arXiv subjects

I. Baraffe

Publications and source records attributed to I. Baraffe.

At least 19 recordsLinked to original sources

arXiv2026

Lithium-rich M-dwarfs at the ZAMS: Evidence for planetary engulfment?

We identify 6 early M-dwarfs, in 3 open clusters (NGC 2451a, Blanco 1 and NGC 2516) at ages of 50-200 Myr, that are anomalously enriched in lithium compared with Li-depleted siblings of similar spectral type. The Li-rich outliers represent 2-3 per cent of stars with $3560 < T_{\rm eff}/{\rm K} < 4045$ in clusters at those ages but are otherwise indistinguishable in their positions, parallaxes and kinematics from other cluster members; their placement in absolute colour-magnitude diagrams is incompatible with being much younger Li-rich interlopers, only one shows evidence of binarity and they are all slow rotators. The enhanced Li abundances are consistent with the engulfment of 3-10 $M_\oplus$ of volatile-depleted planetary material after the formation of a radiative core has ended rapid pre main sequence Li depletion. Published planetary formation simulations featuring engulfment via dynamical interactions, and the preponderance of Earth-like exoplanets in close orbits around M-dwarfs, offer some support to this scenario. The observed occurrence rate would be a lower limit to the frequency with which such engulfment events occur between ages of $\sim (30-200)$ Myr, that depends in the timescale for ongoing Li depletion at the ZAMS.

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arXiv2025

Mass dependence of overshooting beneath convective envelopes

Although the dependence of convective core overshooting on mass has attracted much attention, no corresponding work exists for overshooting below a convective envelope. We aim to quantify this relationship for pre-main sequence stars of intermediate mass ranging from $1.2 M_{\mathsf{sun}}$ to $6 M_{\mathsf{sun}}$. These stars have a similar thermal and density structure, making this a suitable choice to isolate the effect of changing mass. We produce a series of two-dimensional global simulations of stars using MUSIC, a fully compressible, time-implicit hydrodynamics code. The stars that we select for this study are near the end of the pre-main sequence and are convectively unstable above 80% of their stellar radius; they thus have a convective envelope that is shallower than the current sun. For this series of stellar models, a simple scaling with luminosity, with a scaling exponent of 1/4, accounts for the increasing overshooting with stellar mass. This result has interesting similarities with the scaling found by Baraffe et al. [2023] for a range of intermediate mass and massive stars at the zero-age main sequence (ZAMS) that have convective cores.

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arXiv2025

Discovery of the pre-main-sequence eclipsing binary MML 48

We present the discovery of the eclipsing binary MML 48, which is a member of Upper Centaurus Lupus, has an associated age of 16 Myr, and is composed of two young, low-mass stars. We used space- and ground-based observations to characterize the system with both time-series photometry and spectroscopy. Given the extreme mass ratio between the stars, q_EB = 0.209 +- 0.014, we modeled a single-lined spectroscopic and eclipsing binary system. The orbital period, 2.0171068 +- 0.0000004 d, is measured from the highest precision light curves. We derive a primary mass of 1.2 +- 0.07 Msun using stellar models, and with radial velocities we measured a secondary mass of 0.2509 +- 0.0078 Msun. The radii are large, as expected for pre-main-sequence stars, and are measured as 1.574 +- 0.026 +- 0.050 Rsun and 0.587 +- 0.0095 +- 0.050 Rsun, for the primary and secondary stars, respectively. MML 48 joins the short list of known low-mass, pre-main-sequence eclipsing binaries (EBs), being one of only five systems with intermediate ages (15-25 Myr), and the system with the most extreme mass ratio. The primary star is currently at the "fusion bump", undergoing an over-production of energy in the core due to the build-up of 3He before reaching its equilibrium abundance set by the proton-proton (p-p) I chain. MML 48 A is the first young star in an eclipsing system that has been found during its fusion bump. MML 48 is thus an important benchmark for low-mass stellar evolution at a time when the stars are rapidly changing, which allows for a tight constraint on the corresponding isochrone given the uneven mass ratio.

