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			<titleStmt><title level='a'>TOI-3785 b: A Low-density Neptune Orbiting an M2-dwarf Star</title></titleStmt>
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				<publisher></publisher>
				<date>07/04/2023</date>
			</publicationStmt>
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				<bibl> 
					<idno type="par_id">10435508</idno>
					<idno type="doi">10.3847/1538-3881/acd8bf</idno>
					<title level='j'>The Astronomical Journal</title>
<idno>0004-6256</idno>
<biblScope unit="volume">166</biblScope>
<biblScope unit="issue">2</biblScope>					

					<author>Luke C. Powers</author><author>Jessica Libby-Roberts</author><author>Andrea S. Lin</author><author>Caleb I. Cañas</author><author>Shubham Kanodia</author><author>Suvrath Mahadevan</author><author>Joe P. Ninan</author><author>Guđmundur Stefánsson</author><author>Arvind F. Gupta</author><author>Sinclaire Jones</author><author>Henry A. Kobulnicky</author><author>Andrew Monson</author><author>Brock A. Parker</author><author>Tera N. Swaby</author><author>Chad F. Bender</author><author>William D. Cochran</author><author>Leslie Hebb</author><author>Andrew J. Metcalf</author><author>Paul Robertson</author><author>Christian Schwab</author><author>John Wisniewski</author><author>Jason T. Wright</author>
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			<abstract><ab><![CDATA[Abstract                          Using both ground-based transit photometry and high-precision radial velocity spectroscopy, we confirm the planetary nature of TOI-3785 b. This transiting Neptune orbits an M2-Dwarf star with a period of ∼4.67 days, a planetary radius of 5.14 ± 0.16              R              ⊕              , a mass of                                                                                                                                            14.95                                                              −                      3.92                                                              +                      4.10                                                                                                  M              ⊕              , and a density of                                                                                                  ρ                  =                                                            0.61                                                              −                      0.17                                                              +                      0.18                                                                                                  g cm              −3              . TOI-3785 b belongs to a rare population of Neptunes (4              R              ⊕              <              R                              p                            < 7              R              ⊕              ) orbiting cooler, smaller M-dwarf host stars, of which only ∼10 have been confirmed. By increasing the number of confirmed planets, TOI-3785 b offers an opportunity to compare similar planets across varying planetary and stellar parameter spaces. Moreover, with a high-transmission spectroscopy metric of ∼150 combined with a relatively cool equilibrium temperature of              T              eq              = 582 ± 16 K and an inactive host star, TOI-3785 b is one of the more promising low-density M-dwarf Neptune targets for atmospheric follow up. Future investigation into atmospheric mass-loss rates of TOI-3785 b may yield new insights into the atmospheric evolution of these low-mass gas planets around M dwarfs.]]></ab></abstract>
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<div xmlns="http://www.tei-c.org/ns/1.0"><head n="1.">Introduction</head><p>The success of the Kepler <ref type="bibr">(Borucki et al. 2010</ref>) and TESS missions <ref type="bibr">(Ricker et al. 2015)</ref> have produced a catalog of over 5000 confirmed exoplanets. Multiple studies have leveraged these detections to derive planetary occurrence rates across a wide range of parameter spaces. Planetary occurrence rates around M-dwarf stars (the most common spectral type in our galaxy) are of particular interest. Using Kepler, <ref type="bibr">Dressing &amp; Charbonneau (2013)</ref> found that small, short-period planets (such as super-Earths and sub-Neptunes, 1.4 R &#8853; &lt; R p &lt; 4 R &#8853; ) are more common around M dwarfs than that of the Neptuneand Jupiter-sized planets. According to the NASA Exoplanet Archive <ref type="bibr">(Akeson et al. 2013)</ref> there are only &#8764;10 transiting planets within the Neptune radii bounds (4 R &#8853; &lt; R p &lt; 7 R &#8853; ) with confirmed masses orbiting M-dwarf stars, significantly less than the terrestrial population. The processes by which these larger Neptunes orbiting low-mass stars form is still an open question-one that requires a larger sample of planets to answer. Discovering and characterizing more of these planets with precise radius and mass measurements will continue to aid efforts to quantify occurrence and understand the specific mechanisms behind M-dwarf planetary formation.