A view of the Galactic halo using beryllium as a time scale
Rodolfo Smiljanic, L. Pasquini, P. Bonifacio, D. Galli, B. Barbuy, R. Gratton, S. Randich
备注：
To appear in Proceedings of the International Astronomical Union, IAU Symposium, Volume 265, Chemical abundances in the Universe: connecting first stars to planets, K. Cunha, M. Spite and B. Barbuy, eds. 2 Pages, 2 figures
Beryllium stellar abundances were suggested to be a good tracer of time in the early Galaxy. In an investigation of its use as a cosmochronometer, using a large sample of local halo and thick-disk dwarfs, evidence was found that in a log(Be/H) vs. [alpha/Fe] diagram the halo stars separate into two components. One is consistent with predictions of evolutionary models while the other is chemically indistinguishable from the thick-disk stars. This is interpreted as a difference in the star formation history of the two components and suggests that the local halo is not a single uniform population where a clear age-metallicity relation can be defined.
The single stable isotope of beryllium is a pure product of cosmic-ray spallation in the ISM. Assuming that the cosmic-rays are globally transported across the Galaxy, the beryllium production should be a widespread process and its abundance should be roughly homogeneous in the early-Galaxy at a given time. Thus, it could be useful as a tracer of time. In an investigation of the use of Be as a cosmochronometer and of its evolution in the Galaxy, we found evidence that in a log(Be/H) vs. [alpha/Fe] diagram the halo stars separate into two components. One is consistent with predictions of evolut…
[abridged] Beryllium is a pure product of cosmic ray spallation. This implies a relatively simple evolution in time of the beryllium abundance and suggests its use as a time-like observable. We study the evolution of Be in the early Galaxy and its dependence on kinematic and orbital parameters. We investigate the formation of the halo and the thick disk of the Galaxy and the use of Be as a cosmochronometer. Beryllium abundances are determined from high resolution, high signal to noise UVES spectra with spectrum synthesis in the largest sample of halo and thick disk stars analyzed to date. We p…
Data from Gaia DR2 and APOGEE surveys revealed a relatively new component in the inner Galactic halo, which is likely the dynamical remnant of a disrupted dwarf galaxy named Gaia-Enceladus that collided with the Milky Way about 10 Gyrs ago. This merging event offers an extraordinary opportunity to study chemical abundances of elements in a dwarf galaxy, since they are generally hampered in external galaxies. Here, we focus on Li and Be in dwarf stars which are out of reach even in Local Group galaxies.Searching in GALAH, Gaia-ESO survey and in literature, we found several existing 7Li abundanc…
Abundances of beryllium in metal-poor stars scale linearly with metallicity down to [Fe/H] ~ -3.0. In the stars where Be has been detected at this extremely metal-poor regime, an increased abundance scatter has been previously reported. This scatter could indicate a flattening of the relation between Be and [Fe/H]. Our aim is to perform a new investigation of Be abundances in extremely metal-poor stars and try to clarify whether a Be abundance plateau exists. We revisited the Be abundances in a sample of nine dwarfs with [Fe/H] ~ -3.0. Additionally, we analysed the Be lines in the spectra of s…
Using Lithium and Beryllium to Study Structure and Evolution of Rotating Stars: Spite Plateau of Halo Stars
School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）；International Centre of Supernovae, Yunnan Key Laboratory of Supernova Research, Yunnan Observatories, Chinese Academy of Sciences（中国科学院云南天文台超新星国际研究中心、云南省超新星研究重点实验室）；Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台光学天文重点实验室）
Beryllium is a light element with one single stable isotope, 9Be, which is a pure product of cosmic-ray spallation in the interstellar medium. Beryllium abundances in late-type stars can be used in studies about evolutionary mixing, Galactic chemical evolution, planet engulfment, and the formation of globular clusters. Some of these uses of Be abundances figure among the science cases of the Cassegrain U-Band Efficient Spectrograph (CUBES), a new near-UV low- and medium-resolution spectrograph under development for the Very Large Telescope. Here, we report on a study about beryllium abundances…
I discuss a search for red giant stars in the Galactic halo with light-element abundances similar to second-generation globular cluster stars, and discuss the implications of such a population for globular cluster formation models and the balance between in situ star formation and accretion for the assembly of the Galactic halo.
