arXiv subjects

Kohei Ichikawa

Publications and source records attributed to Kohei Ichikawa.

At least 73 records · Page 4Linked to original sources

arXiv2021

The eROSITA Final Equatorial-Depth Survey (eFEDS): The AGN Catalogue and its X-ray Spectral Properties

Context: After the successful launch of the Spectrum-Roentgen-Gamma (SRG) mission in July 2019, eROSITA, the soft X-ray instrument aboard SRG, performed scanning observations of a large contiguous field, namely the eROSITA Final Equatorial Depth Survey (eFEDS), ahead of the planned four-year all-sky survey. eFEDS yielded a large sample of X-ray sources with very rich multi-band photometric and spectroscopic coverage. Aims: We present here the eFEDS Active Galactic Nuclei (AGN) catalog and the eROSITA X-ray spectral properties of the eFEDS sources. Methods: Using a Bayesian method, we perform a systematic X-ray spectral analysis for all eFEDS sources. The appropriate model is chosen based on the source classification and the spectral quality, and, in the case of AGN, including the possibility of intrinsic (rest-frame) absorption and/or soft excess emission. Hierarchical Bayesian modeling (HBM) is used to estimate the spectral parameter distribution of the sample. Results: X-ray spectral properties are presented for all eFEDS X-ray sources. There are 21952 candidate AGN, which comprise 79% of the eFEDS sample. Despite a large number of faint sources with low photon counts, our spectral fitting provides meaningful measurements of fluxes, luminosities, and spectral shapes for a majority of the sources. This AGN catalog is dominated by X-ray unobscured sources, with an obscured (logNH>21.5) fraction of 10% derived by HBM. The power-law slope of the catalog can be described by a Gaussian distribution of 1.94+-0.22. Above a photon counts threshold of 500, nine out of 50 AGN have soft excess detected. For the sources with blue UV to optical color (type-I AGN), the X-ray emission is well correlated with the UV emission with the usual anti-correlation between the X-ray to UV spectral slope α_{OX} and the UV luminosity.

astro-ph.HE↗

arXiv2021

kEDM: A Performance-portable Implementation of Empirical Dynamic Modeling using Kokkos

Empirical Dynamic Modeling (EDM) is a state-of-the-art non-linear time-series analysis framework. Despite its wide applicability, EDM was not scalable to large datasets due to its expensive computational cost. To overcome this obstacle, researchers have attempted and succeeded in accelerating EDM from both algorithmic and implementational aspects. In previous work, we developed a massively parallel implementation of EDM targeting HPC systems (mpEDM). However, mpEDM maintains different backends for different architectures. This design becomes a burden in the increasingly diversifying HPC systems, when porting to new hardware. In this paper, we design and develop a performance-portable implementation of EDM based on the Kokkos performance portability framework (kEDM), which runs on both CPUs and GPUs while based on a single codebase. Furthermore, we optimize individual kernels specifically for EDM computation, and use real-world datasets to demonstrate up to $5.5\times$ speedup compared to mpEDM in convergent cross mapping computation.

cs.DC↗

arXiv2021

Optical Spectroscopy of Dual Quasar Candidates from the Subaru HSC-SSP program

We report on a spectroscopic program to search for dual quasars using Subaru Hyper Suprime-Cam (HSC) images of SDSS quasars which represent an important stage during galaxy mergers. Using Subaru/FOCAS and Gemini-N/GMOS, we identify three new physically associated quasar pairs having projected separations less than 20 kpc, out of 26 observed candidates. These include the discovery of the highest redshift ($z=3.1$) quasar pair with a separation $<$ 10 kpc. Based on the sample acquired to date, the success rate of identifying physically associated dual quasars is $19\%$ when excluding stars based on their HSC colors. Using the full sample of six spectroscopically confirmed dual quasars, we find that the black holes in these systems have black hole masses ($M_{BH} \sim 10^{8-9}M_{\odot}$) similar to single SDSS quasars as well as their bolometric luminosities and Eddington ratios. We measure the stellar mass of their host galaxies based on 2D image decomposition of the five-band ($grizy$) optical emission and assess the mass relation between supermassive black holes (SMBHs) and their hosts. Dual SMBHs appear to have elevated masses relative to their host galaxies. Thus mergers may not necessarily align such systems onto the local mass relation, as suggested by the Horizon-AGN simulation. This study suggests that dual luminous quasars are triggered prior to the final coalescence of the two SMBHs, resulting in early mass growth of the black holes relative to their host galaxies.