</p><p>We present a new planet inhabiting this sparsely populated M-dwarf Neptune parameter space, TOI-3785 b. We used a combination of ground-based photometric (transit) and spectroscopic (radial velocity) follow up to confirm this TESS discovered planet which we describe in Section 2. Using stellar spectra, we update the stellar parameters (Section 3) confirming that TOI-3785 is an inactive M dwarf. We derive precise mass and radius measurements for TOI-3785 b in Section 4. In Section 5 we highlight TOI-3785 b's place across a variety of stellar and planetary parameters and discuss its Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. potential for various in-depth studies into comparative planetology. We conclude and summarize this work in Section 6.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.">Observations</head></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.1.">TESS Photometry</head><p>TOI-3785 (Table <ref type="table">1</ref>) was first observed in TESS Sector 20, from 2019 December 24 to 2020 January 20. Similar to the TOI-1899 <ref type="bibr">(Ca&#241;as et al. 2020</ref>) and TOI-3629 <ref type="bibr">(Ca&#241;as et al. 2022</ref>) systems, we identified TOI-3785 b as a planetary candidate using a custom pipeline to search for transiting candidates in short and long-cadence TESS data. This target was independently identified by the Quick Look Pipeline <ref type="bibr">(Huang et al. 2020</ref>) when a 4.67 days transiting signal was flagged during an observation in long-cadence mode (1800 s exposure). An identical periodic signal from TOI-3785 was again observed by TESS in Sector 47 from 2021 December 30 to 2022 January 28 with a two-minute exposure time. We retrieved both long-and short-cadence sectors using the lightkurve package (Lightkurve <ref type="bibr">Collaboration et al. 1812)</ref>. The Pre-search Data Conditioning Simple Aperture Photometry <ref type="bibr">(Jenkins et al. 2016)</ref> flux was used during our analysis <ref type="bibr">(Caldwell et al. 2020)</ref>. We show this photometry along with the best-fit model from our joint fit in Figure <ref type="figure">1</ref>.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.2.">Ground-based Photometric Follow Up</head><p>2.2.1. Red Buttes Observatory 0.6 m One transit of TOI-3785 b was observed on 2021 November 11 using the 0.6 m telescope at the Red Buttes Observatory (RBO) in Wyoming <ref type="bibr">(Kasper et al. 2016)</ref>. We observed TOI-3785 b using the Bessell I filter at an exposure time of 240 s, from an airmass of 1.26 to 1.08. The post-transit observations were cut short due to increased cloud cover (Figure <ref type="figure">1</ref>).</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.2.2.">ARC 3.5 m Telescope</head><p>We obtained one transit of TOI-3785 b on the night of 2022 April 5 using the Astrophysical Research Consortium (ARC) Telescope Imaging Camera (ARCTIC; <ref type="bibr">Huehnerhoff et al. 2016)</ref> at the ARC 3.5 m Telescope at Apache Point Observatory (APO). This target was observed with ARCTIC's narrow-band Semrock filter (between 842 and 873 nm; <ref type="bibr">Stefansson et al. 2017</ref><ref type="bibr">Stefansson et al. , 2018))</ref>, with an exposure time of 56 s, in the quad amplifier, fast readout mode, and with 4 &#215; 4 onchip binning mode in effect. Relatively photometric skies and the use of this narrow-band Semrock filter (designed to avoid regions of telluric water absorption), enabled us to obtain highprecision photometry even at a significant airmass change (airmass 1.38-3.81) over the entirety of the transit event. The increasing airmass toward the end (airmass &gt;3) resulted in significant scatter in the post-transit baseline (Figure <ref type="figure">1</ref>).</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.2.3.">NESSI at WIYN</head><p>The NN-EXPLORE Exoplanet Stellar Speckle Imager (NESSI; Scott 2018) is mounted on the WIYN 3.5 m telescope at Kitt Peak National Observatory (KPNO). We used NESSI speckle photometry to search for faint stellar targets in close proximity to TOI-3785 that may contaminate the primary, or introduce additional photometric error. We observed this target on 2022 April 17 in the Sloan &#162; z filter (865-960 nm). The 5&#963; contrast curve in Figure <ref type="figure">2</ref> reveals no bright (&#916;z&#8242; mag &lt; 4) stellar companions within a 0.3&#8243;-1.2&#8243; range of TOI-3785. We also include the 2D NESSI speckle image for TOI-3785 as an inset.</p><p>Table 1 Stellar Parameters Parameter Description Value Source Main identifiers: TOI TESS object of interest 3785 ExoFOP-TESS (NExScI 2022) TIC TESS input catalog 458419328 ExoFOP-TESS (NExScI 2022) 2MASS ... J08433613 + 6304413 ExoFOP-TESS (NExScI 2022) Gaia DR3 ... 1044013542142711296 ExoFOP-TESS (NExScI 2022) APASS ... 