arXiv subjects

Sami Dib

Publications and source records attributed to Sami Dib.

At least 55 records · Page 3Linked to original sources

arXiv2023

The massive relic galaxy NGC 1277 is dark matter deficient. From dynamical models of integral-field stellar kinematics out to five effective radii

According to the $Λ$CDM cosmology, present-day galaxies with stellar masses $M_\star>10^{11} {\rm M}_\odot$ should contain a sizable fraction of dark matter within their stellar body. Models indicate that in massive early-type galaxies (ETGs) dark matter should account for $\sim60\%$ of the dynamical mass within five effective radii ($5 R_{\rm e}$). Most massive ETGs have been shaped through a two-phase process: the rapid growth of a compact core was followed by the accretion of an extended envelope through mergers. The exceedingly rare galaxies that have avoided the second phase, the so-called relic galaxies, are thought to be the frozen remains of the massive ETG population at $z\gtrsim2$. The best relic galaxy candidate discovered to date is NGC 1277, in the Perseus cluster. We used deep integral field GCMS data to revisit NGC 1277 out to an unprecedented radius of 6 kpc (corresponding to $5 R_{\rm e}$). By using Jeans anisotropic modelling we find a negligible dark matter fraction within $5 R_{\rm e}$ ($f_{\rm DM}(5 R_{\rm e})<0.05$; two-sigma confidence level), which is in tension with the expectation. Since the lack of an extended envelope would reduce dynamical friction and prevent the accretion of an envelope, we propose that NGC 1277 lost its dark matter very early or that it was dark matter deficient ab initio. We discuss our discovery in the framework of recent proposals suggesting that some relic galaxies may result from dark matter stripping as they fell in and interacted within galaxy clusters. Alternatively, NGC 1277 might have been born in a high-velocity collision of gas-rich proto-galactic fragments, where dark matter left behind a disc of dissipative baryons. We speculate that the relative velocities of $\approx2000 {\rm km/s}$ required for the latter process to happen were possible in the progenitors of the present-day rich galaxy clusters.

astro-ph.GA↗

arXiv2023

Stellar collisions in globular clusters: Constraints on the initial mass function of the first generation of stars

Globular clusters display an anticorrelation between the fraction of the first generation of stars ($N({\rm G1})/N({\rm tot})$) and the slope of the present-day mass function of the clusters ($α_{pd}$), which is particularly significant for massive clusters. In the framework of the binary-mediated collision scenario for the formation of the second-generation stars in globular clusters, we test the effect of a varying stellar initial mass function (IMF) of the G1 stars on the $(N({\rm G1})/N({\rm tot}))-α_{pd}$ anticorrelation. We use a simple collision model that has only two input parameters, the shape of the IMF of G1 stars and the fraction of G1 stars that coalesce to form second-generation stars. We show that a variable efficiency of the collision process is necessary in order to explain the $(N({\rm G1})/N({\rm tot}))-α_{pd}$ anticorrelation; however, the scatter in the anticorrelation can only be explained by variations in the IMF, and in particular by variations in the slope in the mass interval $\approx$ (0.1-0.5) M$_{\odot}$. Our results indicate that in order to explain the scatter in the $(N({\rm G1})/N({\rm tot}))-α_{pd}$ relation, it is necessary to invoke variations in the slope in this mass range between $\approx -0.9$ and $\approx -1.9$. Interpreted in terms of a Kroupa-like broken power law, this translates into variations in the mean mass of between $\approx 0.2$ and $0.55$ M$_{\odot}$. This level of variation is consistent with what is observed for young stellar clusters in the Milky Way and may reflect variations in the physical conditions of the globular cluster progenitor clouds at the time the G1 population formed or may indicate the occurrence of collisions between protostellar embryos before stars settle on the main sequence.

astro-ph.GA↗

arXiv2022

Brane cosmology with variable tension

We study brane-world models and demonstrate that such models do not admit self-similar solutions through the matter collineation approach. By introducing the hypothesis of variable brane tension, $λ,$ we outline the new effective field equation (EFE) in the most simple case (symmetric embedding) under the assumption that the fundamental constants in 5D are constants. In this case, we find the exact form that each physical quantity may take in order that the EFE become invariant under scale transformations. By taking into account such assumptions, we find that in 4D, the gravitational constant $κ^{2}\thicksimλ$ while the cosmological constant $Λ\thicksimλ^{2}$ are always decreasing. These results are quite general and valid for any homogeneous self-similar metric. Nevertheless, the study of the EFE under scale symmetries suggests that $ρ\thicksimλ$ (as a functional relationship). This allows to get a growing $κ^{2}$ but, in this case, the fundamental constants in 5D must vary as well. We outline a toy model allowing such a possibility.

