Quantifying the Effect of Short-timescale Stellar Activity Upon Transit Detection in M Dwarfs

Dana Clarice Yaptangco; Sarah Ballard; Jason Dittmann; Mariangel Albornoz

doi:10.3847/1538-3881/ada898

1. Introduction

While the solar system has historically been the default blueprint for a planetary system in our galaxy, it is atypical in the Milky Way. M dwarfs, in reality, comprise 70%–80% of the galaxy's stars and host most of its rocky planets (T. J. Henry et al. 2004; C. D. Dressing & D. Charbonneau 2015; G. D. Mulders et al. 2015; K. K. Hardegree-Ullman et al. 2019; M. Y. He et al. 2020; K. Ment & D. Charbonneau 2023). M dwarf stars also differ from Sun-like stars in that they are "active" for billions of years or more (A. A. West et al. 2008; E. R. Newton et al. 2016). Decades of research have elucidated the physical processes linked to stellar "activity," a term used to describe a range of phenomena associated with the strength of the star's magnetic field: X-ray emission, Hα in emission, rotation periods generally inferred from photometric monitoring, and starspot and faculae coverage (M. S. Giampapa & J. Liebert 1986; D. R. Soderblom et al. 1991; I. N. Reid et al. 1995; S. L. Hawley et al. 1996; X. Delfosse et al. 1998; S. L. Hawley et al. 1999; J. R. Barnes et al. 2004; D. O'Neal et al. 2004; J. Irwin et al. 2011; E. R. Newton et al. 2017). Below the mass limit at which M dwarfs are fully convective, there is evidence for two divergent populations in the M spectral class (see e.g., J. Irwin et al. 2011; E. R. Newton et al. 2017; R. Kiman et al. 2021; M. Popinchalk et al. 2021; E. Gaidos et al. 2023; Y. Shan et al. 2024): "active" faster rotators exhibiting Hα in emission, and slower/"inactive" rotators exhibiting Hα in absorption. This gap is likely attributable to a period of short but rapid spin down of mid-to-late M dwarfs. However, measuring a slow/"inactive" rotator still requires stellar starspots on its surface to rotate in and out of view, so even an inactive rotator is not completely inactive.

Stellar activity contributes noise to high-precision photometric observations in ways that are varied and complex. Some, like stellar rotation, spot evolution, and large flares, can be modeled and removed (see e.g., S. L. Hawley et al. 2014; S. Aigrain et al. 2015; J. R. A. Davenport 2016), although stellar rotation periods at the same period as potential orbiting planets can complicate detection. In other ways, the identification of the effects of stellar activity upon lightcurves is ongoing: photometric "flicker" on ~8 hr timescales was only detected in 2013, for example (F. A. Bastien et al. 2013, 2016). The effects of pulsations, granulation, long-term evolution of active regions, and magnetic cycles are also present, but can be difficult to resolve and model. Several tools including SOAP (I. Boisse et al. 2012; X. Dumusque et al. 2014) and StarSim (E. Herrero et al. 2016) exist for ameliorating these effects, often by modeling photometry and radial velocity in tandem. Because timescales associated with stellar activity range from minutes to years (G. Basri et al. 2013; A. Suárez Mascareño et al. 2016; A. A. Medina et al. 2022; L. Mignon et al. 2023), resolving the signatures of activity in a given lightcurve depends upon its precision, cadence, duty cycle, and duration.