astro-ph.GA↗

arXiv2021

BAT AGN Spectroscopic Survey-XXIII. A New Mid-Infrared Diagnostic for Absorption in Active Galactic Nuclei

In this study, we use the SWIFT/BAT AGN sample, which has received extensive multiwavelength follow-up analysis as a result of the BAT AGN Spectroscopic Survey (BASS), to develop a diagnostic for nuclear obscuration by examining the relationship between the line-of-sight column densities ($N_{\rm{H}}$), the 2-10 keV-to-$12\,\rm{μm}$ luminosity ratio, and WISE mid-infrared colors. We demonstrate that heavily obscured AGNs tend to exhibit both preferentially ''redder'' mid-infrared colors and lower values of $L_{\rm{X,\,Obs.}}$/$L_{12\,\rm{μm}}$ than less obscured AGNs, and we derive expressions relating $N_{\rm{H}}$ to the $L_{\rm{X,\,Obs.}}$/$L_{12\,\rm{μm}}$ and $L_{22\,\rm{μm}}$/$L_{4.6\,\rm{μm}}$ luminosity ratios as well as develop diagnostic criteria using these ratios. Our diagnostic regions yield samples that are $\gtrsim80$% complete and $\gtrsim60$% pure for AGNs with log($N_{\rm{H}})\geq24$, as well as $\gtrsim85$% pure for AGNs with $\rm{log}(N_{\rm{H}})\gtrsim23.5$. We find that these diagnostics cannot be used to differentiate between optically star forming galaxies and active galaxies. Further, mid-IR contributions from host galaxies that dominate the observed $12~\rm{μm}$ emission can lead to larger apparent X-ray deficits and redder mid-IR colors than the AGNs would intrinsically exhibit, though this effect helps to better separate less obscured and more obscured AGNs. Finally, we test our diagnostics on two catalogs of AGNs and infrared galaxies, including the XMM-Newton XXL-N field, and we identify several known Compton-thick AGNs as well as a handful of candidate heavily obscured AGNs based upon our proposed obscuration diagnostics.

astro-ph.GA↗

arXiv2020

Cometary records revise Eastern Mediterranean chronology around 1240 CE

Eirene Laskarina, empress of John III Batatzes of the exiled Byzantine Empire of Nicaea (1204--1261 CE), was an important Eastern Mediterranean figure in the first half of the thirteenth century. We reassess the date of Eirene's death, which has been variously dated between late 1239 and 1241, with the understanding that narrowing the range in which this event occurred contributes much to understanding the political situation in the area around 1240. George Akropolites, a famous official of the Empire, gives an account that connects Eirene's death to a comet that appeared "six months earlier", thus pointing to two comet candidates that were visible from the Eastern Mediterranean between 1239 and 1241, one recorded on "3 June 1239" and the other on "31 January 1240". Recent historians prefer the former, based on historical circumstances and without a critical assessment of the comet records. We revisit the historical records and reveal that the "3 June 1239" candidate was not a comet. On the other hand, the other candidate, sighted on "31 January 1240", was a comet, as supported by multiple historical records in multiple regions, and is also a good fit with Akropolites's narrative. Therefore, we conclude that Eirene died six months after the comet that was seen on 31 January 1240, which places her death in the summer of 1240. Given that the date of her death is crucial for determining some other contemporary events across the Eastern Mediterranean, our results offer a solid basis for further research on the thirteenth-century Eastern Mediterranean.

physics.hist-ph↗

arXiv2020

Massively Parallel Causal Inference of Whole Brain Dynamics at Single Neuron Resolution

Empirical Dynamic Modeling (EDM) is a nonlinear time series causal inference framework. The latest implementation of EDM, cppEDM, has only been used for small datasets due to computational cost. With the growth of data collection capabilities, there is a great need to identify causal relationships in large datasets. We present mpEDM, a parallel distributed implementation of EDM optimized for modern GPU-centric supercomputers. We improve the original algorithm to reduce redundant computation and optimize the implementation to fully utilize hardware resources such as GPUs and SIMD units. As a use case, we run mpEDM on AI Bridging Cloud Infrastructure (ABCI) using datasets of an entire animal brain sampled at single neuron resolution to identify dynamical causation patterns across the brain. mpEDM is 1,530 X faster than cppEDM and a dataset containing 101,729 neuron was analyzed in 199 seconds on 512 nodes. This is the largest EDM causal inference achieved to date.

