The Occurrence of Small, Short-period Planets Younger than 200 Myr with TESS

Young stars present additional challenges during the detrending processes of their light curves as a result of heightened activity. Photometric variations on the scale of 1%–2% due to rapid stellar rotation, along with stellar flares, require special attention.

We perform iterative sigma clipping outlier rejection for major flare rejection and then model and subtract the photometric signal induced by rapid stellar rotation. Our detrending method is as follows.

• 1.  
  Perform an initial spline fit of the stellar rotational variability via the routine described in Vanderburg et al. (2019).
• 2.  
  Identify flare rejection masks via 10 iterations of upward outlier rejection at the 5σ level with standard deviation calculated by scaling the measured median absolute deviation value.
• 3.  
  Refit stellar variability via the spline model to the raw light curve with the flare rejection masks applied and flatten the resulting light curve (e.g., see Figure 10).

With the detrended light curves, we perform a box least-squares (BLS; Kovács et al. 2002) search to identify planetary transits in the TESS light curves. We sample 100,000 periods linearly spaced between 0.5 and 20 days and 500 transit durations linearly sampled between 0.008 times and 0.08 times each tested orbital period.

We identify any signal with a calculated signal-to-pink noise ratio (Hartman & Bakos 2016) ≥8 to be a threshold-crossing event (TCE). For each individual TCE, we perform a visual inspection to vet for false positives resulting from both astrophysical events and detrending artifacts. Each candidate event is inspected to determine if the signal that triggered the TCE is transit shaped. Further, we require a minimum of three transit events in order to determine a period.

We search for the presence of secondary eclipses and differences in the depths between even and odd transits to determine if the transit is from an obvious EB. For identified TCEs, we fit for the transit depth of even and odd transits respectively to rule out EB scenarios. To measure the transit depth, we fix all parameters except for transit depth, δ. The transits are modeled using batman (Kreidberg 2015). We explore the best-fit transit depth and posteriors with a Markov Chain Monte Carlo run implemented with emcee (Foreman-Mackey et al. 2013). We require the difference in our calculated odd and even transit depths to be <5σ to not be classified as an EB, though no reported candidate has an odd–even difference > 3σ in our sample. We visually vet for secondary eclipses by phase folding the detrended TESS light curves at the derived TCE period and transit time. The entire phase-folded light curve is visually inspected for signs of secondary eclipses. Targets exhibiting EB-like secondary eclipses, including those in eccentric orbits, are excluded as planet candidates.

We check for obvious nearby eclipsing binaries (NEBs) by comparing the pixel-by-pixel light curves centered around the target star to determine if the signal that triggered the TCE is consistent with being on target. We then perform a centroid analysis with the TESS FFIs to create difference images using the transit-diffImage code base ¹² following the techniques described in Bryson et al. (2013). For each candidate in each sector, we produce a difference image between the in-transit and out-of-transit pixel stamps. We calculate the centroid of the target star via the TESS pixel response function fit to the difference image. The calculated centroid is compared against the expected centroid of the target star based on a catalog projection. Some offset in the difference image is expected if nearby stars are present, as the centroid naturally shifts away from the dimming star during transit. We flag any centroid offset > 1 pixel for visual inspection to determine if the high centroid offset is due to an astrophysical false positive.

Remaining candidates were then checked for planetary multiplicity. We masked the initial signal that triggered the TCE in the nondetrended light curves and then repeated the detrending and transit search (see Sections 4.1 and 4.2). Any signal that passes our S/N criteria is visually vetted in the same method as mentioned above. We additionally check for aliasing of the original signal recovered. All remaining candidates are compared to the list of TOIs and known planets.

Our stellar sample contained 26 TOIs (see Table 2), 22 of which were within our search parameters (0.5 days ≤ P ≤ 20 days and 1 R_⊕ ≤ R_P ≤ 8 R_⊕), as well as two previously previously confirmed transiting planets from K2. Of these, 16 have both FFI light curves and 2 minute cadence light curves (see Table 2), as well as the two K2 planets. Of the 22 known TOIs within our survey parameters, 20 are either planet candidates or confirmed planets, the remaining two have been ruled as either false alarms or false positives by the TESS Follow-up Observing Program Working Groups (TFOP WG; SG1 and SG2).