hep-th↗

arXiv2022

Self-similar cosmological solutions in f(R,T) gravity theory

We study the $f(R,T)$ cosmological models under the self-similarity hypothesis. We determine the exact form that each physical and geometrical quantity may take in order that the Field Equations (FE) admit exact self-similar solutions through the matter collineation approach. We study two models: the case$\ f(R,T)=f_{1}(R)+f_{2}(T)$ and the case $f(R,T)=f_{1}(R)+f_{2} (R)f_{3}(T)$. In each case, we state general theorems which determine completely the form of the unknown functions $f_{i}$ such that the field equations admit self-similar solutions. We also state some corollaries as limiting cases. These results are quite general and valid for any homogeneous self-similar metric$.$ In this way, we are able to generate new cosmological scenarios. As examples, we study two cases by finding exact solutions to these particular models.

astro-ph.CO↗

arXiv2022

The galaxy-wide stellar initial mass function in the presence of cluster-to-cluster IMF variations

We calculate the integrated galactic initial stellar mass function (IGIMF) in the presence of IMF variations in clusters. IMF Variations for a population of clusters are taken into account in the form of Gaussian distributions of the IMF parameters. For the tapered power law function used here, these are the slopes at the high and low mass ends, $Γ$ and $γ$, and the characteristic mass $M_{ch}$. Variations are modeled by varying the width of the Gaussian distributions. The reference values are the standard deviations of the parameters observed for young clusters in the present-day Milky Way $σ_Γ=0.6$, $σ_γ=0.25$, and $σ_{M_{ch}}=0.27$ M$_{\odot}$. Increasing the dispersions of $γ$ and $Γ$ moderately flattens the IGIMF at the low and high mass ends. Increasing $σ_{M_{ch}}$ shifts the peak of the IGIMF to lower masses, rendering the IGIMF more bottom heavy. This can explain the bottom heavy stellar mass function of Early-type galaxies as they are the result of the merger of disk galaxies where the physical conditions of the star forming gas vary significantly both in time and space. The effect of IMF variations is compared to that due to other effects such as variations in the shape of the initial cluster mass function, metallicity, and galactic SFR. We find that the effect of IMF variations is a dominant factor that always affects the characteristic mass of the IGIMF. We compare our results to a sample of ultra-faint dwarf satellite galaxies (UFDs). Their present-day stellar mass function is an analog to their IGIMF at the time their stellar populations have formed. We show that the slope of the IGIMF of the UFDs can only be reproduced when IMF variations of the same order as those measured in the present-day Milky Way are included. (Abridged)

astro-ph.GA↗

arXiv2022

Stellar collisions in globular clusters: the origin of multiple stellar populations

Two generations of stars, G1 and G2, typically populate Galactic globular clusters (GCs). The origin of G2 stars is unclear. We uncover two empirical dependencies between GC characteristics, which can be explained by the formation of G2 Main-Sequence (MS) stars due to collision\merging of their primordial counterparts (G1). A similar genesis of both G2 stars and peculiar objects like LMXBs and millisecond pulsars is also implied. Indeed, we find a significant (at a confidence level > 99,9%) anti-correlation between the fraction of G1 red giants ($N_{G1}/N_{tot}$) and stellar encounter rates among 51 GCs. Moreover, a Milky Way-like initial mass function (IMF) requires at least ~50% of MS stars located in the mass range [0.1-0.5] $M\odot$. Unlike cluster mass loss, stellar collisions\merging retain these G1 stars by converting them into more massive G2 ones, with mainly M_ms > 0.5 $M\odot$. This process coupled with a decreasing relative mass loss with increasing GC masses implies a smaller ($N_{G1}/N_{tot}$) in more massive GCs with a shallower present day MF. From data for 35 GCs, we find that such an anti-correlation is significant at 98.3% confidence level (Spearman's correlation) for 12 most massive GCs ($M_{GC} > 10^{5.3}$) and it is at a confidence level of 89% for the 12 least massive GCs ($M_{GC} < 10^{5.1} M_\odot$). Other fractions of G1 and G2 stars observed at the bottom of the MS as compared with the red giant branch in a few GCs are consistent with the scenario proposed.

