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Meng Zhai

Publications and source records attributed to Meng Zhai.

At least 19 recordsLinked to original sources

The capability of CSST in characterizing planetary atmospheres. I. transmission spectroscopy of hot Jupiters

Transmission spectroscopy has become a primary tool for probing exoplanetary atmospheres, enabling constraints on their chemical compositions and providing limited information on their thermal properties. We assess the potential of the upcoming Chinese Space Station Telescope (CSST) for exoplanet atmospheric characterization through transmission spectroscopy. Theoretical spectra of hot gas planets are generated and used to simulate slitless spectroscopic observations with the CSST across the ultraviolet-to-near-infrared range. Atmospheric retrievals performed on the simulated data are compared with the input models to assess the robustness and accuracy of parameter determinations. We find that multi-band observations across three wavelength channels, each with two transits can place meaningful constraints on key atmospheric parameters. For multi-band observations that account for correlated (red) noise, future CSST observations are expected to achieve constraints that are comparable to, or in some cases slightly weaker than, those of the Hubble Space Telescope (HST), depending on the noise level and observing strategy. We conclude that CSST will provide unique and complementary constraints on the chemical compositions and physical properties of exoplanetary atmospheres, particularly for atomic species, metal-bearing molecules, and scattering processes accessible in the UV and optical, thereby complementing JWST's infrared sensitivity to molecular species.

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The 3D Architecture of a pair of 6:1 Resonant Brown Dwarfs around the Naked-eye star $\nu$ Ophiuchi

We present a revisiting study of the brown dwarf pair orbiting the naked-eye ($V=3.3$) K-giant $\nu$~Ophiuchi, located only 44\,pc from our Solar system. By jointly analysing archival radial-velocity measurements together with astrometric data from \textit{Hipparcos} and the \textit{Gaia} second and third data releases, we determine the three-dimensional architecture of the system and robustly constrain the masses of both companions. We find brown dwarf masses of $m_{\mathrm{b}} = 24.2^{+6.4}_{-2.8}\,M_{\mathrm{J}}$ and $m_{\mathrm{c}} = 26.8^{+4.3}_{-2.9}\,M_{\mathrm{J}}$. The mathematical constraint, derived from the posterior distribution of the mutual inclination based on MCMC samples, yields a mutual inclination of $\psi_{\mathrm{bc}}=46^{+27}_{-24}\!\,^{\circ}$, while direct calculations based on the maximum a posteriori and posterior median orbital parameters yield values of $\sim$$10^{\circ}$ and $\sim$$20^{\circ}$, respectively. Resonance analysis indicates that the two companions can still be trapped in a 6:1 mean-motion resonance in the maximum a posteriori configuration. To place an upper limit for the mutual inclination, dynamical stability analysis over a 1~Myr timescale further constrains it to be no larger than $\sim$$15^{\circ}$. Systems hosting brown dwarf pairs are rare, yet they provide important constraints on theories of planetary formation and dynamical evolution. Current detections suggest that brown dwarf pairs preferentially reside at large separations from their host stars and are more common in less mature systems. This supports a star-like formation pathway via gravitational instability in disk.

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Detection of CO, H$_2$O, and OH in WASP-18b with JWST/NIRISS using Direct-Extracted Spectra and Cross-Correlation

The James Webb Space Telescope (JWST) has revolutionized the characterization of exoplanetary atmospheres, offering unprecedented sensitivity to probe their chemical and physical properties. Recently, a growing trend has emerged to obtain atmospheric information directly from pixel-level planetary spectra. In this work, we re-analyzed the WASP-18b NIRISS/SOSS dataset by employing a direct extraction method. This new method preserves the spectral information at the native instrumental resolution, thereby enabling the application of cross-correlation techniques and providing atmospheric retrievals with enhanced precision and richer information content. With this methodology, we report detections of CO at $4.4\sigma$ significance, H$_2$O at $3.4\sigma$, and OH at $7.8\sigma$, where CO and OH were previously unseen. Building on these unambiguous detections, our subsequent retrieval analysis significantly improves the constraints on atmospheric abundances. Our results demonstrate that the cross-correlation technique effectively extracts molecular signals from medium-resolution JWST data, enhancing detection sensitivity. By revisiting JWST archival data with cross-correlation and retrieval analysis, we can achieve a more comprehensive survey of planetary atmospheric chemistry, thereby placing precise constraints on key parameters such as planetary metallicity and C/O ratio.

