TESS Duotransit Candidates from the Southern Ecliptic Hemisphere

Discovering transiting exoplanets with long orbital periods allows us to study warm and cool planetary systems with temperatures similar to the planets in our own Solar system. The TESS mission has photometrically surveyed the entire Southern Ecliptic Hemisphere in Cycle 1 (August 2018 - July 2019), Cycle 3 (July 2020 - June 2021) and Cycle 5 (September 2022 - September 2023). We use the observations from Cycle 1 and Cycle 3 to search for exoplanet systems that show a single transit event in each year - which we call duotransits. The periods of these planet candidates are typically in excess of 20 days, with the lower limit determined by the duration of individual TESS observations. We find 85 duotransit candidates, which span a range of host star brightnesses between 8<$T_{mag}$<14, transit depths between 0.1 per cent and 1.8 per cent, and transit durations between 2 and 10 hours with the upper limit determined by our normalisation function. Of these candidates, 25 are already known, and 60 are new. We present these candidates along with the status of photometric and spectroscopic follow-up.


INTRODUCTION
Longer period transiting exoplanets allow us to measure the densities of warm and cool planets, assisting with studies of atmospheric composition from transit spectroscopy (e.g.Albrecht et al. 2012;Wang et al. 2021).Planetary obliquity is an indicator of planetary migration mechanisms (e.g.Albrecht et al. 2012), and long period planets are amenable to studies of the Rossiter-McLaughlin effect (e.g.Ulmer-Moll et al. 2023) to enable determination of the spin-orbit alignment of the system.When compared to short period hot Jupiter planets, the few well-studied long period planets discovered to date appear to be more aligned (Rice et al. 2022), indicating possible migration mechanisms operating within the protoplanetary disk (e.g.Madhusudhan et al. 2017).Since the launch of TESS (Transiting Exoplanet Survey Satellite; Ricker et al. 2015), a total of 3921 exoplanets have been confirmed using TESS data (NASA Exoplanet Archive; Akeson et al. 2013).Of these systems, only 56 have orbital periods longer than the typical TESS Sector time span of 27 days.
The Kepler mission (Borucki et al. 2010) monitored a single 105 square degree field for approximately four years, and was therefore able to discover long period transiting exoplanets.However, most of the host stars are fainter than the capabilities of modern spectrographs to measure planetary masses and the planets cannot be confirmed and fully characterised.Hsu et al. (2019) placed a limit on the occurrence rate of ≲0.247 planets per FGK star on orbital periods from 237-500 days.The Kepler exoplanet sample includes 42 planets with determined periods longer than 20 days with a robust mass determination from radial velocity confirmation.
The TESS spacecraft has completed surveys of the Southern Ecliptic Hemisphere on two occasions -in Cycle 1 (July 2018 to July 2019) and in Cycle 3 (July 2020 to July 2021).TESS has also re-observed the Southern Ecliptic Hemisphere in Cycle 5 (September 2022 to September 2023), but many of these observations are unavailable at the time of writing and thus are not included in this work.During these surveys a number of stars have shown a single transit (a monotransit), whereby one transit like feature is found in the lightcurve but is not seen to repeat.With only one transit we are not able to determine the orbital period of the planet, although with prior knowledge of the star we can calculate the probability distribution for the orbital period, e.g.Osborn et al. (2022a).A small number of these TESS monotransit candidates have been confirmed, e.g.Gill et al. (2020a,c) and Lendl et al. (2020a).
In addition to the TESS monotransit candidates, there exist candidates that transit exactly once in Cycle 1 and once in Cycle 3.These candidates are biennial duotransits, as opposed to candidates that may have two transits in a single TESS cycle.For the remainder of this paper we use the term duotransit to refer only to such biennial duotransits.These duotransits confer two main advantages over monotransit candidates.Firstly, the true period of a duotransit candidate is limited to a discrete set of possible periods,   , given by where Δ is the time difference between the Cycle 1 and the Cycle 3 transit event and  is a whole number ranging from n=1 for the longest possible period to   for the shortest possible period.Since the duration of a TESS sector is ≈27 days, we find    is typically in the region of 20 days unless there is more than one Sector of data in the TESS Cycle 1 or Cycle 3 observations.The limited set of possible periods means it is possible to check specific orbital periods via photometric monitoring of the duotransit candidate at specific times.This is much more efficient than the continuous monitoring required to find the periods of monotransit candidates.Secondly, duotransits are more robust against false positive signals.We can check that the two transit signals for a duotransit candidate match in depth, total duration, ingress and egress duration, limb darkening parameters, and impact parameter.By contrast, we are far less certain that a single monotransit event is not caused by some systematic or non-planetary astrophysical event.Cooke et al. (2018) predicted that hundreds of long-period planets would be detectable as monotransit events in the TESS sample, with similar results found by Villanueva et al. (2019).Furthermore, Cooke et al. (2021) found that many of these will have a second detectable transit in Cycle 3 of TESS data, making the true orbital period one of an average of 38 period aliases.
Both mono-and duotransits require extensive follow-up with both photometric and radial velocity observations in order to confirm the transit signal, orbital period, radius and mass.Constraining the period of a candidate can greatly reduce the number of radial velocity measurements needed to confirm the exoplanet and measure its mass (e.g.Gill et al. 2020c).
In this paper we set out our search for duotransits from the Cycle 1 and Cycle 3 TESS FFI (Full-Frame Image) lightcurves.In Section 2 we describe the TESS data that we use to search for duotransit candidates.In Section 3 we outline our search algorithm and vetting procedure.In Section 4 we set out the results of our search, including the details of the 85 duotransit candidates.Finally in Section 5 we discuss the prospects for confirming these duotransit candidates via follow-up photometric and spectroscopic programmes.