astro-ph.GA↗

arXiv2021

The structure and characteristic scales of the HI gas in galactic disks

The spatial distribution of the HI gas in galaxies holds important clues on the physical processes that shape the structure and dynamics of the interstellar medium (ISM). In this work, we quantify the structure of the HI gas in a sample of 33 nearby galaxies taken from the THINGS Survey using the delta-variance spectrum. The THINGS galaxies display a large diversity in their spectra, however, there are a number of recurrent features. In many galaxies, we observe a bump in the spectrum on scales of a few to several hundred pc. We find the characteristic scales associated with the bump to be correlated with galactic SFR for values of the SFR > 0.5 M$_{sol}$ yr$^{-1}$ and also with the median size of the HI shells detected in those galaxies. On larger scales, we observe the existence of two self-similar regimes. The first one, on intermediate scales is shallow and the power law that describes this regime has an exponent in the range [0.1-1] with a mean value of 0.55 which is compatible with the density field being generated by supersonic turbulence in the cold phase of the HI gas. The second power law is steeper, with a range of exponents between [0.5-1.5] and a mean value of 1.5. These values are associated with subsonic turbulence which is characteristic of the warm phase of the HI gas. The spatial scale at which the transition between the two regimes occurs is found to be $\approx 0.5 R_{25}$ which is similar to the size of the molecular disk in the THINGS galaxies. Overall, our results suggest that on scales < $0.5 R_{25}$, the structure of the ISM is affected by the effects of supernova explosions. On larger scales (> 0.5 $R_{25}$), stellar feedback has no significant impact, and the structure of the ISM is determined by large scale processes that govern the dynamics of the gas in the warm neutral medium such as the flaring of the HI disk and the effects of ram pressure stripping.

astro-ph.GA↗

arXiv2021

Cloud Motion and magnetic fields: Four clouds in the Cepheus Flare region

The Cepheus Flare region consists of a group of dark cloud complexes that are currently active in star formation. The aim of this work is to estimate the motion of four clouds, L1147/1158, L1172/1174, L1228 and L1251 located at relatively high Galactic latitude (b $\gt$ 14$^{\circ}$) in the Cepheus Flare region. We study the relationship between the motion of the cloud with respect to the magnetic field and the clump orientations with respect to both the magnetic field and the motion. We estimated the motion of the molecular clouds using the proper motion and the distance estimates of the young stellar objects (YSOs) associated with them using the Gaia EDR3 data. By assuming that the YSOs are associated with the clouds and share the same velocity, the projected direction of motion of the clouds are estimated. We estimated a distance of 371$\pm$22 pc for L1228 and 340$\pm$ 7 pc for L1251 implying that all four complexes are located at almost the same distance. Assuming that both the clouds and YSOs are kinematically coupled, we estimated the projected direction of motion of the clouds using the proper motions of the YSOs. All the clouds in motion are making an offset of $\sim$ 30$^{\circ}$ with respect to the ambient magnetic fields except in L1172/1174 where the offset is $\sim$ 45$^{\circ}$. In L1147/1158, the starless clumps are found to be oriented predominantly parallel to the magnetic fields while prestellar clumps show random distribution. In L1172/1174, L1228 and L1251,the clumps are oriented randomly with respect to magnetic field. With respect to the motion of the clouds, there is a marginal trend that the starless clumps are oriented more parallel in L1147/1158 and L1172/1174. In L1228, the clumps major axis are oriented more randomly. In L1251, we find a bimodal trend in case of starless clumps.