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arXiv2024

JWST/NIRSpec Observations of Brown Dwarfs in the Orion Nebula Cluster

We have used the multiobject mode of the Near-Infrared Spectrograph (NIRSpec) on board the James Webb Space Telescope (JWST) to obtain low-resolution 1-5um spectra of 22 brown dwarf candidates in the Orion Nebula Cluster, which were selected with archival images from the Hubble Space Telescope. One of the targets was previously classified as a Herbig-Haro (HH) object and exhibits strong emission in H I, H2, and the fundamental band of CO, further demonstrating that HH objects can have bright emission in that CO band. The remaining targets have late spectral types (M6.5 to early L) and are young based on gravity sensitive features, as expected for low-mass members of the cluster. According to theoretical evolutionary models, these objects should have masses that range from the hydrogen burning limit to 0.003-0.007 Msun. Two of the NIRSpec targets were identified as proplyds in earlier analysis of Hubble images. They have spectral types of M6.5 and M7.5, making them two of the coolest and least massive known proplyds. Another brown dwarf shows absorption bands at 3-5um from ices containing H2O, CO2, OCN-, and CO, indicating that it is either an edge-on class II system or a class I protostar. It is the coolest and least massive object that has detections of these ice features. In addition, it appears to be the first candidate for a protostellar brown dwarf that has spectroscopy confirming its late spectral type.

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arXiv2024

The shape of convection in 2D and 3D global simulations of stellar interiors

Theoretical descriptions of convective overshooting often rely on a one-dimensional parameterization of the flow called the filling factor for convection. Several definitions of the filling factor have been developed, based on: (1) the percentage of the volume, (2) the mass flux, and (3) the convective flux that moves through the boundary. We examine these definitions of the filling factor with the goal of establishing their ability to explain differences between 2D and 3D global simulations of stellar interiors that include fully compressible hydrodynamics and realistic microphysics for stars. We study pairs of identical two- and three-dimensional global simulations of stars produced with MUSIC, a fully compressible, time-implicit hydrodynamics code. We examine (1) a $3 M_\odot$ red giant star near the first dredge-up point, (2) a $1 M_\odot$ pre-main-sequence star with a large convection zone, (3) the current sun, and (4) a $20 M_\odot$ main-sequence star with a large convective core. Our calculations of the filling factor based on the volume percentage and the mass flux indicate asymmetrical convection near the surface for each star with an outer convection zone. However, near the convective boundary, convective flows achieve inward-outward symmetry; for 2D and 3D simulations, these filling factors are indistinguishable. A filling factor based on the convective flux is contaminated by boundary-layer-like flows, making theoretical interpretation difficult. We present two new alternatives to these standard definitions, which compare flows at two different radial points. The first is the penetration parameter of Anders et al. (2022). The second is a new statistic, the plume interaction parameter. We demonstrate that both of these parameters capture systematic differences between 2D and 3D simulations around the convective boundary.

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arXiv2023

JWST/NIRSpec Observations of the Coldest Known Brown Dwarf

We present 1-5um spectroscopy of the coldest known brown dwarf, WISE J085510.83-071442.5 (WISE 0855), performed with the Near-Infrared Spectrograph (NIRSpec) on board the James Webb Space Telescope (JWST). NIRSpec has dramatically improved the measurement of spectral energy distribution of WISE 0855 in terms of wavelength coverage, signal-to-noise ratios, and spectral resolution. We have performed preliminary modeling of the NIRSpec data using the ATMO 2020 models of cloudless atmospheres, arriving at a best fitting model that has T_eff=285 K. That temperature is ~20 K higher than the value derived by combining our luminosity estimate with evolutionary models (i.e., the radius in the model fit to the SED is somewhat smaller than expected from evolutionary models). Through comparisons to the model spectra, we detect absorption in the fundamental band of CO, which is consistent with an earlier detection in a ground-based spectrum and indicates the presence of vertical mixing. Although PH_3 is expected in Y dwarfs that experience vertical mixing, it is not detected in WISE 0855. Previous ground-based M-band spectroscopy of WISE 0855 has been cited for evidence of H_2O ice clouds, but we find that the NIRSpec data in that wavelength range are matched well by our cloudless model. Thus, clear evidence of H_2O ice clouds in WISE 0855 has not been identified yet, but it may still be present in the NIRSpec data. The physical properties of WISE 0855, including the presence of H_2O clouds, can be better constrained by more detailed fitting with both cloudless and cloudy models and the incorporation of unpublished 5-28um data from the Mid-infrared Instrument on JWST.

