arXiv subjects

Stephen A. Shectman

Publications and source records attributed to Stephen A. Shectman.

At least 37 records · Page 2Linked to original sources

arXiv2022

TOI-1075 b: A Dense, Massive, Ultra-Short Period Hot Super-Earth Straddling the Radius Gap

Populating the exoplanet mass-radius diagram in order to identify the underlying relationship that governs planet composition is driving an interdisciplinary effort within the exoplanet community. The discovery of hot super-Earths - a high temperature, short-period subset of the super-Earth planet population - has presented many unresolved questions concerning the formation, evolution, and composition of rocky planets. We report the discovery of a transiting, ultra-short period hot super-Earth orbiting TOI-1075 (TIC 351601843), a nearby ($d$ = 61.4 pc) late K-/early M-dwarf star, using data from the Transiting Exoplanet Survey Satellite (TESS). The newly discovered planet has a radius of $1.791^{+0.116}_{-0.081}$ $R_{\oplus}$, and an orbital period of 0.605 days (14.5 hours). We precisely measure the planet mass to be $9.95^{+1.36}_{-1.30}$ $M_{\oplus}$ using radial velocity measurements obtained with the Planet Finder Spectrograph (PFS), mounted on the Magellan II telescope. Our radial velocity data also show a long-term trend, suggesting an additional planet in the system. While TOI-1075 b is expected to have a substantial H/He atmosphere given its size relative to the radius gap, its high density ($9.32^{+2.05}_{-1.85}$ $\rm{g/cm^3}$) is likely inconsistent with this possibility. We explore TOI-1075 b's location relative to the M-dwarf radius valley, evaluate the planet's prospects for atmospheric characterization, and discuss potential planet formation mechanisms. Studying the TOI-1075 system in the broader context of ultra-short period planetary systems is necessary for testing planet formation and evolution theories, density enhancing mechanisms, and for future atmospheric and surface characterization studies via emission spectroscopy with JWST.

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arXiv2022

3-D selection of 167 sub-stellar companions to nearby stars

We analyze 5108 AFGKM stars with at least five high precision radial velocity points as well as Gaia and Hipparcos astrometric data utilizing a novel pipeline developed in previous work. We find 914 radial velocity signals with periods longer than 1000\,d. Around these signals, 167 cold giants and 68 other types of companions are identified by combined analyses of radial velocity, astrometry, and imaging data. Without correcting for detection bias, we estimate the minimum occurrence rate of the wide-orbit brown dwarfs to be 1.3\%, and find a significant brown dwarf valley around 40 $M_{\rm Jup}$. We also find a power-law distribution in the host binary fraction beyond 3 au similar to that found for single stars, indicating no preference of multiplicity for brown dwarfs. Our work also reveals nine sub-stellar systems (GJ 234 B, GJ 494 B, HD 13724 b, HD 182488 b, HD 39060 b and c, HD 4113 C, HD 42581 d, HD 7449 B, and HD 984 b) that have previously been directly imaged, and many others that are observable at existing facilities. Depending on their ages we estimate that an additional 10-57 sub-stellar objects within our sample can be detected with current imaging facilities, extending the imaged cold (or old) giants by an order of magnitude.

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arXiv2022

The MegaMapper: A Stage-5 Spectroscopic Instrument Concept for the Study of Inflation and Dark Energy

In this white paper, we present the MegaMapper concept. The MegaMapper is a proposed ground-based experiment to measure Inflation parameters and Dark Energy from galaxy redshifts at $2<z<5$. In order to achieve path-breaking results with a mid-scale investment, the MegaMapper combines existing technologies for critical path elements and pushes innovative development in other design areas. To this aim, we envision a 6.5-m Magellan-like telescope, with a newly designed wide field, coupled with DESI spectrographs, and small-pitch robots to achieve multiplexing of at least 26,000. This will match the expected achievable target density in the redshift range of interest and provide a 10x capability over the existing state-of the art, without a 10x increase in project budget.

