arXiv subjects

S. Sousa

Publications and source records attributed to S. Sousa.

At least 37 records · Page 2Linked to original sources

arXiv2021

Determination of stellar parameters for Ariel targets: a comparison analysis between different spectroscopic methods

Ariel has been selected as the next ESA M4 science mission and it is expected to be launched in 2028. During its 4-year mission, Ariel will observe the atmospheres of a large and diversified population of transiting exoplanets. A key factor for the achievement of the scientific goal of Ariel is the selection strategy for the definition of the input target list. A meaningful choice of the targets requires an accurate knowledge of the planet hosting star properties and this is necessary to be obtained well before the launch. In this work, we present the results of a bench-marking analysis between three different spectroscopic techniques used to determine stellar parameters for a selected number of targets belonging to the Ariel reference sample. We aim to consolidate a method that will be used to homogeneously determine the stellar parameters of the complete Ariel reference sample. Homogeneous, accurate and precise derivation of stellar parameters is crucial for characterizing exoplanet-host stars and in turn is a key factor for the accuracy of the planet properties.

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arXiv2020

Atmospheric Rossiter-McLaughlin effect and transmission spectroscopy of WASP-121b with ESPRESSO

WASP-121b is one of the most studied Ultra-hot Jupiters: many recent analyses of its atmosphere report interesting features at different wavelength ranges. In this paper we analyze one transit of WASP-121b acquired with the high-resolution spectrograph ESPRESSO at VLT in 1-telescope mode, and one partial transit taken during the commissioning of the instrument in 4-telescope mode. We investigate the anomalous in-transit radial velocity curve and study the transmission spectrum of the planet. By analysing the in-transit radial velocities we were able to infer the presence of the atmospheric Rossiter-McLaughlin effect. We measured the height of the planetary atmospheric layer that correlates with the stellar mask (mainly Fe) to be 1.052$\pm$0.015 Rp and we also confirmed the blueshift of the planetary atmosphere. By examining the planetary absorption signal on the stellar cross-correlation functions we confirmed the presence of a temporal variation of its blueshift during transit, which could be investigated spectrum-by-spectrum. We detected significant absorption in the transmission spectrum for Na, H, K, Li, CaII, Mg, and we certified their planetary nature by using the 2D tomographic technique. Particularly remarkable is the detection of Li, with a line contrast of $\sim$0.2% detected at the 6$σ$ level. With the cross-correlation technique we confirmed the presence of FeI, FeII, CrI and VI. H$α$ and CaII are present up to very high altitudes in the atmosphere ($\sim$1.44 Rp and $\sim$2 Rp, respectively), and also extend beyond the transit-equivalent Roche lobe radius of the planet. These layers of the atmosphere have a large line broadening that is not compatible with being caused by the tidally-locked rotation of the planet alone, and could arise from vertical winds or high-altitude jets in the evaporating atmosphere.

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arXiv2020

Planetary system LHS 1140 revisited with ESPRESSO and TESS

LHS 1140 is an M dwarf known to host two known transiting planets at orbital periods of 3.77 and 24.7 days. The external planet (LHS 1140 b) is a rocky super-Earth that is located in the middle of the habitable zone of this low-mass star, placing this system at the forefront of the habitable exoplanet exploration. We further characterize this system by improving the physical and orbital properties and search for additional planetary-mass components in the system, also exploring the possibility of co-orbitals. We collected 113 new radial velocity observations with ESPRESSO over a 1.5-year time span with an average photon-noise precision of 1.07 m/s. We determine new masses with a precision of 6% for LHS 1140 b ($6.48 \pm 0.46~M_{\oplus}$) and 9% for LHS 1140 c ($m_c=1.78 \pm 0.17~M_{\oplus}$), reducing by half the previously published uncertainties. Although both planets have Earth-like bulk compositions, the internal structure analysis suggests that LHS 1140 b might be iron-enriched. In both cases, the water content is compatible to a maximum fraction of 10-12% in mass, which is equivalent to a deep ocean layer of $779 \pm 650$ km for the habitable-zone planet LHS 1140 b. Our results also provide evidence for a new planet candidate in the system ($m_d= 4.8\pm1.1~M_{\oplus}$) on a ~78.9-day orbital period, which is detected through three independent methods. The analysis also allows us to discard other planets above 0.5 $M_{\oplus}$ for periods shorter than 10 days and above 2 $M_{\oplus}$ for periods up to one year. Finally, our analysis discards co-orbital planets of LHS 1140 b down to 1 $M_{\oplus}$. Indications for a possible co-orbital signal in LHS 1140 c are detected in both radial velocity and photometric data, however. The new characterization of the system make it a key target for atmospheric studies of rocky worlds at different stellar irradiations