cs.DC↗

arXiv2020

Faint Quasars Live in the Same Number Density Environments as Lyman Break Galaxies at z ~ 4

Characterizing high-z quasar environments is key to understanding the co-evolution of quasars and the surrounding galaxies. To restrict their global picture, we statistically examine the g-dropout galaxy overdensity distribution around 570 faint quasar candidates at z ~ 4, based on the Hyper Suprime-Cam Subaru Strategic Program survey. We compare the overdensity significances of g-dropout galaxies around the quasars with those around g-dropout galaxies, and find no significant difference between their distributions. A total of 4 (22) out of the 570 faint quasars, 0.7_{-0.4}^{+0.4} (3.9_{-0.8}^{+0.8}) %, are found to be associated with the > 4 sigma overdense regions within an angular separation of 1.8 (3.0) arcmin, which is the typical size of protoclusters at this epoch. This is similar to the fraction of g-dropout galaxies associated with the > 4 sigma overdense regions. This result is consistent with our previous work that 1.3_{-0.9}^{+0.9} % and 2.0_{-1.1}^{+1.1} % of luminous quasars detected in the Sloan Digital Sky Survey exist in the > 4 sigma overdense regions within 1.8 and 3.0 arcmin separations, respectively. Therefore, we suggest that the galaxy number densities around quasars are independent of their luminosity, and most quasars do not preferentially appear in the richest protocluster regions at z ~ 4. The lack of an apparent positive correlation between the quasars and the protoclusters implies that: i) the gas-rich major merger rate is relatively low in the protocluster regions, ii) most high-z quasars may appear through secular processes, or iii) some dust-obscured quasars exist in the protocluster regions.

astro-ph.GA↗

arXiv2020

NuSTAR Non-detection of a Faint Active Galactic Nucleus in an Ultraluminous IR Galaxy with Kpc-scale Fast Wind

Large-scale outflows are generally considered as a possible evidence that active galactic nuclei (AGNs) can severely affect their host galaxies. Recently an ultraluminous IR galaxy (ULIRG) at $z=0.49$, AKARI J0916248+073034, was found to have a galaxy-scale [OIII] $λ$5007 outflow with one of the highest energy-ejection rates at $z<1.6$. However, the central AGN activity estimated from its torus mid-IR (MIR) radiation is weak relative to the luminous [OIII] emission. In this work we report the first NuSTAR hard X-ray follow-up of this ULIRG to constrain its current AGN luminosity. The intrinsic 2-10 keV luminosity shows a 90% upper-limit of $3.0\times10^{43}$ erg s$^{-1}$ assuming Compton-thick obscuration ($N_{\rm H}=1.5\times10^{24}$ cm$^{-2}$), which is only 3.6% of the luminosity expected from the extinction corrected [OIII] luminosity. With the NuSTAR observation, we succeed to identify that this ULIRG has a most extreme case of X-ray deficit among local ULIRGs. A possible scenario to explain the drastic declining in both of the corona (X-ray) and torus (MIR) is that the primary radiation from the AGN accretion disk is currently in a fading status, as a consequence of a powerful nuclear wind suggested by its powerful ionized outflow in the galaxy scale.

astro-ph.GA↗

arXiv2020

BAT AGN Spectroscopic Survey-XX: Molecular Gas in Nearby Hard X-ray Selected AGN Galaxies

We present the host galaxy molecular gas properties of a sample of 213 nearby (0.01 10^44 erg/s) increases by ~10-100 between a molecular gas mass of 10^8.7 Msun and 10^10.2 Msun. Higher Eddington ratio AGN galaxies tend to have higher molecular gas masses and gas fractions. Higher column density AGN galaxies (Log NH>23.4) are associated with lower depletion timescales and may prefer hosts with more gas centrally concentrated in the bulge that may be more prone to quenching than galaxy wide molecular gas. The significant average link of host galaxy molecular gas supply to SMBH growth may naturally lead to the general correlations found between SMBHs and their host galaxies, such as the correlations between SMBH mass and bulge properties and the redshift evolution of star formation and SMBH growth.

