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DOE OSTI2025

FLAMINGO: combining kinetic SZ effect and galaxy–galaxy lensing measurements to gauge the impact of feedback on large-scale structure

Energetic feedback processes associated with accreting supermassive black holes can expel gas from massive haloes and significantly alter various measures of clustering on $\sim$Mpc scales, potentially biasing the values of cosmological parameters inferred from analyses of large-scale structure (LSS) if not modelled accurately. Here, we use the state-of-the-art FLAMINGO suite of cosmological hydrodynamical simulations to gauge the impact of feedback on large-scale structure by comparing to Planck + ACT stacking measurements of the kinetic Sunyaev–Zel’dovich (kSZ) effect of SDSS BOSS galaxies. We make careful like-with-like comparisons to the observations, aided by high precision KiDS and DES galaxy–galaxy lensing measurements of the BOSS galaxies to inform the selection of the simulated galaxies. In qualitative agreement with several recent studies using dark matter only simulations corrected for baryonic effects, we find that the kSZ effect measurements prefer stronger feedback than predicted by simulations which have been calibrated to reproduce the gas fractions of low redshift X-ray-selected groups and clusters. We find that the increased feedback can help to reduce the so-called $S_8$ tension between the observed and CMB-predicted clustering on small scales as probed by cosmic shear (although at the expense of agreement with the X-ray group measurements). However, the increased feedback is only marginally effective at reducing the reported offsets between the predicted and observed clustering as probed by the thermal SZ (tSZ) effect power spectrum and tSZ effect – weak lensing cross-spectrum, both of which are sensitive to higher halo masses than cosmic shear.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Reduction of the type Ia supernova host galaxy step in the outer regions of galaxies

Using 1533 type Ia supernovae (SNe Ia) from the 5-yr sample of the Dark Energy Survey (DES), we investigate the relationship between the projected galactocentric separation of the SNe and their host galaxies and their light curves and standardization. We show, for the first time, that the difference in SN Ia post-standardization brightnesses between high- and low-mass hosts reduces from $0.078\pm 0.011$ mag in the full sample to $0.036 \pm 0.018$ mag for SNe Ia located in the outer regions of their host galaxies, while increasing to $0.100 \pm 0.014$ mag for SNe in the inner regions. The difference in the size of the mass step between inner and outer regions is $0.064\pm 0.023$ mag. In these inner regions, the step can be reduced (but not removed) using a model where the $R_V$ of dust along the line of sight to the SN changes as a function of galaxy properties. We investigate the remaining difference using the distributions of the SN Ia stretch parameter to test the inferred age of SN progenitors. Comparing red (older) environments only, outer regions have a higher proportion of high-stretch SNe and a more homogeneous stretch distribution. However, this effect cannot explain the reduction in significance of any Hubble residual step in outer regions. We conclude that the standardized distances of SNe Ia located in the outer regions of galaxies are less affected by their global host galaxy properties than those in the inner regions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Low-mass Active Galaxies in the SAMI Galaxy Survey with Spatially Resolved Spectroscopy

The smallest supermassive black holes (BHs), which provide constraints on BH seeds, reside in low-mass galaxies. Here, we present a systematic analysis of 990 low-mass galaxies in the SAMI Galaxy Survey to identify emission from accreting BHs using integral field spectroscopy (IFS). Employing a novel automated scoring algorithm based on spatially resolved narrow emission-line diagnostics, we find signatures of active galactic nuclei (AGNs) in 41 galaxies, as well as an additional 46 (less secure) candidates. The galaxies have stellar masses between 10 9.4 ≲ M ⋆ /M ⊙ ≲ 10 10 (down to 10 8.5 , including less secure candidates), redshifts z ≲ 0.06, and morphologies ranging from early-type ellipticals to late-type spirals. Our AGN fraction of 4% (9% if we include the less secure candidates) is significantly higher than those reported by studies using single-fiber spectroscopy (≲1%–2%). Indeed, our additional analysis of single-fiber spectra of the objects in our sample demonstrates that many of our AGN candidates detected via IFS are missed. This work highlights the advantages of IFS, especially the ability to capture extended or decentralized emission from accreting BHs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Luminosity and Stellar Mass Functions of Faint Photometric Satellites around Spectroscopic Central Galaxies from DESI Year-1 Bright Galaxy Survey