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arXiv2023

First light of VLT/HiRISE: High-resolution spectroscopy of young giant exoplanets

A major endeavor of this decade is the direct characterization of young giant exoplanets at high spectral resolution to determine the composition of their atmosphere and infer their formation processes and evolution. Such a goal represents a major challenge owing to their small angular separation and luminosity contrast with respect to their parent stars. Instead of designing and implementing completely new facilities, it has been proposed to leverage the capabilities of existing instruments that offer either high contrast imaging or high dispersion spectroscopy, by coupling them using optical fibers. In this work we present the implementation and first on-sky results of the HiRISE instrument at the very large telescope (VLT), which combines the exoplanet imager SPHERE with the recently upgraded high resolution spectrograph CRIRES using single-mode fibers. The goal of HiRISE is to enable the characterization of known companions in the $H$ band, at a spectral resolution of the order of $R = \lambda/\Delta\lambda = 100\,000$, in a few hours of observing time. We present the main design choices and the technical implementation of the system, which is constituted of three major parts: the fiber injection module inside of SPHERE, the fiber bundle around the telescope, and the fiber extraction module at the entrance of CRIRES. We also detail the specific calibrations required for HiRISE and the operations of the instrument for science observations. Finally, we detail the performance of the system in terms of astrometry, temporal stability, optical aberrations, and transmission, for which we report a peak value of $\sim$3.9% based on sky measurements in median observing conditions. Finally, we report on the first astrophysical detection of HiRISE to illustrate its potential.

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arXiv2023

Two-dimensional simulations of internal gravity waves in a 5 $M_{\odot}$ Zero-Age-Main-Sequence model

Main-sequence intermediate-mass stars present a radiative envelope that supports internal gravity waves (IGWs). Excited at the boundary with the convective core, IGWs propagate towards the stellar surface and are suspected to impact physical processes such as rotation and chemical mixing. Using the fully compressible time-implicit code MUSIC, we study IGWs in two-dimensional simulations of a zero-age-main-sequence 5 solar mass star model up to 91\% of the stellar radius with different luminosity and radiative diffusivity enhancements. Our results show that low frequency waves excited by core convection are strongly impacted by radiative effects as they propagate. This impact depends on the radial profile of radiative diffusivity which increases by almost 5 orders of magnitude between the centre of the star and the top of the simulation domain. In the upper layers of the simulation domain, we observe an increase of the temperature. Our study suggests that this is due to heat added in these layers by IGWs damped by radiative diffusion. We show that non-linear effects linked to large amplitude IGWs may be relevant just above the convective core. Both these effects are intensified by the artificial enhancement of the luminosity and radiative diffusivity, with enhancement factors up to $10^4$ times the realistic values. Our results also highlight that direct comparison between numerical simulations with enhanced luminosity and observations must be made with caution. Finally, our work suggests that thermal effects linked to the damping of IGWs could have a non-negligible impact on stellar structure.

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arXiv2023

A study of convective core overshooting as a function of stellar mass based on two-dimensional hydrodynamical simulations

We perform two-dimensional numerical simulations of core convection for zero-age-main-sequence stars covering a mass range from 3 $M_\odot$ to 20 $M_\odot$. The simulations are performed with the fully compressible time-implicit code MUSIC. We study the efficiency of overshooting, which describes the ballistic process of convective flows crossing a convective boundary, as a function of stellar mass and luminosity. We also study the impact of artificially increasing the stellar luminosity for 3 $M_\odot$ models. The simulations cover hundreds to thousands of convective turnover timescales. Applying the framework of extreme plume events previously developed for convective envelopes, we derive overshooting lengths as a function of stellar masses. We find that the overshooting distance ($d_{\rm ov}$) scales with the stellar luminosity ($L$) and the convective core radius ($r_{\rm conv}$). We derive a scaling law $d_{\rm ov} \propto L^{1/3} r_{\rm conv}^{1/2}$ which is implemented in a 1D stellar evolution code and the resulting stellar models are compared to observations. The scaling predicts values for the overshooting distance that significantly increase with stellar mass, in qualitative agreement with observations. Quantitatively, however, the predicted values are underestimated for masses $\gtrsim 10 M_\odot$. Our 2D simulations show the formation of a nearly-adiabatic layer just above the Schwarzschild boundary of the convective core, as exhibited in recent 3D simulations of convection. The most luminous models show a growth in size with time of the nearly-adiabatic layer. This growth seems to slow down as the upper edge of the nearly-adiabatic layer gets closer to the maximum overshooting length and as the simulation time exceeds the typical thermal diffusive timescale in the overshooting layer.

