arXiv subjects

Masashi Chiba

Publications and source records attributed to Masashi Chiba.

At least 37 records · Page 2Linked to original sources

arXiv2024

Detection of a Spatially Extended Stellar Population in M33: A Shallow Stellar Halo?

We analyze the outer regions of M33, beyond 15 kpc in projected distance from its center using Subaru/HSC multi-color imaging. We identify Red Giant Branch (RGB) stars and Red Clump (RC) stars using the surface gravity sensitive $NB515$ filter for the RGB sample, and a multi-color selection for both samples. We construct the radial surface density profile of these RGB and RC stars, and find that M33 has an extended stellar population with a shallow power-law index of $α> -3$, depending on the intensity of the contamination. This result represents a flatter profile than the stellar halo which has been detected by the previous study focusing on the central region, suggesting that M33 may have a double-structured halo component, i.e. inner/outer halos or a very extended disk. Also, the slope of this extended component is shallower than those typically found for halos in large galaxies, implying intermediate-mass galaxies may have different formation mechanisms (e.g., tidal interaction) from large spirals. We also analyze the radial color profile of RC/RGB stars, and detect a radial gradient, consistent with the presence of an old and/or metal-poor population in the outer region of M33, thereby supporting our proposal that the stellar halo extends beyond 15 kpc. Finally, we estimate that the surface brightness of this extended component is $μ_{\it V} = 35.72 \pm 0.08$ mag arcsec$^{-2}$. If our detected component is the stellar halo, this estimated value is consistent with the detection limit of previous observations.

astro-ph.GA↗

arXiv2024

Chemo-dynamical Evolution of Simulated Satellites for a Milky Way-like Galaxy

The chemical abundances of Milky Way's satellites reflect their star formation histories (SFHs), yet, due to the difficulty of determining the ages of old stars, the SFHs of most satellites are poorly measured. Ongoing and upcoming surveys will obtain around ten times more medium-resolution spectra for stars in satellites than are currently available. To correctly extract SFHs from large samples of chemical abundances, the relationship between chemical abundances and SFHs needs to be clarified. Here, we perform a high-resolution cosmological zoom-in simulation of a Milky Way-like galaxy with detailed models of star formation, supernova feedback, and metal diffusion. We quantify SFHs, metallicity distribution functions, and the $α$-element (Mg, Ca, and Si) abundances in satellites of the host galaxy. We find that star formation in most simulated satellites is quenched before infalling to their host. Star formation episodes in simulated satellites are separated by a few hundred Myr owing to supernova feedback; each star formation event produces groups of stars with similar [$α$/Fe] and [Fe/H]. We then perform a mock observation of the upcoming Subaru Prime Focus Spectrograph (PFS) observations. We find that Subaru PFS will be able to detect distinct groups of stars in [$α$/Fe] vs. [Fe/H] space, produced by episodic star formation. This result means that episodic SFHs can be estimated from the chemical abundances of $\gtrsim$ 1,000 stars determined with medium-resolution spectroscopy.

astro-ph.GA↗

arXiv2024

Final Results of Search for New Milky Way Satellites in the Hyper Suprime-Cam Subaru Strategic Program Survey: Discovery of Two More Candidates

We present the final results of our search for new Milky Way (MW) satellites using the data from the Hyper Suprime-Cam (HSC) Subaru Strategic Program (SSP) survey over $\sim 1,140$ deg$^2$. In addition to three candidates that we already reported, we have identified two new MW satellite candidates in the constellation of Sextans at a heliocentric distance of $D_{\odot} \simeq 126$kpc, and Virgo at $D_{\odot} \simeq 151$kpc, named Sextans II and Virgo III, respectively. Their luminosities (Sext II:$M_V\simeq-3.9$mag; Vir III:$M_V\simeq-2.7$mag) and half-light radii (Sext II:$r_h\simeq154$ pc; Vir III:$r_h\simeq 44$ pc) place them in the region of size-luminosity space of ultra-faint dwarf galaxies (UFDs). Including four previously known satellites, there are a total of nine satellites in the HSC-SSP footprint. This discovery rate of UFDs is much higher than that predicted from the recent models for the expected population of MW satellites in the framework of cold dark matter models, thereby suggesting that we encounter a too many satellites problem. Possible solutions to settle this tension are also discussed.

astro-ph.GA↗

arXiv2024

Uncovering the Ghostly Remains of an Extremely Diffuse Satellite in the Remote Halo of NGC 253