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arXiv2020

The Gaia-ESO Survey: Calibrating the lithium-age relation with open clusters and associations. I. Cluster age range and initial membership selections

Previous studies of open clusters have shown that lithium depletion is not only strongly age dependent but also shows a complex pattern with other parameters that is not yet understood. For pre- and main-sequence late-type stars, these parameters include metallicity, mixing mechanisms, convection structure, rotation, and magnetic activity. We perform a thorough membership analysis for a large number of stars observed within the Gaia-ESO survey (GES) in the field of 20 open clusters, ranging in age from young clusters and associations, to intermediate-age and old open clusters. Based on the parameters derived from the GES spectroscopic observations, we obtained lists of candidate members for each of the clusters in the sample by deriving RV distributions and studying the position of the kinematic selections in the EW(Li) versus Teff plane to obtain lithium members. We used gravity indicators to discard field contaminants and studied [Fe/H] metallicity to further confirm the membership of the candidates. We also made use of studies using recent data from the Gaia DR1 and DR2 releases to assess our member selections. We identified likely member candidates for the sample of 20 clusters observed in GES (iDR4) with UVES and GIRAFFE, and conducted a comparative study that allowed us to characterize the properties of these members, as well as identify field contaminant stars, both lithium-rich giants and non-giant outliers. This work is the first step towards the calibration of the lithium-age relation and its dependence on other GES parameters. During this project we aim to use this relation to infer the ages of GES field stars, and identify their potential membership to young associations and stellar kinematic groups of different ages.

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arXiv2020

The Gaia-ESO Survey: Spectroscopic-asteroseismic analysis of K2 stars in Gaia-ESO

The extensive stellar spectroscopic datasets that are available for studies in Galactic Archeaology thanks to, for example, the Gaia-ESO Survey, now benefit from having a significant number of targets that overlap with asteroseismology projects such as Kepler, K2 and CoRoT. Combining the measurements from spectroscopy and asteroseismology allows us to attain greater accuracy with regard to the stellar parameters needed to characterise the stellar populations of the Milky Way. The aim of this Gaia-ESO Survey special project is to produce a catalogue of self-consistent stellar parameters by combining measurements from high-resolution spectroscopy and precision asteroseismology. We carried out an iterative analysis of 90 K2@Gaia-ESO red giants. The spectroscopic values of Teff were used as input in the seismic analysis to obtain log(g) values. The seismic estimates of log(g) were then used to re-determine the spectroscopic values of Teff and [Fe/H]. Only one iteration was required to obtain parameters that are in good agreement for both methods and thus, to obtain the final stellar parameters. A detailed analysis of outliers was carried out to ensure a robust determination of the parameters. The results were then combined with Gaia DR2 data to compare the seismic log(g) with a parallax-based log(g) and to investigate instances of variations in the velocity and possible binaries within the dataset. This analysis produced a high-quality catalogue of stellar parameters for 90 red giant stars observed by both K2 and Gaia-ESO that were determined through iterations between spectroscopy and asteroseismology. We compared the seismic gravities with those based on Gaia parallaxes to find an offset which is similar to other studies that have used asteroseismology. Our catalogue also includes spectroscopic chemical abundances and radial velocities, as well as indicators for possible binary detections.

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arXiv2020

The Gaia-ESO survey: the non-universality of the age-chemical-clocks-metallicity relations in the Galactic disc

