TOI-4562b: A Highly Eccentric Temperate Jupiter Analog Orbiting a Young Field Star

The transiting planet candidate around TOI-4562 was first identified from observations by TESS. TOI-4562 lies in the southern continuous viewing zone of TESS and therefore received near-uninterrupted photometric monitoring during years 1 and 3 of operations. The target received observations at 30 minute cadence during sectors 1–8 (2018 July 25 to 2019 February 28) and sectors 10–13 (2019 March 26 to 2019 July 18) and 2 minute target-pixel-stamp observations during sectors 27–39 (2020 July 4 to 2021 June 24). The transit signature of TOI-4562b was detected by the TESS Science Processing Operations Center (Jenkins et al. 2016) at NASA Ames Research Center during a transit search of sectors 27 through 39 with an adaptive, noise-compensating matched filter (Jenkins 2002; Jenkins et al. 2010, 2020). The transit signature passed all the diagnostic tests in the data validation report (Twicken et al. 2018) and was fitted with an initial limb-darkened transit model (Li et al. 2019). In particular, the transit signal passed the difference image centroiding test, which localized the source of the transits to within 10 ± 25. The TESS Science Office reviewed the diagnostic information and released an alert to the community for TOI-4562b on 2021 October 28 (Guerrero et al. 2021).

We make use of the MIT Quicklook pipeline (Huang et al. 2020) photometric extraction from the full-frame image observations. In addition, where available, we make use of the 2 minute cadence target-pixel-file observations from the crowding and flux fraction corrected Simple Aperture Photometry light curves (Twicken et al. 2010; Morris et al. 2020) made available by SPOC. Because of the large stellar variability seen in the light curve, we used the Simple Aperture Photometry (SAP) light curves rather than the Pre-search Data Conditioning SAP flux and performed the detrending using a high-order spline interpolation (Vanderburg & Johnson 2014)

The full TESS light curve covering all sectors of observations is presented in Figure 1. During the 2 (nonconsecutive) yr of near-continuous observations, a total of four transits were captured by TESS. Figure 2 shows the zoomed-in region around each of these transits.

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TOI-4562 was first identified as a potential young star due to its strong rotational modulation (Zhou et al. 2021) as part of our program to survey for planets around young field stars. We performed a search for transiting signals around TOI-4562 via a box-least-squares period search (Kovacs et al. 2002) after removal of the stellar modulation signal with the splines. This detrending was not the one used for the transit modeling, described in Section 4.1.

We obtained follow-up photometric confirmation of the planetary transit via the Las Cumbres Observatory Global Network (LCOGT; Brown et al. 2013). Transit opportunities for a 225 day period planet are rare from the ground (see Table 3). We captured the full transit of TOI-4562b on 2022 January 3 UTC from the South African Astronomical Observatory (SAAO) node of LCOGT via two 1 m telescopes. The observations were obtained with the Sinistro 4 K × 4 K cameras in the Sloan $i^{\prime}$ filter. The observations were calibrated via the BANZAI pipeline (McCully et al. 2018), and light curves were extracted via the AstroImageJ package (Collins et al. 2017) using circular apertures with radius 47, which exclude flux from all known nearby Gaia EDR3 and TESS Input Catalog stars. The combined light curves (after removing systematics) and best-fit model are shown in Figure 2.

In addition, a transit on 2022 August 16 was attempted from the SAAO node of LCOGT via one 1 m telescope, as well as the Antarctica Search for Transiting ExoPlanets (ASTEP) facility (Guillot et al. 2015; Mekarnia et al. 2016), located at the East Antarctic plateau. A 25 minute segment was captured out of transit, but no portions of a transit event were recorded, and the data set is not included in the modeling presented below.

To characterize the radial-velocity orbit of TOI-4562b and constrain the properties of the host star, we obtained 84 spectroscopic observations of TOI-4562 using the CHIRON facility. To capture the long orbital period of TOI-4562b, the velocities spanned two observing seasons, from 2020 December 9 to 2022 January 23; the resulting radial velocities are given in Table 4. CHIRON is a fiber-fed, high-resolution echelle spectrograph on the 1.5 m SMARTS telescope at Cerro Tololo Inter-American Observatory, Chile (Tokovinin et al. 2013). Due to the faintness of the host star, spectral observations were obtained in the "fiber" mode of CHIRON, yielding a resolving power of R ∼ 28,000 over the wavelength range of 4100–8700 Å and an average signal-to-noise of ∼100 per resolution element at the Mg b line wavelength region.

We make use of the extracted spectra from the standard CHIRON pipeline described in Paredes et al. (2021). Radial velocities were derived from the observations via a least-squares deconvolution against a nonrotating ATLAS9 spectral template (Castelli & Kurucz 2004). The resulting broadening profile is fitted via a kernel describing the effects of radial-velocity shift and rotational, macroturbulent, and instrumental broadening. The derived velocities are presented in Table 4 and shown in Figure 4.

