TOI-1728b: The Habitable-zone Planet Finder Confirms a Warm Super-Neptune Orbiting an M-dwarf Host

TOI-1728 (TIC 285048486, UCAC4 774-029023, Gaia DR2 1094545653447816064) was observed by TESS in Sector 20 from 2019 December 24 to 2020 January 19 at two-minute cadence. It has one transiting planet candidate, TOI-1728.01, with a period of ∼3.49 days (Figure 1) that was detected by the TESS science processing pipeline (Jenkins et al. 2016). For our subsequent analysis, we used the entire presearch data conditioned time-series light curves (Ricker & Vanderspek 2018) available at the Mikulski Archive for Space Telescopes (MAST) for Sector 20. We exclude points marked as anomalous by the TESS data quality flags (see Table 28 in Tenenbaum & Jenkins 2018).

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2.2.1. Perkin 0.43 m

2.2.2. Penn State Davey CDK 0.6 m Telescope

We observed TOI-1728 using HPF (Mahadevan et al. 2012, 2014), a high-resolution (R ∼ 55,000), NIR (8080–12780 Å) precision RV spectrograph located at the 10 meter Hobby–Eberly Telescope (HET) in Texas. The HET is a fully queue-scheduled telescope with all observations executed in a queue by the HET resident astronomers (Shetrone et al. 2007). HPF is a fiber-fed instrument with a separate science, sky, and simultaneous calibration fiber (Kanodia et al. 2018). It is actively temperature-stabilized and achieves ∼1 mK temperature stability (Stefansson et al. 2016). We use the algorithms in the tool HxRGproc for bias noise removal, nonlinearity correction, cosmic-ray correction, slope/flux and variance image calculation (Ninan et al. 2018) of the raw HPF data. We use this variance estimate to calculate the S/N of each HPF exposure (Table 1). Each visit was divided into two exposures of 945 s each. The median S/N goal was 144 per resolution element. Even though HPF has the capability for simultaneous calibration using a NIR Laser Frequency Comb (LFC), we chose to avoid simultaneous calibration to minimize the impact of scattered calibrator light in the science target spectra. Instead, the stabilized instrument allows us to correct for the well calibrated instrument drift by interpolating the wavelength solution from other LFC exposures from the night of the observations as discussed in Stefansson et al. (2020). This methodology has been shown to enable precise wavelength calibration and drift correction up to ∼30 cm s⁻¹ per observation, a value smaller than our estimated per observation RV uncertainty (instrumental + photon noise) for this object of ∼10 m s⁻¹ (in 945 s exposures).

We follow the methodology described in Stefansson et al. (2020) to derive the RVs, by using a modified version of the SpEctrum Radial Velocity AnaLyser pipeline (SERVAL; Zechmeister et al. 2018). SERVAL uses the template-matching technique to derive RVs (e.g., Anglada-Escudé & Butler 2012), where it creates a master template from the target star observations, and determines the Doppler shift for each individual observation by minimizing the χ² statistic. This master template was generated by using all observed spectra while explicitly masking any telluric regions identified using a synthetic telluric-line mask generated from telfit (Gullikson et al. 2014), a Python wrapper to the Line-by-line Radiative Transfer Model package (Clough et al. 2005). We used barycorrpy, the Python implementation (Kanodia & Wright 2018) of the algorithms from Wright & Eastman (2014) to perform the barycentric correction. We obtained a total of 36 exposures on this target, of which three were excluded from RV analysis since they were taken during a transit of the planet (JD 2458909.61466) and could add a potential systematic due to the Rossiter–McLaughlin effect (McLaughlin 1924; Rossiter 1924; Triaud 2017). Including these RVs in our analysis does not change the results, however, we still choose to exclude these in an abundance of caution. Furthermore, three exposures were discarded due to bad weather conditions. The remaining 30 945 s exposures, are listed in Table 1 and plotted in Figure 2. A generalized Lomb–Scargle (GLS) periodogram (Zechmeister & Kürster 2009) on these 30 RV points shows a signal at ∼3.5 days with a False Alarm Probability ∼6% (Figure 4) calculated with a bootstrap simulation using astropy which computes periodograms on simulated data given the errors. This period is consistent with the orbital period obtained from the TESS photometry.

