TOI-712: A System of Adolescent Mini-Neptunes Extending to the Habitable Zone

TESS is an all-sky photometric survey, launched on 2018 April 18. Its primary mission is to detect small planets around nearby, bright stars, ideal for follow-up observations for further characterization. Using four cameras, each 24° × 24°, TESS observes the sky in 24° × 96° strips. In the 2 yr prime mission, these strips generally spanned from one of the ecliptic poles to near the ecliptic plane. Each observing sector lasts 27.4 days before stepping ∼ 27° to the next antisolar sector. After a year (13 sectors) observing the southern ecliptic hemisphere, the spacecraft oriented to observe the north for a year. ²⁶ Overlap of the fields of view of successive sectors at high ecliptic latitudes results in longer observation time spans, extending to nearly continuous year-long coverage at the poles.

TIC 150151262 (TOI-712) was preselected for 2-minute-cadence observations by the TESS mission on the basis of the star's size, brightness, and position on the sky near the southern ecliptic pole, the combination of which was expected to enable detection of small transiting planets. TOI-712 was observed on Camera 4 during the prime and extended missions between 2018 September 20 UTC and 2021 June 24 (sectors 3, 4, 6, 7, 9, 10, 11, 13, 27, 29, 30, 31, 32, 33, 34, 36, 37, and 39). During the extended mission, TOI-712 was selected for 20 s cadence observations in sector 27 as part of two Guest Investigator programs: G03068 (PI D. Kipping) and G03278 (PI A. Mayo).

The raw photometric data from TESS were processed by the TESS Science Processing Operations Center (SPOC) located at NASA Ames Research Center. The SPOC pipeline (Jenkins et al. 2010a, 2016) extracts the light curve using Simple Aperture Photometry (SAP) and also corrects the light curve for instrument systematics using the Presearch Data Conditioning (PDC) algorithm (see Stumpe et al. 2012). The resulting light curves are available through the Mikulski Archive for Space Telescopes (MAST) archive. After filtering for stellar variability and residual noise, the light curve was searched for transit signals using the SPOC Transiting Planet Search (TPS; Jenkins 2002; Jenkins et al. 2010b, 2020), which revealed two periodic transit events with periods of 9.53 and 51.69 days. An initial limb-darkened transit model was fitted to the data (Li et al. 2019), and a suite of diagnostic tests were conducted to make or break confidence in the planetary interpretation of the signatures (Twicken et al. 2018). The two candidates passed all the diagnostic tests, and the sources of the transits were localized to within 19500 ± 41489 and 20800 ± 45217, respectively. The TESS Science Office reviewed the data validation (DV) reports and issued an alert in 2019 May (Guerrero et al. 2021). These were released as TESS Objects of Interest (TOIs), TOI-712.01 and TOI-712.02. An additional candidate with a period of 53.7 days was released as TOI-712.03, but only one transit event looked believable, and a system with 51- and 53-day planets would not be dynamically stable.

We note that the algorithms applied by SPOC are successful for the vast majority of stars, but the stellar variability of young stars often requires a boutique analysis to properly remove stellar signal and identify real transits (see, e.g., Rizzuto et al. 2017; Hedges et al. 2021). Given the apparent presence of this additional transit-like event, we chose to re-extract the light curve while correcting for spacecraft systematics, following Vanderburg et al. (2019). We started with the SPOC SAP light curve and fit a model to the time series consisting of a basis spline (with breakpoints spaced every 1.0 days to adequately model the stellar variability) and systematics parameters relating to the means and standard deviations of the spacecraft quaterion time series within each exposure (see Vanderburg et al. 2019), the fast timescale (band 3) cotrending basis vectors from the SPOC PDC analysis, and a high-pass-filtered time series of the flux in the SPOC background aperture. We fit for up to quadratic relationships in each systematics parameter. We solved for the best-fit coefficients of our free parameters using a matrix inversion technique, iteratively excluding 3σ outliers from the fit until it reached convergence. We then subtracted the best-fit systematics vectors from the SAP light curve and corrected for diluting flux in the optimal aperture using the SPOC crowdsap parameter, to yield a final, corrected light curve. While there are 24 stars within two TESS pixels, none of them are brighter than T = 17, and as a result the aperture typically includes only about 2% dilution. The uncertainty in this correction, propagated to the derived parameters, is negligible compared to other sources of uncertainty. We performed the same extraction for the sector 27 20 s data and then binned to 2 minutes. While the overall scatter in our extracted light curve is similar to the PDCSAP scatter, the systematics during periods of increased pointing jitter are reduced. This helped us identify additional transits of the third candidate, for which we determined a period of 84.839 days. We note that SPOC later identified another transit of this candidate in the extended mission. It was assigned a period of 678.7 days (8 times too long) and released as TOI-712.04, though we now know that both TOI-712.03 (53 days) and TOI-712.04 (679 days) correspond to the 84.8-day candidate. The three candidates have transit depths close to 1 mmag, implying sizes between 2 and 3 R_⊕, and durations ranging from 1.7 to 5.7 hr, as expected for the range of orbital periods. Details of the transit fitting are discussed in Section 4. Our extracted light curve is shown in Figure 1.