To estimate the spectroscopic properties of the host star, we matched each spectrum against an observed library of ∼10,000 spectra preclassified by the spectroscopic classification pipeline (Buchhave et al. 2012). The matching was performed by first training the preclassified library via a gradient-boosting classifier using scikit-learn and then classifying the observed spectrum. We found that TOI-4562 has an effective temperature of T_eff = 6096 ± 50 K, a surface gravity of log g = 4.4 ± 0.1 dex, a bulk metallicity of [M/H] =0.1 ± 0.1 dex, and a line-of-sight projected stellar rotational velocity of v sin i = 17 ± 0.5 km s⁻¹. Since the CHIRON data set overwhelms the other data sets we obtained for TOI-4562 in quantity, we adopt these parameters as Gaussian priors in the global analysis of the system described in Section 4. We note a general consensus between the spectral parameters from CHIRON and those presented below in Section 2.4.

We also check for the possibility that the velocity variations we observe are due to a spectroscopically blended companion rather than the host star. We compare the broadening measured from the line profiles against the velocities and find no correlation. If a blended companion is causing the radial-velocity offset, then the line profiles should be broadest at the orbital quadratures and narrowest at the conjunctions. We therefore find no evidence that the velocity variations originate from a blended companion.

The FEROS spectrograph, attached to the MPG/ESO 2.2 m (Kaufer et al. 1999) telescope at La Silla Observatory, gathered 11 spectra of TOI-4562. Spectra are coadded with a signal-to-noise ratio per spectra ranging between 52 and 82, and atmospheric parameters are derived using ZASPE (Brahm et al. 2017b). We find T_eff = 6280 ± 100 K, log g = 4.49 ± 0.10, [M/H] = 0.24 ± 0.05 dex, and v sin i = 15.7 ± 0.5 km s⁻¹. We chose not to include the FEROS data in the RV modeling. All points fall near phases (−0.4, 0.025, and 0.35) where the RV signal is close to 0 and therefore do not meaningfully contribute while adding one instrument and the associated extra parameters. Using the ceres pipeline (Brahm et al. 2017a), we also recover chromospheric emission indices, tracers of stellar activity. The core emission of the H_α line at 6562.808 Å is H_α = 0.160 ± 0.005 (following Boisse et al. 2009). Using regions defined by Duncan et al. (1991) and calibrations from Noyes et al. (1984), we measure the core emission of the Ca ii H and K lines around 3933 Å and 3968 Å to be log ${R}_{\mathrm{HK}}^{{\prime} }$ = −4.503 ± 0.044. This value is consistent with a young active star (Mamajek & Hillenbrand 2008). Finally, legacy spectra from the GALAH survey (Buder et al. 2021) found T_eff = 6034 ± 77 K, log g = 4.36 ± 0.18, [M/H] = 0.08 ± 0.06, and v sin i = 15.6 ± 2.2 km s⁻¹.

A first high-resolution image of TOI-4562 was obtained on 2022 March 17 with the Zorro Speckle camera on the 8.1 m Gemini South telescope (Howell & Furlan 2022) and is shown in the top panel of Figure 3. Simultaneous observations were obtained at 562 and 832 nm, respectively. Contrast curves were retrieved following Howell et al. (2011) for both wavelengths, and neither shows sign of a companion in the vicinity of TOI-4562b. A difference in magnitude Δm of 5 is achieved at a separation of ∼01. This allows us to rule out the presence of bright stellar objects in the same TESS pixel as TOI-4562 that would meaningfully impact the transit light curve to a projected distance of ∼35 au (given TOI-4562's distance of 350.0 ± 1.2 pc).

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On 2022 April 19, another high-resolution image was acquired with the HRCam instrument on the 4.1 m SOAR telescope. TOI-4562 was observed as part of the SOAR TESS survey (Ziegler et al. 2020, 2021), and the data were reduced following Tokovinin (2018). The image shown in the bottom panel of Figure 3 and shows a contrast in the I band of 5 mag within 1'' with no sign of a companion, in agreement with the Gemini South observation.

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Young stars on the zero-age main sequence spin rapidly. Over the course of a few billion years, mass loss from stellar winds spin down Sunlike stars. The rotation period of Sunlike stars can be a tracer for their age. Rotation–color–age relationships such as those from Barnes (2007) and Mamajek & Hillenbrand (2008) are calibrated against coeval clusters and associations and can provide useful metrics to estimate stellar ages. Recent theoretically motivated models, which are based on wind-braking models and can incorporate core–envelope coupling, also provide such relationships (e.g., Spada & Lanzafame 2020).

The 25 sectors of observations gathered by TESS provide the means for a good estimation of the rotation period of TOI-4562. As shown in Figure 5, we ran the PyAstronomy implementation of the generalized Lomb–Scargle periodogram (GLS; Lomb 1976; Scargle 1982; Zechmeister & Kurster 2009) on the entire data set and measured a rotation period of P_⋆ =${3.86}_{-0.08}^{+0.05}$ days. To obtain P_⋆, we first computed separate GLS periodograms for individual sectors (each covering ∼7 P_⋆) previously binned to a 10 minute cadence. The median and 1σ values of all obtained periods were then used to derive P_⋆ and the associated uncertainties.

