The elemental and isotopic abundances of volatiles like carbon oxygen and nitrogen may trace a planets formation location relative to HSUB2SUBO COSUB2SUB CO NHSUB3SUB and NSUB2SUB snowlines or the distance from the star at which these volatile elements sublimate. By comparing the CO and SUP12SUPCSUP13SUPC ratios measured in giant exoplanet atmospheres to complementary measurements of their host stars we can determine whether the planet inherited stellar abundances from formation inside the volatile snowlines or nonstellar CO and SUP13SUPC enrichment characteristic of formation beyond the snowlines. To date there are still only a handful of exoplanet systems where we can make a direct comparison of elemental and isotopic CNO abundances between an exoplanet and its host star. Here we present a SUP12SUPCSUP13SUPC abundance analysis for host star WASP77A whose hot Jupiters SUP12SUPCSUP13SUPC abundance was recently measured. We use MARCS stellar atmosphere models and the radiative transfer code TurboSpectrum to generate synthetic stellar spectra for isotopic abundance calculations. We find a SUP12SUPCSUP13SUPC ratio of 51  6 for WASP77A which is subsolar 91 but may still indicate SUP13SUPC enrichment in its companion planet WASP77A b SUP12SUPCSUP13SUPC  26  16 previously reported. Together with the inventory of carbon and oxygen abundances in both the host and companion planet these chemical constraints point to WASP77A bs formation beyond the HSUB2SUBO and COSUB2SUB snowlines and provide chemical evidence for the planets migration to its current location 0.024 au from its host star.
['Planet hosting stars', 'Exoplanet systems', 'Hot Jupiters', 'Exoplanet migration', 'Exoplanet formation', 'Exoplanet atmospheric composition', 'Chemical abundances', 'Stellar abundances', 'Isotopic abundances', '1242', '484', '753', '2205', '492', '2021', '224', '1577', '867', 'Astrophysics - Earth and Planetary Astrophysics', 'Astrophysics - Solar and Stellar Astrophysics']
The Wanderer Charting WASP77A bs Formation and Migration Using a Systemwide Inventory of Carbon and Oxygen Abundances
{"The Wanderer: Charting WASP-77A b's Formation and Migration Using a System-Wide Inventory of Carbon and Oxygen Abundances": 'David R. Coria , 1 Neda Hejazi , 1 Ian J. M. Crossfield, 1 and Maleah Rhem 1  \n1 Department of Physics & Astronomy, University of Kansas, Lawrence, KS, USA', 'ABSTRACT': "The elemental and isotopic abundances of volatiles like carbon, oxygen, and nitrogen may trace a planet's formation location relative to H 2 O, CO 2 , CO, NH 3 , and N 2 'snowlines', or the distance from the star at which these volatile elements sublimate. By comparing the C/O and 12 C/ 13 C ratios measured in giant exoplanet atmospheres to complementary measurements of their host stars, we can determine whether the planet inherited stellar abundances from formation inside the volatile snowlines, or non-stellar C/O and 13 C enrichment characteristic of formation beyond the snowlines. To date, there are still only a handful of exoplanet systems where we can make a direct comparison of elemental and isotopic CNO abundances between an exoplanet and its host star. Here, we present a 12 C/ 13 C abundance analysis for host star WASP-77A (whose hot Jupiter's 12 C/ 13 C abundance was recently measured). We use MARCS stellar atmosphere models and the radiative transfer code TurboSpectrum to generate synthetic stellar spectra for isotopic abundance calculations. We find a 12 C/ 13 C ratio of 51 ± 6 for WASP-77A, which is sub-solar ( ∼ 91) but may still indicate 13 C-enrichment in its companion planet WASP-77A b ( 12 C/ 13 C = 26 ± 16, previously reported). Together with the inventory of carbon and oxygen abundances in both the host and companion planet, these chemical constraints point to WASP-77A b's formation beyond the H 2 O and CO 2 snowlines and provide chemical evidence for the planet's migration to its current location ∼ 0.024 AU from its host star.  \nKeywords: Planet hosting stars - Exoplanet Systems - Hot Jupiters - Exoplanet Migration Exoplanet formation - Exoplanet atmospheric composition - Elemental abundances Isotopic abundances", '1.1. Refractory Abundances and the Star-Planet Connection': "Stellar composition has long been implicated in planet formation- after all, stars and planets form out of the same disk of gas and dust albeit through different mechanisms. Different protoplanetary disk compositions and planet formation mechanisms have diverse outcomes which produce rocky terrestrial planets, super-Earths, sub-Neptunes, and even gas giants like Jupiter and Saturn. Since stellar atmospheres evolve slowly, the elemental abundances of exoplanet hosts tend to reflect the composition of their planet-forming disks (Brewer et al. 2016) and have the potential to yield constraints on planet formation processes and, in turn, even the  \nphysical properties of exoplanets themselves (Bedell et al. 2018). One of the best known links between stellar abundances and exoplanets is stellar metallicity. The occurrence rate of close-in ( < 1 au) Jupiter-class planets is increased around higher metallicity stars (Valenti and Fischer 2005; Johnson 2010; Mortier et al. 2013). This relation is interpreted as support for the core accretion model: protoplanetary disks around more metalrich stars often have higher masses and metal contents (Andrews et al. 2013) and can sustain solids for longer periods (Bitsch and Mah 2023), which allows giant planets to form more efficiently. Planet formation is therefore predicted to be unlikely in in metal-poor environments lacking sufficient metals to form planetary cores and kick-start accretion (Andrews et al. 2013; Boley et al. 2021; Bitsch and Mah 2023). The relation with hoststar metallicity, though weaker, has also been observed for sub-Neptunes and Super-Earths (Wang and Fischer 2015; Petigura et al. 2018; Boley et al. 2024). Besides  \nstellar metallicity, there is also a correlation between the abundances of individual refractory elements like (Mg, Si, Al, Ti) and planetary occurrence rates (Adibekyan et al. 2012). For example, giant-planet host stars exhibit higher refractory-to-iron abundance ratios than non-host stars. In Neptune-class planet hosts, there is notable increase in [Ti/Fe], [Si/Fe], [Al/Fe], and [Mg/Fe] compared to non-host stars.  \nRefractory-to-volatile ratios also become useful in tracing giant exoplanet formation and migration for the hot and ultra-hot Jupiter-class exoplanets (Hands and Helled. 2022; Lothringer et al. 2021). In these planets with equilibrium temperatures greater than 2000 K, refractory elements like Fe, Mg, and Si are not condensed, except perhaps on the night side, but rather gaseous and observable in the planet's atmosphere (Lothringer et al. 2021). Using these atmospheric refractory-to-volatile abundance ratios, we may infer a planet's rock-to-ice fraction and constrain planet formation and migration scenarios (Lothringer et al. 2021). Furthermore, formation of a planet beyond the water snowline followed by inward migration results in excess accretion of oxygenpoor, refractory-rich material leading to super-stellar alkali metal abundances but stellar water abundances in the planet's atmosphere (Hands and Helled. 