arXiv subjects

Shi Shao

Publications and source records attributed to Shi Shao.

At least 19 recordsLinked to original sources

arXiv2026

The Fate of the Milky Way--Andromeda System: To Merge or Not?

It has long been predicted that the Milky Way (MW) will eventually merge with Andromeda (M31), a view reinforced by \textit{HST} measurements indicating a small M31 transverse velocity. However, using updated \textit{Gaia}-based proper motions (PMs) and including the dynamical influence of the Large Magellanic Cloud (LMC) and M33, Sawala et al. reported an MW--M31 merger probability of $\sim$50\% within 10 Gyr, leaving the fate of the Local Group (LG) uncertain. Adopting their semi-analytic framework, we revisit this problem with the latest and most precise \textit{Gaia}-based PMs for M31 and M33, corrected for systematic offsets in \textit{Gaia} astrometry. In our fiducial model, the MW--M31 merger probability rises to 90\%, with a median merger time of $6.5_{-1.5}^{+1.3}$ Gyr, broadly restoring the classical picture. A sensitivity analysis shows that the merger probability depends strongly on the adopted M31 PM through two channels: a direct effect via the radial-tangential balance of the MW-M31 orbit, and a satellite-mediated effect, where the M31 PM fixes the orbital plane and determines how satellite-induced barycentric reflex motions project onto it, either promoting or suppressing a merger. Given this sensitivity, current measurements, while favoring a high merger probability, remain inconclusive, spanning from 64.7\% to 100\% across the 2$\sigma$ PM region. Future PM measurements with uncertainty of $\lesssim2\,\upmu\mathrm{as\,yr^{-1}}$ will be required to reach a firm conclusion, i.e., to constrain the probability range within 10\% at the 2$\sigma$ level.

astro-ph.GA↗

arXiv2025

Particle loads for cosmological simulations with equal-mass dark matter and baryonic particles

Traditional cosmological hydrodynamical simulations usually assume equal-numbered but unequal-mass dark matter and baryonic particles, which can lead to spurious collisional heating due to energy equipartition. To avoid such a numerical heating effect, a simulation setup with equal-mass dark matter and baryonic particles, which corresponds to a particle number ratio of $N_{\rm DM}:N_{\rm gas} = \Omega_{\rm cdm} / \Omega_{\rm b}$, is preferred. However, previous studies have typically used grid-based particle loads to prepare such initial conditions, which can only reach specific values for $N_{\rm DM}:N_{\rm gas}$ due to symmetry requirements. In this study, we propose a method based on the glass approach that can generate two-component particle loads with more general $N_{\rm DM}:N_{\rm gas}$ ratios. The method simultaneously relaxes two Poisson particle distributions by introducing an additional repulsive force between particles of the same component. We show that the final particle load closely follows the expected minimal power spectrum, $P(k) \propto k^{4}$, exhibits good homogeneity and isotropy properties, and remains sufficiently stable under gravitational interactions. Both the dark matter and gas components individually also exhibit uniform and isotropic distributions. We apply our method to two-component cosmological simulations and demonstrate that an equal-mass particle setup effectively mitigates the spurious collisional heating that arises in unequal-mass simulations. Our method can be extended to generate multi-component uniform and isotropic distributions. Our code based on Gadget-2 is available at https://github.com/liaoshong/gadget-2glass .

astro-ph.CO↗

arXiv2025

A North-South Metallicity Asymmetry in the Outer Galactic disk -- Evidence for the Pericentric Passage of the Sagittarius Dwarf Galaxy

We present maps of the mean metallicity distributions on the Galactocentric $R$--$Z$ plane at different azimuthal angles using red clump stars selected from the LAMOST and APOGEE surveys. In the inner disk ($R < $ 11\,kpc), the metallicity distribution is symmetric between the upper and lower disk. However, we find a North-South metallicity asymmetry in the outer disk ($R > 11$\,kpc), especially towards the anti-Galactic center ($-5^\circ < \Phi < 15^\circ$) direction. By further dissecting the map in age space, we detect this asymmetry across all mono-age stellar populations. However, the asymmetry is less pronounced in older populations ($\tau > 8$ Gyr) compared to younger ones ($\tau < 6$\,Gyr). This reduced significance likely stems from three factors: larger age uncertainties, fewer stars in the outer disk, and the kinematically hotter nature of older populations. The observed metallicity asymmetry may be the consequence of the purturbation of the recent pericentric passage through the Galactic disk and tidal force of the well-known Sagittarius dwarf galaxy.