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We conducted ground-based photometric follow-up observations for TOI-712 as part of the TESS Follow-up Observing Program ²⁷ (TFOP; Collins 2019). We used the TESS Transit Finder, which is a customized version of the Tapir software package (Jensen 2013), to schedule our transit observations. The observations are described below and summarized in Table 1.

Table 1. Ground-based Transit Observations of TOI-712

Date (UT)	Telescope	Filter	Coverage
TOI-712 b
2019-09-11	LCO-SSO-1.0 m	Zs	Egress
2019-12-15	LCO-SAAO-1.0 m	Zs	Full
2020-01-04	LCO-SAAO-1.0 m	Zs	Full
2020-01-23	LCO-CTIO-1.0 m	B	Ingress
2020-10-15	LCO-SAAO-1.0 m	B	Full
2020-11-13	LCO-SSO-1.0 m	Zs	Full
2020-12-12	LCO-CTIO-1.0 m	ip	Full
TOI-712 c
2019-12-25 a	LCO-SSO-1.0 m	Zs	Egress
2019-12-25 a	Hazelwood-0.32 m	Rc	Ingress
2020-02-15	LCO-CTIO-1.0 m	Zs	Ingress
2020-05-28	ASTEP-0.4 m	∼Rc	Full
2020-09-09	LCO-SAAO-1.0 m	Zs	Egress
2021-04-03	ASTEP-0.4 m	∼Rc	Ingress
2021-05-25	ASTEP-0.4 m	∼Rc	Full
2021-09-05	ASTEP-0.4 m	∼Rc	Ingress

Note.

^a Indicates an observation that was not used in the global fit. The LCOGT filter designations Zs and ip indicate Pan-STARRS z-short band and Sloan $i^{\prime}$ band, respectively. The LCOGT 1 m telescope nodes used are at Siding Spring Observatory (SSO), Cerro Tololo Inter-American Observatory (CTIO), and South Africa Astronomical Observatory (SAAO). See text regarding the ASTEP observation band.

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2.2.1. LCOGT

2.2.2. ASTEP

2.2.3. Hazelwood

We obtained three spectra of TOI-712 with the CHIRON high-resolution echelle spectrograph on the 1.5 m SMARTS telescope at the Cerro Tololo Inter-American Observatory (CTIO), Chile (Tokovinin et al. 2013). Observations were taken on UT 2019 September 20, 2019 October 31, and 2021 April 10 in slicer mode, which employs a fiber-fed image slicer to deliver light to the spectrograph, achieving a resolving power of R ∼ 80,000 across the wavelength range 4100–8700 Å. The CHIRON spectra can be used to characterize the stellar properties, search for massive outer companions, and rule out false-positive scenarios that would induce large RV variations or exhibit line profile variations.

We extracted the RVs of TOI-712 by fitting the line profiles of each spectrum, which were measured via least-squares deconvolution (LSD) of the observed spectra against synthetic templates (Donati et al. 1997). The RVs, which reveal no significant velocity variation beyond the uncertainties (∼50 m s⁻¹), are listed in Table 2. We also find no evidence for a composite spectrum or line profile variations.