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Thermal emission spectra of the ultra-hot Jupiter WASP-33 b

Observations of exoplanetary atmospheres provide critical insights into their chemical composition, formation and evolution history. Ultra-hot Jupiters serve as excellent targets for atmospheric characterization; studies of these planets may yield key understanding of gas giant's formation and evolution history. We present a thermal emission study of WASP-33 b's dayside atmosphere, based on two secondary eclipse observations with CFHT/WIRCam in two specific narrow band filters, namely the CO and CH4$_{\rm on}$ filters, and archival data with HST/WFC3 and Spitzer. Stellar pulsations of the host star induce some quasi-periodic photometric variations, particularly in the CH4$_{\rm on}$ band, which are modelled and corrected in the high-precision differential light curves. An eclipse depth of $1565.2^{+228.6}_{-237.5}$ ppm and $914.3^{+56.1}_{-57.0}$ ppm is determined for the CO and CH4$_{\rm on}$ bands, respectively. Combined with HST/WFC3 and Spitzer data, our joint retrieval of WASP-33 b's dayside atmosphere reveals a high metallicity ([Fe/H] $= 1.52^{+0.35}_{-0.52}$), high C/O ratio (C/O $= 0.78^{+0.03}_{-0.04}$), and a thermal inversion layer, suggesting a formation history involving metal-rich gas accretion. We confirm the presence of the molecules H$_{2}$O, H$^{-}$ and CO, and report a tentative detection of TiO in the dayside atmosphere of WASP-33 b. Future higher precision observations with JWST may provide better understand constraints on the chemical abundances of oxygen and refractory element abundances to better WASP-33 b's formation and evolutionary pathway.

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Unraveling Year-Long Radial Velocity Variations in Red Clump Region -- I: Comprehensive analysis of a K0 Giant star, 2 Draconis

Slow-rotating evolved stars frequently exhibit radial velocity (RV) variations on annual timescales, complicated by instrumental systematics and aliasing in the one-year regime. Here we investigate the origin of the near-yearly periodicity in 2 Dra, a star located in the red-clump region, assessing possible causes between stellar activity, instrumental profile (IP) effects, sampling alias, and planetary companions. We applied two independent approaches: (1) constraining diagnostic signals and performing a correlation analysis ($r$) between period-confined signals, and (2) evaluating phase stability by partitioning Keplerian fits. These methods enabled us to examine the physical connections and phase coherence among stellar activity indicators, RV measurements, and IP diagnostics. Our analysis suggests a stellar rotation period of $\simeq270\text{--}320$\,d for 2~Dra. The 340-d RV signal does not appear to originate from stellar activity in this chromospherically quiet star ($|r| \lesssim 0.33$), nor from instrumental systematics near the annual period ($|r| \lesssim 0.1$). This conclusion is supported by contrasting phase behavior: the RV and stellar activity phases remain stable, whereas the IP phases do not. We therefore propose that the 340-d variation likely arises from either small-amplitude intrinsic variability or a tentative gas giant companion with potential weak activity-induced modulation. The case of 2~Dra provides a framework for distinguishing the origins of $\sim$1-yr RV variations in other evolved stars.

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HST/WFC3 Constraints on the Abundances of OH and FeH in the Atmosphere of the Ultra-Hot Neptune LTT-9779 b

