EDEN Survey: Small Transiting Planet Detection Limits and Constraints on the Occurrence Rates of Planets around Late-M Dwarfs within 15 pc

We observed with seven telescopes across the Northern Hemisphere: four located in Arizona, two in Europe, and one in Taiwan (see Table 1 in Gibbs et al. 2020). Under ideal scheduling and weather conditions, this longitudinal coverage allows for continuous observations of target stars visible from all EDEN sites. The telescope apertures range in size from 0.8 to 2.3 m. The Schulman 0.8 m telescope is robotically operated, while the CAHA 1.2 m is remotely operated. The rest require an on-site operator/observer each night. We took sky flat or dome flats, as well as bias frames, whenever possible. Dark frames are no longer acquired as we found no difference between data calibrated with or without darks, as the dark current is near zero at all telescopes and the targets have high S/Ns (Gibbs et al. 2020). We tried to observe a given target star for at least three hours per night, which is roughly three times the expected transit duration of a planet on a close-in orbit. This strategy allows us to observe multiple targets in one night if we cannot spend the entire night on one star (e.g., if the star is relatively southern and is only visible for half the night).

We used the GG495 filter from Schott, ¹⁸ which is a longpass filter that reaches 50% transparency at ∼500 nm and extends into the near-IR, due to its greater transmission (>90%) than narrowband filters across visible and near-IR wavelengths. Some observations required a narrowband filter, usually due to moon brightness or for TESS transit follow up. We usually used 60 s exposures unless the target was too bright/faint, or if higher time precision was required (e.g., for a transit timing variation (TTV) analysis of transit follow-up targets). In certain cases, we slightly defocused the star to both mitigate inter- and intra-pixel sensitivity differences and to avoid saturation for longer exposures on brighter targets (for further information see, e.g., Southworth et al. 2009; Gibbs et al. 2020).

Our detectors enter a nonlinear regime of photon/electron counts at about 2/3 of the well limit; we thus aimed to stay below 60% of the full-well level for bright targets. Our data reduction pipeline adjusts for saturation in the target and best reference stars, with brighter reference stars discarded if they are saturated. For most of our CCDs, the field of view is on the order of 10', but the plate pixel scales differ, and in many cases the observations were binned in order to decrease the readout times. We built our data reduction pipeline to be robust and agnostic to different plate scales, and only run photometry for one given night from one given telescope at a time.

The Project EDEN target list is comprised of all known single nonvariable stars of spectral type M7–L0 within 15 pc and with declinations >−20°. At the beginning of our survey, we removed known binaries and active flare stars as indicated by SIMBAD from the 15 pc sample because they are likely to contaminate the light curves, making it more difficult to find a transiting planet. Once we removed the stars that do not fit the above criteria, we were left with 22 stars that became the focus of the survey.

It has been shown that the removal of binary stars from samples of demographic studies can introduce biases, mainly in the form of overestimating giant planet occurrence rates (Moe & Kratter 2021). While close binaries may pose a threat to M dwarf planetary systems, they are relatively rare around low-mass stars (e.g., Shan et al. 2015; Susemiehl & Meyer 2022). M dwarf binaries also tend to have 10× higher flare activity than single M dwarfs (Huang et al. 2020). The close binary fraction is also relatively constant across the M dwarf range, which suggests that there is no introduction of a systematic error with their removal (Offner et al. 2022). Additionally, M dwarf binary systems with planets or planet candidates tend to have wide separations between the stellar components (e.g., Clark et al. 2022a). To identify multiple stars in our sample, we searched the RECONS M dwarf binary catalogs (Winters et al. 2019; Vrijmoet et al. 2020), the Gaia EDR3 binary catalog (El-Badry et al. 2021), the recent results from Robo-AO (Salama et al. 2021, 2022), the M dwarf TESS objects of interest (TOIs) companion catalog (Clark et al. 2022a), and the POKEMON speckle catalog (Clark et al. 2022b). We found two binaries within our sample, EDEN Input Catalog (EIC) 10 and EIC 14.

