TOI-824 b: A New Planet on the Lower Edge of the Hot Neptune Desert

TOI-824 (SCR J1448-5735, TYC 8688-915-1, TIC 193641523, 2MASS J14483982-5735175) is a V = 11.15 (Winters et al. 2011) K-type dwarf star located at 64.4 ± 0.03 pc (ϖ = 15.6142 ± 0.0348 mas; Gaia Collaboration et al. 2018). The star has not drawn much previous attention, having been first pointed out as a high-proper-motion, potentially nearby star by Finch et al. (2007; identified as SCR J1448-5735). As the star had a preliminary photometric distance estimate of only 18 pc by Finch et al. (2007), Winters et al. (2011) measured Krons–Cousins VRI photometry as part of the SuperCOSMOS RECONS survey and provided an updated distance estimate of 62.4 ± 9.7 pc, not far from the current Gaia DR2 estimate (Bailer-Jones et al. 2018). Astrometry and photometry for TOI-824 are summarized in Table 1. The star's position, proper motion, parallax, and Gaia photometry are drawn from Gaia DR2. Optical photometry is adopted from Tycho-2 (B_T V_T; Høg et al. 2000), APASS DR9 (BVr"i"; Henden et al. 2015, 2016), and Gaia DR2 (Gaia Collaboration et al. 2018), while infrared photometry is adopted from the Two Micron All Sky Survey (2MASS; JHK_s; Cutri et al. 2003) and the Wide-field Infrared Survey Explorer (WISE; Cutri et al. 2012).

Table 1.  Stellar Parameters for TOI-824

Parameter	Value	Source
Designations	TIC 193641523	Stassun et al. (2019)
	SCR J1448-5735	Finch et al. (2007)
	2MASS J14483982-5735175	Cutri et al. (2003)
R.A. (hh:mm:ss)	14:48:39.71	Gaia DR2
Decl. (dd:mm:ss)	−57:35:19.92	Gaia DR2
μ R.A. (mas yr−1)	−51.6035 ± 0.068	Gaia DR2
μ Decl. (mas yr−1)	−152.392 ± 0.079	Gaia DR2
Parallax (mas)	15.696 ± 0.049	Gaia DR2a
Distance (pc)	63.71 ± 0.20	Gaia DR2
SpT	K4V	This work
B	12.263 ± 0.005	APASS/DR9
V	11.153 ± 0.008	APASS/DR9
V	11.15 ± 0.03:	Winters et al. (2011)
$r^{\prime}$	10.717 ± 0.025	APASS/DR9
$i^{\prime}$	10.303 ± 0.053	APASS/DR9
TESS	10.0732 ± 0.006	TIC8
G	${10.762}_{-0.001}^{+0.02}$	Gaia DR2
GBP	${11.406}_{-0.001}^{+0.02}$	Gaia DR2
GRP	${10.021}_{-0.001}^{+0.02}$	Gaia DR2
J	9.145 ± 0.018	2MASS
H	8.557 ± 0.046	2MASS
Ks	8.432 ± 0.038	2MASS
W1	8.154 ± 0.083	WISE
W2	8.326 ± 0.021	WISE
W3	6.948 ± 0.017	WISE
W4	3.372 ± 0.020	WISE
U (km s−1)	−0.220 ± 0.152	This work
V (km s−1)	−45.803 ± 0.181	This work
W (km s−1)	−33.886 ± 0.140	This work

Note.

^aCorrection of +82 μas applied to the Gaia parallax as per Stassun & Torres (2018).

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TOI-824 was observed by TESS from UT 2019 April 22 through 2019 May 20 as part of the Sector 11 campaign and again from UT 2019 May 21 through 2019 June 18 as part of Sector 12. The star fell on CCD 3 of Camera 2 during Sector 11 and then on CCD 4 of Camera 2 during Sector 12.

The SPOC data (Jenkins et al. 2016) for TOI-824, available at the the Mikulski Archive for Space Telescopes (MAST) website,³⁹ includes both simple aperture photometry (SAP) flux measurements (Twicken et al. 2010; Morris et al. 2017) and presearch data conditioned simple aperture photometry (PDCSAP) flux measurements (Smith et al. 2012; Stumpe et al. 2012, 2014). The instrumental variations present in the SAP flux are removed in the PDCSAP result. At the start of each orbit, thermal effects and strong scattered light impact the systematic error removal in PDC (see TESS data release notes DRN16 and DNR17). Before the fitting process described in Section 3.8, we use the quality flags provided by SPOC to mask out unreliable segments of the time series. We then further detrend the TESS data set by breaking it into the individual spacecraft orbits (two per sector) and fitting each with a low-order spline to address residual trends in the light curve (Figure 1).

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We acquired ground-based time-series follow-up photometry of TOI-824 during the times of transit predicted by the TESS data. We used the TESS Transit Finder, which is a customized version of the Tapir software package (Jensen 2013), to schedule our transit observations.

We observed a full transit of TOI-824 on UTC 2019 July 1 in the ${R}_{{\rm{c}}}$ band from the Perth Exoplanet Survey Telescope (PEST) near Perth, Australia. The 0.3 m telescope is equipped with a 1530 × 1020 SBIG ST-8XME camera with an image scale of 12 pixel⁻¹, resulting in a 31' × 21' field of view. A custom pipeline based on C-Munipack⁴⁰ was used to calibrate the images and extract differential photometry for TOI-824 and all other stars detected within 25 of TOI-824, using apertures with radius 62. The images have typical stellar point spread functions (PSFs) with an FWHM of 36.

Four full transits of TOI-824 b were observed using the Las Cumbres Observatory Global Telescope (LCOGT) 1 m network (Brown et al. 2013) on UTC 2019 June 30, 2019 July 13, 2019 July 27, and 2019 August 5 in Pan-STARSS z, B, B, and Pan-STARSS z bands, respectively. All observations were obtained by the LCOGT node at Cerro Tololo Inter-American Observatory, except the August 5 observations, which were obtained by the LCOGT node at Siding Spring Observatory. The telescopes are equipped with 4096 × 4096 LCO SINISTRO cameras having an image scale of 0389 pixel⁻¹, resulting in a 26' × 26' field of view. The images were calibrated by the standard LCOGT BANZAI pipeline, and the photometric data were extracted using the AstroImageJ (AIJ) software package (Collins et al. 2017). Circular apertures with radius of 12 pixels (47) were used to extract the differential photometry. The image sets have average stellar PSF FWHMs ranging from 14 on August 5 to 24 on July 14.

