A Revised Exoplanet Yield from the Transiting Exoplanet Survey Satellite (TESS)

The first step was made relatively straightforward by the availability of the CTL—a prioritized list of target stars that the TESS Target Selection Working Group has determined represent the stars most suitable for detection of small planets by TESS. The properties of about 500 million stars were assembled in the TIC (Stassun et al. 2017), and the CTL includes several million of those stars that are most suitable for small transit detection. We used CTL version 6.1,⁴ which includes 3.8 million stars with properties such as stellar radii, masses, distances, and apparent brightness in various bandpasses. The CTL stars were then ranked using a simple metric based on stellar brightness and radius, along with the degree of blending and flux contamination (especially important given the large TESS pixels). The CTL does not include all stars. Save for stars on specially curated target lists (e.g., Muirhead et al. 2018), stars with reduced proper motions (RPMs) that indicate they are red giants (Collier Cameron et al. 2007), stars with a temperature below 5500 K and a TESS magnitude fainter than 12, or stars with temperature above 5500 K and a TESS magnitude fainter than 13 are excluded from the CTL. Such broad cuts were required in order to assemble a small enough population of stars to practically manage.

We then determined which of these stars are likely to be observed by the mission. We used tvguide (Mukai & Barclay 2017) on each star to determine whether and for how long it is observable with TESS. We arbitrarily selected a central ecliptic longitude for the first sector of 277°, which equates to an antisolar date of June 28 (the precise timing of the first sector is dependent on commissioning duration). Until we have on-orbit measurements of focal plane geometry, tvguide assumes that the cameras are uniform square detectors projected on the sky, placed precisely 24° apart in ecliptic latitude and with identical ecliptic longitude. Gaps between CCDs are assumed to be 025. We ended up with a total of 3.18 million individual stars on silicon.

We also needed to simulate which of these stars are likely to be observed at 2-minute cadence and ensure compliance with the TESS mission requirement that states that over the 2 yr mission more than 200,000 total stars should be targeted, and 10,000 stars should be observed for at least 120 days. It is somewhat less trivial than one would initially assume to simulate this requirement because we could not simply select the top 200,000 stars with the highest priority in the CTL because this would place far too many stars in the CVZ than can actually be observed there at 2-minute cadence. To ensure a realistic distribution of targets, we first divided each ecliptic hemisphere into 15 sections: a polar section with everything within 13° of the pole, representing stars that primarily fall into Camera 4; an ecliptic section including everything within 6° of the ecliptic to represent stars that are not observed in the prime mission; and then the remaining area was divided longitudinally into 13 northern and 13 southern adjacent sections, representing stars observable with Cameras 1–3 in Sectors 1–26. This yielded a total of 28 sections of the sky with observable stars.

A star that fell in a camera overlap region is observed in multiple sectors but only represented one unique target. We found that we could make a reasonable approximation to satisfy the requirements of 200,000 unique targets if in each polar section we selected the 6000 stars in that region with the highest priority in the CTL, and then for each longitudinal section (representing the footprint of Cameras 1–3 in each sector) we selected the 8,200 highest-priority stars in each of the regions. After removing stars that fall into CCD and camera gaps, this yielded 214,000 unique stars. We assumed that any star in an overlap region is observed in every possible sector. Figure 2 shows the breakdown of how many targets are observed in each sector.

While the CTL includes a great deal of curation, it is not infallible. A particular weakness inherent to stellar catalogs based on photometric colors is in distinguishing between dwarf stars and subgiants (Huber et al. 2014; Mathur et al. 2017). CTL versions up through 6.2 use parallax information when available to determine stellar radii (and therefore luminosity class), but the vast majority of stars depend on the use of RPM cuts to distinguish dwarfs from giants. While GAIA DR2 will shortly provide reliable parallaxes for most CTL stars (Davenport 2017; Huber et al. 2017; Stassun et al. 2018), the CTL will not be significantly modified until 2019. Furthermore, while the RPM method is highly reliable at distinguishing dwarfs and subgiants as a group from giant stars, it is generally not useful for distinguishing dwarfs from subgiants. Of the CTL stars that are classified as dwarfs based on the RPM cut, about 40% are actually subgiants, although roughly 35% of the CTL stars have parallax measurements confirming their spectral class. To account for this effect, we simulated a misclassified population of subgiants by increasing the stellar radius of 40% of those AFGK stars that had been selected with the RPM cut by a factor of 2, with the affected stars drawn at random. That included 25% of all the AFGK stars in the CTL. This approach somewhat overestimates the radii of A-type subgiants, but the effect on total planet yield is limited, because A-type stars have large radii, making detecting transiting planets challenging, and thus are already a relatively small fraction of the high-priority CTL stars.