TESS OBSERVATIONS
TESS is a space-based NASA mission focusing on the discovery of transiting exoplanets around bright stars (Ricker et al. 2015).TESS has four cameras, each equipped with a grid of four CCDs for a total combined field-of-view of TESS of 24°× 96°.In Cycle 1 (2018Jul 25 -2019 Jul 17), TESS observed almost the entire Southern Ecliptic Hemisphere in 13 Sectors, each observed for a period of approximately 27 days.Each TESS sector has a gap of approximately 2.4 days, during which time the satellite downlinks data.There is a similar gap in between Sectors.Other gaps in the data can be due to technical problems with the spacecraft or scattered light (mostly from the Earth) making some image frames unusable (e.g.Dalba et al. 2020).Select stars were observed with 2 minute cadence, while the full frame images (FFIs) were observed with a cadence of 30 minutes.
TESS reobserved the Southern Ecliptic Hemisphere in Cycle 3 (2020 Jul 5 -2021 Jun 24), with the FFIs collected with a shorter cadence of 10 minutes.During Cycle 3, TESS slightly shifted its survey fields in order to cover spatial gaps in between the Cycle 1 Sectors.
For our search for duotransit candidates, we use the TESS fullframe image (FFI) light curves produced by the Science Processing Operations Center pipeline (SPOC; Jenkins et al. 2016), which are publicly available from the Mikulski Archive for Space Telescopes (MAST)2 .The SPOC pipeline produces FFI light curves for approximately 160,000 stars per sector, based on selection criteria set out in Caldwell et al. (2020).
We focus solely on the Southern Ecliptic Hemisphere, as at the time of writing TESS had completed its campaign of the Southern Ecliptic in two cycles.We use Sector 1-13 data from Cycle 1, and Sector 27-38 data from Cycle 3. In total, this results in a sample of 1,422,473 stars.We search light curves from the Presearch Data Conditioning Simple Aperture Photometry (PDCSAP; Stumpe et al. 2012Stumpe et al. , 2014;;Smith et al. 2012) lightcurves, which have instrumental systematic trends removed from the Simple Aperture Photometry (SAP) flux, but should retain stellar variability including any transit events.
In addition to using flux measurements from the FFI PDCSAP lightcurves, we also make use of the sky background and momentum centroiding measurements provided in the PDCSAP lightcurve files via the keywords SAPBKG and MOMCENTR1/MOMCENTR2 respectively.These data allow us to rule out a large number of false candidates as described in Section 3.2.

DUOTRANSIT SEARCH
Our search for TESS duotransit candidates arises out of a more general search for TESS monotransits.We therefore begin by searching the entire set of 1,422,473 SPOC PDCSAP FFI light-curves for monotransit events, and then we match up events to detect duotransit candidates.

Searching for Monotransit Events
We begin by downloading the SAP and PDCSAP SPOC FFI lightcurve products from MAST.To remove bad data points from the lightcurves we discarded data points with quality bit values above 0. We read the meta information for each light-curve, including the TIC ID, effective temperature, stellar radius, and metallicity if available.We assume a solar metallicity of 0 dex for stars with no metallicity value available.We split each lightcurve into segments defined by gaps in excess of 2.4 hours and normalise each separately.This accounts for gaps in individual orbits due to spacecraft data download times and regions of data flagged by the SPOC algorithm.For each segment, we smooth the lightcurve using an iterative Savitzky-Golay filter (5 iterations using a threshold of 3-) with a window size 48 hours (e.g.Hattori et al. 2022).This window size strikes a balance of removing stellar activity but ultimately sets an upper limit on the width of transit events our algorithm can detect.Our tests show that transit widths below ∼ 2.3 days are easily detectable using this filter width.For events wider than this, we find that the Savitzky-Golay filter begins to confuse transit signals with stellar activity and thus the event is not recovered.In addition, our tests showed that the change in cadence between Cycle 1 (30 minutes) and Cycle 3 (10 minutes) had a negligible effect on the filter.For a warm Jupiter in a circular orbit around a Solar type star, we estimate an upper limit to the possible recovered orbital periods of in excess of 1000 days.
Once the lightcurves are normalised and flattened, we pass them to monofind, our custom monotransit detection algorithm.monofind searches for monotransit events in the lightcurve where three consecutive 30-minute data points are 3 median absolute deviations below the normalised median of the lightcurve.An example of this method is shown in Figure 1, as applied to TOI-2447 (Gill et al., submitted).For the Cycle 1 light-curves we use the native 30 minute data points, while for the Cycle 3 lightcurves we bin the native 10-minute cadence by three to a 30-minute cadence to achieve a consistent detection threshold for transit events.