In the era of large spectroscopic surveys, massive databases of high-quality spectra provide tools to outline a new picture of our Galaxy. In this framework, an important piece of information is provided by our ability to infer stellar ages. We aim to provide empirical relations between stellar ages and abundance ratios for a sample of solar-like stars. We investigate the dependence on metallicity, and we apply our relations to Gaia-ESO samples of open clusters and field stars. We analyse high-resolution and high-S/N HARPS spectra of a sample of solar-like stars to obtain precise determinations of their atmospheric parameters and abundances through differential spectral analysis and age through isochrone fitting. We investigate the relations between ages and abundance ratios. For the abundance ratios with a steeper dependence on age, we perform multivariate linear regressions, including the dependence on metallicity. We apply our relations to a sample of open clusters located in 4 7 kpc. In these clusters, the content of s-elements is lower than expected from chemical evolution models, and consequently the [s/$α$] are lower than in clusters of the same age located in the solar neighbourhood. With our chemical evolution model and a set of empirical yields, we suggest that a strong dependence on the star formation history and metallicity-dependent yields of s-elements can substantially modify the slope of the [s/$α$]-[Fe/H]-age relation in different regions of the Galaxy. Our results point towards a non-universal relation [s/$α$]-[Fe/H]-age, indicating the existence of relations at different R$_{GC}$ or for different star formation history. A better understanding of the s-process at high metallicity is necessary to fully understand the origin of these variations.

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arXiv2020

Revisiting Proxima with ESPRESSO

We aim to confirm the presence of Proxima b using independent measurements obtained with the new ESPRESSO spectrograph, and refine the planetary parameters taking advantage of its improved precision. We analysed 63 spectroscopic ESPRESSO observations of Proxima taken during 2019. We obtained radial velocity measurements with a typical radial velocity photon noise of 26 cm/s. We ran a joint MCMC analysis on the time series of the radial velocity and full-width half maximum of the cross-correlation function to model the planetary and stellar signals present in the data, applying Gaussian process regression to deal with stellar activity. We confirm the presence of Proxima b independently in the ESPRESSO data. The ESPRESSO data on its own shows Proxima b at a period of 11.218 $\pm$ 0.029 days, with a minimum mass of 1.29 $\pm$ 0.13 Me. In the combined dataset we measure a period of 11.18427 $\pm$ 0.00070 days with a minimum mass of 1.173 $\pm$ 0.086 Me. We find no evidence of stellar activity as a potential cause for the 11.2 days signal. We find some evidence for the presence of a second short-period signal, at 5.15 days with a semi-amplitude of merely 40 cm/s. If caused by a planetary companion, it would correspond to a minimum mass of 0.29 $\pm$ 0.08 Me. We find that the FWHM of the CCF can be used as a proxy for the brightness changes and that its gradient with time can be used to successfully detrend the radial velocity data from part of the influence of stellar activity. The activity-induced radial velocity signal in the ESPRESSO data shows a trend in amplitude towards redder wavelengths. Velocities measured using the red end of the spectrograph are less affected by activity, suggesting that the stellar activity is spot-dominated. The data collected excludes the presence of extra companions with masses above 0.6 Me at periods shorter than 50 days.

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arXiv2019

Hot, rocky and warm, puffy super-Earths orbiting TOI-402 (HD 15337)

TESS is revolutionising the search for planets orbiting bright and nearby stars. In sectors 3 and 4, TESS observed TOI-402 (TIC-120896927), a bright V=9.1 K1 dwarf also known as HD 15337, and found two transiting signals with period of 4.76 and 17.18 days and radius of 1.90 and 2.21\,\Rearth. This star was observed as part of the radial-velocity search for planets using the HARPS spectrometer, and 85 precise radial-velocity measurements were obtained over a period of 14 years. In this paper, we analyse the HARPS radial-velocity measurements in hand to confirm the planetary nature of these two signals. By reanalysing TESS photometry and host star parameters using EXOFASTv2, we find that TOI-402.01 and TOI-402.02 have periods of 4.75642$\pm$0.00021 and 17.1784$\pm$0.0016 days and radii of 1.70$\pm$0.06 and 2.52$\pm$0.11\,\Rearth\,(precision 3.6 and 4.2\%), respectively. By analysing the HARPS radial-velocity measurements, we find that those planets are both super-Earths with masses of 7.20$\pm$0.81 and 8.79$\pm$1.67\,\Mearth\,(precision 11.3 and 19.0\%), and small eccentricities compatible with zero at 2$σ$. Although having rather similar masses, the radius of these two planets is really different, putting them on different sides of the radius gap. With stellar irradiation 160 times more important than Earth for TOI-402.01 and only 29 times more for TOI-402.02, it is likely that photo-evaporation is at the origin of this radius difference. Those two planets, being in the same system and therefore being in the same irradiation environment are therefore extremely important to perform comparative exoplanetology across the evaporation valley and thus bring constraints on the mechanisms responsible for the radius gap.