Planets residing within the hot-Neptune Desert are rare, and studying their atmospheres can provide valuable insights into their formation and evolutionary processes. We present the atmospheric characterization of the first known ultra-hot Neptune, LTT-9779 b, using transmission spectroscopic observations obtained with the HST/WFC3 G141 and G102 grisms. Using the Iraclis pipeline and TauREx3 retrieval code, we find that LTT-9779 b likely possesses a H/He-dominated primary atmosphere with an opaque aerosol layer and the pure cloudy, flat-line model is rejected with approximately 2.7-$\sigma$ confidence. Although we do not find conclusive evidence supporting the presence of any molecular species, we place 95% confidence level upper limits on the volume mixing ratios (VMRs) of hydroxyl radical (OH) and iron hydride (FeH) at $7.18\times10^{-2}$ and $1.52\times10^{-8}$, respectively. Notably, the retrieval results are inconsistent with predictions from equilibrium chemistry models, which favor higher $\rm H_2O$ abundances over OH. This discrepancy suggests that disequilibrium processes, such as photochemistry or vertical mixing, may have altered the atmospheric composition. Comparisons between HST, Spitzer and JWST data reveal no evidence of temporal variations in the atmospheric composition of the terminator region. Our results highlight the need for higher-resolution spectroscopy and secondary eclipse observations to resolve LTT-9779 b's temperature-pressure (T-P) profile and chemical inventory definitively.

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The Terminator Region Atmosphere of the hot Jupiter WASP-77Ab with ESPRESSO/VLT observations

Atmospheric studies are essential for elucidating the formation history, evolutionary processes, and atmospheric dynamics of exoplanets. High-resolution transmission spectroscopy offers the advantage of detecting subtle variations in stellar spectral profiles, thereby enabling the identification of the sources of observed signals. In this study, we present the transmission spectra of the exoplanet WASP-77Ab, a hot Jupiter with a 1.36-day orbital period around a G8 host star with $V=11.29$ mag. These observations were conducted using the high-resolution spectrograph ESPRESSO at the Very Large Telescope over three transit events. We analyze the Rossiter-McLaughlin effect for WASP-77A and determine a projected spin-orbit angle of ${\lambda = 16.131^{\circ}}^{+2.106}_{-2.324}$, indicating that the planet's orbit is nearly aligned. Following the generation of transmission spectra for the three nights, we model and correct for center-to-limb variation and the Rossiter-McLaughlin effects. In the residual transmission spectra, we detect H$\alpha$, H$\beta$ and CaII H with a significance exceeding 3.5$\sigma$. After applying 0.1-0.5 \r{A} masks to the cores of these lines to mitigate stellar contamination, all them still shows visible absorptions although not significant, suggesting at least partial planet contribution to them. Therefore, we are yet unable to confirm or reject the planetary origin of these spectral signals based on the current data set. Further investigation of WASP-77Ab's atmosphere, particularly in areas beyond the terminator region, is essential to illuminate the planet's two-dimensional atmospheric structure.

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GASTLI: An open-source coupled interior-atmosphere model to unveil gas giant composition

The metal mass fractions of gas giants are a powerful tool to constrain their formation mechanisms and evolution. The metal content is inferred by comparing mass and radius measurements with interior structure and evolution models. In the midst of the JWST, CHEOPS, TESS, and the forthcoming PLATO era, we are at the brink of obtaining unprecedented precision in radius, age and atmospheric metallicity measurements. To prepare for this wealth of data, we present the GAS gianT modeL for Interiors (GASTLI), an easy-to-use, publicly available Python package. The code is optimized to rapidly calculate mass-radius relations, and radius and luminosity thermal evolution curves for a variety of envelope compositions and core mass fractions. Its applicability spans planets with masses $17 \ M_{\oplus} < M < 6 \ M_{Jup}$, and equilibrium temperatures $T_{eq} < 1000$ K. The interior model is stratified in a core composed of water and rock, and an envelope constituted by H/He and metals (water). The interior is coupled to a grid of self-consistent, cloud-free atmospheric models to determine the atmospheric and boundary interior temperature, as well as the contribution of the atmosphere to the total radius. We successfully validate GASTLI by comparing it to previous work and data of the Solar System's gas giants and Neptune. We also test GASTLI on the Neptune-mass exoplanet HAT-P-26 b, finding a bulk metal mass fraction between 0.60-0.78 and a core mass of 8.5-14.4 $M_{\oplus}$. Finally, we explore the impact of different equations of state and assumptions, such as C/O ratio and transit pressure, in the estimation of bulk metal mass fraction. These differences between interior models entail a change in radius of up to 2.5% for Jupiter-mass planets, but more than 10\% for Neptune-mass. These are equivalent to variations in core mass fraction of 0.07, or 0.10 in envelope metal mass fraction.