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arXiv2022

Impact of a new H/He equation of state on the evolution of massive brown dwarfs. New determination of the hydrogen burning limit

We have explored the impact of the latest equation of state (EOS) for dense hydrogen-helium mixtures (Chabrier \& Debras 2021), which takes into account the interactions between hydrogen and helium species, upon the evolution of very low mass stars and brown dwarfs (BD). These interactions modify the thermodynamic properties of the H/He mixture, notably the entropy, a quantity of prime importance for these fully convective bodies, but also the onset and the development of degeneracy throughout the body. This translates into a faster cooling rate, i.e. cooler isentropes for a given mass and age, and thus larger brown dwarf masses and smaller radii for given effective temperature and luminosity than the models based on previous EOSs. This means that objects of a given mass and age, in the range $M\lesssim 0.1\,\msol$, $\tau\gtrsim 10^8$ yr, will have cooler effective temperatures and fainter luminosities. Confronting these new models with several observationally determined BD dynamical masses, we show that this improves the agreement between evolutionary models and observations and resolves at least part of the observed discrepancies between the properties of dynamical mass determinations and evolutionary models. A noticeable consequence of this improvement of the dense H/He EOS is that it yields a larger H-burning minimum mass, now found to be $0.075\,\msol$ ($78.5\,\mjup$) with the ATMO atmosphere models for solar metallicity. These updated brown dwarf models are made publicly available.

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arXiv2022

Connecting SPHERE and CRIRES+ for the characterisation of young exoplanets at high spectral resolution: status update of VLT/HiRISE

New generation exoplanet imagers on large ground-based telescopes are highly optimised for the detection of young giant exoplanets in the near-infrared, but they are intrinsically limited for their characterisation by the low spectral resolution of their integral field spectrographs ($R<100$). High-dispersion spectroscopy at $R \gg 10^4$ would be a powerful tool for the characterisation of these planets, but there is currently no high-resolution spectrograph with extreme adaptive optics and coronagraphy that would enable such characterisation. With project HiRISE we propose to use fiber coupling to combine the capabilities of two flagship instruments at the Very Large Telescope in Chile: the exoplanet imager SPHERE and the high-resolution spectrograph CRIRES+. The coupling will be implemented at the telescope in early 2023. We provide a general overview of the implementation of HiRISE, of its assembly, integration and testing (AIT) phase in Europe, and a brief assessment of its expected performance based on the final hardware.

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arXiv2022

Impact of radial truncation on global 2D hydrodynamic simulations for a Sun-like model

Stellar convection is a non-local process responsible for the transport of heat and chemical species. It can lead to enhanced mixing through convective overshooting and excitation of internal gravity waves (IGWs) at convective boundaries. The relationship between these processes is still not well understood and requires global hydrodynamic simulations to capture the important large-scale dynamics. The steep stratification in stellar interiors suggests that the radial extent of such simulations can affect the convection dynamics, the IGWs in the stably stratified radiative zone, and the depth of the overshooting layer. We investigate these effects using two-dimensional global simulations performed with the fully compressible stellar hydrodynamics code MUSIC. We compare eight different radial truncations of the same solar-like stellar model evolved over approximately 400 convective turnover times. We find that the location of the inner boundary has an insignificant effect on the convection dynamics, the convective overshooting and the travelling IGWs. We relate this to the background conditions at the lower convective boundary which are unaffected by the truncation, as long as a significantly deep radiative layer is included in the simulation domain. However, we find that extending the outer boundary by only a few percent of the stellar radius significantly increases the velocity and temperature perturbations in the convection zone, the overshooting depth, the power and the spectral slope of the IGWs. The effect is related to the background conditions at the outer boundary, which are determined in essence by the hydrostatic stratification and the given luminosity.