We measure the luminosity functions (LFs) and stellar mass functions (SMFs) of photometric satellite galaxies around spectroscopically identified isolated central galaxies (ICGs). The photometric satellites are from the DESI Legacy Imaging Surveys (DR9), while the spectroscopic ICGs are selected from the DESI Year-1 BGS sample. We can measure satellite LFs down to r-band absolute magnitudes of M r,sat ∼ −7, around ICGs as small as 7.1 < log 10 M *,ICG /M ⊙ < 7.8, with the stellar mass of ICGs measured by the DESI Fastspecfit pipeline. The satellite SMF can be measured down to log 10 M *,sat /M ⊙ ~ 5.5. Interestingly, we discover that the faint/low-mass end slopes of satellite LFs/SMFs become steeper with the decrease in the stellar masses of host ICGs, with smaller and nearby host ICGs capable of being used to probe their fainter satellites. The steepest slopes can be −2.298 ± 0.656 and −2.888 ± 0.916 for satellite LF and SMF, respectively. Detailed comparisons are performed between the satellite LFs around ICGs selected from DESI BGS or from the SDSS NYU-VAGC spectroscopic Main galaxies over 7.1 < log 10 M *,ICG /M ⊙ < 11.7, showing reasonable agreement, but we show that differences between DESI and SDSS stellar masses for ICGs play a role to affect the results. We also compare measurements based on DESI Fastspecfit and Cigale stellar masses used to bin ICGs, with the latter including the modeling of active galactic nuclei based on Wide-field Infrared Survey Explorer photometry, and we find good agreements in the measured satellite LFs by using either of the DESI stellar mass catalogs.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

DESI 2024 V: Full-Shape galaxy clustering from galaxies and quasars

We present the measurements and cosmological implications of the galaxy two-point clustering using over 4.7 million unique galaxy and quasar redshifts in the range 0.1 < z < 2.1 divided into six redshift bins over a ∼ 7,500 square degree footprint, from the first year of observations with the Dark Energy Spectroscopic Instrument (DESI Data Release 1). By fitting the full power spectrum, we extend previous DESI DR1 baryon acoustic oscillation (BAO) measurements to include redshift-space distortions and signals from the matter-radiation equality scale. For the first time, this Full-Shape analysis is blinded at the catalogue-level to avoid confirmation bias and the systematic errors are accounted for at the two-point clustering level, which automatically propagates them into any cosmological parameter. When analyzing the data in terms of compressed model-agnostic variables, we obtain a combined precision of 4.7% on the amplitude of the redshift space distortion (RSD) signal reaching a similar precision with just one year of DESI data than with twenty years of observation from the previous generation survey. We also analyze the data to directly constrain the cosmological parameters within the ΛCDM model using perturbation theory and combine this information with the reconstructed DESI DR1 galaxy BAO. Using a Big Bang Nucleosynthesis Gaussian prior on the baryon density parameter, ω b , and a weak Gaussian prior on the spectral index, n s , we constrain the matter density is Ω m = 0.296±0.010 and the Hubble constant H 0 = (68.63 ± 0.79)[km s -1 Mpc -1 ]. Additionally, we measure the amplitude of clustering σ 8 = 0.841±0.034. The DESI DR1 galaxy clustering results are in agreement with the ΛCDM model based on general relativity with parameters consistent with those from Planck. The cosmological interpretation of these results in combination with DESI DR1 Ly-α forest data and external datasets are presented in the companion paper [1].