Selecting Duotransit Candidates
After searching all the TESS Cycle 1 and Cycle 3 SPOC FFI lightcurves for monotransit events, we cross match detections to search for stars which show exactly one monotransit event in Cycle 1 and one monotransit event in Cycle 3.This yielded a list of 9718 duotransit candidates.
We then performed a visual inspection of these 9718 lightcurves to check which of these showed two events that could possibly be transit events.This allowed us to remove obvious false positives that had triggered the monofind algorithm but did not have two transit-shaped events in the lightcurve.In most instances these were some kind of variable star.This quick visual inspection took us down to a total of 736 reasonable duotransit candidates.The majority of candidates that did not pass this vetting step were caused by asteroids passing through the target and/or background pixel apertures, systematics noise events due to the spacecraft, or changes in the amplitude of variable stars (see examples presented in Figure 2).
We examined each of these duotransit candidates in order to ascertain which appeared to be good transiting exoplanet candidates, and which were false-positives.Examples of false-positive scenarios included those causing transit-like events such as eclipsing binary stars, TESS spacecraft systematics (in particular momentum dumps), stellar variability, and Solar System asteroids passing through the background and target photometric aperture.
We are able to identify events caused by asteroids crossing the photometric aperture by checking for variations in the sky background (SAPBKG) that correlate with the monotransit event.We also noticed that such events were typically very asymmetrical in shape, and therefore unlike a bona-fide monotransit event.In total, we identified 170 of our initial duotransit candidates as being due to asteroids crossing the photometric aperture in Cycle 1 or Cycle 3.
We identified monotransit events that were likely caused by eclips-ing binaries by examining the results from the transit/eclipse fit from monofind.We designated any event with a modeled companion radius > 2 R J (∼ 22 R ⊕ ) to be an eclipsing binary, and removed it from our duotransit candidate list.Such well-separated planets are not expected to be inflated like hot Jupiters (e.g.see figure 2 from Lopez & Fortney 2016) and thus this limit is justified.We also designated a candidate as an eclipsing binary if there was evidence of a secondary eclipse in the lightcurve.Furthermore, we excluded events which had significant depth differences between Cycles 1 and 3.In total we identified 384 eclipsing binaries from our our initial duotransit candidate list.We searched for blended eclipsing binaries by inspecting the lightcurves of nearby stars, by checking for centroiding offsets during the monotransit events, and by examining the Target Pixel File (TPF) using our custom spoctpf tool.spoctpf allows us to make a lightcurve for any pixel or set of pixel in the TPF, and helps determine if the monotransit event is on the star of interest, or is on a nearby star.In total we identified 58 blended eclipsing binaries from our our initial duotransit candidate list.
We also examined the pre-normalised and pre-flattened PDCSAP lightcurves, as well as the SAP lightcurves.This was to ensure that neither the PDCSAP algorithm nor our own normalisation and flattening had significantly altered the shape of the detected monotransit events.We also inspected by-eye the full unflagged SPOC lightcurve for additonal transit events that may have been excluded from the PDCSAP data.
Finally we checked if any of the duotransit candidates had an associated Data Validation Report (DVR, Twicken et al. 2019).DVRs are created for potential TESS planets candidates processed with the SPOC pipeline and contain initial findings about the system including a detailed model fit and analysis of nearby stars to exclude blend scenarios.If a DVR determined a candidate to be a false-positive, we investigated the target further to assess if it warranted exclusion from our list.Some candidates displayed depth differences between the Cycle 1 and Cycle 3 events.SPOC lightcurves use unique masks for each individual Sector which may lead to different amounts of dilution from neighboring stars depending on telescope pointing and orientation for each sector (Bryant et al. 2023).This should be accounted for in the detrended SPOC data (PDCSAP) but might not be perfect, and thus small sector-dependent depth differences are expected (⪅2 ppt), particularly in crowded fields.Some candidates had larger depth and width differences, which could be multi-planet systems or blended eclipsing binaries.However, since they do not meet our criteria for selection as duotransit candidates, they were excluded from our list.We also found 39 duotransit candidates that we associate with spacecraft systematics (stray light, momentum dumps etc.3 ).This number also includes a few events resulting from stellar variability that was poorly matched by our detrending model.
A flowchart illustrating the candidate search and vetting process, and the associated numbers of candidates categorised at each stage, is shown in Figure 3.
In summary, out of the 1,422,473 unique TIC IDs, 9718 duotransit candidates were identified by the monofind algorithm, and after visual inspection this was reduced to 736 candidates pre-vetting.As a result of the vetting process, 58 objects were classified as blended eclipsing binaries ('blends'), 170 as Solar System asteroids, 384 as eclipsing binaries, and 39 as events caused by either spacecraft systematics or poorly-detrended stellar variability.We list a sample of these events along with their designation in Table A4.The vetting process left us with a final number of 85 duotransit candidates that we present as likely planetary in nature in this paper.