The abundance of beryllium in the oldest, most metal-poor stars acts as a probe of early star formation and Galactic chemical evolution. We have analyzed high-resolution, high signal-to-noise Keck/HIRES spectra of 24 stars with [Fe/H] from -2.3 to -3.5 in order to determine the history of Be abundances and explore the possibility of a Be plateau. We have determined stellar parameters spectroscopically. Oxygen abundances have been derived from three OH features which occur in the same spectral region. We have supplemented this sample with reanalyzed spectra of 25 stars from previous observation…
Most of the previous studies on beryllium abundances in metal-poor stars have taken different Galactic populations as a whole when investigating the production and evolution of Be. In this Letter, we report on the detection of systematic differences in [α/H]-A(Be) relationships between the low- and high-α stars which were identified by previous works. We remind that one should be more careful in investigating the Galactic evolution of Be with a sample comprising different Galactic populations, because such a mixed sample may lead to inaccurate Be-Fe/Be-O relationships.
The mass of the Galactic dark matter halo is under vivid discussion. A recent study by Xue et al. (2008, ApJ, 684, 1143) revised the Galactic halo mass downward by a factor of ~2 relative to previous work, based on the line-of-sight velocity distribution of ~2400 blue horizontal-branch (BHB) halo stars. The observations were interpreted in a statistical approach using cosmological galaxy formation simulations, as only four of the 6D phase-space coordinates were determined. Here we concentrate on a close investigation of the stars with highest negative radial velocity from that sample. For one …
In Martell & Grebel (2010) we reported the discovery in the Sloan Digital Sky Survey-II/SEGUE spectroscopic database of a small subset of halo red giants, 2.5%, with CN and CH band strengths indicative of globular-cluster-like carbon and nitrogen abundances. Because the formation of stars with unusual light-element abundances is thought to be restricted to high-density environments like globular clusters, this result has strong implications for both cluster formation processes and the assembly history of the Galactic halo. Here we discuss two efforts to expand upon that work.
M3 and M13 are Galactic globular clusters with previous reports of surrounding stellar halos. We present the results of a search for members and extratidal cluster halo stars within and outside of the tidal radius of these clusters in the LAMOST Data Release 1. We find seven candidate cluster members (inside the tidal radius) of both M3 and M13 respectively. In M3 we also identify eight candidate extratidal cluster halo stars at distances up to ~9.8 times the tidal radius, and in M13 we identify 12 candidate extratidal cluster halo stars at distances up to ~13.8 times the tidal radius. These r…
The rotation of the galactic objects has been seen by asymmetric Doppler shift in the CMB data. Molecular hydrogen clouds at virial temperature may contribute to the galactic halo dark matter and they might be the reason for the observed rotational asymmetry in the galactic halos. We present a method to constrain the parameters of these virial clouds given that they are composed of a single fluid. The method is such that it should be possible to extend it to more than one fluid.
The motivation for this paper is to review the limits set on the MACHO content of the Galactic halo by microlensing experiments in the direction of the Large Magellanic Cloud. This has been prompted by recent measurements of the Galactic rotation curve, which suggest that the limits have been biassed by the assumption of an over-massive halo. The paper first discusses the security of the detection efficiency calculations which are central to deriving the MACHO content of the Galactic halo. It then sets out to compare the rotation curves from various halo models with recent observations, with a…
We estimate the 3D density profile of the Galactic dark matter (DM) halo within $r \lesssim 30$ kpc from the Galactic centre by using the astrometric data for halo RR Lyrae stars from Gaia DR2. We model both the stellar halo distribution function and the Galactic potential, fully taking into account the survey selection function, the observational errors, and the missing line-of-sight velocity data for RR Lyrae stars. With a Bayesian MCMC method, we infer the model parameters, including the density flattening of the DM halo $q$, which is assumed to be constant as a function of radius. We find …
External spiral galaxies seen edge-on exhibit X-shape magnetic fields in their halos. Whether the halo of our own Galaxy also hosts an X-shape magnetic field is still an open question. We would like to provide the necessary analytical tools to test the hypothesis of an X-shape magnetic field in the Galactic halo. We propose a general method to derive analytical models of divergence-free magnetic fields whose field lines are assigned a specific shape. We then utilize our method to obtain four particular models of X-shape magnetic fields in galactic halos. In passing, we also derive two particul…