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To measure spectroscopic T_eff, $\mathrm{log}g$, and [Fe/H] values of the host star, we use the HPF spectral matching methodology from Stefansson et al. (2020), which is based on the SpecMatch-Emp algorithm from Yee et al. (2017). In short, we compare our high-resolution HPF spectra of TOI-1728 to a library of high S/N as-observed HPF spectra. The library consists of slowly rotating reference stars with well characterized stellar parameters from Yee et al. (2017).

To perform the comparison, we shift the observed target spectrum to a library wavelength scale and rank all of the targets in the library using a χ² goodness-of-fit metric. Following the initial χ² minimization step, we pick the five best-matching reference spectra (in this case: GJ 1172, GJ 488, BD+29 2279, HD 88230, and HD 28343) to construct a linear combination weighted composite spectrum to better match to the target spectrum (see Figure 6). In this step, each of the five stars receives a best-fit weight coefficient. We then assign the target stellar parameter T_eff, $\mathrm{log}g$, and Fe/H values as the weighted average of the five best stars using the best-fit weight coefficients. Our final parameters are listed in Table 2, using the cross-validation error estimates from Stefansson et al. (2020). As an additional check, we performed the library comparison using six other HPF orders that have low levels of tellurics, all of which resulted in consistent stellar parameters. Lastly, during both optimization steps, we note that we account for any potential $v\sin i$ broadening by artificially broadening the library spectra with a $v\sin i$ broadening kernel (Gray 1992) to match the rotational broadening of the target star. For TOI-1728 no significant rotational broadening was needed, and we thus place an upper limit of $v\sin i\lt 2\,\mathrm{km}\,{{\rm{s}}}^{-1}$, which is the lower limit of measurable $v\sin i$ values given HPF's spectral resolving power of R ∼ 55,000.

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Table 2.  Summary of Stellar Parameters for TOI-1728

Parameter	Description	Value	Reference
Main identifiers:
TOI	TESS Object of Interest	1728	TESS mission
TIC	TESS Input Catalog	285048486	Stassun
2MASS	⋯	J08022653 + 6447489	2MASS
Gaia DR2	⋯	1094545653447816064	Gaia DR2
Equatorial Coordinates, Proper Motion and Spectral Type:
αJ2000	R.A.	08:02:26.55	Gaia DR2
δJ2000	decl.	+64:47:48.93	Gaia DR2
μα	Proper motion (R.A., mas yr−1)	104.078 ± 0.044	Gaia DR2
μδ	Proper motion (Decl., mas yr−1)	52.919 ± 0.046	Gaia DR2
d	Distance in pc	${60.80}_{-0.13}^{+0.14}$	Bailer-Jones
AV,max	Maximum visual extinction	0.01	Green
Optical and near-infrared magnitudes:
B	Johnson B mag	13.693 ± 0.073	APASS
V	Johnson V mag	12.400 ± 0.035	APASS
g'	Sloan g' mag	13.086 ± 0.112	APASS
r'	Sloan r' mag	11.788 ± 0.041	APASS
i'	Sloan i' mag	11.096 ± 0.029	APASS
J	J mag	9.642 ± 0.019	2MASS
H	H mag	8.953 ± 0.028	2MASS
Ks	Ks mag	8.803 ± 0.020	2MASS
W1	WISE1 mag	8.691 ± 0.022	WISE
W2	WISE2 mag	8.742 ± 0.021	WISE
W3	WISE3 mag	8.598 ± 0.026	WISE
W4	WISE4 mag	8.250 ± 0.234	WISE
Spectroscopic Parametersa:
Teff	Effective temperature in K	3975 ± 77	This work
[Fe/H]	Metallicity in dex	0.09 ± 0.13	This work
log(g)	Surface gravity in cgs units	4.67 ± 0.05	This work
Model-dependent Stellar SED and Isochrone fit Parametersb:
Teff	Effective temperature in K	${3980}_{-32}^{+31}$	This work
[Fe/H]	Metallicity in dex	0.25 ± 0.10	This work
$\mathrm{log}(g)$	Surface gravity in cgs units	4.657 ± 0.017	This work
M*	Mass in M⊙	${0.646}_{-0.022}^{+0.023}$	This work
R*	Radius in R⊙	${0.6243}_{-0.0097}^{+0.010}$	This work
L*	Luminosity in L⊙	0.088 ± 0.002	This work
ρ*	Density in g cm−3	3.78 ± 0.19	This work
Age	Age in Gyr	7.1 ± 4.6	This work
Av	Visual extinction in mag	${0.0050}_{-0.0035}^{+0.0034}$	This work
Other Stellar Parameters:
$v\sin {i}_{* }$	Rotational velocity in km s−1	<2	This work
ΔRV	"Absolute" radial velocity in km s−1	−43.2 ± 0.3	Gaia DR2
U, V, W	Galactic velocities in km s−1	53.8 ± 0.2, −9.8 ± 0.1, 1.8 ± 0.15	This work