59229225 ExoFOP-TESS (NExScI 2022) Equatorial coordinates: &#945; J2000 R.A. 8:43:36 ExoFOP-TESS (NExScI 2022) &#948; J2000 decl. +65:03:41 ExoFOP-TESS (NExScI 2022) Proper motion: &#956; &#945; Proper motion (R.A.) -42.86 &#177; 0.01 GAIA (DR3; Gaia Collaboration et al. 2022) &#956; &#948; Proper motion (decl.) -16.95 &#177; 0.01 GAIA (DR3; Gaia Collaboration et al. 2022) Distance and maximum extinction: d Geometric distance (pc) 79.4 &#177; 0.1 Bailer-Jones et al. (2021) A V,max Maximum visual extinction 0.03 Green et al. (2019) Magnitudes: TESS TESS mag 12.496 &#177; 0.007 ExoFOP-TESS (NExScI 2022) g PS1 g'mag 15.244 &#177; 0.013 PS1 Chambers et al. (2016), Magnier et al. (2020) r PS1 r'mag 14.076 &#177; 0.008 PS1 Chambers et al. (2016), Magnier et al. (2020) y PS1 y'mag 12.248 &#177; 0.022 PS1 Chambers et al. (2016), Magnier et al. (2020) J 2M J mag 11.051 &#177; 0.026 2MASS (Cutri et al. 2003) H 2M H mag 10.387 &#177; 0.029 2MASS (Cutri et al. 2003) K 2M K mag 10.165 &#177; 0.022 2MASS (Cutri et al. 2003) W1 WISE1 mag 10.034 &#177; 0.023 WISE (Wright et al. 2010) W2 WISE2 mag 9.966 &#177; 0.019 WISE (Wright et al. 2010) W3 WISE3 mag 9.860 &#177; 0.045 WISE (Wright et al. 2010)</p><p>Additionally, we use Gaia Data Release 3 (DR3; Gaia Collaboration et al. 2022) to further rule out stellar companions within a 25&#8243; range. According to <ref type="bibr">Ziegler et al. (2018)</ref>, Gaia has the capabilities to recover 93% of targets at a distance &gt; 2&#8243;. In TOI-3785&#700;s case, Gaia DR3 reveals the closest object at 26&#8243;. Therefore, considering data from NESSI and Gaia, we can conclude that no source of significant photometric dilution is present from nearby stellar companions.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.3.">Radial Velocity Follow Up</head></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.3.1.">The Habitable-zone Planet Finder</head><p>The Habitable-zone Planet Finder (HPF; <ref type="bibr">Mahadevan et al. 2012</ref><ref type="bibr">Mahadevan et al. , 2014) )</ref> is designed to obtain high-precision near-infrared (808-1278 nm) radial velocity observations. Located on the 10 m Hobby-Eberly Telescope (HET; <ref type="bibr">Ramsey et al. 1998;</ref><ref type="bibr">Hill et al. 2021)</ref> in Texas, this spectrograph is rigorously environmentally controlled <ref type="bibr">(Stefansson et al. 2016</ref>) and fiber fed, allowing for simultaneous science and sky observations <ref type="bibr">(Kanodia et al. 2018)</ref>. From the raw HPF data, we correct for bias noise, cosmic rays, and nonlinearity using HxRGproc <ref type="bibr">(Ninan et al. 2018)</ref>.  We apply a modified version of the SpEctrum Radial Velocity AnaLyser pipeline (SERVAL; <ref type="bibr">Zechmeister et al. 2018)</ref>, as outlined in <ref type="bibr">Metcalf et al. (2019)</ref>, to derive the binned radial velocity (RV) points. To accomplish this, SERVAL combines all observations of TOI-3785 to extract a master spectrum (Anglada-Escud&#233; &amp; Butler 2012) after first identifying and masking telluric and sky emission lines. SERVAL then fits this template to each individual spectrum by shifting it in wavelength space to minimize &#967; 2 . We use the python package barycorrpy <ref type="bibr">(Kanodia &amp; Wright 2018)</ref> to further correct for barycentric motion.</p><p>We observed TOI-3785 with HPF for 34 visits, with most visits consisting of two 15 minutes exposures per night that were then binned, between 2020 November 4 and 2022 April 19. A median signal-to-noise ratio (S/N) of 69 was calculated at a wavelength of 1070 nm. Of the 34 collected RV points, 29 were kept for the final analysis. Discarded points were done so on the grounds of either unideal weather conditions or significant deviation from the average S/N. Binned RV points along with their errors are listed under Table <ref type="table">2</ref>, and the final binned HPF RVs are plotted as dark red points in Figure <ref type="figure">3</ref>.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="2.3.2.">NEID</head><p>NEID <ref type="bibr">(Halverson et al. 2016;</ref><ref type="bibr">Schwab et al. 2016</ref>) is a highresolution (R &#8764;110,000) spectrograph located on the WIYN 3.5 m telescope at KPNO. NEID covers optical/near-infrared wavelengths ranging from 380 to 930 nm. We observed TOI-3785 between 2021 November 10 and 2022 May 16, obtaining 10 RV points with NEID in high-resolution mode. As NEID allows for longer exposure times than HPF, we obtained a single spectrum per visit with an exposure time of 1800 s, resulting in a median S/N of 15 at 850 nm. The raw spectra were reduced through the NEID Data Reduction Pipeline, 21 and we retrieved the Level-2 2D extracted spectra. 22 We derived RVs using a modified SERVAL pipeline designed specifically for NEID data <ref type="bibr">(Stef&#224;nsson et al. 2022)</ref>. NEID RVs and errors are reported in Table <ref type="table">3</ref> and plotted in gold in Figure <ref type="figure">3</ref>.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="3.">Stellar Parameters</head><p>We used the HPF spectra and HPF-SpecMatch (Stefansson et al. 2020) to derive the effective temperature (T eff ), metallicity (Fe/H), v i sin , and g log priors for the host star, TOI-3785. Based on <ref type="bibr">Yee et al. (2017)</ref>, HPF-SpecMatch uses a spectral database of well-characterized stellar targets with high S/N HPF observations comparing each star to that of TOI-3785. By creating a composite of library spectra and minimizing the &#967; 2 of the composite, we obtain best-fit values for each parameter. Uncertainties in the spectroscopic parameters were then determined from cross-validation estimates (for additional details see <ref type="bibr">Stefansson et al. 2020)</ref>. We estimate the following stellar priors,</p><p>4.747 0.0458, and Fe/H = 0.099 &#177; 0.117 (Table <ref type="table">4</ref>).