Reiners & Basri (2009) identified EIC 10 (LP 775-031/Gaia DR3 3171631420210205056) as a double-lined spectroscopic binary (SB2) consisting of two nearly equal brightness components. Recent high-resolution imaging efforts have been unable to resolve the companion (Winters et al. 2019; Vrijmoet et al. 2020). C. Clark et al. (2023, in preparation) observed EIC 10 using speckle imaging, but were not able to resolve a companion. Speckle imaging is sensitive to separations >01, constraining the binary separation to ≲1 au at a system distance of 10.6 pc. Indeed, Gaia DR3 revealed this target to have an orbital astrometric solution with a period of 105.56 days (Gaia Collaboration et al. 2022). Assuming EIC 10 consists of two equal mass M7 stars (0.09 M_⊙), Kepler's third law places the component separation at 0.25 au, corresponding to 0023, below the sensitivity of speckle imaging.

Salama et al. (2022) identified EIC 14 (Gaia DR3 1097353325107339776) as a binary with an angular separation of 04 and a ${\rm{\Delta }}i^{\prime}$ magnitude of 2.28, but the observation was conducted in 2012. Clark et al. (2023, in preparation) more recently resolved EIC 14 as a binary with an angular separation of 029 and a Δ880 nm magnitude of 1.62. The angular separations at two different epochs place the binary companion between 3.5 and 5 au at a system distance of 12.3 pc. We kept this target in our sample due to the wide separation of the binary and implemented a flux-correction factor (see Section 4.1).

The sample of stars matching our criteria (including the wide-separation binary) is shown in Tables 1 and 2. As the completeness of our targets within 15 pc neared 100% during the survey, we extended our observations to stars in the 15–21 pc range, as well as many targets outside the criteria (either in distance or in spectral type) as interesting candidates during the time when no <15 pc target was seasonally observable, as well as interesting candidates for other scientific purposes (e.g., the high-frequency flare star Wolf 359; Lin et al.2021). These targets are shown in Table 3. In addition, we performed targeted follow-up observations of exoplanet candidate stars found by TESS (see Table 4).

We began our photometric process by calibrating the target frames using combined flats and biases. This step is coded to be optional in cases of bad or unavailable calibration files, which only rarely occur (<5% of nights) and do not significantly reduce the quality of our light curves. We then performed aperture photometry using photutils (Bradley et al. 2019), including calculating an astrometric solution using astrometry.net (Lang et al. 2010). We selected an aperture size between 5 and 50 pixels in steps of 1 pixel that minimizes the rms scatter in the light curve of the target and a sky background median value of a 60 × 60 pixel box around the target after other sources are removed. Finally, we ran a simple comparison detrending of the light curve. The six reference stars in the field (or as many as possible in the rare cases where there are few reference stars) with the lowest average deviation within bins of 20 exposures across the light curve were median-combined into a single unbinned light curve, which was then divided out from the target light curve (see, e.g., Section 3.4 in Gibbs et al. 2020). Further detrending was performed as part of the transit search, as described in the following section.

As is usual for ground-based, high-precision photometry, our data are impacted by relatively slowly changing systematics, usually arising from airmass changes, telescope positional drift, and seeing variations. In order to correct for these systematics, we performed a detailed detrending analysis similar to that laid out in Section 4.2 of Gibbs et al. (2020). Specifically, we followed these steps:

• 1.  
  We divided the normalized light curve by a 2nd-order polynomial that we fit to the original data.
• 2.  
  We performed a median filter over a 2 hr window.
• 3.  
  We removed any data points 2σ above the median but not below to avoid removing transits much shorter (1–2 hr) than the length of the overall light curve (>3 hr).
• 4.  
  We fit a 2nd-order multivariate polynomial, based on the airmass, background level, and pixel x, y positions and divided it out.