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We note the clear second periodogram peak in Figure 5, close to P_⋆. This could be showing differential rotation (i.e., the variation of P_⋆ as a function of stellar latitude). This has been largely observed in Kepler stars (Reinhold et al. 2013). We could suppose that the rotational modulation of two distinct clumps of surface stellar spots evolving at a different latitude would be at the origin of the double peak (Lanza et al. 1993).

In addition, TOI-4562 received 4 yr of monitoring with the Wide Angle Search for Planets (WASP) Consortium (Pollacco et al. 2006) Southern SuperWASP facility from 2008 to 2012. WASP-South is located at SAAO and consists of an array of eight commonly mounted 200 mm f/1.8 Canon telephoto lenses, each with a 2 K × 2 K detector. A period analysis of the WASP-South light curves reveals periods of 3.74, 3.84, 3.82, and 3.84 days for the 2008/2009, 2009/2010, 2010/2011, and 2011/2012, respectively, in agreement with the TESS light curves. The long-term stability of the signal helps to confirm it as the correct alias of the rotational modulation signal. We note that WASP did not cover any transit event.

Finally, we run periodograms on the available light curves from the All-Sky Automated Survey for Supernovae (ASAS-SN; Shappee et al. 2014; Jayasinghe et al. 2019). Sloan g-band data spanning from 2017 October to 2022 April show very strong peaks in the periodogram at 3.84, 3.87, and 3.82 days for the 2018/2019, 2019/2020, and 2020/2021 seasons, respectively (2017 and 2022 data sets are of poorer quality), agreeing with the other photometric data sets. The Johnson V-band data was obtained between October 2016 and September 2018. Despite being less extensive and less densely sampled than the g-band photometry, a moderate peak (FAP ∼ 0.2%) is found at 3.64 days, close to P_⋆.

Using the age–rotation relationship from Mamajek & Hillenbrand (2008), we found TOI-4562b to be 110–490 (3σ) Myr old. We note that age estimates from this relationship assume that the star lies on the slow sequence of the age–rotation relationship. Stars are often found to be more rapidly rotating than such sequences for a given age, which has been attributed to binarity in cluster populations (e.g., Douglas et al. 2016; Gillen et al. 2020). Though there is no evidence for TOI-4562 being part of a binary system, caveats still apply for gyrochronology-based age estimates. For a 1.2 M_⊙ star with P_⋆ = ${3.86}_{-0.08}^{+0.05}$, the model from Spada & Lanzafame (2020) gives a consistent age estimate of 300–400 Myr.

The top plot of Figure 6 shows the rotation period of TOI-4562 compared with stars of known nearby clusters and associations. TOI-4562's P_⋆ is consistent with that of stars belonging to Group X (Messina et al. 2022; Newton et al. 2022), with an estimated age of 300 Myr.

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The convective envelope of low-mass stars (M_⋆ < 1.5 M_⊙) allows efficient transport of lithium to deeper and hotter regions in a star's interior, where it gets destroyed by proton capture. Calibrated with stars in clusters and associations, this lithium depletion can be used as a proxy for stellar age. Using CHIRON spectra (see Section 2.3), we measured the equivalent width of the lithium doublet at 6707.76 and 6707.91 Å. We fit two Gaussian line profiles of the same depth at the respective wavelengths of the lithium doublet and one auxiliary with a different depth to account for the nearby Fe i line at 6707.43 Å usually blended with the Li doublet. All profiles share the same width as per the rotational broadening of the star. We measure a lithium equivalent width of 0.084 ± 0.007 Å from a median-combined spectrum of all our CHIRON observations. These data are displayed in Figure 6. On the same figure, we show the lithium equivalent width as a function of effective temperature for stars belonging to clusters with well-constrained ages, the Pleiades (∼ 125 Myr), Group X (∼ 300 Myr), and Praesepe (∼ 670 Myr). TOI-4562 exhibits a Li equivalent width shallower than most of the Pleiades stars and of comparable strength to stars from the Praesepe cluster, at an effective temperature of 6000 K. Combined with the gyrochronology analysis, TOI-4562's age is consistent with a star younger than the Praesepe/Hyades clusters (i.e., ≲700 Myr).