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Evolution of structure growth during dark energy domination: Insights from the cross-correlation of DESI galaxies with CMB lensing and galaxy magnification

We use a hybrid effective field theory (HEFT) model to constrain the evolution of low-redshift (z≲0.4) matter fluctuations by cross-correlating DESI Bright Galaxy Survey (BGS) legacy imaging with the latest cosmic microwave background (CMB) lensing maps from Planck and Atacama cosmology telescope. Our tomographic BGS analysis finds that the evolution and amplitude of matter fluctuations align with CMB-conditioned Λ cold dark matter predictions. When including DESI baryon acoustic oscillation (BAO) measurements we obtain σ8=0.876-0.067+0.051 from BGS alone. Jointly analyzing BGS and luminous red galaxy (LRG) cross-correlations with the same CMB lensing maps yields σ8=0.791±0.021. As a complementary approach we isolate the galaxy magnification signal from the cross-correlation of nonoverlapping BGS and LRG photometric redshift bins, ruling out the null-magnification hypothesis at 11σ. For the first time, we constrain quasilinear structure growth from the (finite-difference calibrated) galaxy magnification signal and find σ8=0.720±0.047(stat)±0.050(sys) assuming a linear bias model and including BAO data.

Sailer, Noah↗
DOE OSTI2025

Comprehensive Neural Posterior Estimation for Galaxy-Galaxy Strong Lensing

We present a deep learning model based on neural posterior estimation (NPE) for comprehensive extraction of astrophysical parameters from galaxy-scale strong gravitational lenses. The unprecedentedly large amount of galaxy-scale strong lenses expected in future cosmological surveys (${\cal O}(10^5)$) promises to enable valuable statistical constraints in various studies ranging from galaxy formation to the nature of dark matter, but it also poses a significant challenge for traditional modelling pipelines. To this end, our automated model includes several new, state-of-the-art features and approaches leveraging the framework of simulation-based inference (SBI). We infer a total of 20 parameters describing the mass and light profiles of both lens and source galaxies, using simulated raw multi-band data modelled under noise and observing conditions expected by the Legacy Survey of Space and Time (LSST), with its summary statistics generated by a residual network. We examine the efficacy of multi-band data in extracting nearly 20 model parameters simultaneous from strong lensing images including lens light. Finally, We perform a comprehensive set of diagnostics for SBI models, evaluating the model's prediction accuracy, stability, and uncertainty quantification.

Zhao, Roy J. [Chicago U., KICP]↗
DOE OSTI2025

SITCOMTN-165: Surface brightness profiles around massive galaxies in LSSTComCam data

Low surface brightness photometry of massive galaxies can probe the extended stellar halos and intracluster light but is often limited by background subtraction and masking systematics. Here we present radial surface brightness profiles for the brightest cluster galaxy of Abell 360 and 2dFGRS TGS323Z113 using Rubin Observatory Commissioning Camera (LSSTComCam) Data Preview 1 in the g, r, and z bands. Our results show that the LSSTComCam data can go down to ~28 mag arcsec^-2 in the r band. Comparison to DECaLS measurements processed with Legacyhalos shows good agreement of surface brightness profiles at small radii while the LSSTComCam data extend deeper at larger radii.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Self-interacting Dark Matter, Core Collapse, and the Galaxy–Galaxy Strong-lensing Discrepancy

Abstract Gravitational lensing by galaxy clusters has emerged as a powerful tool to probe the standard cold dark matter (CDM) paradigm of structure formation in the Universe. Despite the remarkable explanatory power of CDM on large scales, tensions with observations on small scales have been reported. Recent studies find that the observational cross section for galaxy–galaxy strong lensing (GGSL) in clusters exceeds the CDM prediction by more than an order of magnitude and persists even after rigorous examination of various possible systematics. We investigate the impact of modifying the internal structure of cluster dark matter subhalos on GGSL and report that altering the inner density profile, given by r γ , to steeper slopes with γ > 2.5 can alleviate the GGSL discrepancy. This is steeper than slopes obtained with the inclusion of the contribution of baryons to the inner regions of these subhalos. Deviating from the γ ~ 1.0 cusps that CDM predicts, these steeper slopes could arise in models of self-interacting dark matter undergoing core collapse. Our results motivate additional study of subhalo core collapse in dense cluster environments.