</p><p>We then estimate the stellar mass, radius, and age by modeling the spectral energy distribution (SED) using the MIST model grids <ref type="bibr">Dotter (2016)</ref>  <ref type="table">4</ref>). These parameters, combined with the SED derived effective temperature of 3580 &#177; 47 K, classifies the star as a M2-dwarf spectraltype star <ref type="bibr">(Damiani et al. 2016)</ref>.</p><p>To evaluate the activity of TOI-3785, we examine a Lomb-Scargle periodogram <ref type="bibr">(Lomb 1976</ref>) derived from the short cadence TESS light curve. We find no significant peaks corresponding to stellar rotation. We also used the publicly available photometry from the Zwicky Transient Facility (ZTF; <ref type="bibr">Bellm et al. 2019)</ref> in the &#162; g and &#162; r filters and the All-Sky Automated Survey for Supernovae <ref type="bibr">(Kochanek et al. 2017)</ref> in its V filter. The Lomb-Scargle analysis from both sources again reports no statistically significant rotation signals in the photometry. This lack of detection is expected given our estimated v i sin is below our detection threshold from HPF-SpecMatch (&lt;2 km s -1 ). We further support this claim by investigating the Calcium Infrared Triplet lines <ref type="bibr">(Mallik 1997;</ref><ref type="bibr">Andretta et al. 2005;</ref><ref type="bibr">Cincunegui et al. 2007;</ref><ref type="bibr">Martin et al. 2017)</ref> observed by HPF and H&#945; lines observed by NEID. No lines exhibited signs of emission, suggesting low activity in the chromosphere of TOI-3785 <ref type="bibr">(Newton et al. 2016</ref>). Thus, we conclude that TOI-3785 is a slowly rotating, inactive M2dwarf star.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="4.">Analysis</head></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="4.1.">Data Reduction</head><p>We use AstroImageJ <ref type="bibr">(Collins et al. 2016)</ref> to perform the reductions of TOI-3785&#700;s ground-based photometry. For each of the ground-based observations, we subtract a median master bias file, and for the RBO photometry, we additionally subtract a median master dark current file (at short exposure times there is no significant dark current for the ARCTIC observations). Table 3 NEID RV Points BJD TDB RV (m s -1 ) &#963; (m s -1 ) S/N 2459529.01052 15.7 5.26 15 2459532.01789 -4.52 3.91 20 2459533.01626 11.74 5.07 16 2459533.91777 12.63 3.69 21 2459538.97354 -9.06 4.43 18 2459569.04250 -9.32 7.27 11 2459586.75088 -8.23 5.89 14 2459619.89833 7.11 5.43 15 2459629.91089 0.82 7.47 11 2459715.67442 18.02 6.51 13 Table 4 TOI-3785 b System Parameters Parameter Label (Units) Value Orbital parameters: RV semiamplitude K (m s -1 ) 9.24 &#177; 2.68 Orbital period P (days) 4.6747373 &#177; 0.0000038 Transit midpoint T 0 (BJD) 2458861.49553 - + 0.00058 0.00060 Scaled radius R p /R * 0.0962 &#177; 0.0017 Scaled semimajor axis a/R * 18.89 - + 0.44 0.45 Impact parameter b 0.60 - + 0.03 0.02 Planetary parameters: Eccentricity e -+ 0.11 0.08 0.10 (2&#963; &lt; 0.26) Inclination i (degrees) 88.1&#177;0.01 Omega &#969; (degrees) 96.26 - + 143.93 51.25 Transit duration T Dur (days) 0.071 &#177; 0.001 Transit depth ( ) * R R p 2 (ppm) 9254 &#177; 3 Mass M p (M &#8853; ) 14.95 - + 3.92 4.10 Radius R p (R &#8853; ) 5.14&#177;0.16 Density &#961; p (g/cm 3 ) 0.61 - + 0.17 0.18 Semimajor axis a (AU) 0.043&#177;0.001 Isolation S p (S &#8853; ) 19.1&#177;2.0 Equilibrium temperature T eq (K) 582&#177;16 Stellar parameters: Mass M * (M e ) 0.52 &#177; 0.02 Radius R * (R e ) 0.50 &#177; 0.01 Luminosity L * (L e ) -+ 0.0367 0.0009 0.0008 Effective temperature T eff (Kelvin) 3576 &#177; 88 K Surface gravity g log (cgs) 4.747&#177;0.0458 Rotational velocity v i sin (km s -1 ) &lt;2 Metallicity [Fe/H] (dex) 0.099 &#177; 0.117 Age (Gyr) -+ 8.0 4.8 4.1</p><p>The bias and dark corrected images were then divided by their respective normalized sky flats.</p><p>After initial data reductions were completed, we select appropriate aperture sizes for the target and reference stars to minimize both the background noise and any potential stellar interference in our photometry. We then perform differential aperture photometry using AstroImageJ, of the primary target and five to seven reference stars assuming a constant aperture size with a radius of 5.48&#8243; and 7.8&#8243; for APO and RBO, respectively. Background values were measured by assuming a median value derived from annuli around each star with an inner and outer radius of 9.12&#8243;, 14.6&#8243; for APO and 10.4&#8243;, 13.0&#8243; for the RBO data. Uncertainties were calculated by AstroImageJ assuming photon noise from the star, background, and dark current (for RBO) and respective read noise for the individual instruments. In post-processing, we found it was unnecessary to detrend the light curves using any external parameters (airmass, background, etc.).