Finally, we used the more recent baffles package (Stanford-Moore et al. 2020) to derive an age estimate. baffles is a Bayesian framework in which lithium abundance, the log $R{{\prime} }_{\mathrm{HK}}$ index, and B − V color are used to infer an age posterior for the studied star. The likelihood functions used are calibrated against stars belonging to open clusters and associations (i.e., with well-constrained ages). For log $R{{\prime} }_{\mathrm{HK}}$=−4.503 (from the FEROS spectra), Li 6708 EW = 84 ± 7 mÅ, and B − V = 0.52 ± 0.03 (corrected from extinction), we recover a 1σ age estimate of 340-715-1500 Myr. This is slightly higher than our previous estimate, but we note that baffles uses an age posterior extending by default to 12 Gyr. Compared to the star sample used in Morris (2020) belonging to well-studied star clusters, TOI-4562's photometric variability and rotation period are respectively larger and smaller than any stars of age 1 Gyr, therefore pointing to a younger age. Applying a conservative maximum age cutoff of 1.5 Gyr to the age posterior when running baffles yields a 1σ age of 320-619-1100 Myr, closer to previously quoted values.

All parameters for TOI-4562 are summarized in Table 1.

Despite the 225 day orbital period of TOI-4562b, the extensive observations of TOI-4562 by TESS allowed four transits to be observed. Spot-modulated variability at the ∼3% level is seen on the TESS light curve due to the active nature of TOI-4562, as expected given its young age. For the purposes of the transit modeling, we detrend the region around each transit epoch with a fourth-order polynomial. The polynomial is fitted using the out-of-transit regions of the light curve within 0.5 days of the transit center. We model the transits as per Mandel & Agol (2002) via the batman package (Kreidberg 2015). Free parameters that describe the transit model include the transit center T_c at each transit epoch, radius ratio R_p/R_⋆, line-of-sight inclination of the transit i, and the eccentricity parameters $\sqrt{e}\cos \omega$ and $\sqrt{e}\sin \omega$. A quadratic model was used to account for limb darkening using coefficients μ_1TESS and μ_2TESS, fixed to those interpolated from Claret (2017) at the atmospheric parameters of TOI-4562 for the TESS transits. We note that a/R_⋆ was not directly sampled but rather computed from the free parameters P_orb, M_⋆, R_⋆ and planet mass M_p. For the two (same epoch, different telescopes) SAAO LCOGT transits, the limb-darkening coefficients ${\mu }_{{1}_{\mathrm{LCO}}}$ and ${\mu }_{{2}_{\mathrm{LCO}}}$ are computed for the SDSS i' band from Claret & Bloemen (2011), using the interpolation routine from Eastman et al. (2013) with T_eff = 6000 K, log g = 4.5, and [M/H] = 0.1, computed with the least-squares method (LSM). For the SAAO LCOGT data, we also incorporate the effects of instrumental systematic variations that are common to ground-based photometric observations via a simultaneous detrending of the light curve against parameters describing the observation air mass to which we add a linear trend with respect to time. All detrended light curves and the best transit-model fits are shown in Figure 2.

Even though the transit shape points to a very eccentric orbit, this can be degenerate with the mean stellar density ρ_⋆. To cross-validate the eccentric nature of TOI-4562b's orbit, we compared the stellar density obtained from isochrone fitting, which we call ρ_⋆, to the stellar density obtained from a forced circular orbit, which we call ρ_circ. To obtain ρ_circ, we run a transit-only model, imposing e = 0 and with the following free parameters: ρ_circ, transit center T_c for each transit, radius ratio R_p/R_⋆, impact parameter b, limb-darkening coefficients (${\mu }_{{1}_{\mathrm{LCO}}}$, ${\mu }_{{2}_{\mathrm{LCO}}}$, ${\mu }_{{1}_{\mathrm{TESS}}}$ and ${\mu }_{{2}_{\mathrm{TESS}}}$), and instrument systematics parameters (for the SAAO LCOGT transits). Leveraging this photoeccentric effect (Dawson et al. 2012) allows us to recover the space of possible parameters for e and w (see Dawson et al. 2015). On Figure 8, we show in blue the resulting 2D distribution of e and w that agree with the derived ratio for ρ_circ/ρ_⋆, given ⁴⁰ :

$\begin{eqnarray}&&\displaystyle \frac{{\rho }_{\mathrm{circ}}}{{\rho }_{\star }}=\displaystyle \frac{{(1+e\,\sin w)}^{3}}{{(1-{e}^{2})}^{3/2}}.\end{eqnarray} \tag{ 1 }$

This grants us increased confidence of the true eccentric nature of TOI-4562b's orbit.

The radial velocities obtained over the two consecutive orbits of TOI-4562b were modeled using a Keplerian orbit. Some fitted parameters are shared with the transits and stellar isochrone fitting, such as T_c, P_orb, a/R_⋆(derived), R_⋆, M_⋆, i, $\sqrt{e}\cos \omega$ , and $\sqrt{e}\sin \omega$. To model the velocities, we add the planet mass M_p, a radial-velocity offset γ_rel, and a white-noise term, σ_Y1. The semiamplitude of the planetary signature K_amp was computed from the above parameters. The orbital solution and the associated likelihood from the fit to the data are computed from K_amp, T_c, P_orb, $\sqrt{e}\,\cos \,\omega$, and $\sqrt{e}\,\sin \,\omega$ via the radvel package (Fulton et al. 2018).