TOI-824 was observed by the CHIRON spectrograph (Tokovinin et al. 2013) to determine whether its stellar parameters were well suited to precision RV follow-up efforts. CHIRON is a high-resolution spectrograph fed by an image slicer and a fiber bundle, located on the 1.5 m SMARTS telescope at Cerro Tololo Inter-American Observatory (CTIO), Chile. CHIRON has a spectral resolving power of R ≃ 80,000 over the wavelength region from 4100 to 8700 Å. Two spectra were obtained for TOI-824 on UT 2019 July 5 and 6.

We collected AO images with the Very Large Telescope (VLT)/NaCo on UT 2019 August 2 using the Brγ filter centered on 2.166 μm (Lenzen et al. 2003; Rousset et al. 2003). We collected a total of nine frames, each with an exposure time of 22 s, and dithered the telescope position between each frame. This allows a sky background to be constructed by median combining the dithered frames. A standard data reduction was carried out using a custom IDL code. This procedure included bad pixel removal, flat-fielding, and subtraction of the sky background. Frames were then aligned and coadded.

TOI-824 was added as a target in two RV TESS follow-up efforts using the Planet Finder Spectrograph (PFS) on the 6.5 m Magellan Clay telescope (Crane et al. 2006, 2008, 2010) at Las Campanas Observatory and the High-Accuracy Radial velocity Planet Searcher (HARPS) spectrograph (Mayor et al. 2003) on the ESO 3.6 m telescope at La Silla Observatory.

PFS is a custom-designed precision RV echelle spectrometer that, with the exception of the focus, has no moving parts. PFS is embedded in an insulated box where the temperature is maintained at 27°C ± 0.01°C. The wavelength range extends from 3900 to 6700 Å. In 2018 January, the old PFS CCD (a 4 K × 4 K detector with 15 μm pixels) was replaced with a next-generation 10 K × 10 K detector with 9 μm pixels, improving the sampling by 40%. The peak resolution of PFS when using the 03 slit, as was done for all observations of TOI-824, is R ≃ 130,000. An iodine cell placed in the converging beam of the telescope is used to provide a precise wavelength metric for velocity measurements (Marcy & Butler 1992). The gaseous iodine blankets the region from 5000 to 6200 Å with a dense forest of sharp absorption lines. The PFS iodine cell was scanned with the NIST FTS spectrometer (Nave 2017) at a resolution of 1 million. The raw data is reduced to 1D spectra with a custom-built raw reduction package. Velocities were generated from an updated version of the iodine modeling package outlined in Butler et al. (1996), and the BJD time stamps were computed using the PEXO software package (Feng et al. 2019).

In contrast, the HARPS spectrograph makes use of multiple observing fibers, one of which is placed on the stellar target while the other is fed by a Fabry–Perot interferometer for a simultaneous wavelength reference. HARPS produces spectra from 3800 to 6900 Å, the entirety of which can be used to measure a star's RV shift, and has a peak resolving power of R ≃ 115,000 (Pepe et al. 2002). Once an observation is complete, a 2D spectrum is optimally extracted from the resulting FITS file. The spectrum is cross-correlated with a numerical mask corresponding to the appropriate spectral type (F0, G2, K0, K5, or M4; we used the G2, which has undergone the most development during the HARPS observing span), and the resulting cross-correlation function is fit with a Gaussian curve to produce an RV measurement (Baranne et al. 1996; Pepe et al. 2002) and calibrated to determine the RV photon-noise uncertainty σ_RV.

A total of 24 PFS radial observations were obtained in 2019 July and August, binned into 12 velocity measurements, with a mean internal uncertainty of 0.94 ${\rm{m}}\,{{\rm{s}}}^{-1}$. A total of eight HARPS observations, binned into five velocity measurements, were obtained in 2019 July, with a mean internal uncertainty of 2.24 ${\rm{m}}\,{{\rm{s}}}^{-1}$ (Table 2).

Table 2.  Binned RV Data of TOI-824

Date (BJD)	RV $({\rm{m}}\,{{\rm{s}}}^{-1}$)	${\sigma }_{\mathrm{RV}}$ $({\rm{m}}\,{{\rm{s}}}^{-1})$	Instrument
2458674.64056	4.73	1.91	HARPS
2458675.67088	22.39	2.57	HARPS
2458676.56075	4.42	0.94	PFS
2458677.54783	−11.54	0.92	PFS
2458679.57467	15.06	0.83	PFS
2458680.55934	−3.35	0.79	PFS
2458681.56315	−4.86	1.07	PFS
2458682.54917	12.28	0.84	PFS
2458684.64071	6.30	2.12	HARPS
2458685.53003	11.15	1.03	PFS
2458689.59665	24.17	2.31	HARPS
2458690.61645	18.20	2.30	HARPS
2458703.54142	7.28	0.97	PFS
2458705.51575	−11.65	0.98	PFS
2458708.49699	−4.44	0.73	PFS
2458712.49177	−16.84	1.18	PFS
2458714.48836	14.16	1.03	PFS

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Sixteen transits of TOI-824 b were detected in both the MIT Quick Look Pipeline (QLP), which searches for evidence of planet candidates in the TESS 30 minute cadence full-frame images, and in the SPOC pipeline, which analyzes the 2 minute cadence data that TESS obtains for preselected target stars (Jenkins et al. 2016). Initial analyses of the TESS QLP results found a transit signal with a period of 1.393 days, a depth of ∼1900 ppm, a duration of 1.3 hr, and the classic flat-bottomed trough shape that is characteristic of a planetary transit. These transit parameters translated to a planet with radius R_p = 3.4 ${R}_{\oplus }$ when using the stellar parameters for TOI-824 listed in the eighth installment of the TESS Input Catalog (TIC; Stassun et al. 2019).