Although we adopted steps from Gibbs et al. (2020), we also explored whether alternative detrending approaches may yield better results. Specifically, we tested multiple detrending procedures from the Wōtan package (Hippke et al. 2019), including combinations of biweight filtering, median filtering, spline fitting, and Savitsky–Golay polynomial fitting. For injected planet transit tests, none of the above versions of detrending procedures provided a lower scatter in the out-of-injected-transit baselines without also overfitting and at least partially removing the injected transit from the data set. Specifically, biweight filtering is best at removing signals from raw data sets that have much longer timescales than the transit signal. For short-timescale signals across the duration of one observing night, biweight filtering did not improve the results. Therefore, our tests did not demonstrate that alternative approaches result in significant improvements, and we thus decided to continue using our original detrending procedure.

A potential source for false-positive detections are variations of precipitable water vapor (PWV) in Earth's atmosphere, in particular for red target stars such as the ones in our survey (e.g., Bailer-Jones & Lamm 2003; Blake et al. 2008). These variations may affect the accuracy of photometric time series in magnitudes and timescales that could be comparable to transit signals (Berta et al. 2012).

The filter bands in which EDEN observations are done are sometimes affected by PWV, as they overlap with several water vapor bands. The magnitude of light-curve impairment due to PWV depends on the spectral energy distributions of the target and comparison stars, the amount of water vapor in the atmospheric column along the line of sight of the telescope and its variation in time, and the bandwidths and wavelengths of the used filters. Mitigation strategies have been put forward, such as evaluating the contribution of PWV across global, all-sky light curves and/or monitoring using local environmental sensors (Pedersen et al. 2023), as well as concurrent satellite remote sensing observations to drive a correction (Meier Valdés et al. 2021).

Given the above, if PWV affects light curves significantly, it is expected to introduce false positives. However, there is no evidence for such an effect in our data set: the fact that we only detected one transit candidate (see Section 7.2) in >2450 hr of photometry shows that PWV is not a major source of false positives for the combination of filter choice and telescope locations of the EDEN survey. However, in the case of a signal that survives the initial validation steps, we will need to evaluate the possibility of a false-positive scenario caused by PWV.

We first analyzed all the data we had on each target by eye via the EDEN Interactive Viewer, which shows the light curve for the night along with airmass, moon altitude, sky background, reference and target star flux, and x, y pixel positions. Transit-like features were manually flagged for potential follow up, but most variations in the data can be attributed to observing conditions or stellar activity. We account for the dilution of potential transit depths from the binary star EIC 14 by implementing a correction factor following Equation (4) from Furlan et al. (2017), with Δm = 1.62. We note that our GG495 longpass filter is not the same as the narrowband 880 nm filter of the speckle observations, making this Δm value an approximation. Assuming a planet orbits the primary, brighter star in the system, the correction factor is ∼1.1.

To search for signatures of planetary transits in the EDEN photometry more thoroughly, we used the Transit Least Squares (TLS; Hippke & Heller 2019) search algorithm, which is based on a template signal shape informed by small-planet detections of the Kepler mission. We applied the algorithm to all stars in our sample with data cuts at 0.3%, 0.6%, 0.9%, and 10% precision levels. Each of these runs returns a periodogram, model light curve (including phase folding), and best-fit parameters (period, duration, depth/radius ratio, mid-transit time for first transit in our data, and false-alarm probability) for the expected transits. We note that TLS always attempts to fit a transit model, and that many of the output parameters are likely not actual transits but instead false positives that are the result of attempting to fit a transit to short-period and short-duration noise residuals in the light curves. We vetted all the signals and discarded any transit models with a high false-alarm probability (>0.01) as well as those signals with low false-alarm probabilities but with parameters for planets that are unlikely to exist and be detected with our observations: transit durations ≲15 minutes, orbital periods <0.25 days, and transit depths corresponding to planets <0.1 R_⊕.