We recovered all known TOIs in our planet search using the SPOC light curves, including 15 planet candidates within our search parameters and the known planets V1298 Tau c and d. Our QLP planet search recovered all 20 TOIs within our parameters but was unable to recover V1298 Tau c and d. Our pipeline identified a signal corresponding to V1298 Tau c, with a signal-to-pink noise ratio of 6.29, which did not trigger a TCE. Upon visual inspection of the FFI light curves for V1298 Tau, the long cadence of the FFIs and the heightened stellar activity subsequently diluted the transit signal in our detection pipeline.

We identified new planet candidates TIC 88785435.01, TIC 150070085.01, TIC 434398831.01, and TIC 434398831.02 (S. Vach et al. 2024, in preparation) in our QLP search. Out of the new planet candidates, only TIC 150070085.01 also has SPOC data and is independently identified by our SPOC search. These candidates are described in detail in Appendix C.

Our planet detection pipeline recovered 14 confirmed planets within our SPOC parent sample, and 16 confirmed planets in the QLP parent sample. For planets with confirmed planet dispositions by the TFOP WGs, we adopt a false-positive rate of zero, as these planets have undergone extensive spectroscopic and photometric follow-up observations to rule out false-positive scenarios.

Five remaining planet candidates have not received sufficient follow up to be categorized as verified or validated planets. As such, there exists a possibility that they are the result of astrophysical false-positive scenarios, instrumental systematics, stellar variability, detrending artifacts, etc. There are insufficient planet candidates around young stars from which we can derive a secure false-positive rate estimate.

To attain false-positive estimates, we make use of the publically available TRICERATOPS (Giacalone et al. 2021) code to estimate the probability that a transit signal is planetary in nature or the result of an astrophysical false positive. We explore the impact on the false-positive rates when derived using blend analyses codes, including TRICERATOPS and MOLUSC (Wood et al. 2021). The false-positive rates from TRICERATOPS are adopted in our occurrence rate calculations hereafter and are typically 1%–5% for a given candidate. When we adopt TRICERATOPS and MOLUSC together, the false-positive rate approaches 0% for all candidates, and its impact on the calculated occurrence rates is the same as if we assume all candidates are true planets. This upper-bound case is further explored in Appendix B. We do not attempt to differentiate the false-positive rates between multi- and single-planet systems. We present our calculated false-positive rates in Table 2.

We adopt a false-positive rate of 0% for TIC 434398831.01 and TIC 434398831.02, which are presented in this work. These are characterized as confirmed planets as space- and ground-based follow up have ruled out any false-positive scenarios (see Appendix C).

We perform a series of checks to illustrate our false-positive rate assumptions do not significantly influence our derived occurrence rates (see Appendix B).

We identify nine planets or planet candidates that are not included in our occurrence rate calculations. These are presented in Table 2. HIP 67522 b (10.1 R_⊕; Rizzuto et al. 2020), HD 114082 (single transit, 11.2 R_⊕; Zakhozhay et al. 2022), and TOI-6550.01 (14.1 R_⊕, P = 20.3 days) were recovered in both our SPOC and QLP pipelines, but are not included in our occurrence rate calculations as they fall outside the bounds our survey investigates. We note that TOI-2519.01 (QLP only) and TOI-4596.01 (SPOC and QLP), which we recover in our survey, both show no Li features in ground-based follow-up observations. Upon visual inspection, their respective light curves are also not consistent with youth. We therefore exclude them from our occurrence rate calculations as they are likely not members of their respective clusters. TOI-4596 has an additional single transit event, but we are unable to constrain the period.

TOI-6555.01 is excluded as our vetting processes did not find it to be consistent with being on target. Additionally, TOI-6555.01 was not alerted until Sector 65, which was not made available until after 2023 February.

We identify two new additional candidates, TIC 36332984.01 and TIC 238395674.01, which both pass all of our initial vetting procedures, but we are unable to uniquely determine the orbital periods. TIC 238395674 is likely a multiplanet system, where we observe two transits of TIC 238395674.01 and an additional single transit of TIC 238395674.02. Therefore we do not include these candidates in our occurrence rate calculations.