astro-ph.GA↗

arXiv2020

Tracing the co-evolution path of super massive black holes and spheroids with AKARI-selected ultra-luminous IR galaxies at intermediate redshifts

We present the stellar population and ionized-gas outflow properties of ultra-luminous IR galaxies (ULIRGs) at $z=$ 0.1-1.0, which are selected from AKARI FIR all-sky survey. We construct a catalog of 1077 ULIRGs to examine feedback effect after major mergers. 202 out of the 1077 ULIRGs are spectroscopically identified by SDSS and Subaru/FOCAS observations. Thanks to deeper depth and higher resolution of AKARI compared to the previous IRAS survey, and reliable identification from WISE MIR pointing, the sample is unique in identifying optically-faint (i$\sim$20) IR-bright galaxies, which could be missed in previous surveys. A self-consistent spectrum-SED decomposition method, which constrains stellar population properties in SED modeling based on spectral fitting results, has been employed for 149 ULIRGs whose optical continua are dominated by host galaxies. They are massive galaxies ($M_{\rm star}\sim10^{11}$-$10^{12}$ M$_{\odot}$), associated with intense star formation activities (SFR $\sim$ 200-2000 M$_{\odot}$ yr$^{-1}$). The sample covers a range of AGN bolometric luminosity of $10^{10}$-$10^{13}$ L$_{\odot}$, and the outflow velocity measured from [OIII] 5007A line shows a correlation with AGN luminosity. Eight galaxies show extremely fast outflows with velocity up to 1500-2000 km s$^{-1}$. However, the co-existence of vigorous starbursts and strong outflows suggests the star formation has not been quenched during the ULIRG phase. By deriving stellar mass and mass fraction of young stellar population, we find no significant discrepancies between stellar properties of ULIRGs with weak and powerful AGNs. The results are not consistent with the merger-induced evolutionary scenario, which predicts that SF-dominated ULIRGs show smaller stellar mass and younger stellar populations compared to AGN-dominated ULIRGs.

astro-ph.GA↗

arXiv2020

Wide and Deep Exploration of Radio Galaxies with Subaru HSC (WERGS). III. Discovery of a z = 4.72 Radio Galaxy with Lyman Break Technique

We report a discovery of $z = 4.72$ radio galaxy, HSC J083913.17+011308.1, by using the Lyman break technique with the Hyper Suprime-Cam Subaru Strategic Survey (HSC-SSP) catalog for VLA FIRST radio sources. The number of known high-$z$ radio galaxies (HzRGs) at $z > 3$ is quite small to constrain the evolution of HzRGs so far. The deep and wide-area optical survey by HSC-SSP enables us to apply the Lyman break technique to a large search for HzRGs. For an HzRG candidate among pre-selected $r$-band dropouts with a radio detection, a follow-up optical spectroscopy with GMOS/Gemini has been performed. The obtained spectrum presents a clear Ly$α$ emission line redshifted to $z=4.72$. The SED fitting analysis with the rest-frame UV and optical photometries suggests the massive nature of this HzRG with $\log{M_*/M_{\odot}} = 11.4$. The small equivalent width of Ly$α$ and the moderately red UV colors indicate its dusty host galaxy, implying a chemically evolved and dusty system. The radio spectral index does not meet a criterion for an ultra-steep spectrum: $α^{325}_{1400}$ of $-1.1$ and $α^{150}_{1400}$ of $-0.9$, demonstrating that the HSC-SSP survey compensates for a sub-population of HzRGs which are missed in surveys focusing on an ultra-steep spectral index.

astro-ph.GA↗

arXiv2020

Application of X-Ray Clumpy Torus Model (XCLUMPY) to 10 Obscured Active Galactic Nuclei Observed with Suzaku and NuSTAR