</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="4.2.">Joint Fitting</head><p>Using the python package exoplanet (Foreman-Mackey et al. 2021), we perform a joint fit of all transit photometry (TESS + ARCTIC + RBO) and RV measurements (HPF + NEID). We derived the final transit and radial velocity models in addition to a collection of stellar and planetary parameters that were previously estimated in the AstroImageJ fit. Tables <ref type="table">4</ref> and <ref type="table">5</ref> list the finalized transit and system parameters produced by this joint fit.</p><p>From the transit observations, we derive a best-fit a/R * , impact parameter (b), transit depth (R p /R s ) 2 , and midtransit ephemeris. We reparameterized and then fit the limb-darkening parameters as suggested in <ref type="bibr">Kipping (2013)</ref> to ensure uninformative sampling of quadratic parameters. As each instrument employs a different bandpass, we fit for individual quadratic limb-darkening terms. We also include a photometric noise jitter term added in quadrature to the error bars and the addition of a flux offset value to each light curve.</p><p>Due to TESS&#700;s large pixel sizes, photometric dilution is a common source of error in transit depth estimations <ref type="bibr">(Sullivan et al. 2015)</ref>. TESS dilution may cause photometric variation in our reported transit depth causing our errors to inflate. We account for this by fitting a separate dilution term multiplied to the transit depth for each TESS Sector (as described in Bryant . Our high-precision uncontaminated ground-based photometry from ARCTIC (which we use as the baseline fixed to a dilution of 1) enabled us to properly account for this variation.</p><p>Figure <ref type="figure">1</ref> displays our best-fit photometric transit models. These folded light curves report a transit depth of 0.9254% &#177; 0.0003% and transit duration of T duration = 0.071 &#177; 0.001 days (&#8764;1.7 hr). Each transit plot presents a 10 minute bin of the reduced data and residuals as well as values of median photometric error.</p><p>For the radial velocity observations, we include linear RV trend terms for both HPF and NEID to account for any slight positive or negative slopes in the RVs caused by instrumental drift. In addition, we report the instrument-specific factors of RV jitter and offset. The jitter term is used to estimate the degree of RV error inflation in order to meet an expected RV fit. All photometric and radial velocity correction terms are reported in Table <ref type="table">5</ref>. We plot, in Figure <ref type="figure">3</ref>, the exoplanet RV fit including all HPF and NEID points. The best-fit model indicates an RV semiamplitude of 9.24 &#177; 2.68 m s -1 and an eccentricity of = -+ e 0.11 0.08 0.10 . From this analysis, we determine that TOI-3785 b has a radius of 5.14 &#177; 0.16 R &#8853; and a mass of</p><p>-+ &#197; M 14.95 3.92 4.10</p><p>. Table <ref type="table">4</ref> lists the finalized planetary and orbital parameters produced by this joint fit.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="4.3.">Planetary Companions</head><p>Further analyzing the transit data, we search for additional periodic signals by implementing a box least squared (BLS; <ref type="bibr">Kov&#225;cs et al. 2002)</ref> algorithm of all available TESS data extracted from the MAST archive (MAST Team 2021). The known transit of TOI-3785 b in both Sectors 20 and 47 were masked to twice the duration in order to search for other potential period detections that may indicate additional transiting planets in the TOI-3785 system. The masked BLS periodograms report no significant peaks over the false alarm probability (FAP) of 10%.</p><p>Additionally, periodograms of HPF and NEID also show no additional significant peaks (stellar or planetary in nature). The existing data does not reveal the presence of a close-period companion in this system as the known signal of TOI-3785 b recovers the lowest FAP at 10%. However, the limited</p><p>Table 5 Photometry/Radial Velocity Correctional Terms Parameter Label (Units) Value Photometric parameters: TESS S20 TESS S47 APO RBO Linear limb-darkening coefficient u 1 0.36 - + 0.26 0.39 0.26 - + 0.19 0.31 0.27 - + 0.19 0.26 0.35 - + 0.25 0.43 Quadratic limb-darkening coefficient u 2 0.17 - + 0.37 0.37 0.14 - + 0.27 0.32 0.046 - + 0.214 0.268 0.10 - + 0.31 0.37 Photometric jitter &#963; phot (ppm) 53 - + 33 55 110 - + 67 103 3056 - + 91 98 3830 - + 360 430 Dilution factor D 0.97 - + 0.05 0.06 0.92&#177;0.05 *** *** RV parameters: HPF NEID RV jitter &#963; RV (m s -1 ) -+ 2.9 2.1 3.1 -+ 7.7 2.6 3.5 RV offset &#947; RV (m s -1 ) 4.7 &#177;3.3 1.1 &#177;2.9 RV trend a &#61478; g (mm s -1 day -1 ) -2.1 - + 4.3 4.2</p><p>Absolute RV a &#916;RV (m s -1 ) 4657 &#177; 152</p><p>Note.</p><p>a Not instrument specific coverage of this system with both TESS and RV monitoring cannot rule out the potential for additional long-period planets.</p><p>From our available transit and RV data, we see no detection of additional orbiters, but a more in-depth analysis is required for a concrete claim to be made.