We present the discovery of NGC253-SNFC-dw1, a new satellite galaxy in the remote stellar halo of the Sculptor Group spiral, NGC 253. The system was revealed using deep resolved star photometry obtained as part of the Subaru Near-Field Cosmology Survey that uses the Hyper Suprime-Cam on the Subaru Telescope. Although rather luminous ($\rm{M_{V}} = -11.7 \pm 0.2$) and massive ($M_* \sim 1.25\times 10^7~\rm{M}_{\odot}$), the system is one of the most diffuse satellites yet known, with a half-light radius of $\rm{R_{h}} = 3.37 \pm 0.36$ kpc and an average surface brightness of $\sim 30.1$ mag arcmin$^{-2}$ within the $\rm{R_{h}}$. The colour-magnitude diagram shows a dominant old ($\sim 10$ Gyr) and metal-poor ($\rm{[M/H]}=-1.5 \pm 0.1$ dex) stellar population, as well as several candidate thermally-pulsing asymptotic giant branch stars. The distribution of red giant branch stars is asymmetrical and displays two elongated tidal extensions pointing towards NGC 253, suggestive of a highly disrupted system being observed at apocenter. NGC253-SNFC-dw1 has a size comparable to that of the puzzling Local Group dwarfs Andromeda XIX and Antlia 2 but is two magnitudes brighter. While unambiguous evidence of tidal disruption in these systems has not yet been demonstrated, the morphology of NGC253-SNFC-dw1 clearly shows that this is a natural path to produce such diffuse and extended galaxies. The surprising discovery of this system in a previously well-searched region of the sky emphasizes the importance of surface brightness limiting depth in satellite searches.

astro-ph.GA↗

arXiv2024

New insights on the dynamics of satellite galaxies: effects of the figure rotation of a host galaxy

We investigate a mechanism to form and keep a planar spatial distribution of satellite galaxies in the Milky Way (MW), which is called the satellite plane. It has been pointed out that the ΛCDM cosmological model hardly explains the existence of such a satellite plane, so it is regarded as one of the serious problems in the current cosmology. We here focus on a rotation of the gravitational potential of a host galaxy, i.e., so-called a figure rotation, following the previous suggestion that this effect can induce the tilt of a so-called tube orbit. Our calculation shows that a figure rotation of a triaxial potential forms a stable orbital plane perpendicular to the rotational axis of the potential. Thus, it is suggested that the MW's dark halo is rotating with its axis being around the normal line of the satellite plane. Additionally, we find that a small velocity dispersion of satellites is required to keep the flatness of the planar structure, namely the standard derivation of their velocities perpendicular to the satellite plane needs smaller than their mean rotational velocity on the plane. Although not all the MW's satellites satisfy this condition, some fraction of them called member satellites, which are prominently on the plane, satisfy it. We suggest that this picture explaining the observed satellite plane can be achieved by the filamentary accretion of dark matter associated with the formation of the MW and a group infall of member satellites along this cosmic filament.

astro-ph.GA↗

arXiv2024

JASMINE: Near-Infrared Astrometry and Time Series Photometry Science

Japan Astrometry Satellite Mission for INfrared Exploration (JASMINE) is a planned M-class science space mission by the Institute of Space and Astronautical Science, the Japan Aerospace Exploration Agency. JASMINE has two main science goals. One is the Galactic archaeology with Galactic Center Survey, which aims to reveal the Milky Way's central core structure and formation history from Gaia-level (~25 $μ$as) astrometry in the Near-Infrared (NIR) Hw-band (1.0-1.6 $μ$m). The other is the Exoplanet Survey, which aims to discover transiting Earth-like exoplanets in the habitable zone from NIR time-series photometry of M dwarfs when the Galactic center is not accessible. We introduce the mission, review many science objectives, and present the instrument concept. JASMINE will be the first dedicated NIR astrometry space mission and provide precise astrometric information of the stars in the Galactic center, taking advantage of the significantly lower extinction in the NIR. The precise astrometry is obtained by taking many short-exposure images. Hence, the JASMINE Galactic center survey data will be valuable for studies of exoplanet transits, asteroseismology, variable stars and microlensing studies, including discovery of (intermediate mass) black holes. We highlight a swath of such potential science, and also describe synergies with other missions.