To each star in our list we assigned zero or more planets. The number of planets assigned to each star was drawn from a Poisson distribution. The mean (referred to here as λ) of the Poisson distribution we used differs between AFGK dwarf stars and M dwarfs because there is strong evidence that M dwarfs host more planets on short orbital periods (Burke et al. 2015; Mulders et al. 2015). For AFGK stars we used the average number of planets per star with orbital periods of up to 85 days of λ = 0.689 (Fressin et al. 2013), while for M stars λ = 2.5 planets are reported with orbital periods up to 200 days (Dressing & Charbonneau 2015).

Each planet was then assigned six physical properties drawn at random: an orbital period (P), a radius (R_p), an eccentricity, a periastron angle, an inclination to our line of sight (i), and a midtime of first transit. The orbital period and radius were selected using the exoplanet occurrence rate estimate of Fressin et al. (2013) for AFGK stars and Dressing & Charbonneau (2015) for M stars. Both Fressin et al. (2013) and Dressing & Charbonneau (2015) reported occurrence rates in period/radius bins. We drew at random from each of these bins with the probability to draw from a given bin weighted by the occurrence rate in that bin divided by the total occurrence rate of planets. For example, Dressing & Charbonneau (2015) reported a 4.3% occurrence rate for planets with radii 1.25–2.0 R_⊕ and orbital period 10–17 days, so in our simulation we drew planets from that bin with a frequency of 4.3 divided by the total occurrence rate in all bins. We normalized by the total occurrence rate of planets since we already took account of systems with zero or multiple planets in the Poisson draw. Once we knew which bin to select a planet from, we drew from a uniform distribution over the bin area to select an orbital period–radius pair, except for the giant-planet bin where we draw from a power-law distribution in planet radius with exponent −1.7, which mirrors Sullivan et al. (2015). This nonuniform giant-planet size distribution reduces the number of nonphysical inflated planets, as discussed by Mayorga & Thorngren (2018). Occurrence rates from both Fressin et al. (2013) and Dressing & Charbonneau (2015) are based on Kepler data and are limited in orbital period to 0.5–85 days and 0.5–200 days, respectively.

Following Kipping (2014), the orbital eccentricity was selected from a Beta distribution, with parameters α = 1.03 and β = 13.6, which Van Eylen & Albrecht (2015) found were appropriate for transiting planets. The periastron angle was drawn from a uniform distribution between −π and +π. The cosine of inclination was chosen to be uniform between zero and one. Planets in multiple-planet systems were assumed to be coplanar—i.e., they have the same $\cos i$—which is a reasonable assumption because multiple-exoplanet systems have been found to be highly coplanar (Xie et al. 2016). Finally, we chose a time of first transit to be uniform between zero and the orbital period—note that this may be greater than the total observation duration, in which case no transit was recorded. We then computed the number of transits observed using the observation duration calculated previously (the number of sectors where a target is observed).

We intentionally kept planets that cross the orbit of other planets in the system because, while they are likely on unphysical orbits, to remove them would change the distribution of the number of planets per star, which is an observed property. We also assumed that none of these planets experience a significant amount of transit timing variations (S. Hadden et al. 2018, in preparation, address transit timing variations and period ratios in detail).

Armed with a sample of planets and host stars, we then determined which planets are detectable. To do this, we derived a transit depth modified by several factors: the flux contamination of nearby stars, the number of transits, and the transit duration. It should be noted that flux contamination is significantly more problematic for TESS than with Kepler because TESS has pixels that are 28 times larger than Kepler's.

