Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Disks”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

Quantifying Chemical and Kinematical Properties of Galactic Disks

We aim to quantify the chemical and kinematical properties of Galactic disks with a sample of 119,558 giant stars having abundances and 3D velocities taken or derived from the APOGEE DR17 and Gaia EDR3 catalogs. A Gaussian mixture model is employed to distinguish the high-α and low-α sequences along the metallicity by simultaneously using chemical and kinematical data. Four disk components are identified and quantified; they are named the hαmp, hαmr, lαmp, and lαmr disks and correspond to the high-α or low-α, and metal-poor or metal-rich properties. Combined with the spatial and stellar-age information, we confirm that they are well interpreted by the two-infall formation model. The first infall of turbulent gas quickly forms the hot and thick hαmp disk with consequent thinner hαmr and lαmr disks. Then the second gas accretion forms a thinner and outermost lαmp disk. We find that the inside-out and upside-down scenario does not only satisfy the overall Galactic disk formation of these two major episodes but is also presented in the formation sequence of the three inner disks. Importantly, we reveal the inverse age–[M/H] trend of the lαmr disk, which means its younger stars are more metal-poor, indicating that the rejuvenated gas from the second accretion gradually dominates later star formation. Meanwhile, the recently formed stars converge to [M/H] ~ –0.1 dex, demonstrating a sufficient mixture of gas from two infalls.

79 ASTRONOMY AND ASTROPHYSICS↗

Changing-look Active Galactic Nuclei Powered by Disk Tearing

Changing-look active galactic nuclei (CLAGN) feature order-of-magnitude variability in both the continuum and broad line luminosities on months-to-years-long timescales, and are currently unexplained. Simulations have demonstrated that rotating black holes (BHs) sometimes tear apart tilted accretion disks. These tearing events violently restructure the disk on timescales much shorter than a viscous timescale, hinting at a connection to CLAGN. Here, we show that disk tearing can power changing-look events. We report synthetic observations of an extremely high-resolution, three-dimensional, general-relativistic magnetohydrodynamic simulation of a geometrically thin, tilted accretion disk around a rapidly rotating, 10 8 M ⊙ BH. We perform ray-tracing calculations that follow the thermal disk emission to both a line-of-sight camera and to a distribution of cameras in a prescribed torus-like broad-line region (BLR). The continuum photoionizes the BLR, and we calculate the resulting spectrum. Both the continuum and line luminosities undergo order-of-magnitude swings on months-to-years-long timescales. We find shorter, week-long variability driven by the geometric precession of the inner disk and an intraday quasiperiodic oscillation driven by radial breathing of the inner disk. When the torn disk precesses, it causes asymmetric illumination of the BLR, driving time-evolving red-to-blue asymmetries of the broad emission lines that may be a smoking gun for disk tearing. We also make predictions for future photometric observations from ULTRASAT and Vera Rubin Observatory, given a Shakura–Sunyaev–like effective temperature profile, both of which may play an important role in detecting future changing-look events. Future work should consider nonthermal emission, especially from the time-variable corona.

accretion↗

Igniting Weak Interactions in Neutron Star Postmerger Accretion Disks

The merger of two neutron stars or a neutron star and a black hole typically results in the formation of a postmerger accretion disk. Outflows from disks may dominate the overall ejecta from mergers and be a major source of r-process nuclei in our universe. We explore the parameter space of such disks and their outflows and r-process yields by performing 3D general-relativistic magnetohydrodynamic simulations with weak interactions and approximate neutrino transport. We discuss the mapping between the initial binary parameters and the parameter space of the resulting disks, chiefly characterized by their initial accretion rate. We demonstrate the existence of an ignition threshold for weak interactions at around ~10 -3 M⊙ s -1 for typical parameters by means of analytic calculations and numerical simulations. We find a degenerate, self-regulated, neutrino-cooled regime above the threshold and an advection-dominated regime below the threshold. Excess heating in the absence of neutrino cooling below the threshold leads to ≳60% of the initial disk mass being ejected in outflows, with typical velocities of ~(0.1–0.2)c, compared to ≲40% at ~(0.1–0.15)c above the threshold. While disks below the threshold show suppressed production of light r-process elements, disks above the threshold can produce the entire range of r-process elements, in good agreement with the observed solar system abundances. Disks below the ignition threshold may produce an overabundance of actinides seen in actinide-boost stars. As gravitational-wave detectors start to sample the neutron star merger parameter space, different disk realizations may be observable via their associated kilonova emission.