Notes. References are: Stassun (Stassun et al. 2018), 2MASS (Cutri et al. 2003), Gaia DR2 (Gaia Collaboration et al. 2018), Bailer-Jones (Bailer-Jones et al. 2018), Green (Green et al. 2019), APASS (Henden et al. 2018), WISE (Wright et al. 2010).

^aDerived using the HPF spectral matching algorithm from Stefansson et al. (2020). ^bEXOFASTv2 derived values using MIST isochrones with the Gaia parallax and spectroscopic parameters in (a) as priors.

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In addition to the spectroscopic stellar parameters derived above, we use EXOFASTv2 (Eastman et al. 2019) to model the SED of TOI-1728 (Figure 7) to derive model-dependent constraints on the stellar mass, radius, and age of the star. For the SED fit, EXOFASTV2 uses the the BT-NextGen stellar atmospheric models (Allard et al. 2012). We assume Gaussian priors on the (i) 2MASS JHK magnitudes, (ii) SDSS g'r'i' and Johnson B and V magnitudes from APASS, (iii) Wide-field Infrared Survey Explorer magnitudes W1, W2, W3, and W4, (Wright et al. 2010), (iv) spectroscopically derived host star effective temperature, surface gravity, and metallicity, and (v) distance estimate from Bailer-Jones et al. (2018). We apply a uniform prior on the visual extinction and place an upper limit using estimates of Galactic dust by Green et al. (2019; Bayestar19) calculated at the distance determined by Bailer-Jones et al. (2018). We convert the Bayestar19 upper limit to a visual magnitude extinction using the R_v = 3.1 reddening law from Fitzpatrick (1999). We use GALPY (Bovy 2015) to calculate the UVW velocities, which along with the BANYAN tool (Gagné et al. 2018) classify TOI-1728 as a field star in the thin disk (Bensby et al. 2014).

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The stellar priors and derived stellar parameters with their uncertainties are listed in Table 2. We use the T_eff estimate of $={3980}_{-32}^{+31}$ K to classify TOI-1728 as an M star (T_eff < 4000 K), which is consistent with results obtained from the PPMXL catalog (Roeser et al. 2010; Frith et al. 2013).

To estimate the stellar rotation period, we accessed the publicly available data from the ZTF (Masci et al. 2019) and the All Sky Automated Survey for SuperNovae (ASAS-SN; Kochanek et al. 2017) for this target to perform a Lomb–Scargle (Lomb 1976; Scargle 1982) periodogram analysis. We do not detect any rotation signal present in the photometry. The photometry spans JD 2458202–2458868 (∼660 days) for ZTF (zg) and JD 2455951–2458934 (∼3000 days) for ASAS-SN (in the V and g band). We repeated this on the photometry from the TESS PDCSAP pipeline (Smith et al. 2012; Ricker & Vanderspek 2018) and do not see any statistically significant signals which would suggest potential rotation modulation signal in the photometry.

The lack of photometric rotational modulation in the long baseline photometry suggests an inactive star, and this claim is further bolstered by the lack of emission or any detectable temporal changes in the cores of the Calcium II NIR triplet (Mallik 1997; Cincunegui et al. 2007; Martin et al. 2017) in the HPF spectra. This combination of low stellar activity and $v\sin i$ upper limit of 2 km s⁻¹ (Section 4) suggests a slow rotating old and inactive star, which is consistent with our age estimate from the EXOFASTv2 fit of 7 ± 4.6 Gyr.