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arXiv2021

The Magellan-TESS Survey I: Survey Description and Mid-Survey Results

$Kepler$ revealed that roughly one-third of Sun-like stars host planets orbiting within 100 days and between the size of Earth and Neptune. How do these planets form, what are they made of, and do they represent a continuous population or multiple populations? To help address these questions, we began the Magellan-TESS Survey (MTS), which uses Magellan II/PFS to obtain radial velocity (RV) masses of 30 TESS-detected exoplanets and develops an analysis framework that connects observed planet distributions to underlying populations. In the past, small planet RV measurements have been challenging to obtain due to host star faintness and low RV semi-amplitudes, and challenging to interpret due to the potential biases in target selection and observation planning decisions. The MTS attempts to minimize these biases by focusing on bright TESS targets and employing a quantitative selection function and observing strategy. In this paper, we (1) describe our motivation and survey strategy, (2) present our first catalog of planet density constraints for 27 TESS Objects of Interest (TOIs; 22 in our population analysis sample, 12 that are members of the same systems), and (3) employ a hierarchical Bayesian model to produce preliminary constraints on the mass-radius (M-R) relation. We find that the biases causing previous M-R relations to predict fairly high masses at $1~R_\oplus$ have been reduced. This work can inform more detailed studies of individual systems and offer a framework that can be applied to future RV surveys with the goal of population inferences.

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arXiv2021

Wolf 503 b: Characterization of a Sub-Neptune Orbiting a Metal-Poor K Dwarf

Using radial velocity measurements from four instruments, we report the mass and density of a $2.043\pm0.069 ~\rm{R}_{\oplus}$ sub-Neptune orbiting the quiet K-dwarf Wolf 503 (HIP 67285). In addition, we present improved orbital and transit parameters by analyzing previously unused short-cadence $K2$ campaign 17 photometry and conduct a joint radial velocity-transit fit to constrain the eccentricity at $0.41\pm0.05$. The addition of a transit observation by $Spitzer$ also allows us to refine the orbital ephemeris in anticipation of further follow-up. Our mass determination, $6.26^{+0.69}_{-0.70}~\rm{M}_{\odot}$, in combination with the updated radius measurements, gives Wolf 503 b a bulk density of $ρ= 2.92\pm ^{+0.50}_{-0.44}$ $\rm{g}~\rm{cm}^{-3}$. Using interior composition models, we find this density is consistent with an Earth-like core with either a substantial $\rm{H}_2\rm{O}$ mass fraction ($45^{+19.12}_{-16.15}\%$) or a modest H/He envelope ($0.5\pm0.28\%$). The low H/He mass fraction, along with the old age of Wolf 503 ($11\pm2$ Gyrs), makes this sub-Neptune an opportune subject for testing theories of XUV-driven mass loss while the brightness of its host ($J=8.3$ mag) makes it an attractive target for transmission spectroscopy.

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arXiv2021

TOI-942b: A Prograde Neptune in a ~60 Myr old Multi-transiting System

Mapping the orbital obliquity distribution of young planets is one avenue towards understanding mechanisms that sculpt the architectures of planetary systems. TOI-942 is a young field star, with an age of ~60 Myr, hosting a planetary system consisting of two transiting Neptune-sized planets in 4.3- and 10.1-day period orbits. We observed the spectroscopic transits of the inner Neptune TOI-942b to determine its projected orbital obliquity angle. Through two partial transits, we find the planet to be in a prograde orbit, with a projected obliquity angle of |lambda| = 1/+41-33 deg. In addition, incorporating the light curve and the stellar rotation period, we find the true three-dimensional obliquity to be 2/+27-23 deg. We explored various sources of uncertainties specific to the spectroscopic transits of planets around young active stars, and showed that our reported obliquity uncertainty fully encompassed these effects. TOI-942b is one of the youngest planets to have its obliquity characterized, and one of even fewer residing in a multi-planet system. The prograde orbital geometry of TOI-942b is in line with systems of similar ages, none of which have yet been identified to be in strongly misaligned orbits.

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arXiv2021

TOI-1231 b: A Temperate, Neptune-Sized Planet Transiting the Nearby M3 Dwarf NLTT 24399

We report the discovery of a transiting, temperate, Neptune-sized exoplanet orbiting the nearby ($d$ = 27.5 pc), M3V star TOI-1231 (NLTT 24399, L 248-27, 2MASS J10265947-5228099). The planet was detected using photometric data from the Transiting Exoplanet Survey Satellite and followed up with observations from the Las Cumbres Observatory and the Antarctica Search for Transiting ExoPlanets program. Combining the photometric data sets, we find that the newly discovered planet has a radius of 3.65$^{+0.16}_{-0.15}$ R$_{\oplus}$, and an orbital period of 24.246 days. Radial velocity measurements obtained with the Planet Finder Spectrograph on the Magellan Clay telescope confirm the existence of the planet and lead to a mass measurement of 15.5$\pm$3.3 M$_{\oplus}$. With an equilibrium temperature of just 330K TOI-1231 b is one of the coolest small planets accessible for atmospheric studies thus far, and its host star's bright NIR brightness (J=8.88, K$_{s}$=8.07) make it an exciting target for HST and JWST. Future atmospheric observations would enable the first comparative planetology efforts in the 250-350 K temperature regime via comparisons with K2-18 b. Furthermore, TOI-1231's high systemic radial velocity (70.5 k\ms) may allow for the detection of low-velocity hydrogen atoms escaping the planet by Doppler shifting the H I Ly-alpha stellar emission away from the geocoronal and ISM absorption features.