2022).", '1.2. Volatile Element Abundances as Formation Diagnostics': "Similarly, the stellar abundances of volatile elements like H, C, N, O, and S may shed light on giant exoplanet formation mechanisms, planet composition and atmospheric evolution (Bedell et al. 2018; Brewer and Fischer 2016; Fortney 2012; Delgado Mena et al. 2021; Turrini et al. 2021; Crossfield 2023). Stellar carbon and oxygen abundances are particularly important formation diagnostics because of their influence on exoplanet ice, gas, and rock chemistry. Formation mechanisms such as gravitational instability for brown dwarfs and core accretion for Jupiter-class exoplanets each leave behind unique carbon and oxygen signatures in the atmospheres of these sub-stellar objects. Formation via gravitational instability occurs more rapidly than core accretion, on sub-Myr timescales, which results in brown dwarfs with stellar to super-stellar C/O ratios and abundances characteristic of their progenitor molecular clouds, similar to binary star systems (Ilee et al. 2017; Hawkins et al. 2020). Core accretion, on the other hand, is a much slower process, occurring on Myr timescales, which allows for protoplanets to incorporate varying quantities of gas and solids into their atmospheres, potentially resulting in a wide range of atmospheric metallicities and  \nC/O ratios, but maintaining sub-stellar carbon and oxygen abundances (Xuan et al. 2024b).  \nMultiple studies also explore the possibility of using elemental abundance ratios like the carbon-to-oxygen ratio (Oberg et al. 2011; Madhusudhan et al. 2014; Mordasini et al. 2016; Ali-Dib et al. 2017; Reggiani et al. 2022; Seligman et al. 2022) to constrain a planet's formation location relative to 'snowlines', or the distance from a star where volatile molecules like H 2 O, CH 4 , CO, and CO 2 condense into ice grains. When a planet forms within the H 2 O and CO snowlines, like Jupiter and Saturn for example, the planet is expected to inherit the same C/O ratio as its host star. When the planet forms outside the volatile snowlines, there are two main scenarios that affect the volatile abundances of these planets: (1) the planet migrates before dissipation of the protoplanetary disk resulting in atmospheric C/O ratios < 0 . 5 and super-solar metallicities due to the accretion of oxygen-rich planetesimals or (2) the planet migrates after dissipation of the protoplanetary disk resulting in atmospheric C/O ratios ∼ 1 and sub-solar metallicities (Oberg et al. 2011; Madhusudhan et al. 2014, 2017; Madhusudhan 2019). See also (Schneider and Bitsch 2021a,b; Bitsch et al. 2022; Pacetti et al. 2022) for an in-depth analysis on how inward drifting evaporating pebbles affect volatile abundances in exoplanet atmospheres along with a couple example giant exoplanet formation scenarios.  \nThough precise stellar abundances provide useful context for interpreting the atmospheric composition of their companion exoplanets (Reggiani et al. 2022, 2024), there is still a need to investigate the connection between atmospheric composition, protoplanetary disk chemistry, and planetary formation inferences (Molliere et al. 2022). After all, the chemical composition of giant planets and their atmospheres are greatly affected by the accretion of gas and solids as they form and migrate to their final locations, deviating significantly from abundances of the protoplanetary disk (Pacetti et al. 2022). Comparisons of the atmospheric abundances of exoplanets to planet formation simulations provide additional, complementary constraints on planet formation pathways. The condensation sequence of H 2 O, CO 2 , CH 4 , and CO results in an increase of the gas phase C/O ratio with radial distance from the host star, which makes the planetary C/O ratio an ideal signature of a planet's accretion history (Bitsch et al. 2022). Besides C/O, other volatile ratios like C/N, N/O, and S/N appear to follow monotonic trends with the extent of migration- the deviation from stellar values increases with the extent of disk-driven migration (Pacetti et al. 2022). By measuring these volatile element abundances in an exoplanet's  \natmosphere, comparing them to the host star's abundances as well as planet formation models, we may predict how and where in the disk the planet formed and infer subsequent migration.", '1.3. Isotopologue Abundance Ratios as Formation Diagnostics': "In the era of the James Webb Space Telescope (JWST), ground-based 8m- class telescopes, upcoming 30m- class telescopes, and ultra high-resolution spectroscopy, we are suddenly sensitive to the signatures of much weaker molecular absorption lines in dwarf stars, brown dwarfs and even exoplanets. In addition to the major isotopologues of CO, CH, H 2 O, NH 3 , we are now detecting minor isotopologues such as 13 C 16 O, 12 C 18 O, 13 CH, H 2 17 O, H 2 18 O, and 15 NH 3 which allow for the measurements of 12 C/ 13 C, 14 N/ 15 N, 16 O/ 18 O, and 17 O/ 18 O isotopologue ratios. The most widely observed of the CNO isotope ratios is the 12 C/ 13 C ratio. Measurements have been made in young stellar objects (Smith et al. 2015), solar twin stars (Botelho et al. 2020; Coria et al. 2023), M dwarf stars (Crossfield et al. 2019; Xuan et al. 2024a), brown dwarfs (e.g. L dwarf 2M0355, T dwarf, 2M0415, M dwarf HD 984 B, and several others) (Zhang et al. 2021b; Costes et al. 2024; Hood et al. 2024; Xuan et al. 2024b; de Regt et al. 2024), shortorbit hot-Jupiters (e.g. WASP-77A b and HD 189733 b) (Line et al. 2021; Finnerty et al. 2024) and wide-orbit Jupiters (e.g. TYC-8998 b and VHS 1256 b) (Zhang et al. 2021a; Gandhi et al. 2023) using instruments and observatories such as VLT/CRIRES, ESO/HARPS, NASA IRTF/iSHELL, Keck/KPIC, Keck/NIRSpec, Gemini/IGRINS, and JWST/NIRSpec.  \nThese isotopic ratios are not only useful in constraining Galactic Chemical Evolution (GCE) models (Kobayashi et al. 2020; Prantzos et al. 2018; Romano et al. 2020; Romano 2022; Coria et al. 2023), but also in understanding planet formation pathways and accretion histories (Woods and Willacy 2009; Atreya et al. 2016; Zhang et al. 2021a,b; Barrado et al. 2023). The first study investigating carbon isotope fractionation in protoplanetary disks finds that the 12 C/ 13 C ratio of a system varies with radius and height in the disk (Woods and Willacy 2009). Complementary observations and measurements of the 12 C/ 13 C ratio in solar system objects provide a hint of 13 C-enrichment of the ice giants located beyond our Sun's CO snowline (Woods 2009). Since then, observations of 12 C/ 13 C in protoplanetary disks have unveiled different isotopic reservoirs that may imprint their signatures in exoplanet atmospheres (Zhang et al. 2017; Nomura et al. 2023; Bergin et al. 2024; Yoshida et al. 2024). Beyond the CO  \nsnowline at around 20 AU for sun-like stars, Bergin et al. (2024) finds one reservoir enriched in 12 C composed mainly of methane/hydrocarbon ices and a second, 13 Cenriched reservoir dominated by gaseous CO. Zhang et al. (2021a) instead proposes 13 C-enriched ice, found beyond the CO snowline, as a source for observed giant planet 13 C enrichment.  \nSimilar to elemental carbon and oxygen abundances, different formation mechanisms also produce signature atmospheric 12 C/ 13 C ratios. The sub-Myr timescales of formation via gravitational instability result in brown dwarfs with solar to super-solar 12 C/ 13 C ratios while the longer, Myr timescales of formation via core accretion allow for protoplanets to accrete 13 C-rich ice/gas. Although there are few planetary growth models that incorporate isotopolgue ratios, this particular pattern is arising from 12 C/ 13 C ratio measurements made in brown dwarfs (e.g. L dwarf 2M0355, T dwarf, 2M0415, M dwarf HD 984 B) (Zhang et al. 2021b; Costes et al. 2024; Hood et al. 2024), and lower-mass super-Jupiters (e.g. WASP-77A b, HD 189733 b, TYC-8998 b and VHS 1256 b) (Line et al. 2021; Finnerty et al. 2024; Zhang et al. 2021a; Gandhi et al. 2023). Furthermore, the icegas partitioning of these carbon isotopes allows for the 12 C/ 13 C ratio to be used as a tracer of a planet's formation location and migration. Planets forming within the CO snowline are expected to inherit the host star's 12 C/ 13 C ratio while those forming beyond the CO snowline ( 20 AU) are expected to accrete 13 C-rich ice/gas which lower the planet's 12 C/ 13 C ratio. The formation scenarios and corresponding C/O and 12 C/ 13 C ratios outlined above assume in-situ formation. However, if there is a mismatch between a planet's C/O ratio, 12 C/ 13 C ratio, its current location, and the host star's C/O and 12 C/ 13 C ratio, this could be an indicator for planetary migration. Recent observations of both hot Jupiters (e.g. WASP-77A b and HD 189733 b) (Line et al. 2021; Finnerty et al. 2024) and wide-orbit, directly imaged planets (e.g. VHS 1256 b and TYC 8998-760-1 b) (Gandhi et al. 2023; Zhang et al. 2021a) reveal similar 13 C enrichment, supporting the hypothesis that hot Jupiters likely did not form in situ.  \nTo test how planetary 12 C/ 13 C ratios change with distance with their host stars and relative to various volatile snowlines, it is necessary to measure volatile abundances in three types of targets: (1) planets located inside the CO snowline, (2) planets located outside the CO snowline, and (3) exoplanet host stars. Jupiter-class planets are the most amenable to these system-wide abundance surveys. Short-period superJupiters close to their host stars (within the CO snowline) can have their C/O and 12 C/ 13 C ratios measured  \nusing transmission spectroscopy (as in Line et al. (2021)) while bright super-Jupiters outside the CO snowline, like TYC-8998-760-1 b (Zhang et al. 2021a), can have their C/O and 12 C/ 13 C ratios measured using a combination of spectroscopy and direct imaging techniques (Molliere et al. 2019). Although FGK-type host stars routinely have their abundances measured using standard methods (Brewer and Fischer 2016; Bedell et al. 2018), cooler mid- to late- type K and M dwarfs pose a bigger challenge due to their intrinsic faintness and overwhelming molecular absorption in their spectra. However, with high-resolution, high signal-to-noise spectra and a careful analysis we may successfully measure abundances in these stars as well (Souto et al. 2017, 2018, 2022; Hejazi et al. 2023, 2024). Contemporary researchers use both the stellar and planetary abundances to model exoplanet atmospheres, to infer the structure and composition of the exoplanet's interior, and to understand how atmospheres and interiors co-evolve over time (Madhusudhan 2012; Unterborn et al. 2014; Brewer et al. 2016; Unterborn et al. 2017; Lincowski et al. 2018, 2019).  \nIn this paper, we focus on the complementary stellar and planetary isotopic abundances of the volatile elements: carbon and oxygen. We present the 12 C/ 13 C ratio measured in exoplanet host star WASP-77A using optical CH absorption features. We then compare archival carbon and oxygen abundances and our novel 12 C/ 13 C ratio in WASP-77A to those in its companion, the hot-Jupiter WASP-77A b. Our isotope ratio measurement corroborates previous findings from stellar and planetary elemental abundance analyses that favor formation beyond the H 2 Oand CO 2 snowlines, rather than an in-situ formation, for WASP-77A b.  \nIn Section 2, we provide an overview of three previous elemental abundance analyses for the host star (WASP-77A) with data from Keck/HIRES, MPG/ESO/FEROS, and ARC/ARCES. We also summarize the constraints placed on the companion planet's (WASP-77A b) C/O and 12 C/ 13 C abundance ratios derived from thermal emission spectroscopy. WASP77A b is a well-studied hot Jupiter, so we include the companion's abundance measurements using data from three facilities: Gemini/IGRINS, HST/WFC3, and JWST/NIRSpec.  \nSection 3 provides details on our Keck/HIRES and VLT/ESPRESSO spectra, and our methodology for determining 12 C/ 13 C for the host star WASP-77A. In Section 4, we discuss WASP-77A b's formation scenario and the possible migration mechanisms that may have transformed a once cool-Jupiter to the hot-Jupiter we see today. Finally, in Section 5, we summarize the results of our stellar 12 C/ 13 C analysis and discuss the prospects  \nfor measuring more complementary stellar isotopologue ratios.", '2. PREVIOUS OBSERVATIONS OF THE WASP-77 SYSTEM': "The WASP-77 system is a visual binary otherwise known as BD -07 436. The primary star (WASP-77 A) is a moderately bright, solar metallicity G8V star (V mag = 10 . 3) and the secondary star (WASP-77 B) is a fainter K dwarf at a separation of approximately 3 '' . Maxted et al. (2013) discovered a transiting, tidally-locked planetary mass companion (WASP-77A b) to the primary with an orbital period of 1.36 days. WASP-77A b is slightly larger than Jupiter with a mass of 1 . 76 ± 0 . 06 M Jup and radius of 1 . 21 ± 0 . 02 R Jup and rather hot with an effective temperature of 1740 K(Maxted et al. 2013). Both WASP-77 A and its companion planet are well-studied, well-characterized, and prime targets for chemical composition analyses as summarized below.", '2.1. Host Star: WASP-77A High-resolution Spectroscopy with Keck/HIRES, MPG/ESO/FEROS, & ARC/ARCES': "Polanski et al. (2022) uses high-resolution, high signalto-noise optical spectra from Keck/HIRES and KeckSpec and a machine-learning-based tool to derive fundamental stellar parameters and abundances for 25 prime JWST target exoplanet host stars. Please refer to Table 1 for their adopted effective temperature, surface gravity, and [Fe/H]. Although they provide stellar abundances for 15 elements, here we include only the constraints placed on WASP-77A's carbon, oxygen, and [Fe/H] abundances. They report stellar [C/H] = -0 . 02 ± 0 . 05, [O/H] = 0 . 06 ± 0 . 07, C/O = 0 . 46 ± 0 . 09, and [Fe/H] = +0 . 01 ± 0 . 03.  \nKolecki et al. (2022) works with an MPG/ESO/FEROS spectrum (S/N = 116) to derive chemical abundances of elements most informative to planet formation and composition (C, N, O, Na, Mg, Si, S, K, and Fe). Here, we include only the stellar [C/H] = -0 . 04 ± 0 . 04, [O/H] = -0 . 04 ± 0 . 04, C/O = 0 . 59 ± 0 . 08, and [Fe/H] = -0 . 15 ± 0 . 06. Again please refer to Table 1 for the adopted stellar parameters. Notice that although they measure carbon and oxygen abundances consistent with solar values, they do, however, find a slightly subsolar [Fe/H].  \nReggiani et al. (2022) also determined the effective temperature, surface gravity, and [Fe/H] for WASP77A using an optical spectrum (from ARC/ARCES at the Apache Point Observatory), ATLAS9 model atmospheres (Castelli and Kurucz 2003), the MOOG radiative transfer code (Sneden 1973; Sneden et al. 2012),  \nand the isochrones package (Morton et al. 2015). Please refer to Table 1 for their adopted stellar parameters. They infer elemental abundances for WASP-77A using the equivalent width method and find [C/H] = 0 . 1 ± 0 . 09, [O/H] = 0 . 23 ± 0 . 02, and C/O = 0 . 44 ± 0 . 07. These abundances are mostly consistent with previous publications: Maxted et al. (2013), Kolecki et al. (2022), and Polanski et al. (2022). These abundances for WASP-77A b and its host star are indicative of formation beyond the H 2 O snowline, rather than in situ. We discuss this further in Section 4.", '2.2. Differences Between Abundance Measurements': 'The relevant stellar parameters and abundances discussed above are shown in Table 1. All three studies above find a slightly subsolar iron abundance for WASP77A and a solar to slightly subsolar C/O ratio. Though mostly consistent, there are a few notable discrepancies in effective temperature, [Fe/H], carbon and oxygen abundance values. Oxygen abundances are notoriously difficult to determine, particularly when using optical spectra where there is a shortage of detectable atomic oxygen lines with both observational and theoretical complications (Ting et al. 2018). In this case, however, the differences are likely due to the slightly different T eff and [Fe/H] values adopted.  \nGenerally, significant differences in abundance measurements can be caused by a number of factors including the choice of input stellar parameters (T eff , log g, [Fe/H]), the selected stellar model atmospheres, the radiative transfer code used for generating synthetic spectra, and the preferred atomic and molecular line lists. We refer the reader to Kolecki et al. (2022) Section 5.2 and the references therein for a more detailed discussion of abundance discrepancies. For future isotopologue analyses, this means that an elemental abundance fit prior to measuring isotopic abundances is necessary to ensure the best possible fit between the base model spectrum and the observed spectrum as this is the starting point for generating the 12 C/ 13 C model grid.', '2.3. WASP-77A b Thermal Emission Spectroscopy': "WASP-77A b is an excellent candidate for transit spectroscopy and is actually one of the highest signal-tonoise ratio planets for thermal emission measurements in the near-infrared (Kempton et al. 2018)- making this hot Jupiter an ideal target for atmospheric characterization.  \nLine et al. (2021) provides secondary eclipse spectroscopy of WASP-77A b. The single 4.7 hour timeseries sequence was taken with Gemini-South/IGRINS (Park et al. 2014; Mace et al. 2018) on December 14,  \n2020. The resulting spectrum is high-resolution (R ∼ 45,000) with wavelength coverage spanning 1.43 - 2.42 µ m.  \nThe IGRINS analysis reports a planetary [C/H] = -0 . 46 +0 . 17 -0 . 16 , [O/H] = -0 . 49 +0 . 14 -0 . 12 , and a carbon-tooxygen ratio C/O = 0 . 59 ± 0 . 08. More importantly, they also retrieve a constraint on the 12 CO/ 13 CO ratio: 10.2-42.6 at 68% confidence. The sub-solar carbon and oxygen abundances in WASP-77A b suggest an atmosphere depleted in metals, at least based on extrapolation from the solar system planets. Although a comparison to solar abundances is a natural first step, the key is to make the comparison with the planet's host star abundances. Refer to Section 4 for an abundance comparison between the host star WASP-77A and the companion planet WASP-77A b and see Table 1 for a list of all available carbon and oxygen abundances and metallicities for the WASP-77A system.  \nMansfield et al. (2022) presents another set of secondary eclipse observations for WASP-77A b, this time with the Hubble Space Telescope's WFC3 covering wavelengths 1.1-1.7 µ m and Spitzer/IRAC at 3.6 and 4.5 µ m. This atmospheric retrieval places a 3 σ lower limit on the atmospheric H 2 O abundance: log(n H 2 O ) > -4 . 78 but was unable to constrain the CO abundance and individual [C/H] and [O/H] abundances. There are no carbon-bearing molecule features resolved in this emission spectrum, which results in a poor constraint on the C/O ratio: a 2 σ upper limit of C/O = 0.78. The retrieval's best fit metallicity is [M/H] = 0.43 +0 . 36 -0 . 28 . This value is much higher and less precise than that derived from the high-resolution Gemini/IGRINS observations. After performing a grid fit to a combination of the WFC3 and Spitzer data, they derive a metallicity of [M/H] = 0.10 +0 . 43 -0 . 31 , which is more consistent with the high-resolution measurement.  \nRecent secondary eclipse observations of WASP-77A b with JWST/NIRSpec (August et al. 2023) cover the wavelength range 2.8-5.2 µ m and contains several H 2 O and CO features but no CO 2 . The atmospheric retrieval finds a sub-solar metallicity [M/H] = -0 . 91 +0 . 24 -0 . 16 and a C/O ratio = 0 . 36 +0 . 10 -0 . 09 as well as molecular abundances of log 10 (n H 2 O ) = -4 . 26 +0 . 14 -0 . 10 for water and log 10 (n CO ) = -4 . 58 +0 . 27 -0 . 24 for carbon monoxide. These results agree with the Gemini/IGRINS abundances from Line et al. (2021) within ∼ 1 σ for [Fe/H] and ∼ 1 . 8 σ for the C/O ratio.", '3.1. The Spectrum': "We observed WASP-77A with the HIRES spectrograph (Vogt et al. 1994) at the Keck Observatory. The  \n582-second exposure of WASP-77A was taken on February 22, 2021 06:03 UT by the California Planet Search collaboration (Lead: Andrew Howard, Caltech). They use the C2 decker under effective seeing conditions of roughly 1.3 '' . Standard reduction routines and telluric corrections are applied resulting in a spectrum of R ∼ 45,000 and median signal-to-noise of 82. The final spectrum covers a wavelength range of 3600-4400 ˚ A . This is the same spectrum analysed in Polanski et al. (2022). Additionally, we also utilize publicly available ESO data for WASP-77A. This 14400-second exposure of WASP-77A was taken on October 29, 2021 02:03 UTC using VLT/ESPRESSO's ultra-high-resolution (UHR) mode. The data is reduced using the ESPRESSO data-reduction software (DRS) pipeline, and the final extracted, wavelength-calibrated spectrum has R ∼ 140 , 000, S/N = 511 and covers a wavelength range of 3770-7898 ˚ A .", '3.2. Generating the Synthetic Spectra Grid': 'We will measure CH isotopologue abundances in WASP-77A by comparing the observed spectrum to synthetic spectra generated from custom 1D hydrostatic MARCS stellar atmosphere models (Gustafsson et al. 2008) and the LTE radiative transfer code TurboSpectrum (Version 15.1) (Plez et al. 2012). Although there is an extensive grid of MARCS models, we further used the interpolation routine developed by Thomas Masseron 1 to interpolate models with the same physical parameters as those of our target star. We also use the set of atomic and molecular line lists, assuming solar abundances from (Grevesse et al. 2007), as described in Hejazi et al. (2023). This includes atomic line data from the Vienna Atomic Line Database (VALD, Ryabchikova et al. (2015)) and molecular line lists from multiple sources including VALD for TiO, the Kurucz (Smithsonian) Atomic and Molecular Database (Kurucz et al. 1995), and the high resolution transmission molecular absorption database (HITRAN, Rothman et al. (2021)). The most important molecular bands for this study are: FeH (Dulick et al. 2003), CN (Brooke et al. 2014; Sneden et al. 2014), and CH (Masseron et al. 2014).  \nInitially, we adopt the effective temperature, surface gravity, and [Fe/H] (as a proxy for the bulk stellar metallicity) values for WASP-77 A derived from our Keck/HIRES spectrum using the machine-learning tool KeckSpec: T eff = 5569 ± 77 K, log g = 4 . 45 ± 0 . 09, and [Fe/H] = 0 . 01 ± 0 . 03 (Polanski et al. 2022). At this point, we have not altered individual elemental abun-  \nces from solar values. However, the base model generated from these parameters did not appear to fit the spectral lines surrounding several target 13 CH lines in the HIRES spectrum, particularly for atomic iron lines and molecular CH lines. The problem persists for a couple lines in the higher-quality ESPRESSO spectrum, but the overall fit is greatly improved. This leads us to believe that the issue with these specific lines lies in the opacity calculations or the atomic and molecular line lists incorporated in synthesizing spectra rather than the base stellar parameters. Rather than choose a set of effective temperature, surface gravity, and [Fe/H] (as a proxy for the bulk stellar metallicity) from one particular study, we instead adopt weighted averages (weights = 1 /σ 2 where σ is the parameter uncertainty) for the stellar parameters since the effective temperature and surface gravity values are similar for the three previous host star studies (Polanski et al. 2022; Reggiani et al. 2022; Kolecki et al. 2022): T eff = 5545 ± 22 K, log g = 4 . 45 ± 0 . 02. Please refer to Section 3.7 for further explanation of how our choice of fundamental stellar parameters affects the derived 12 C/ 13 C ratio.  \nFrom these chosen stellar parameters, we then generate a grid of synthetic spectra with 12 C/ 13 C ratios of 30, 50, 60 80, 90, 100, 110, 130, 160. These model spectra cover wavelengths 3600 - 4400 ˚ A where there are numerous 12 CH and 13 CH lines suitable for this isotopologue abundance analysis.', '3.3. Line Selection': "We utilize TurboSpectrum's built-in equivalent-width calculation feature to generate a list of equivalent widths of the 12 CH and 13 CH lines from the base model. From that list, we remove all 13 CH lines with EW < 1 . 5 ˚ A and are left with 95 candidate absorption lines. We narrow down this line list via a visual inspection of our base model spectrum. Lines from the final set are later accepted or rejected from the final 12 C/ 13 C calculation depending on overall model fit and continuum renormalization. Please refer to Table 2 for our final 13 CH line list. We also include information for atomic and molecular lines located within the renormalization window of our 13 CH lines of interest.", '3.4. Continuum Re-normalization': 'After applying a Gaussian filter to smooth the model spectra to a spectral resolution ∼ 45,000 for the HIRES spectrum and ∼ 140,000 for the ESPRESSO spectrum, and performing an RV correction to the observed spectrum, we begin the continuum selection and renormalization following the methods described in Hejazi et al. (2023). The 13 CH features in the optical  \nare significantly weaker than the 13 CO features identified in the M-band (4.5-5.0 µ m) and so this isotopic abundance analysis demands a more precise continuumselection and re-normalization process than in Coria et al. (2023). Otherwise, even a slight misalignment between the observed spectrum and the model grid (either wavelength or continuum normalization misalignment) makes determining the best fit model nearly impossible.  \nFor each of the selected 13 CH lines, we visually inspect a 4-5 ˚ A window around the line center. We then carefully select the continuum/pseudocontinuum regions around the line-of-interest, making sure to exclude all other absorption features. From the selected continuum points, we perform an iterative sigma-clipping, 2 σ then 1.5 σ , to keep only those continuum/pseudocontinuum points with the best fit between the base model and the observed spectrum. For those remaining continuum/pseudocontinuum points, we perform a polynomial fit to the residuals R = O/M, where O is the observed flux and M is the interpolated model flux at each shifted, observed wavelength. Finally, we divide the observed spectrum by the polynomial fit to re-normalize and align continuum/pseudocontinuum levels of the observed spectrum to the models. See Figure 1 for an example renormalization using an isolated 13 CH line.  \nUnfortunately, even after a careful line-by-line renormalization, there are still regions of the observed spectrum that our models are not able to reproduce successfully. This may be due to spectral noise and bad pixels in the observed spectrum, insufficiencies in model assumptions and opacity calculations as well as atomic and molecular line lists incorporated in synthesizing spectra. Other factors such as NLTE effects are typically negligible in solar type stars (Nissen et al. 2018). Magnetic field effects are also negligible when measuring CNO abundances (Shchukina et al. 2016) but may result in an underestimate of iron abundances (Fabbian et al. 2012). Regardless, this means that we must remove lines from our analysis where the poor fit interferes with our ability to reliably determine the stellar 12 C/ 13 C ratio. This leaves only three candidate lines for the HIRES spectrum and five lines for the ESPRESSO spectrum where both the continuum/pseudo-continuum and nearby atomic absorption lines of the model spectra align well with that of the observed spectrum.', '3.5. Statistical Significance': 'We remind the reader that our HIRES spectrum has a resolution R ∼ 45,000 and a median signal-to-noise ratio of 82 over the wavelength range of 3600-4400 ˚ A. Although this spectrum is fairly high S/N, the 13 CH lines in this study are exceedingly weak. Therefore, we calcu-  \ne the BIC factor (BIC = χ 2 + n dof *ln(N data ), where n dof is the number of degrees of freedom = 1, and N data is the number of data points used in the fit) for the selected 13 CHlines to test the statistical significance of our detection. We determine ∆BIC 160 -BF (BIC between the observed spectrum and the model with 12 C/ 13 C = 160 minus BIC between the observed spectrum and the best-fit 12 C/ 13 C model) for the 13 CH lines in Table 3. This ∆BIC 160 -BF tells us if the observed spectrum significantly favors low 13 C-enrichment (or the 12 C/ 13 C = 160 model) or higher 13 C-enrichment (or the best fit 12 C/ 13 C model). Table 3 demonstrates a clear difference in the BIC factor, for each of our selected 13 CH lines, for both the HIRES and ESPRESSO analysis. This means that both observed spectra favor models with solar to super-solar 13 C enrichment.', '3.6. Deriving Individual Line 12 C/ 13 C Ratios': 'We measure the 12 C/ 13 C ratio in WASP-77 A following a similar process to that described in Crossfield et al. (2019); Coria et al. (2023). We calculate χ 2 between the re-normalized observed spectrum and each model spectrum, for each line over a wavelength range (typically 0.1-0.3 Angstroms) previously determined during the continuum selection process. For each set of χ 2 values, we use a cubic spline fit to interpolate the minimum χ 2 which corresponds to the best-fit 12 C/ 13 C abundance. We infer 1 σ confidence intervals using the region where ∆ χ 2 ≤ 1 (Avni et al. 1976). This gives us an estimate of the stellar 12 C/ 13 C ratio for each selected 13 CH line. Figures 2 - 4 show the renormalized spectra, a zoom-in on the 13 CH line, the χ 2 minimization, and the derived 12 C/ 13 C ratio for our selected lines in the HIRES and ESPRESSO spectra. Table 3 contains more details on the χ 2 minimization including the χ 2 fit window, the number of points fit, the χ 2 at the minimum associated with the best fit 12 C/ 13 C ratio for each line. We obtain three individual 12 C/ 13 C from the HIRES analysis and five from the ESPRESSO analysis, respectively. These values range from 12 C/ 13 C = 47 - 75. Please refer to Table 3 for the list of 12 C/ 13 C ratios and their statistical uncertainties.', '3.7. Systematic Uncertainties': 'Prior to determining the final 12 C/ 13 C ratio for WASP-77A, we must consider the systematic uncertainties involved, particularly those associated with our choice of fundamental stellar parameters and elemental abundances. To test how the selection of fundamental stellar parameters impacts the derived 12 C/ 13 C ratios, we generate several more model grids, this time varying effective temperature, surface gravity, bulk stellar metallicity, and individual C, O, Ti, and Fe abundances. We  \nfind that changing individual elemental abundances (of species in close proximity to selected 13 CH lines: [Fe/H], [Ti/H], [C/H], [O/H]) over the range reported in the literature values (+0.1, -0.2 dex), hardly change the model fit and the derived 12 C/ 13 C ratios at all. However, effective temperature, surface gravity, bulk stellar metallicity do have a noticeable effect on the derived 12 C/ 13 C ratios.  \nTo determine systematic uncertainties of the derived 12 C/ 13 C ratio due to changes in effective temperature, we vary the stellar effective temperature over span comparable various literature measurements, in steps of 25 K around our chosen value of 5545 K, while holding log g and metallicity constant. We find that this plausible range of effective temperature values produces 12 C/ 13 C ratios ranging from 90-110 for the 13 CH line at 4231.412 ˚ A. However, the changes in 12 C/ 13 C due to the step change in effective temperature ( σ T = 3) are much smaller than the statistical uncertainties on our measurement of 12 C/ 13 C derived from the HIRES spectrum ( σ = 17). Thus, we are not limited by the uncertainties on the stellar parameters in this case. For the ESPRESSO spectrum, where the data is much more precise, the changes in 12 C/ 13 C due to the step change in effective temperature ( σ T = 4) are larger than the statistical uncertainties on our measurement of 12 C/ 13 C ( σ = 1). In this case, we are somewhat limited by uncertainties on the stellar parameters.  \nWe repeat the process to determine systematic uncertainties of the derived 12 C/ 13 C ratio due to changes in surface gravity. We now vary the stellar surface gravity in steps of 0.05 around our chosen value of 4.45, while holding effective temperature and metallicity constant. We find systematic uncertainties in the derived 12 C/ 13 C due to the change in log g to be: σ G = 2 for the HIRES analysis and σ G = 3 for the ESPRESSO analysis. Again, these uncertainties limit the precision of the 12 C/ 13 C ratio derived from the higher-quality ESPRESSO spectrum, but not the HIRES spectrum.  \nFinally, to determine systematic uncertainties of the derived 12 C/ 13 C ratio due to changes in metallicity (Z), we deviate Z in steps of 0.1 dex. These steps are larger than the uncertainties of stellar metallicity reported in the literature ( < 0 . 05 dex), but we did this to inspect if non-solar metallicities would better reproduce spectral lines such as Ti, Mn, and CH. So, we vary the stellar metallicity in steps of 0.1 dex around our chosen value of +0.00 dex, while holding effective temperature and log g constant. We find that this plausible range of Z values produces a much broader range of 12 C/ 13 C ratios ranging from 80-140. However, none of the reasonable Z values produce a model spectrum that significantly im-  \nproves the fit to nearby spectral lines such as Ti, Mn, and CH. In the ESPRESSO spectrum, the models derived using Z = +0.00 dex fit much better than they do the HIRES spectrum.  \nWe find that the derived 12 C/ 13 C changes by σ Z = 7 for the HIRES analysis and σ Z = 6 for the ESPRESSO spectrum with each step of ± 0 . 1 dex in bulk metallicity Z. These σ Z are overestimates, however, since the actual uncertainties on the stellar metallicity are less than half of our chosen step size. Therefore, we report final systematic uncertainties in the derived 12 C/ 13 Cratio due to changes in stellar metallicity as σ Z = 3 . 5 for the HIRES analysis and σ Z = 3 for the ESPRESSO analysis.  \nFinally, we calculate the quadrature sum of σ T , σ G , and σ Z as the final systematic uncertainties in the 12 C/ 13 C ratio: σ sys = 5 for the HIRES analysis and σ sys = 6 for the ESPRESSO analysis.', '3.8. Deriving the Stellar 12 C/ 13 C Ratio': "Because the target 13 CH spectral lines have low statistical significance and are barely visible by eye when considered individually, we derive the final stellar 12 C/ 13 C ratio from these individual estimates collectively using both statistical uncertainties and the systematic uncertainties discussed above. We determine a final, weighted average of 12 C/ 13 C = 66 ± 18 for WASP-77 A with our HIRES spectrum analysis, and a consistent, but more precise 12 C/ 13 C = 51 ± 6 from our ESPRESSO spectrum analysis. We use the methods detailed in Barlow et al. (2004) Section 2.8, 'Model 2' to calculate a weighted mean using asymmetric uncertainties.  \nContrary to frequent assumptions, we do not find a solar 12 C/ 13 C ratio for WASP-77A, but rather a subsolar and even near-ISM 12 C/ 13 C ratio (solar 12 C/ 13 C = 91 . 4 ± 1 . 3, ISM 12 C/ 13 C ≈ 68) (Ayres et al. 2013). Compared to its host star, WASP-77A b appears slightly enriched in 13 C with 12 C/ 13 C = 26 . 4 ± 16 . 2 (Line et al. 2021). We further discuss what these new abundance ratios may mean for WASP-77A b's formation in the following section.  \n<!-- image -->  \n13  \n<!-- image -->  \n<!-- image -->  \n13  \nFigure 1. Pre- and post- renormalization for strong, isolated 13 CH lines (Top: Line at 4231.412 ˚ A in the HIRES spectrum; Bottom: Line at 4268.304 ˚ A in the ESPRESSO spectrum). The area within the orange lines shows the χ 2 fit window dominated by 13 CH line centered at 3982.247 Angstroms, while the regions covered by the red and black lines (left plot) are excluded from the continuum/pseudocontinuum selection routine. The starred points are the selected continuum/pseudocontinuum points used for renormalization. The pink points represent the residuals R = O/M for the selected continuum/pseudocontinuum points and the black curve is the polynomial fit which, when divided out of the observed spectrum, provides a significantly better alignment to the target 13 CH line. The figures on the right highlight the location of our selected 13 CH lines and other nearby atomic lines.  \n<!-- image -->  \n<!-- image -->  \n<!-- image -->  \n<!-- image -->  \n<!-- image -->  \n<!-- image -->  \nFigure 2. Interpolating the stellar 12 C/ 13 C ratio from our high-resolution and high signal-to-noise Keck/HIRES spectrum. On the left, we show our three selected 13 CH lines, post-renormalization. We have labeled, in black, some nearby atomic and molecular lines that help us determine the best-fit base model spectrum. Refer to Table 2 for the complete line list. On the right, we zoom in on the χ 2 fit windows to better see the separation between model spectra with high and low 12 C/ 13 C ratios. We then calculate χ 2 values between the model spectra and the observed spectrum for each target line, and fit the points with a cubic spline. The minimum of the spline represents the best fit 12 C/ 13 C for the individual 13 CH line.  \n<!-- image -->  \n<!-- image -->  \n<!-- image -->  \n<!-- image -->  \n<!-- image -->  \n13CH @ 4223.934 Angstroms  \n<!-- image -->  \nFigure 3. Interpolating the stellar 12 C/ 13 C ratio from the publicly available, high-resolution, and high signal-to-noise VLT/ESPRESSO spectrum. Similar to Figure 2, we show our selected 13 CH lines, post-renormalization on the left. On the right, we show a zoom-in on the χ 2 fit windows and the χ 2 minimization used to determine 12 C/ 13 C for individual 13 CH lines.  \n<!-- image -->  \n<!-- image -->  \n<!-- image -->  \n<!-- image -->  \nFigure 4. Interpolating the stellar 12 C/ 13 C ratio from the publicly available, high-resolution, and high signal-to-noise VLT/ESPRESSO spectrum. Similar to Figure 2, we show our selected 13 CH lines, post-renormalization on the left. On the right, we show a zoom-in on the χ 2 fit windows and the χ 2 minimization used to determine 12 C/ 13 C for individual 13 CH lines.  \n<!-- image -->  \nTable 1. WASP-77 A (Host) vs. WASP-77 Ab (Planet) Abundances  \nNote -Parameters and system-wide abundance inventory for host star WASP-77A and its hot Jupiter companion WASP-77A b. **This Paper. We derive the stellar 12 C/ 13 Cratio for WASP-77A using the same HIRES spectrum as Polanski et al. (2022) and a publicly available VLT/ESPRESSO spectrum.  \nTable 2 . Line List  \nTable 2 continued  \nTable 2 (continued)  \nNote -We include species, line center, and equivalent width for atomic and molecular lines within the renormalization window for each of our 13 CH lines of interest (starred). CH line lists are from Masseron et al. (2014). Atomic lines are from the Vienna Atomic Line Database (Ryabchikova et al. 2015). Equivalent widths are calculated using TurboSpectrum (Plez et al. 2012). Lines without equivalent widths were identified by eye.  \nC/O (solar C/O = 0 . 59 ± 0 . 08 (Asplund et al. 2021)), and slightly sub-solar metallicity. Additionally, we now see a potential difference between the solar 12 C/ 13 C ratio (91 . 