We test the hypothesis that the classical and ultra-faint dwarf spheroidal satellites of the our Galaxy have been the building blocks of the Galactic halo by comparing their [O/Fe] and [Ba/Fe] vs. [Fe/H] patterns with the ones observed in Galactic halo stars. The [O/Fe] ratio deviates substantially from the observed abundance ratios in the Galactic halo stars for [Fe/H] > -2 dex, while they overlap for lower metallicities. On the other hand, for the neutron capture elements, the discrepancy is extended at all the metallicities, suggesting that the majority of stars in the halo are likely to ha…
With the use of a detailed Milky Way nonaxisymmetric potential, observationally and dynamically constrained, the effects of the bar and the spiral arms in the Galaxy are studied in the disc and in the stellar halo. Especially the trapping of stars in the disc and Galactic halo by resonances on the Galactic plane, induced by the Galactic bar, has been analysed in detail. To this purpose, a new method is presented to delineate the trapping regions using empirical diagrams of some orbital properties obtained in the Galactic potential. In these diagrams we plot in the inertial Galactic frame a cha…
We have learned recently that the inner halo of the Milky Way contains a kinematically coherent component (Gaia-Enceladus) from a significant merger 10 Gyrs ago. By contrast the inner halo (defined to exclude the Magellanic Stream) contains no similar intruder stellar population of billion year age. The tracer we use to set the corresponding upper limit is Gaia asymptotic giant branch stars, rather than Gaia kinematics. The primary sample is drawn from Gaia DR2 with SkyMapper photometry. This is supplemented with PanSTARRS and 2MASS photometry. As the Gaia mission proceeds, a star formation hi…
The contribution of the thermal dust component in galactic halo rotation is explored based on the microwave data of Planck satellite. The temperature asymmetry of Doppler nature revealed for several edge-on galaxies at several microwave frequencies is analyzed regarding the contribution of the thermal dust emission. We derive the dust contribution to the galactic halo rotation using the data in three bands, 353GHz, 545GHz and 857GHz for two nearby galaxies M81 and M82. The relevance of the revealed properties on the halo rotation is then discussed in the context of the modified gravity theorie…
We present an analysis of Galactic halo structure and substructure traced by ~500 RR Lyrae stars in the SDSS stripe 82 region. The main result of this study is a 2D map of the Galactic halo that reaches distances of 100 kpc and traces previously known and new halo substructures, such as the Sagittarius and Pisces tidal streams. We also present strong direct evidence, based on both RR Lyrae and main sequence stars, that the halo stellar number density profile significantly steepens beyond 30 kpc from the Galactic center. Using a novel photometric metallicity method that simultaneously combines …
We use the $Gaia$ DR2 RR Lyrae sample to gain an uninterrupted view of the Galactic stellar halo. We dissect the available volume in slices parallel to the Milky Way's disc to show that within $\sim30$ kpc from the Galactic centre the halo is triaxial, with the longest axis misaligned by $\sim70^{\circ}$ with respect to the Galactic $x$-axis. This anatomical procedure exposes two large diffuse over-densities aligned with the semi-major axis of the halo: the Hercules-Aquila Cloud and the Virgo Over-density. We reveal the kinematics of the entire inner halo by mapping out the amplitudes and dire…
We explore the hypothesis that the classical and ultra-faint dwarf spheroidal satellites of the Milky Way have been the building blocks of the Galactic halo by comparing their [O/Fe] and [Ba/Fe] versus [Fe/H] patterns with the ones observed in Galactic halo stars. Oxygen abundances deviate substantially from the observed abundances in the Galactic halo stars for [Fe/H] values larger than -2 dex, while they overlap for lower metallicities. On the other hand, for the [Ba/Fe] ratio the discrepancy is extended at all [Fe/H] values, suggesting that the majority of stars in the halo are likely to ha…
A method to diagnose the gas distribution in the Galactic halo using a shock wave from the Galactic Centre (GC) is presented. Propagation of a shock wave caused by central explosion with released energy $\sim 10^{55}$ erg is calculated for various models of the gaseous halo, and the shock front morphology is compared with the observed North- (NPS) and South-Polar Spurs (SPS). The observed bipolar hyper-shell (BHS) structure of the spurs is reproduced, when a semi-exponential halo model with radially-variable scale height is adopted. A spherical halo model ($β$ model) is shown to be not appropr…
