Engineering topics

Pieres, A. (ORCID:0000000191866042)

Publications and source records attributed to Pieres, A. (ORCID:0000000191866042).

At least 19 records

DOE OSTI2025

High-significance detection of correlation between the unresolved gamma-ray background and the large-scale cosmic structure

Our understanding of the γ-ray sky has improved dramatically in the past decade, however, the unresolved γ-ray background (UGRB) still has a potential wealth of information about the faintest γ-ray sources pervading the Universe. Statistical cross-correlations with tracers of cosmic structure can indirectly identify the populations that most characterize the γ-ray background. In this study, we analyze the angular correlation between the γ-ray background and the matter distribution in the Universe as traced by gravitational lensing, leveraging more than a decade of observations from the Fermi-Large Area Telescope (LAT) and 3 years of data from the Dark Energy Survey (DES). We detect a correlation at signal-to-noise ratio of 8.9. Most of the statistical significance comes from large scales, demonstrating, for the first time, that a substantial portion of the UGRB aligns with the mass clustering of the Universe as traced by weak lensing. Blazars provide a plausible explanation for this signal, especially if those contributing to the correlation reside in halos of large mass (∼ 10 14 M ⊙ ) and account for approximately 30–40% of the UGRB above 10 GeV. Additionally, we observe a preference for a curved γ-ray energy spectrum, with a log-parabolic shape being favored over a power-law. We also discuss the possibility of modifications to the blazar model and the inclusion of additional γ-ray sources, such as star-forming galaxies, misalinged active galactic nuclei, or particle dark matter.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Monitoring of asteroids in cometary orbits and activated asteroids through archival images and new observations

Transitional objects are minor bodies that share some characteristics with asteroids and others with comets. These objects include asteroids in cometary orbits (ACOs), which behave dynamically like comets, but lack observed activity, while activated asteroids (AAs) follow typical asteroidal orbits, but have shown dust ejections. The monitoring of a set of these objects carried out in 2015 and 2016 is continued using archival images from various observatories and new data from the IMPACTON telescope in Brazil. Two techniques were applied to detect activity: (i) surface brightness profiles were compared with those of field stars to identify widening, and (ii) the magnitudes reported in the Minor Planet Center, combined with our observations, were reduced and analyzed to identify abrupt brightness increases as a function of heliocentric distance. We analyzed the surface brightness profiles of 133 ACOs and 7 AAs. To study the reduced magnitude, we obtained data from the 705 ACOs that were known at the time of the analysis. Together with the data from our previous work, our analysis covered 23% of the total known ACOs; 8 deviated slightly in the surface brightness profile, 6 brightened in the reduced magnitude, and one object is in common in both samples. A very low percentage of objects might show activity (4% of the sample with brightness profiles and <1% in the reduced magnitudes). These results would rule out a slow transition from active to inert. Regarding AAs, 4 showed activity, and 3 of them matched previously reported periods, while the data we analyzed for P/2015 X 6 were obtained 19 days before the first existing activity report. The activity episodes of these objects are very restricted in time and do not always occur in the same region of the orbit.

asteroids: general↗

DOE OSTI2025

Year six photometric measurements of known Trans-Neptunian Objects and Centaurs by the Dark Energy Survey

ABSTRACT We identified known Trans-Neptunian Objects (TNOs) and Centaurs in the complete Dark Energy Survey (DES) year six catalogue (DES Y6) through the Sky Body Tracker (SkyBoT) tool. We classified our data set of 144 objects into a widely used 4-class taxonomic system of TNOs. No such previous classification was available in the literature for most of these objects. From absolute magnitudes and average albedos, an estimation of the diameters of all these objects is obtained. Correlations involving colours, orbital parameters, dynamical classes, and sizes are also discussed. In particular, our largest reddest object has a diameter of $390^{+68}_{-53}$ km and our largest cold classical, $255^{+19}_{-17}$ km. Also, a weak correlation between colour and inclination is found within the population of resonant TNOs in addition to weak correlations between colour and phase slope in different bands.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