Because of their abundance in nature, it is of interest to investigate the sensitivity of transit surveys to exoplanets around M dwarf stars. Across the M spectral class, the "active" duration of a star's life varies from 1 Gyr in the case of M0 dwarfs to 8 Gyr or more for spectral type M8 (A. A. West et al. 2008, 2015); by spectral type M6, at least half of field stars are active (though this is also dependent upon galactic radius and height; J. S. Pineda et al. 2013). The relevance to transit searches is strong: active stars present photometric variability over a range of timescales, but crucially, some are extremely close to the transit durations of transiting planets. A Gaussian process regression of photometry of Proxima Centauri by D. M. Kipping et al. (2017) showed a characteristic correlation length of 130 minutes. A. A. Medina et al. (2022) identified that the characteristic variability of Hα emission of 20–25 minutes corresponded to variability on that timescale in photometry as well. A study of the hot Jupiter HD 189733b by P. W. Cauley et al. (2017) found that the depth of its transit in the Hα line varied between transits over the host star's activity cycle. Additionally, this variability did not correlate significantly with traditional activity indicators like the Ca H&K lines, suggesting that decorrelating planet signals from stellar activity signals will require more complicated approaches. If Hα variability is tied to photometric variability in active stars, we can expect correlated noise timescales of 15 minutes–1 hr for late-type dwarfs (E. A. Kruse et al. 2010; K. J. Bell et al. 2012; A. G. Soto et al. 2023). Indeed, J. R. A. Davenport (2016) estimate that Proxima Centauri exhibits a 0.5% brightness increase once every ~20 minutes (on average). This is in comparison with an average transit duration of 2.5 hr among the M dwarf exoplanets identified by the Kepler Mission (J. J. Swift et al. 2015).

We describe here an empirical analysis to characterize the effect of shorter-timescale stellar activity in late-type M dwarfs upon photometric transit detection. While each star's activity signature will be unique, we aim to quantify the extent to which sensitivity to transits degrades on average. We design an experiment by which we identify a sample of M dwarfs of common temperature, radius, and apparent magnitude, all observed by NASA's Transiting Exoplanet Survey Satellite (TESS; G. R. Ricker et al. 2014). We then split the sample into "active" and "inactive" M dwarfs, using the the presence of Hα in emission from A. A. Medina et al. (2020), E. R. Newton et al. (2017), M. Coréts Contreras (2016), and F. J. Alonso-Floriano et al. (2015) as our criterion. We remove the more readily identifiable signatures of activity: stellar rotation and flares. We then conduct an injection-and-recovery analysis of transit signals for each lightcurve, varying planetary orbital period and radius. Finally, we investigate the extent to which the ability to recover transit signals is affected, comparing the resulting sensitivity maps from the active and inactive samples.

This manuscript is organized as follows. In Section 2, we describe our sample selection. We detail our methodology for injecting transit signals and then detrending the lightcurves, which we apply to the active and inactive lightcurves in a uniform way. We then attempt to blindly recover the injected signals using publicly available transit search packages. In Section 3, we examine the difference in transit sensitivity between the two samples. We quantify, based on averaged sensitivity maps between a fiducial "active" and "inactive" star, the effect to which transit signal-to-noise ratio (SNR) is degraded in the photometry of active stars, even when obvious signs of activity are removed. In Section 4, we summarize our findings and conclude.

2. Methods

To determine the detectability of transiting planets orbiting active versus inactive M dwarfs, we first select a sample of stars with extant transit photometry from the TESS (G. R. Ricker et al. 2014). We describe this procedure in Section 2.1. With the sample selected, we then detrend the lightcurves to remove signatures of stellar rotation and flaring. We detail the detrending process, which we apply in the same way to both active and inactive stars, in Section 2.2. In order to explore the parameter space of interest, we conduct injection-and-recovery tests for planetary transits across a range of orbital period and radius. We lay out our framework for conducting this injection-and-recovery analysis in Section 2.3.

2.1. Stellar Sample

We draw the stellar sample from among nearby M dwarfs observed in optical spectroscopy by A. A. Medina et al. (2020), E. R. Newton et al. (2017), M. Coréts Contreras (2016), and F. J. Alonso-Floriano et al. (2015). These works identify the presence of Hα in emission or absorption for the sample, in addition to noting the near-universality of Hα emission among rapidly rotating stars. There are many signifiers of stellar activity, and here we adopt Hα in emission as our diagnostic criterion. From these stars, we identify those with an associated TESS Input Catalog (P. S. Muirhead et al. 2017; K. G. Stassun et al. 2019) ID within our dataset. We then remove binaries by filtering out stars with companions within two magnitudes of the target star (or brighter) in a 1'' radius. We also ensure that none of the stars in our sample host a bona fide TESS Object of Interest (N. M. Guerrero et al. 2021).