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arXiv2017

The Gaia-ESO Survey: radial distribution of abundances in the Galactic disc from open clusters and young field stars

The spatial distribution of elemental abundances in the disc of our Galaxy gives insights both on its assembly process and subsequent evolution, and on the stellar nucleogenesis of the different elements. Gradients can be traced using several types of objects as, for instance, (young and old) stars, open clusters, HII regions, planetary nebulae. We aim at tracing the radial distributions of abundances of elements produced through different nucleosynthetic channels -the alpha-elements O, Mg, Si, Ca and Ti, and the iron-peak elements Fe, Cr, Ni and Sc - by using the Gaia-ESO idr4 results of open clusters and young field stars. From the UVES spectra of member stars, we determine the average composition of clusters with ages >0.1 Gyr. We derive statistical ages and distances of field stars. We trace the abundance gradients using the cluster and field populations and we compare them with a chemo-dynamical Galactic evolutionary model. Results. The adopted chemo-dynamical model, with the new generation of metallicity-dependent stellar yields for massive stars, is able to reproduce the observed spatial distributions of abundance ratios, in particular the abundance ratios of [O/Fe] and [Mg/Fe] in the inner disc (5 kpc<RGC <7 kpc), with their differences, that were usually poorly explained by chemical evolution models. Often, oxygen and magnesium are considered as equivalent in tracing alpha-element abundances and in deducing, e.g., the formation time-scales of different Galactic stellar populations. In addition, often [alpha/Fe] is computed combining several alpha-elements. Our results indicate, as expected, a complex and diverse nucleosynthesis of the various alpha-elements, in particular in the high metallicity regimes, pointing towards a different origin of these elements and highlighting the risk of considering them as a single class with common features.

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arXiv2017

The $Gaia$-ESO Survey: the inner disk intermediate-age open cluster NGC 6802

Milky Way open clusters are very diverse in terms of age, chemical composition, and kinematic properties. Intermediate-age and old open clusters are less common, and it is even harder to find them inside the solar Galactocentric radius, due to the high mortality rate and strong extinction inside this region. NGC 6802 is one of the inner disk open clusters (IOCs) observed by the $Gaia$-ESO survey (GES). This cluster is an important target for calibrating the abundances derived in the survey due to the kinematic and chemical homogeneity of the members in open clusters. Using the measurements from $Gaia$-ESO internal data release 4 (iDR4), we identify 95 main-sequence dwarfs as cluster members from the GIRAFFE target list, and eight giants as cluster members from the UVES target list. The dwarf cluster members have a median radial velocity of $13.6\pm1.9$ km s$^{-1}$, while the giant cluster members have a median radial velocity of $12.0\pm0.9$ km s$^{-1}$ and a median [Fe/H] of $0.10\pm0.02$ dex. The color-magnitude diagram of these cluster members suggests an age of $0.9\pm0.1$ Gyr, with $(m-M)_0=11.4$ and $E(B-V)=0.86$. We perform the first detailed chemical abundance analysis of NGC 6802, including 27 elemental species. To gain a more general picture about IOCs, the measurements of NGC 6802 are compared with those of other IOCs previously studied by GES, that is, NGC 4815, Trumpler 20, NGC 6705, and Berkeley 81. NGC 6802 shows similar C, N, Na, and Al abundances as other IOCs. These elements are compared with nucleosynthetic models as a function of cluster turn-off mass. The $α$, iron-peak, and neutron-capture elements are also explored in a self-consistent way.

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arXiv2017

The Gaia-ESO Survey: Structural and dynamical properties of the young cluster Chamaeleon I