Modelling Candidate Duotransit Events
In order to derive planetary parameters for the candidates, as well as the most likely period aliases, we must fit the available transits.However, most transit model fitting requires a priori knowledge of the orbital periods, and is certainly not optimised to sample the extremely narrow but widely-separated period regions found for duotransits.We used the MonoTools package (Osborn 2022) which fits transits in a way agnostic of orbital period and then computes the posterior density function of the planet candidate from the orbital velocity implied from the transit impact parameter, radius ratio and duration.This has previously been used to model other duotransiting planet candidates that were subsequently confirmed (e.g.Osborn et al. 2021Osborn et al. , 2022a)).
MonoTools fits transits using the exoplanet python library (Foreman-Mackey et al. 2021).Stellar parameters from the TESS Input Catalogue (TICv8; Stassun et al. 2019) were used as priors for each of the fits; as was the Kipping (2013) eccentricity prior, the Espinoza & Jordán (2016) impact parameter prior, and quadratic limb-darkening parameters constrained using theoretical predictions for the TESS bandpass of Claret (2017).In the majority of cases, a cubic spline was fit to the transit-masked TESS PDCSAP flux in order to pre-flatten the lightcurve and a window of 5.5 transit durations was cut around the transit.However, after modelling some of these fits appeared to poorly model the out-of-transit variability.In these cases we turned to a simple harmonic oscillator (SHOTerm) celerite Gaussian process (Foreman-Mackey et al. 2017), which we constrained by first sampling out-of-transit data and then using the inferred hyperparameter distributions as priors for a combined model fit.A log scatter parameter was used to encapsulate additional noise for each transit.The transit model was then sampled using the Hamiltonian Monte Carlo of Salvatier et al. (2016) using a burn-in phase of 800 steps and 1500 samples on each of four independent chains, resulting in typical effective sample sizes of 2500-3000 for each parameter for each candidate.The derived parameters are shown in full online but summarised in Table A3.The probabilistic planetary period distributions are shown in Table A3 and in Figure 4 ordered from shortest to longest.

85 Duotransit Planet Candidates
Following the methods described in Section 3, we have found a total of 85 duotransit planet candidates from our monofind search and vetting of the SPOC FFI lightcurves for the Southern Ecliptic TESS fields (Sectors 1-13, 27-34).The stellar properties of our candidates are set out in Table A1, where N sec denotes the total number of TESS sectors in which the target was observed.The transit event parameters are set out in Tables A2 & A3, including the central transit times  c1 and  c2 of the Cycle 1 and Cycle 3 events respectively, and the separation between the two events in days Δ   .We also include the Gaia flags of NSS (Non-Single Star), where 0 denotes a good single-star solution, 1 denotes an astrometric binary, 2 denotes a spectroscopic binary and 3 denotes an eclipsing binary; and the Gaia robust radial velocity (RV) amplitude in km s −1 , calculated using the standard deviations of individual RV measurements as set out in Gaia Data Release 3 (DR3, Gaia Collaboration 2022).We do not remove candidates from our target list based on these values, however, since an NSS designation is often consistent with the presence of a planet and it is not clear how robust the Gaia DR3 RV amplitudes are (e.g.Seabroke et al. 2021).In Table A3, we also show the most probable value of   ( marg ) and the corresponding value of  ( alias ).
The transit events for all 85 duotransit candidates are plotted in Figures A1-A5.We plot the best fit transit and eclipse model for each event from the monofind algorithm (see Section 3.1).We also plot the sky distribution of the candidates in Figure 5.
Figure 6 shows where our duotransit candidate host stars lie on the HR diagram, with most on the main-sequence spanning spectral types A-K, some on the main-sequence turn off, and one in the hot sub-dwarf regime (see Section 4.2).Our candidates span a range of brightness between 8 < T mag < 14, with most candidates lying between 10 < T mag < 13; see Figure 11.This magnitude range is largely governed by the magnitude distribution of the SPOC FFI lightcurves that cuts off at around T mag = 13.5 due to the number of lightcurves per sector being restricted to approximately 160,000 (Jenkins et al. 2016).
We calculated the total SNRs (Signal-to-Noise Ratios) for each of our candidates as a function of the SNRs of each individual transit event.The SNR of each transit event was estimated using the double box approximation model described by Kipping (2023).Using this square well transit model, the SNR for each transit event with a depth  in ppm, a duration  dur in hours, light curve noise  in ppm, and a contamination ratio  was calculated using Equation 2: The contamination ratio and noise value were both extracted directly from the headers of the SPOC lightcurves.In some cases these values were missing from the headers of the Cycle 3 lightcurves, in such instances we used the same noise as the Cycle 1 lightcurve.To combine the SNR across both transit events we add the individual SNR for each event in quadrature.
We plot the distribution of the total SNR values for our 85 candidates in Figure 7, and find that most candidates have a SNR between 10-70, with the distribution peaking at SNR values of 25-30.There is one candidate with a total SNR value below 10 and four candidates with a SNR value above 100.

Candidates of Special Interest
Based on our Gaia H-R diagram in Figure 6, we identify three candidates that are distinct from the rest.