Additionally, TOI-6715, previously identified as PATHOS 31 (Nardiello et al. 2020), has both QLP and SPOC data. However, as of 2023 February only the QLP data were available, therefore we only include TOI-6715 in our QLP occurrence rate calculations, but not in our SPOC occurrence rate calculations.

We identified seven TOIs that failed our own vetting process but were identified as TOIs by QLP and/or SPOC Transiting Planet Search. These TOIs are presented in Table 2.

Follow-up observations by the TFOP WGs rule five as nearby planet candidates, meaning the signal triggering the TCE is from a planet transiting a nearby star, or ambiguous planet candidates. TFOP WG SG2 identified the remaining two as a NEB and an EB respectively.

We perform a forward modeling test to compare the demographics of planets around young stars against that of the Kepler distribution. We synthesize a population of planets using the Kepler statistics as presented in Kunimoto & Matthews (2020) and compute the expected number of recovered planets as per our survey efficiency. The forward modeling process allows us to compare the expected characteristics of the planet population against those that we identify from the young stellar sample.

We adopt the Kunimoto & Matthews (2020) Kepler occurrence rates for F, G, and K stars. We draw the occurrence rates assuming half-Gaussians based on the asymmetric uncertainties in Kunimoto & Matthews (2020) for each of the simulations. For each star in our parent sample, we simulate a planetary system based on its Kepler period–radius planet frequency grid for its specific stellar type. ¹³ The planets are first randomly assigned into a period–radius cell based on the two-dimensional cumulative probability. Then, their period and radius are drawn within the cell assuming log-uniform distributions in both axes. We then account for transit probability and detection probability as per the injection and recovery exercise described in Section 5. For each planet, the transit probability is calculated as 0.8 × R_⋆/a, as we reject near-grazing candidates with impact parameters of b > 0.8 due to their difficulty for confirmation. Detection probability is computed as the percentage of recovered planets within a single period–radius bin as shown in Figure 6 from our injection and recovery exercise. This forward modeling process is performed 100 times each for the QLP and SPOC samples to quantify its associated uncertainties. The resulting comparison between the expected population and that identified from the TESS sample is presented in Figure 7.

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We compare the predicted planet yield from the forward modeling to the detected sample further in Section 6.3. The forward modeling comparison accounts for intrinsic differences in occurrence rates due to the differing host star populations sampled by the QLP and SPOC samples from TESS and the Kepler sample. Such differences, such as that of SPOC preferentially sampling later-type stars, may contribute to an intrinsic shift in the planet occurrence rates compared to that from the Kepler sample, as well as a difference in the measured occurrence rates between the two TESS subsamples.

We use a population Monte Carlo approximate Bayesian computation (ABC-PMC; Beaumont et al. 2009) method to estimate the occurrence rates of young planets. We use the ABC-PMC algorithm implemented in the python sampler cosmoabc (Ishida et al. 2015), described in Kunimoto & Matthews (2020), which requires three elements:

• 1.  
  a prior probability distribution, where we adopt the per-bin polynomial distribution as implemented in Kunimoto & Matthews (2020),
• 2.  
  a forward modeled population, used to generate a simulated set of data to compare to observations, and
• 3.  
  a distance function, used to determine the consensus between the simulated data and the observations.

We use the prior probability distribution described in Kunimoto & Matthews (2020) and modify their forward modeling method and distance function to accurately represent the characteristics of the TESS data, rather than Kepler data. Typically, in Kepler occurrence studies, the recoverability of transit signals is computed by a function dependent on their estimated S/Ns based on injection and recovery experiments (e.g., Christiansen et al. 2015). In our study, we also require recoverability to be a function of the host star spectral type, such that the differences in stellar variability and transit duration are accounted for. This approach is also computationally more efficient compared to the per-star recovery map method detailed in our Section 6.1. We use one realization of an ABC-PMC run to test that the S/N recovery curve approach yields similar occurrence rates compared to the per-star recovery map approach and use the recovery curves for the final occurrence rate results presented in Section 7.