Although the measured transit depth and flat-bottomed shape were positive indicators of a transit signal being planetary in nature, the TESS vetting process is designed to guard against a variety of false positives that can mimic this combination. The primary sources of false positives in the TESS data are eclipsing binaries, whether in the form of transiting stars on grazing orbits or as background blends that reduce the amplitude of foreground transit signals, causing them to be deceptively small (e.g., Cameron 2012). Thus, during the TESS vetting process, we carefully inspected the star's Data Validation Report (DVR; Twicken et al. 2018; Li et al. 2019), which is based on the SPOC 2 minute cadence data for TOI-824. The multisector DVR was found to show no evidence of secondary eclipses, inconsistencies in depth between the even and odd transits, nor correlations between aperture size and transit depth, any of which would be interpreted as a sign of the signal being caused by a nearby eclipsing binary. Additionally, the DVR shows that the location of the transit source is consistent with the position of the target star. After passing these verification steps, the transit signal was assigned the identifier TOI-824.01 and was announced on the MIT TESS data alerts website⁴¹ so that additional follow-up efforts could be coordinated.

TESS has large ∼21'' pixels and ∼1' stellar FWHM, resulting in photometric apertures that typically extend ∼1' from the central target star location. The large apertures are often contaminated with many nearby stars bright enough to produce the TESS detection. We used our higher spatial resolution follow-up time-series images to search for the location of the periodic flux deficits that caused the detection of TOI-824 b in the TESS data. We checked the light curves of all 338 Gaia DR2 stars within 25 of TOI-824 that are bright enough to have caused the TESS detection and ruled out nearby eclipsing binaries (EBs) as the source. Furthermore, we detected five transits of TOI-824 b in our ground-based data using target star apertures with radii as small as 12 centered on TOI-824. The nearest Gaia DR2 or TICv8 star to TOI-824 at the epoch of our follow-up observations is 77 west. Thus, most of the flux from known nearby stars is excluded from even our larger 47 target star apertures. We therefore confirm that the source of the flux deficit that is responsible for the TESS detection occurs within a 12 radius of TOI-824. Our multiband light curves in B, R_c, and Pan-STARRS z bands show that the transits have depths that are consistent across optical wavelengths and with the deblended depth in the TESS data. This rules out certain classes of bound or background EBs that could be blended in the small follow-up photometric apertures as potential sources of the transit detections. Blended EBs that have primary and secondary stars with significantly different effective temperatures are ruled out, while those with similar effective temperatures could still possibly produce the transit signals based on the photometric data alone.

Adopting the position, proper motion, parallax, and absolute RV provided by Gaia Collaboration et al. (2018), we compute the barycentric galactic velocity of TOI-824 to be U, V, W = −0.220 ± 0.152, −45.803 ± 0.181, −33.886 ± 0.140 k ${\rm{m}}\,{{\rm{s}}}^{-1}$, with U measured toward the Galactic center, V in the direction of Galactic rotation, and W toward the North Galactic Pole (ESA 1997). Adopting the local standard of rest (LSR) from Schönrich et al. (2010), we find this velocity translates to U_LSR, V_LSR, W_LSR = 10.9, −33.6, −26.6 k ${\rm{m}}\,{{\rm{s}}}^{-1}$. Using the velocity ellipsoids and population normalizations from Bensby et al. (2003), we estimate the probabilities of kinematic membership of TOI-824 to the thin disk, thick disk, and halo to be 83.9%, 16%, and 0.1%, respectively. Hence, TOI-824 is kinematically most consistent with being a thin disk star. The kinematic parameters corroborate the chemical abundance information provided by TOI-824's color–magnitude diagram position (in the middle of the main sequence for field stars) and near-solar spectroscopic metallicity ([Fe/H] ≃ −0.1), suggesting that TOI-824 is a typical thin disk star.

The combined NaCo images show that no additional candidates were detected within the field of view, and that TOI-824 appears single to the limit of our resolution and contrast. The sensitivity of our observations was calculated as a function of radius by injecting fake companions and scaling their brightness until they could be detected with 5σ confidence. The contrast sensitivity is 5 mag at 250 mas and 5.5 mag in the wide field. The contrast sensitivity as a function of radius and a high-resolution image of the star are shown in Figure 2. The lack of companions strongly suggests that the transit signal originates from a planetary companion to TOI-824 b, rather than a background EB, and that the measured radius is not being diluted by a stellar companion (Ciardi et al. 2015).

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We also searched for wide companions sharing a similar proper motion and parallax in the Gaia DR2 astrometric catalog (Gaia Collaboration et al. 2018). Any bound companions would likely be seen at separations smaller than the star's tidal (Jacobi) radius (r_t ≃ 1.35 pc (${M}_{* }/{M}_{\odot }{)}^{1/3}$), which for the star's mass of 0.72 M_⊙ should correspond to about 1.21 pc (Jiang & Tremaine 2010; Mamajek et al. 2013), or 109 at the Gaia DR2 distance. A search of the Gaia DR2 catalog for stars with parallaxes within 25% of that of TOI-824 within 2r_t (218) yielded 234 stars. Within a projected separation of one tidal radius (109, 1.21 pc), none had a proper motion within 60 mas yr⁻¹ (Δv_tan ≃ 18 km s⁻¹) of that of TOI-824. Within two tidal radii, no Gaia DR2 stars had proper motion within 20 mas yr⁻¹ (Δv_tan ≃ 6.1 km s⁻¹) of TOI-824. Additionally, among stars within two tidal radii, no other Gaia DR2 candidates lacking parallaxes were found with proper motions within ±20 mas yr⁻¹ of that of TOI-824.