We also try to add a Gaussian process using a quasiperiodic kernel, implemented through radvel to model the stellar noise apparent in the data. The resulting parameter values do not yield a significant difference, therefore not justifying the necessity to use a correlated noise model to account for the stellar intrinsic variability seen in the radial velocities. With one data point a day at most, the sampling is too sparse for the Gaussian process to correctly grasp the ∼4 day stellar period. Crudely assuming a spot covering 0.6%–1.2% (δ_spot) of the stellar surface, we can approximate an activity-induced radial-velocity semiamplitude K_act of v sin i × δ_spot ∼ 100–200 m s⁻¹, comparable to the jitter level seen in Figure 4.

We attempted to fit a second longer-period circular planet to the radial velocities. We used uniform priors for the period (${ \mathcal U }[300:2000]$ days), planet mass (${ \mathcal U }[0.002:0.1]$ M_⊙), and t₀ (${ \mathcal U }[1398:3398]$ TESS Barycentric Julian Date). The posterior distributions are not clearly converging, favoring larger periods and smaller masses. With a K_amp of ∼70 m s⁻¹, the best solution is clearly below the activity level and therefore not trustworthy. Long-term data is needed to attempt to constrain a longer-period companion.

To constrain the host star parameters R_⋆, M_⋆, [M/H], and T_eff we also model the spectral energy distribution (SED) of TOI-4562 simultaneously to the transit and radial-velocity models. The stellar parameters are modeled using the MESA Isochrones and Stellar Tracks (Paxton et al. 2011, 2013, 2015; Choi et al. 2016). We interpolate evolution tracks using the minimint package (Koposov 2021) against M_⋆, age, [M/H], and the photometric bands B, V, Gaia G, Bp, Rp, and 2MASS bands J, H, and K. R_⋆ is derived from the isochrone-predicted values for log g and M_⋆. To account for uncertainties in the stellar evolution models, we adopt a 4% uncertainty floor in stellar radius and 5% floor in stellar mass, where appropriate (Tayar et al. 2022). For the effective temperature T_eff, we apply a Gaussian prior such that the predicted T_eff interpolated from the isochrone is compared against that measured from the CHIRON spectra as an additional likelihood term. Predicted fluxes from the SED model are corrected for interstellar reddening with the PyAstronomy unred package, which uses the parameterization from Fitzpatrick (1999). Extinction is a free parameter, with a maximum value of E(B − V) = 0.1542 mag, as estimated from the Schlafly & Finkbeiner (2011) maps over a 5' radius ⁴¹ around TOI-4562. We also incorporate a Gaussian prior on the distance modulus via the observed Gaia parallax to TOI-4562. We offset Gaia DR3's parallax value by −0.023861 mas, the parallax zero-point offset estimated using the routine from Lindegren et al. (2021a), ⁴² and function of ecliptic latitude, magnitude, and color. At each Markov Chain Monte Carlo (MCMC) jump step, the observed SED is compared against the interpolated MIST model predictions for a given tested stellar parameter.

Table 1. TOI-4562 Parameters

Parameters	Description	Prior	Value	Reference
Name and position
TOI	TESS Object of Interest	·	4562
TIC	TESS Input Catalog	·	349576261	ST18
Gaia	DR2 Source ID	·	5288681857665822080	Gaia EDR3
R.A.	Right ascension (HH:MM:SS, J2000, epoch 2015.5)	·	07:28:02.41	Gaia EDR3
Decl.	decl. (DD:MM:SS, J2000, epoch 2015.5)	·	·63:31:04	Gaia EDR3
μR.A.	R.A. proper motion (mas yr−1)	·	·5.899 ± 0.015	Gaia EDR3
μdecl.	decl. proper motion (mas yr−1)	·	10.491 ± 0.011	Gaia EDR3
Type	Spectral type	·	F7V
ϖ	Parallax (mas)	${ \mathcal G }[2.857,0.05]$ a	2.85692${}_{-0.00990}^{+0.01009}$	This work
D	Distance (parsec)	·	350.0 ± 1.2	This work
Photospheric parameters
Teff	Effective temperature (K)	·	6096 ± 32 K	This work (CHIRON)
log g	Surface gravity (dex)	·	4.39 ± 0.01	This work
[M/H]	Bulk metallicity (dex)	${ \mathcal G }[0.2,0.3]$	0.08 ± 0.06	This work
v sin i	Rotational velocity (km s−1)	·	17 ± 0.5	This work (CHIRON)
Physical parameters
M⋆	Mass (M⊙)	${ \mathcal U }[0,2]$	1.192 ± 0.057	This work
R⋆	Radius (R⊙)		1.152 ± 0.046	This work
Age	Age (Myr)		<700	This work
Activity parameters
P⋆	Equatorial rotation period (days)	·	${3.86}_{-0.08}^{+0.05}$	This work
Li 6708 EW	Li doublet (∼6708 Å) equivalent width (Å)	·	0.076 ± 0.022	This work
log $R{{\prime} }_{{HK}}$		·	·4.503 ${}_{-0.052}^{+0.028}$	This work (FEROS)
Photometric parameters
E(B-V)	Interstellar extinction (mag)	${ \mathcal U }[0,0.1542]$ b	<0.01 (3σ)	This work
T	TESST(mag)	·	11.533 ± 0.006	ST18
V	Johnson V(mag)	·	12.098 ± 0.014	H16
B	Johnson B (mag)	·	12.698 ± 0.025	H16
G	Gaia G(mag)	·	11.948 ± 0.020 c	Gaia EDR3
Bp	Gaia Bp(mag)	·	12.262 ± 0.020 c	Gaia EDR3
Rp	Gaia Rp(mag)	·	11.467 ± 0.020 c	Gaia EDR3
J	2MASS J(mag)	·	10.931 ± 0.023	SK06
H	2MASS H(mag)	·	10.693 ± 0.025	SK06
Ks	2MASS Ks(mag)	·	10.619 ± 0.023	SK06
W1	WISE W1(mag)	·	10.578 ± 0.023	W10,C13
W2	WISE W2(mag)	·	10.618 ± 0.020	W10,C13
W3	WISE W3(mag)	·	10.590 ± 0.061	W10,C13
NUV	GALEX/NUV calibrated AB magnitude (mag)	·	17.133 ± 0.023	B17