We follow Kovács et al. (2002) to derive the expected S/N of an injected transit signal for the SPOC observations. We adopt a similar S/N calculation for the QLP light curves, modified to account for its varying cadences (30 and 10 minutes), ¹⁴ and we modify the calculation as follows.

For each injected planet with transit depth δ, we split the light curves of the star into two segments with the same cadence, and estimate the number of transits, ${N}_{{tr},i}$, and the average number of points in transit, N_in,i for each segment. The expected S/N is then expressed as:

$$\begin{eqnarray}&&{\rm{S}}/{{\rm{N}}}_{\star }=\delta \sqrt{\displaystyle \sum _{i}\displaystyle \frac{{N}_{{tr},i}{N}_{{in},i}}{{\sigma }_{i}^{2}}},\end{eqnarray} \tag{ 1 }$$

where σ_i is the per-point noise level, and is calculated as 1.48× the median average deviation of the light curve.

Figure 8 shows our computed recoverability as a function of S/N by stellar type in the QLP and SPOC survey. Our recoverability for both surveys plateaus at ∼80%.

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In addition, we adopt a distance function similar to Kunimoto & Matthews (2020) Equation (21) but require the computation to be done over the radius, period, and stellar-type bins, rather than just radius and period. This allows us to account for the differences in stellar types in our parent stellar samples.

Following Hsu et al. (2019) and Kunimoto & Matthews (2020), we first fit for the occurrence rates over a fine period–radius grid. We break the period–radius space into bins between periods of 0.78, 1.56, 3.125, 6.25, 12.5, and 20 days and radii of 0.5, 0.71, 1.41, 2.0, 2.83, 4.0, 5.66, 8.0, 11.31, and 16 R_⊕. For each period–radius cell, the occurrence rate is obtained from fitting five radius bins (two on each side in radius dimension) simultaneously. The edge radius bins (0.5–1.41 R_⊕ and 8–16 R_⊕) are then excluded from the reported occurrence rates. These finer-resolution occurrence rate values are then combined into the final occurrence rates we report in larger cells in Section 7.

To account for the radius uncertainty of each planet and false-positive probability of the unconfirmed planet candidates in our sample, we perform multiple realizations of the occurrence rate calculations. At each realization, the radius of each planet is drawn from a Gaussian distribution about their fitted mean and standard deviation values. Each unconfirmed planet candidate is included, or excluded, based on a random draw as per their false-positive probability (see Section 4.4). 10 realizations of the SPOC and QLP samples are performed, with their resulting posteriors concatenated to attain the final occurrence rate posterior distribution, such that the uncertainties associated with planet radius and false-positive rate are incorporated into our reported occurrence rates.

Additionally, we account for the possibility of stars falsely identified as members of kinematically young comoving groups in our parent stellar population. Our survey uses catalogs collated from Gaia kinematic associations described in Gagné et al. (2018), Kounkel & Covey (2019), Ujjwal et al. (2020), and Moranta et al. (2022). Our analysis of the rotational variability of the stars in our parent sample indicates 10%–30% of the stellar population does not exhibit rotational variations consistent with the literature ages. To incorporate this uncertainty in our parent stellar population, we randomly sample 70%–90% of the parent stellar population in each of our 10 realizations to estimate our occurrence rates. Each of the identified planet candidates and confirmed planets shows signs of variability consistent with literature ages; as such we do not resample the planet population.

Due to our visual vetting process, we induce nonreproducible biases, especially near the detection limit, as signals induced by smaller planets are more challenging to identify by eye. This would manifest as an underrepresentation of the derived occurrence rates for small planets. In this work, we do not correct our completeness maps to account for the possibility of planets being mislabeled as false positives or false alarms in our vetting process. We therefore do not attempt to derive an occurrence rate for the 1–2 R_⊕ bin, which would be most heavily impacted by this bias.

We find general agreement between the forward modeling results and the occurrence rate calculations. The results from our forward model exercises are presented in Figure 7.

