets per star, respectively. Hsu et al. (2020) found occurrence rates of Kepler M-dwarf planet hosts to be 4.2 ± 0.6 or ${8.2}_{-1.1}^{+1.2}$, depending on their choice of priors in sampling their distribution, for the ranges P ∈ [0.5, 256] days, and R_P ∈ [0.5, 4] R_⊕. Hsu et al. (2020) also found that for small planets at short periods, in the range P ∈ [2, 32] days and R_P ∈ [1, 2.5] R_⊕, their occurrence rate is ${0.9}_{-0.1}^{+0.2}$ or ${1.6}_{-0.2}^{+0.3}$ (depending on the prior chosen).

As mentioned in Section 5.3.2, our integrated occurrence rate for the ranges P ∈ [1, 9] days and R_P ∈ [0.5, 11] R_⊕ is 2.49 ± 1.58 planets per star, when including known transiting planets, TOI, and DIAmante planet candidates. This occurrence rate is within the uncertainty of the estimations of occurrence rates from previous studies in similar period–radius parameter space. Of our 29 planet candidates, 24 of them have planet radii <4 R_⊕, with measurable planet masses (see Table 3), and can thus contribute to fulfilling the level one science requirement of the TESS mission. ¹⁵

Although there are more M-dwarfs observed by TESS with 30-minute cadences than with two-minute cadences, the lack of time resolution limits the types of transit that can be detected. Using Equations (5) and 16, for a planet with a radius of 1 R_⊕ transiting a small star with M = 0.1 M_⊙, R = 0.1 R_⊙ once per day, the transit duration is about 17 minutes with an S/N ∼127 for a two-minute cadence and an S/N ∼33 for a 30-minute cadence. For a larger star (M = 0.5 M_⊙, R = 0.5 R_⊙) and the same transiting planet, the transit duration is about 47 minutes with an S/N of about 8 for a two-minute cadence, and an S/N of about 2 for a 30-minute cadence.

With sufficient coverage of observed transit events, it is possible to detect these short-duration, small-transit events in FFI data, but with the various instrumental systematics and astrophysical noise presented by each of these faint targets, these 1–2 data points per transit may be removed during data processing, owing to common data-reduction practices such as smoothing or outlier removal. With our single-sector approach to searching for transit events, the types of transits we can detect with the 30-minute cadence data is somewhat limited, as shown in Figure 13, where we maintain a detection sensitivity of roughly 30% for radii larger than 1 R_⊕. In years three and four of the TESS extended mission, the FFIs will be observed with a 10-minute cadence, which will certainly increase the detection of these types of transit events, as they are likely to have higher S/Ns due to the improved time resolution.

Another challenge encountered in this survey lies in ensuring that our automatically selected apertures remained on-target throughout the observations in each sector of data. As mentioned in Section 3.2, we utilized a bivariate quadratic function to approximate the core of a point-spread function for each FFI cutout, where we chose pixels that were brighter than 7.5 standard deviations above the median brightness of the time series. For isolated targets, this works fairly well, but for crowded fields, particularly for dim targets (TESS magnitude >15), our centroiding procedure often fails, and the selected aperture centers on other bright stars in the 11 × 11 pixel cutouts.

Early in the testing phase of our pipeline's application, we noticed that each sector of TESS data has varying degrees of instrumental effects due to telescope jitter or glare in the TESS field of view from Earth and/or the Moon near the beginning or ends of data collection in each orbit of the satellite. For this reason, we opted to focus on performing transit searches on individual sectors, thereby restricting the upper limit in terms of the longest periods we could search per sector, to about nine days. This choice was cautiously selected early in the development of our pipeline, so as to avoid increasing the amount of false positives encountered via a multisector approach that could possibly be attributed to residual instrumental effects in our processed light curves.

We intend to continue our survey to cover TESS sectors 6–13 in the southern hemisphere, and 14–26 in the northern sectors, in order to gain a longer baseline of coverage for our M-dwarf target lists, and to extend the range of periods to search for transits using a multisector approach. With a longer baseline of observations, we can also consider searching for multiple planets per target with a higher degree of confidence than in our single-sector approach, by analyzing other peaks in the TLS power spectrum with strong SDEs (see Appendix B, TOI 270). We also intend to vet those threshold crossing events with lower SDEs in the range of 6–10, in order to potentially find transit detections that may have been missed due to the use of a higher threshold.

Although we were cautious in our promotion of planet candidates from TCEs, there is still an element of human judgement, and the potential for bias. As a quick check, and an alternative analysis to our vetting report, we used the automated EDI-Vetter Unplugged tool, which uses our TLS outputs to conduct false-positive tests, as described in Section 4.2. Additional community tools, such as TESS-ExoClass (TEC ¹⁶ ), or Discovery and Vetting of Exoplanets (DAVE; Kostov et al. 2019b) are vetting tools built upon the Kepler vetting algorithm RoboVetter (Coughlin et al. 2016), and were developed for use in K2 (Hedges et al. 2019) and TESS data (Crossfield et al. 2019, Kostov et al. 2019a). For our future endeavors, to minimize opportunities for human selection bias, and to reduce the overall human vetting time, we may explore automating our vetting process, or the use of tools such as DAVE or TEC for the first round of vetting in our overall vetting process.

In future work, we may also revisit our centroiding process, or employ a multi-aperture approach similar to that used in other FFI pipelines (Feinstein et al. 2019; Nardiello et al. 2019; Bouma et al. 2019; Montalto et al. 2020). We currently keep track of the change in pixel directions during any detected transit-like events, and exclude threshold crossing events with change in pixel direction of more than five standard deviations, to help reduce the amount of false-positive detections, but an alternative approach to centroiding may prove more consistent for targets fainter than TESS magnitude >15.

All of these candidates were observed by TESS roughly two years ago, and the southern hemisphere is already being observed once again by TESS in year three of its extended mission. In the extended TESS mission, FFIs will have an improved time resolution of 10-minute cadences, whereas for years one and two, the time resolution was 30 minutes. After working through the data from years one and two, we also intend to extract light curves from the year three data, in order to revisit our planet candidates based on an improved time resolution. Armed with a longer baseline, by virtue of analyzing the FFI data from both the TESS mission and its extended mission, we also intend to revisit the detection recoverability, sensitivity, and survey completeness of our NEMESIS pipeline for longer orbital periods. With additional future planet candidate detections, we can also revisit our estimation of planet occurrence rates for M-dwarf host stars with improved resolution in the orbital period–planet radius domain.