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We searched for close visual companions to TOI-712 in I band using the HRCam speckle imager on the 4.1 m Southern Astrophysical Research (SOAR) telescope (Tokovinin 2018; Ziegler et al. 2018) on UT 2019 October 16, and simultaneously at 562 nm and 832 nm using the Zorro speckle imager on the 8 m Gemini South Telescope (Scott et al. 2021) on UT 2020 January 10. We achieved contrast ratios better than 5 mag at a separation of 01 and > 7 mag beyond ∼ 05 in the Zorro 832 nm data, which have a field of view of 25 × 25 and are therefore sensitive to companions within about 12 of TOI-712. Outside of 15, Gaia can exclude the presence of stellar sources bright enough to produce the observed transit signals (Ziegler et al. 2018). Closer stars unresolved by Gaia will often manifest as elevated astrometric noise (see, e.g., Evans 2018), but TOI-712 has RUWE = 0.994, providing no evidence for excess astrometric motion. ²⁸ The 5σ contrast curves from our speckle imaging are shown in Figure 3.

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We extract the effective temperature (T_eff), surface gravity ($\mathrm{log}g$), and metallicity ($\left[\mathrm{Fe}/{\rm{H}}\right]$) of TOI-712 from the CHIRON spectrum by matching against a library of observed spectra that have been previously classified by SPC (Buchhave et al. 2012), with interpolation performed via a gradient-boosting regressor implemented in the scikit-learn Python module. We find T_eff = 4767 ± 50 K, $\mathrm{log}g=4.63\pm 0.10$, and $\left[\mathrm{Fe}/{\rm{H}}\right]\,=-0.15\pm 0.08$. The projected rotational velocity, $v\sin {i}_{\star }$, is derived following Gray (2005) and Zhou et al. (2018), fitting broadening kernels to the instrumental, macroturbulent, and rotational line profiles. We estimate $v\sin {i}_{\star }=2.0\,\pm 1.0$ km s⁻¹ and v_mac = 1.4 ± 1.0 km s⁻¹, though the instrumental resolving power is only 3.7 km s⁻¹; for such slow rotation, these estimates may suffer systematic offsets. The projected rotational velocity is consistent with the equatorial rotation velocity calculated from the stellar radius and rotation period, but it is not precise enough to confidently state that the stellar spin and orbital axes are well aligned.

3.2.1. Gyrochronology

The TESS light curve of TOI-712 shows rotational modulation with an amplitude of ∼2%, indicative of active regions on the stellar surface like those expected for a young star. We estimate the rotation period with multiple techniques, first using a Lomb–Scargle periodogram (Lomb 1976; Scargle 1982). We assign the rotation period to the period of maximum power, with the uncertainty taken to be the half-width at half-maximum. However, the analysis is slightly complicated by the long time span of observations. Visual inspection of the light curve (Figure 1) reveals changes in the morphology of the rotational phase curve on a relatively short timescale. The first year of TESS observations includes two epochs of a more complex, double-peaked phase curve and two epochs of a single-peaked phase curve. The third year is primarily single peaked. If the dominant spot latitudes also change between the prime and extended missions, we might expect a slight change in the measured rotation period due to differential rotation, which is both predicted (e.g., Küker & Rüdiger 2011) and measured for some rapidly rotating stars (e.g., Collier Cameron 2007). A periodogram of the full time series would then be sensitive to the phasing of the signals, even though we should not expect or require them to be in phase. Indeed, this is what we see in Figure 4, which shows that the periodogram of the combined TESS light curve only allows a few discrete periods, while individual years of data each exhibit broader peaks that are consistent with one another. We therefore measure the rotation period in each year separately.

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From the TESS year 1 light curves, we measure a stellar rotation period of 12.505 ± 0.441 days, and the TESS year 3 light curves yield a rotation period of 12.452 ± 0.629 days. Additionally, WASP photometry spanning five observing seasons from 2008 to 2012 measures a rotation period of 12.503 days. The periodograms from the TESS and WASP observations are shown in Figure 4, and the binned TESS light curve, phase folded to the measured rotation period, is shown in Figure 4. As a check on the Lomb–Scargle periods, we also fit the full TESS light curve using a Gaussian process with a quasi-periodic kernel. This yields a period consistent with the Lomb–Scargle results, P_rot = 12.538 days. We adopt a weighted average of rotation periods from individual seasons, P_rot = 12.454 days.