astro-ph.IM↗

arXiv2024

The Milky Way Tomography with Subaru Hyper Suprime-Cam. I. Halo substructures

We analyze the photometric data in the Wide layer of the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) over $\sim 1,200$ deg$^{2}$ to uncover new halo substructures beyond the distance, $D_{\odot}\sim$ 30 kpc, from the Sun. For this purpose, we develop an isochrone filter for an old, metal-poor stellar system to extract the faint main-sequence stars at a range of distances. With this method, we detect, not only the previously discovered substructures such as the Orphan Stream, but also the new overdensity toward Boötes at about $D_{\odot}\sim$ 60 kpc and the new stream-like feature toward Pisces at around $D_{\odot}\sim$ 60 kpc. It has been suggested that a small-scale overdensity exists in this direction of Pisces (the so-called Pisces Overdensity), but our results show that the overdensity is widely spread with a tidally elongated feature. Combining our results with the ongoing Hyper Suprime-Cam narrow-band survey and the near-future spectroscopic survey with Prime Focus Spectrograph (PFS) will allow us to place strong constraints on the origin of these halo substructures.

astro-ph.GA↗

arXiv2023

Study of structural parameters and systemic proper motion of Sextans dwarf spheroidal galaxy with Subaru Hyper Suprime-Cam data

We use the Subaru Hyper Suprime-Cam (HSC) data to study structural parameters and systemic proper motion of the Sextans dwarf spheroidal galaxy at the heliocentric distance of 86 kpc, which is one of the most important targets for studies of dark matter nature and galaxy formation physics. Thanks to the superb image quality and wide area coverage of the Sextans field, the HSC data enables a secure selection of member star candidates based on the colour-magnitude cut, yielding about 10,000 member candidates at magnitudes down to $i\sim 24$. We use a likelihood analysis of the two-dimensional distribution of stars to estimate the structural parameters of Sextans taking into account the contamination of foreground halo stars in the Milky Way, and find that the member star distribution is well-fitted by an elliptical King profile with ellipticity $ε\simeq 0.25$ and the core and tidal radii of $R_c=(368.4\pm 8.5)$ pc and $R_t=(2.54\pm 0.046)$ kpc, respectively. Then using the two HSC datasets of 2.66 years time baseline on average, we find the systemic proper motions of Sextans to be $(μ_α, μ_δ)=(-0.448\pm{0.075},0.083\pm{0.078})$ $\mathrm{mas}\ \mathrm{yr}^{-1}$, which is consistent with some of the previous works using the $Gaia$ data of relatively bright member stars in Sextans. Thus, our results give a demonstration that a ground-based, large-aperture telescope data which covers a wide solid angle of the sky and has a long time baseline, such as the upcoming LSST data, can be used to study systemic proper motions of dwarf galaxies.

astro-ph.GA↗

arXiv2023

Dark matter halo properties of the Galactic dwarf satellites: implication for chemo-dynamical evolution of the satellites and a challenge to $Λ$CDM

Elucidating dark matter density profiles in the Galactic dwarf satellites is essential to understanding not only the quintessence of dark matter, but also the evolution of the satellites themselves. In this work, we present the current constraints on dark matter densities in the Galactic ultra-faint dwarf (UFD) and diffuse galaxies. Applying our constructed non-spherical mass models to the currently available kinematic data of the 25 UFDs and 2 diffuse satellites, we find that whereas most of the galaxies have huge uncertainties on the inferred dark matter density profiles, Eridanus~II, Segue~I, and Willman~1 favor cuspy central profiles even considering effects of a prior bias. We compare our results with the simulated subhalos on the plane between the dark matter density at 150~pc and the pericenter distance. We find that the most observed satellites and the simulated subhalos are similarly distributed on this plane, except for Antlia~2, Crater~2, and Tucana~3, which are less than one tenth of the density. Despite considerable tidal effects, the subhalos detected by commonly-used subhalo finders have difficulty in explaining such a huge deviation. We also estimate the dynamical mass-to-light ratios of the satellites and confirm the ratio is linked to stellar mass and metallicity. Tucana~3 deviates largely from these relations, while it follows the mass-metallicity relation. This indicates that Tucana~3 has a cored dark matter halo, despite a significant uncertainty in its ratios.