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arXiv2021

A Complete Census of Circumgalactic MgII at Redshift z<~ 0.5

We present a survey of MgII absorbing gas in the vicinity of 380 random galaxies, using 156 background quasi-stellar objects(QSOs) as absorption-line probes. The sample comprises 211 isolated (73 quiescent and 138 star-forming galaxies) and 43 non-isolated galaxies with sensitive constraints for both MgII absorption and Ha emission. The projected distances span a range from d=9 to 497 kpc, redshifts of the galaxies range from z=0.10 to 0.48, and rest-frame absolute B-band magnitudes range from $M_{\rm B}=-16.7$ to $-22.8$. Our analysis shows that the rest-frame equivalent width of MgII, $W_r$(2796), depends on halo radius($R_h$), $B$-band luminosity($L_{\rm B}$) and stellar mass ($M_{\rm star}$) of the host galaxies, and declines steeply with increasing $d$ for isolated, star-forming galaxies. $W_r$(2796) exhibits no clear trend for either isolated, quiescent galaxies or non-isolated galaxies. The covering fraction of MgII absorbing gas $\langle κ\rangle$ is high with $\langle κ\rangle\gtrsim 60$% at $<40$ kpc for isolated galaxies and declines rapidly to $\langle κ\rangle\approx 0$ at $d\gtrsim100$ kpc. Within the gaseous radius, $\langle κ\rangle$ depends sensitively on both $M_{\rm star}$ and the specific star formation rate inferred from Ha. Different from massive quiescent halos, the observed velocity dispersion of MgII gas around star-forming galaxies is consistent with expectations from virial motion, which constrains individual clump mass to $m_{\rm cl} \gtrsim 10^5 \,\rm M_\odot$ and cool gas accretion rate of $\sim 0.7-2 \,M_\odot\,\rm yr^{-1}$. We find no strong azimuthal dependence of MgII absorption for either star-forming or quiescent galaxies. Our results highlight the need of a homogeneous, absorption-blind sample for establishing a holistic description of chemically-enriched gas in the circumgalactic space.

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arXiv2021

TESS discovery of a super-Earth and three sub-Neptunes hosted by the bright, Sun-like star HD 108236

We report the discovery and validation of four extrasolar planets hosted by the nearby, bright, Sun-like (G3V) star HD~108236 using data from the Transiting Exoplanet Survey Satellite (TESS). We present transit photometry, reconnaissance and precise Doppler spectroscopy as well as high-resolution imaging, to validate the planetary nature of the objects transiting HD~108236, also known as the TESS Object of Interest (TOI) 1233. The innermost planet is a possibly-rocky super-Earth with a period of $3.79523_{-0.00044}^{+0.00047}$ days and has a radius of $1.586\pm0.098$ $R_\oplus$. The outer planets are sub-Neptunes, with potential gaseous envelopes, having radii of $2.068_{-0.091}^{+0.10}$ $R_\oplus$, $2.72\pm0.11$ $R_\oplus$, and $3.12_{-0.12}^{+0.13}$ $R_\oplus$ and periods of $6.20370_{-0.00052}^{+0.00064}$ days, $14.17555_{-0.0011}^{+0.00099}$ days, and $19.5917_{-0.0020}^{+0.0022}$ days, respectively. With V and K$_{\rm s}$ magnitudes of 9.2 and 7.6, respectively, the bright host star makes the transiting planets favorable targets for mass measurements and, potentially, for atmospheric characterization via transmission spectroscopy. HD~108236 is the brightest Sun-like star in the visual (V) band known to host four or more transiting exoplanets. The discovered planets span a broad range of planetary radii and equilibrium temperatures, and share a common history of insolation from a Sun-like star ($R_\star = 0.888 \pm 0.017$ R$_\odot$, $T_{\rm eff} = 5730 \pm 50$ K), making HD 108236 an exciting, opportune cosmic laboratory for testing models of planet formation and evolution.