The raw transit depth was computed assuming a uniform disk (i.e., transit depth ${T}_{d}={({R}_{p}/{R}_{\star })}^{2}$, where R_⋆ is the stellar radius). That is, we ignored the effects of limb darkening and grazing transits. We calculated the reduction in transit depth due to dilution from nearby stars using the value of contamination for the CTL as T_d/(1+d), where d is the dilution, the fraction of light coming from stars that are not the target divided by the total star light. We then multiplied the transit depth by the square root of the transit duration (T_dur) in hours, with transit duration following Winn (2010) defined as

$$\begin{eqnarray}&&{T}_{\mathrm{dur}}=\displaystyle \frac{P}{\pi }\arcsin \left[\displaystyle \frac{{R}_{\star }}{a}\displaystyle \frac{\sqrt{(1+{R}_{p}/{R}_{\star })-{b}^{2}}}{\sqrt{1-{\cos }^{2}i}}\right],\end{eqnarray} \tag{ 1 }$$

where P is the orbital period, i is the orbital inclination relative to our line of sight, a/R_⋆ is the semimajor axis in units of stellar radius, b is the impact parameter, and R_p/R_⋆ is the planet-to-star radius ratio, to derive an effective transit depth. The effective transit depth, T_d', is defined as

$$\begin{eqnarray}&&{T}_{d}^{{\prime} }={({R}_{p}/{R}_{\star })}^{2}\times \sqrt{{T}_{\mathrm{dur}}}\times \sqrt{N}\times \displaystyle \frac{1}{1+d},\end{eqnarray} \tag{ 2 }$$

where N is the number of transits observed.

We took the TESS photometric noise level from Stassun et al. (2017), who used the properties described by Ricker et al. (2016) and tested whether the effective transit depth was greater than the TESS photometric noise at the stellar brightness of the host stars multiplied by 7.3 (i.e., signal-to-noise ratio [S/N] ≥ 7.3). A 7.3σ detection is the nominal value used by Sullivan et al. (2015) and is calculated in a similar manner to the detection threshold used by Kepler (Jenkins et al. 2010). We also required that the impact parameter of the transit is less than 1.0 and that we observed at least two transits. Requiring an impact parameter of less than 1 removes a small number of grazing transits, but these are difficult to distinguish from eclipsing binaries anyway (Armstrong et al. 2017). These detection thresholds are relatively aggressive; Section 4.2 describes using more conservative detection thresholds of at least three transits and S/N of 10.

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For the TESS mission to be successful, it must find planets smaller than 4 R_⊕ with a measurable RV signal. We predict that TESS will find more than 2100 planets smaller than 4 R_⊕, but many of these will orbit stars whose brightness makes follow-up challenging or impossible with current-precision RV facilities. While planets orbiting very faint stars have had their mass determined via RV studies (e.g., Koppenhoefer et al. 2013), it is typically challenging to measure masses of planets around stars fainter than V = 12. We predict that TESS will find 1300 planets smaller than 4 R_⊕ around stars brighter than V = 12. Therefore, with more than 1000 potential targets, TESS will have a plethora of targets to choose from when selecting promising RV targets. Even if just 20% are good RV targets, this will more than triple the number of planets smaller than 4 R_⊕ with measured masses.

There are 160 planets in our sample that are smaller than 2 R_⊕ and orbit stars brighter than V = 12. We currently have mass and radius constraints on fewer than 60 planets smaller than 2 R_⊕, so TESS will potentially greatly increase this number, although the precise number will depend on whether individual stars are suitable for precise RV measurements.

A second aim of the TESS mission is to find targets suitable for transmission spectroscopy using JWST. Until on-sky performance is measured, particularly the systematic noise level, there is considerable uncertainty on how JWST will perform (Batalha et al. 2017). However, we can identify the properties of planets that would make them good JWST targets using a few simple cuts. The host star should be bright in the infrared, and the star should be small. We identified simulated planets whose host stars have K_s < 10, T_eff < 3410 K, which equates to M3V stars with a radius of approximately 0.37 solar radii (Pecaut & Mamajek 2013). In total, there were 70 planets fulfilling these criteria. We show in Figure 11 the simulated small planets we think make interesting candidate JWST targets in terms of insolation fluxes. There are 10 planets in the boxed region in Figure 11, which highlights planets that fell into the optimistic habitable zone (Kopparapu et al. 2013) and had radii between 1.25 and 2.5 R_⊕, implying a puffed-up atmosphere (Lopez & Fortney 2014). These planets, along with those orbiting TRAPPIST-1 (Gillon et al. 2017) and other low-mass stars (Greene et al. 2016; Kreidberg & Loeb 2016; Morley et al. 2017; Louie et al. 2018), will form a reference sample of temperate worlds for observation by JWST.