Finally, we caution that we are observing the rotation period at the latitude of the active regions. The unknown strength of differential rotation and current spot latitudes contribute additional (systematic) uncertainties if interpreting the observed rotation period as the equatorial rotation period. If differential rotation in TOI-712 is similar to that of the Sun, then the true equatorial rotation period could be different by 10% or more.

We adopt the activity–rotation–age relation as described in Mamajek & Hillenbrand (2008), to estimate the age of TOI-712. In particular, we use the equation

$$\begin{eqnarray}&&{P}_{{\rm{rot}}}\left(B-V,t\right)=a{\left[\left(B-V\right)-c\right]}^{b}{t}^{n},\end{eqnarray} \tag{ 1 }$$

where P_rot is the rotational period of the star in days, t is the stellar age in Myr, B − V is the color index, a = 0.407 ± 0.021 and b = 0.325 ± 0.024 are gyrochronology constants, c =0.495 ± 0.010 is the "color singularity," and n = 0.566 ±0.008 is the time-dependent power law. Using the stellar rotation period above and B − V = 1.265 ± 0.152, we estimate a gyrochronological age of 492 ± 103 Myr. However, we caution that the formal uncertainty is quite likely underestimated. First, systematic errors may affect the determination of P_rot, as described above. More importantly, TOI-712 is outside of the color range (0.5 < B − V < 0.9) in which the Mamajek & Hillenbrand (2008) relation is well calibrated, as their sample consisted of primarily Sun-like stars and TOI-712 is relatively red. More recent investigations of the gyrochronology of K dwarfs, enabled by precise photometry of adolescent stars from K2 and TESS, suggest that in contrast to the G dwarfs, K dwarfs experience an epoch of stalled spin-down. While it is true that K dwarfs are expected to have rotation periods similar to TOI-712 at 500 Myr, they may also have the same rotation period at twice that age (Curtis et al. 2019a). As a result, from its rotation alone, we can only estimate the age of TOI-712 to be between about 0.5 and 1.1 Gyr.

3.2.2. Comparison with Stellar Populations

Since recent work has identified many new members of known stellar groups, we explore whether TOI-712 might belong to a known association. We use the online tool BANYAN Σ (Gagné et al. 2018) to assess possible membership in known groups, but the result suggests that it is not part of any previously known groups.

Similarly, there are likely many sparse groups that are currently unrecognized, but the large volume of public data (from Gaia, TESS, broadband photometric surveys, and spectroscopic surveys) makes possible a targeted search for comoving, coeval companions to a star of interest. We searched for evidence of a previously unknown comoving population of stars via Friend Finder. ²⁹ Within 25 pc of TOI-712, we find only two stars with similar kinematics, but this is likely no more than would be expected by chance. TOI-712 has either escaped from its birth environment or formed in such a small environment that almost none of its stellar siblings remain within <25 pc. While no convincing kinematic matches were found, the age can also be constrained by the precise UV photometry provided by GALEX (e.g., Shkolnik et al. 2011; Findeisen & Hillenbrand 2010). Friend Finder illustrates that the near-UV (NUV) flux of TOI-712 is consistent with the NUV sequence of the stars populating the Hyades (see Figure 5), which has a well-constrained age of ∼625 Myr (see, e.g., Perryman et al. 1998; Martín et al. 2018). Older stars should exhibit lower levels of NUV flux. This provides supporting evidence that the age of TOI-712 is consistent with the age of the Hyades, though if NUV flux and rotation evolve together, it is possible that NUV flux would plateau while spin-down stalls. If that were the case, then the NUV flux of Hyades K dwarfs could be similar to that of somewhat older stars. Richey-Yowell et al. (2019, 2022) show that while both the far-UV (FUV) flux and NUV flux are inversely related to stellar age in K dwarfs, there is only a statistically significant distinction between Hyades-aged stars and field stars in the FUV excess. NUV sequences in slightly older clusters like NGC 752 (1.3 Gyr; Agüeros et al. 2018) and Ruprecht 147 (2.7 Gyr; e.g., Torres et al. 2020; Curtis et al. 2020) might help resolve the age of TOI-712, but because of their distance, GALEX provides only noninformative upper limits for most of the K dwarf members.