4 ± 1 . 3) and our measurement of WASP-77A's 12 C/ 13 C ratio (51 ± 6).", '4. DISCUSSION': "We now see slight deviations from solar abundances in WASP-77A's photosphere. The weighted average of the three stellar abundance values from (Polanski et al. 2022; Reggiani et al. 2022; Kolecki et al. 2022) are [C/H] = -0 . 02 ± 0 . 03, [O/H] = 0 . 17 ± 0 . 02, C/O = 0 . 49 ± 0 . 05, and [Fe/H] = -0 . 05 ± 0 . 02. WASP-77A potentially has [C/H] consistent with solar, elevated [O/H], sub-solar  \nNow, by comparing host star WASP-77A's carbon, oxygen, and metallicity values to those of its hot Jupiter companion, we notice WASP-77A b's sub-stellar [C/H] = -0 . 46 ± 0 . 17, significant oxygen depletion with [O/H] = -0 . 49 ± 14, C/O = 0 . 50 ± 0 . 06 consistent with its host star, and sub-stellar metallicity with [M/H] = -0 . 60 ± 0 . 13.  \nTable 3. χ 2 Minimization and Individual 12 C/ 13 C Ratios  \nNote -The first two columns show the location of our selected 13 CH lines. Columns 3 describes the location of the χ 2 fit window including the number data points fit (Column 4), the calculated χ 2 minimum (Column 5), and the ∆BIC 160 -Best (Column 6) associated with the best fit 12 C/ 13 C ratios for the HIRES (H) and ESPRESSO (E) spectra (Columns 7 and 8, respectively). ∆BIC 160 -Best is calculated as the BIC difference between the lowest 13 C-enriched model with 12 C/ 13 C = 160, and the best-fit model.", "4.1. WASP-77A b's Formation Location": "Hot Jupiter systems are of particular interest for abundance studies because of their amenability for observation, but also because of their formation histories. There is only sufficient material for in-situ hot Jupiter formation in large protoplanetary disks where there are also likely to be multiple cold Jupiters in the outer disk (Batygin et al. 2016). This does not appear to be the case for WASP-77A b. Thus, we expect non-stellar abundances in hot-Jupiter atmospheres, characteristic of the planet's formation location and accretion history elsewhere in the disk. The following formation scenario for WASP-77 A b relies on the volatile abundance inventory for the WASP-77 A system (Table 1: including both host star and planetary C/H, O/H, C/O, and 12 C/ 13 C ratios) and its usage in determining formation and migration diagnostics as discussed in Sections 1.2 and 1.3.  \nA sub-stellar C/O ratio would indicate radial migration where the planet accumulates O-rich and C-poor material, however, WASP-77A b's C/O ratios are mostly consistent with its host star (Line et al. 2021; August et al. 2023). While the similar C/O ratios alone may be indicative of formation close to the star (within the H 2 O snowline at 5 AU), it is critical to take into account individual carbon and oxygen abundances as well. The sub-stellar carbon and oxygen abundances measured in WASP-77A b's atmosphere are a signature of formation in the outer disk, beyond the H 2 O and CO 2 snowlines (located at around 5 and 10 AU respectively), where most carbon and oxygen is trapped in grains, leaving the planet-feeding gas depleted in volatiles (Bosman et al. 2021). Planets forming in this outer region of the  \ndisk are expected to have sub-stellar C/H and O/H. In fact, the sub-solar C/H, O/H, and solar C/O ratios of WASP-77A b are well reproduced by planet formation and accretion models which predict the planet's formation beyond the CO 2 evaporation front (Bitsch et al. 2022). Overall, WASP-77A b's sub-stellar atmospheric carbon and oxygen abundances and stellar C/O ratio are indicative of this planet's formation beyond the host's H 2 O and CO 2 snowlines located at ∼ 5AU and 10 AU respectively (Oberg et al. 2011; Reggiani et al. 2022; Bitsch et al. 2022).  \nThough elemental abundances alone constrain WASP77A b's formation location to be beyond both the H 2 O and CO 2 snowlines, or somewhere at a separation greater than 10 AU, our goal was to make a complementary measurement of the stellar 12 C/ 13 C ratio to determine whether (1) WASP-77A b's 13 C enrichment was inherited from the host star, placing the formation location between the CO 2 snowline at 10 AU and the CO snowline at 20 AU or (2) whether WASP-77A b's 13 C enrichment was due to the accretion of 13 C-rich material found beyond the CO snowline at 20 AU. Our additional finding that WASP-77A has a sub-solar 12 C/ 13 C ratio of 51 ± 6 shows that the hot Jupiter WASP-77A b may indeed have 13 C enrichment ( 12 C/ 13 C = 10.2-42.6), but perhaps not as significant as when we were assuming a solar 12 C/ 13 C for the host star. Again, protoplanetary disk chemistry models produce a broad range of 12 C/ 13 C in CO as mid-plane height and radial distance from the star varies (Zhang et al. 2017; Nomura et al. 2023; Bergin et al. 2024; Yoshida et al. 2024; Line et al. 2021; Woods and Willacy 2009). Although this host star and exoplanet 12 C/ 13 C ratio comparison appears  \nconsistent with previous studies that place WASP-77A b's formation beyond the stellar H 2 O and CO 2 snowlines located at 5 and 10 AU respectively, it is unclear whether the difference is considerable enough to suggest formation beyond the stellar CO snowline where significant 13 C enrichment is expected occur (Zhang et al. 2021a; Bergin et al. 2024). Notably, WASP-77A b has a 12 C/ 13 C ratio inconsistent with that of any planet in our own solar system, but this is perhaps unexpected as WASP-77A b's formation and accretion history is thought to be much different than that of our solar system planets. The 13 C-enrichment found in WASP-77A b's atmosphere, relative to its host star, and the elemental carbon and oxygen abundances in the system disfavor an 'in situ' formation scenario nonetheless. This new piece of evidence corroborates our understanding of hot Jupiter formation from a dynamical standpoint. That is, hot-Jupiters likely did not form in situ, but rather migrated to their current positions from the outer disk. Refer to Section 4.2 for a brief dynamical explanation on how hot Jupiters form.  \nWe emphasize that the interpretation of abundance ratios measured in giant exoplanet atmospheres relies on the abundance ratios measured in the host star's photosphere and on planet formation and accretion models. For a further analysis of the interplay between a planet's atmospheric carbon and oxygen abundances and different planet formation pathways in the context of the WASP-77 system, we refer the reader to Bitsch et al. (2022).", '4.2. Possible Migration Mechanisms': "There are several mechanisms for migration that could transform a warm/cool Jupiter into a short-period hot Jupiter. These include coplanar high-eccentricity migration (Petrovich et al. 2015b), secular chaos (Wu and Lithwick 2011), and Lidov-Kozai cycling (Wu and Murray 2003; Petrovich et al. 2015a). A recent study based on data from the California Legacy Survey (Rosenthal et al. 2021) argues that coplanar high-eccentricity migration is the most likely formation pathway for hot-Jupiter formation (Zink and Howard 2023). In this scenario, there are two cold gas giant planets that through the exchange of angular momentum and tidal interactions with the host star, culminate in a hot Jupiter. Zink and Howard (2023) finds that giant planet multiplicity is ubiquitous with an average of 1 . 3 +1 . 0 -0 . 6 companions per hot Jupiter and 1 . 0 ± 0 . 