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="5.">Discussion</head></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="5.1.">TOI-3785 b in Parameter Space</head><p>In order to emphasize the unique planetary characteristics of TOI-3785 b we compare this system to other confirmed exoplanet targets in Figure <ref type="figure">4</ref>. We plot TOI-3785 b in both planetary mass-radius (Figure <ref type="figure">4</ref>; top) and T eff -radius (Figure <ref type="figure">4</ref>; bottom) space. These systems were compiled from the NASA Exoplanet Archive <ref type="bibr">(Akeson et al. 2013</ref>) as of 2023 March 1 using the following parameter constraints: an upper planetary radius limit of 14 R &#8853; and a radius and mass significance cut off at &gt;3&#963;. For the mass-radius plot we limit the stellar effective temperature to &lt;4000 K (the upper temperature boundary of M dwarfs; <ref type="bibr">Casagrande et al. 2008</ref>) and include planetary density contour lines at 0.5, 1, 3, and 10 g cm -3 .</p><p>The parameter spaces of Figure <ref type="figure">4</ref> both show TOI-3785 b, indicated by a blue circle, to be a meaningful addition to the current number of known M-dwarf-hosted targets. Due to its planetary radius , TOI-3785 b occupies the rare M-dwarf Neptune population (4 R &#8853; &lt; R p &lt; 7 R &#8853; ) of which only eight others have been confirmed with a &gt;3&#963; mass and radius (Figure <ref type="figure">4</ref>). This dearth in the Neptune population becomes clear when the vast number of lower radii targets (&lt;3R &#8853; ) is considered. It is widely known that lower mass M dwarfs have a higher occurrence rate for smaller (and likely terrestrial in composition) close-in planets with <ref type="bibr">Dressing &amp; Charbonneau (2013)</ref> discovering a sharp decrease in occurrence rate at 4 R &#8853; .</p><p>The M-dwarf Jupiter population (&gt;7 R &#8853; ) is seen to be relatively sparse compared to FGK occurrence totaling only &#8764;15 mass significant targets. M-dwarf Jupiters do not come close to rivaling the M-dwarf Earth population (&lt;3 R &#8853; ) in which &#8764;35 &gt;3&#963; mass targets are known. Still, first approximations of occurrence rates have been derived for close-in Jupiters orbiting M dwarfs, even with this small sample size (&#8764;1%; <ref type="bibr">Bryant et al. 2023;</ref><ref type="bibr">Gan et al. 2023</ref>). However, the occurrence of M-dwarf Neptunes (4 &lt; R p &lt; 7 R &#8853; ) has yet to be the focus of a targeted study-in part due to the &lt;10 confirmed detections. TESS&#700;s focus on nearby M dwarfs is steadily growing the Neptune population. With the discovery of additional Neptunes similar to TOI-3785 b, we may soon derive the first occurrence rates for Neptunes and move closer toward a complete picture regarding the occurrence of all M-dwarf populations.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="5.2.">Constraints on M-dwarf Planetary Formation</head><p>The leading theory of Neptune formation around M dwarfs is core accretion <ref type="bibr">(Laughlin et al. 2004)</ref>, in which the formation of a solid core generates a disk of gas and dust from surrounding debris that is slowly accreted onto the surface of the protoplanet. In cases of ample material and undisturbed mass accumulation, a protoplanet may reach a critical mass triggering runaway accretion in which a planet's mass exponentially increases. This is the traditional formation pathway for many Jupiter mass planets (e.g., <ref type="bibr">Bodenheimer &amp; Pollack 1986;</ref><ref type="bibr">Pollack et al. 1996)</ref>. In the case of the less massive Neptune population, there must be an inhibitor to prevent runaway accretion from taking place: either the protoplanet lacks sufficient material to accrete onto its surface or it lacks sufficient time to grow to a critical mass <ref type="bibr">(Deleuil et al. 2020)</ref>. <ref type="bibr">Laughlin et al. (2004)</ref> argues that due to the smaller M-dwarf disk masses, gas giant cores require additional time to form. If they reach the critical mass threshold to begin accumulating H/He, their runaway growth stage is cut short due to disk dispersion.</p><p>TOI-3785 b appears to support this formation theory. Using the Exoplanet Compositional Interpolator<ref type="foot">foot_1</ref> based on models from <ref type="bibr">Lopez &amp; Fortney (2014)</ref>, we estimate a H/He mass fraction of 20% (&#8764;3 M &#8853; ) with a heavy-element (core) mass fraction of 80% (11.95 M &#8853; ) for TOI-3785 b. As this is slightly more massive than the predicted core mass required for runaway accretion, we conclude that TOI-3785 b&#700;s core must have formed slowly following the predicted pathway highlighted in <ref type="bibr">Laughlin et al. (2004)</ref>. With 20% of its mass in a H/ He envelope, it appears TOI-3785 b was poised to begin runaway accretion. However, this accretion stalled potentially due to the disk dispersing or the planet migrating inwards to its present-day location. By further investigating TOI-3785 b&#700;s composition, we may constrain the formation timeline of M-dwarf hosting Neptunes to derive reasonable evolutionary pathways for these rare targets.