Dutra, Isaque (ORCID:0000000170404930)↗
DOE OSTI2025

The AGORA High-resolution Galaxy Simulations Comparison Project. VIII. Disk Formation and Evolution of Simulated Milky Way Mass Galaxy Progenitors at 1 < z < 5

We investigate how differences in the stellar feedback produce disks with different morphologies in Milky Way–like progenitors over 1 ≤ z ≤ 5, using eight state-of-the-art cosmological hydrodynamics simulation codes in the AGORA project. In three of the participating codes, a distinct, rotation-dominated inner core emerges with a formation timescale of ≲300 Myr, largely driven by a major merger event, while two other codes exhibit similar signs of wet compaction—gaseous shrinkage into a compact starburst phase—at earlier epochs. The remaining three codes show only weak evidence of wet compaction. Consequently, we divide the simulated galaxies into two groups: those with strong compaction signatures and those with weaker ones. Galaxies in these two groups differ in size, stellar age gradients, and disk-to-total mass ratios. Specifically, codes with strong wet compaction build their outer disks in an inside-out fashion, leading to negative age gradients, whereas codes with weaker compaction feature flat or positive age gradients caused primarily by outward stellar migration. Although the stellar half-mass radii of these two groups diverge at z ∼ 3, the inclusion of dust extinction brings their sizes and shapes in mock observations closer to each other and to observed galaxies. We attribute the observed morphological differences primarily to variations in the stellar feedback implementations—such as delayed cooling timescales, and feedback strengths—that regulate both the onset and duration of compaction. Overall, our results suggest that disk assembly at high redshifts is highly sensitive to the details of the stellar feedback prescriptions in simulations.

Jung, Minyong [Seoul National Univ. (Korea, Republ↗
DOE OSTI2025

Improving galaxy cluster selection with the outskirt stellar mass of galaxies

The number density and redshift evolution of optically selected galaxy clusters offer an independent measurement of the amplitude of matter fluctuations, 𝑆 8 . However, recent results have shown that clusters chosen by the redMaPPer algorithm show richness-dependent biases that affect the weak lensing signals and number densities of clusters, increasing uncertainty in the cluster mass calibration and reducing their constraining power. Here, in this work, we evaluate an alternative cluster proxy, outskirt stellar mass, 𝑀 out , defined as the total stellar mass within a [50, 100] kpc envelope centered on a massive galaxy. This proxy exhibits scatter comparable to redMaPPer richness, 𝜆, but is less likely to be subject to projection effects. We compare the Dark Energy Survey Year 3 redMaPPer cluster catalog with a 𝑀 out selected cluster sample from the Hyper-Suprime Camera survey. We use weak lensing measurements to quantify and compare the scatter of 𝑀 out and 𝜆 with halo mass. Our results show 𝑀 out has a scatter consistent with 𝜆, with a similar halo mass dependence, and that both proxies contain unique information about the underlying halo mass. We find 𝜆-selected samples introduce features into the measured Δ⁢Σ signal that are not well fit by a log-normal scatter only model, absent in 𝑀 out selected samples. Our findings suggest that 𝑀 out offers an alternative for cluster selection with more easily calibrated selection biases, at least at the generally lower richnesses probed here. Combining both proxies may yield a mass proxy with a lower scatter and more tractable selection biases, enabling the use of lower mass clusters in cosmology. Finally, we find the scatter and slope in the 𝜆 −𝑀 out scaling relation to be 0.49 ±0.02 and 0.38 ±0.09.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

The DESI Single Fiber Lens Search. I. Four Thousand Spectroscopically Selected Galaxy–Galaxy Gravitational Lens Candidates

We present 4110 strong gravitational lens candidates, 3887 of which are new discoveries, selected from a sample of 5,837,154 luminous red galaxies (LRGs) observed with the Dark Energy Spectroscopic Instrument (DESI). Candidates are identified via the presence of background ionized oxygen [O II ] nebular emission lines in the foreground LRG spectra, which may originate from the lensing of higher-redshift star-forming galaxies. Using the measured foreground redshift, background redshift, and integrated flux of the background [O II ] doublet, we integrate over impact parameters to compute the probability that each candidate is a lens. We expect 53% of candidates to be true lenses with Einstein radii ranging from 0$^{''}_.$1–4", which can be confirmed with high-resolution imaging. Confirmed strong lenses from this sample will form a valuable cosmological data set, as strong gravitational lensing is the only method to directly measure dark matter halo substructure at cosmological distances. We independently recover the host of the multiply imaged gravitationally lensed type Ia supernova iPTF16geu. Monitoring these lenses for future multiply lensed transients will enable (a) H 0 measurements via time-delay cosmography and (b) substructure measurements via flux ratios.