Stellar streams provide unique probes of galactic potentials, with the longer streams normally providing the cleaner measurements. In this paper, we show an example of a short tidal stream that is particularly sensitive to the shape of the Milky Way's dark matter halo: the globular cluster tidal stream NGC 5466. This stream has an interesting deviation from a smooth orbit at its western edge. We show that such a deviation favours an underlying oblate or triaxial halo (irrespective of plausible variations in the Milky Way disc properties and the specific halo parametrisation chosen); spherical …
In the Galactic halo, metal-bearing Galactic halo material mixes into high velocity clouds (HVCs) as they hydrodynamically interact. This interaction begins long before the clouds completely dissipate and long before they slow to the velocity of the Galactic material. In order to make quantitative estimates of the mixing efficiency and resulting metal enrichment of HVCs, we made detailed 2 and 3 dimensional simulations of cloud-ISM interactions. Our simulations track the hydrodynamics and time dependent ionization levels. They assume that the cloud originally has a warm temperature and extreme…
Binary mergers (NSMs) of double neutron star (and black hole-neutron star) systems are suggested to be major sites of r-process elements in the Galaxy by recent hydrodynamical and nucleosynthesis studies. It has been pointed out, however, that the estimated long lifetimes of neutron star binaries are in conflict with the presence of r-process-enhanced halo stars at metallicities as low as [Fe/H] ~ -3. To resolve this problem, we examine the role of NSMs in the early Galactic chemical evolution on the assumption that the Galactic halo was formed from merging sub-halos. We present simple models …
We examine the constraints imposed by Faraday rotation measures of extragalactic point sources on the structure of the magnetic field in the halo of our Galaxy. Guided by radio polarization observations of external spiral galaxies, we look in particular into the possibility that field lines in the Galactic halo have an X shape. We employ the analytical models of spiraling, possibly X-shape magnetic fields derived in a previous paper to generate synthetic all-sky maps of the Galactic Faraday depth, which we fit to an observational reference map with the help of Markov Chain Monte Carlo simulati…
Two observational results, the density profile from simulations performed in the $Λ$CDM scenario and the observed flat galactic rotation curves, are taken as input with the aim of showing that the galactic halo possesses some of the characteristics needed to support traversable wormholes. This result should be sufficient to provide an incentive for scientists to seek observational evidence for wormholes in the galactic halo region.
Based on a large spectroscopic sample of $\sim$ 4,300 RR Lyrae stars with metallicity, systemic radial velocity and distance measurements, we present a detailed analysis of the chemical and kinematic properties of the Galactic halo. Using this sample, the metallicity distribution function (MDF) as a function of $r$ and the velocity anisotropy parameter $β$ profiles (for different metallicity populations) are derived for the stellar halo. Both the chemical and kinematic results suggest that the Galactic halo is composed of two distinct parts, the inner halo and outer halo. The cutoff radius ($\…
According to the current cosmological cold dark matter paradigm, the Galactic halo could have been the result of the assemblage of smaller structures. Here we explore the hypothesis that the classical and ultra-faint dwarf spheroidal satellites of the Milky Way have been the building blocks of the Galactic halo by comparing their [$α$/Fe] and [Ba/Fe] versus [Fe/H] patterns with the ones observed in Galactic halo stars. The $α$ elements deviate substantially from the observed abundances in the Galactic halo stars for [Fe/H] values larger than -2 dex, while they overlap for lower metallicities. …
We present an analytic model of a magnetized galactic halo surrounding a Mestel gravitating disc. The magnetic field is taken to be in energy equipartition with the pressure dominant rotating halo gas ({\it not} with the cosmic rays), and the whole system is in a steady state. A more flexible `anisotropic equipartition' model is also explored. A definite pressure law is required to maintain the equilibrium, but the halo density is constant. The velocity/magnetic system is scale-free. The objective is to find the rotational velocity lag in such a halo. The magnetic field is not force-free so th…
Assuming the dark matter halo of the Milky Way as a non-spherical potential (i.e. triaxial, prolate, oblate), we show how the assembling process of the Milky Way halo, may have left long lasting stellar halo kinematic fossils only due to the shape of the dark matter halo. In contrast with tidal streams, associated with recent satellite accretion events, these stellar kinematic groups will typically show inhomogeneous chemical and stellar population properties. However, they may be dominated by a single accretion event for certain mass assembling histories. If the detection of these peculiar ki…