3 companions per warm or cold Jupiter. This provides plenty of opportunities for hot Jupiter formation via coplanar high-eccentricity migration. Most notably, this study finds that hot Jupiterclass planets tend to have an outer companion with at  \nleast three times its mass. In the WASP-77 system, we do not see an additional, Jupiter-class companion with mass M > 3 M J that may have driven this type of migration, but we do see a possible suspect in the secondary star, WASP-77B. This star is not well characterized, but studies find it is spectral type K5 with an effective temperature T eff = 4810 ± 100 K which places it a mass anywhere from 0.5-0.8 solar masses based on mass-effective-temperature relationships for stars on the main sequence (Evans et al. 2016). This is at least three times more massive than WASP-77A b, and may be the cause of the planet's migration to its current location ∼ 0 . 02 AU from its host star.", '4.3. WASP-77B Contamination': "Although we have mostly discussed the primary star WASP-77A and its, companion planet WASP-77A b, there is a third member of the system: a K dwarf star WASP-77B at a separation of approximately 3 arcseconds (Maxted et al. 2013). It could be argued that the peculiar abundances observed in WASP-77A b may be a result of chemical contamination from the secondary star WASP-77B. However, there is no clear avenue for determining elemental abundances for this star. There are only ∼ 4 low signal-to-noise (Average S/N = 30) ESO/HARPS spectra of WASP-77B in the literature, no effective temperature, surface gravity, or metallicity, constraints and therefore no elemental abundances for this star in the literature. Nonetheless, such contamination seems unlikely as the seeing for our Keck/HIRES spectrum was 1.3' and 0.45' for the VLT/ESPRESSO spectrum.", '5.1. Summary': "Using the James Webb Space Telescope, ground-based 8m- class telescopes, and ultra high-resolution spectroscopy, we are able to characterize the composition of exoplanet atmospheres like never before. However, it is necessary to properly contextualize these atmospheric abundance constraints by comparing them to their host star's abundances rather than to solar abundances. In the case of hot Jupiter WASP-77A b and its host star WASP-77A, metallicity, carbon, and oxygen abundances provide us an insight into the planet's origins beyond the H 2 O and CO 2 snowlines (Reggiani et al. 2022; Bitsch et al. 2022). In this paper, we derive the 12 C/ 13 C ratio for WASP-77A to complement a similar measurement in WASP-77A b made by Line et al. (2021). The subsolar and near-ISM 12 C/ 13 Cratio we find for WASP-77A (51 ± 6) provides additional evidence for WASP-77A b's formation beyond the H 2 O and CO 2 snowlines.", '5.2. Prospects for Measuring Nitrogen and Oxygen Isotopologue Ratios in Cool Dwarf Stars': 'With the advent of some astounding exoplanet abundance constraints (Line et al. 2021; Finnerty et al. 2024; Zhang et al. 2021a; Gandhi et al. 2023), we must continue building the catalogue of elemental and isotopic host star abundances as in Souto et al. (2017, 2018); Crossfield et al. (2019); Hejazi et al. (2023); Coria et al. (2023); Hejazi et al. (2024) with an emphasis on carbon, nitrogen, and oxygen. Stellar [N/H] and 14 N/ 15 N abundances are best measured using optical CN (Sneden et al. 2014; Ryabchikova et al. 2022) and possibly NH lines. While [C/H] and 12 C/ 13 C may be measured using optical CH lines as we do here, they are preferentially measured for cooler K and M dwarfs in the near-infrared using CO isotopologue lines (Goorvitch 1994; Gordon et al. 2017). In the near-infrared, we may also derive [O/H], 16 O/ 18 O, and possibly 17 O/ 18 O using CO, OH and H 2 O isotopologue lines (Goorvitch 1994; Goldman 1982; Barber et al. 2006; Xuan et al. 2024a).', '5.3. CNO Abundances in Brown Dwarfs': 'Besides exoplanets, brown dwarf abundances also play an important role in understanding planet formation. Y dwarfs specifically are cool enough that we may see absorption from molecules that dissociate in the atmospheres of short period hot-Jupiters and wide-orbit young Jupiters. Recent studies are able to measure 12 C/ 13 C (Lew et al. 2024; Hood et al. 2024; Costes et al. 2024), 14 N/ 15 N (Barber et al. 2006), and 16 O/ 18 O (Zhang et al. 2021b) in the atmospheres of cool brown dwarfs like 2M0355, WISE J1828, and 2M0415. CNO isotopologue ratios may provide chemical distinctions between brown dwarfs and super-Jupiters, or top-down vs. bottom-up formation models, as we start seeing ISM- or greater isotopologue ratios in brown dwarfs, but sub-stellar and sub-ISM isotopologue ratios in the superJupiters.', '5.4. CNO Abundances in the Context of Other Planetary Systems': "Jupiter-class exoplanets and their host stars provide the most practical systems with which to test how carbon, oxygen, and their respective isotopic abundance ratios change with radial distance from the host star. Specifically, the most amenable planetary systems to complementary abundance analyses are those in the WASP (Wide Angle Search for Planets) catalog (Pol-  \nlacco et al. 2006) and the young, wide separation, directly imaged Jupiter-class planet systems. These planetary systems are routinely targeted by JWST and ground-based observatories for transmission and emission spectroscopy and provide the best avenue for the direct comparison of stellar and planetary carbon and oxygen abundances, both elemental and isotopic. These complementary abundance surveys do, however, come with several challenges exemplified by the WASP-121 and TYC 8998-760-1 systems. WASP-121 and its ultrahot Jupiter companion WASP-121 b (Delrez et al. 2016) are well studied both in transmission and secondary eclipse observations (Mikal-Evans et al. 2018, 2019; Kovacs et al. 2019; Sing et al. 2019). Though these observations may retrieve carbon and oxygen abundance constraints for the companion planet, complementary host star measurements are made much more difficult (and isotopic abundance measurements, impossible) by the star's fast rotation. The recently discovered TYC8998-760-1 is a young, K2IV star host to two wideseparation Jupiter-class planets (Bohn et al. 2020). As ESO/SPHERE direct imaging and spectroscopy prioritize observations of the planets (Zhang et al. 2021b), the chemical composition of the host star remains obscure. Furthermore, the strong magnetic fields prevalent in these young stars make it difficult to model their spectra and determine fundamental effective temperature, surface gravity, and metallicity values- let alone elemental abundances- without some significant processing of the stellar spectrum (Lopez-Valdivia et al. 2021). More work must be done to identify planetary systems where we may determine carbon, oxygen, and their respective isotopic abundances in both the host star and companion planet.  \nThe authors of this work would like to thank the California Planet Search team for providing the HIRES spectrum (originally analyzed in Polanski et al. (2022)) that was used in this analysis. We also thank the referee for an excellent discussion on the statistical significance of our measurements and the systematic uncertainties associated with our choice of model parameters which both greatly improved this paper. Finally, the authors would also like to acknowledge the support of National Science Foundation grant AST-2108686 and NASA ICAR grant A21-0406-S003.  \nFacilities: W. M. Keck Observatory", 'REFERENCES': 'Adibekyan, V. Z., Sousa, S. G., Santos, N. C., et al. 2012, A&A, 545, A32, doi: 10.1051/0004-6361/201219401  \nAli-Dib, M. 2017, MNRAS, 467, 2845, doi: 10.1093/mnras/stx260  \nTing, Y.-S., Conroy, C., Rix, H.-W., and Asplund, M. 2018, ApJ, 860, 159, doi: 10.3847/1538-4357/aac6c9  \nTurrini, D., Schisano, E., Fonte, S., et al. 2021, ApJ, 909, 40, doi: 10.3847/1538-4357/abd6e5  \nUnterborn, C. T., Hull, S. D., Stixrude, L. P., et al. 2017, arXiv, https://arxiv.org/abs/1706.10282  \nUnterborn, C. T., Kabbes, J. E., Pigott, J. S., Reaman, D. M., and Panero, W. 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