To ensure as homogeneous a sample as possible in terms of predicted transit SNR, we construct our sample to fall within a narrow range in stellar radius and apparent magnitude. We aim to characterize the effect of low-level, frequently occurring flares on transit detection, as one of the likely contributing factors to decreased transit sensitivity for active stars. This necessitates a tradeoff in our sample criteria between flare amplitude, frequency, and predicted transit SNR. We aimed to have our marginally detectable injected transits induce the approximate same photometric offset as flares occurring with frequency similar to the (~2 hr) transit duration timescale, to ensure that confusion between flares and transits will occur as part of our survey design. J. R. A. Davenport (2016) found that flares of 5 mmag amplitude occur on average 63 times per day on the active M dwarf Proxima Centauri (roughly 1 every 20 minutes), with more energetic flares occurring less often in relationship characterized by a power law. In the TESS magnitude range of 10–11, flares larger than this relative amplitude of 5 × 10⁻³ are detectable nearly 100% of the time (M. N. Günther et al. 2020). We concluded that flares occurring with a frequency near a typical transit duration (~2 hr), necessarily >5 mmag, would therefore be detectable and removable in our TESS lightcurves if we select stars in this approximate magnitude range. Limiting ourselves to brighter targets, however, skews the sample toward earlier spectral types, for which fewer stars are active. In order to maintain a nominal sample size of 16 active and 14 inactive stars with a common range of stellar radius and magnitude, we identified the fiducial radius of 0.2R_⊙ as optimal for our sample: at this radius, there are (a) sufficient stars (both active and inactive) in the A. A. Medina et al. (2020), E. R. Newton et al. (2017), M. Coréts Contreras (2016), and F. J. Alonso-Floriano et al. (2015); samples that (b) meet the magnitude criterion for which (c) there exists at least one sector of TESS 2 minutes cadence photometry. In Table 1 we list the 30 targets we decided upon: all of the stellar radii fall within the range of 0.18–0.23 R_⊙ (0.05R_⊙ is typical uncertainty on stellar radius, per T. A. Berger et al. 2023). These stars also all have similar brightness, with TESS magnitudes between 10 and 11.5. Though some stars in our sample were observed during more than one TESS sector, we select only one sector for each star. While there exist gaps within the lightcurves dependent upon the TESS sector in which the star was observed, we ensure that the duty cycle varies by no more than 10% across the sample. In Figure 1 we show the TESS magnitude and stellar radius of our resulting sample of 30 stars.

Table 1. TESS Input Catalog IDs and Sectors of the 30 Stars in Our Sample (14 Inactive, 16 Active), with Corresponding Activity Flags Drawn from A. A. Medina et al. (2020), E. R. Newton et al. (2017), M. Coréts Contreras (2016), and F. J. Alonso-Floriano et al. (2015)

TIC ID	TESS Sector	Activity	Source Paper
347695698	10	1	E. R. Newton et al. (2017)
238865036	59	1	E. R. Newton et al. (2017)
29168887	21	1	E. R. Newton et al. (2017)
233068870	14	1	E. R. Newton et al. (2017)
35760711	4	1	E. R. Newton et al. (2017)
137025855	15	1	E. R. Newton et al. (2017)
84649454	19	1	M. Coréts Contreras (2016)
255932726	24	1	M. Coréts Contreras (2016)
156491690	15	1	F. J. Alonso-Floriano et al. (2015)
155113423	56	1	F. J. Alonso-Floriano et al. (2015)
234526939	1	1	M. Coréts Contreras (2016)
201878287	2	1	A. A. Medina et al. (2020)
7723060	4	1	A. A. Medina et al. (2020)
170636897	4	1	A. A. Medina et al. (2020)
123480394	7	1	A. A. Medina et al. (2020)
411248800	23	1	E. R. Newton et al. (2017)
11893637	48	0	E. R. Newton et al. (2017)
274626553	24	0	E. R. Newton et al. (2017)
340807280	55	0	E. R. Newton et al. (2017)
115131636	19	0	E. R. Newton et al. (2017)
446098056	19	0	E. R. Newton et al. (2017)
224269420	2	0	E. R. Newton et al. (2017)
345874162	25	0	E. R. Newton et al. (2017)
286582903	26	0	E. R. Newton et al. (2017)
188640773	24	0	E. R. Newton et al. (2017)
331681541	13	0	A. A. Medina et al. (2020)
328465904	4	0	A. A. Medina et al. (2020)
371493573	21	0	M. Coréts Contreras (2016)
389687183	1	0	A. A. Medina et al. (2020)
16530308	20	0	M. Coréts Contreras (2016)

Note. Here 1 is "active," signifying Hα in emission, and 0 is "inactive."