We apply XCLUMPY, an X-ray spectral model from a clumpy torus in an active galactic nucleus (AGN), to the broadband X-ray spectra of 10 obscured AGNs observed with both Suzaku and NuSTAR. The infrared spectra of these AGNs were analyzed with the CLUMPY code. Since XCLUMPY adopts the same clump distribution as that in the CLUMPY, we can directly compare the torus parameters obtained from the X-ray spectra and those from the infrared ones. The torus angular widths determined from the infrared spectra ($σ_{\mathrm{IR}}$) are systematically larger than those from the X-ray data ($σ_{\mathrm{X}}$); the difference ($σ_{\mathrm{IR}}-σ_{\mathrm{X}}$) correlates with the inclination angle determined from the X-ray spectrum. These results can be explained by the contribution from dusty polar outflows to the observed infrared flux, which becomes more significant at higher inclinations (more edge-on views). The ratio of the hydrogen column density and V-band extinction in the line of sight absorber shows large scatter ($\simeq$1 dex) around the Galactic value, suggesting that a significant fraction of AGNs have dust-rich circumnuclear environments.

astro-ph.HE↗

arXiv2020

The BAT AGN Spectroscopic Survey -- XVIII. Searching for Supermassive Black Hole Binaries in the X-rays

Theory predicts that a supermassive black hole binary (SMBHB) could be observed as a luminous active galactic nucleus (AGN) that periodically varies on the order of its orbital timescale. In X-rays, periodic variations could be caused by mechanisms including relativistic Doppler boosting and shocks. Here we present the first systematic search for periodic AGNs using $941$ hard X-ray light curves (14-195 keV) from the first 105 months of the Swift Burst Alert Telescope (BAT) survey (2004-2013). We do not find evidence for periodic AGNs in Swift-BAT, including the previously reported SMBHB candidate MCG+11$-$11$-$032. We find that the null detection is consistent with the combination of the upper-limit binary population in AGNs in our adopted model, their expected periodic variability amplitudes, and the BAT survey characteristics. We have also investigated the detectability of SMBHBs against normal AGN X-ray variability in the context of the eROSITA survey. Under our assumptions of a binary population and the periodic signals they produce which have long periods of hundreds of days, up to $13$% true periodic binaries can be robustly distinguished from normal variable AGNs with the ideal uniform sampling. However, we demonstrate that realistic eROSITA sampling is likely to be insensitive to long-period binaries because longer observing gaps reduce their detectability. In contrast, large observing gaps do not diminish the prospect of detecting binaries of short, few-day periods, as 19% can be successfully recovered, the vast majority of which can be identified by the first half of the survey.

astro-ph.HE↗

arXiv2020

Universal transition diagram from dormant to actively accreting supermassive black holes

The vast majority of supermassive black holes (SMBHs) in the local universe exhibit levels of activity much lower than those expected from gas supplying rates onto the galactic nuclei, and only a small fraction of silent SMBHs can turn into active galactic nuclei. Revisiting observational data of very nearby SMBHs whose gravitational spheres of influence are spatially reached by the Chandra X-ray satellite, we find that the level of BH activity drastically increases from the quiescent phase when the inflow rate outside of the BH influence radius is higher than 0.1% of the Eddington accretion rate. We also show that the relation between the nuclear luminosity and gas accretion rate from the BH influence radius measured from X-ray observations is well described by the universal state transition of accreting SMBHs, as predicted by recent hydrodynamical simulations with radiative cooling and BH feedback. After the state transition, young massive stars should form naturally in the nucleus, as observed in the case of the nearest SMBH, Sagittarius A$^\ast$, which is currently quiescent but was recently active.

astro-ph.GA↗

arXiv2020

ALMA polarimetry measures magnetically aligned dust grains in the torus of NGC 1068

The obscuring structure surrounding active galactic nuclei (AGN) can be explained as a dust and gas flow cycle that fundamentally connects the AGN with their host galaxies. This structure is believed to be associated with dusty winds driven by radiation pressure. However, the role of magnetic fields, which are invoked in almost all models for accretion onto a supermassive black hole and outflows, is not thoroughly studied. Here we report the first detection of polarized thermal emission by means of magnetically aligned dust grains in the dusty torus of NGC 1068 using ALMA Cycle 4 polarimetric dust continuum observations ($0.07"$, $4.2$ pc; 348.5 GHz, $860$ $μ$m). The polarized torus has an asymmetric variation across the equatorial axis with a peak polarization of $3.7\pm0.5$\% and position angle of $109\pm2^{\circ}$ (B-vector) at $\sim8$ pc east from the core. We compute synthetic polarimetric observations of magnetically aligned dust grains assuming a toroidal magnetic field and homogeneous grain alignment. We conclude that the measured 860 $μ$m continuum polarization arises from magnetically aligned dust grains in an optically thin region of the torus. The asymmetric polarization across the equatorial axis of the torus arises from 1) an inhomogeneous optical depth, and 2) a variation of the velocity dispersion, i.e. variation of the magnetic field turbulence at sub-pc scales, from the eastern to the western region of the torus. These observations and modeling constrain the torus properties beyond spectral energy distribution results. This study strongly supports that magnetic fields up to a few pc contribute to the accretion flow onto the active nuclei.