Superclustering with the Atacama Cosmology Telescope and Dark Energy Survey. II. Anisotropic Large-scale Coherence in Hot Gas, Galaxies, and Dark Matter

Statistics that capture the directional dependence of the baryon distribution in the cosmic web enable unique tests of cosmology and astrophysical feedback. We use constrained oriented stacking of thermal Sunyaev–Zel’dovich (tSZ) maps to measure the anisotropic distribution of hot gas 2.5–40 Mpc away from galaxy clusters embedded in massive filaments and superclusters. The cluster selection and orientation (at a scale of ∼15 Mpc) use Dark Energy Survey (DES) Year 3 data, while expanded tSZ maps from the Atacama Cosmology Telescope Data Release 6 enable a ∼3× more significant measurement of the extended gas compared to the technique’s proof-of-concept. Decomposing stacks into cosine multipoles of order m , we detect a dipole ( m = 1) and quadrupole ( m = 2) at 8σ–10σ, as well as evidence for m = 4 signal at up to 6σ, indicating sensitivity to late-time non-Gaussianity. We compare to Cardinal simulations with spherical gas models pasted onto dark matter halos. The fiducial tSZ data can discriminate between two models that deplete pressure differently in low-mass halos (mimicking astrophysical feedback), preferring higher average pressure in extended structures. However, uncertainty in the amount of cosmic infrared background contamination reduces the constraining power. Additionally, we apply the technique to DES galaxy density and weak lensing to study for the first time their oriented relationships with tSZ. In the tSZ-to-lensing relation, averaged on 7.5 Mpc (transverse) scales, we observe dependence on redshift but not shape or radial distance. Thus, on large scales, the superclustering of gas pressure, galaxies, and total matter is coherent in shape and extent.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

The Dark Energy Survey Supernova Program: slow supernovae show cosmological time dilation out to z ~ 1.

ABSTRACT We present a precise measurement of cosmological time dilation using the light curves of 1504 Type Ia supernovae from the Dark Energy Survey spanning a redshift range $0.1\lesssim z\lesssim 1.2$. We find that the width of supernova light curves is proportional to $(1+z)$, as expected for time dilation due to the expansion of the Universe. Assuming Type Ia supernovae light curves are emitted with a consistent duration $\Delta t_{\rm em}$, and parametrizing the observed duration as $\Delta t_{\rm obs}=\Delta t_{\rm em}(1+z)^b$, we fit for the form of time dilation using two methods. First, we find that a power of $b \approx 1$ minimizes the flux scatter in stacked subsamples of light curves across different redshifts. Secondly, we fit each target supernova to a stacked light curve (stacking all supernovae with observed bandpasses matching that of the target light curve) and find $b=1.003\pm 0.005$ (stat) $\pm \, 0.010$ (sys). Thanks to the large number of supernovae and large redshift-range of the sample, this analysis gives the most precise measurement of cosmological time dilation to date, ruling out any non-time-dilating cosmological models at very high significance.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

OzDES Reverberation Mapping Program: Stacking analysis with Hβ, Mg ii , and C iv

ABSTRACT Reverberation mapping is the leading technique used to measure direct black hole masses outside of the local Universe. Additionally, reverberation measurements calibrate secondary mass-scaling relations used to estimate single-epoch virial black hole masses. The Australian Dark Energy Survey (OzDES) conducted one of the first multi-object reverberation mapping surveys, monitoring 735 AGN up to z ∼ 4, over 6 years. The limited temporal coverage of the OzDES data has hindered recovery of individual measurements for some classes of sources, particularly those with shorter reverberation lags or lags that fall within campaign season gaps. To alleviate this limitation, we perform a stacking analysis of the cross-correlation functions of sources with similar intrinsic properties to recover average composite reverberation lags. This analysis leads to the recovery of average lags in each redshift-luminosity bin across our sample. We present the average lags recovered for the Hβ, Mg ii, and C iv samples, as well as multiline measurements for redshift bins where two lines are accessible. The stacking analysis is consistent with the Radius–Luminosity relations for each line. Our results for the Hβ sample demonstrate that stacking has the potential to improve upon constraints on the R–L relation, which have been derived only from individual source measurements until now.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