The Gaia DR2 data for entries in the vicinity of TOI-824 are reasonably complete with both parallaxes and proper motions down to G ≃ 20.0 (M_G = 16.0), and with increasing incompleteness down to G ≃ 21.4. Among nearby stars within 25 pc, the absolute magnitude M_G ≃ 16 compares well to the M8.5V star 2MASS J11240487 + 3808054 (M_G = 15.96, M_Ks = 18.47; Cruz et al. 2003; Cutri et al. 2003; Gaia Collaboration et al. 2018), whose M_Ks value corresponds to mass 0.08 M_⊙ (Mann et al. 2019), just above the H-burning limit. So our search of the Gaia DR2 catalog for wide companions is likely complete to just above the H-burning limit or ∼0.08 M_⊙.

When we combine our high-contrast imaging data, RV data, and analysis of the Gaia DR2 astrometry for stars in TOI-824's vicinity, thus far the star appears to be a single star, although objects straddling the H-burning limit or brown dwarfs on wide orbits can not yet be ruled out.

We performed an analysis of the broadband spectral energy distribution (SED) together with the Gaia DR2 parallax in order to determine an empirical measurement of the stellar radius, following the procedures described in Stassun & Torres (2016) and Stassun et al. (2017, 2018). Together, the available photometry described in Section 2 and Table 1 spans the full stellar SED over the wavelength range 0.4–22 μm (see Figure 3). Noting the large excess in the WISE3 and WISE4 bands due to a nearby infrared-bright star (IRAS 14448–5722, TIC 1133968082, Tmag = 19.72), we chose to exclude them from the fit.

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We performed the fit using NextGen stellar atmosphere models, with priors set on the star's effective temperature (${T}_{\mathrm{eff}}$), surface gravity (log g), and metallicity ([Fe/H]) drawn from the TIC-8. We set the extinction (A_V) to zero due to the proximity of the star, which is consistent with the A_V = 0.025 ± 0.06 value from Lallement et al. (2018). The resulting fit is very good (Figure 3) with a reduced χ² of 2.3 and best-fit T_eff = 4450 ± 100 K. Integrating the model SED gives the bolometric flux at Earth of F_bol = (1.442 ± 0.034) × 10⁻⁹ erg s cm⁻². Taking the F_bol and T_eff together with the Gaia parallax, adjusted by +0.082 mas to account for the systematic offset reported by Stassun & Torres (2018), gives the stellar radius as R_⋆ = 0.719 ± 0.033 ${R}_{\odot }$, which is consistent with the updated stellar parameters listed in TIC-8.

In order to better estimate the potential flux contamination of the nearby infrared-bright star ∼25'' (∼1 TESS pixel) from TOI-824, we also performed an SED fit to that source. In this case we also fit for A_V, which we limited to the maximum line-of-sight extinction from the Schlegel et al. (1998) dust maps. We used Gaia G, 2MASS JHK_S, WISE W1–W4, and BV magnitudes from the SPM4.0 catalog (Girard et al. 2011) and zy photometry from the VISTA catalog (Cross et al. 2012). We obtained a best-fit T_eff = 2750 ± 250 K and A_V = 5.8 ± 1.9. The Gaia DR2 parallax for this star is negative, so we instead used the Bayesian distance estimator from Bailer-Jones et al. (2018), which together with the integrated F_bol gives an estimated stellar radius of R_⋆ = 1100 ± 200 R_⊙. The infrared-bright source is evidently a distant, highly extincted red supergiant. We find that the brightness ratio between TOI-824 and this faint supergiant is ∼7000 in the TESS bandpass, and therefore we conclude that it is unable to affect our measurement of the planet's radius at a detectable level given the final radius error bars of ±0.1 ${R}_{\oplus }$.

We matched the CHIRON spectra against a library of ∼10,000 observed spectra classified by the Stellar Parameter Classification (SPC) pipeline (Buchhave et al. 2012), interpolated via a gradient-boosting regressor. From this analysis, we find the effective temperature, metallicity, surface gravity, and rotational velocity of TOI-824 to be T_eff = 4665 ± 100 K, log g = 4.68 ± 0.10 dex, [m/H] = −0.28 ± 0.10 dex, and $v\sin i=4.5\pm 0.5\,\mathrm{km}\,{{\rm{s}}}^{-1}$, all of which suggested that TOI-824 was suitable for precision radial velocity follow-up efforts.

To determine more precise constraints of the stellar parameters for TOI-824, which have a large influence on the derived planetary parameters, we took one of the spectra from HARPS (which is higher resolution than the spectra provided by CHIRON) and analyzed it using the SPC pipeline described above. From the HARPS spectrum, SPC reports that the star has an effective temperature T_eff = 4569 ± 50 K, a surface gravity of log(g) = 4.56 ± 0.10, and a metallicity of [m/H] = −0.12 ± 0.08. We performed a secondary check by running the same HARPS spectra through the SpecMatch-emp software package (Yee et al. 2017), which reported similar results that produced minimal changes when used to derive planetary parameters for TOI-824 b. Given this general agreement, we adopt the HARPS + SPC stellar parameters as the priors for our final EXOFASTv2 analysis of the combined data sets.

To determine the abundances of specific elements in TOI-824, we combined the individual HARPS spectra into a single, high signal-to-noise ratio (S/N) spectrum and applied the SPECIES code (Soto & Jenkins 2018). SPECIES computes the atmospheric parameters (${T}_{\mathrm{eff}}$, $\mathrm{log}g$, $\left[\mathrm{Fe}/{\rm{H}}\right]$, v_t) by measuring the equivalent widths (EWs)⁴² for a set of iron lines. These, together with an ATLAS9 model atmosphere (Castelli & Kurucz 2004), are used to solve the radiative transfer equation in the atmosphere of the star using MOOG (Sneden 1973). Abundances for individual ions are estimated by computing the EWs for a set of lines and using the derived parameters from before to create an appropriate atmospheric model to input to MOOG. Physical parameters, including stellar mass and radius, were obtained by interpolating through a grid of MIST models (Dotter 2016), using the isochrones Python module (Morton 2015). The atmospheric parameters, along with the magnitude of the star at different filters and its parallax (Table 1), were used as priors for the interpolation. Finally, the macroturbulence velocity was obtained from the effective temperature, and the projected rotational velocity by broadening the profiles of a set of absorption lines. The lines used in the fitting procedure, along with the absorption lines used in the abundance determination, are listed in Soto & Jenkins (2018). The results from SPECIES are shown in Table 3.