We conduct a joint data analysis of all photometry (TESS and ground-based), and the RVs using two independent tools: juliet (Espinoza et al. 2019) and exoplanet (Foreman-Mackey et al. 2020). The juliet package uses the dynamic nest-sampling algorithm dynesty (Speagle 2020) for parameter estimation, whereas exoplanet uses the PyMC3 Hamiltonian Monte Carlo package (Salvatier et al. 2016). We confirm that the results of the two independent methods are consistent to 1σ for all derived planetary properties, and present the results of the juliet analysis in this paper for brevity.

juliet uses batman (Kreidberg 2015) to model the photometry and radvel (Fulton et al. 2018) to model the velocimetry. The RV model is a standard Keplerian model while the photometric model is based on the analytical formalism of Mandel & Agol (2002) for a planetary transit and assumes a quadratic limb-darkening law. In the photometric model we include a dilution factor, D, to represent the ratio of the out-of-transit flux of TOI-1728 to that of all the stars within the TESS aperture. We assume that the ground-based photometry has no dilution, since we use the ground-based transits to estimate the dilution in the TESS photometry. We assume the transit depth is identical in all bandpasses and use our ground-based transits to determine the dilution required in the TESS data to be D_TESS = 0.860 ± 0.045; including which increases the radius from ${4.71}_{-0.11}^{+0.14}{R}_{\oplus }$ to ${5.04}_{-0.17}^{+0.16}{R}_{\oplus }$. We also set a prior on the stellar density using the value determined from our EXOFASTv2 SED fit. For both the photometry and RV modeling, we include a simple white-noise model in the form of a jitter term that is added in quadrature to the error bars of each data set.

The photometric model includes a Gaussian Process (GP) model to account for any correlated noise behavior in the TESS photometry. We use the celerite implementation of the quasi-periodic covariance function (Equation (56) in Foreman-Mackey et al. 2017) available in juliet. The celerite covariance parameters are chosen such that the combination of parameters replicates the same behavior as a quasi-periodic kernel (Rasmussen & Williams 2006). We follow the example in Foreman-Mackey et al. (2017) and set broad uniform priors on the hyperparameters for the GP.

juliet uses the default stopping criterion from dynesty (Speagle 2020), which stops the run when the estimated contribution of the remaining prior volume to that of the total evidence falls below a preset threshold. For this analysis, we defined that threshold to be 1%, i.e., the run stopped when the remaining prior volume was lower than 1% of the total evidence. Furthermore, we verify this result using a Hamiltonian Monte Carlo parameter estimation implemented in PyMC3 (Salvatier et al. 2016) under exoplanet (Foreman-Mackey et al. 2020), which uses the Gelman–Rubin statistic ($\hat{R}\leqslant 1.1;$ Ford 2006) to check for convergence.

In Figure 1 we show the photometry and the best-fit transit model, in Figure 2 we show the RV time series and the model from this joint fit, showing the residuals in the bottom panel, Figure 8 shows the phase folded RVs. Table 3 lists the priors used in juliet, Table 4 provides a summary of the inferred system parameters and respective confidence intervals, and Figure 9 shows a corner plot of the posteriors. The data reveal a companion having a radius of ${5.05}_{-0.17}^{+0.16}$ R_⊕ and mass ${26.78}_{-5.13}^{+5.43}$ M_⊕.

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Table 3.  Summary of Priors Used for the Three Joint Transit and RV Fits Performed