Comparing bulk planet occurrence rates between different host star populations can be made difficult by the numerous factors on which planet frequencies depend. A number of works have demonstrated that the occurrence rate of small planets depends strongly on spectral type (e.g., Kunimoto & Matthews 2020). The forward modeling approach accounts for spectral type dependencies of the host population.

The forward modeled planet yield agrees well with that recovered from the young planet population for mini-Neptunes, and for short-period (1.6–6.2 days) planets. This agreement is also reflected in the occurrence rate results, where the differences between our survey results and those from the Kepler sample differ by <2σ. We find an excess of super-Neptunes, and planets at longer period orbits compared to that expected from the forward model, resulting in a noteably higher occurrence rate for these subpopulations as discussed in Section 7.1.

The derived occurrence rates for our SPOC and QLP samples are presented in Figure 9. There exist differences between the QLP and SPOC samples at the 1–1.5σ level. We find a generally lower planet occurrence rate in the QLP sample compared to the SPOC sample. The small planet and parent stellar population sample size makes it difficult to interpret the validity of this difference.

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Figure 2 shows the QLP parent sample is skewed toward earlier-type stars. Kunimoto & Matthews (2020) find K dwarfs to host 2–3× more planets in the 2–8 R_⊕ range compared to F dwarfs. The potential differences in the QLP and SPOC occurrence rates highlight the difficulty in a direct interpretation of planet frequency results without also accounting for the bulk parent stellar type. If such stellar-type dependencies are validated, it points to the paucity of small planets around F stars being developed early in their evolutionary history, as expected due to the differing levels of irradiation received by these planets around early-type stars.

Target stars selected as a part of the initial TESS mission and TESS Guest Investigator Programs to have their light curves sampled at 2 minute cadences may bias the derived SPOC occurrence rate. These young stars may have been known to host planets (i.e., V1298 Tau) or have been identified as planet candidate hosts in the FFIs subsequently receiving SPOC observations during the extended TESS mission, resulting in an overall higher occurrence rate compared to the QLP sample. Further, the SPOC sample favors later-type stars, which are known to have higher occurrence rates (e.g., Kunimoto & Matthews 2020).

It is also likely the contamination rate for cluster membership of the parent population is different for QLP and SPOC. The low occurrence rate of planets in the QLP sample is more consistent with that of the mature planet population. To investigate the impact of our false-positive rate for cluster membership on the derived occurrence rates, we repeat our occurrence rate calculations as described in Section 6 without resampling the parent stellar population for the 10%–30% assumed contamination rate. Using the full stellar population observed by SPOC, we derive an occurrence rate of ${28}_{-8.5}^{+11}$% for mini-Neptunes and ${25}_{-7}^{+8.6}$% for super-Neptunes. For the full QLP population, we calculate an occurrence rate of ${17}_{-5.0}^{+6.4} \%$ for mini-Neptunes and ${8}_{-2.3}^{+2.9} \%$ for super-Neptunes. The excess of super-Neptunes is still prevalent in these calculations, indicating that the uncertainties on our occurrence rates (see Section 7.1) are derived from the small planet number statistics rather than the membership contamination rate of our parent sample. Similarly, we find the excess of Neptune-sized planets with periods of 6.2–12 days as well in the full stellar sample. We derive an occurrence rate of ${17}_{-5.6}^{+7.3}$% for the 6.2–12 day bin with the SPOC sample and ${8}_{-2.6}^{+3.5} \%$ with QLP. Secure young star membership lists may help future studies resolve the discrepancies between the derived SPOC and QLP occurrence rates.

In both the QLP and SPOC samples, we find (1) a mild excess of super-Neptunes in the young planet population and (2) a significant excess of Neptune-sized planets at ∼10 day orbital periods in the young planet population.

7.1.1. We Find a Mild Excess of Super-Neptunes Orbiting Young Stars

7.1.2. We Find a Significant Excess of ∼10 day Period Planets Around Young Stars

Mapping the distribution of young planets has the potential to disentangle otherwise degenerate modes of planet formation. Some super-Earths and Neptune-sized planets may have formed in close-in volatile- and gas-depleted regions of the protoplanet disk (e.g., Lee et al. 2014), while others may be composed of water-rich envelopes and were formed further out (e.g., Zeng et al. 2019; Luque & Pallé 2022). These different formation modes produce planets of similar bulk physical properties in the mature planet distribution. In the water-rich scenario, the planets may have formed in the outer ice-rich protoplanet disk, migrating inward to their current locations (e.g., Mordasini et al. 2009). These planets may have silicate cores, icy mantles, and steam atmospheres (e.g., Rogers & Seager 2010; Zeng et al. 2019).