Notes.

^a Adopted from Gaia EDR3 Gaia Collaboration et al. (2016, 2021), corrected using a zero-point offset value of −0.024 mas, following Lindegren et al. (2021a). ^b Adopted from Schlafly & Finkbeiner (2011). ^c These are inflated uncertainties from the Gaia photometric bands, following the convention from Eastman et al. (2013). Priors: ${ \mathcal U }$ a, b uniform priors with boundaries a and b; ${ \mathcal G }$[μ,σ] Gaussian priors.

References. (Gaia EDR3) Gaia Collaboration et al. (2016, 2021); (ST18) Stassun et al. (2018); (SK06) Skrutskie et al. (2006); (W10) Wright et al. (2010); (C13) Cutri et al. (2021); (B17) Bianchi et al. (2017); (H16) Henden et al. (2016).

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The global model includes simultaneous fits of the TESS and ground-based photometric data sets (4.1), the CHIRON velocities (4.3), and stellar isochrone model (4.4), as shown in Figures 2, 4, and 7, respectively. We explore the best-fit parameters and the posterior distribution via the affine invariant MCMC ensemble sampler emcee (Foreman-Mackey et al. 2013). The resulting parameters for TOI-4562b are given in Table 2.

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Table 2. TOI-4562b Parameters

Parameters	Description	Priors	Values
Transit parameters
Tc,1 a	Transit mid-time (BJDTDB)	${ \mathcal U }$[1456.83,1456.93]	1456.87991${}_{-0.00120}^{+0.00142}$
Tc,2 a	Transit mid-time (BJDTDB)	${ \mathcal U }$[1681.94,1682.04]	1681.98324${}_{-0.00142}^{+0.00136}$
Tc,3 a	Transit mid-time (BJDTDB)	${ \mathcal U }$[2132.17,2132.27]	2132.21577${}_{-0.00095}^{+0.00088}$
Tc,4 a	Transit mid-time (BJDTDB)	${ \mathcal U }$[2357.29,2357.39]	2357.34544${}_{-0.00080}^{+0.00079}$
Tc,5 a	Transit mid-time (BJDTDB)	${ \mathcal U }$[2582.41,2582.51]	2582.46321${}_{-0.00036}^{+0.00142}$
Tc a	Derived linear ephemeris	${ \mathcal U }$[1456.83,1456.93]	1456.87168${}_{-0.00101}^{+0.00101}$
Porb a	Orbital period (days)	Derived linear ephemeris	225.11781${}_{-0.00022}^{+0.00025}$
T14	Transit total duration (hours)	·	4.32 ± 0.04
Rp/R⋆	Radius ratio	${ \mathcal U }[0,0.2]$	0.09980${}_{-0.00092}^{+0.00084}$
a/R⋆	Normalized semimajor axis, derived from [M⋆,R⋆,Porb,Mp]	·	147.4${}_{-1.26}^{+1.44}$
b	Impact parameter	·	0.60${}_{-0.04}^{+0.03}$
δ	Transit depth (ppm)	·	9961${}_{-184}^{+167}$
$\sqrt{e}\cos \omega$ a	Reparameterization of e and ω	${ \mathcal U }[-1,1]$	0.442${}_{-0.131}^{+0.110}$
$\sqrt{e}\sin \omega$ a	Reparameterization of e and ω	${ \mathcal U }[-1,1]$	0.752${}_{-0.063}^{+0.058}$
i	Planet orbit inclination (°)	${ \mathcal U }[84,90]$	89.06 ± 0.04
${\mu }_{{1}_{\mathrm{TESS}}}$ b	Quadratic limb-darkening law coefficient 1 (TESS)	Fixed	0.28
${\mu }_{{2}_{\mathrm{TESS}}}$ b	Quadratic limb-darkening law coefficient 2 (TESS)	Fixed	0.29
${\mu }_{{1}_{\mathrm{LCO}}}$ c	Quadratic limb-darkening law coefficient 1 (LCO)	Fixed	0.28
${\mu }_{{2}_{\mathrm{LCO}}}$ c	Quadratic limb-darkening law coefficient 2 (LCO)	Fixed	0.29
Radial velocities parameters
K	RV semiamplitude (m s−1)	-	106${}_{-26}^{+24}$
Mp	Mass (M⊙)	${ \mathcal U }[0,0.2]$	0.0022 ± 0.0005
γCHIRON	RV offset (m s−1)	${ \mathcal U }[5200,5400]$	5347±13
σY1	RV jitter, first orbit (m s−1)	${ \mathcal U }[0,600]$	${73}_{-15}^{+15}$
Derived parameters
Rp	Radius (R⊕)	·	12.53 ± 0.15
	Radius (RJ)	·	${1.118}_{+0.013}^{-0.014}$
Mp	Mass (M⊕)	·	732${}_{-149}^{+152}$
	Mass (MJ)	·	2.30${}_{-0.47}^{+0.48}$
e	Eccentricity	·	0.76${}_{-0.02}^{+0.02}$
w	Argument at periapse (°)	·	60${}_{-8}^{+9}$
ρp	Density (g cm−3)	·	2.06${}_{-0.44}^{+0.42}$
a	Semimajor axis (au)	·	0.768${}_{-0.005}^{+0.005}$
〈Teq〉	Temporal average equilibrium temperature (K) d	·	318 ± 4
Tperi	Equilibrium temperature at periapsis (K)	·	717${}_{-37}^{+29}$
Tapo	Equilibrium temperature at apoapsis (K)	·	262${}_{-2}^{+3}$