astro-ph.GA↗

arXiv2025

ViT-based Local Volume dwarf galaxy Identificationin (VIDA) in the CSST survey

Identifying dwarf galaxies within the Local Volume is crucial for constraining the luminosity function of satellite galaxies in the nearby universe. We report the detection capabilities of dwarf galaxies within the Local Volume using the Chinese Space Station Telescope (CSST). Based on the simulated imaging data of CSST, we develop a detection and classification pipeline that combines traditional image-based search techniques with advanced machine learning classification models. The simulated Local Volume dwarf galaxies can be identified using a pre-processing method for "extended source detection", followed by classification with a pretrained ViT-Base model. This pipeline achieves a true positive rate (TPR) exceeding 85% with a false positive rate (FPR) of only 0.1%. We quantify the detection completeness of Local Volume dwarf galaxies across a three-dimensional parameter space defined by absolute magnitude ($M_V$), half-light radius ($R_h$), and heliocentric distance, based on simulated single-exposure CSST wide-field imaging survey data. For unresolved or semi-resolved dwarf galaxies, our method achieves a significantly deeper absolute magnitude detection limit compared to catalog-based approaches, reaching $M_V = -7$ within 10 \Mpc. By combining this image-based approach with traditional stellar catalog-based "matched filter" techniques, our automated framework established in this work can identify dwarf galaxies within 20 \Mpc for the CSST mission.

astro-ph.GA↗

arXiv2025

The Shape and Mass of the Galactic Dark Matter Halo from the Axisymmetric Jeans Model

We explore the density profile, shape, and virial mass of the Milky Way's dark matter halo using K giants (KG) from LAMOST and SDSS/SEGUE, as well as blue horizontal branch (BHB) stars from SDSS. Incorporating Gaia DR3 proper motions, we first investigate the velocity ellipsoid distribution within the $(R, |z|)$ space. The ellipsoids projected onto the $(v_R, v_z)$ plane exhibit near-spherical alignment. We then probe the underlying dark matter distribution using the axisymmetric Jeans equations with multi-Gaussian expansion (MGE) and the spherically aligned Jeans anisotropic modelling (JAM${\rm sph}$), allowing for different flattened dark matter density models. For each model, we apply two fitting approaches: fitting the KGs and BHBs separately or fit them simultaneously as two dynamical tracers in one gravitational potential. We find consistent results on the dark matter density profiles, $r_{200}$, and $M_{200}$ within a 1-$\sigma$ confidence region for models constrained by KGs, BHBs, and both. We find the strongest consistency between KGs and BHBs in constraining dark matter profiles for models incorporating radially varying halo flattening ($q(r_{\rm gc})$), which suggests the Milky Way's dark matter halo shape evolves with Galactocentric distance ($r_{\rm gc}$). Specifically, the halo flattening parameter $q_h$ decreases within $r_{\rm gc} < 20$ kpc and increases for $r_{\rm gc} > 20$ kpc. In this model, $M_{\rm tot} (< 60~{\rm kpc}) = 0.533^{+0.061}_{-0.054} \times 10^{12}$ $M_{\odot}$, $r_{200}$ is $188\pm15$ kpc, with $M_{200}$ estimated at $0.820^{+0.210}_{-0.186} \times 10^{12} M_{\odot}$.

astro-ph.GA↗

arXiv2025

Where are the Population III star relics in the simulated Milky Way analogues?

Using 6 Milky Way analogues with two different numerical resolutions from the Auriga simulation, we investigate the total mass, spatial distribution and kinematics of the Population III star relics in the Milky Way analogues at $z=0$. These relics (primarily second generation stars) formed over a wide redshift range, from about $z=22$ to $z=4$, with an average formation redshift of $z \sim 10.0$, and comprise about $2\times10^{-5}$ of the entire galactic stellar population. The disk and bulge components host only a small fraction of these relics, contributing less than $12$ percent in total. The stellar halo, in particular the outer stellar halo of which galactic radius $r>30$ kpc, hosts the largest fraction (about 46 percent on average), with an average of one relic star for per $4,000$ to $10,000$ stars, making it a promising region for observational searches. Additionally, around $18$ percent of the Population III star relics are found in satellite galaxies, with smaller and older satellite galaxies tending to contain a higher proportion of these stars. Thus, low-mass and early-formed satellite galaxies are also ideal targets for finding such relics, although some satellite galaxies may lack them entirely. The spatial distribution and kinematics of these stars show good numerical convergence across different simulation resolutions. Our results provide valuable guidance for searches of the Population III star relics and offer insights for interpreting findings from ongoing and future stellar archaeology surveys.