We build upon Ordering Points To Identify Clustering Structure (OPTICS), a hierarchical clustering algorithm well-known to be a robust data-miner, in order to produce Halo-OPTICS, an algorithm designed for the automatic detection and extraction of all meaningful clusters between any two arbitrary sizes. We then apply Halo-OPTICS to the 3D spatial positions of halo particles within four separate synthetic Milky Way type galaxies, classifying the stellar and dark matter structural hierarchies. Through visualisation of the Halo-OPTICS output, we compare its structure identification to the state-o…
We test the X-ray emission predictions of galactic fountain models against XMM-Newton measurements of the emission from the Milky Way's hot halo. These measurements are from 110 sight lines, spanning the full range of Galactic longitudes. We find that a magnetohydrodynamical simulation of a supernova-driven interstellar medium, which features a flow of hot gas from the disk to the halo, reproduces the temperature but significantly underpredicts the 0.5-2.0 keV surface brightness of the halo (by two orders of magnitude, if we compare the median predicted and observed values). This is true for v…
We study the disk-halo interaction, in the context of orbits and Giant Molecular loops (GMLs) in the Galactic center (GC) region. We present a large scale survey in the central kpc in SiO(J=2-1), HCO$^+$(J=1-0) and H$^{13}$CO$^+$ (J=1-0), observations in 3mm lines toward a region in two clumps M+5.3-0.3 and M-3.8+0.9 placed in the foot point of two molecular loops, and observations toward selected positions, to trace accretion of the gas from the halo
We extend the Halo Occupation Distribution (HOD) framework to generate mock galaxy catalogs exhibiting varying levels of "galactic conformity", which has emerged as a potentially powerful probe of environmental effects in galaxy evolution. Our model correlates galaxy colours in a group with the concentration of the common parent dark halo through a "group quenching efficiency" $ρ$ which makes older, more concentrated halos $\textit{at fixed mass}$ preferentially host redder galaxies. We find that, for a specific value of $ρ$, this 1-halo conformity matches corresponding measurements in a group…
Comparisons between observational surveys and galaxy formation models find that the mass of dark matter haloes can largely explain galaxies' stellar mass. However, it remains uncertain whether additional environmental variables, generally referred to as assembly bias, are necessary to explain other galaxy properties. We use the Illustris Simulation to investigate the role of assembly bias in producing galactic conformity by considering 18,000 galaxies with $M_{stellar}$ > $2 \times 10^9$ $M_{\odot}$. We find a significant signal of galactic conformity: out to distances of about 10 Mpc, the mea…
A self-consistent model of a one-dimensional cosmic-ray (CR) halo around the Galactic disk is formulated with the restriction to a minimum number of free parameters. It is demonstrated that the turbulent cascade of MHD waves does not necessarily play an essential role in the halo formation. Instead, an increase of the Alfven velocity with distance to the disk leads to an efficient generic mechanism of the turbulent redshift, enhancing CR scattering by the self-generated MHD waves. As a result, the calculated size of the CR halo at lower energies is determined by the halo sheath, an energy-depe…
Various profiles of matter distribution in galactic halos (such as Navarro-Frenk-White, Burkert, Hernquist, Moore, Taylor-Silk and others) are considered here as the source term for the Einstein equations. We solve these equations and find exact solutions which represent the metric of a central black hole immersed in a galactic halo. Even though in the general case the solution is numerical, very accurate general analytical metric, which includes all the particular models, are found in the astrophysically relevant regime, when the mass of the galaxy is much smaller than the characteristic scal…
We present predictions for galactic halo baryon fractions from cosmological hydrodynamic simulations with a well-constrained model for galactic outflows. Without outflows, halos contain roughly the cosmic fraction of baryons, slightly lowered at high masses owing to pressure support from hot gas. The star formation efficiency is large and increases monotonically to low masses, in disagreement with data. With outflows, the baryon fraction is increasingly suppressed in halos to lower masses. A Milky Way-sized halo at z=0 has about 60% of the cosmic fraction of baryons, so "missing" halo baryons …
In this work the space-time geometry of the halo region in spiral galaxies is obtained considering the observed flat galactic rotation curve feature, invoking the Tully-Fisher relation and assuming the presence of cold dark matter in the galaxy. The gravitational lensing analysis is performed treating the so obtained space-time as a gravitational lens. It is found that the aforementioned space-time as the gravitational lens can consistently explain the galaxy-galaxy weak gravitational lensing observations and the lensing observations of the well-known Abell 370 galaxy cluster.