Table 3.  SPECIES Results for TOI-824

Parameter	Value	Uncertainty
[Fe/H] (dex)	−0.15	0.02
Teff (K)	4616	51
log g ([cm s−2])	4.613	0.12
vt (km s−1)	0.188	0.10
v sin i (km s−1)	2.165	0.21
vmac (km s−1)	1.542	0.02
No. Fe i lines	131
No. Fe ii lines	8
Element	Value	Number of Lines
[Na/H]	0.08 ± 0.20	1
[Mg/H]	−0.23 ± 0.12	3
[Al/H]	−0.18 ± 0.12	3
[Si/H]	−0.18 ± 0.12	3
[Ca/H]	−0.48 ± 0.08	7
[Ti i/H]	0.00 ± 0.08	6
[Ti ii/H]	0.27 ± 0.14	2
[Cr/H]	−0.12 ± 0.06	12
[Mn/H]	0.03 ± 0.09	5
[Ni/H]	−0.04 ± 0.09	5
[Cu/H]	0.39 ± 0.12	3
[Fe i/H]	−0.07 ± 0.06	13
[Fe ii/H]	−0.02 ± 0.10	4
Parameter	Value	54% Confidence Level
Mass (${M}_{\odot }$)	0.69	${}_{0.007}^{0.009}$
Age (Gyr)	10.9	${}_{3.1}^{1.8}$
log giso (cm s−1)	4.612	${}_{0.007}^{0.011}$
Radius (${R}_{\odot }$)	0.68	0.005
log(L/L${}_{\odot }$)	−0.72	${}_{0.012}^{0.009}$

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3.7.1. Upper Age Constraint from [α/Fe]

3.7.2. Lower Age Constraint from the Li 6707 Å Line

To fully characterize the TOI-824 system, we used the EXOFASTv2 software package (Eastman 2017; Eastman et al. 2019) to perform a simultaneous fit to the TESS photometry, the ground-based SG1 photometry, and the RVs from PFS and HARPS. The detrending of the ground-based photometry, to correct for observational effects such as changes in the star's air mass throughout the transit, is handled within EXOFASTv2 using parameters provided by the AIJ software.

3.8.1. EXOFASTv2 Priors and Starting Values

We enforced Gaussian priors on the star's effective temperature (T_eff = 4569 ± 114 K) and metallicity ([Fe/H] = −0.12 ± 0.08) using the SPC analysis results of the HARPS spectrum described in Section 3.6, and on the stellar radius (R_⋆ = 0.719 ± 0.0333 R_⊙) using the results of the SED fit described in Section 3.5. We also placed a Gaussian prior on the star's parallax from Gaia's DR2 results (π = 15.696178 ± 0.04934 mas) after applying the correction from Stassun & Torres (2018). All starting values were further refined using the results of earlier, shorter EXOFASTv2 fits.

The orbit of planet b was defined to be circular in our analysis, as initial EXOFASTv2 fits to the data found eccentricity values consistent with zero and previous studies of small, short-period planets have generally found low eccentricities (Van Eylen & Albrecht 2015; Hadden & Lithwick 2017). We also allowed for a linear slope to be applied to the RV data during the fitting process. The EXOFASTv2 RV model fits for velocity offsets between the PFS and HARPS data sets as well as different instrumental jitter values, terms that are added in quadrature to the estimated measurement uncertainties from PFS and HARPS to account for systematic effects. To constrain the star's age, we use EXOFASTv2's implementation of the MESA Isochrones and Stellar Tracks (MIST) stellar evolution models (Paxton et al. 2013, 2015; Choi et al. 2016; Dotter 2016).

We also fit a dilution term to the TESS photometry to check whether additional correction is needed to address blending from nearby stars. The dilution factor of the TESS photometry is determined by comparing the TESS transit depth to the transit depth measured in the ground-based light curves. The ground-based photometric data has higher spatial resolution, so we expect these transits to experience less flux contamination. We performed two instances of the EXOFASTv2 fit. In the first, which is the version that we use for the final planet parameters presented in Table 4, the TESS dilution parameter is unconstrained. In the second, we enforce a Gaussian prior of 0.0 ± 0.03 on the TESS dilution. If the SPOC pipeline that produced the TESS light curves corrected the blending effects properly, then the best fit to the dilution parameter should be close to zero, regardless of fitting priors.

Table 4.  Median Values and 68% Confidence Interval for EXOFASTv2 Results on TOI-824