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="5.3.">The Neptune Desert</head><p>The Neptune desert is a region of parameter space in which remarkably few Neptune-sized targets have been confirmed around FGK stars. Targets that inhabit this region are defined by their Neptune radii as well as low orbital periods and high insolations. TOI-3785 b lies within the Neptune-desert regime as defined in radius-period space in <ref type="bibr">Mazeh et al. (2016;</ref><ref type="bibr">Figure 5;</ref><ref type="bibr">top)</ref>. However, the bounds of this desert were derived from FGK targets confirmed by the Kepler mission. M-dwarf targets, such as TOI-3785 b, may have misleading placements within the desert as low-temperature stars will produce planets with low insolation even at short periods. TOI-3785 b possesses a short orbital period of 4.67 days and its cooler host star yields a significantly smaller insolation (19&#215; Earth Insolation) when compared to planets around FGK stars that normally yield insolations within the range of 100-1000 S &#8853; . Therefore, the Neptune Desert should be considered in radiusinsolation space for M-dwarf hosting systems. TOI-3785 b sits outside of the Insolation Neptune Desert space as defined by <ref type="bibr">Kanodia et al. (2021;</ref><ref type="bibr">Figure 5;</ref><ref type="bibr">bottom)</ref>. TOI-532 b <ref type="bibr">(Kanodia et al. 2021</ref>) is a similarly-sized planet compared to TOI-3785 b orbiting a slightly larger M0 dwarf. TOI-532 b is also the only M-dwarf Neptune that possesses a large enough insolation (94 S &#8853; ) to be considered within the FGK bounds of the insolation Neptune Desert. While similarly sized, this planet possesses a substantially higher mass and density than all other M-dwarf Neptunes suggesting it experienced significant H/He escape during its lifetime. With its low insolation, TOI-3785 b likely experienced little to no atmospheric escape during its evolution.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="5.4.">Atmospheric Comparative Planetology</head><p>TOI-3785 b joins the growing list of promising targets for atmospheric characterization (Table <ref type="table">6</ref>). We calculate its transmission spectroscopy metric (TSM) following Equation (1) in <ref type="bibr">Kempton et al. (2018)</ref> finding a TSM value of 147 (Figure <ref type="figure">6</ref>). TOI-3785 b possesses one of the highest TSMs for any planet cooler than 600 K-with AU Mic b the only other planet in this temperature regime with a higher TSM. Since AU Mic is an active star <ref type="bibr">(Plavchan et al. 2020)</ref>, difficulties probing AU Mic b's atmosphere may arise due to stellar interference.</p><p>Thus, the inactivity of TOI-3785 b's host star makes it the best target for exploring this temperature regime.</p><p>TOI-3785 b also possesses similar planetary and stellar parameters as two Neptunes with well-characterized transmission spectra: GJ 3470 b (e.g., <ref type="bibr">Crossfield et al. 2013;</ref><ref type="bibr">Ehrenreich et al. 2014;</ref><ref type="bibr">Dragomir et al. 2015)</ref> and GJ 436 b (e.g., <ref type="bibr">Knutson et al. 2014</ref>). Both of these targets possess featureless spectra Colored points represent &gt;3&#963; mass precision while targets under this threshold are grayed out. We also highlight the lack of planetary confirmation between (4000 K &lt; T eff &lt; 4700 K). This is most likely a result of the shallow transit depths that are characteristic of K-dwarf stars. This creates a detection bias as K-dwarf planets produce weaker transiting signals. In both figures, similar M-dwarf Neptunes to TOI-3785 b are labeled and listed in Table <ref type="table">6</ref>. within Hubble's Wide Field Camera 3 bandpass (1.1-1.7 &#956;m) indicating hazy atmospheres; a characteristic that TOI-3785 b could share <ref type="bibr">(Yu et al. 2021;</ref><ref type="bibr">Dymont et al. 2022)</ref>. By leveraging JWST's NIRSpec-Prism longer wavelength coverage, the hazes should become translucent at wavelengths beyond 3 microns allowing for both characterization of the haze layer and the atmospheric composition beneath <ref type="bibr">(Kawashima et al. 2019)</ref>. TOI-3785 b therefore presents an opportunity to not only explore the atmosphere of a warm-Neptune but also enable insightful atmospheric comparisons with similar planets around similar stars. Interestingly, both GJ 3470 b and GJ 436 b have along with similarities between this system and GJ 3470 (stellar parameters) makes it a promising target for helium follow up.</p></div>