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The JWST CVZ is located within 5° of the ecliptic poles and is contained within the TESS CVZ, shown in Figure 1. However, because of gaps between the TESS CCDs on Camera 4 (each camera is composed of a 2 × 2 grid of CCDs), the central 2° has limited coverage. In our sample we have 74 planets with ecliptic latitude $| b| \gt 85^\circ$, of which 29 are 2-minute cadence targets and 11 are smaller than 2 R_⊕.

In addition to the nominal 2-minute cadence target selection laid out in Section 2.1, we also considered alternative strategies of selecting a higher or lower fraction of targets in the CVZ, which we call scenarios (a) and (b), respectively. There are justifications for both approaches. Placing more of the 2-minute cadence targets in the CVZ increases the overall number of 2-minute targets where TESS is sensitive to long-period planets, and potentially to smaller planets via increased S/N. On the other hand, placing more of the 2-minute targets outside the CVZ should increase the overall number of planets detected, since 13 stars can be observed in regions with single-sector coverage for each target in the CVZ.

To test these scenarios, we selected targets in an identical manner to that described in Section 2.1, except that in scenario (a) we included 12,000 stars in the CVZ and 2200 stars in the other cameras per sector, while in scenario (b) we select 3000 CVZ targets and 11,200 stars in the remaining cameras.

Under these two different selection strategies, we examined the number of planets found in 2-minute cadence data, compared to our nominal selection strategy. In scenario (a) we found a total of 740 ± 50 planets, and in scenario (b) we found 1380 ± 60 planets, which compares with 1250 ± 70 planets in the nominal strategy (where the reported value is the median, and uncertainties are the central 90% of the distribution, calculated by 300 Monte Carlo simulations). These results suggest that the nominal selection strategy was reasonably successful at accomplishing the goal of maximizing the number of planets with 2-minute cadence photometry, which in turn maximizes the number of planets where we can derive precise stellar parameters through asteroseismology (Campante et al. 2016). Scenario (b) yielded 10% more planets, but the results were comparable within uncertainties, and the number of planets with orbital periods beyond 15 days was cut by about 10% in scenario (b). Scenario (a) extended the tail of the orbital period distribution—the 95th percentile shifts from 30 to 42 days—but because of the large decrease in the total number of planets, the absolute number of long-period planets was unchanged.

In each scenario the total number of planets detected remained unchanged because almost all planets could be found equally well in 2-minute cadence and FFI data, so the precise stellar selection had limited impact on the primary mission goals.

Our analysis so far has made two fairly optimistic assumptions: (1) that we can identify a transiting planet by observing just two transits from TESS, and (2) that we can detect all planets with an S/N ≥ 7.3. In actuality, planets with fewer than three observed transits are very difficult to uniquely identify using photometric survey data alone (see Mullally et al. 2018; Thompson et al. 2018). Planets have been detected using K2 mission data (Howell et al. 2014) with one (Vanderburg et al. 2015) and two (Crossfield et al. 2015) transits, but these cases occurred in systems where additional space-based follow-up assets were exploited or there were two other planets in the system, so the validity of the planets was less ambiguous (Lissauer et al. 2012). While with sufficient observing resources characterizing these planets is feasible, they remain a challenge. Furthermore, analyses of Kepler data have shown that using a detection threshold below 8σ–10σ leads to many spurious detections (Christiansen et al. 2016; Mullally et al. 2018; Thompson et al. 2018). In K2, a threshold of S/N > 12 was typically applied (Crossfield et al. 2016) before expending follow-up resources on a candidate planet.

With these limits in mind, we took the fiducial catalog and cut planets that either had fewer than three transits or had a combined transit S/N < 10. This resulted in a moderate cut in the total number of planets found to 2609 total planets, of which 820 came from the 2-minute cadence data. This was a 60% overall decrease in the total number of planets detected, but it was most significant for small planets. The number of planets with radii below 2 R_⊕ decreased by a factor of two from 279 to 128 planets, with similar fractional losses in the 2–4 R_⊕ bin, but there was only a 25% decrease in detected giant planets. Figure 12 shows the size distribution of planets found under the conservative detection model.

The decrease in the number of planets amenable to RV follow-up was roughly a factor of two, with planets smaller than 4 R_⊕ orbiting stars with V < 12 dropping from 1312 to 616, and those smaller than 2 R_⊕ from 151 to 67. The number of habitable zone planets dropped from 69 to 28 and left just four smaller than 2 R_⊕. The number of premium JWST targets sees a modest decrease. The number of planets orbiting stars cooler than 3410 K, with K_s < 10, drops from 71 to 58, and the number in the dashed box in Figure 11 dropped from 10 to 7. While these drops were significant, they are unlikely to seriously impact the primary mission goal, because there were still hundreds of small planets orbiting bright stars in the sample.