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arXiv2022

Two-dimensional simulations of solar-like models with artificially enhanced luminosity. II. Impact on internal gravity waves

Artificially increasing the luminosity and the thermal diffusivity of a model is a common tactic adopted in hydrodynamical simulations of stellar convection. In this work, we analyse the impact of these artificial modifications on the physical properties of stellar interiors and specifically on internal gravity waves. We perform two-dimensional simulations of solar-like stars with the MUSIC code. We compare three models with different luminosity enhancement factors to a reference model. The results confirm that properties of the waves are impacted by the artificial enhancement of the luminosity and thermal diffusivity. We find that an increase in the stellar luminosity yields a decrease in the bulk convective turnover timescale and an increase in the characteristic frequency of excitation of the internal waves. We also show that a higher energy input in a model, corresponding to a larger luminosity, results in higher energy in high frequency waves. Across our tests with the luminosity and thermal diffusivity enhanced together by up to a factor of 104, our results are consistent with theoretical predictions of radiative damping. Increasing the luminosity also has an impact on the amplitude of oscillatory motions across the convective boundary. One must use caution when interpreting studies of internal gravity waves based on hydrodynamical simulations with artificially enhanced luminosity.

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arXiv2021

Dynamics in a stellar convective layer and at its boundary: Comparison of five 3D hydrodynamics codes

Our ability to predict the structure and evolution of stars is in part limited by complex, 3D hydrodynamic processes such as convective boundary mixing. Hydrodynamic simulations help us understand the dynamics of stellar convection and convective boundaries. However, the codes used to compute such simulations are usually tested on extremely simple problems and the reliability and reproducibility of their predictions for turbulent flows is unclear. We define a test problem involving turbulent convection in a plane-parallel box, which leads to mass entrainment from, and internal-wave generation in, a stably stratified layer. We compare the outputs from the codes FLASH, MUSIC, PPMSTAR, PROMPI, and SLH, which have been widely employed to study hydrodynamic problems in stellar interiors. The convection is dominated by the largest scales that fit into the simulation box. All time-averaged profiles of velocity components, fluctuation amplitudes, and fluxes of enthalpy and kinetic energy are within $\lesssim 3\sigma$ of the mean of all simulations on a given grid ($128^3$ and $256^3$ grid cells), where $\sigma$ describes the statistical variation due to the flow's time dependence. They also agree well with a $512^3$ reference run. The $128^3$ and $256^3$ simulations agree within $9\%$ and $4\%$, respectively, on the total mass entrained into the convective layer. The entrainment rate appears to be set by the amount of energy that can be converted to work in our setup and details of the small-scale flows in the boundary layer seem to be largely irrelevant. Our results lend credence to hydrodynamic simulations of flows in stellar interiors. We provide in electronic form all outputs of our simulations as well as all information needed to reproduce or extend our study.

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arXiv2021

Two-dimensional simulations of solar-like models with artificially enhanced luminosity -- I. Impact on convective penetration

We perform 2D, fully compressible, time-implicit simulations of convection in a solar-like model with the MUSIC code. Our main motivation is to explore the impact of a common tactic adopted in numerical simulations of convection that use realistic stellar conditions. This tactic is to artificially increase the luminosity and to modify the thermal diffusivity of the reference stellar model. This work focuses on the impact of these modifications on convective penetration (or overshooting) at the base of the convective envelope of a solar-like model. We explore a range of enhancement factors for the energy input and confirm the increase in the characteristic overshooting depth with the increase in the energy input. Our results highlight the importance of the impact of penetrative downflows on the thermal background below the convective boundary. This is a result of compression and shear which induce local heating and thermal mixing. The artificial increase in the energy flux intensifies the heating process by increasing the velocities in the convective zone and at the convective boundary, revealing a subtle connection between the local heating of the thermal background and the plume dynamics. This heating also increases the efficiency of heat transport by radiation which may counterbalance further heating and helps to establish a steady state. The modification of the thermal background by penetrative plumes impacts the width of the overshooting layer. Our results suggest that an artificial modification of the radiative diffusivity in the overshooting layer, rather than only accelerating the thermal relaxation, could also alter the dynamics of the penetrating plumes and thus the width of the overshooting layer. Results from simulations with an artificial modification of the energy flux and of the thermal diffusivity should be regarded with caution if used to determine an overshooting width.