Parameter	Description	Model
Orbital parameters:
P (days)	Orbital period	${ \mathcal N }(3.48,0.1)$
TC	Transit midpoint (BJDTDB)	${ \mathcal N }(2458843.276,0.1)$
Rp/R*	Scaled radius	${ \mathcal U }(0,1)$
a/R*	Scaled semimajor axis	${ \mathcal J }(1,90)$
b	Impact parameter	${ \mathcal U }(0,1)$
$\sqrt{e}$ cos ω	e − ω parameterization	${ \mathcal U }(-1,1)$
$\sqrt{e}$ sin ω	e − ω parameterization	${ \mathcal U }(-1,1)$
K	RV semiamplitude (m s−1)	${ \mathcal J }(0.001,100)$
Other constraints:
ρ*	Stellar density (g cm−3)	${ \mathcal N }(3.78,0.19)$
Jitter and other instrumental terms:
u1a	Limb-darkening parameter	${ \mathcal U }(0,1)$
u2a	Limb-darkening parameter	${ \mathcal U }(0,1)$
σphotb	Photometric jitter (ppm)	${ \mathcal J }({10}^{-6},5000)$
μphotb	Photometric baseline	${ \mathcal N }(0,0.1)$
DTESS	Photometric dilution	${ \mathcal U }(0,1)$
DDavey	Photometric dilution	Fixed(1)
DPerkin	Photometric dilution	Fixed(1)
σHPF	HPF RV jitter (m s−1)	${ \mathcal J }(0.001,1000)$
γ	Systemic velocity (m s−1)	${ \mathcal N }(0,100)$
dv/dt	HPF RV trend (mm s−1 day−1)	${ \mathcal N }(0,500)$
TESS Quasiperiodic GP parametersc:
PGP	GP kernel period (days)	${ \mathcal J }(0.001,1000)$
B	Amplitude	${ \mathcal J }({10}^{-6},1)$
C	Constant scaling term	${ \mathcal J }({10}^{-3},{10}^{3})$
L	Characteristic timescale	${ \mathcal J }(1,{10}^{3})$

Notes. ${ \mathcal N }(\mu ,\sigma )$ denotes a normal prior with mean μ, and standard deviation σ; ${ \mathcal U }(a,b)$ denotes a uniform prior with a start value a and end value b, ${ \mathcal J }(a,b)$ denotes a Jeffreys prior truncated between a start value a and end value b. A Gaussian prior on the stellar density was placed for all fits. The dilution parameters in juliet were fixed to 1 for all ground-based transit observations.

^aWe use the same uniform priors for pairs of limb-darkening parameters q₁ and q₂ (parameterization from Kipping et al. 2013, and use separate limb-darkening parameters for each instrument). ^bWe placed a separate photometric jitter term and baseline offset term for each of the photometric instruments (TESS, Penn State Davey CDK 0.6 m and Perkin 17''). ^cWe do not use a GP for the two ground-based photometric instruments (Penn State Davey CDK 0.6 m and Perkin 17'') since the total observation duration for each was only about 4 hr.

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Table 4.  Derived Parameters for the TOI-1728 System

Parameter	Units	Value
Orbital parameters:
Orbital period	P (days)	${3.491510}_{-0.000057}^{+0.000062}$
Time of periastron	TP (BJDTDB)	${2458843.707}_{-1.010}^{+0.697}$
Eccentricity	e	${0.057}_{-0.039}^{+0.054}$
Argument of periastron	ω (degrees)	${45}_{-187}^{+104}$
Semiamplitude velocity	K (m s−1)	${15.12}_{-2.87}^{+3.04}$
Systemic velocitya	γ (m s−1)	${1.86}_{-1.91}^{+1.84}$
RV trend	dv/dt (mm s−1 day−1)	0.001 ± 0.025
RV jitter	σHPF (m s−1)	${0.46}_{-0.44}^{+3.36}$
Transit parameters:
Transit midpoint	TC (BJDTDB)	2458843.27427 ± 0.00043
Scaled radius	Rp/R*	0.074 ± 0.002
Scaled semimajor axis	a/R*	13.48 ± 0.20
Orbital inclination	i (degrees)	${88.31}_{-0.40}^{+0.58}$
Impact parameter	b	${0.39}_{-0.15}^{+0.11}$
Transit duration	T14 (hr)	1.96 ± 0.03
Photometric jitterb	σTESS (ppm)	${0.02}_{-0.02}^{+1.96}$
	σDavey(ppm)	${2334.64}_{-196.66}^{+197.77}$
	σPerkin (ppm)	${1062.40}_{-272.43}^{+261.22}$
Dilutionc	DTESS	0.860 ± 0.045
Planetary parameters:
Mass	Mp (M⊕)	${26.78}_{-5.13}^{+5.43}$
Radius	Rp (R⊕)	${5.05}_{-0.17}^{+0.16}$
Density	ρp (g cm−3)	${1.14}_{-0.24}^{+0.26}$
Surface gravity	gp (cm s−2)	${1037}_{-30}^{+29}$
Semimajor axis	a (au)	0.0391 ± 0.0009
Average incident flux	$\langle F\rangle$ (105 W m−2)	${0.785}_{-0.035}^{+0.033}$
Planetary insolation	S (S⊕)	57.78 ± 3.48
Equilibrium temperatured	Teq (K)	767 ± 8

Notes.