astro-ph.GA↗

arXiv2024

Apostle--Auriga: Effects of stellar feedback subgrid models on the evolution of angular momentum in disc galaxies

Utilizing the Apostle--Auriga simulations, which start from the same zoom-in initial conditions of Local Group-like systems but run with different galaxy formation subgrid models and hydrodynamic solvers, we study the impact of stellar feedback models on the evolution of angular momentum in disc galaxies. At $z = 0$, Auriga disc galaxies tend to exhibit higher specific angular momenta compared to their cross-matched Apostle counterparts. By tracing the evolution history of the Lagrangian mass tracers of the in-situ star particles in the $z = 0$ galaxies, we find that the specific angular momentum distributions of the gas tracers from the two simulations at the halo accretion time are relatively similar. The present-day angular momentum difference is mainly driven by the physical processes occurring inside dark matter haloes, especially galactic fountains. Due to the different subgrid implementations of stellar feedback processes, Auriga galaxies contain a high fraction of gas that has gone through recycled fountain (${\sim} 65$ per cent) which could acquire angular momentum through mixing with the high angular momentum circumgalactic medium (CGM). In Apostle, however, the fraction of gas that has undergone the recycled fountain process is significantly lower (down to ${\sim} 20$ per cent for Milky Way-sized galaxies) and the angular momentum acquisition from the CGM is marginal. As a result, the present-day Auriga galaxies overall have higher specific angular momenta.

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arXiv2024

How does the velocity anisotropy of halo stars, dark matter and satellite galaxies depend on host halo properties?

We investigate the mass ($M_{200}$) and concentration ($c_{200}$) dependencies of the velocity anisotropy ($\beta$) profiles for different components in the dark matter halo, including halo stars, dark matter and subhalos, using systems from the IllustrisTNG simulations. Beyond a critical radius, $\beta$ becomes more radial with the increase of $M_{200}$, reflecting more prominent radial accretion around massive halos. The critical radius is $r\sim r_s$, $0.3~r_s$ and $r_s$ for halo stars, dark matter and subhalos, with $r_s$ the scale radius of host halos. This dependence on $M_{200}$ is the strongest for subhalos, and the weakest for halo stars. In central regions, $\beta$ of halo stars and dark matter particles gets more isotropic with the increase of $M_{200}$ in TNG300 due to baryons. By contrast, $\beta$ of dark matter from the dark matter only TNG300-Dark run shows much weaker dependence on $M_{200}$ within $r_s$. Dark matter in TNG300 is slightly more isotropic than in TNG300-Dark at $0.2~r_s r_s$ as $\beta_\mathrm{star}-\beta_\mathrm{DM}=(-0.028 \pm 0.008)\log_{10}M_{200}/M_\odot + (0.690\pm0.010)$.

astro-ph.GA↗

arXiv2024

Effectiveness of halo and galaxy properties in reducing the scatter in the stellar-to-halo mass relation

The stellar-to-halo mass relation (SHMR) is a fundamental relationship between galaxies and their host dark matter haloes. In this study, we examine the scatter in this relation for primary galaxies in the semi-analytic L-Galaxies model and two cosmological hydrodynamical simulations, \eagle{} and \tng{}. We find that in low-mass haloes, more massive galaxies tend to reside in haloes with higher concentration, earlier formation time, greater environmental density, earlier major mergers, and, to have older stellar populations, which is consistent with findings in various studies. Quantitative analysis reveals the varying significance of halo and galaxy properties in determining SHMR scatter across simulations and models. In \eagle{} and \tng{}, halo concentration and formation time primarily influence SHMR scatter for haloes with $M_{\rm h}<10^{12}~\rm M_\odot$, but the influence diminishes at high mass. Baryonic processes play a more significant role in \lgal{}. For halos with $M_{\rm h} <10^{11}~\rm M_\odot$ and $10^{12}~\rm M_\odot 10^{13}~\rm M_\odot$, supermassive black hole mass becomes more important. Interestingly, it is found that AGN feedback may increase the amplitude of the scatter and decrease the dependence on halo properties at high masses.