The young (~2 Myr) cluster Chamaeleon I is one of the closest laboratories to study the early stages of star cluster dynamics in a low-density environment. We studied its structural and kinematical properties combining parameters from the high-resolution spectroscopic survey Gaia-ESO with data from the literature. Our main result is the evidence of a large discrepancy between the velocity dispersion (sigma = 1.14 \pm 0.35 km s^{-1}) of the stellar population and the dispersion of the pre-stellar cores (~0.3 km s^{-1}) derived from submillimeter observations. The origin of this discrepancy, which has been observed in other young star clusters is not clear. It may be due to either the effect of the magnetic field on the protostars and the filaments, or to the dynamical evolution of stars driven by two-body interactions. Furthermore, the analysis of the kinematic properties of the stellar population put in evidence a significant velocity shift (~1 km s^{-1}) between the two sub-clusters located around the North and South main clouds. This result further supports a scenario, where clusters form from the evolution of multiple substructures rather than from a monolithic collapse. Using three independent spectroscopic indicators (the gravity indicator $γ$, the equivalent width of the Li line, and the H_alpha 10\% width), we performed a new membership selection. We found six new cluster members located in the outer region of the cluster. Starting from the positions and masses of the cluster members, we derived the level of substructure Q, the surface density Σand the level of mass segregation $Λ_{MSR}$ of the cluster. The comparison between these structural properties and the results of N-body simulations suggests that the cluster formed in a low density environment, in virial equilibrium or supervirial, and highly substructured.

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arXiv2016

EELT-HIRES the high-resolution spectrograph for the E-ELT

The first generation of E-ELT instruments will include an optical-infrared High Resolution Spectrograph, conventionally indicated as EELT-HIRES, which will be capable of providing unique breakthroughs in the fields of exoplanets, star and planet formation, physics and evolution of stars and galaxies, cosmology and fundamental physics. A 2-year long phase A study for EELT-HIRES has just started and will be performed by a consortium composed of institutes and organisations from Brazil, Chile, Denmark, France, Germany, Italy, Poland, Portugal, Spain, Sweden, Switzerland and United Kingdom. In this paper we describe the science goals and the preliminary technical concept for EELT-HIRES which will be developed during the phase A, as well as its planned development and consortium organisation during the study.

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arXiv2015

Gaia FGK benchmark stars: abundances of alpha and iron-peak elements

In the current era of large spectroscopic surveys of the Milky Way, reference stars for calibrating astrophysical parameters and chemical abundances are of paramount importance. We determine elemental abundances of Mg, Si, Ca, Sc, Ti, V, Cr, Mn, Co and Ni for our predefined set of Gaia FGK benchmark stars. By analysing high-resolution and high-signal to noise spectra taken from several archive datasets, we combined results of eight different methods to determine abundances on a line-by-line basis. We perform a detailed homogeneous analysis of the systematic uncertainties, such as differential versus absolute abundance analysis, as well as we assess errors due to NLTE and the stellar parameters in our final abundances. Our results are provided by listing final abundances and the different sources of uncertainties, as well as line-by-line and method-by-method abundances. The Gaia FGK benchmark stars atmospheric parameters are already being widely used for calibration of several pipelines applied to different surveys. With the added reference abundances of 10 elements this set is very suitable to calibrate the chemical abundances obtained by these pipelines.

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arXiv2014

ESPRESSO: The next European exoplanet hunter

The acronym ESPRESSO stems for Echelle SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observations; this instrument will be the next VLT high resolution spectrograph. The spectrograph will be installed at the Combined-Coudé Laboratory of the VLT and linked to the four 8.2 m Unit Telescopes (UT) through four optical Coudé trains. ESPRESSO will combine efficiency and extreme spectroscopic precision. ESPRESSO is foreseen to achieve a gain of two magnitudes with respect to its predecessor HARPS, and to improve the instrumental radial-velocity precision to reach the 10 cm/s level. It can be operated either with a single UT or with up to four UTs, enabling an additional gain in the latter mode. The incoherent combination of four telescopes and the extreme precision requirements called for many innovative design solutions while ensuring the technical heritage of the successful HARPS experience. ESPRESSO will allow to explore new frontiers in most domains of astrophysics that require precision and sensitivity. The main scientific drivers are the search and characterization of rocky exoplanets in the habitable zone of quiet, nearby G to M-dwarfs and the analysis of the variability of fundamental physical constants. The project passed the final design review in May 2013 and entered the manufacturing phase. ESPRESSO will be installed at the Paranal Observatory in 2016 and its operation is planned to start by the end of the same year.