<div xmlns="http://www.tei-c.org/ns/1.0"><head n="6.">Summary</head><p>Using both ground-based and TESS transit photometry as well as spectroscopic RV follow up of the TOI-3785 system, we confirm the existence of a single planetary companion, TOI-3785 b, a warm-Neptune with a 4.67 days circular orbit around an M2V-dwarf star. Using the package exoplanet we model both the transit observations and RVs to derive a planetary mass of -+ &#197; M 14.95 3.92 4.10 and radius of 5.14 &#177; 0.16R &#8853; . The confirmation of TOI-3785 b proves to be a valuable addition to the small number of M-dwarf-hosted Neptunes as increased target confirmation in this space may support Neptune formation models such as the joint efforts of core accretion and situational disk dispersion. Future investigations into this target via transmission spectroscopy are warranted as it possesses an ideal TSM along with favorable constraints on atmospheric hazing. The noteworthy similarities to GJ 3470 b and GJ 436 b may also demonstrate similarly influential results on the composition and formation pathways of M-dwarf gas planets. Furthermore, we discuss TOI-3785 b's place relative to the radius-period and radius-insolation Neptune Deserts and the necessary cautions that accompany M-type hosts and desert classifications.  Table 6 and are noted with colors varying by their respective planetary radii, while planets orbiting FGK-dwarf stars are plotted as gray points. TOI-3785 b (navy blue circle) possesses one of the highest TSMs for any planet cooler than 600 K, making it a promising target for future transmission spectroscopy observations. planetary target. The Center for Exoplanets and Habitable Worlds is supported by Penn State and the Eberly College of Science. Computations for this research were performed on the Penn State&#700;s Institute for Computational and Data Sciences' Advanced Cyber Infrastructure (ICDS-ACI). This content is solely the responsibility of the authors and does not necessarily represent the views of the Institute for Computational and Data Sciences. The Pennsylvania State University campuses are located on the original homelands of the Erie, Haudenosaunee <ref type="bibr">(Seneca, Cayuga, Onondaga, Oneida, Mohawk, and Tuscarora)</ref>, Lenape (Delaware Nation, Delaware Tribe, Stockbridge-Munsee), Shawnee (Absentee, Eastern, and Oklahoma), Susquehannock, and Wahzhazhe (Osage) Nations. As a land grant institution, we acknowledge and honor the traditional caretakers of these lands and strive to understand and model their responsible stewardship. We also acknowledge the longer history of these lands and our place in that history. W.D.C. acknowledges support from NSF grant AST 2108801.</p><p>These results are based on observations obtained with the Habitable-zone Planet Finder Spectrograph on the HET. We acknowledge support from NSF grants AST-1006676, <ref type="bibr">AST-1126413, AST-1310885, AST-1310875, AST-1910954, AST-1907622, AST-1909506, ATI 2009889, ATI-2009982, AST-2108512, and</ref> the NASA Astrobiology Institute (NNA09-DA76A) in the pursuit of precision radial velocities in the NIR. The HPF team also acknowledges support from the Heising-Simons Foundation via grant 2017-0494. The Hobby-Eberly Telescope is a joint project of the University of Texas at Austin, the Pennsylvania State University, Ludwig-Maximilians-Universit&#228;t M&#252;nchen, and Georg-August Universit&#228;t Gottingen. The HET is named in honor of its principal benefactors, William P. Hobby and Robert E. Eberly. The HET collaboration acknowledges the support and resources from the Texas Advanced Computing Center. We thank the Resident Astronomers and Telescope Operators at the HET for the skillful execution of our observations with HPF. We would like to acknowledge that the HET is built on Indigenous land. Moreover, we would like to acknowledge and pay our respects to the Carrizo &amp; Comecrudo, Coahuiltecan, Caddo, Tonkawa, Comanche, Lipan Apache, Alabama-Coushatta, Kickapoo, Some of the data presented in this paper were obtained from MAST at STScI. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts. This work includes data collected by the TESS mission, which are publicly available from MAST. Funding for the TESS mission is provided by the NASA Science Mission directorate.</p><p>This work presents results from the European Space Agency (ESA) space mission Gaia. Gaia data are being processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC is provided by national institutions, in particular the institutions participating in the Gaia MultiLateral Agreement (MLA). The Gaia mission website is <ref type="url">https://www.  cosmos.esa.int/gaia</ref>.</p><p>The Gaia archive website is <ref type="url">https://  archives.esac.esa.int/gaia</ref>. This research has made use of the Exoplanet Follow-up Observation Program (ExoFOP, NExScI 2022) website, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. C.I.C. acknowledges support by NASA Headquarters through an appointment to the NASA Postdoctoral Program at the Goddard Space Flight Center, administered by USRA through a contract with NASA and the NASA Earth and Space Science Fellowship Program through grant 80NSSC18K1114.</p><p>Facilities: TESS, APO (ARCTIC), RBO, Gaia, HET (HPF), WIYN (NEID), NESSI.</p></div><note xmlns="http://www.tei-c.org/ns/1.0" place="foot" xml:id="foot_0"><p>The Astronomical Journal, 166:44 (13pp), 2023 August Powers et al.</p></note>
			<note xmlns="http://www.tei-c.org/ns/1.0" place="foot" n="24" xml:id="foot_1"><p>https://tools.emac.gsfc.nasa.gov/ECI/</p></note>
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