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arXiv2021

Physical Parameters of the Multi-Planet Systems HD 106315 and GJ 9827

HD 106315 and GJ 9827 are two bright, nearby stars that host multiple super-Earths and sub-Neptunes discovered by K2 that are well suited for atmospheric characterization. We refined the planets' ephemerides through Spitzer transits, enabling accurate transit prediction required for future atmospheric characterization through transmission spectroscopy. Through a multi-year high-cadence observing campaign with Keck/HIRES and Magellan/PFS, we improved the planets' mass measurements in anticipation of HST transmission spectroscopy. For GJ 9827, we modeled activity-induced radial velocity signals with a Gaussian process informed from the Calcium II H&K lines in order to more accurately model the effect of stellar noise on our data. We found planet masses of M$_b$=$4.87\pm 0.37$ M$_\oplus$, M$_c$=$1.92\pm 0.49$ M$_\oplus$, and M$_d$=$3.42\pm 0.62$ M$_\oplus$. For HD 106315, we found that such activity-radial velocity decorrelation was not effective due to the reduced presence of spots and speculate that this may extend to other hot stars as well (T$_{\rm {eff}}>6200$ K). We found planet masses of M$_b$=$10.5\pm 3.1$ M$_\oplus$ and M$_c$=$12.0\pm 3.8$ M$_\oplus$. We investigated all of the planets' compositions through comparing their masses and radii to a range of interior models. GJ 9827 b and GJ 9827 c are both consistent with an Earth-like rocky composition, GJ 9827 d and HD 106315 b both require additional volatiles and are consistent with moderate amounts of water or hydrogen/helium, and HD 106315 c is consistent with 10% hydrogen/helium surrounding an Earth-like rock and iron core.

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arXiv2020

Development of the ROSIE Integral Field Unit on the Magellan IMACS Spectrograph

We are building an image slicer integral field unit (IFU) to go on the IMACS wide-field imaging spectrograph on the Magellan Baade Telescope at Las Campanas Observatory, the Reformatting Optically-Sensitive IMACS Enhancement IFU, or ROSIE IFU. The 50.4" x 53.5" field of view will be pre-sliced into four 12.6" x 53.5" subfields, and then each subfield will be divided into 21 0.6" x 53.5" slices. The four main image slicers will produce four pseudo-slits spaced six arcminutes apart across the IMACS f/2 camera field of view, providing a wavelength coverage of 1800 Angstroms at a spectral resolution of 2000. Optics are in-hand, the first image slicer is being aluminized, mounts are being designed and fabricated, and software is being written. This IFU will enable the efficient mapping of extended objects such as nebulae, galaxies, or outflows, making it a powerful addition to IMACS.

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arXiv2020

Revisiting the HD 21749 Planetary System with Stellar Activity Modeling

HD 21749 is a bright ($V=8.1$ mag) K dwarf at 16 pc known to host an inner terrestrial planet HD 21749c as well as an outer sub-Neptune HD 21749b, both delivered by TESS. Follow-up spectroscopic observations measured the mass of HD 21749b to be $22.7\pm2.2\ M_{\oplus}$ with a density of $7.0^{+1.6}_{-1.3}$ g~cm$^{-3}$, making it one of the densest sub-Neptunes. However, the mass measurement was suspected to be influenced by stellar rotation. Here we present new high-cadence PFS RV data to disentangle the stellar activity signal from the planetary signal. We find that HD 21749 has a similar rotational timescale as the planet's orbital period, and the amplitude of the planetary orbital RV signal is estimated to be similar to that of the stellar activity signal. We perform Gaussian Process (GP) regression on the photometry and RVs from HARPS and PFS to model the stellar activity signal. Our new models reveal that HD 21749b has a radius of $2.86\pm0.20\ R_{\oplus}$, an orbital period of $35.6133\pm0.0005$ d with a mass of $M_{b}=20.0\pm2.7\ M_{\oplus}$ and a density of $4.8^{+2.0}_{-1.4}$ g~cm$^{-3}$ on an eccentric orbit with $e=0.16\pm0.06$, which is consistent with the most recent values published for this system. HD 21749c has an orbital period of $7.7902\pm0.0006$ d, a radius of $1.13\pm0.10\ R_{\oplus}$, and a 3$σ$ mass upper limit of $3.5\ M_{\oplus}$. Our Monte Carlo simulations confirm that without properly taking stellar activity signals into account, the mass measurement of HD 21749b is likely to arrive at a significantly underestimated error bar.