The Dark Energy Survey Supernova Program: Cosmological Biases from Host Galaxy Mismatch of Type Ia Supernovae

Abstract Redshift measurements, primarily obtained from host galaxies, are essential for inferring cosmological parameters from type Ia supernovae (SNe Ia). Matching SNe to host galaxies using images is nontrivial, resulting in a subset of SNe with mismatched hosts and thus incorrect redshifts. We evaluate the host galaxy mismatch rate and resulting biases on cosmological parameters from simulations modeled after the Dark Energy Survey 5 Yr (DES-SN5YR) photometric sample. For both DES-SN5YR data and simulations, we employ the directional light radius method for host galaxy matching. In our SN Ia simulations, we find that 1.7% of SNe are matched to the wrong host galaxy, with redshift differences between the true and matched hosts of up to 0.6. Using our analysis pipeline, we determine the shift in the dark energy equation of state parameter (Δ w ) due to including SNe with incorrect host galaxy matches. For SN Ia–only simulations, we find Δ w = 0.0013 ± 0.0026 with constraints from the cosmic microwave background. Including core-collapse SNe and peculiar SNe Ia in the simulation, we find that Δ w ranges from 0.0009 to 0.0032, depending on the photometric classifier used. This bias is an order of magnitude smaller than the expected total uncertainty on w from the DES-SN5YR sample of ∼0.03. We conclude that the bias on w from host galaxy mismatch is much smaller than the uncertainties expected from the DES-SN5YR sample, but we encourage further studies to reduce this bias through better host-matching algorithms or selection cuts.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Designing an Optimal Kilonova Search Using DECam for Gravitational-wave Events

We address the problem of optimally identifying all kilonovae detected via gravitational-wave emission in the upcoming LIGO/Virgo/KAGRA observing run, O4, which is expected to be sensitive to a factor of ~7 more binary neutron star (BNS) alerts than previously. Electromagnetic follow-up of all but the brightest of these new events will require >1 m telescopes, for which limited time is available. We present an optimized observing strategy for the DECam during O4. We base our study on simulations of gravitational-wave events expected for O4 and wide-prior kilonova simulations. We derive the detectabilities of events for realistic observing conditions. We optimize our strategy for confirming a kilonova while minimizing telescope time. For a wide range of kilonova parameters, corresponding to a fainter kilonova compared to GW170817/AT 2017gfo, we find that, with this optimal strategy, the discovery probability for electromagnetic counterparts with the DECam is ~80% at the nominal BNS gravitational-wave detection limit for O4 (190 Mpc), which corresponds to an ~30% improvement compared to the strategy adopted during the previous observing run. For more distant events (~330 Mpc), we reach an ~60% probability of detection, a factor of ~2 increase. For a brighter kilonova model dominated by the blue component that reproduces the observations of GW170817/AT 2017gfo, we find that we can reach ~90% probability of detection out to 330 Mpc, representing an increase of ~20%, while also reducing the total telescope time required to follow up events by ~20%.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

Identification of Galaxy–Galaxy Strong Lens Candidates in the DECam Local Volume Exploration Survey Using Machine Learning

We perform a search for galaxy–galaxy strong lens systems using a convolutional neural network (CNN) applied to imaging data from the first public data release of the DECam Local Volume Exploration Survey, which contains ~520 million astronomical sources covering ~4000 deg 2 of the southern sky to a 5σ point–source depth of g = 24.3, r= 23.9, i = 23.3, and z = 22.8 mag. Following the methodology of similar searches using Dark Energy Camera data, we apply color and magnitude cuts to select a catalog of ~11 million extended astronomical sources. After scoring with our CNN, the highest-scoring 50,000 images were visually inspected and assigned a score on a scale from 0 (not a lens) to 3 (very probable lens). We present a list of 581 strong lens candidates, 562 of which are previously unreported. We categorize our candidates using their human-assigned scores, resulting in 55 Grade A candidates, 149 Grade B candidates, and 377 Grade C candidates. We additionally highlight eight potential quadruply lensed quasars from this sample. Due to the location of our search footprint in the northern Galactic cap (b > 10 deg) and southern celestial hemisphere (decl. < 0 deg), our candidate list has little overlap with other existing ground-based searches. Where our search footprint does overlap with other searches, we find a significant number of high-quality candidates that were previously unidentified, indicating a degree of orthogonality in our methodology. We report properties of our candidates including apparent magnitude and Einstein radius estimated from the image separation.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Synchronous Rotation in the (136199) Eris–Dysnomia System