^aIn addition to the absolute RV from Table 2. ^bJitter (per observation) added in quadrature to photometric instrument error. ^cDilution due to presence of background stars in TESS aperture. ^dThe planet is assumed to be a blackbody.

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He 10830 Å observations have recently emerged as a powerful ground-based probe to detect and constrain atmospheric outflow from hot Jupiters and warm Neptunes (Seager & Sasselov 2000; Oklopčić & Hirata 2018). The low bulk density of this planet makes it a promising candidate for large atmospheric mass outflows. We estimated an upper limit on the He 10830 Å signature from the spectrum obtained during the transit of TOI-1728. We observed a total of three spectra inside transit, with a median S/N of ∼100 per pixel on 2020 March 1. A high S/N template of the out-of-transit spectrum was created by averaging all the spectra we obtained for RV measurement outside the transit window. Careful subtraction of the sky emission line is crucial so as to not confuse sky lines with the He 10830 Å signal. We subtracted the simultaneous sky spectrum measured in the HPF's sky fiber after scaling by the throughput ratio obtained from twilight observations. Figure 10 shows the ratio of in-transit to the out-of-transit spectrum during the transit. The error bars propagated through our pipeline are also shown in the plot. To calculate the upper limit we injected artificial absorption lines and ran Markov Chain Monte Carlo (MCMC) fits using PyMC3 (Salvatier et al. 2016) to test detectability. The line width was taken to be HPF's instrument resolution, with the wavelength fixed to the two strong unresolved lines in the He 10830 Å triplet, and the continuum normalized to 1. The posterior distribution of the amplitude of the absorption line was used to calculate its credible interval. With 90% probability, we obtain the upper limit of the absorption trough to be <1.1% (see Figure 10). Deeper levels of He 10830 Å absorption have been detected in other planet atmospheres at the 90% confidence level using similar techniques by HPF and CARMENES (Ninan et al. 2020; Palle et al. 2020).

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In Figure 11 we show where TOI-1728b lies in exoplanet parameter phase space compared to other known exoplanets. For the purposes of illustration, we draw our sample from the NASA Exoplanet Archive (Akeson et al. 2013) and further include recent transiting planets discovered by TESS around M-dwarf stellar hosts, we include only those planets with either mass measurements or upper limits. For Figures 11(a)–(c) we restrict our sample to T_eff < 4000 K and planetary radii R_p < 6R_⊕, whereas for Figure 11(c) we impose an additional requirement of a 3σ mass measurement. For Figure 11(d), we restrict our sample to planets with T_eff < 7000 K, planetary radius—3 R_⊕ < R_p < 6 R_⊕, and eccentricity errors <0.1. We also looked at the exoplanet sample for host stars of mass up to 0.75 M^⊙, however this did not add any super-Neptunes comparable to TOI-1728b to the discussion, and hence we limit our planet sample to exoplanets around M dwarfs with T_eff < 4000 K.

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TOI-1728b (M0 host star) has an orbital period comparable to GJ 3470b and GJ 436b (Figure 11(a)), which orbit a M1.5V and M2.5V host star, respectively. Due to the hotter effective temperature, TOI-1728b receives higher insolation flux than the other two comparable warm Neptunes (Figure 11(b)). TOI-1728b also represents an important addition to the mass–radius plane (Figure 11(c)) for M-dwarf exoplanets. The current sample of transiting M-dwarf exoplanets consists of about 40 planets with mass measurements (and not only upper limits). Of these, the only other comparable planets are GJ 3470b and GJ 436b. There have been numerous studies which find differences in the occurrence rates for planets around M dwarfs versus earlier type stars (Hardegree-Ullman et al. 2019; Hsu et al. 2020), as well as the empirical distributions of mass and radius for said planets (Bonfils et al. 2013; Dressing & Charbonneau 2015). These results motivate independent statistical studies of M-dwarf exoplanet populations (Cloutier & Menou 2020; Kanodia et al. 2019). However, the aforementioned studies suffer from a small M-dwarf planet sample. Furthermore, the large range of stellar masses in the M-dwarf spectral type (0.65 M_⊙–0.08 M_⊙) means that we can possibly expect differences in planetary formation and properties within the spectral subtype due to variation in luminosity, protoplanetary disk mass, and composition. We need a larger sample of M-dwarf exoplanets to study these trends in planetary formation and evolution, for which TOI-1728b represents a step forward.