Parameter	Units	Values
EXOFASTv2 Gaussian Priors:
R*	Stellar radius (${R}_{\odot }$)	0.719 ± 0.033
${T}_{\mathrm{eff}}$	Effective temperature (K)	4569 ± 114
$[\mathrm{Fe}/{\rm{H}}]$	Metallicity (dex)	−0.12 ± 0.080
ϖ	Parallax (mas)	15.696178 ± 0.04934
${A}_{v}$	V-band extinction (mag)	0.025 ± 0.06
EXOFASTv2 Hard Bounds on Parameters:
$\mathrm{log}g$	Surface gravity (cgs)	[3, 5]
Age	Age (Gyr)	[0, 10]
${T}_{\mathrm{eff}}$	Effective temperature (K)	[4000, 8000]
$[\mathrm{Fe}/{\rm{H}}]$	Metallicity (dex)	[−1, 0.5]
Stellar Parameters:
M*	Mass (${M}_{\odot }$)	${0.710}_{-0.031}^{+0.032}$
R*	Radius (${R}_{\odot }$)	0.695 ± 0.027
L*	Luminosity (${L}_{\odot }$)	${0.195}_{-0.025}^{+0.028}$
${\rho }_{* }$	Density (cgs)	${2.98}_{-0.27}^{+0.30}$
$\mathrm{log}g$	Surface gravity (cgs)	4.605 ± 0.026
${T}_{\mathrm{eff}}$	Effective temperature (K)	${4600}_{-100}^{+110}$
$[\mathrm{Fe}/{\rm{H}}]$	Metallicity (dex)	$-{0.092}_{-0.077}^{+0.076}$
${[\mathrm{Fe}/{\rm{H}}]}_{0}$	Initial metallicity	$-{0.080}_{-0.079}^{+0.077}$
Age	Age (Gyr)	${7.5}_{-2.9}^{+1.8}$
EEP	Equal evolutionary phase	${333.7}_{-13}^{+7.1}$
$\dot{\gamma }$	RV slope (m s−1 day−1)	−0.138 ± 0.067
AD	TESS dilution from neighboring stars	$-{0.26}_{-0.13}^{+0.11}$
Planetary Parameters:		b
P	Period (days)	${1.392978}_{-0.000017}^{+0.000018}$
RP	Radius ($\,{R}_{{\rm{E}}}$)	${2.926}_{-0.191}^{+0.202}$
MP	Mass ($\,{M}_{{\rm{E}}}$)	${18.467}_{-1.875}^{+1.843}$
TC	Time of conjunction (${\mathrm{BJD}}_{\mathrm{TDB}}$)	${2458597.81419}_{-0.00065}^{+0.00063}$
T0	Optimal conjunction time (${\mathrm{BJD}}_{\mathrm{TDB}}$)	2458639.60354 ± 0.00035
a	Semimajor axis (au)	0.02177 ± 0.00032
i	Inclination (degrees)	${83.65}_{-0.38}^{+0.39}$
Teq	Equilibrium temperature (K)	${1253}_{-37}^{+38}$
${\tau }_{\mathrm{circ}}$	Tidal circularization timescale (Gyr)	${0.57}_{-0.16}^{+0.23}$
K	RV semiamplitude (m s−1)	${13.2}_{-1.3}^{+1.2}$
$\mathrm{log}K$	Log of RV semiamplitude	${1.121}_{-0.044}^{+0.039}$
${R}_{P}/{R}_{* }$	Radius of planet in stellar radii	${0.0387}_{-0.0019}^{+0.0018}$
$a/{R}_{* }$	Semimajor axis in stellar radii	${6.73}_{-0.21}^{+0.22}$
δ	Transit depth (fraction)	0.00149 ± 0.00014
Depth	Flux decrement at midtransit	0.00149 ± 0.00014
τ	Ingress/egress transit duration (days)	${0.00386}_{-0.00034}^{+0.00037}$
T14	Total transit duration (days)	${0.04806}_{-0.00080}^{+0.00081}$
TFWHM	FWHM transit duration (days)	${0.04419}_{-0.00085}^{+0.00084}$
b	Transit impact parameter	${0.745}_{-0.024}^{+0.022}$
${\delta }_{S,3.6\mu {\rm{m}}}$	Blackbody eclipse depth at 3.6 μm (ppm)	${86}_{-11}^{+12}$
${\delta }_{S,4.5\mu {\rm{m}}}$	Blackbody eclipse depth at 4.5 μm (ppm)	${126}_{-15}^{+16}$
${\rho }_{P}$	Density (cgs)	${4.03}_{-0.78}^{+0.98}$
log gP	Surface gravity	${3.323}_{-0.070}^{+0.069}$
Θ	Safronov number	0.0136 ± 0.0016
$\langle F\rangle$	Incident flux (${10}^{9}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$)	${0.561}_{-0.063}^{+0.070}$
TP	Time of periastron (${\mathrm{BJD}}_{\mathrm{TDB}}$)	${2458597.81419}_{-0.00065}^{+0.00063}$
${M}_{P}/{M}_{* }$	Mass ratio	${0.0000782}_{-0.0000076}^{+0.0000074}$
$d/{R}_{* }$	Separation at midtransit	${6.73}_{-0.21}^{+0.22}$
Telescope Parameters:		HARPS	PFS
${\gamma }_{\mathrm{rel}}$	Relative RV offset (m s−1)	12.9 ± 2.4	1.3 ± 1.0
${\sigma }_{J}$	RV jitter (m s−1)	${4.3}_{-2.1}^{+3.0}$	${3.21}_{-0.81}^{+1.3}$
${\sigma }_{J}^{2}$	RV jitter variance	${18}_{-14}^{+35}$	${10.3}_{-4.5}^{+9.6}$
$\mathrm{RMS}$	rms of RV residuals (m s−1)	2.58	2.71

Note. Notes from Eastman et al. (2019): The star's age is calculated using the MIST isochrones. The optimal conjunction time (T₀) is the time of conjunction that minimizes the covariance with the planet's period and therefore has the smallest uncertainty. The equilibrium temperature of the planet (T_eq) is calculated using Equation (1) of Hansen & Barman (2007) and assumes no albedo and perfect heat redistribution. The tidal circularization timescale (${\tau }_{\mathrm{circ}}$) is calculated using Equation (3) from Adams & Laughlin (2006) and assumes Q = 10⁶. The 3.6 and 4.6 μm secondary occultation depths use a blackbody approximation of the stellar flux, F_⋆, at ${T}_{\mathrm{eff}}$ and of the planetary flux, F_p, at ${T}_{\mathrm{eq}}$ and are calculated using ${\delta }_{S,\lambda }=\tfrac{{({R}_{{\rm{p}}}/{R}_{\star })}^{2}}{{({R}_{{\rm{p}}}/{R}_{\star })}^{2}+({F}_{\star }/{F}_{{\rm{p}}})}$.

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3.8.2. EXOFASTv2 Results

The median EXOFASTv2 parameters for the TOI-824 system are shown in Table 4, and the best fits to the TESS photometry and PFS and HARPS RV data are shown in Figure 4. The mass of TOI-824 b is measured to be 18.47 ± 1.84 ${M}_{\oplus }$, which, when combined with the measured planet radius of 2.93 ± 0.20 ${R}_{\oplus }$, results in a bulk density of 4.03${}_{-0.78}^{+0.98}$ ${\rm{g}}\,{\mathrm{cm}}^{-3}$, making the planet more than twice as dense as Neptune (Figure 5). This radius measurement is roughly 15% smaller than the R = 3.4 ${R}_{\oplus }$ estimate based on the TESS data alone (Section 3.1), and we address this difference in Section 4. We find that our assumption of a circular orbit is further supported by the fact that the tidal circularization timescale (τ_circ ∼ 0.57 Gyr) is short compared to the star's age (${7.5}_{-2.9}^{+1.8}$ Gyr).