We combine photometry of Eris from a 6 month campaign on the Palomar 60 inch telescope in 2015, a 1 month Hubble Space Telescope WFC3 campaign in 2018, and Dark Energy Survey data spanning 2013–2018 to determine a light curve of definitive period 15.771 ± 0.008 days (1σ formal uncertainties), with nearly sinusoidal shape and peak-to-peak flux variation of 3%. This is consistent at part-per-thousand precision with the P = 15.785 90 ± 0.00005 day sidereal period of Dysnomia's orbit around Eris, strengthening the recent detection of synchronous rotation of Eris by Szakáts et al. with independent data. Photometry from Gaia are consistent with the same light curve. We detect a slope of 0.05 ± 0.01 mag per degree of Eris's brightness with respect to illumination phase averaged across g, V, and r bands, intermediate between Pluto's and Charon's values. Variations of 0.3 mag are detected in Dysnomia's brightness, plausibly consistent with a double-peaked light curve at the synchronous period. The synchronous rotation of Eris is consistent with simple tidal models initiated with a giant-impact origin of the binary, but is difficult to reconcile with gravitational capture of Dysnomia by Eris. The high albedo contrast between Eris and Dysnomia remains unexplained in the giant-impact scenario.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Cool Cores in Clusters of Galaxies in the Dark Energy Survey

We search for the presence of cool cores in optically selected galaxy clusters from the Dark Energy Survey (DES) and investigate their prevalence as a function of redshift and cluster richness. Clusters were selected from the redMaPPer analysis of three years of DES observations that have archival Chandra X-ray observations, giving a sample of 99 clusters with a redshift range of 0.11 < z < 0.87 and a richness range of 25 < λ < 207. Using the X-ray data, the core temperature was compared to the outer temperature to identify clusters where the core temperature is a factor of 0.7 or less than the outer temperature. We found a cool core fraction of approximately 20% with no significant trend in the cool core fraction with either redshift or richness.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

The Dark Energy Survey Supernova Program: Corrections on Photometry Due to Wavelength-dependent Atmospheric Effects

Abstract Wavelength-dependent atmospheric effects impact photometric supernova flux measurements for ground-based observations. We present corrections on supernova flux measurements from the Dark Energy Survey Supernova Program’s 5YR sample (DES-SN5YR) for differential chromatic refraction (DCR) and wavelength-dependent seeing, and we show their impact on the cosmological parameters w and Ω m . We use g − i colors of Type Ia supernovae to quantify astrometric offsets caused by DCR and simulate point-spread functions (PSFs) using the GalSIM package to predict the shapes of the PSFs with DCR and wavelength-dependent seeing. We calculate the magnitude corrections and apply them to the magnitudes computed by the DES-SN5YR photometric pipeline. We find that for the DES-SN5YR analysis, not accounting for the astrometric offsets and changes in the PSF shape cause an average bias of +0.2 mmag and −0.3 mmag, respectively, with standard deviations of 0.7 mmag and 2.7 mmag across all DES observing bands ( griz ) throughout all redshifts. When the DCR and seeing effects are not accounted for, we find that w and Ω m are lower by less than 0.004 ± 0.02 and 0.001 ± 0.01, respectively, with 0.02 and 0.01 being the 1 σ statistical uncertainties. Although we find that these biases do not limit the constraints of the DES-SN5YR sample, future surveys with much higher statistics, lower systematics, and especially those that observe in the u band will require these corrections as wavelength-dependent atmospheric effects are larger at shorter wavelengths. We also discuss limitations of our method and how they can be better accounted for in future surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