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Figure 1. Refer to the following caption and surrounding text. — **Figure 1.** Our stellar sample, selected from A. A. Medina et al. (2020), E. R. Newton et al. (2017), M. Coréts Contreras (2016), and F. J. Alonso-Floriano et al. (2015) for extant TESS photometry of stars of similar size and magnitude. Our sample comprises of 16 active and 14 inactive stars between 0.18 R_⊙ and 0.23 R_⊙ with apparent TESS magnitudes between 10.0 and 11.5. We show histograms of these distributions above and to the side of the plot. This sample of stars are similar enough in physical properties to serve as a useful benchmark sample for this study.
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2.2. Detrending of TESS Lightcurves

For each of our 30 stars, we detrend the TESS lightcurves to remove readily identifiable signatures of stellar activity. We employ a Gaussian process model for stellar variability, using the exoplanet (D. Foreman-Mackey et al. 2021) Python package. We utilize the Lomb–Scargle estimator with a minimum period of 0.1 days, a maximum period of 30.0 days, and 50 samples per peak. We modeled this detrending (in the functional form for the Gaussian process kernel) on that of K. Ment & D. Charbonneau (2023), who detrended 363 TESS lightcurves of nearly M dwarfs with a similar treatment.

Upon generating the rotation model, we normalize the original lightcurve (with transits injected; see Section 2.3) by dividing it by the model. We identify and remove flares by identifying individual flux measurements more than 5σ above the median, before clipping all points within a 3 hr window of these identified points. We apply this treatment uniformly to both active and inactive stars, ensuring consistency in detrending across the sample. In Figure 2, we show the nondetrended SPOC photometry from one sector for each of our 30 sample stars, as well as the resulting detrended photometry.

Figure 2. Refer to the following caption and surrounding text. — **Figure 2.** TESS lightcurves of all thirty stars in our sample. Panel (a) to left shows the active sample and panel (b) to the right shows the inactive sample. The left side of each panel shows the original nondetrended SPOC (J. M. Jenkins et al. 2016) photometry in black. We have overplotted the Gaussian process stellar rotation model in yellow, and identified flare events in red. The right side of each panel displays the treated lightcurve, normalized by the rotation model and with flares (and points within 3 hr of flare data points) excised.
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2.3. Injection and Recovery

To account for the possibility of transit suppression from the process of detrending, we inject transits into the lightcurve prior to the detrending stage. We employ the TESS-SPOC lightcurves (J. M. Jenkins et al. 2016), and draw the stellar parameters of mass and radius from E. R. Newton et al. (2017) and K. G. Stassun et al. (2019), with a standard deviation equal to that reported in these works.

In order to construct a sample of transiting planet parameters, we draw values in both period and radius using the same log uniform distribution as S. Ballard (2019). This choice will also enable the ultimate ease of comparison between our empirical maps we generate here and the average theoretical M dwarf sensitivity maps in that paper. We employ an inset of period parameter space from 0.8 to 5.7 days, and radius from 0.28 to 1.44 R_⊕. We selected the center of this range in order to sample planetary signals with an approximate SNR of 7, where we expected transit sensitivity to meaningfully vary (see, e.g., J. L. Christiansen et al. 2016). For each lightcurve, we inject a transiting planet with each possible combination of period and radius ten times, each time shifting the transit phase, t₀, of the planet by 3 hr per iteration in order to be sure to fully sample the effect of stellar variability on each individual star. Additionally, we assume the orbital eccentricity of all injected planets to be zero. We generate the model transit lightcurves using the batman (L. Kreidberg 2015) Python package (normalized to unity), and inject this lightcurve into the simulated TESS lightcurve by multiplication, completing the injection step.

Following the injection, we detrend the lightcurve, as detailed previously in Section 2.2. Once the rotation model is divided out and flares are removed, we utilize the TransitLeastSquares (M. Hippke & R. Heller 2019) Python package, generating a periodogram and estimating the most likely period for the transiting exoplanet. We define a transit as "detected" if the False Alarm Probability (FAP) value is less than 0.001, and the estimated period is within 1% of the true injected period. In this sense, we do not consider aliases of the injected period to constitute "detection."