A1V type host star, TIC-221915858
TIC-221915858 (candidate 45) is the most luminous star in our sample and resides in the region of the colour-magnitude diagram where the main-sequence approaches the sub-giant branch (Figure 6).This is complemented by Gaia DR3 stellar parameters suggesting that TIC-221915858 is a hot ( eff = 9000 K) A1 star with a RUWE of 0.814 indicative of a good astrometric solution.The fitted spectral energy distribution in TIC V8, which uses Gaia DR2 along with 2MASS colours, suggests TIC-221915858 is a main sequence A1 ( eff = 9475 ± 187 K) star with mass and radius of 2.41 ± 0.33 M ⊙ and 2.47 ± 0.09 R ⊙ respectively.In addition to being the most luminous host star in our sample, TIC-221915858 is also the hottest on the main sequence and represents a under-sampled population of exoplanets around hot stars.If a planet is confirmed around TIC-221915858, it would be the hottest planet host star discovered by the TESS mission4 .The 5.74 ppt transit depth is detectable with ground-based photometric facilities and so it is possible to recover the orbital period with ground-based instruments.However, recovering the spectroscopic orbit will be challenging, in-part due to the typical rotation and lack of absorption lines in A-type stars making it difficult to measure a precise CCF (Cross-Correlation Function) centre.Doppler tomography (e.g. Watson et al. 2019) has been used successfully to determine the radial-velocity semi-amplitude of fastrotating stars with broad CCFs (Temple et al. 2018(Temple et al. , 2019) ) and could be applicable to TIC-221915858 once the orbital period is known.We provide the light curves and transit models for this candidate in Figure A2.

Late K-dwarf host, TOI-4310/TIC-303317324
While the majority of our duotransit candidates orbit F, G and early K type dwarf stars, the candidate TOI-4310 (TIC-303317324, candidate 65) is a late K-dwarf star with  eff = 4159 K.This is an outlier amongst our candidates on the Gaia colour-magnitude diagram (Fig 6), positioned much further down the main sequence than any of our other candidates.The estimated radius of TOI-4130 is 0.72 R ⊙ , and the transit model indicates the transiting planet would have a radius of 2.67 R ⊕ , making it one of the smallest of our duotransit planet candidates.We provide the light curves and transit models for this candidate in Appendix Figure A1.6 outside of the main population of exoplanet hosts from our candidates.Hot subdwarfs are evolved compact stars, mainly resulting from enhanced mass-loss at the tip of the red giant branch, which likely occurred due to binary interaction (Han et al. 2002(Han et al. , 2003;;Maxted et al. 2001;Pelisoli et al. 2020).This makes them targets of interest for probing the survivability of planets to both stellar evolution and binary environments.Most hot subdwarf companions fall into two populations containing either close white dwarf or M-dwarf/brown dwarf companions or wide FGK-type companions (e.g.Schaffenroth et al. 2022), with no planetary companions confirmed to date (e.g.Van Grootel et al. 2021;Thuillier et al. 2022).
Parameters from TICv8 poorly constrain the mass and a radius of the host to 0.5 ± 0.3 M ⊙ and 0.15 ± 0.11 R ⊙ (log  = 5.8 ± 0.9), which are consistent with a hot subdwarf and make it the smallest candidate host star in our list.Jeffery et al. (2021) obtained for this star a  eff of 45, 600 ± 1000 K and a consistent log  of 6.08 ± 0.04 and classified it as helium-rich sdO (He-sdO).They reported no radius or mass estimate.To derive a radius consistent with the precise  eff and log  of Jeffery et al. (2021), we performed a spectral energy distribution (SED) fit using speedyfit 5 .We employed spectral models from the Tübingen NLTE Model-Atmosphere Package (TMAP, Werner & Dreizler 1999;Werner et al. 2003;Rauch & Deetjen 2003).Initial attempts revealed the existence of excess flux towards the red/near-infrared compared to the hot subdwarf model.We therefore included a second component in the fit, modelled with ATLAS9 spectra (Castelli & Kurucz 2003).The log  was kept fixed at the spectroscopic value for the hot subdwarf (as it is poorly constrained by a SED fit), and a Gaussian prior was applied on the temperature.The temperature of the companion star was allowed to vary freely within 3500 and 6000 K (restricted by the lack of contribution to the spectrum in Jeffery et al. 2021, : higher temperatures would lead to visible lines in the spectrum; for lower temperatures, the hot subwarf would completely dominate and a companion would have no effect) and the log  was left to vary in the range of 4 to 5. A prior on the Gaia parallax was also applied, which enables the determination of precise radii.The MCMC fit converged to radii of 0.18 +0.06 −0.03 R ⊙ and 0.88 +0.30  −0.15 R ⊙ for the hot subdwarf and the companion, respectively.
5 https://speedyfit.readthedocs.io/ The companion T eff was found to be 5100 ± 120 K, consistent with a K-type main sequence star.FGK-type companions are found with 30 per cent of hot subdwarfs (Stark & Wade 2003), and their periods are in the range of 100-1000 days (e.g.Vos et al. 2019), which could be consistent with the orbital period of the duotransit signal.We note that there is also another much deeper (5.8%) transit/eclipse signal with a 32 day period that is reported in TFOP, and was the reason this candidate was flagged as a TOI.However that signal is distinct from the duotransit signal that we report in this paper.We provide the light curves and transit models for this candidate in Appendix Figure A4.