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Given the age ambiguity associated with the stalled spin-down of K dwarfs, we ultimately adopt an age of ${830}_{-280}^{+250}$ Myr and bounded between 0.3 and 1.3 Gyr, as determined by the global fit described in Section 4.

3.2.3. The Stellar Flare Rate of TOI-712

In the previous section, we presented a model of the planetary system orbiting TOI-712, but we have not formally validated the signals as bona fide planets. In particular, we note that while we detect the transits of TOI-712 b and c from the ground in small apertures that localize the transit signal to within a few arcseconds of TOI-712, there is no ground-based transit detection of TOI-712 d. Given the large TESS pixels, the signal could potentially be produced by a faint, NEB. Gaia detects 25 stars within 2 pixels (420), though the centroid analysis made available in the SPOC DV report rules out NEBs more distant than 180. The brightest of the remaining stars is 8.1 mag fainter in the TESS bandpass and therefore contributes a flux fraction of only 0.0006 (0.6 mmag). The transit of TOI-712 d is deeper than 1 mmag, so none of the nearby stars can be responsible for the transit signal. The high-resolution imaging and Gaia astrometry discussed in Section 2.4 rule out nearly all stellar companions within 1'', and the CHIRON RVs exclude many close, bound eclipsing binaries that would have accelerated TOI-712 during the 600-day observing time span.

Previous analysis has shown that the overwhelming majority of Kepler candidates in multiplanet systems are real planets, and moreover that systems with more than two candidates are even more likely to be real (e.g., Latham et al. 2011; Lissauer et al. 2012). The same cannot be assumed for TESS, mainly because of the increased potential for NEBs due to its large pixels and, in some cases, crowded fields. However, our follow-up observations have excluded the presence of contaminating eclipsing binaries even more confidently than is the case for Kepler candidates. As a result, we consider TOI-712 b, c, and d to be bona fide planets.

Upon subtracting the best-fit EXOFASTv2 three-planet model from the TESS light curve, we perform a transit least-squares (TLS; Hippke & Heller 2019) analysis on the residuals to search for the signature of any additional transiting planets. TLS reveals a ∼4.32-day candidate signal. We refer to this signal as TOI-712.05. A new EXOFASTv2 fit including all four candidates converged, with no change to the stellar parameters or properties of the other three candidates. The derived properties of this candidate are shown in Table 5, and the phase-folded TESS light curve is shown in Figure 6. If real, TOI-712.05 would be slightly smaller than Earth, R_P =0.81 R_⊕.

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Table 5. Parameters of the Candidate TOI-712.05

Parameter	Description (Units)	Values
P	Period (days)	${4.321298}_{-0.000069}^{+0.000093}$
RP	Radius (R⊕)	0.81 ± 0.11
RP /R*	Radius of planet in stellar radii	0.0110 ± 0.0015
${\left({R}_{P}/{R}_{* }\right)}^{2}$	Planet-to-star area ratio	${0.000120}_{-0.000031}^{+0.000035}$
δTESS	Transit depth in TESS band	0.000122 ± 0.000022
TC	Time of conjunction (BJDTDB)	${1388.3796}_{-0.012}^{+0.0076}$
a	Semimajor axis (AU)	${0.04679}_{-0.00040}^{+0.00041}$
a/R*	Semimajor axis in stellar radii	${14.90}_{-0.29}^{+0.31}$
i	Inclination (deg)	${87.09}_{-0.38}^{+1.1}$
b	Transit impact parameter	${0.757}_{-0.28}^{+0.093}$
e	Eccentricity	0.0 (fixed)
ω*	Argument of periastron (deg)	90.0 (fixed)
T14	Total transit duration (hours)	${1.49}_{-0.26}^{+0.48}$

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We present the results for TOI-712.05 separately because we have less confidence that it is real. Notably, the signal is not clearly present in the full-frame images (FFIs). While this could be due to smearing of the short-duration transit in the 30- and 10-minute cadence data, it may also be due to a difference in the apertures used to produce the FFI and 2-minute light curves. If this were the case, it could suggest that the signal originates on a nearby star at the edge of the 2-minute aperture. To test this possibility, we ran two experiments. First, we extracted FFI light curves for each of the stars within $2.5^{\prime}$ and folded them at the ephemeris of TOI-712.05. None showed signs of an eclipse that would cause the observed signal. Because the sensitivity of the FFIs to a shallow, short-duration event may be compromised, we also extracted 2-minute light curves using different apertures.