astro-ph.GA↗

arXiv2024

A younger Universe implied by satellite pair correlations from SDSS observations of massive galaxy groups

Many of the satellites of galactic-mass systems such as the Miky Way, Andromeda and Centaurus A show evidence of coherent motions to a larger extent than most of the systems predicted by the standard cosmological model. It is an open question if correlations in satellite orbits are present in systems of different masses. Here , we report an analysis of the kinematics of satellite galaxies around massive galaxy groups. Unlike what is seen in Milky Way analogues, we find an excess of diametrically opposed pairs of satellites that have line-of-sight velocity offsets from the central galaxy of the same sign. This corresponds to a $\pmb{6.0σ}$ ($\pmb{p}$-value $\pmb{=\ 9.9\times10^{-10}}$) detection of non-random satellite motions. Such excess is predicted by up-to-date cosmological simulations but the magnitude of the effect is considerably lower than in observations. The observational data is discrepant at the $\pmb{4.1σ}$ and $\pmb{3.6σ}$ level with the expectations of the Millennium and the Illustris TNG300 cosmological simulations, potentially indicating that massive galaxy groups assembled later in the real Universe. The detection of velocity correlations of satellite galaxies and tension with theoretical predictions is robust against changes in sample selection. Using the largest sample to date, our findings demonstrate that the motions of satellite galaxies represent a challenge to the current cosmological model.

astro-ph.GA↗

arXiv2023

Subhalo abundance and satellite spatial distribution in Milky Way-Andromeda-like paired haloes

We study the subhalo and satellite populations in haloes similar to the Milky Way (MW)-Andromeda paired configuration in the Millennium II and P-Millennium simulations. We find subhaloes are $5\%-15\%$ more abundant in paired haloes than their isolated counterparts that have the same halo mass and large-scale environmental density. Paired haloes tend to reside in a more isotropic environment than isolated haloes, the shear tensor of their large-scale tidal field is possibly responsible for this difference. We also study the thickness of the spatial distribution of the top 11 most massive satellite galaxies obtained in the semi-analytic galaxy sample constructed from the Millennium II simulation. Moreover, satellites that have lost their host subhaloes due to the resolution limit of the simulation have been taken into account. As a result, we find that the difference in the distribution of the satellite thickness between isolated and paired haloes is indistinguishable, which suggests that the paired configuration is not responsible for the observed plane of satellites in the Milky Way. The results in this study indicate the paired configuration could bring some nonnegligible effect on the subhalo abundance in the investigation of the Milky Way's satellite problems.

astro-ph.GA↗

arXiv2023

The galaxy size to halo spin relation of disk galaxies in cosmological hydrodynamical simulations

In the standard disk galaxy formation model, the sizes of galactic disks are tightly related to the spin parameters $λ$ of their dark matter haloes. The model has been wildly adopted by various semi-analytic galaxy formation models which have been extremely successful to interpret a large body of observational data. However, the size-$λ$ correlation was rarely seen in most modern hydrodynamical simulations of galaxy formation. In this short paper, we make use of 4 sets of large hydrodynamical simulations to explore the size-spin parameter relation with a large sample of simulated disk galaxies, and compare it with a popular disk galaxy formation model of Mo et al. (1998). Intriguingly, galactic sizes correlate strongly with spin parameters of their dark matter haloes in the simulations developed by the IllustrisTNG collaborations, albeit the relation does not always agree with prediction of MMW98 model over all stellar mass range we examined. There is also a size-spin correlation for the Milky way analogies in the EAGLE simulations, while it is relatively weaker than that of the IllustrisTNG counterparts. For the dwarfs in the simulations from the EAGLE collaboration, there is NULL correlation. We conclude that either the detailed subgrid physics or hydrodynamics solvers account for the size-spin relation, which will be explored in our future work.