astro-ph.GA↗

arXiv2023

Revealing mass distributions of dwarf spheroidal galaxies in the Subaru-PFS era

The Galactic dwarf spheroidal galaxies (dSphs) provide valuable insight into dark matter (DM) properties and its role in galaxy formation. Their close proximity enables the measurement of line-of-sight velocities for resolved stars, which allows us to study DM halo structure. However, uncertainties in DM mass profile determination persist due to the degeneracy between DM mass density and velocity dispersion tensor anisotropy. Overcoming this requires large kinematic samples and identification of foreground contamination. With 1.25 deg$^2$ and 2394 fibers, PFS plus pre-imaging with Hyper Suprime Cam will make significant progress in this undertaking.

astro-ph.GA↗

arXiv2022

Origin of highly $r$-process-enhanced stars in a cosmological zoom-in simulation of a Milky Way-like galaxy

The $r$-process-enhanced (RPE) stars provide fossil records of the assembly history of the Milky Way and the nucleosynthesis of the heaviest elements. Observations by the $R$-Process Alliance (RPA) and others have confirmed that many RPE stars are associated with chemo-dynamically tagged groups, which likely came from accreted dwarf galaxies of the Milky Way (MW). However, we do not know how RPE stars are formed. Here, we present the result of a cosmological zoom-in simulation of an MW-like galaxy with $r$-process enrichment, performed with the highest resolution in both time and mass. Thanks to this advancement, unlike previous simulations, we find that most highly RPE ($r$-II; [Eu/Fe] $> +0.7$) stars are formed in low-mass dwarf galaxies that have been enriched in $r$-process elements for [Fe/H] $\,<-2.5$, while those with higher metallicity are formed in situ, in locally enhanced gas clumps that were not necessarily members of dwarf galaxies. This result suggests that low-mass accreted dwarf galaxies are the main formation site of $r$-II stars with [Fe/H] $\,<-2.5$. We also find that most low-metallicity $r$-II stars exhibit halo-like kinematics. Some $r$-II stars formed in the same halo show low dispersions in [Fe/H] and somewhat larger dispersions of [Eu/Fe], similar to the observations. The fraction of simulated $r$-II stars is commensurate with observations from the RPA, and the distribution of the predicted [Eu/Fe] for halo $r$-II stars matches that observed. These results demonstrate that RPE stars can be valuable probes of the accretion of dwarf galaxies in the early stages of their formation.

astro-ph.GA↗

arXiv2022

Elemental abundances in M31: Individual and Coadded Spectroscopic [Fe/H] and [α/Fe] throughout the M31 Halo with SPLASH

We present spectroscopic chemical abundances of red giant branch (RGB) stars in Andromeda (M31), using medium resolution ($R\sim6000$) spectra obtained via the Spectroscopic and Photometric Landscape of Andromeda's Stellar Halo (SPLASH) survey. In addition to individual chemical abundances, we coadd low signal-to-noise ratio (S/N) spectra of stars to obtain a high enough to measure average [Fe/H] and [$α$/Fe] abundances. We obtain individual and coadded measurements for [Fe/H] and [$α$/Fe] for M31 halo stars, covering a range of 9--180 kpc in projected radius from the center of M31. With these measurements, we greatly increase the number of outer halo ($R_{\mathrm{proj}} > 50$ kpc) M31 stars with spectroscopic [Fe/H] and [$α$/Fe], adding abundance measurements for 45 individual stars and 33 coadds from a pool of an additional 174 stars. We measure the spectroscopic metallicity ([Fe/H]) gradient, finding a negative radial gradient of $-0.0050\pm0.0003$ for all stars in the halo, consistent with gradient measurements obtained using photometric metallicities. Using the first measurements of [$α$/Fe] for M31 halo stars covering a large range of projected radii, we find a positive gradient ($+0.0026\pm0.0004$) in [$α$/Fe] as a function of projected radius. We also explore the distribution in [Fe/H]--[$α$/Fe] space as a function of projected radius for both individual and coadded measurements in the smooth halo, and compare these measurements to those stars potentially associated with substructure. These spectroscopic abundance distributions highlight the substantial evidence that M31 has had an appreciably different formation and merger history compared to our own Galaxy.