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Two long-period giant planets around two giant stars: HD 112570 and HD 154391

We present the discoveries of two giant planets orbiting the red giant branch (RGB) star HD 112570 and the red clump (RC) star HD 154391, based on the radial velocity (RV) measurements from Xinglong station and Okayama Astrophysical Observatory (OAO). Spectroscopic and asteroseismic analyses suggest that HD 112570 has a mass of $1.15\pm0.12\,M_{\odot}$, a radius of $9.85\pm0.23\,R_{\odot}$, a metallicity [Fe/H] of $-0.46\pm0.1$ and a ${\rm log}\,g$ of $2.47\pm0.1$. With the joint analysis of RV and Hipparcos-Gaia astrometry, we obtain a dynamical mass of $M_{\rm p}={3.42}_{-0.84}^{+1.4}\ M_{\rm Jup}$, a period of $P={2615}_{-77}^{+85}$ days and a moderate eccentricity of $e={0.20}_{-0.14}^{+0.16}$ for the Jovian planet HD 112570 b. For HD 154391, it has a mass of $2.07\pm0.03\,M_{\odot}$, a radius of $8.56\pm0.05\,R_{\odot}$, a metallicity [Fe/H] of $0.07\pm0.1$ and a ${\rm log}\,g$ of $2.86\pm0.1$. The super-Jupiter HD 154391 b has a mass of $M_{\rm p}={9.1}_{-1.9}^{+2.8}\ M_{\rm Jup}$, a period of $P={5163}_{-57}^{+60}$ days and an eccentricity of $e={0.20}_{-0.04}^{+0.04}$. We found HD 154391 b has one of the longest orbital period among those ever discovered orbiting evolved stars, which may provide a valuable case in our understanding of planetary formation at wider orbits. Moreover, while a mass gap at $4\,M_{\rm Jup}$ seems to be present in the population of giant stars, there appears to be no significant differences in the distribution of metallicity among giant planets with masses above or below this threshold. Finally, The origin of the abnormal accumulation near 2 au for planets around large evolved stars ($R_{\star}>21\,R_{\odot}$), remains unclear.

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The Tianlin Mission: a 6m UV/Opt/IR space telescope to explore the habitable worlds and the universe

[Abridged] It is expected that the ongoing and future space-borne planet survey missions including TESS, PLATO, and Earth 2.0 will detect thousands of small to medium-sized planets via the transit technique, including over a hundred habitable terrestrial rocky planets. To conduct a detailed study of these terrestrial planets, particularly the cool ones with wide orbits, the exoplanet community has proposed various follow-up missions. The currently proposed ESA mission ARIEL is capable of characterization of planets down to warm super-Earths mainly using transmission spectroscopy. The NASA 6m UV/Opt/NIR mission proposed in the Astro2020 Decadal Survey may further tackle down to habitable rocky planets, and is expected to launch around 2045. In the meanwhile, China is funding a concept study of a 6-m class space telescope named Tianlin (A UV/Opt/NIR Large Aperture Space Telescope) that aims to start its operation within the next 10-15 years and last for 5+ years. Tianlin will be primarily aimed to the discovery and characterization of rocky planets in the habitable zones (HZ) around nearby stars and to search for potential biosignatures mainly using the direct imaging method. Transmission and emission spectroscopy at moderate to high resolution will be carried out as well on a population of exoplanets to strengthen the understanding of the formation and evolution of exoplanets. It will also carry out in-depth studies of the cosmic web and early galaxies, and constrain the nature of the dark matter and dark energy. We describe briefly the primary scientific motivations and main technical considerations based on our preliminary simulation results. We find that a monolithic off-axis space telescope with a primary mirror diameter larger than 6m equipped with a high contrast chronograph can identify water in the atmosphere of a habitable-zone Earth-like planet around a Sun-like star.