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arXiv2020

Rotational spectral modulation of cloudless atmospheres for L/T Brown Dwarfs and Extrasolar Giant Planets

The rotational spectral modulation (spectro-photometric variability) of brown dwarfs is usually interpreted as a sign of the presence of inhomogeneous cloud covers in the atmosphere. This paper aims at exploring the role of temperature fluctuations in these spectral modulations. These fluctuations could naturally arise in a convective atmosphere impacted by diabatic processes such as complex chemistry, i.e. the recently proposed mechanism to explain the L/T transition: CO/CH4 radiative convection. We use the 1D radiative/convective code ATMO with ad-hoc modifications of the temperature gradient to model the rotational spectral modulation of 2MASS 1821, 2MASS 0136, and PSO 318.5-22. Modeling the spectral bright-to-faint ratio of the modulation of 2MASS 1821, 2MASS 0136, and PSO 318.5-22 shows that most spectral characteristics can be reproduced by temperature variations alone. Furthermore, the approximately anti-correlated variability between different wavelengths can be easily interpreted as a change in the temperature gradient in the atmosphere which is the consequence we expect from CO/CH4 radiative convection to explain the L/T transition. The deviation from an exact anti-correlation could then be interpreted as a phase shift similar to the hot-spot shift a different bandpasses in the atmosphere of hot Jupiters. Our results suggest that the rotational spectral modulation from cloud-opacity and temperature variations are degenerate. The detection of direct cloud spectral signatures, e.g. the silicate absorption feature at 10 um, would help to confirm the presence of clouds and their contribution to spectral modulations. Future studies looking at the differences in the spectral modulation of objects with and without the silicate absorption feature may give us some insight on how to distinguish cloud-opacity fluctuations from temperature fluctuations.

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arXiv2020

Direct characterization of young giant exoplanets at high spectral resolution by coupling SPHERE and CRIRES+

Studies of atmospheres of directly imaged exoplanets with high-resolution spectrographs have shown that their characterization is predominantly limited by noise on the stellar halo at the location of the studied exoplanet. An instrumental combination of high-contrast imaging and high spectral resolution that suppresses this noise and resolves the spectral lines can therefore yield higher quality spectra. We study the performance of the proposed HiRISE fiber coupling between the SPHERE and CRIRES+ at the VLT for spectral characterization of directly imaged planets. Using end-to-end simulations of HiRISE we determine the S/N of the detection of molecular species for known exoplanets in $H$ and $K$ bands, and compare them to CRIRES+. We investigate the ultimate detection limits of HiRISE as a function of stellar magnitude, and we quantify the impact of different coronagraphs and of the system transmission. We find that HiRISE largely outperforms CRIRES+ for companions around bright hosts like $\beta$ Pic or 51 Eri. For an $H=3.5$ host, we observe a gain of a factor of up to 16 in observing time with HiRISE to reach the same S/N on a companion at 200 mas. More generally, HiRISE provides better performance than CRIRES+ in two-hour integration times between 50-350 mas for hosts with $H<8.5$ and between 50-700 mas for $H<7$. For fainter hosts like PDS 70 and HIP 65426, no significant improvements are observed. We find that using no coronagraph yields the best S/N when characterizing known exoplanets due to higher transmission and fiber-based starlight suppression. We demonstrate that the overall transmission of the system is in fact the main driver of performance. Finally, we show that HiRISE outperforms the best detection limits of SPHERE for bright stars, opening major possibilities for the characterization of future planetary companions detected by other techniques.

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arXiv2020

Comparison of two- and three-dimensional compressible convection in a pre-main sequence star

Extending our recent studies of two-dimensional stellar convection to 3D, we compare three-dimensional hydrodynamic simulations to identically set-up two-dimensional simulations, for a realistic pre-main sequence star. We compare statistical quantities related to convective flows including: average velocity, vorticity, local enstrophy, and penetration depth beneath a convection zone. These statistics are produced during stationary, steady-state compressible convection in the star's convection zone. Our simulations with the MUSIC code confirm the common result that two-dimensional simulations of stellar convection have a higher magnitude of velocity on average than three-dimensional simulations. Boundary conditions and the extent of the spherical shell can affect the magnitude and variability of convective velocities. The difference between 2D and 3D velocities is dependent on these background points; in our simulations this can have an effect as large as the difference resulting from the dimensionality of the simulation. Nevertheless, radial velocities near the convective boundary are comparable in our 2D and 3D simulations. The average local enstrophy of the flow is lower for two-dimensional simulations than for three-dimensional simulations, indicating a different shape and structuring of 3D stellar convection. We perform a statistical analysis of the depth of convective penetration below the convection zone, using the model proposed in our recent study (Pratt et al. 2017). Here we analyze the convective penetration in three dimensional simulations, and compare the results to identically set-up 2D simulations. In 3D the penetration depth is as large as the penetration depth calculated from 2D simulations.

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