astro-ph.GA↗

arXiv2020

Metal-THINGS: On the metallicity and ionization of ULX sources in NGC 925

We present an analysis of the optical properties of three Ultra Luminous X-ray (ULX) sources identified in NGC 925. We use Integral field unit data from the George Mitchel spectrograph in the context of the Metal-THINGS survey. The optical properties for ULX-1 and ULX-3 are presented, while the spaxel associated with ULX-2 had a low S/N, which prevented its analysis. We also report the kinematics and dimensions of the optical nebula associated with each ULX using ancillary data from the PUMA Fabry-Perot spectrograph. A BPT analysis demonstrates that most spaxels in NGC 925 are dominated by star-forming regions, including those associated with ULX-1 and ULX-3. Using the resolved gas-phase metallicities, a negative metallicity gradient is found, consistent with previous results for spiral galaxies, while the ionization parameter tends to increase radially throughout the galaxy. Interestingly, ULX-1 shows a very low gas metallicity for its galactocentric distance, identified by two independent methods, while exhibiting a typical ionization. We find that such low gas metallicity is best explained in the context of the high-mass X-ray binary population, where the low-metallicity environment favours active Roche lobe overflows that can drive much higher accretion rates. An alternative scenario invoking accretion of a low-mass galaxy is not supported by the data in this region. Finally, ULX-3 shows both a high metallicity and ionization parameter, which is consistent with the progenitor being a highly-accreting neutron star within an evolved stellar population region.

astro-ph.GA↗

arXiv2020

The structure and characteristic scales of molecular clouds

The structure of molecular clouds (MCs) holds important clues on the physical processes that lead to their formation and subsequent evolution. While it is well established that turbulence imprints a self-similar structure to the clouds, other processes, such as gravity and stellar feedback, can break their scale-free nature. The break of self-similarity can manifest itself in the existence of characteristic scales that stand out from the underlying structure generated by turbulent motions. We investigate the structure of the Cygnus-X North and the Polaris MCs which represent two extremes in terms of their star formation activity. We characterize the structure of the clouds using the delta-variance ($Δ$-variance) spectrum. In Polaris, the structure of the cloud is self-similar over more than one order of magnitude in spatial scales. In contrast, the $Δ$-variance spectrum of Cygnus-X exhibits an excess and a plateau on physical scales of ~0.5-1.2 pc. In order to explain the observations for Cygnus-X, we use synthetic maps in which we overlay populations of discrete structures on top of a fractal Brownian motion (fBm) image. The properties of these structures such as their major axis sizes, aspect ratios, and column density contrasts are randomly drawn from parameterized distribution functions. We show that it is possible to reproduce a $Δ$-variance spectrum that resembles the one of the Cygnus-X cloud. We also use a "reverse engineering" approach in which we extract the compact structures in the Cygnus-X cloud and re-inject them on an fBm map. The calculated $Δ$-variance using this approach deviates from the observations and is an indication that the range of characteristic scales observed in Cygnus-X is not only due to the existence of compact sources, but is a signature of the whole population of structures, including more extended and elongated structures

astro-ph.GA↗

arXiv2019

Star formation activity and the spatial distribution and mass segregation of dense cores in the early phases of star formation

We examine the spatial distribution and mass segregation of dense molecular cloud cores in a number of nearby star forming regions that span about four orders of magnitude in star formation activity. We use an approach based on the calculation of the minimum spanning tree, and for each region, we calculate the structure parameter Q and the mass segregation ratio measured for various numbers of the most massive cores. Our results indicate that the distribution of dense cores in young star forming regions is very substructured and that it is likely that this substructure will be imprinted onto the nascent clusters that will emerge out of these clouds. With the exception of Taurus in which there is nearly no mass segregation, we observe mild-to-significant levels of mass segregation for the ensemble of the 6, 10, and 14 most massive cores in Aquila, CrA, and W43, respectively. Our results suggest that the clouds' star formation activity are linked to their structure, as traced by their population of dense cores. We also find that the fraction of massive cores that are the most mass segregated in each region correlates with the surface density of star formation in the clouds. The Taurus region with low star-forming activity is associated with a highly hierarchical spatial distribution of the cores (low Q value) and the cores show no sign of being mass segregated. On the other extreme, the mini-starburst region W43-MM1 has a higher Q that is suggestive of a more centrally condensed structure and it possesses a higher fraction of massive cores that are segregated by mass. While some limited evolutionary effects might be present, we attribute the correlation between the star formation activity of the clouds and their structure to a dependence on the physical conditions that have been imprinted on them by the large scale environment at the time they started to assemble

astro-ph.GA↗

arXiv2019

Physical properties and chemical composition of the cores in the California molecular cloud