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For the sake of completeness, we check the S-index and H-index activity indicators extracted from the PFS data set for periodicities that could cause the 1.39 day signal. These activity indicators serve as proxies for chromospheric activity in the visible stellar hemisphere at the moments when the spectra were obtained. The S-index is calculated by measuring the emission reversal at the cores of the Fraunhofer H and K lines of Ca ii located at 3968 Å and 3934 Å, respectively (Duncan et al. 1991), while the H-index quantifies the amount of flux within the Hα Balmer line core compared to the local continuum. Details on the prescription used to measure these indicators in the PFS data set can be found in Butler et al. (2017). We analyze the resulting S- and H-index values by computing Lomb–Scargle periodograms for each of the activity indicators as well as for the PFS RV values and then looking for any well-defined peaks with false-alarm probabilities <0.1% in the vicinity of the planet's period (Figure 6).

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The RV signal of TOI-824 b is apparent in the Lomb–Scargle periodogram of the PFS RVs (Figure 6). Neither the S- nor H-index periodogram displays any significant peaks at periods close to the planetary signal, however, which means stellar activity is unlikely to skew or otherwise influence our measurement of the planet's mass. Indeed, based upon these periodograms, TOI-824 appears to be a relatively quiet star.

Given the match in both period and phase between the TESS signal and the planet signal seen in the combined RV data set, along with the lack of any significant periodicity in the spectral activity indicators, we consider this to be a decisive confirmation of the planetary nature of TOI-824 b.

We model the interior of TOI-824 by assuming a pure iron core, a silicate mantle, a pure water layer, and a H–He atmosphere. We follow the structure model of Dorn et al. (2017), with the equation of state (EOS) of the iron core taken from Hakim et al. (2018), the EOS of the silicate mantle calculated using PERPLE_X by Connolly (2009) given thermodynamic data of Stixrude & Lithgow-Bertelloni (2011), and Saumon et al. (1995) for the H–He envelope assuming protosolar composition. For the water, we use the quotidian equation of state presented in Vazan et al. (2013) for low pressures and the tabulated EOS from Seager et al. (2007) for pressures above 44.3 GPa. We then use a generalized Bayesian inference analysis using a nested sampling scheme (e.g., Buchner 2016) to quantify the degeneracy between interior parameters and produce posterior probability distributions. We use the stellar Fe/Si and Mg/Si ratios as a proxy for the planet, and we assume an envelope luminosity of L = 10^22.52 erg s⁻¹ (equal to Neptune's luminosity).

Table 5 lists the inferred mass fractions of the core, mantle, water layer, and H–He atmosphere from our structure models. We find a median H–He mass fraction of 2.8%, which is a lower bound because enriched H–He atmospheres are more compressed and can therefore increase the planetary H–He mass fraction. Indeed, formation models of mini-Neptunes suggest that it is very unlikely to form such planets without envelope enrichment (Venturini & Helled 2017). The core, mantle, and water layer have relative mass fractions between 27%, 38%, and 31% with large sigma. This regime of the mass–radius relation is very degenerate, and therefore it is not possible to accurately determine the mass ratios of the core, mantle, and water layer.

Table 5.  Inferred Interior Structure Properties of TOI-824 b

${M}_{\mathrm{core}}/{M}_{\mathrm{total}}$	${0.27}_{-0.11}^{+0.23}$
${M}_{\mathrm{mantle}}/{M}_{\mathrm{total}}$	${0.38}_{-0.18}^{+0.25}$
${M}_{\mathrm{water}}/{M}_{\mathrm{total}}$	${0.31}_{-0.18}^{+0.24}$
${M}_{\mathrm{atm}}/{M}_{\mathrm{total}}$	${0.028}_{-0.007}^{+0.008}$

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One of the most intriguing results of NASA's Kepler mission is clear evidence that the overall distribution of small, short-period planets has been sculpted by processes that erode atmospheres (e.g., Lopez et al. 2012; Owen & Wu 2013, 2017; Chen & Rogers 2016; Jin & Mordasini 2018). This evidence includes both the clear gap in the planet radius distribution uncovered by Fulton (2017) and better documented in Fulton et al. (2017) and Fulton & Petigura (2018), as well as the clear dearth of nonrocky 2–4 ${R}_{\oplus }$ planets in the most strongly irradiated orbits (e.g., Sanchis-Ojeda et al. 2014; Lundkvist et al. 2016; McDonald et al. 2019), which is frequently referred to as the hot Neptune desert. This desert is normally shown by examining the distribution of planetary radii and insolations, as in Figure 9, but this is closely related to similar concepts like the "cosmic shoreline" described in Zahnle & Catling (2017), which compares planetary insolation and escape velocity, as well as the mass-loss thresholds found by comparing planetary binding energies to the high ionizing X-ray and EUV irradiation they receive (e.g., Lecavelier Des Etangs 2007; Lopez & Fortney 2013, 2014; Owen & Wu 2013). Indeed, the hot Neptune desert and the radius gap closely match prior predictions from models of extreme atmospheric escape due to XUV-driven photoevaporative escape (e.g., Owen & Jackson 2012; Lopez & Fortney 2013; Owen & Wu 2013; Jin et al. 2014; Lopez 2017), although other extreme escape mechanisms have subsequently been proposed to explain these features (e.g., Schlichting et al. 2015; Ginzburg et al. 2018).