In order to probe the underlying planet population through our detection statistics, a thorough understanding of our survey completeness is necessary. Besides the geometric probability of a planet to transit given our line of sight to its host star, the completeness of our survey is limited by our ability to detect transit signatures. Our sensitivity is mostly limited by the photometric precision of our light curves and by the performance of our detection pipeline.

For close-to-ideal surveys not suffering from nonuniform sampling and significant data gaps, analytic expressions exist to estimate the sensitivity for transit signals (e.g., Pepper et al. 2003). In the case of our ground-based survey with its inevitable irregularities, we instead employed injection-and-retrieval simulations. Our approach was to inject planet signatures on a grid of orbital period versus planet radius and recover them. We used a log-spaced grid of 20 orbital period bins from 0.5 to 10 days, but if we had fewer than 10 nights of data on a target we truncated the grid to the number of nights we had. We also used a log-spaced grid of 12 planet radius bins from 0.6 to 3.5 R_⊕. For targets with data covering fewer than 10 nights, we artificially cut off the injections to periods where we would see at least two transits of the injected planet.

We created 250 planets with a random orbital period, orbital phase, and planet radius within each of the given grid bins, where the random values were drawn from a uniform distribution within each bin. This differs from the process in Gibbs et al. (2020), where they injected enough planets to retrieve 10 observable transiting planets per bin. This is due to increased noise levels generated by the previous method (see Figure 5 in Gibbs et al. 2020). In addition, we assumed the orbits to be circular, we randomly drew the impact parameter from a uniform distribution between 0 and 0.7 to avoid grazing transits, and we used the Claret (1998) limb-darkening law with coefficients u₁ = 0.84 and u₂ = 0.125. We injected the transit signals of each artificial planet into our observed photometric time series, detrended the resulting light curve, and ran the TLS algorithm to attempt to recover the injected planets. An example detrended light curve with an injected transit is shown in Figure 2. The results of our transit search are described in Section 5.2.

Zoom In Zoom Out Reset image size

We considered our injected planets to be detected and positively recovered if the period was within 0.02 days (or 24 minutes) of the injected period, which corresponds to a fractional difference ≤4% based on the actual given period. We also accounted for undersampled periods due to the scarcity of our data by looking at light curves with at least two transits found and checking to see if the given period for the injected planet still matched the injected transits recovered. We created a separate detection filter for single transits found and discarded those, as we cannot place our desired constraint on the orbital period of a planet with only one transit recovered.

Our survey yielded a rich data set of detrended light curves with ∼1–10 mmag scatter for 22 EDEN target stars ranging in spectral types from M7V to L0, and in distance from 5.7 to 14.8 pc. For most target stars, our data set provides the highest-quality photometric monitoring to date, often with a unique combination of relatively high cadence (∼60 s), sensitivity, and monitoring baseline. The light curves were used in this study to search for transiting exoplanets and place upper limits on their occurrence rates, but they can also be exploited for studies of stellar activity and stellar rotation, among other uses (see, e.g., Lin et al. 2021; Murray et al. 2022). Although not included here, our data set also provides similar photometric monitoring information for typically a dozen other stars in the same fields of view of our target stars.

Our careful manual and algorithmic analyses of the light curves resulted in no convincing transit detections. Roughly 20 potential transit signals were flagged in all of our data, and there was one repeating, transit-like signal, which we followed up with additional observations and found no further evidence of a transit (see Section 7.2). Many TLS results were discarded as being unphysical false positives via the vetting procedure mentioned in Section 4.1. Therefore, we conclude that TLS found no real transit signals in the data from any of our targets. The fact that our light curves did not show many false positives—yet remained very sensitive to exoplanets down to Earth radii—demonstrates the efficiency of our data reduction and analysis approach.