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arXiv2023

Dark against luminous matter around isolated central galaxies: a comparative study between modern surveys and Illustris-TNG

Based on independent shear measurements using the DECaLS/DR8 imaging data, we measure the weak lensing signals around isolated central galaxies (ICGs) from SDSS/DR7 at $z\sim0.1$. The projected stellar mass density profiles of surrounding satellite galaxies are further deduced, using photometric sources from the Hyper Suprime-Cam (HSC) survey (pDR3). The signals of ICGs $+$ their extended stellar halos are taken from Wang et al.(2021). All measurements are compared with predictions by the Illustris-TNG300-1 simulation. We find, overall, a good agreement between observation and TNG300. In particular, a correction to the stellar mass of massive observed ICGs is applied based on the calibration of He et al.(2013), which brings a much better agreement with TNG300 predicted lensing signals at $\log_{10}M_\ast/M_\odot>11.1$. In real observation, red ICGs are hosted by more massive dark matter halos, have more satellites and more extended stellar halos than blue ICGs at fixed stellar mass. However, in TNG300 there are more satellites around blue ICGs at fixed stellar mass, and the outer stellar halos of red and blue ICGs are similar. The stellar halos of TNG galaxies are more extended compared with real observed galaxies, especially for blue ICGs with $\log_{10}M_\ast/M_\odot>10.8$. We find the same trend for TNG100 galaxies and for true halo central galaxies. The tensions between TNG and real galaxies might indicate that satellite disruptions are stronger in TNG. In both TNG300 and observation, satellites approximately trace the underlying dark matter distribution beyond $0.1R_{200}$, but the fraction of total stellar mass in TNG300 does not show the same radial distribution as real galaxies.

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arXiv2022

The spatial distribution of satellites in galaxy clusters

The planar distributions of satellite galaxies around the Milky Way and Andromeda have been extensively studied as potential challenges to the standard cosmological model. Using the Sloan Digital Sky Survey and the Millennium simulation we extend such studies to the satellite galaxies of massive galaxy clusters. We find that both observations and simulations of galaxy clusters show an excess of anisotropic satellite distributions. On average, satellites in clusters have a higher degree of anisotropy than their counterparts in Milky-Way-mass hosts once we account for the difference in their radial distributions. The normal vector of the plane of satellites is strongly aligned with the host halo's minor axis, while the alignment with the large-scale structure is weak. At fixed cluster mass, the degree of anisotropy is higher at higher redshift. This reflects the highly anisotropic nature of satellites accretion points, a feature that is partly erased by the subsequent orbital evolution of the satellites. We also find that satellite galaxies are mostly accreted singly so group accretion is not the explanation for the high flattening of the planes of satellites.

astro-ph.GA↗

arXiv2021

Measuring the Mass of Missing Baryons in the Halo of Andromeda Galaxy with Gamma-Ray Observations

One of the biggest mysteries in the modern cosmology and galaxy formation is the hideout of the "missing baryons". The leading theory of galaxy formation predicts that a huge amount of baryons resides around galaxies extending out to their virial radii in the form of diffuse and hot gas of $10^6-10^7\,$K, which is also known as the major component of the circumgalactic medium (CGM). Studies by various groups via different techniques, however, have not reached a consensus on the role of CGM in accounting for the missing baryons, with the estimated contribution ranging from a minor fraction to enclosing the baryon budget of the galaxy. In this work we attempt to measure the mass of missing baryons in CGM with a novel method based on the gamma-ray observations of the extended halo of the Andromeda Galaxy. Since cosmic-ray particles that are generated inside the galaxy will eventually escape to the CGM, they will produce gamma-ray emission via the proton-proton collision with CGM. Different from some traditional measurements which are sensitive only to gas in certain specific temperature range, the hadronic gamma-ray flux is sensitive to baryonic gases in all phases and does not rely on the metallicity in the halo. Our result suggests that the total baryon mass contained within the virial radius is less than $(1.4-5)\times 10^{10}M_\odot$ according to the gamma-ray intensity obtained with a model-dependent analysis. It implies that the CGM of Andromeda Galaxy may not account for more than $30\%$ of the missing baryons, but the result is subject to uncertainties from the gamma-ray intensity upper limit, diffusion coefficient of the CRs in the halo as well as the stellar mass and dark matter halo mass of the galaxy. This method will become more constraining provided better understandings on these issues and more sensitive gamma-ray telescopes in the future.