Karp, Juliana S. M. [Univ. of Washington, Seattle,↗
DOE OSTI2024

Model independent approach for calculating galaxy rotation curves for low S/N MaNGA galaxies

Internal kinematics of galaxies, traced through the stellar rotation curve or two dimensional velocity map, carry important information on galactic structure and dark matter. With upcoming surveys, the velocity map may play a key role in the development of kinematic lensing as an astrophysical probe. Here, we improve techniques for extracting velocity information from integral field spectroscopy at low signal-to-noise (S/N), without a template, and demonstrate substantial advantages over the standard Penalized PiXel-Fitting method (pPXF) approach. Robust rotation curves can be derived down to S/N ≈ 2 using our method.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Study of the connected four-point correlation function of galaxies from the DESI Data Release 1 luminous red galaxy sample

We present a measurement of the non-Gaussian four-point correlation function (4PCF) from the DESI DR1 luminous red galaxy (LRG) sample. For the gravitationally induced parity-even 4PCF, we detect a signal with a significance of 14.7⁢𝜎 using our fiducial setup. We assess the robustness of this detection through a series of validation tests, including auto and cross-correlation analyses, sky partitioning across multiple patch combinations, and variations in radial scale cuts. Due to the low completeness of the sample, we find that differences in fiber assignment implementation schemes can significantly impact estimation of the covariance and introduce biases in the data vector. After correcting for these effects, all tests yield consistent results. This is one of the first measurements of the connected 4PCF on the DESI LRG sample; the good agreement between the simulation and the data implies that the amplitude of the density fluctuation inferred from the connected 4PCF is consistent with the Planck Λ⁢ CDM cosmology. The methodology and diagnostic framework established in this work provide a foundation for interpreting parity-odd 4PCF.

Cosmology↗
DOE OSTI2026

The Extended Baryonic Tully–Fisher Relation for SDSS MaNGA Galaxies

The baryonic Tully–Fisher relation (BTFR), a relationship between the rotational velocity and baryonic mass in spiral galaxies, probes the relative content of baryonic and total mass in galaxies and thus provides a good test of dark matter content in galaxies. Using Hα kinematics, we model the rotation curves of the Sloan Digital Sky Survey MaNGA DR17 spiral galaxies. To extend the BTFR to higher masses with elliptical galaxies, we estimate their total masses from their stellar velocity dispersions using the virial theorem and define the effective rotational velocity as the velocity a rotation-supported galaxy would exhibit given this mass. The baryonic mass of spiral galaxies is composed of stellar, H I , H 2 , and He mass, while only the stellar mass is used for the baryonic content of ellipticals. We construct joint BTFRs for 5743 MaNGA spiral and elliptical galaxies, TNG100 simulated galaxies with baryonic masses greater than 10 9 M ⊙ , and a cross-matched subsample between these two datasets (3149 spiral and 1423 elliptical galaxies). For the cross-matched subsample, we find agreement in the slopes between observed and simulated galaxies. We find a slope of $3.8{6}_{-0.62}^{+0.92}$ for the full MaNGA sample, which agrees well with the slope of 4.0 predicted by MOND and the fitted slope of $3.5{8}_{-0.38}^{+0.48}$ for the TNG100 galaxies. We find that a sample of lower-mass galaxies is necessary to differentiate between the two models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Bounds on galaxy stochasticity from halo occupation distribution modeling