We report the percentage of planets recovered with properties similar to the injected ones and created a map of the recovery probability in our sensitivity maps (see Figure 3 for the average map and full detection probability from the EDEN survey and Appendix A for the full set of 22 sensitivity maps).

Zoom In Zoom Out Reset image size

Our average sensitivity to approximately Neptune-sized planets (R ∼ 3.5 R_⊕) on very short (P ∼ 0.5 days) orbits for most of our target stars is ∼85%–90% (see the top left corner of the top panel of Figure 3), which can be extended as a conservative estimate to larger planets as well. Due to the nightly cadence of observations, we tend to see a higher sensitivity for our targets at periods that are integer multiples of one day. Overall, our light curves are very sensitive to short-period (P < 1.5 days) super-Earths and larger (R > 1.5 R_⊕) exoplanets, and, for most of our targets, we can exclude that such transiting planets orbit our targets.

We note that EIC 7 (2MASS J05310004-0052452) and EIC 21 (2MASS J15345704-1418486) have significantly lower sensitivities than the other targets, which occur due to a combination of low overall time observed (<50 hr), southern declinations, and relatively high light-curve scatter for more observations than the other targets. However, these two targets do not significantly affect the overall average sensitivity map, and we include them here for completeness.

Using the above-described Monte Carlo method to compare the results of the simulated surveys of hypothetical exoplanet populations to the actual results of our survey statistically, we first tested the hypothesis that "TRAPPIST-1 b analogs orbit every late-M dwarf star", or f_Trb = 100%. Although simplistic, this hypothesis is a sensible starting point for the exploration of the exoplanet population around late-M dwarfs, since short-period planets like TRAPPIST-1 b are among the easiest to detect in the known late-M dwarf population.

In order to do so, we simulated our EDEN transit survey 10,000 times to determine in what fraction of these surveys would the predicted results be consistent with our actual survey. Assuming isotropic orbit orientations, we injected a planet with probability P_geom = (R_⋆ + R_p )/a, which approximates the geometric transit probability for a planet with radius R_p in a circular orbit with semimajor axis a around a star with radius R_⋆. In the case of a transit occurring, we injected the photometric signature of a planet with a random orbital phase and TRAPPIST-1 b's orbital period and planet radius (P = 1.511 days, R = 1.116 R_⊕, respectively; Agol et al. 2021) and tested its detection by our pipeline. In 15% of our simulated surveys, we would have seen at least one planet out of our sample of 22 stars. Our sensitivity (probability to detect a transiting TRAPPIST-1 b) is ∼18%, whereas the completeness (probability of detecting a planet, so the sensitivity multiplied by the geometric transit probability) is ∼0.8%.

We also tested the hypothesis that "TRAPPIST-1-like planetary systems orbit every late-M dwarf star" (${f}_{\mathrm{Tr}}\lt 100 \%$) as an extension to the TRAPPIST-1 b hypothesis. The additional planets in the full TRAPPIST-1 system make the system as a whole more likely to be discovered, even with individual planets decreasing in detection likelihood going outwards in the system. We took all of the planet period and radius values from Agol et al. (2021), and set a random system inclination and a Rayleigh distribution for mutual inclinations around 2° (e.g., Fabrycky et al. 2014; although Luger et al. 2017 measured the TRAPPIST-1 mutual orbital inclinations to be around 03). Planets g and h were included for the survey sensitivity—as if they had an orbital period of 10 days—because their orbital periods are >10 days. Again the EDEN transit survey was simulated 10,000 times, and in 21% of the surveys we would have detected at least one planet.