This study and other planet yield simulations (e.g., Sullivan et al. 2015) have not paid particular attention to the physical properties of giant planets, primarily because these are not a focus for the TESS mission team. Nevertheless, we are anticipating groundbreaking scientific advances in our understanding of the atmospheres of giant planets from follow-up observations of planets found by TESS—particularly from Spitzer, Hubble Space Telescope, and JWST. As pointed out by Mayorga & Thorngren (2018), in the first version of this paper there were significant numbers of giant planets that were beyond the limit of inflation for their equilibrium temperatures (Thorngren & Fortney 2018). The cause of this is that in the occurrence rate estimates of Fressin et al. (2013) the giant-planet bin spans 6–22 R_⊕ while temperate planets should rarely be larger than 12 R_⊕. As a result of this feedback from Mayorga & Thorngren (2018), we changed the selection function in the giant-planet bins from a lognormal function to a power law. This reduced the number of phantom planets from 8% of the total population to 1%. We caution giant-planet aficionados that there are 45 overinflated giant planets in our simulation.

The nature of the TESS orbit means that a subset of observations will be obscured by the Earth or Moon passing through the field of view. Cameras that receive a significant amount of scattered light from the Earth or Moon will experience larger background flux, and photometry in any camera that receives a large portion of direct light from the Earth or Moon will likely be impossible because of saturation and bleed. However, the Earth and Moon move relatively quickly through the field of view, and Earth or Moon crossings are relatively infrequent (Ricker et al. 2015). Bouma et al. (2017) estimated that the Earth and Moon will significantly affect photometric performance for 9% of all exposures, although the lost cadences will not be evenly distributed in time or focal plane location. Camera 1 and, to a lesser degree, Camera 2 are impacted, but the effect was expected to be limited for Cameras 3 and 4. Estimating how this affects the yield is nontrivial, but we can try by using the Bouma et al. estimates that 23% of observations in Camera 1 and 12% of observations in Camera 2 will be affected. We can then assume that the S/N of transits will scale with the square root of the number of observations, so Camera 1 targets will have 11% lower S/N, and Camera 2 targets will have 6% lower S/N. This causes a 13% drop in total planets detected in our simulation and a 9% decrease in the number of planets orbiting 2-minute cadence targets. Early commissioning results have suggested that the effect of the Moon may be more complex than anticipated, and owing to the substantial uncertainty in the impact of Earth and Moon crossings, we have not included Earth and Moon crossings in our yield statistics.

Sullivan et al. (2015) performed a careful analysis of the sources and rates of false positives expected in the TESS 2-minute cadence data, and we have not reproduced that work here. They estimated that TESS will find over 1000 astrophysical false positives in 2-minute cadence data, but they described promising mitigation strategies that utilize follow-up observations and statistical methods to reduce this by a factor of 4 or more.

The ratio of false positives to detected planets will not be uniform over all stars observed by TESS, but it will vary as a function of hit rate. In Section 3 we showed that the hit rate for 2-minute cadence targets is a factor of 5.5 higher than FFI-only stars. Assuming that each star has the same chance of yielding a detection of an astrophysical false positive, the fraction of true planets found to false positives will be lower for the FFI-only detections than for 2-minute cadence targets. The reason is that fewer planets are found per stars observed but the same number of false positives are detected. Using the false-positive rate from Sullivan et al. (2015) of 1 false positive per 180 stars observed yields one astrophysical false positive per planet detection. However, for the FFI-only targets the ratio of false positives to planets detected increases to more than five per true planet discovered.

Furthermore, stars on the CTL that are not included in our 2-minute cadence sample are, on average, 2 mag fainter than the 200,000 stars observed at 2-minute cadence. This means that mitigation strategies that rely on follow-up observations will be significantly more challenging. Given that essentially all small planets will be found in the 2-minute cadence data, only the most intrepid of exoplaneteers will want to commit significant resources to discovering and following up planets in FFI data.