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arXiv2020

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

We report the detection of a transiting hot Neptune exoplanet orbiting TOI-824 (SCR J1448-5735), a nearby (d = 64 pc) K4V star, using data from the \textit{Transiting Exoplanet Survey Satellite} (TESS). The newly discovered planet has a radius, $R_{\rm{p}}$ = 2.93 $\pm$ 0.20 R$_{\oplus}$, and an orbital period of 1.393 days. Radial velocity measurements using the Planet Finder Spectrograph (PFS) and the High Accuracy Radial velocity Planet Searcher (HARPS) spectrograph confirm the existence of the planet and we estimate its mass to be $M_{\rm{p}}$ = 18.47 $\pm$ 1.84 M$_{\oplus}$. The planet's mean density is $ρ_{\rm{p}}$ = 4.03$^{+0.98}_{-0.78}$ g cm$^{-3}$ making it more than twice as dense as Neptune. TOI-824 b's high equilibrium temperature makes the planet likely to have a cloud free atmosphere, and thus an excellent candidate for follow up atmospheric studies. The detectability of TOI-824 b's atmosphere from both ground and space is promising and could lead to the detailed characterization of the most irradiated, small planet at the edge of the hot Neptune desert that has retained its atmosphere to date.

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arXiv2020

Search for Nearby Earth Analogs. III. Detection of ten new planets, three planet candidates, and confirmation of three planets around eleven nearby M dwarfs

Earth-sized planets in the habitable zones of M dwarfs are good candidates for the study of habitability and detection of biosignatures. To search for these planets, we analyze all available radial velocity data and apply four signal detection criteria to select the optimal candidates. We find ten strong candidates satisfying these criteria and three weak candidates showing inconsistency over time due to data samplings. We also confirm three previous planet candidates and improve their orbital solutions through combined analyses of updated data sets. Among the strong planet candidates, HIP 38594 b is a temperate super-Earth with a mass of $8.2 \pm 1.7$ $M_\oplus$ and an orbital period of $60.7\pm0.1$ days, orbiting around an early-type M dwarf. Early-type M dwarfs are less active and thus are better hosts for habitable planets than mid-type and late-type M dwarfs. Moreover, we report the detection of five two-planet systems, including two systems made up of a warm or cold Neptune and a cold Jupiter, consistent with a positive correlation between these two types of planets. We also detect three temperate Neptunes, four cold Neptunes, and four cold Jupiters, contributing to a rarely explored planet population. Due to their proximity to the Sun, these planets on wide orbits are appropriate targets for direct imaging by future facilities such as HabEx and ELT.

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arXiv2020

Vanadium Abundance Derivations in 255 Metal-poor Stars

We present vanadium (V) abundances for 255 metal-poor stars, derived from high-resolution optical spectra from the Magellan Inamori Kyocera Echelle spectrograph on the Magellan Telescopes at Las Campanas Observatory, the Robert G. Tull Coudé Spectrograph on the Harlan J. Smith Telescope at McDonald Observatory, and the High Resolution Spectrograph on the Hobby-Eberly Telescope at McDonald Observatory. We use updated V I and V II atomic transition data from recent laboratory studies, and we increase the number of lines examined (from 1 to 4 lines of V I, and from 2 to 7 lines of V II). As a result, we reduce the V abundance uncertainties for most stars by more than 20% and expand the number of stars with V detections from 204 to 255. In the metallicity range $-$4.0 $<$ [Fe/H] $< -$1.0, we calculate the mean ratios [V I/Fe I]$ = -0.10 \pm 0.01 (σ= 0.16)$ from 128 stars with $\geq$ 2 V I lines detected, [V II/Fe II] $= +0.13 \pm 0.01 (σ= 0.16)$ from 220 stars with $\geq$ 2 V II lines detected, and [V II/V I] $= +0.25 \pm 0.01 (σ= 0.15)$ from 119 stars. We suspect this offset is due to non-LTE effects, and we recommend using [V II/Fe II], which is enhanced relative to the solar ratio, as a better representation of [V/Fe]. We provide more extensive evidence for abundance correlations detected previously among scandium, titanium, and vanadium, and we identify no systematic effects in the analysis that can explain these correlations.