In the following, we provide an estimate of the occurrence rate of close-in giant planets around late-M dwarfs based on our survey's completeness in this parameter domain. Our constraint is based on the same numerical Monte Carlo experiment as above for the TRAPPIST-1 b analogs. As a conservative approximation, we assumed for these planets the sensitivity we found for the largest artificial planets that we injected in our sensitivity analysis (3.5 R_⊕; see Section 4.2). For a host-star radius representative of an M8V dwarf (R_⋆ = 0.114 R_⊙; Pecaut & Mamajek 2013), the geometric transit probability P_geom ≈ 11% for a planet in a 1.05 day orbit. Even assuming such close orbits, 98% of our mock surveys yield zero detections if giant planets occur around 2% of late-M dwarfs (Ghezzi et al. 2018). If instead every such star hosts a giant planet, we would expect to detect at least one giant planet in our survey in 73% of the cases. If we decrease the orbital period down to 0.5 day orbital periods, the average sensitivity to a transiting planet increases by a factor of ∼1.6, and we can constrain the giant planet occurrence rate down to 75% with 95% confidence.

Our EDEN observations provide the most extensive set of light curves for the majority of our 22 target stars. Table 1 summarizes our targets and the total length of observations for each. Even though our targets are close to the solar system (d < 15 pc), the majority of the target stars are too faint for wide-array or all-sky surveys—such as HAT (Bakos et al. 2002), MEarth (Irwin et al. 2009), or TESS (Ricker et al. 2015)—to search for planets. For example, a comparison of our targets (with typical spectral types of M7–M9) to the stellar effective temperature and planet radius distribution of TOIs as of 2022 April (see Figure 1) illustrates how well our observations complement the TESS survey: there are currently no TOIs with spectral types beyond M7. This paucity of TOIs for late spectral types is primarily due to the fact that TESS's sensitivity—in spite of its extreme photometric stability—is limited to brighter stars by its small collecting area. The MEarth project, which utilized arrays of small robotic telescopes to search for transiting planets around bright mid-to-late-M dwarfs (Nutzman & Charbonneau 2008), reports photometric precisions of 0.2%–1.0% at a typical cadence of ∼25 minutes (Berta et al. 2013).

In comparison to these other current M dwarf surveys, the EDEN survey, due to the large apertures and uniform observing and data reduction strategies, accomplishes uniquely long monitoring both with high cadence and high sensitivity. Specifically, our targets are observed for at least 25 hr (the equivalent of about four typical, clear nights) and 1/3 of our targets were observed for over 100 hr (the equivalent of about 15 typical, clear nights) with ∼60 s cadence. As the light curves collected in our EDEN survey will likely be of use for a variety of future studies (e.g., stellar activity and rotation measurements), we make the reduced and calibrated light curves available to the community as an online data set accompanying this paper. The non-EDEN targets observed in our survey (Tables 3 and 4) represent a less homogeneous data set. Those light curves and the ensemble of images obtained are available on a collaborative basis and will be made fully available in the near future.

During observation runs in fall–winter 2020, we identified transit-like features in the light curves of EIC 9 (2MASS J04195212+4233304), i.e., a 0.5%–1% dip with a duration of ∼45 minutes. Similar features occurred twice on the same day of 2020 November 18 (UT), once observed by the Lulin One-meter Telescope (LOT) in Taiwan and again about 14 hr later by the Kuiper 61'' Telescope in Arizona. The Vatican Advanced Technology Telescope (VATT) in Arizona observed another feature on 2020 December 22 (UT). The VATT and Kuiper features were both 1% depths, whereas the LOT feature was 0.5%, and the LOT and Kuiper features were both ∼40–45 minutes in duration, whereas the VATT feature was ∼60 minutes (see Figures 5 and 6). The weather at the sites for all three events was nominal—no clouds during the LOT and VATT events, and light cirrus at the Kuiper site in the east as the target was setting. Our observations are done with intra-exposure guiding every few seconds on a bright star near the target, and there were no guiding errors during the observations so the target and reference star centroids remained consistent.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

This star was also observed by TESS in Sector 19, and was found to have stellar variability with an amplitude of ∼1% on a 0.99 day period. Once that trend was removed, a low-confidence recurring event (S/N = 4.9, and signal detection efficiency ∼ 6.5) was found with a period of 2.883 days and a transit depth of 0.7%. Notably, the ephemerides aligned with both the LOT and VATT detections—12 orbits of separation with a period of 2.883 days between the two sets of data. However, additional observations from Lulin and Calar Alto ruled out additional transits during those observation windows, casting doubt on the veracity of the original transit observations.