In Section 2.1 we simulated planets orbiting stars that are in CTL version 6.1. This totals roughly 3.2 million stars but includes only those stars that the TESS Target Selection Working Group considered as potential 2-minute cadence targets. The limited number of slots available for 2-minute cadence requires not just a careful consideration of the overall potential for planet detections around a given star but also comparison of the relative planet detection potential between stars, along with the scientific value of the resulting planets. The CTL was constructed to permit a quantitative relative ranking of the best stars to select for the 2-minute cadence slots, not to identify all stars with detectable planets. While in this work we have adopted the set of several million stars in the CTL as the primary sample to investigate, stars not in the CTL might also yield some planet detections in the FFI data. The reason we adopted this approach is the same reason for the construction of the CTL in the first place—our analysis of planet yield among a population of several million stars is much more tractable than conducting the analysis for all 470 million stars in TIC-6.

Explicitly removed from the CTL are stars with an RPM that flags them as giants, stars with parallax or other information that flags them as giants or subgiants, dwarf stars that are somewhat hot and relatively faint but not as faint as some dwarf stars that are included, and faint dwarf stars. The magnitude cut used in the CTL is TESS magnitude of 12 for stars hotter than 5500 K and TESS magnitude of 13 for cooler stars, although faint cool dwarfs are explicitly included via a specially curated target list (Muirhead et al. 2018). The CTL therefore generally excludes hot stars, faint stars, and evolved stars, in favor of bright, cool dwarfs.

Only a handful of transiting planets have been detected around red giants (e.g., Burrows et al. 2000; Huber et al. 2013; Barclay et al. 2015; Grunblatt et al. 2016; Van Eylen et al. 2016; Grunblatt et al. 2017) because finding these planets is extremely challenging. Transit depth scales with the square of the stellar radius, so planets orbiting large stars are hard to find. Therefore, the frequency of planets orbiting giant stars is relatively poorly constrained. However, TESS will observe hundreds of thousands of red giants brighter than 11th mag in the TESS bandpass (Huber 2017) and will certainly detect planets orbiting these stars. However, Kepler observed roughly 16,000 red giants (Yu et al. 2018) and found only a handful of planets. With a factor 20 or so increase in the number of red giants from TESS, we might expect of order 100 new planets. This estimate is comparable to that of Campante et al. (2016), who performed a much more careful analysis and predicted that TESS will find roughly 50 planets orbiting red giants.

The brightness cuts applied to the TIC in creating the CTL have a larger impact on our yield estimates. At 12th mag the TESS 1 hr integrated noise level is 600 ppm. This equates to detecting a Neptune-size planet with three transits around a solar-radius star, while at 13th mag the noise is 1200 ppm, which is equivalent to a 6 R_⊕ planet. So it is certainly the case that many stars not included in the CTL may have planets detectable with TESS. To detect a Jupiter with three transits around a Sun-like star would require a maximum 1 hr integrated noise of approximately 4000 ppm, which corresponds to a TESS magnitude of 14.7. The TIC lists 16.0 million stars with temperatures above 5500 K, log g above 3.9, and TESS magnitude of 12–14.7 and 4.2 millions stars with temperature between 4000 and 5500 K, $\mathrm{log}g$ above 4.2, and brightness between 13 and 14.7 (where we cut at 4000 K because the cooler stars are included via the cool star curated list). In our fiducial sample, the frequency of detected planets larger than 4 R_⊕ was 0.069%. Assuming an equal detection rate for fainter stars in the 4+ R_⊕ bin as for brighter stars, we would expect to find 14,000 additional giant planets. Even under our conservative model, the rate is 0.050%, or 10,000 additional planets.

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While these planets will appear in the FFI data, they are not prime targets, hence their exclusion from the CTL, because the planets will be hard to detect and harder to follow up and confirm owing to their faintness and higher crowding. Using the logic described in Section 4.5, the astrophysical false-positive rate in this part of the parameter space is also very high. With a hit rate around 0.05% and a false-positive rate likely to be comparable to that found by Sullivan et al. (2015) of 1 per 180 stars observed, we expect a factor of more than 11-to-1 false-positive to true planets detected. Thus, we caution that searching for planets in this regime is fraught with challenges.

The omission of these potential host stars from our analysis leads to a large underestimate in the overall planet yield of the mission, although that is almost entirely in the giant-planet regime. In Figure 13 we show our final distribution of planet radii and include the sample of giant planets orbiting faint stars, using the conservative yield estimate. This results in a total planet yield of 14,000 transiting planets. However, as discussed, these planets will be resource intensive both to confirm and to meaningfully analyze.