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Atmospheric composition of WASP-85Ab with ESPRESSO/VLT observations

Transit spectroscopy is the most frequently used technique to reveal the atmospheric properties of exoplanets, while that at high resolution has the advantage to resolve the small Doppler shift of spectral lines, and the trace signal of the exoplanet atmosphere can be separately extracted. We obtain the transmission spectra of the extrasolar planet WASP-85Ab, a hot Jupiter in a 2.655-day orbit around a G5, V=11.2 mag host star, observed by high-resolution spectrograph ESPRESSO at the Very Large Telescope array for three transits. We present an analysis of the Rossiter-McLaughlin effect on WASP-85A, and determine a spin-orbit angle ${λ= -16.155^{\circ}}^{+2.916}_{-2.879}$, suggesting that the planet is in an almost aligned orbit. Combining the transmission spectra of three nights, we tentatively detected H$α$ and Ca II absorption with $\gtrapprox 3σ$ via direct visual inspection of the transmission spectra with the Center-to-Limb variation and the Rossiter-McLaughlin effects removed, which still remain visible after excluding the cores of these strong lines with a 0.1 A mask. These spectral signals seems likely to origin from the planetary atmosphere, but we can not fully exclude their stellar origins. Via the cross-correlation analysis of a set of atoms and molecules, Li I is marginally detected at $\sim4σ$ level, suggesting that Li might be present in the atmosphere of WASP-85Ab.

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Detection of rubidium and samarium in the atmosphere of the ultra-hot Jupiter MASCARA-4b

Ultra-hot Jupiters (UHJs) possess the most extreme environments among various types of exoplanets, making them ideal laboratories to study the chemical composition and kinetics properties of exoplanet atmosphere with high-resolution spectroscopy (HRS). It has the advantage of resolving the tiny Doppler shift and weak signal from exoplanet atmosphere and has helped to detect dozens of heavy elements in UHJs including KELT-9b, WASP-76b, WASP-121b. MASCARA-4b is a 2.8-day UHJ with an equilibrium temperature of $\sim2250$ K, which is expected to contain heavy elements detectable with VLT. In this letter, we present a survey of atoms/ions in the atmosphere of the MASCARA-4b, using the two VLT/ESPRESSO transits data. Cross-correlation analyses are performed on the obtained transmission spectra at each exposure with the template spectra generated by petitRADTRANS for atoms/ions from element Li to U. We confirm the previous detection of Mg, Ca, Cr and Fe and report the detection of Rb, Sm, Ti+ and Ba+ with peak signal-to-noise ratios (SNRs) $>$ 5. We report a tentative detection of Sc+, with peak SNRs $\sim$6 but deviating from the estimated position. The most interesting discovery is the first-time detection of elements Rb and Sm in an exoplanet. Rb is an alkaline element like Na and K, while Sm is the first lanthanide series element and is by far the heaviest one detected in exoplanets. Detailed modeling and acquiring more data are required to yield abundance ratios of the heavy elements and to understand better the common presence of them in UHJ's atmospheres.

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Detection of TiO and VO in the atmosphere of WASP-121b and Evidence for its temporal variation

We report the transit observations of the ultra hot Jupiter WASP-121b using the Goodman High Throughput Spectrograph (GHTS) at the 4-meter ground-based telescope Southern Astrophysical Research Telescope (SOAR), covering the wavelength range $502-900$ nm. By dividing the target and reference star into 19 spectroscopic passbands and applying differential spectrophotometry, we derive spectroscopic transit light curves and fit them using Gaussian process framework to determine transit depths for every passbands. The obtained optical transmission spectrum shows a steep increased slope toward the blue wavelength, which seems to be too steep to be accounted for by the Rayleigh scattering alone. We note that the transmission spectrum from this work and other works differ obviously from each other, which was pointed out previously by \citet{Wilson2021} as evidence for temporal atmospheric variation. We perform a free chemistry retrieval analysis on the optical transmission spectra from this work and the literature HST/WFC3 NIR spectrum. We determine TiO, VO and H$_{2}$O with abundances of $-5.95_{-0.42}^{+0.47}$ dex, $-6.72_{-1.79}^{+0.51}$ dex, and $-4.13_{-0.46}^{+0.63}$ dex, respectively. We compare the abundances of all these three molecules derived from this work and previous works, and find that they are not consistent with each other, indicating the chemical compositions of the terminator region may change over long timescales. Future multi-epoch and high-precision transit observations are required to further confirm this phenomena. We note that when combining the transmission spectra in the optical and in NIR in retrieval analysis, the abundances of V and VO, the NIR-to-optical offset and the cloud deck pressure may be coupled with each other.