Continuous Viewing Zone candidates
Three of our candidates lie inside or close to the TESS Continuous Viewing Zone (CVZ), where targets are observed in every Sector.TIC-25194908 (candidate 8) was observed in Sectors 1-13 during Cycle 1, and Sectors 27-38 in Cycle 3, for a total of 24 Sectors, with only two transits detected.TIC-294097549 (candidate 62) was observed in multiple Sectors across Cycle 1 and Cycle 3 for a total of 13 Sectors, also with only two transits detected.This additional TESS coverage rules out most alias periods, and only 2 and 3 periods are possible respectively for these candidates.These are likely to be among the longest periods from our sample, with the remaining allowed periods in the range 337-675 d and 299-599 d respectively (see Table A3).TIC-349091983 (candidate 74) was observed in all Sectors in Cycle 1 with the exception of Sector 5, and again in Cycle 3 in all Sectors with the exception of Sector 35, for a total of 24 Sectors.There is only one possible period for this candidate of approximately ∼ 549 days, and thus the true orbital period is solved from TESS alone.

TOI and CTOI candidates
TESS Objects of Interest (TOIs) are planet candidates that have been vetted by the TESS Science Office (TSO), the TESS Follow-up Observing Program (TFOP) and designated as promising candidates for follow-up and publication.11 of our total 85 candidates have previously been flagged as TESS Objects of Interest (TOI), and these are labelled in Table A1.
Another 14 of our 85 candidates have previously been flagged as Community TESS Objects of Interest (CTOIs), and these are also labelled in Table A1.CTOIs are typically planet candidates submitted by additional community projects outside of the official TOI planet search pipelines, and CTOIs are reviewed by the TESS TOI team before being promoted to TOI status and assigned a number.
The majority of CTOIs have been identified by the WINE (Warm gIaNts with tEss) collaboration (e.g.Schlecker et al. 2020;Jordán et al. 2020;Hobson et al. 2021), the PHT (Planet Hunters TESS) project (Eisner et al. 2021), and the STF (Single-Transit Finder) project.

Confirmed and published candidates
Two of our duotransit planet candidates have already been confirmed and published.TOI-5153 (candidate 25; TIC-124029677) has been published by Ulmer-Moll et al. (2022).The planet is a large warm Jupiter (M = 3.26 +0.18  −0.17 M J , R = 1.06 +0.04 −0.04 R J ) orbiting an F8-type star on a period of 20.33 days.We find that our fitted planetary radius from  A1) so we estimate the distance from the parallax and do not correct for reddening or extinction.Table A3 is in agreement with this published value.TIC-466206508 (candidate 85; TOI-5542) has also been published by Grieves et al. (2022).The planet is an old warm Jupiter orbiting a relatively metalpoor G-dwarf host star on a period of 75.12 days, with a mass of M = 1.32 +0.10 −0.10 M J and a radius of R = 1.01 +0.04 −0.04 R J .Other publica-

Previous TOIs and CTOIs identified as false positives
Some of the candidates that were detected in our transit search but rejected as false positives have previously been announced as TOIs or CTOIs.In all cases, we found these to be examples of passing asteroids that caused peaks in the SAP background time series and hence false dips in the target light curve (see Section 3.2).These false positives are are TOI-4312 (TIC-251086776) and the CTOIs TIC-152070435 and TIC-275180352.

DISCUSSION
From our initial set of 1,422,473 unique TIC IDs, 9718 were identified as duotransit candidates from our monofind algorithm in the first instance, and after a quick visual inspection to reject obvious variable stars this was reduced to 736 candidates pre-vetting (see Section 3.2.From these candidates, 651 were determined to be caused by false-positive scenarios including blended sources, asteroid crossing events, eclipsing binaries, systematics and stellar variability.This leads to a final list of 85 duotransit candidates presented in this work (see Section 4 and Tables A1-A3).We have submitted all of our non-TOI/CTOI duotransit planet candidates to the TESS follow-up program (TFOP) (60 candidates).We hope that this will allow the community to follow-up these interesting systems further with the aim of determining their true orbital periods and providing confirmation and full characterisations of new long-period planets.