The joint probability distribution of matter overdensity and galaxy counts in cells is a powerful probe of cosmology, and the extent to which variance in galaxy counts at fixed matter density deviates from Poisson shot noise is not fully understood. The lack of informed bounds on this stochasticity is currently the limiting factor in constraining cosmology with the galaxy–matter probability distribution function (PDF). We investigate stochasticity in the conditional distribution of galaxy counts along lines of sight with fixed matter density, and we present a halo occupation distribution (HOD)-based approach for obtaining plausible ranges for stochasticity parameters. To probe the high-dimensional space of possible galaxy–matter connections, we derive a set of HODs that conserve the galaxies’ linear bias and number density to produce RED M A G I C-like galaxy catalogs within the A BACUS S UMMIT suite of N -body simulations. We study the impact of individual HOD parameters and cosmology on stochasticity and perform a Monte Carlo search in HOD parameter space subject to the constraints on bias and density. In mock catalogs generated by the selected HODs, shot noise in galaxy counts spans both sub-Poisson and super-Poisson values, ranging from 80% to 133% of Poisson variance for cells with mean matter density. Nearly all of the derived HODs show a positive relationship between local matter density and stochasticity. For galaxy catalogs with higher stochasticity, modeling galaxy bias to second order is required for an accurate description of the conditional PDF of galaxy counts at fixed matter density. The presence of galaxy assembly bias also substantially extends the range of stochasticity in the super-Poisson direction. This HOD-based approach leverages degrees of freedom in the galaxy–halo connection to obtain informed bounds on nuisance model parameters and can be adapted to study other parametrizations of shot noise in galaxy counts, in particular to motivate prior ranges on stochasticity for cosmological analyses.

Britt, Dylan (ORCID:000000019905601X)↗
DOE OSTI2024

Galaxy Zoo DESI: large-scale bars as a secular mechanism for triggering AGNs

ABSTRACT Despite the evidence that supermassive black holes (SMBHs) co-evolve with their host galaxy, and that most of the growth of these SMBHs occurs via merger-free processes, the underlying mechanisms which drive this secular co-evolution are poorly understood. We investigate the role that both strong and weak large-scale galactic bars play in mediating this relationship. Using 48 871 disc galaxies in a volume-limited sample from Galaxy Zoo DESI, we analyse the active galactic nucleus (AGN) fraction in strongly barred, weakly barred, and unbarred galaxies up to $z = 0.1$ over a range of stellar masses and colours. After controlling for stellar mass and colour, we find that the optically selected AGN fraction is $31.6 \pm 0.9$ per cent in strongly barred galaxies, $23.3 \pm 0.8$ per cent in weakly barred galaxies, and $14.2 \pm 0.6$ per cent in unbarred disc galaxies. These are highly statistically robust results, strengthening the tantalizing results in earlier works. Strongly barred galaxies have a higher fraction of AGNs than weakly barred galaxies, which in turn have a higher fraction than unbarred galaxies. Thus, while bars are not required in order to grow an SMBH in a disc galaxy, large-scale galactic bars appear to facilitate AGN fuelling, and the presence of a strong bar makes a disc galaxy more than twice as likely to host an AGN than an unbarred galaxy at all galaxy stellar masses and colours.

Astronomy & Astrophysics↗
DOE OSTI2024

Unravelling the orbits of cluster galaxy populations according to their dominant gas ionization source

ABSTRACT We investigate the kinematical and dynamical properties of cluster galaxy populations classified according to their dominant source of gas ionization, namely: star-forming (SF) galaxies, optical active galactic nuclei (AGNs), mixed SF plus AGN ionization (transition objects, T), and quiescent (Q) galaxies. We stack 8892 member galaxies from 336 relaxed galaxy clusters to build an ensemble cluster and estimate the observed projected profiles of numerical density and velocity dispersion, $\sigma _P(R)$, of each galaxy population. The MAMPOSSt code and the Jeans equations inversion technique are used to constrain the velocity anisotropy profiles of the galaxy populations in both parametric and non-parametric ways. We find that Q (SF) galaxies display the lowest (highest) typical cluster-centric distances and velocity dispersion values. Transition galaxies are more concentrated and tend to exhibit lower velocity dispersion values than SF galaxies. Galaxies that host an optical AGN are as concentrated as Q galaxies but display velocity dispersion values similar to those of the SF population. MAMPOSSt is able to find equilibrium solutions that successfully recover the observed $\sigma _P(R)$ profile only for the Q, T, and AGN populations. We find that the orbits of all populations are consistent with isotropy in the inner regions, becoming increasingly radial with the distance from the cluster centre. These results suggest that Q galaxies are in equilibrium within their clusters, while SF galaxies have more recently arrived in the cluster environment. Finally, the T and AGN populations appear to be in an intermediate dynamical state between those of the SF and Q populations.

Valk, Greique A. (ORCID:0009000827731299)↗