astro-ph.GA↗

arXiv2022

Existence of Tidal Tails for the Globular Cluster NGC 5824

Context. Several dynamically cold streams have been associated with certain globular clusters (GCs) based on orbital energies and angular momenta. Some of these streams are surprisingly far apart from their progenitors and one such pair is Triangulum and NGC 5824. Triangulum can be considered as a piece of NGC 5824 leading tail since the cluster's future orbit matches with the stream's track well. The existence of the leading tail for NGC 5824 is the motivation behind the search for its trailing tail. Aims. Our goal is to confirm the connection between Triangulum and NGC 5824 and seek the trailing tail of the cluster. Methods. The selection of member stars of Triangulum is made through various cuts in metallicity, proper motions (PMs), radial velocity and color-magnitude diagram (CMD). The selected members are compared in phase space to a mock stream which models the disruption of NGC 5824. We then try to detect the trailing tail of the cluster based on a modified matched-filter technique. Stars are assigned weights using their color differences from the cluster's locus in CMD. These weights are further scaled based on stars' departures from expected PMs of the model stream. Results. A total of 26 member stars for Triangulum are obtained and 16 of them are newly identified. These members are consistent with the mock stream in the phase space and their metalicity and position on the CMD are in good agreements with NGC 5824. By applying the matched-filter, a tenuous trailing tail of the cluster is detected, spanning $\sim$ 50$^\circ$ long on sky. The signature matches with the mock stream's trajectory well. Conclusions. Our results support that Triangulum stream acts as a part of the leading tail for NGC 5824. On the trailing side, we have detected a 50$^\circ$ tail extended from the cluster. The existence of both leading and trailing tails for the GC NGC 5824 is verified.

astro-ph.GA↗

arXiv2022

The Missing Satellite Problem Outside of the Local Group. II. Statistical Properties of Satellites of Milky Way-like Galaxies

We present a new observation of satellite galaxies around seven Milky Way (MW)-like galaxies located outside of the Local Group (LG) using Subaru/Hyper Suprime-Cam imaging data to statistically address the missing satellite problem. We select satellite galaxy candidates using magnitude, surface brightness, Sérsic index, axial ratio, full width half maximum, and surface brightness fluctuation cuts, followed by visual screening of false-positives such as optical ghosts of bright stars. We identify 51 secure dwarf satellite galaxies within the virial radius of nine host galaxies, two of which are drawn from the pilot observation presented in Paper I. We find that the average luminosity function of the satellite galaxies is consistent with that of the MW satellites, although the luminosity function of each host galaxy varies significantly. We observe an indication that more massive hosts tend to have a larger number of satellites. Physical properties of the satellites such as the size-luminosity relation is also consistent with the MW satellites. However, the spatial distribution is different; we find that the satellite galaxies outside of LG shows no sign of concentration or alignment, while that of the MW satellites is more concentrated around the host and exhibits a significant alignment. As we focus on relatively massive satellites with $M_V<-10$, we do not expect that the observational incompleteness can be responsible here. This trend might represent a peculiarity of the MW satellites, and further work is needed to understand its origin.

astro-ph.GA↗

arXiv2022

The global structure of the Milky Way's stellar halo based on the orbits of local metal-poor stars

We analyze the global structure of the Milky Way (MW)'s stellar halo including its dominant subcomponent, Gaia-Sausage-Enceladus (GSE). The method to reconstruct the global distribution of this old stellar component is to employ the superposition of the orbits covering over the large MW's space, where each of the orbit-weighting factor is assigned following the probability that the star is located at its currently observed position. The selected local, metal-poor sample with ${\rm [Fe/H]}<-1$ using {\it Gaia} EDR3 and SDSS DR16 shows that the global shape of the halo is systematically rounder at all radii in more metal-poor ranges, such that an axial ratio, $q$, is nearly 1 for ${\rm [Fe/H]}<-2.2$ and $\sim 0.7$ for $-1.4<{\rm [Fe/H]}<-1.0$. It is also found that a halo in relatively metal-rich range of ${\rm [Fe/H]}>-1.8$ actually shows a boxy/peanut-like shape, suggesting a major merger event. The distribution of azimuthal velocities shows a disk-like flattened structure at $-1.4<{\rm [Fe/H]}<-1.0$, which is thought to be the metal-weak thick disk. For the subsample of stars showing GSE-like kinematics and at ${\rm [Fe/H]}>-1.8$, its global density distribution is more spherical with $q \sim 0.9$ than the general halo sample, having an outer ridge at $r\sim20$~kpc. This spherical shape is consistent with the feature of accreted halo components and the ridge suggests that the orbit of GSE's progenitor has an apocenter of $\sim 20$~kpc. Implications for the formation of the stellar halo are also presented.