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Thermal Emission from the hot Jupiter WASP-103b in J and Ks Bands

Hot Jupiters, particularly those with temperature higher than 2000 K are the best sample of planets that allow in-depth characterization of their atmospheres. We present here a thermal emission study of the ultra hot Jupiter WASP-103 b observed in two secondary eclipses with CFHT/WIRCam in J and Ks bands. By means of high precision differential photometry, we determine eclipse depths in J and Ks to an accuracy of 220 and 270 ppm, which are combined with the published HST/WFC3 and Spitzer data to retrieve a joint constraints on the properties of WASP-103 b dayside atmosphere. We find that the atmosphere is best fit with a thermal inversion layer included. The equilibrium chemistry retrieval indicates an enhanced C/O (1.35$^{+0.14}_{-0.17}$) and a super metallicity with [Fe/H]$=2.19^{+0.51}_{-0.63}$ composition. Given the near-solar metallicity of WASP-103 of [Fe/H]=0.06, this planet seems to be $\sim$100 more abundant than its host star. The free chemistry retrieval analysis yields a large abundance of FeH, H$^{-}$, CO$_2$ and CH$_4$. Additional data of better accuracy from future observations of JWST should provide better constraint of the atmospheric properties of WASP-103b.

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Tentative detection of titanium oxide in the atmosphere of WASP-69 b with a 4m ground-based telescope

Transiting planets provide unique opportunities for the atmospheric characterization of exoplanets as they can reveal composition and the temperature structures at the day-night terminator regions in planetary atmospheres, and help understand the atmospheric process and formation environments of exoplanets. Here, we present the optical transmission spectroscopic study of an inflated Saturn-mass planet WASP-69 b, obtained by the 4-meter ground-based telescope Southern Astrophysical Research Telescope (SOAR). We obtain spectroscopic transit light curves in 20 passbands from 502 to 890 nm, and fit them using Gaussian Processes and an analytical transit model to obtain independent transit depths for each. The derived transmission spectrum of WASP-69 b shows a slope with absorption depth increasing towards blue wavelengths, indicating a Rayleigh scattering in the atmosphere consistent with previous works. The retrieval analysis yields a tentative detection of TiO absorption feature in the transmission spectrum. We present the first results from the SOAR telescope to characterize exoplanetary atmospheres proving its capability and precision for hot Jupiters around bright stars in an area dominated by results from large ground-based telescopes or space telescopes.

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The Masses of a Sample of Radial-Velocity Exoplanets with Astrometric Measurements

Being one of the most fundamental physical parameter of astronomical objects, mass plays a vital role in the study of exoplanets, including their temperature structure, chemical composition, formation, and evolution. However, nearly a quarter of the known confirmed exoplanets lack measurements of their masses. This is particularly severe for those discovered via the radial-velocity (RV) technique, which alone could only yield the minimum mass of planets. In this study, we use published RV data combined with astrometric data from a cross-calibrated Hipparcos-Gaia Catalog of Accelerations (HGCA) to jointly constrain the masses of 115 RV-detected substellar companions, by conducting full orbital fits using the public tool \texttt{orvara}. Among them, 9 exoplanets with $M_{\rm p}\,{\rm sin}\,i<13.5\ M_{\rm Jup}$ are reclassified to the brown dwarf (BD) regime, and 16 BD candidates ($13.5\leqslant M_{\rm p}\,{\rm sin}\,i<80\,M_{\rm Jup}$) turn out to be low-mass M dwarfs. We point out the presence of a transition in the BD regime as seen in the distributions of host star metallicity and orbital eccentricity with respect to planet masses. We confirm the previous findings that companions with masses below $42.5\ M_{\rm Jup}$ might primarily form in the protoplanetary disc through core accretion or disc gravitational instability, while those with masses above $42.5\ M_{\rm Jup}$ formed through the gravitational instability of molecular cloud like stars. Selection effects and detection biases which may affect our analysis to some extent, are discussed.