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One further source of additional planets is from M dwarfs in the southern hemisphere. As mentioned in Section 2.1, there is a deficit of cool stars below −30° declination, caused primarily by the lower completion of proper-motion catalogs where Northern Hemisphere telescopes are unable to observe. This manifests in fewer planets detected around cool stars in the south. In the 2-minute cadence data, there are 2.6× as many planets orbiting stars cooler than 3900 K north of declination 30° than south of declination −30°. Including the FFI planets, this increases to 3× as many northern as southern planets (233 vs. 74 planets). With GAIA data release 2 now available, it is probable that new M dwarfs in the south will be identified. This will help to recover additional planets orbiting cool stars not identified as dwarfs in the CTL. Given that this could potentially yield new candidate planets for JWST, there is a pressing need for this work.

Sullivan et al. (2015), Bouma et al. (2017), and Ballard (2018) have previously estimated the planet yield from TESS. These previous studies selected stars from a simulated Galactic model rather than real stars, and therefore we expect that there are moderate differences between our predicted yields and previous studies. Additionally, we used different selection strategies for both 2-minute cadence targets and FFI stars. We built a realistic 2-minute cadence star selection model that limits the stars observed at the pole cameras to just 6000 stars per hemisphere, whereas the previous works assumed that TESS can observe many more stars in the CVZ than is possible with the flight hardware configuration used. We also use a different prioritization metric than previous work, which is based on the metric used by the TESS Target Selection Working Group. For the FFI targets we primarily consider those within the CTL, whereas different cuts on brightness are made in earlier works. Therefore, we expect to see significant differences in the planet yield for giant planets.

Sullivan et al. predicted 1700 planets in 2-minute cadence data, of which 560 are smaller than 2 R_⊕. Bouma et al. used the same methodology and software as Sullivan et al. but fixed a number of software bugs and modified a number of parameters. They also predicted 1700 planets from 2-minute cadence data, of which 430 were smaller than 2 R_⊕. The total 2-minute cadence planet yield in both these studies was about 30% larger than we have predicted, but the number of planets smaller than 2 R_⊕ in our study is lower by a factor of 1.7 and 2.3 than Bouma et al. and Sullivan et al. respectively. However, given the different selection strategies, it may be more reasonable to compare the combined 2-minute cadence and FFI yields. Where Bouma et al. (2017) and Sullivan et al. (2015) differ is in their star selection for FFI targets. Bouma et al. limit their selection to the top ranked 3.8 million stars using a similar priority metric to the one applied in CTL 6.1. This enables easy comparison with our 3.2 million star sample. On the other hand, Sullivan et al. (2015) consider all stars brighter than K_s = 15, totaling 150 million stars, which we can compare with our analysis in Section 4.6.

Our total simulated yield is remarkably similar to Bouma et al., with 41 versus 49 Earth-sized planets, 238 versus 390 super-Earths, 1900 versus 2000 mini-Neptunes, and 2200 versus 2500 giant planets, for this work and Bouma et al., respectively. The only area where we see a significant deviation is for super-Earths, which we attribute to differences between the Galactic model and real stars.

Compared to Sullivan et al. (2015, 2017), we predict lower totals in all bins. However, as mentioned by Bouma et al., the number of Earths and super-Earths is overestimated by around 30% owing to a bug in their calculation of the dilution from background stars. Taking this into account, our number of Earths matches both Bouma et al. and Sullivan et al., while the super-Earths are comparable. Our rate of giant planets predicted in Section 4.6 is consistent with Sullivan et al.

Ballard used the framework and detection rates of Sullivan et al. (2015) but focused entirely on M1–M4 dwarfs and made significant changes to the occurrence rates to account for covariances between planets in the same systems. In comparison, our analysis of the M dwarf population is simplistic. Ballard predicted a 50% increase in the rate of planets orbiting these cool stars compared to the occurrence rates used by Sullivan et al. (and this work). They predicted 990 ± 350 planets around M1–M4 stars, while we predicted 410 planets orbiting stars with temperatures of 3100–3800 K. If the Ballard occurrence rate has a similar impact on our yields to what it had on Sullivan et al., and given comparable yields between our studies, we would expect an additional 50% of planets in this parameter space, which is 200 more planets orbiting cool stars. Assuming that the increase is uniform in planet size, we might expect an increased yield that includes 14 additional Earths, 42 additional super-Earths, and 142 additional mini-Neptunes. The yield could be even higher if we are able to identify additional M dwarfs in the southern sky, as discussed in Section 4.6.