Planetary candidates that are released as TOIs also undergo ephemeris matching against all other signals detected by the pipeline, in order to test for a false positive introduced by a nearby transit-like signal. TOI-712.05 was not released as a TOI, so we performed this test using all signals detected by MIT's Quick Look Pipeline (QLP; Huang et al. 2020a, 2020b), and we did not find any ephemeris matches.

It is also possible that SPOC introduced the transit signal while processing the light curve since TOI-712 is relatively active. As a check, we ran TLS on the unprocessed SAP light curve to see whether the transit is still present. After flattening and removing the transits from the three planets, the phase-folded SAP light curve does show the transit signal for TOI-712.05.

A final concern is that the signal could be introduced by stellar activity. If that were the case, we might expect that the signal would not appear consistent in time owing to evolution of the stellar signal, which is apparent by eye in the unflattened TESS light curve. We tested this by comparing the signal in year 1 to the signal in year 3. To within the uncertainties, the two are consistent, as would be expected for a transiting object.

While TOI-712.05 passed the above tests, it remains a low signal-to-noise ratio (S/N) event, so we present it here as a candidate planet. Its planetary nature may be solidified as the signal strength increases in future TESS extended missions, or perhaps by additional analysis of existing data.

Multiplanet systems provide a laboratory for comparative studies of exoplanets in an environment controlled for stellar properties and age and the ability to leverage dynamical interactions to constrain planetary masses and orbital architectures. This avenue for characterization is especially important when other methods like RV monitoring are difficult—for example, due to stellar activity, faint host stars, or small or long-period planets that induce low-amplitude orbital motion. Because short-period planets are more likely to transit, relatively few systems include long-period planets, and most that do were discovered by Kepler orbiting faint stars. As a result, TOI-712 stands out as one of the brightest long-period planetary systems currently known (see Figure 9). While many mini-Neptunes transit bright stars, most reside close to their star with high equilibrium temperatures, so TOI-712 represents an opportunity to study temperate mini-Neptunes, which are likely to have experienced different formation environments and evolutionary histories than their short-period counterparts.

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Previous investigations of young planets have suggested that they tend to have larger radii than their older counterparts (e.g., Mann et al. 2017; David et al. 2021), which is qualitatively consistent with atmospheric mass loss, but the details of the process and the timescale over which it occurs are not precisely known. Moreover, most known young planets have relatively short orbital periods for which photoevaporation is likely an important process (e.g., Owen & Wu 2013; Jin & Mordasini 2018), but other thermally driven mass-loss mechanisms (e.g., core-powered mass loss; Ginzburg et al. 2018) may drive atmospheric escape on longer timescales (∼2 − 3 Gyr). However, as both core-powered mass loss and mass loss via photoevaporation are dependent on orbital separation, the long-period planets TOI-712 c and d are likely representative of their primordial compositions. We illustrate in Figure 10 that the radii of the TOI-712 planets are smaller than the youngest planets, but there are no young planets with insolation fluxes similar to the outer TOI-712 planets.

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For TOI-712 b, it is unclear whether it is smaller owing to having been subjected to significant atmospheric loss, or rather formed smaller than other known young planets. The first possibility was discussed in Section 3.2; if TOI-712 b is older than 1 Gyr, the small size may not be a powerful constraint. Even at short periods, where the radius valley is well characterized, TOI-712 b is of note. At R_p = 2.049 R_⊕, it sits near the edge of the radius valley for its size and incident flux. If the timescale for core-powered mass loss is as long as 2 Gyr or more, it could be losing atmosphere now and ultimately be destined to become a rocky world. Future advances in understanding K-dwarf gyrochronology and activity may provide a more precise age and a more definitive conclusion about the evolution of these planets.