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Milky Way Mass with K Giants and BHB Stars Using LAMOST, SDSS/SEGUE, and Gaia: 3D Spherical Jeans Equation and Tracer Mass Estimator

We measure the enclosed Milky Way mass profile to Galactocentric distances of $\sim70$ and $\sim50$ kpc using the smooth, diffuse stellar halo samples of Bird et al. The samples are LAMOST and SDSS/SEGUE K giants (KG) and SDSS/SEGUE blue horizontal branch (BHB) stars with accurate metallicities. The 3D kinematics are available through LAMOST and SDSS/SEGUE distances and radial velocities and {\it Gaia} DR2 proper motions. Two methods are used to estimate the enclosed mass: 3D spherical Jeans equation and Evans et al. tracer mass estimator (TME). We remove substructure via the Xue et al. method based on integrals of motion. We evaluate the uncertainties on our estimates due to random sampling noise, systematic distance errors, the adopted density profile, and non-virialization and non-spherical effects of the halo. The tracer density profile remains a limiting systematic in our mass estimates, although within these limits we find reasonable agreement across the different samples and the methods applied. Out to $\sim70$ and $\sim50$ kpc, the Jeans method yields total enclosed masses of $4.3\pm0.95$ (random) $\pm0.6$ (systematic) $\times10^{11}$ M$_\odot$ and $4.1\pm1.2$ (random) $\pm0.6$ (systematic) $\times10^{11}$ M$_\odot$ for the KG and BHB stars, respectively. For the KG and BHB samples we find a dark matter virial mass of $M_{200}=0.55^{+0.15}_{-0.11}$ (random) $\pm0.083$ (systematic) $\times10^{12}$ M$_\odot$ and $M_{200}=1.00^{+0.67}_{-0.33}$ (random) $\pm0.15$ (systematic) $\times10^{12}$ M$_\odot$, respectively.

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Local Group Analogs in $Λ$CDM cosmological simulations

We use semi-analytic galaxy catalogs based on two high-resolution cosmological $N$-body simulations, Millennium-WMAP7 and Millennium-II, to investigate the formation of the Local Group (LG) analogs. Unlike previous studies, we use the observed stellar masses to select the LG member (Milky Way (MW) and M31) analogs, and then impose constrains using the observed separation, isolation, and kinematics of the two main member galaxies. By comparing radial and low-ellipticity orbits between the MW and M31, we find higher tangential velocity results in higher total mass, which are 4.4$^{+2.4}_{-1.5}\times$10$^{12}\rm M_{\odot}$ and 6.6$^{+2.7}_{-1.5}\times$10$^{12}\rm M_{\odot}$ for radial and low-ellipticity orbits. The orbits also influence the individual mass distribution of MW and M31 analogs. For radial orbits, the typical host halo masses of the MW and M31 are 1.5$^{+1.4}_{-0.7}\times$10$^{12}\rm M_{\odot}$ and 2.5$^{+1.3}_{-1.1}\times$10$^{12}\rm M_{\odot}$; for low-ellipticity orbits, the masses are 2.5$^{+2.2}_{-1.4}\times$10$^{12}\rm M_{\odot}$ and 3.8$^{+2.8}_{-1.8}\times$10$^{12} \rm M_{\odot}$. The LG is located primarily in filaments with tails extending toward higher densities up to $δ\sim4.5$. The dark matter velocity anisotropy parameters $β$ of both the MW and M31 analogs are close to zero in the center, increasing to 0.2--0.3 at 50--80 kpc and decreasing slowly outward. The slope is much flatter than computed from the MW satellites, and the amplitude is smaller than traced by halo stars. Values of $β$ from different tracers agree at $\sim$120 kpc where $β\sim$ 0.2. We also find that model predictions agree broadly with observations in the radial distribution and luminosity function of satellites around the MW and M31.

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