Using existing compositional models (Lopez & Fortney 2014) we estimate TOI-1728b to have a H/He atmospheric envelope of 15%–25% mass fraction (H/He + rock). We get comparable estimates from the Baraffe et al. (2008) models which predict a H/He mass fraction >10%. However, we would advise caution on this estimate, because these models (Fortney et al. 2007; Lopez & Fortney 2014; Zeng et al. 2019) use an exoplanet sample that consists mostly of solar-type stellar hosts, while there have been studies that suggest that the planetary formation mechanism has a dependence on stellar mass (Mulders et al. 2015a, 2015b). Also, most of these models are generally limited to rocky planets and sub-Neptunes with R_p < 4–4.5 R_⊕. The H/He envelope of Neptunes orbiting solar-type stars tend to have a higher metallicity [M/H] than Jupiter-sized planets due to planetesimal accretion (Venturini et al. 2016). However it is not clear whether this should be seen in Neptunes orbiting M dwarfs as well, due to different timescales for planetesimal accretion and disk lifetime for M-dwarf hosts versus solar-type host stars (Ogihara & Ida 2009).

The characteristic circularization timescale for most warm Neptunes is typically <5 Gyr, and hence most observed Neptunes should be in circular orbits. However, most warm Neptunes (P < 5 days) tend to exhibit nonzero eccentricity at >1σ (Correia et al. 2020); GJ 436b (Turner et al. 2016) and HAT-P-11b (Yee et al. 2018) are all eccentric at >3σ (Figure 11(d)). This eccentricity distribution of warm Neptunes contrasts with that for hot Jupiters and rocky planets, where the shorter orbital period planets tend to have circular orbits due to tidal dissipation. Correia et al. (2020) discuss multiple mechanisms that oppose bodily tides to slow down this circularization process; a combination of which (thermal tides in the atmosphere, atmospheric escape, or excitation due to a companion) can potentially yield the observed population of eccentric Neptunes.

TOI-1728b is a warm super-Neptune with a period of ∼3.5 days and eccentricity ${0.057}_{-0.039}^{+0.054}$ (Figure 11). The current eccentricity estimate for TOI-1728b is consistent with both a circular and mildly eccentric orbit. While it does rule out a highly eccentric system, it does not have the precision for more substantial claims regarding its place in the eccentric warm Neptune population. This constraint could be greatly improved with additional observations, especially the observation of a secondary eclipse. We also recognize that given the truncated positive semi-definite nature of the eccentricity distribution, there tends to exist a bias toward higher values in eccentricity estimates (Lucy & Sweeney 1971; Shen & Turner 2008). Considering these factors, if TOI-1728b is indeed in a circular orbit, this would contrast with the eccentricity distribution for warm Neptunes seen by Correia et al. (2020), and could be attributed to a few possible hypotheses:

• 1.  
  The TOI-1728 stellar system is old enough to circularize the planet despite the competing mechanisms. From Equation (2) of Correia et al. (2020), the characteristic circularization timescale for TOI-1728b is ∼0.8 Gyr, while our age estimates from the SED fit predict a stellar age of 7.0 ± 4.6 Gyr. This estimate, coupled with the lack of a detectable rotation period in photometry or RVs, and the lack of stellar activity indicate an old stellar host system that has had time to circularize its orbit.
• 2.  
  The initial orbit of TOI-1728b was not as highly eccentric as the other warm Neptunes in the Correia et al. (2020) sample. Since the total time for circularization scales with the initial eccentricity, if TOI-1728b formed in an orbit that was not highly eccentric, then it would be easier to circularize it.
• 3.  
  A companion object can pump up the eccentricity of a planet by the Kozai–Lidov mechanism (Kozai 1962; Lidov 1962) or spin-eccentricity pumping (Correia et al. 2013; Greenberg et al. 2013). For TOI-1728b, the TESS light curve does not show another transiting companion, however this does not rule out nontransiting companions or those with orbital periods ≳27 days. Furthermore, the RV residuals do not show a periodic signal, which at least rules out a massive and short period companion object.