In the alternate scenario, the planets may be born with a thick hydrogen–helium envelope surrounding an iron–silicate core in the volatile-depleted inner regions of the disk (e.g., Lee et al. 2014). Some of these hydrogen–helium-dominated planets may undergo runaway mass loss early in their evolution driven by boil-off (Ginzburg et al. 2016; Owen & Wu 2016), photoevaporation (Lopez & Fortney 2013; Owen & Wu 2013), and core-powered (Ginzburg et al. 2018; Gupta & Schlichting 2019) mechanisms. Owen & Schlichting (2023) suggested that a combination of these mechanisms is likely acting with timescales from ∼100 Myr to gigayears, although the details of this timeline require further study.

These different formation pathways differ most drastically early in their evolution. In particular, hydrogen–helium-dominated atmospheres are expected to experience rapid contraction within the first few hundred million to billion years of evolution (e.g., Lopez et al. 2012; Chen & Rogers 2016), while steam-dominated atmospheres experience very mild radius contraction as they cool (Lopez et al. 2012; Lopez 2017), and our young planet population should resemble that of the Kepler distribution. Furthermore, atmospheric escape mechanisms should be evident with an increased frequency of planets ≳1.8 R_⊕ around younger stars. As some of the planets have their atmospheres stripped and transition to below the radius valley, this frequency should decrease with time.

To test these predictions, we perform a forward modeling exercise using the models presented in Rogers & Owen (2021) and Rogers et al. (2023). These models consider the thermal contraction and photoevaporative mass loss for small, close-in exoplanets hosting hydrogen–helium atmospheres. We apply our forward modeling framework (Section 6.1) to a population of synthesized planets orbiting around our stellar population, to test for consistency between the observed distribution and a synthetic distribution of planets evolving through these physical processes.

For each star in the underlying SPOC and QLP stellar samples presented in Table 1, we forward model 100 planets, assuming the underlying core mass, initial atmospheric mass fraction, core composition, and orbital period distributions inferred in Rogers & Owen (2021). The synthesized planets have ages corresponding to that estimated for each respective association as listed in Table 1. We then randomly draw planets from this sample to match the Kepler occurrence rates, as done in Rogers & Owen (2021). This population therefore represents a sample of young planets orbiting around our observed stellar sample, under the photoevaporation model, which would eventually evolve to reproduce the Kepler sample of ∼5 Gyr old super-Earths and mini-Neptunes.

We compare the predicted yield to our QLP and SPOC planet yields in Figure 7. The models are in agreement at the 0.5–1.5σ level, showing the derived occurrence rates in this work are consistent with the contraction of hydrogen-dominated atmospheres undergoing photoevaporative escape (Rogers & Owen 2021). Of note, one can see that the occurrence rate of super-Neptunes in the Rogers & Owen (2021) models is increased when compared to the Kepler sample in Figure 9. This is because the young mini-Neptunes in this model host significant hydrogen–helium atmospheres that are inflated to super-Neptune sizes for ages < 200 Myr. While the results are generally inconsistent with noncontracting steam-based atmospheres (see Figure 7), we leave model comparisons of evolving hydrogen versus high mean-molecular weight (e.g., steam) atmospheres for future work.

We investigate the impact of binarity on our derived occurrence rates by repeating our occurrence rate calculations without removing high-RUWE stars. We collate our stellar parent population following Section 3. We find 8852 stars with TESS observations. Of which, 8505 were observed in the FFIs and 2243 were observed in the target pixel stamps.