OzDES Reverberation Mapping Programme: Mg ii lags and R − L relation

ABSTRACT The correlation between the broad line region radius and continuum luminosity (R–L relation) of active galactic nuclei (AGNs) is critical for single-epoch mass estimates of supermassive black holes (SMBHs). At z ∼ 1–2, where AGN activity peaks, the R–L relation is constrained by the reverberation mapping (RM) lags of the Mg ii line. We present 25 Mg ii lags from the Australian Dark Energy Survey RM project based on 6 yr of monitoring. We define quantitative criteria to select good lag measurements and verify their reliability with simulations based on both the damped random walk stochastic model and the rescaled, resampled versions of the observed light curves of local, well-measured AGN. Our sample significantly increases the number of Mg ii lags and extends the R–L relation to higher redshifts and luminosities. The relative iron line strength $\mathcal {R}_{\rm Fe}$ has little impact on the R–L relation. The best-fitting Mg iiR–L relation has a slope α = 0.39 ± 0.08 with an intrinsic scatter $\sigma _{\rm rl} = 0.15^{+0.03}_{-0.02}$ . The slope is consistent with previous measurements and shallower than the H β R–L relation. The intrinsic scatter of the new R–L relation is substantially smaller than previous studies and comparable to the intrinsic scatter of the H β R–L relation. Our new R–L relation will enable more precise single-epoch mass estimates and SMBH demographic studies at cosmic noon.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Mapping gas around massive galaxies: cross-correlation of DES Y3 galaxies and Compton- y maps from SPT and Planck

ABSTRACT We cross-correlate positions of galaxies measured in data from the first three years of the Dark Energy Survey with Compton-y maps generated using data from the South Pole Telescope (SPT) and the Planck mission. We model this cross-correlation measurement together with the galaxy autocorrelation to constrain the distribution of gas in the Universe. We measure the hydrostatic mass bias or, equivalently, the mean halo bias-weighted electron pressure 〈bhPe 〉, using large-scale information. We find 〈bhPe 〉 to be $[0.16^{+0.03}_{-0.04},0.28^{+0.04}_{-0.05},0.45^{+0.06}_{-0.10},0.54^{+0.08}_{-0.07},0.61^{+0.08}_{-0.06},0.63^{+0.07}_{-0.08}]$ meV cm−3 at redshifts z ∼ [0.30, 0.46, 0.62, 0.77, 0.89, 0.97]. These values are consistent with previous work where measurements exist in the redshift range. We also constrain the mean gas profile using small-scale information, enabled by the high-resolution of the SPT data. We compare our measurements to different parametrized profiles based on the cosmo-OWLS hydrodynamical simulations. We find that our data are consistent with the simulation that assumes an AGN heating temperature of 108.5 K but are incompatible with the model that assumes an AGN heating temperature of 108.0 K. These comparisons indicate that the data prefer a higher value of electron pressure than the simulations within r500c of the galaxies’ haloes.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Ultracool dwarfs candidates based on 6 yr of the Dark Energy Survey data

ABSTRACT We present a sample of 19 583 ultracool dwarf candidates brighter than z ≤23 selected from the Dark Energy Survey DR2 coadd data matched to VHS DR6, VIKING DR5, and AllWISE covering ∼ 480 deg2. The ultracool candidates were first pre-selected based on their (i–z), (z–Y), and (Y–J) colours. They were further classified using a method that compares their optical, near-infrared, and mid-infrared colours against templates of M, L, and T dwarfs. 14 099 objects are presented as new L and T candidates and the remaining objects are from the literature, including 5342 candidates from our previous work. Using this new and deeper sample of ultracool dwarf candidates we also present: 20 new candidate members to nearby young moving groups and associations, variable candidate sources and four new wide binary systems composed of two ultracool dwarfs. Finally, we also show the spectra of 12 new ultracool dwarfs discovered by our group and presented here for the first time. These spectroscopically confirmed objects are a sanity check of our selection of ultracool dwarfs and photometric classification method.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Characterizing the intracluster light over the redshift range 0.2 < z < 0.8 in the DES-ACT overlap