The results of numerical simulations of the dynamics of galactic disks, which are submerged into nonaxisymmetric dark massive halo are discussed. Galaxy disks dynamics in the nonaxisymmetric (triaxial) dark halo were investigated in detail by the high resolution numerical hydrodynamical methods (TVD \& SPH) and N-body models. The long-lived two arms spiral structure generates for a wide range of parameters. The spiral structure is global and number of turns can be 2-3 in depends of model parameters. Morphology and kinematics of spiral structures were investigated in depends of the halo and the…
We study the behaviors of galactic disks in triaxial halos both numerically and analytically to see if warps can be excited and sustained in triaxial potentials. We consider the following two scenarios: 1) galactic disks that are initially tilted relative to the equatorial plane of the halo (for a pedagogical purpose), and 2) tilted infall of dark matter relative to the equatorial plane of the disk and the halo. With numerical simulations of 100,000 disk particles in a fixed halo potential, we find that in triaxial halos, warps can be excited and sustained just as in spherical or axisymmetric …
We give a review of cosmic ray propagation models. It is shown that the development of the theory of cosmic ray origin leads inevitably to the conclusion that cosmic ray propagation in the Galaxy is determined by effective particle scattering, which is described by spatial diffusion. The Galactic Disk is surrounded by an extended halo, in which cosmic rays are confined before escaping into intergalactic space. For a long time cosmic ray convective outflow from the Galaxy (galactic wind) was believed to be insignificant. However, investigations of hydrodynamic stability and an analysis of ISM d…
Observations of the lengthy tidal streams produced by the destruction of the Sagittarius dwarf spheroidal (Sgr dSph) are capable of providing strong constraints on the shape of the Galactic gravitational potential. However, previous work, based on modeling different stream properties in axisymmetric Galactic models has yielded conflicting results: while the angular precession of the Sgr leading arm is most consistent with a spherical or slightly oblate halo, the radial velocities of stars in this arm are only reproduced by prolate halo models. We demonstrate that this apparent paradox can be r…
Spiral galaxies are surrounded by a widely distributed hot coronal gas and seem to be fed by infalling clouds of neutral hydrogen gas with low metallicity and high velocities. We numerically study plasma waves produced by the collisions of these high-velocity clouds (HVCs) with the hot halo gas and with the gaseous disk. In particular, we tackle two problems numerically: 1) collisions of HVCs with the galactic halo gas and 2) the dispersion relations to obtain the phase and group velocities of plasma waves from the equations of plasma motion as well as further important physical characteristic…
We show how an adequate post--Newtonian generalization can be obtained for Newtonian dark matter halos associated with an empiric density profile. Applying this approach to halos that follow from the well known numerical simulations of Navarro, Frenk and White (NFW), we derive all dynamical variables and show that NFW halos approximatelly follow an ideal gas type of equation of state which fits very well to a polytropic relation in the region outside the core. This fact suggests that ``outer'' regions of NFW halos might be related to equilibrium states in the non--extensive Statistical Mechani…
Tidal debris from infalling satellites can leave observable structure in the phase-space distribution of the Galactic halo. Such substructure can be manifest in the spatial and/or velocity distributions of the stars in the halo. This paper focuses on a class of substructure that is purely kinematic in nature, with no accompanying spatial features. To study its properties, we use a simulated stellar halo created by dynamically populating the Via Lactea II high-resolution N-body simulation with stars. A significant fraction of the stars in the inner halo of Via Lactea share a common speed and me…
In this paper we show that spherically symmetric BEC dark matter halos, with the $\sin r/r$ density profile, that accurately fit galactic rotation curves and represent a potential solution to the cusp-core problem are unstable. We do this by introducing back the density profiles into the fully time-dependent Gross-Pitaevskii-Poisson system of equations. Using numerical methods to track the evolution of the system, we found that these galactic halos lose mass at an approximate rate of half of its mass in a time scale of dozens of Myr. We consider this time scale is enough as to consider these h…