Duotransit candidate properties
We plot the transit depths of our 85 duotransit candidates in Figure 8, and for comparison we overlay the TESS planets that have been confirmed in the Southern Ecliptic Hemisphere6 .The transit depths  of our duotransit candidates range from approximately 0.1 percent to 1.8 percent, peaking around 0.7 percent.This is significantly deeper than is typical for the confirmed TESS exoplanets, the majority of which are less than 0.2 percent.This depth difference is to be expected given that the monofind algorithm is designed to detect individual high-SNR transits, which will naturally be deeper than the general TOI population.
In Figure 9 we plot the best-fitting radii of our duotransit planet candidates, again in comparison with the TESS confirmed planet sample.We find that our sample peaks at around the radius of Jupiter (11 R ⊕ ), which is also to be expected for a sample on individual high-SNR transits.Our sample extends to radii exceeding 16 R ⊕ , and while the sample of confirmed TESS planets also extends to similar radii, these are hot Jupiters with radii inflated by irradiation, which we would not expect for long-period planets (Gu et al. 2003).Nevertheless, rather than applying an arbitrary upper radius cut, we keep these candidates in our sample for completeness and will rely on follow-up observations to determine the upper radius limit of long-period planets.
Figure 10 shows that most of our candidates have significantly longer transit durations than many of the confirmed TESS planets.This is expected as we are probing planets with orbital periods in excess of ∼ 17 days, which is significantly longer than the median orbital period of TESS planets (∼ 5.8 days).
In Figure 11 we plot the TESS magnitudes of the host stars of our candidates, again comparing with the sample of confirmed TESS planets.Here it can be seen that our long-period planet candidates tend to orbit stars that are significantly fainter than the confirmed planet sample (typically T mag of 10-13).This is for three reasons.First, the confirmed TESS sample is biased towards bright stars, partly because brighter stars make it easier to detect shallow transits, and partly because follow-up efforts tend to be focused on bright host stars.Second, the much smaller transit probabilities of wide-separation planets means that long-period transiting candidates are rare, and so the brightest detected examples will be around fainter stars, which are more numerous (the absence of brighter examples is not a selection effect because such systems would readily detected).Third, gas giant planets are inherently rarer than the sub-Neptune sized planets that make up the bulk of the confirmed TESS sample.The steep cut-off in our detected candidates at T mag =13 simply reflects the selection criteria for the SPOC FFI lightcurves (Caldwell et al. 2020).
In Figure 12 we plot the distances of our duotransit candidate host stars from the Gaia DR3 catalog.We find that most candidate host stars are at distances from 200-500 pc, with the furthest object being TIC-218977148 at a distance of ∼ 826 pc, and the closest being TIC-303317324/TOI-4310 at a distance of ∼ 40 pc.
As described in Section 3.3, we use the shape and width of our detected transit events to determine the most probable orbital period for each candidate (e.g.Osborn et al. 2022b).The probability of each allowed alias is indicated on Figure 4 and the most probable period for each candidate is listed in Table A3.We plot a histogram of these most probable period in Figure 13.We find that our distribution peaks at periods around 20-30 days.While these values are the most probable periods according to the information and data available, they are not necessarily the correct values, and the true orbital periods must be determined through follow-up observations.We also note the three candidates in our sample with the longest periods: TIC-294097549 with a value of  marg of 200 days, TIC-25194908 with a value of  marg of 338 days, and TIC-349091983 with a value of  marg of 549 days (see Table A3).

Photometric period determination
The limited number of discrete period alias for duotransit candidates means that precise orbital periods can be determined efficiently with photometric follow-up targeted at predicted transit times for each alias.
Our own team is actively following up the duotransit candidates presented here using the Next Generation Transit Survey (NGTS; Wheatley et al. 2018).NGTS is a ground-based facility located at the ESO Paranal Observatory in Chile that deploys an array of twelve telescopes optimised for photometric detection of exoplanet transits (e.g.Bryant et al. 2020).Our monotransit programme with NGTS confirmed the first planet that was initially identified as a single-transit event with TESS (Gill et al. 2020c), and has since confirmed several other long-period planets (e.g.Ulmer-Moll et al. 2022;Grieves et al. 2022, Gill et al., submitted).We have also confirmed three long-period, low-mass eclipsing binary systems (Gill et al. 2020a;Lendl et al. 2020b;Gill et al. 2020b).
We are also searching TESS Cycle 5 data as it is released for third transits of our duotransit candidates.In some cases this will significantly reduce the number of period aliases to search, although with a similar two-year gap between Cycles 1, 3 and 5 a third transit usually still leaves multiple aliases to be searched.

Radial velocity detections
Our team has also begun a spectroscopic campaign using the CORALIE spectrograph (Queloz et al. 1999) on the Swiss 1.2 m Leonhard Euler Telescope at La Silla Observatory (program ID 500) to help confirm our candidates.With a first CORALIE spectrum, we are able to identify and remove double-line spectroscopic binary (SB2) systems, and detect rapidly rotating stars from the broadening of the cross-correlation function.With a second CORALIE spectrum, taken about one week later, we are able to exclude systems for which the change of measured radial velocity is too large to be consistent with a planetary companion (>1 km s −1 ).Bright targets hosting relatively massive planetary companions exhibit radial velocity variations detectable with CORALIE (∼ 6m s −1 for bright stars; e.g.Marmier et al. 2013) and for other targets we use HARPS.Previous efforts to confirm these mono-and duotransiting planets using spectroscopic observations have been successful (e.g.Ulmer-Moll et al. 2022;Grieves et al. 2022;Ulmer-Moll et al. 2023).

CONCLUSION
We have presented the discovery of 85 duotransit candidates from the TESS-SPOC FFI light curves from the Southern Ecliptic Hemisphere.The candidates were found using our custom-built monofind algorithm through which all SPOC pipeline data products were passed.We also employed a vetting procedure to rule out false-positive scenarios such as eclipsing binaries and asteroids in the sample.A total of 25 of our candidates have previously been flagged as either TOIs or CTOIs, and we found during our vetting process 3 TOI/CTOI objects outside of our duotransits falsely flagged as such that are asteroids.A dedicated program on the NGTS facility is now being used to determine the true orbital periods of these systems, and we welcome other community efforts in this difficult task.We also have programs on instruments such as CORALIE and HARPS to acquire radial velocity measurements to confirm the planetary nature of these systems and to determine the mass of the exoplanets.Once confirmed, these planets will form the basis for characterisation studies into their atmospheric compositions and orbital obliquities, and hence into the formation, evolution and migration of warm and cool gas giant exoplanets.