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arXiv2020

TESS Reveals a Short-period Sub-Neptune Sibling (HD 86226c) to a Known Long-period Giant Planet

The Transiting Exoplanet Survey Satellite mission was designed to find transiting planets around bright, nearby stars. Here we present the detection and mass measurement of a small, short-period ($\approx\,4$\,days) transiting planet around the bright ($V=7.9$), solar-type star HD 86226 (TOI-652, TIC 22221375), previously known to host a long-period ($\sim$1600 days) giant planet. HD 86226c (TOI-652.01) has a radius of $2.16\pm0.08$ $R_{\oplus}$ and a mass of 7.25$^{+1.19}_{-1.12}$ $M_{\oplus}$ based on archival and new radial velocity data. We also update the parameters of the longer-period, not-known-to-transit planet, and find it to be less eccentric and less massive than previously reported. The density of the transiting planet is $3.97$ g cm$^{-3}$, which is low enough to suggest that the planet has at least a small volatile envelope, but the mass fractions of rock, iron, and water are not well-constrained. Given the host star brightness, planet period, and location of the planet near both the ``radius gap'' and the ``hot Neptune desert'', HD 86226c is an interesting candidate for transmission spectroscopy to further refine its composition.

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arXiv2020

The Magellan/PFS Exoplanet Search: A 55-day period dense Neptune transiting the bright ($V=8.6$) star HD 95338

We report the detection of a transiting, dense Neptune planet candidate orbiting the bright ($V=8.6$) K0.5V star HD 95338. Detection of the 55-day periodic signal comes from the analysis of precision radial velocities from the Planet Finder Spectrograph on the Magellan II Telescope. Follow-up observations with HARPS also confirm the presence of the periodic signal in the combined data. HD 95338 was also observed by the Transiting Exoplanet Survey Satellite ({\it TESS}) where we identify a clear single transit in the photometry. A Markov Chain Monte Carlo period search on the velocities allows strong constraints on the expected transit time, matching well the epoch calculated from \tess{} data, confirming both signals describe the same companion. A joint fit model yields an absolute mass of 42.44$^{+2.22}_{-2.08} M_{\oplus}$ and a radius of 3.89$^{+0.19}_{-0.20}$ $R_{\oplus}$ which translates to a density of 3.98$^{+0.62}_{-0.64}$ \gcm\, for the planet. Given the planet mass and radius, structure models suggest it is composed of a mixture of ammonia, water, and methane. HD 95338\,b is one of the most dense Neptune planets yet detected, indicating a heavy element enrichment of $\sim$90\% ($\sim38\, M_{\oplus}$). This system presents a unique opportunity for future follow-up observations that can further constrain structure models of cool gas giant planets.

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arXiv2020

Gravity and the Nonlinear Growth of Structure in the Carnegie-Spitzer-IMACS Redshift Survey

A key obstacle to developing a satisfying theory of galaxy evolution is the difficulty in extending analytic descriptions of early structure formation into full nonlinearity, the regime in which galaxy growth occurs. Extant techniques, though powerful, are based on approximate numerical methods whose Monte Carlo-like nature hinders intuition building. Here, we develop a new solution to this problem and its empirical validation. We first derive closed-form analytic expectations for the evolution of fixed percentiles in the real-space cosmic density distribution, {\it averaged over representative volumes observers can track cross-sectionally\}. Using the Lagrangian forms of the fluid equations, we show that percentiles in $δ$---the density relative to the median---should grow as $δ(t)\proptoδ_{0}^α\,t^β$, where $α\equiv2$ and $β\equiv2$ for Newtonian gravity at epochs after the overdensities transitioned to nonlinear growth. We then use 9.5 sq. deg. of Carnegie-Spitzer-IMACS Redshift Survey data to map {\it galaxy\} environmental densities over $0.2<z<1.5$ ($\sim$7 Gyr) and infer $α=1.98\pm0.04$ and $β=2.01\pm0.11$---consistent with our analytic prediction. These findings---enabled by swapping the Eulerian domain of most work on density growth for a Lagrangian approach to real-space volumetric averages---provide some of the strongest evidence that a lognormal distribution of early density fluctuations indeed decoupled from cosmic expansion to grow through gravitational accretion. They also comprise the first exact, analytic description of the nonlinear growth of structure extensible to (arbitrarily) low redshift. We hope these results open the door to new modeling of, and insight-building into, the galaxy growth and its diversity in cosmological contexts.

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