astro-ph.GA↗

arXiv2020

Dust Destruction by Charging: A Possible Origin of Grey Extinction Curves of Active Galactic Nuclei

Observed extinction curves of active galactic nuclei (AGNs) are significantly different from those observed in the Milky Way. The observations require preferential removal of small grains at the AGN environment; however, the physics for this remains unclear. In this paper, we propose that dust destruction by charging, or Coulomb explosion, may be responsible for AGN extinction curves. Harsh AGN radiation makes a dust grain highly charged through photoelectric emission, and grain fission via the Coulomb explosion occurs when the electrostatic tensile stress of a charge grain exceeds its tensile strength. We show that the Coulomb explosion can preferentially remove both small silicate and graphite grains and successfully reproduce both flat extinction curves and the absence of 2175Å~bump.

astro-ph.GA↗

arXiv2020

Dust Destruction by Drift-Induced Sputtering in Active Galactic Nuclei

Recent mid-infrared high spatial resolution observations have revealed that active galactic nuclei (AGNs) may host a polar dust region with the size of several pc, and such dust may be carried by radiation from the central engine. The polar dust emission often exhibits very weak or absence of the silicate 10-$μ$m emission feature. A possible explanation is that the polar dust is dominated by micron-sized large grains because these grains do not show the silicate feature, while it remains unclear how large grains are preferentially supplied to the polar region. We here propose a new scenario describing the prevalence of large grains at the polar region. We show that grains are accelerated to the hypersonic drift velocity by the radiation pressure from AGN, and the hypersonic drift results in dust destruction via kinetic sputtering. Sputtering destroys small grains faster than the large ones, and thus larger grains will be preferentially blown over longer distance. Although the hypersonic drift, or kinetic sputtering, tends to be suppressed for very small grains due to the Coulomb drag, they might also be disrupted by Coulomb explosion. Removal of small grains and/or survival of large grains may explain the lack of a silicate 10-$μ$m emission feature in polar dust emission.

astro-ph.GA↗

arXiv2019

Obscuring fraction of active galactic nuclei implied by supernova and radiative feedbacks

We study the obscuring structure of circumnuclear disks (CNDs) by considering supernova (SN) feedbacks from nuclear starburst and the effect of anisotropic radiative pressure from AGNs. We suppose that the mass accretion onto a central supermassive black hole (SMBH) is triggered by SN-driven turbulence within CNDs, and we explore how the structures of CNDs depend on the BH mass ($M_{\rm BH}$) and AGN luminosity ($L_{\rm AGN}$). We find that the obscuring fraction ($f_{\rm obs}$) peaks at $\sim10\%$ of the Eddington luminosity ($L_{\rm Edd}$), and its maximal value is $f_\mathrm{obs} \sim 0.6$ for less massive SMBHs (e.g., $M_{\rm BH} < 10^{8}M_{\odot}$). This is because the scale height of CNDs is determined by the SN-driven accretion for a smaller $L_{\rm AGN}$, while the dusty molecular gas in CNDs is blown away by the radiation pressure from AGNs beyond the critical luminosity. On the other hand, for massive SMBHs (e.g., $M_{\rm BH} > 10^{8}M_{\odot}$), $f_{\rm obs}$ is always smaller than $0.2$, and it is almost independent of $L_{\rm AGN}$ because the scale height of CNDs is mainly controlled by the maximal star-formation efficiency ($C_{\rm *, max}$) in CNDs. By comparison with the obscuring fractions suggested from the mid-infrared observations of nearby AGNs, the SN plus radiative feedback model with $C_{\rm *, max} = 10^{-7}\, {\rm yr}^{-1}$ well reproduces the observations for $M_\mathrm{BH} = 10^8 M_\odot$. We also find that the intense starburst or the existence of dust-free absorbers inside CNDs are necessary, to explain X-ray observations.

astro-ph.GA↗