ACKNOWLEDGEMENTS
This paper includes data collected by the TESS mission.Funding for the TESS mission is provided by the NASA Explorer Program.Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center for the production of the SPOC data products.The TESS team shall assure that the masses of fifty (50) planets with radii less than 4 REarth are determined.
This work makes use of data from the European Space Agency (ESA) mission Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and Analysis Consortium (DPAC, https://www.cosmos.esa.int/web/gaia/dpac/consortium).Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement.
We acknowledge the use of public TESS Alert data from pipelines at the TESS Science Office and at the TESS Science Processing Operations Center.
This research makes use of the Exoplanet Follow-up Observation Program website, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.
This paper includes data collected by the TESS mission that are publicly available from the Mikulski Archive for Space Telescopes (MAST).
FH, TR and AO are supported by STFC studentships.ML acknowledges support of the Swiss National Science Foundation under grant number PCEFP2_194576.The contribution of MB, ML, HPO, & SUM have been carried out within the framework of the NCCR PlanetS supported by the Swiss National Science Foundation under grants 51NF40_182901 and 51NF40_205606.JSJ acknowledges support by Fondecyt grant 1201371 and by the ANID BASAL project FB210003.IP acknowledges a Warwick Astrophysics prize postdoctoral fellowship made possible thanks to a generous philanthropic donation.The contributions at the University of Warwick by SG, DB, PJW, RGW and DA have been supported by STFC through consolidated grants ST/P000495/1, ST/T000406/1 and ST/X001121/1.

FLUXFigure 1 .
Figure 1.Upper panel: The TESS Sector 32 lightcurve of TOI-2447 (black) with detrending model (red solid line) and the 3-MAD detection threshold (red dashed line).A single event was detected highlighted in blue.Lower panel: An inspection of the transit event with best fitting transit model (red solid line).

Figure 2 .
Figure 2. Three example duotransit candidates ruled out during the visual inspection of the transit events in the TESS light curves, with an arbitrary flux offset for clarity.The dotted red line indicates the 3 median absolute deviations detection threshold used in monofind.The red triangles indicate the event that triggered the detection by monofind.From top to bottom, these example events are caused by an asteroid passing through the target and background aperture, systematic noise caused by the spacecraft, and changes in amplitude of a variable stars.

Figure 3 .
Figure3.Flowchart of the monofind algorithm candidates and the vetting process that followed, with the number of candidates categorised at each stage as blended eclipsing binaries ('blends'), asteroids, eclipsing binaries, and other systematics and stellar variability features.

Figure 4 .
Figure 4. Probability distribution of possible periods for each duotransit candidate as computed by MonoTools, normalised to the most likely period alias.The vertical colourbars refer to six steps in the log probability of each alias, and the green triangles represent the minimum eccentricity aliases.

Figure 5 .
Figure 5.The ecliptic plane (solid red line) with the positions of the 85 duotransit candidates marked with red-inset black points.

Figure 6 .
Figure 6.Gaia DR3 (Gaia Collaboration 2022) colour-magnitude diagram (corrected for extinction and reddening) showing all stars with TESS full frame image SPOC lightcurves from Cycle 1 and Cycle 3 that have measured Gaia DR3 distances.Blue circles indicate the positions of our 85 duotransit candidates.The colourbar shows the relative number density of stars at each location in the diagram.For six of the duotransit candidates there was no Gaia DR3 distance measurement (see TableA1) so we estimate the distance from the parallax and do not correct for reddening or extinction.

Figure 7 .
Figure 7.The distribution of total transit event SNR values (see Section 4.1) for our 85 duotransit candidates.

Figure 8 .
Figure8.The distribution of transit depths for our duotransit candidates (green) and the confirmed TESS discovered exoplanets from the Southern Ecliptic Hemisphere (grey).

Figure 9 .
Figure9.The distribution of planet radii for our duotransit candidates (green) and the confirmed TESS discovered exoplanets from the Southern Ecliptic Hemisphere (grey).

Figure 10 .
Figure10.The distribution of transit durations for our duotransit candidates (green) and the confirmed TESS discovered exoplanets from the Southern Ecliptic Hemisphere (grey).

Figure 11 .
Figure 11.The distribution of TESS magnitudes for our duotransit candidate host stars (green) and the confirmed TESS discovered exoplanet host stars from the Southern Ecliptic Hemisphere (grey).

Figure A1 .Figure A2 .Figure A3 .Figure A4 .Figure A5 .
Figure A1.Zoomed-in transit events for duotransit candidates TIC-304339227 to TIC-156716001 ordered by transit depth.The left panel shows the Year 1 transit, and the right panel shows the Year 3 transit.The data in blue is the TESS PDCSAP photometry (see Section 2).In cases with < 15 minute cadence blue points represent 30 minute bins with raw photometry shown in grey.The dashed purple lines show the best fit transit model with 1 and 2 standard deviations as shaded purple regions.

Table A1 :
Properties of the host stars of our duotransit candidates.

Table A1 :
Properties of the host stars of our duotransit candidates.

Table A2 :
The transit event properties of our duotransit candidates.

Table A3 :
Properties of our duotransit candidates. alias is the alias number corresponding to the most probable orbital period  marg .

Table A3 :
Properties of our duotransit candidates. alias is the alias number corresponding to the most probable orbital period  marg .

Table A3 :
Properties of our duotransit candidates. alias is the alias number corresponding to the most probable orbital period  marg .

Table A4 .
A sample of events from monofind that were not planetary in nature.This table is available in its entirety online.