The occurrence rates derived from the full sample, without attempting to filter for binarity, agree with our presented occurrence rates at the <1σ level. Similarly to the occurrence rates presented in Figure 9, we find a mild excess of super-Neptunes and a significant excess of Neptune-sized planets at orbital periods ∼ 10 days in the population without filtering for binarity. We search for transiting planets following Section 4, and characterize our pipeline completeness following Section 5. The planet sample recovered is identical to the sample presented in Table 2. We follow Section 6, and perform 10 realizations of both the QLP and SPOC occurrence rate calculations, with each realization randomly sampling 70%–90% of the stellar population to account for the membership contamination rate. See Table 3 full results.

Table 3. Calculated Occurrence Rates

Occurrence Rate Bin	This work a	Without Filtering for Binarity	Confirmed Planets only	All Planets and Planet Candidates
SPOC
Mini-Neputnes (2–4 R⊕)	${35}_{-10}^{+13}$%	${31}_{-9.4}^{+12}$% (0.25σ)	${29}_{-9.3}^{+12}$% (0.38σ)	${36}_{-9.9}^{+12}$% (0.063σ)
Super-Neputnes (4–8 R⊕)	${27}_{-8}^{+10}$%	${21}_{-6.3}^{+8.5}$% (0.51σ)	${27}_{-8.5}^{+10}$% (0σ)	${31}_{-8.9}^{+12}$% (0.29σ)
1.6–3.1 days	${4.6}_{-1.7}^{+2.3}$%	${3.6}_{-1.3}^{+1.9}$% (0.39 σ)	⋯	${4.4}_{-1.6}^{+2.2}$% (0.072σ)
3.1–6.2 days	${6.6}_{-2.4}^{+3.4}$%	${6.5}_{-2.5}^{+5}$% (0.021σ)	${5.7}_{-2}^{+2.9}$% (0.24σ)	${10}_{-3.3}^{+3.6}$% (0.75σ)
6.2–12 days	${18}_{-6.2}^{+7.8}$%	${18}_{-5.9}^{+6.7}$% (0σ)	${19}_{-6.4}^{+8.3}$% (0.098σ)	${21}_{-6.4}^{+8.4}$% (0.29σ)
12−20 days	${31}_{-11}^{+14}$%	${23}_{-8.8}^{+12}$% (0.49σ)	${29}_{-10}^{+14}$% (0.12σ)	${31}_{-11}^{+14}$% (0σ)
QLP
Mini-Neputnes (2–4 R⊕)	${22}_{-6.8}^{+8.6}$%	${18}_{-5.5}^{+7.9}$% (0.39σ)	${17}_{-5.1}^{+7.2}$% (0.51σ)	${19}_{-6.2}^{+8.1}$% (0.28σ)
Super-Neputnes (4–8 R⊕)	${13}_{-3.9}^{+4.9}$%	${9.5}_{-2.9}^{+4}$% (0.63σ)	${8.0}_{-2.3}^{+3.0}$% (0.98σ)	${10}_{-3.1}^{+4.1}$% (0.53σ)
1.6–3.1 days	${2.6}_{-1.1}^{+1.7}$%	${1.6}_{-0.61}^{+0.84}$% (0.63σ)	⋯	${2.0}_{-0.7}^{+1.1}$% (0.36σ)
3.1–6.2 days	${3.7}_{-1.3}^{+1.8}$%	${3.9}_{-1.3}^{+1.8}$% (0.090σ)	${2.8}_{-1}^{+1.3}$% (0.47σ)	${3.5}_{-1.3}^{+2}$% (0.088σ)
6.2–12 days	${9.9}_{-3.3}^{+4.3}$%	${7.8}_{-2.7}^{+3.8}$% (0.42σ)	${7.3}_{-2.6}^{+3.4}$% (0.53σ)	${8.6}_{-2.8}^{+3.7}$% (0.26σ)
12–20 days	${19}_{-6.8}^{+9}$%	${14}_{-5.5}^{+7.6}$% (0.49σ)	${13}_{-4.8}^{+6.9}$% (0.61σ)	${15}_{-5.6}^{+7.7}$% (0.39σ)

Note.

^a Sigma differences are computed against this column. These values are the same as presented in Figure 9.