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arXiv2013

The Homogeneous Study of Transiting Systems (HoSTS) I. The Pilot Study of WASP-13

We present the fundamental stellar and planetary properties of the transiting planetary system WASP-13 within the framework of the Homogeneous Study of Transiting Systems (HoSTS). HoSTS aims to derive the fundamental stellar (Teff, [Fe/H], Mstar, Rstar), and planetary (Mpl, Rpl, Teq) physical properties of known transiting planets using a consistent methodology and homogeneous high-quality dataset. Four spectral analysis techniques are independently applied to a Keck+HIRES spectrum of WASP-13 considering two distinct cases: unconstrained parameters, and constrained log g from transit light curves. We check the derived stellar temperature against that from a different temperature diagnostic based on an INT+IDS Hα spectrum. The four unconstrained analyses render results that are in good agreement, and provide an improvement of 50% in the precision of Teff, and of 85% in [Fe/H] with respect to the WASP-13 discovery paper. The planetary parameters are then derived via the Monte-Carlo-Markov-Chain modeling of the radial velocity and light curves, in iteration with stellar evolutionary models to derive realistic uncertainties. WASP-13 (1.187 +- 0.065 Msun; 1.574 +- 0.048 Rsun) hosts a Saturn-mass, transiting planet (0.500 +- 0.037 MJup; 1.407 +- 0.052 RJup), and is at the end of its main-sequence lifetime (4-5.5 Gyr). Our analysis of WASP-13 showcases that both a detailed stellar characterization, and transit modeling are necessary to well determine the fundamental properties of planetary systems, which are paramount in identifying and determining empirical relationships between transiting planets and their hosts.

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arXiv2013

On the functional form of the metallicity-giant planet correlation

It is generally accepted that the presence of a giant planet is strongly dependent on the stellar metallicity. A stellar mass dependence has also been investigated, but this dependence does not seem as strong as the metallicity dependence. Even for metallicity, however, the exact form of the correlation has not been established. In this paper, we test several scenarios for describing the frequency of giant planets as a function of its host parameters. We perform this test on two volume-limited samples (from CORALIE and HARPS). By using a Bayesian analysis, we quantitatively compared the different scenarios. We confirm that giant planet frequency is indeed a function of metallicity. However, there is no statistical difference between a constant or an exponential function for stars with subsolar metallicities contrary to what has been previously stated in the literature. The dependence on stellar mass could neither be confirmed nor be discarded.

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arXiv2012

A new analysis of the WASP-3 system: no evidence for an additional companion

In this work we investigate the problem concerning the presence of additional bodies gravitationally bounded with the WASP-3 system. We present eight new transits of this planet and analyse all the photometric and radial velocity data published so far. We did not observe significant periodicities in the Fourier spectrum of the observed minus calculated (O-C) transit timing and radial velocity diagrams (the highest peak having false-alarm probabilities of 56 per cent and 31 per cent, respectively) or long-term trends. Combining all the available information, we conclude that the radial velocity and transit timing techniques exclude, at 99 per cent confidence limit, any perturber more massive than M \gtrsim 100 M_Earth with periods up to 10 times the period of the inner planet. We also investigate the possible presence of an exomoon on this system and determined that considering the scatter of the O-C transit timing residuals a coplanar exomoon would likely produce detectable transits. This hypothesis is however apparently ruled out by observations conducted by other researchers. In case the orbit of the moon is not coplanar the accuracy of our transit timing and transit duration measurements prevents any significant statement. Interestingly, on the basis of our reanalysis of SOPHIE data we noted that WASP-3 passed from a less active (log R'_hk=-4.95) to a more active (log R'_hk=-4.8) state during the 3 yr monitoring period spanned by the observations. Despite no clear spot crossing has been reported for this system, this analysis claims for a more intensive monitoring of the activity level of this star in order to understand its impact on photometric and radial velocity measurements.

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arXiv2012

The radius and mass of the close solar twin 18 Sco derived from asteroseismology and interferometry

The growing interest in solar twins is motivated by the possibility of comparing them directly to the Sun. To carry on this kind of analysis, we need to know their physical characteristics with precision. Our first objective is to use asteroseismology and interferometry on the brightest of them: 18 Sco. We observed the star during 12 nights with HARPS for seismology and used the PAVO beam-combiner at CHARA for interferometry. An average large frequency separation $134.4\pm0.3$ $μ$Hz and angular and linear radiuses of $0.6759 \pm 0.0062$ mas and $1.010\pm0.009$ R$_{\odot}$ were estimated. We used these values to derive the mass of the star, $1.02\pm0.03$ M$_{\odot}$.

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