3. Analysis

We apply the methodology in Section 2 to our sample of 16 active and 14 inactive M dwarf stars. In Section 3.1, we compare the sensitivity maps generated using the injection-and-recovery procedure for active and inactive stars. In Section 3.2, we discuss the relevance of our findings to the detectability of transiting exoplanets orbiting active stars.

3.1. Sensitivity in Active versus Inactive Stars

In order to quantify the degradation to the detection probability incurred by the active sample, we employ the fact that contours in the SNR trace the detection probability. F. Fressin et al. (2013) first quantified the SNR corresponding specifically to the 50% detection contour for the Kepler mission, and it has proven to be a useful metric for understanding the mission's completeness (see also J. L. Christiansen et al. 2015). We aim here to quantify the extent to which the SNR requirement for a 50% detection probability changes between active and inactive stars.

For ease of reference, we designate a quantity α = SNR_50%. With an analytically evaluated SNR map, we can translate directly to detection sensitivity. The SNR for a transit signal is analytically calculable from the formula

$\begin{eqnarray}&&\alpha ={{\rm{SNR}}}_{50 \% }=\frac{\rm{depth}\,\cdot\, \sqrt{{N}_{\rm{transits}}}}{\,\rm{photometric\, uncertainty}}\propto {\left(\frac{{R}_{p}}{{R}_{\star }}\right)}^{2}\frac{\sqrt{P}}{\sigma },\end{eqnarray} \tag{ 1 }$

where σ corresponds to the photometric uncertainty on the timescale of the transit. To generate synthetic detection sensitivity maps, we calculate a fiducial SNR value for each {radius, period} pixel, assuming a stellar radius of 0.2R_⊙ and a photometric uncertainty σ drawn from the middle of our sample: the 50th percentile 1 hr uncertainty corresponding to a star with TESS magnitude of 11 is ~400 ppm (we comment in more detail below about the effect of our sample spanning a small but nontrivial range of magnitude and stellar radius). Then, SNR values will scale across our radius and period according to Equation (1). We then identify a given value for α, the SNR corresponding to a detection probability of 50%. We convert the analytic SNR map to a model detection probability map by normalizing the SNR map so that the contour corresponding to that α corresponds to a value of 0.5. We then set all newly normalized pixels with a value >1.0 equal to 1.0. This map can then be directly compared to the empirical measured maps, using the intersample scatter in each pixel to quantify our uncertainty in the probability of detection in that pixel, as shown in Figure 3. In practice, we evaluate this SNR model on an grid oversampled in radius and period by a factor of 10, then bin down to the resolution of the detection probability map.

Figure 3. Refer to the following caption and surrounding text. — **Figure 3.** Detectability sensitivity map of exoplanets around active and inactive stars. These maps represent the average detectability, where "detection" constitutes a FAP < 0.001, and a recovery of the true period within 1%. Detectability ranges from 0% to 100%. Overplotted is the confidence interval for the 50% contour. Top: transiting planet detectability for our active star population. We find that planet recovery decreases significantly below Earth-radii planets at periods longer than 1.6 days. Middle: same as the top panel but for our inactive stellar sample. We find broadly increased recovery of injected planet signals, reaching down to sub-Earth radii and periods as large as 6.0 days. We find that imperfect correction of photometric modulation can significantly degrade the ability to detect transiting planet signals. Bottom: Gaussian distributions for the SNR associated with the 50% detection contour. The 50% detection contour corresponds to an SNR of 7 for inactive stars, and an effective SNR of 14 is required for active stars.
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For each test value of α, we then employ a χ² likelihood to quantify the goodness-of-fit for each model detection probability map (summing over all pixels), where the uncertainty in the denominator of the χ² is set by the scatter in detection probability corresponding to each pixel across the sample. From the resulting minimum in the χ² distribution, we then identify the likeliest effective SNR corresponding to 50% detection. We assume the uncertainty is normally distributed, so that a Δχ² of 1 corresponds to the 1σ confidence interval. In this way, we establish that, for our inactive sample, an SNR of 7 ± 1 corresponds to the 50% detection threshold, while an SNR of 14 ± 1.5 corresponds to the 50% detection threshold for the active sample. Given a common transit depth and number of transits between a typical active and inactive lightcurve, the difference in SNR is attributable to the higher effective photometric noise in the active sample.