astro-ph.HE↗

arXiv2020

The twisted dark matter halo of the Milky Way

We analyse systems analogous to the Milky Way (MW) in the EAGLE cosmological hydrodynamics simulation in order to deduce the likely structure of the MW's dark matter halo. We identify MW-mass haloes in the simulation whose satellite galaxies have similar kinematics and spatial distribution to those of the bright satellites of the MW, specifically systems in which the majority of the satellites (8 out of 11) have nearly co-planar orbits that are also perpendicular to the central stellar disc. We find that the normal to the common orbital plane of the co-planar satellites is well aligned with the minor axis of the host dark matter halo, with a median misalignment angle of only $17.3^\circ$. Based on this result, we infer that the minor axis of the Galactic dark matter halo points towards $(l,b)=(182^\circ,-2^\circ)$, with an angular uncertainty at the 68 and 95 percentile confidence levels of 22$^\circ$ and 43$^\circ$ respectively. Thus, the inferred minor axis of the MW halo lies in the plane of the stellar disc. The halo, however, is not homologous and its flattening and orientation vary with radius. The inner parts of the halo are rounder than the outer parts and well-aligned with the stellar disc (that is the minor axis of the halo is perpendicular to the disc). Further out, the halo twists and the minor axis changes direction by $90^\circ$. This twist occurs over a very narrow radial range and reflects variations in the filamentary network along which mass was accreted into the MW.

astro-ph.GA↗

arXiv2020

The survival of globular clusters in a cuspy Fornax

It has long been argued that the radial distribution of globular clusters (GCs) in the Fornax dwarf galaxy requires its dark matter halo to have a core of size $\sim 1$ kpc. We revisit this argument by investigating analogues of Fornax formed in E-MOSAICS, a cosmological hydrodynamical simulation that self-consistently follows the formation and evolution of GCs in the EAGLE galaxy formation model. In EAGLE, Fornax-mass haloes are cuspy and well described by the Navarro-Frenk-White profile. We post-process the E-MOSAICS to account for GC orbital decay by dynamical friction, which is not included in the original model. Dynamical friction causes 33 per cent of GCs with masses $M_{\rm GC}\geq4\times10^4 {~\rm M_\odot}$ to sink to the centre of their host where they are tidally disrupted. Fornax has a total of five GCs, an exceptionally large number compared to other galaxies of similar stellar mass. In the simulations, we find that only 3 per cent of the Fornax analogues have five or more GCs, while 30 per cent have only one and 35 per cent have none. We find that GC systems in satellites are more centrally concentrated than in field dwarfs, and that those formed in situ (45 per cent) are more concentrated than those that were accreted. The survival probability of a GC increases rapidly with the radial distance at which it formed ($r_{\rm init}$): it is 37 per cent for GCs with $r_{\rm init} \leq 1$ kpc and 92 per cent for GCs with $r_{\rm init} \geq 1$ kpc. The present-day radial distribution of GCs in E-MOSAICS turns out to be indistinguishable from that in Fornax, demonstrating that, contrary to claims in the literature, the presence of five GCs in the central kiloparsec of Fornax does not exclude a cuspy DM halo.

astro-ph.GA↗

arXiv2020

Galaxy properties in the cosmic web of EAGLE simulation

We investigate the dependence of the galaxy properties on cosmic web environments using the most up-to-date hydrodynamic simulation: Evolution and Assembly of Galaxies and their Environments (EAGLE). The baryon fractions in haloes and the amplitudes of the galaxy luminosity function decrease going from knots to filaments to sheets to voids. Interestingly, the value of L$^*$ varies dramatically in different cosmic web environments. At z = 0, we find a characteristic halo mass of $10^{12} h^{-1}\rm M_{\odot}$, below which the stellar-to-halo mass ratio is higher in knots while above which it reverses. This particular halo mass corresponds to a characteristic stellar mass of $1.8\times 10^{10} h^{-1}\rm M_{\odot}$. Below the characteristic stellar mass central galaxies have redder colors, lower sSFRs and higher metallicities in knots than those in filaments, sheets and voids, while above this characteristic stellar mass, the cosmic web environmental dependences either reverse or vanish. Such dependences can be attributed to the fact that the active galaxy fraction decreases along voids, sheets, filaments and knots. The cosmic web dependences get weaker towards higher redshifts for most of the explored galaxy properties and scaling relations, except for the gas metallicity vs. stellar mass relation.

astro-ph.GA↗