Additional analysis of the light curves from the LOT and VATT events found both to be highly dependent on systematics, as the VATT event was at high airmass and the LOT event is canceled out by the detrending procedure (compare the top panel of Figure 5 with the top panel of Figure 6 and the middle panel of Figure 7). The event in the Kuiper telescope light curve remained even through additional detrending. Previous observations by the Bok telescope in 2019 were not sensitive enough to rule out a transit of the given depth, but new data from the Calar Alto 1.23 m telescope in 2021 January ruled out the ∼2.883 day period for the candidate (see Figure 7). Transit fitting of the signal from the Kuiper event put the period at 3.003 days with a 68% confidence interval of [1.735, 3.781] days. Based on our observing coverage of the target, we likely would have seen multiple transits of any planets within a 5 day period.

Zoom In Zoom Out Reset image size

Eventually, we determined that our effective phase coverage was providing diminishing returns on continued observations beyond ∼40 nights of data, so with no further transit signals we suspended the follow up of this target and returned to the standard survey monitoring procedures. The event could be a transit, but we would likely have seen an additional transit in our observations unless the data quality was consistently poor. At this point the origin of the detected signal remains unexplained. It may have been caused by telluric contamination such as variable PWV (see the discussion in Section 3.3), which we shall estimate qualitatively here. Typical amounts of water vapor in the Santa Catalina Mountains of 2 mm have been measured (Warner 1977). For a bandpass similar to GG495, this was estimated to cause a ∼3% flux difference due to PWV for an M8 target star (Murray et al. 2020; Pedersen et al. 2023). According to these data, a PWV variation on the order of 1 mm would be consistent with a 1%-level flux change, making PWV variations a potentially viable source of the observed signal.

The TLS results from the full set of light curves of this target confirm our analysis of the potential signal. There was no strong event matching the period or any multiples of the expected transit from the TESS data, and the best transit model that TLS found had too short of a duration to be a physical transit of an exoplanet. In addition, none of the best-fit models from any of the precision cuts included the Kuiper event as a possible transit match.

Our observations were collected with seven telescopes located on three different continents. We developed a uniform observing protocol and data reduction and analysis approach that provided uniform final products, where differences are primarily due to the sensitivity of the instrument (a combination of the telescopes' light-collecting area and the quantum efficiency of the detectors). Our data reduction and analysis approach was developed to maximize sensitivity (finding many possible transit candidates and following up on them) and efficiency (observing many targets where follow-up monitoring requires a substantial amount of telescope time) simultaneously.

The EDEN survey's sensitivity is demonstrated by the injection-and-retrieval tests we performed (see Section 4.2). Its efficiency is, perhaps counterintuitively, reflected in the overall scarcity of possible detections: our sensitivity analysis shows that our observations can very efficiently detect short-period planets (P <1.5 days), even if they are relatively small (R_p < 1.5 R_⊕). Yet, during our survey of over 2450 hr, we detected only one target with a potential single transit (see Section 7.2). The combination of high sensitivity and the very low number of false positives demonstrates high efficiency and reliability, as well as robust approaches to the data reduction and analysis, which are particularly important for any targeted survey. In order to support future surveys, we commit to making the complete EDEN data analysis package available on a collaborative basis.

Project EDEN survey's extensive data set yielded multiple possible detections, but only EIC 9 was not identified immediately as a false positive. Further observations successfully eliminated it as a potential planet candidate, leaving no detected transit in our survey. Translating nondetections into constraints on the exoplanet demographics and occurrence rates is nontrivial, and requires a careful sensitivity analysis (see, e.g., Obermeier et al. 2016; Kunimoto & Matthews 2020; Sagear et al. 2020).