While α, the SNR corresponding to 50% detection probability, is useful unto itself for establishing underlying planet occurrence, we are concerned here with the extent to which noise is effectively inflated among active stars. By taking a ratio of α_active/α_inactive, according to Equation (1), we are obtaining a value β = σ_active/σ_inactive (all other terms contributing to α cancel, given that we are employing stars with a common radius and magnitude, and a common set of planetary radii and orbital periods). We can thus employ propagation of error to quantify β, the ratio of the inactive photometric uncertainty to the active photometric uncertainty, by computing α_active/α_inactive: using α_active = 14 ± 2 and α_inactive = 7 ± 1, we measure β to be 2.0 ± 0.5.

Considering β to be the factor by which the photometric uncertainty is effectively inflated by correlated noise, on transit duration timescales, F. Pont et al. (2006) quantified it to be

$\begin{eqnarray}&&\beta =\sqrt{1+{\left(\frac{{\sigma }_{{\rm{r}}}}{{\sigma }_{{\rm{w}}}}\right)}^{2}},\end{eqnarray} \tag{ 2 }$

where σ_r corresponds to the "red" (off-diagonal) contribution to the noise budget and σ_w corresponds to the "white" (diagonal) contribution. For noise with no red component, β = 1. Thus, given our likeliest β = 2, derived empirically, we estimate that among active stars in our sample, correlated noise and shot noise contribute approximately equally to the noise budget on transit timescales.

3.2. Relevance for M Dwarf Planet Occurrence

In Figure 4, we show the result of random injection and recovery of planets into the detectability metric from the sensitivity maps from Figure 3, revealing the region where there is a discrepancy between the detectability rates between active and inactive stars. This region is significant because there are known exoplanets in this region, such as, for example, the TRAPPIST-1 planets (M. Gillon et al. 2016). This means that despite this being a crucial region to constrain detectability due to planetary abundance, our ability to detect exoplanets around active stars in this region is depreciated. Calculation of occurrence rates—such as in C. D. Dressing et al. (2017) or meaningfully constraining models of planet formation (which require an accurate census of planetary systems)—therefore depend on accurately correcting for this population of planets that will be "missed" in current surveys. We generate this plot by selecting random points in the orbital period/radius parameter surveyed by the sensitivity maps, and then selecting a random number, and then determining if it falls within the probability that a planet would have been detected around that type of star. If it is within the probability, it was marked as "detected" around that type of star. Our recovery fractions, as expected, deviate most strongly between "active" and "inactive" in the parameter space with the most difference between the maps.

Figure 4. Refer to the following caption and surrounding text. — **Figure 4.** Planets are randomly injected at different points on the sensitivity maps from Figure 3 then assigned a value of "detected" or "not detected" based on the corresponding probabilities of detection at that point. Red planets are not detected around active nor inactive stars. Yellow planets are only detected around inactive stars. Green planets are only detected around active stars. Finally, blue planets are detected around both. The orbital periods and radii of TRAPPIST-1b, c, and d (M. Gillon et al. 2016) are overplotted as star symbols. We find that some TRAPPIST-1 planets are not detectable under a TESS-like survey and therefore existing TESS objects of interest may in fact be a TRAPPIST-1 like system that remains unexplored or not fully understood. As TRAPPIST-1 is itself an active star, this further degrades the probability of detecting a similar system blindly in TESS data.
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As expected, if a planet is large with a small orbital period, it is detected around both active and inactive stars. On the other extreme, small planets with large orbital periods are not detected around active nor inactive stars. The region of interest is where planets were detected by only an active or (more likely) an inactive star. Most often, planets are only detected around the inactive star in this region. As shown in Figure 4, the three inner-most planets orbiting TRAPPIST-1 (M. Gillon et al. 2017) fall within this region. We emphasize here that TRAPPIST-1 itself is an "active" host star which also is at a dimmer magnitude than the active and inactive stars surveyed here: we include them to contextualize the difficulty of identifying planets of this size and orbital period in TESS lightcurves even of bright (10th and 11th magnitude) stars.