ABSTRACT We characterize the properties and evolution of bright central galaxies (BCGs) and the surrounding intracluster light (ICL) in galaxy clusters identified in the Dark Energy Survey and Atacama Cosmology Telescope Survey (DES-ACT) overlapping regions, covering the redshift range 0.20 < z < 0.80. Over this redshift range, we measure no change in the ICL’s stellar content (between 50 and 300 kpc) in clusters with log10(M200m,SZ/M⊙) >14.4. We also measure the stellar mass–halo mass (SMHM) relation for the BCG+ICL system and find that the slope, β, which characterizes the dependence of M200m,SZ on the BCG+ICL stellar mass, increases with radius. The outskirts are more strongly correlated with the halo than the core, which supports that the BCG+ICL system follows a two-phase growth, where recent growth (z < 2) occurs beyond the BCG’s core. Additionally, we compare our observed SMHM relation results to the IllustrisTNG300-1 cosmological hydrodynamic simulations and find moderate qualitative agreement in the amount of diffuse light. However, the SMHM relation’s slope is steeper in TNG300-1 and the intrinsic scatter is lower, likely from the absence of projection effects in TNG300-1. Additionally, we find that the ICL exhibits a colour gradient such that the outskirts are bluer than the core. Moreover, for the lower halo mass clusters (log10(M200m,SZ/M⊙) < 14.59), we detect a modest change in the colour gradient’s slope with lookback time, which combined with the absence of stellar mass growth may suggest that lower mass clusters have been involved in growth via tidal stripping more recently than their higher mass counterparts.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Timing the r -process Enrichment of the Ultra-faint Dwarf Galaxy Reticulum II

The ultra-faint dwarf galaxy Reticulum II (Ret II) exhibits a unique chemical evolution history, with ${72}_{-12}^{+10}$% of its stars strongly enhanced in r-process elements. We present deep Hubble Space Telescope photometry of Ret II and analyze its star formation history. As in other ultra-faint dwarfs, the color–magnitude diagram is best fit by a model consisting of two bursts of star formation. If we assume that the bursts were instantaneous, then the older burst occurred around the epoch of reionization, forming ~80% of the stars in the galaxy, while the remainder of the stars formed ~3 Gyr later. When the bursts are allowed to have nonzero durations, we obtain slightly better fits. The best-fitting model in this case consists of two bursts beginning before reionization, with approximately half the stars formed in a short (100 Myr) burst and the other half in a more extended period lasting 2.6 Gyr. Considering the full set of viable star formation history models, we find that 28% of the stars formed within 500 ± 200 Myr of the onset of star formation. The combination of the star formation history and the prevalence of r-process-enhanced stars demonstrates that the r-process elements in Ret II must have been synthesized early in its initial star-forming phase. We therefore constrain the delay time between the formation of the first stars in Ret II and the r-process nucleosynthesis to be less than 500 Myr. This measurement rules out an r-process source with a delay time of several Gyr or more, such as GW170817.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

DeepZipper. II. Searching for Lensed Supernovae in Dark Energy Survey Data with Deep Learning

Gravitationally lensed supernovae (LSNe) are important probes of cosmic expansion, but they remain rare and difficult to find. Current cosmic surveys likely contain 5–10 LSNe in total while next-generation experiments are expected to contain several hundred to a few thousand of these systems. We search for these systems in observed Dark Energy Survey (DES) five year SN fields—10 3 sq. deg. regions of sky imaged in the griz bands approximately every six nights over five years. To perform the search, we utilize the DeepZipper approach: a multi-branch deep learning architecture trained on image-level simulations of LSNe that simultaneously learns spatial and temporal relationships from time series of images. We find that our method obtains an LSN recall of 61.13% and a false-positive rate of 0.02% on the DES SN field data. DeepZipper selected 2245 candidates from a magnitude-limited (m i < 22.5) catalog of 3,459,186 systems. We employ human visual inspection to review systems selected by the network and find three candidate LSNe in the DES SN fields.

79 ASTRONOMY AND ASTROPHYSICS↗