We aim to reveal the physical properties and chemical composition of the cores in the California molecular cloud (CMC), so as to better understand the initial conditions of star formation. We made a high-resolution column density map (18.2") with Herschel data, and extracted a complete sample of the cores in the CMC with the \textsl{fellwalker} algorithm. We performed new single-pointing observations of molecular lines near 90 GHz with the IRAM 30m telescope along the main filament of the CMC. In addition, we also performed a numerical modeling of chemical evolution for the cores under the physical conditions. We extracted 300 cores, of which 33 are protostellar and 267 are starless cores. About 51\% (137 of 267) of the starless cores are prestellar cores. Three cores have the potential to evolve into high-mass stars. The prestellar core mass function (CMF) can be well fit by a log-normal form. The high-mass end of the prestellar CMF shows a power-law form with an index $α=-0.9\pm 0.1$ that is shallower than that of the Galactic field stellar mass function. Combining the mass transformation efficiency ($\varepsilon$) from the prestellar core to the star of $15\pm 1\%$ and the core formation efficiency (CFE) of 5.5\%, we suggest an overall star formation efficiency of about 1\% in the CMC. In the single-pointing observations with the IRAM 30m telescope, we find that 6 cores show blue-skewed profile, while 4 cores show red-skewed profile. [$\rm {HCO}^{+}$]/[HNC] and [$\rm {HCO}^{+}$]/$\rm [N_{2}H^{+}]$ in protostellar cores are higher than those in prestellar cores; this can be used as chemical clocks. The best-fit chemical age of the cores with line observations is $\sim 5\times 10^4$~years.

astro-ph.GA↗

arXiv2018

Properties of an accretion disc with a power-law stress-pressure relationship

Recent numerical simulations of magnetized accretion discs show that the radial-azimuthal component of the stress tensor due to the magnetorotational instability (MRI) is well represented by a power-law function of the gas pressure rather than a linear relation which has been used in most of the accretion disc studies. The exponent of this power-law function which depends on the net flux of the imposed magnetic field is reported in the range between zero and unity. However, the physical consequences of this power-law stress-pressure relation within the framework of the standard disc model have not been explored so far. In this study, the structure of an accretion disc with a power-law stress-pressure relation is studied using analytical solutions in the steady-state and time-dependent cases. The derived solutions are applicable to different accreting systems, and as an illustrative example, we explore structure of protoplanetary discs using these solutions. We show that the slopes of the radial surface density and temperature distributions become steeper with decreasing the stress exponent. However, if the disc opacity is dominated by icy grains and value of the stress exponent is less than about $0.5$, the surface density and temperature profiles become so steep that make them unreliable. We also obtain analytical solutions for the protoplanetary discs which are irradiated by the host star. Using these solutions, we find that the effect of the irradiation becomes more significant with decreasing the stress exponent.

astro-ph.GA↗

arXiv2018

The emergence of the galactic stellar mass function from a non-universal IMF in clusters

We investigate how a single generation galactic mass function (SGMF) depends on the existence of variations in the initial stellar mass functions (IMF) of stellar clusters. We show that cluster-to-cluster variations of the IMF lead to a multicomponent SGMF where each component in a given mass range can be described by a distinct power-law function. We also show that a dispersion of $\approx 0.3$ M$_{\odot}$ in the characteristic mass of the IMF, as observed for young Galactic clusters, leads to a low mass slope of the SGMF that matches the observed Galactic stellar mass function even when the IMFs in the low mass end of individual clusters are much steeper.

astro-ph.GA↗

arXiv2017

Structure and mass segregation in Galactic stellar clusters

We quantify the structure of a very large number of Galactic open clusters and look for evidence of mass segregation for the most massive stars in the clusters. We characterise the structure and mass segregation ratios of 1276 clusters in the Milky Way Stellar Cluster (MWSC) catalogue containing each at least 40 stars and that are located at a distance of up to $\approx 2$ kpc from the Sun. We use an approach based on the calculation of the minimum spanning tree of the clusters, and for each one of them, we calculate the structure parameter \Q\ and the mass segregation ratio $Λ_{\rm MSR}$. Our findings indicate that most clusters possess a \Q\ parameter that falls in the range 0.7-0.8 and are thus neither strongly concentrated nor do they show significant substructure. Only 27\% can be considered centrally concentrated with \Q\ values $> 0.8$. Of the 1276 clusters, only 14\% show indication of significant mass segregation ($Λ_{\rm MSR} > 1.5$). Furthermore, no correlation is found between the structure of the clusters or the degree of mass segregation with their position in the Galaxy. A comparison of the measured \Q\ values for the young open clusters in the MWSC to N-body numerical simulations that follow the evolution of the \Q\ parameter over the first 10 Myrs of the clusters life suggests that the young clusters found in the MWSC catalogue initially possessed local mean volume densities of $ρ_{*} \approx 10-100$ M$_{\odot}$ pc$^{-3}$.