Notes. Priors: ${ \mathcal U }$ [a, b] uniform priors with boundaries a and b.

^a Parameters common to the transit and RV models. ^b Adopted form  the TESS band from Claret (2017), using ATLAS model with T_eff = 6000 K, log g = 4.5, and [M/H] = 0.1 and computed with the LSM. ^c Computed for the SDSS i' band from Claret & Bloemen (2011), using the interpolation routine from Eastman et al. (2013) with T_eff = 6000 K, log g = 4.5, and [M/H] = 0.1 and computed with the LSM. ^d Computed for an elliptical orbit from Mendez & Rivera-Valentin (2017), using an albedo of A = 0.4, = 1, and β = 0.74.

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Figure 8 illustrates the contribution of each part of the model to constrain the high eccentricity of TOI-4562b. In gray we show the distribution stemming from the value of ρ_⋆ when imposing a circular orbit to the planet and fitting only for transits (see Section 4.2). Then, a model containing both the transits and isochrones, shown in red, greatly constrain the eccentricity. Finally, the addition of RVs (shown in yellow) only slightly improves the constraint of the eccentricity, due to both the large stellar activity and the poor coverage of the periastron passages.

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At the end of their accretion phase, newly formed gas giants are expected to have radii larger than 1 R_J. As the planet core radiates its primordial internal heat, Jovian mass planets will cool down via the Kelvin–Helmholtz contraction to ∼1 R_J. Only hot Jupiters, orbiting extremely close to their parent star, are expected to remain inflated due to their increased irradiation. According to cooling models (Baraffe et al. 2003; Fortney et al. 2007; Baraffe et al. 2008; Linder et al. 2019), shown in Figure 10, the most drastic changes in radius occur at the earliest ages. Measuring radii of young gas giants like TOI-4562b is therefore essential to set constraints on these such models, as emphasized in Fortney et al. ( 2007).

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The current picture is unclear as the recently measured mass of V1298 Tau b & e (Suárez Mascareño et al. 2022) yield much denser planets than predicted at 20 Myr old and require dramatic heavy element enrichment to somewhat reconcile with cooling models (see Figure 10). Conversely, TOI-4562b's radius is as expected for its age. At the closest approach to its host star (∼0.18 au), it receives stellar irradiation of ∼ 9.3 × 10 ⁴ W m⁻², or ∼ 68 times that of Earth. Although above the ∼1.6 ×10 ⁴ W m⁻² threshold to trigger inflation, given by Sestovic et al. (2018) for planets more massive than 2.5 M_J, TOI-4562b's orbital eccentricity means this level of irradiation affects the planet for a very short fraction of the orbit, not sufficient to trigger radius inflation.