astro-ph.GA↗

arXiv2022

The Diversity of Core Halo Structure in the Fuzzy Dark Matter Model

In the fuzzy dark matter (FDM) model, gravitationally collapsed objects always consist of a solitonic core located within a virialised halo. Although various numerical simulations have confirmed that the collapsed structure can be described by a cored NFW like density profile, there is still disagreement about the relation between the core mass and the halo mass. To fully understand this relation, we have assembled a large sample of cored haloes based on both idealised soliton mergers and cosmological simulations with various box sizes. We find that there exists a sizeable dispersion in the core-halo mass relation that increases with halo mass, indicating that the FDM model allows cores and haloes to coexist in diverse configurations. We provide a new empirical equation for a core halo mass relation with uncertainties that can encompass all previously found relations in the dispersion, and emphasise that any observational constraints on the particle mass using a tight one-to-one core-halo mass relation should suffer from an additional uncertainty on the order of 50 % for halo masses $ \ge 10^9 (8 \times 10^{-23} eV/ (mc^2))^{3/2} M_\odot$. We suggest that tidal stripping may be one of the effects contributing to the scatter in the relation.

astro-ph.CO↗

arXiv2021

The nature of the Milky Way's stellar halo revealed by the three integrals of motion

We developed a new selection method of halo stars in the phase-space distribution defined by the three integrals of motion in an axisymmetric Galactic potential, ($E$, $L_z$, $I_3$), where $I_3$ is the third integral of motion. The method is used to explore the general chemo-dynamical structure of the halo based on stellar samples from SDSS-SEGUE DR7 and DR16-APOGEE, matched with Gaia-DR2. We found, (a) halo stars can be separated from disk stars by selecting over (1) $0 < L_z < 1500$ \kpckms, $(2I_3)^{1/2} > 1000$ \kpckms (orbital angle $θ_{\rm orb}$ $>$ 15-20 deg), and $E < -1.5 \times 10^5$ km$^2$ s$^{-2}$, and (2) $L_z < 0$ \kpckms. These selection criteria are free from kinematical biases introduced by the simple high-velocity cuts adopted in recent literature; (b) the averaged, or {\it coarse-grained}, halo phased-space distribution shows a monotonic exponential decrease with increasing $E$ and $I_3$ like the Michie-Bodenheimer models; (c) the inner stellar halo described in \citet{carollo2007,carollo2010} is found to comprise a combination of Gaia Enceladus debris (GE; \citealt{helmi2018}), lowest-$E$ stars (likely in-situ stars), as well as metal-poor prograde stars missed by the high velocity cuts selection; (d) the very metal poor outer halo, ([Fe/H] $< -$2.2), exhibits both retrograde and prograde rotation, with an asymmetric $L_z$ distribution towards high retrograde motions, and larger $θ_{\rm orb}$ than those possessed by the GE dominated inner halo; (e) the Sgr dSph galaxy could induce a long-range dynamical effect on local halo stars. Implication for the formation of the stellar halo are also discussed.

astro-ph.GA↗

arXiv2020

Proper motion measurements for stars up to $100$ kpc with Subaru HSC and SDSS Stripe 82

We present proper motion measurements for more than $0.55$ million main-sequence stars, by comparing astrometric positions of matched stars between the multi-band imaging datasets from the Hyper Suprime-Cam (HSC) Survey and the SDSS Stripe 82. In doing this we use $3$ million galaxies to recalibrate the astrometry and set up a common reference frame between the two catalogues. The exquisite depth and the nearly $12$ years of time baseline between HSC and SDSS enable high-precision measurements of statistical proper motions for stars down to $i\simeq 24$. A validation of our method is demonstrated by the agreement with the $Gaia$ proper motions, to the precision better than $0.1$ mas yr$^{-1}$. To retain the precision, we make a correction of the subtle effects due to the differential chromatic refraction in the SDSS images based on the comparison with the $Gaia$ proper motions against colour of stars, which is validated using the SDSS spectroscopic quasars. Combining with the photometric distance estimates for individual stars based on the precise HSC photometry, we show a significant detection of the net proper motions for stars in each bin of distance out to $100$ kpc. The two-component tangential velocities after subtracting the apparent motions due to our own motion display rich phase-space structures including a clear signature of the Sagittarius stream in the halo region of distance range $[10,\ 35]$ kpc. We also measure the tangential velocity dispersion in the distance range $5-20$ kpc and find that the data are consistent with a constant isotropic dispersion of $80\pm 10\ {\rm km/s}$. More distant stars appear to have random motions with respect to the Galactic centre on average.

astro-ph.GA↗