astro-ph.GA↗

arXiv2017

The extended law of star formation: the combined role of gas and stars

We present a model for the origin of the extended law of star formation in which the surface density of star formation ($Σ_{\rm SFR}$) depends not only on the local surface density of the gas ($Σ_{g}$), but also on the stellar surface density ($Σ_{*}$), the velocity dispersion of the stars, and on the scaling laws of turbulence in the gas. We compare our model with the spiral, face-on galaxy NGC 628 and show that the dependence of the star formation rate on the entire set of physical quantities for both gas and stars can help explain both the observed general trends in the $Σ_{g}-Σ_{\rm SFR}$ and $Σ_{*}-Σ_{\rm SFR}$ relations, but also, and equally important, the scatter in these relations at any value of $Σ_{g}$ and $Σ_{*}$. Our results point out to the crucial role played by existing stars along with the gaseous component in setting the conditions for large scale gravitational instabilities and star formation in galactic disks.

astro-ph.GA↗

arXiv2016

Structure of radiation dominated gravitoturbulent quasar discs

Self-gravitating accretion discs in a gravitoturbulent state, including radiation and gas pressures, are studied using a set of new analytical solutions. While the Toomre parameter of the disc remains close to its critical value for the onset of gravitational instability, the dimensionless stress parameter is uniquely determined from the thermal energy reservoir of the disc and its cooling rate. Our solutions are applicable to the accretion discs with dynamically important radiation pressure like in the quasars discs. We show that physical quantities of a gravitoturbulent disc in the presence of radiation are significantly modified compared to solutions with only gas pressure. We show that the dimensionless stress parameter is an increasing function of the radial distance so that its steepness strongly depends on the accretion rate. In a disc without radiation its slope is 4.5, however, we show that in the presence of radiation, it varies between 2 and 4.5 depending on the accretion rate and the central mass. As for the surface density, we find a shallower profile with an exponent -2 in a disc with sub-Eddington accretion rate compared to a similar disc, but without radiation, where its surface density slope is -3 independent of the accretion rate. We then investigate gravitational stability of the disc when the stress parameter reaches to its critical value. In order to self-consistently determine the fragmentation boundary, however, it is shown that the critical value of the stress parameter is a power-law function of the ratio of gas pressure and the total pressure and its exponent is around 1.7. We also estimate the maximum mass of the central black hole using our analytical solutions.

astro-ph.GA↗

arXiv2016

Massive stars reveal variations of the stellar initial mass function in the Milky Way stellar clusters

We investigate whether the stellar initial mass function (IMF) is universal, or whether it varies significantly among young stellar clusters in the Milky Way. We propose a method to uncover the range of variation of the parameters that describe the shape of the IMF for the population of young Galactic clusters. These parameters are the slopes in the low and high stellar mass regimes, $γ$ and $Γ$, respectively, and the characteristic mass, $M_{ch}$. The method relies exclusively on the high mass content of the clusters, but is able to yield information on the distributions of parameters that describe the IMF over the entire stellar mass range. This is achieved by comparing the fractions of single and lonely massive O stars in a recent catalog of the Milky Way clusters with a library of simulated clusters built with various distribution functions of the IMF parameters. The synthetic clusters are corrected for the effects of the binary population, stellar evolution, sample incompleteness, and ejected O stars. Our findings indicate that broad distributions of the IMF parameters are required in order to reproduce the fractions of single and lonely O stars in Galactic clusters. They also do not lend support to the existence of a cluster mass-maximum stellar mass relation. We propose a probabilistic formulation of the IMF whereby the parameters of the IMF are described by Gaussian distribution functions centered around $γ=0.91$, $Γ=1.37$, and $M_{ch}=0.41$ M$_{\odot}$, and with dispersions of $σ_γ=0.25$, $σ_Γ=0.60$, and $σ_{M_{ch}}=0.27$ M$_{\odot}$ around these values.

astro-ph.GA↗