However, if TOI-712 is as young as 500 Myr, then the small planet sizes are more likely to reflect the formation process rather than (or in addition to) the mass-loss history. In particular, TOI-712 c and d orbit at greater distances from their host star than other known young planets, and they may differ in composition. Under the assumption that mini-Neptunes form in situ, local conditions in the protoplanetary disk during formation would differ for the long-period TOI-712 planets, the outer of which resides at the edge of the HZ. As the outer planets are too distant to have been subjected to significant atmospheric loss, they are likely representative of their primordial compositions. More data, such as transmission spectroscopy, could shed light on the compositional differences between hot and temperate planets, as well as the formation environment of typical mini-Neptunes, specifically within the HZ in the case of TOI-712 d.

As discussed above, young planets—including those orbiting TOI-712—open avenues for observational constraints on the dynamical and physical evolution of planetary systems; further, the outer two planets could provide complementary information about formation by probing primordial compositions, while mass-loss models for TOI-712 b may unveil information about its internal structure and composition shortly after formation. While young stars can be challenging to observe, future observations of the TOI-712 system remain promising.

Our modest-precision RVs suggest some variation beyond the internal uncertainty estimates, which is consistent with expectations for an adolescent star with rotating surface features. Given the rotation ($v\sin {i}_{\star }=2$ km s⁻¹) and the amplitude of photometric modulation (∼1%), we estimate that there should be tens of meters per second RV variation from stellar surface features (see, e.g., Saar & Donahue 1997). Since the predicted RV amplitudes induced by the planets are only a few meters per second (see Table 4), attempts to measure the planet masses with stabilized spectrographs would be difficult without significant advances in stellar activity modeling.

Dynamical interactions between the planets, if detected via transit timing variations or transit duration variations, could help determine their masses and eccentricities. There is currently no evidence for transit timing variations, but TOI-712 will be observed by TESS in future extended missions, providing longer baselines over which to measure transit timing variations. Moreover, the S/N of the TOI-712.05 transit should increase if it is a real companion, and we can therefore more confidently confirm or refute its existence. Similarly, additional transiting planets in the system may become apparent with the inclusion of more data. In particular, we showed in Section 5 that there are dynamically stable orbits for small planets in the HZ of TOI-712. We also know that systems of small planets tend to be packed, so it would not be surprising to find an additional planet between TOI-712 b and c (10 days ≲ P ≲ 51 days). While planets larger than TOI-712 b (2 R_⊕) would have likely been detected already, smaller planets may be revealed in future TESS data. Better knowledge of the system architecture and improved measurements of orbital properties will make dynamical modeling more powerful, which also feeds back into improved planetary properties.

As discussed in Section 7.1, the atmospheric composition of the outer planets could inform our understanding of the formation of temperate mini-Neptunes. We note that TOI-712 is located 14 from the south ecliptic pole, in the James Webb Space Telescope (JWST) continuous viewing zone, and it stands out as one of the brightest stars hosting long-period transiting planets (Figure 9). The star is relatively small, and as a result, transmission spectroscopy of the planets may be possible. Following Kempton et al. (2018), we calculate the Transmission Spectroscopy Metric (TSM) of the planets to assess the prospect for transmission spectroscopy with JWST. We find TSM_b = 53.22, TSM_c = 41.35, and TSM_d = 31.88. Based on expected yields from TESS, Kempton et al. (2018) suggested that a survey with JWST should adopt a TSM threshold of 92 for planets of this size. However, this threshold is purely based on the S/N and ignores the outsized scientific value of some individual planets that happen to have lower expected S/Ns. TOI-712 c and d are examples of planets that would not meet the cutoff for such a survey, but they may still be worth observing. Figure 11 shows the TSM values of transiting mini-Neptunes (2.0 R_⊕ ≤ R_P ≤ 4.0 R_⊕) as a function of equilibrium temperature and stellar effective temperature. It is clear that although the planets lie below the TSM threshold for the predicted TESS yield, they stand out among the real sample as two of the best temperate mini-Neptunes. When also considering the age of the system, these planets become more scientifically valuable and may form the basis for a comparative study of temperate planets as a function of age.

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