We performed injection-and-recovery-based Monte Carlo sensitivity assessments for our targets and data sets, which mimic signals which would have been introduced by planets. In the initial EDEN survey paper (Gibbs et al. 2020), where our method was initially introduced, the efficiency was compared to (blind) injection and recovery by four team members. We found that the human team's ability to identify randomly injected planets is comparable to the algorithmic identifications. Therefore, the automatic injection-and-recovery sensitivity maps presented in Appendix A can be considered as a highly reliable assessment of the sensitivity of our data set for each planet as a function of planet period and radius. The nondetection, in combination with the carefully characterized sensitivity limits, provides an important opportunity to place constraints on the occurrence rates of exoplanets around late-M dwarfs.

While we obtain a sensitivity of ∼30% to transiting TRAPPIST-1b-like planets, the completeness with regard to these planets is low due to the small transit probabilities. Our Monte Carlo assessment of 10,000 mock surveys showed that even if every star had a TRAPPIST-1 b-like planet or TRAPPIST-1 planetary system analog, we would detect planets either 15% or 21% of the time. In addition, Burn et al. (2021) found in planet formation models that the occurrence rates of planets of all sizes drop from early-M dwarfs to late-M dwarfs. Based on a pebble accretion formation model, Mulders et al. (2021) suggest a drop in rocky planets toward the substellar boundary.

We can compare our results to other measurements from ultracool dwarf (UCD) surveys. The full TRAPPIST survey analysis (Lienhard et al. 2020) found that their expected number of detections, given every UCD had a TRAPPIST-1 b-like planet in the system, is 0.52. Thus, the detection of TRAPPIST-1 b in the survey sample of 40 UCDs implies a lower limit for the occurrence rate of TRAPPIST-1 b-like planets of 10% at 95% confidence. Sestovic & Demory (2020) examined the K2 light curves of 702 UCDs and were able to rule out TRAPPIST-1-like planetary systems around every UCD with 96% confidence, while Sagear et al. (2020) examined 827 K2 UCD light curves and found that the occurrence rate of TRAPPIST-1b analogs was limited to <57%. The EDEN survey, with roughly half the number of targets as the full TRAPPIST survey analysis, shows a similar expected number of detections. Thus, even a targeted EDEN-like survey expanded out to >100 UCDs would still have at least a 50% chance of detecting no planets.

The case of giant planets is a separate consideration. Compared to FGK stars, M dwarfs host fewer giant planets (Endl et al. 2006; Johnson et al. 2010; Bonfils et al. 2013; Sabotta et al. 2021), which is in line with predictions of current planet formation models (e.g., Miguel & Ida 2016; Liu et al. 2019; Burn et al. 2021; Mulders et al. 2021). Giant planet occurrence appears to decline linearly with decreasing stellar mass (Johnson et al. 2010; Ghezzi et al. 2018), although the continuation of this trend into the less-explored late-M dwarf regime has recently been questioned (Jordán et al. 2022; Schlecker et al. 2022). Under the optimistic assumption of a short-period (P ∼ 1 day) giant planet around every star, 27% of the simulated EDEN surveys would still yield zero detections. Our data thus allows us to reject the hypothesis of one giant planet per star at a 73% significance level. For ultrashort-period giant planets (P = 0.5 days), our constraint on the occurrence rate at 95% confidence is f_large < 75%. We conclude that our nondetection is consistent with previous giant planet occurrence rates while not ruling out a moderate increase around late-M dwarfs as recently suggested by Schlecker et al. (2022). A larger sample will be needed to provide stronger constraints. Assuming a comparable completeness for an extension of the survey, we find that a sample with at least ∼50 stars is needed to exclude the hypothesis that every star hosts a (hot) giant planet with 95% confidence.