4. Conclusion

We have investigated the detectability of transiting exoplanets around M dwarfs, with a focus upon the effects of stellar activity. By identifying a sample of common stellar radius and apparent magnitude, that differs only in "activity" status, we can directly assess the extent to which stellar activity (which occurs over a wide range of timescales and amplitudes) affects the detection of transiting planets in practice. We crafted our sample in order to allow for confusion between (a) flares occurring with frequency near the typical ~2 hr transit duration and (b) marginally detectable transiting planets (which is, the two have similar predicted amplitude). Of course, this finding is limited in scope, as flaring on all timescales will affect transit detection, as well the detrending necessarily to remove stellar rotation. As predicted, our sensitivity to transiting planets is degraded around active stars. We quantify this affect by estimating β, the inflation of the photometric uncertainty in active stellar lightcurves due to the presence of correlated noise. While we have limited our study here to stars with radius ~0.2R_⊙ and TESS magnitudes between 10 and 11.5, the estimation of β to be 2 ± 0.5 may be useful in a broader context as a normalization in the sensitivity to transits around active versus inactive M dwarfs.

We find that the types of planets that are detected around inactive but not active stars fall in an important parameter space where terrestrial exoplanets are known to occur. Particularly, we find that a realistic noise budget for active stars makes the detection of additional TRAPPIST-1 like systems challenging in current TESS data even of bright stars. The use of TESS data for the calculation of occurrence rate, particularly at the low-mass end of the stellar main sequence where active lifetimes are long and stellar variability is high, requires a more thorough understanding of how variability manifests in lightcurves. Future work quantifying this effect is warranted as well as future work exploring other methods for mitigating the effect of stellar activity on transit detection. The habitable zone of these stars falls in the regions of interest explored in this work, and so developing a census and target list of potentially habitable rocky planets for future missions will heavily depend on our ability to mitigate and understand stellar activity in these transit lightcurves.

Acknowledgments

We thank Quadry Chance, Sheila Sagear, Christopher Lam, Natalia Guerrero, William Schap III, and Kristo Ment for useful discussions that have helped inform and enrich this work. We also thank the anonymous reviewer for the helpful comments and suggestions that shaped this work. This material is based on work supported in part by the University of Florida Undergraduate Scholars Program and the William Oegerle Scholarship in Physics and Astronomy.

We acknowledge that for thousands of years the area now comprising the state of Florida has been, and continues to be, home to many Native Nations. We further recognize that the main campus of the University of Florida is located on the ancestral territory of the Potano and of the Seminole peoples. The Potano, of Timucua affiliation, lived here in the Alachua region from before European arrival until the destruction of their towns in the early 1700s. The Seminole, also known as the Alachua Seminole, established towns here shortly after but were forced from the land as a result of a series of wars with the United States known as the Seminole Wars. We, the authors, acknowledge our obligation to honor the past, present, and future Native residents and cultures of Florida.

This research made use of exoplanet (D. Foreman-Mackey et al. 2021) and its dependencies (Astropy Collaboration et al. 2013, 2018; D. M. Kipping 2013; J. Salvatier et al. 2016; Theano Development Team 2016; R. Kumar et al. 2019; R. Luger et al. 2019; E. Agol et al. 2020).

Software: exoplanet (D. Foreman-Mackey et al. 2021), batman (L. Kreidberg 2015), TransitLeastSquares (M. Hippke & R. Heller 2019).

Appendix: Comparison to Literature Results

To benchmark our methods against existing similar studies in the literature, we show in Figure 5 our sensitivity map to TIC 11893637. This star is one of the 363 M dwarfs studied by K. Ment & D. Charbonneau (2023), who also characterized the sensitivity to transits in TESS lightcurves. We have inverted the axes and show radius ratio, rather than planetary radius, in order to allow for direct comparison. We note broad consistency in the detection contours, though our resolution in orbital period and radius space differs.

Figure 5. Refer to the following caption and surrounding text. — **Figure 5.** Sensitivity map for TIC 11893637, using the methodology described in Section 2. We show a comparison to K. Ment & D. Charbonneau (2023) to show consistency in completeness across methodologies. Axes drawn from K. Ment & D. Charbonneau (2023).
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