In its current observed state, TOI-4562b's semimajor axis and eccentricity (see Figure 11) are not in favor of a high-eccentricity migration scenario as a circularization of its orbit would take orders of magnitudes longer than the age of the universe (τ_circ ∼ 1 ×10⁷ Gyr; Goldreich & Soter 1966). It is possible, however, that the planet is experiencing ongoing eccentricity cycles and we happen to be observing it at a lower eccentricity. Reduction of the star–planet distance at the periastron at the eccentricity peak of such cycles might allow the circularization process to be triggered as described in Dong et al. (2014). Disk–planet interactions can in principle excite the eccentricity of the orbit (Duffell & Chiang 2015), but this is restricted to low (e ≲ 0.2) values, as shown with the red area in Figure 11. Debras et al. (2021) proposed that migration inside wide gaps carved in protoplanetary disks could result in gas giants with eccentricities up to 0.4. This is still insufficient to explain the very high eccentricity from TOI-4562b's orbit.

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Another possible scenario to account for TOI-4562b's very high eccentricity is in situ formation (or alternatively, smooth disk migration), followed by excitation from a companion. This can occur via secular interactions or slow angular momentum exchanges with another body located further out, either periodically through, e.g., von Zeipel–Lidov–Kozai cycles (von Zeipel 1910; Kozai 1962; Lidov 1962; Nagasawa et al. 2008; Naoz 2016), or chaotically in secular chaos (Wu & Lithwick 2011; Hamers et al. 2017). High eccentricity can also be triggered sporadically in planet–planet scattering (Weidenschilling & Marzari 1996; Rasio & Ford 1996; Ford & Rasio 2006; Chatterjee et al. 2008) or stellar flybys (Shara et al. 2016; Rodet et al. 2021). Planet–planet scattering could have happened quickly and potentially early if triggered by the dissipation of the gas disk or if the planets were initially closely spaced. Constraints on an outer companion (if not ejected as a result of scattering) could provide crucial insights on dynamical evolution timescales, given the young age of the system.

The five transits of TOI-4562b show modest deviation from a linear ephemeris fit on the 5–20 minute level (see Figure 12). This potential detection of a transit-timing variation signal suggests the presence of a companion in the system, to which TOI-4562b probably owes its high eccentricity. The existing data are not sufficient to set meaningful constraints on the companion, and most configurations for period (i.e., inner or outer companion), eccentricity, and mutual inclination remain possible. TOI-4562b will be observed by TESS again in its second extended mission in 2023. In Table 3, we show future opportunities to continue monitoring transits of TOI-4562b in the years to come. Combining these with long-term radial-velocity follow-up might enable us to unravel the 3D architecture and dynamical history of this system, as has been successfully performed for Kepler-419 b and c (Dawson et al. 2012, 2014). We also note that no transit-duration variations were found.

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The orbital astrometric motion of an outer companion could be retrieved from Gaia in the upcoming release of astrometric solutions for ∼1.3 billion stars (Lindegren et al. 2021b). When archival Hipparchos and Gaia observations have been analyzed jointly for previous brighter systems (e.g., Venner et al. 2021), astrometric accelerations have often yielded constraints for outer-stellar massed companions to key exoplanet systems. Additional Gaia observations over the next ∼10 yr will allow us to achieve similar constraints for TOI-4562. Combined with the diffraction-limited adaptive optics observations estimated to reach ∼35 au (see Section 2.5), these constraints can inform the presence of exterior stellar companions and provide means to distinguish between evolution scenarios.

Another candidate tracer for dynamical history is the angle between the star's rotation axis and the planet's orbital axis, or (sky-projected) obliquity. From P_⋆, R_⋆, and v sin i, we estimate the stellar inclination with respect to the line of sight to have a 3σ lower bound of 70° as per Masuda & Winn (2020), consistent with being well aligned. Similarly to other planetary characteristics, the young (<1 Gyr) end of the obliquity distribution is undersampled. Recent measurements resulting from TESS discoveries reveal a remarkable systematic alignment of young systems, including the Jupiter-sized planet HIP 67522 b (Rizzuto et al. 2020; Heitzmann et al. 2021), as well as a number of smaller planets (e.g., AU Mic b and c, Martioli et al. 2020; Palle et al. 2020; Hirano et al. 2020; Plavchan et al. 2020; Addison et al. 2021; DS Tuc Ab, Newton et al. 2019; Montet et al. 2020; Zhou et al. 2020; TOI 942 b and c, Wirth et al. 2021; and TOI 251, Zhou et al. 2021). The estimated amplitude of the Rossiter–McLaughlin effect (Rossiter 1924; McLaughlin 1924) for TOI-4562b is ΔV ∼ 70–150 m s⁻¹. Given the ∼4 hr transit duration, combined with a brightness of V = 12.098 and a rotational broadening of v sin i = 17.5 km s⁻¹, this is well within the grasp of a 4m class telescope, and such an eccentric system would provide a precious addition to the age-obliquity distribution. It is important to note that the long orbital period remains a major obstacle to transit spectroscopy for ground-based facilities.

In the coming years, we aim to conduct extensive follow-ups of the TOI-4562 system to unravel the full architecture of the system and potentially provide insights into the processes shaping the current gas-giant planet distribution. Such follow-up will include radial velocities, ground- and space-based photometry, astrometry and transit spectroscopy for obliquity measurements, and/or atmospheric characterization.