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TOI-824 b is particularly interesting in the context of the hot Neptune desert because, along with a handful of other recent discoveries, it appears to lie at the lower edge of the desert (see Figure 9). Its mass and radius, however, indicate that TOI-824 b must possess a significant primary atmosphere. Assuming a rock and iron core, thermal evolution models from Lopez & Fortney (2014) suggest a H+He envelope fraction of 2.4${}_{-1.7}^{+1.1}$%, consistent with the findings in Section 5.1. This is well within the typical range of the warmest Neptune planets discovered by Kepler, although of course those are typically much less irradiated than TOI-824 b is. This poses an interesting question: how could this planet have possibly retained a significant gaseous envelope despite receiving extreme radiation?

Planet evolution and escape models may be able to explain this conundrum. Along with other recent discoveries in and around the desert such as K2-100b (Barragán et al. 2019), HD 219666 b (Esposito et al. 2019), NGTS-4 b (West et al. 2019), TOI-132 b (Díaz et al. 2020), and LTT 9779 b (J. T. Jenkins 2020, private communication), TOI-824 b is exceptionally massive given its radius. All of these planets have masses in excess of 16 ${M}_{\oplus }$ despite the fact that planets in this size range (3–5 ${R}_{\oplus }$) are more typically 6–10 ${M}_{\oplus }$(Wolfgang et al. 2016; Ning et al. 2018). Such high masses mean that these planets are more resilient to atmospheric escape because a planet's timescale to lose its atmosphere to photoevaporative escape scales roughly as ${M}_{{\rm{p}}}^{-2}$ (Lopez & Fortney 2013). Indeed, when viewed in the context of their gravitational binding energy and their XUV irradiation (Figure 10), these new discoveries appear more typical, lying close to but not beyond the limits of potential survival to escape, similar to other previously known hot Neptunes and sub-Neptunes.

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Although the large planet mass may help explain how TOI-824 b's atmosphere survived, the existence of these large planet masses alone poses intriguing questions for theorists. Structure models indicate that most of this large mass is likely in the planet's heavy element core (Lopez & Fortney 2014). Given its extremely short orbital period, however, we must ask how TOI-824 b and similar planets accumulated such a large amount of heavy elements on such an irradiated orbit in the first place. Theorists have long argued that hot Jupiters likely migrate in from much more distant orbits, but it has been debated whether this is also true of lower mass planets. Studies of ultrashort-period rocky planets and of the overall distribution of Kepler planets indicate that there is likely some mass enhancement in the inner parts of planetary disks compared to the classic minimum mass solar nebula (e.g., Chiang & Laughlin 2013). However, with ∼18.6 ${M}_{\oplus }$ and an orbital period of only 1.4 days, systems like TOI-824 may require an even stronger concentration or migration of heavy elements in the inner part of the planetary disk.

Hot Neptunes are particularly compelling targets for follow-up atmosphere characterization. Their high equilibrium temperatures make it more likely that their atmospheres are cloud-free (Crossfield & Kreidberg 2017). Their elevated temperatures also mean that they are good targets for thermal emission measurements taken during secondary eclipse, which are less affected by clouds and hazes than transmission spectra (Fortney 2005). The number of Neptune-sized planets in this desired insolation range is currently very limited, however, and only a small number have been studied in depth and had their atmospheres confirmed. Most notable among this population are GJ 436 b (Butler et al. 2004; Morley et al. 2017), GJ 3470 b (Bonfils et al. 2012; Benneke et al. 2019), and HAT-P-11b (Bakos et al. 2010; Fraine et al. 2014), which are denoted by the square points in Figure 9.

TOI-824 b is also a compelling target because its mass is precisely known. Batalha et al. (2019) showed that in order to infer the atmospheric properties of an exoplanet, the planet's mass must be measured to at least the 20% level. Otherwise the widths of the posterior distributions of the atmospheric properties are dominated by the uncertainties in the planet's mass.

Absorption features from several key molecular species in the atmosphere of TOI-824 b may be detectable with current ground- and space-based facilities. Hubble/WFC3 observations in the near-infrared could reveal water features, assuming a cloud-free, 100× solar metallicity atmosphere. Molecular features from water and CO may also be accessible with high-resolution ground-based spectrographs such as CRIRES+ at the VLT (Follert et al. 2014). In addition to these molecular species, TOI-824 b is hot enough that alkali metals may be present in the gas phase in the atmosphere, in contrast to previously characterized small planets (Morley et al. 2015). The ESPRESSO spectrograph on VLT (Pepe et al. 2014), for example, should be able to detect sodium in the atmosphere of TOI-824 b. Many additional chemical species will be observable with next-generation facilities like the ELTs that have broader wavelength coverage.

We note that the expected S/N for atmospheric features for TOI-824 b is not the highest for all sub-Neptunes discovered by TESS. It sits just barely above the cutoff suggested by Kempton et al. (2018), at a transmission spectroscopy metric (TSM) of 85 compared to the suggested inclusion criteria of TSM ≥ 84, which was designed to yield a statistical sample of planets in this size range that are accessible with a modest amount of James Webb Space Telescope time per planet. That threshold S/N assumes the atmospheres are cloud-free, however, which is not necessarily the case (Crossfield & Kreidberg 2017). If TOI-824 b follows the trend noted in Crossfield & Kreidberg (2017), then it may have relatively large spectral features due to its high temperature. Atmosphere characterization is worth pursuing to test this hypothesis.

TOI-824 b is also a promising target for the detection of atmospheric escape. At the edge of the hot Neptune desert, the planet has likely experienced significant photoevaporation over its lifetime and into the present. Observations of the helium near-IR triplet may reveal atmospheric escape in action and constrain the rate of evaporative mass loss (Salz et al. 2018; Spake et al. 2018; Ninan et al. 2020), and similar studies could be carried out using observations of Hα (Jensen et al. 2012, 2018; Cauley et al. 2017; Yan & Henning 2018) and Lyα (Ehrenreich et al. 2015; Bourrier et al. 2018). Conveniently, TOI-824 b has a K dwarf host star, which is the optimal stellar spectral type to excite neutral helium atoms (Oklopčić & Hirata 2018; Oklopčić 2019).

As of now, the detectability of TOI-824 b's atmosphere from both ground and space is promising and could lead to detailed characterization of the most irradiated small planet at the edge of the desert that has retained its atmosphere to date.