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To investigate the degree to which our adopted false-positive rate assumptions via TRICERATOPS impact our derived occurrence rates, we explore the bounding cases where (a) all planet candidates are counted as confirmed planets and (b) only verified/published planets are included in our occurrence rate calculation and all planet candidates are treated as false alarms. We calculate the occurrence rates following Section 6.

In both bounding cases, we find that the main conclusions presented in Section 7 are also present: a mild excess of super-Neptunes and a significant excess of planet with orbital periods ∼ 10 days when compared to the Kepler statistics. Our full results are presented in Table 3.

TIC 150070085 was observed by TESS in Sectors 20 and 47, receiving both 2 minute target pixel stamps and FFI observations. TIC 150070085.01 was identified in both our SPOC and QLP planet search with a signal-to-pink noise ratio of 8.2 and 9.5 respectively. Our vetting diagnostic figure for TIC 150070085.01 is shown in Figure 10. We utilize the 2 minute cadence observations for our global model.

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TIC 150070085 (T_eff = 6070 ± 146 K) is located in the Theia 214 moving group. We use our derived age to inform our model by constraining the stellar age. Our global best-fit model for the TIC 150070085 system finds R_P = 3.64 ± 0.41 R_⊕, t₀ = 2458843.8908 ± 0.0041 BJD, P = 10.4745 ± 0.0036 days, and t_dur = 0.1466 ± 0.0031 days. The stellar rotation period, P_rot = 3.0 days, calculated from the QLP light curves shows the rotational spread for Theia 214 is consistent with the literature age ∼ 100 Myr.

TIC 88785435 was observed by TESS in Sectors 11 and 38 in the FFIs. TIC 88785435.01 was identified in our QLP planet search with a signal-to-pink noise ratio of 9.47. Figure 11 shows our vetting diagnostic figure for TIC 88785435.01.

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TIC 88785435 (T_eff = 4000 ± 150 K) is located in the UCL/LCC moving group. We use our derived age to inform our model by constraining the stellar age. Our global best-fit model for the TIC 88785435 system finds R_P = 4.88 ± 0.28 R_⊕, t₀ = 2458609.2308 ± 0.0036 BJD, P = 10.508907 ± 0.000035 days, and t_dur = 0.1466 ± 0.0031 days. The stellar rotation period, P_rot = 8.6 days, is calculated from the QLP light curves, consistent with the literature age of UCL/LCC.

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TIC 434398831 (S. Vach et al. 2024, in preparation) received FFI observations over TESS Sectors 6, 33, 43, 44, and 45. Our planet search identifies two planet candidates, TIC 434398831.01 (signal-to-pink noise ratio of 11.8) and TIC 434398831.02 (signal-to-pink noise ratio of 15.7). Our best-fit parameters for TIC 434398831.01 are R_P = 3.65 ± 0.28 R_⊕, P = 3.68551266 ± 0.000019 days, t₀ = 2458468.6318 ± 0.0052 BJD, and t_dur = 0.1061 ± 0.0014 days, and for TIC 434398831.02 they are R_P = 5.41 ± 0.32 R_⊕ P = 6.210377 ± 0.000017 days, t₀ = 2458470.6110 ± 0.0027 BJD, and t_dur = 0.1289 ± 0.010 days. Figure 12 shows our vetting diagnostic plots for TIC 434398831.01 and 02.

The host star TIC 434398831 is on the premain sequence, with an effective temperature of T_eff = 5554 ± 144 K. Previous works place TIC 434398831 in the Theia 116 moving group. We measure the stellar rotation period, P_rot = 2.0 days, using the FFI light curves. After analyzing the members of Theia 116, we find the rotational spread to be consistent with ∼50 Myr, agreeing with the isochrone-derived age.

Three transits of TIC 434398831.01 and two transits of TIC 434398831.02 have been observed by ESA's CHEOPS mission (AO-4 program PR230002). Paired with extensive LCO ground-based follow up of TIC 434398831.01 and TIC 434398831.02, we were able to clear the field of NEBs and rule out any false-positive scenarios. Therefore, we classify TIC 434398831.01 and TIC 4343988310.02 as confirmed planets in our occurrence rate calculations and adopt false-positive rates of zero for both (see Table 2).