Based on energy conservation, in a planet heated by host star's irradiation, the atmosphere mass escape rate is proportional to the XUV²⁴ flux falling on the planet, and inversely proportional to the density of the planet (Sanz-Forcada et al. 2011). We summarize the detections for He 10830 Å and Lyα absorption for GJ436b, GJ3470b—both warm Neptunes around M dwarfs—as well as HAT-P-11b, a warm Neptune around a mid-K dwarf, as they represent the closest analogues to TOI-1728b with intensive transmission spectroscopy follow-up.

He 10830 Å: Transit spectroscopy measurements have detected absorption in the NIR corresponding to ionized He 10830 Å for GJ3470b (Ninan et al. 2020; Palle et al. 2020), and also HAT-P-11b (Allart et al. 2018; Mansfield et al. 2018; Yee et al. 2018). At the same time, no absorption corresponding to this feature has been detected for GJ436b (Nortmann et al. 2018) or for TOI-1728b (this work).

Lyα measurements: Lyα observations using Hubble Space Telescope (HST) have detected significant atmospheric mass outflows in GJ 3470b (Bourrier et al. 2018) and GJ 436b (Kulow et al. 2014; Ehrenreich et al. 2015).

GJ 436b represents a particularly interesting case with Lyα detection in the UV, but lack of He 10830 Å absorption. This could be due to a lower helium ionizing flux in comparison to the hydrogen ionizing flux, and even to certain extent a fractional under-abundance of Helium in the exosphere of GJ 436b (Hu et al. 2015).

Similarly for TOI-1728b, despite having lower planet density, and higher stellar irradiance than GJ3470b, our upper limit of 1.1% in He 10830 Å absorption for TOI-1728b is less than the 1.5% absorption detection seen in GJ 3470b. This could imply a lesser helium ionizing flux from TOI-1728 than GJ 3470, and a scenario similar to that for GJ 436b. Given the similarity in planetary properties for these planets, we encourage the follow-up of TOI-1728 using the HST for Lyα exosphere detection, as well as further NIR observations to put tighter constraints on the upper limit on He 10830 Å absorption.

In addition to the atmospheric escape transmission spectroscopy observations detailed in the previous section, TOI-1728b is also a promising candidate for atmospheric abundance characterization.

Warm Neptunes (800–1200 K) represent equilibrium temperatures where the chemical and dynamical timescales become comparable and the assumption of chemical equilibrium breaks down (Guzmán Mesa et al. 2020). An example of this is GJ 436b, where transmission spectroscopy in the infrared with Spitzer has revealed that the relative abundances of CO to CH₄ are higher than expectations (Madhusudhan & Seager 2011). Crossfield & Kreidberg (2017) calculate the correlations between the detectability of H₂O signal for Neptunes with the equilibrium temperature and the H/He. These, when applied to TOI-1728b indicate a potential scale height for water of 1–2 (in units of H/He scale height), which would make TOI-1728b a good target for atmospheric characterization.

The Transmission Spectroscopy Metric (TSM; Kempton et al. 2018) for TOI-1728b is ∼130, which is the fifth highest TSM of sub-Jovian M-dwarf planets (R_p < 9 R_⊕) with mass measurements. We limit our TSM plot (Figure 12) to planets with mass measurements (3σ or better), because mass measurements are required to place priors on the atmospheric scale height, which is used to estimate the S/N of transmission spectroscopy observations. TOI-1728b has a density of ${1.14}_{-0.24}^{+0.26}$ g cm⁻³ and an inflated nature that lends itself to be particularly suitable for transmission spectroscopy. Our mass measurement precision of 5.1σ is essential in order to derive posteriors for atmospheric features that are not limited by the uncertainties in mass (Batalha et al. 2019).

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