79 ASTRONOMY AND ASTROPHYSICS↗

DIISC-II: Unveiling the Connections between Star Formation and Interstellar Medium in the Extended Ultraviolet Disk of NGC 3344

We present our investigation of the extended ultraviolet (XUV) disk galaxy, NGC 3344, conducted as part of Deciphering the Interplay between the Interstellar medium, Stars, and the Circumgalactic medium survey. We use surface and aperture photometry of individual young stellar complexes to study star formation and its effect on the physical properties of the interstellar medium. We measure the specific star formation rate (sSFR) and find it to increase from 10 –10 yr –1 in the inner disk to >10 –8 yr –1 in the extended disk. This provides evidence for inside-out disk growth. If these sSFRs are maintained, the XUV disk stellar mass can double in ~0.5 Gyr, suggesting a burst of star formation. The XUV disk will continue forming stars for a long time due to the high gas depletion times (τ dep ). The stellar complexes in the XUV disk have high-Σ H I and low-Σ SFR with τ dep ~ 10 Gyr, marking the onset of a deviation from the traditional Kennicutt–Schmidt law. We find that both far-ultraviolet (FUV) and a combination of FUV and 24 μm effectively trace star formation in the XUV disk. Hα is weaker in general and prone to stochasticities in the formation of massive stars. Investigation of the circumgalactic medium at 29.5 kpc resulted in the detection of two absorbing systems with metal-line species: the stronger absorption component is consistent with gas flows around the disk, most likely tracing inflow, while the weaker component is likely tracing corotating circumgalactic gas.

79 ASTRONOMY AND ASTROPHYSICS↗

A Tale of Two Disks: Mapping the Milky Way with the Final Data Release of APOGEE

We present new maps of the Milky Way disk showing the distribution of metallicity ([Fe/H]), α-element abundances ([Mg/Fe]), and stellar age, using a sample of 66,496 red giant stars from the final data release (DR17) of the Apache Point Observatory Galactic Evolution Experiment survey. We measure radial and vertical gradients, quantify the distribution functions for age and metallicity, and explore chemical clock relations across the Milky Way for the low-α disk, high-α disk, and total population independently. The low-α disk exhibits a negative radial metallicity gradient of -0.06 ± 0.001 dex kpc -1 , which flattens with distance from the midplane. The high-α disk shows a flat radial gradient in metallicity and age across nearly all locations of the disk. The age and metallicity distribution functions shift from negatively skewed in the inner Galaxy to positively skewed at large radius. Significant bimodality in the [Mg/Fe]–[Fe/H] plane and in the [Mg/Fe]–age relation persist across the entire disk. The age estimates have typical uncertainties of ~0.15 in log(age) and may be subject to additional systematic errors, which impose limitations on conclusions drawn from this sample. Nevertheless, these results act as critical constraints on galactic evolution models, constraining which physical processes played a dominant role in the formation of the Milky Way disk. We discuss how radial migration predicts many of the observed trends near the solar neighborhood and in the outer disk, but an additional more dramatic evolution history, such as the multi-infall model or a merger event, is needed to explain the chemical and age bimodality elsewhere in the Galaxy.

79 ASTRONOMY AND ASTROPHYSICS↗

First Images of the Protoplanetary Disk around PDS 201

Scattered light imaging has revealed nearly a dozen circumstellar disks around young Herbig Ae/Be stars—enabling studies of structures in the upper disk layers as potential signs of ongoing planet formation. We present the first images of the disk around the variable Herbig Ae star PDS 201 (V* V351 Ori) and an analysis of the images and spectral energy distribution through 3D Monte Carlo radiative transfer simulations and forward modeling. The disk is detected in three data sets with the Large Binocular Telescope Interferometer/Large Binocular Telescope mid-infrared camera at the Large Binocular Telescope, including direct observations in the Ks and L′ filters, and an L′ observation with the 360° vector apodizing phase plate coronagraph. The scattered light disk extends to a very large radius of ∼250 au, which places it among the largest of such disks. Exterior to the disk, we establish detection limits on substellar companions down to ∼5 M {sub Jup} at ≳1.″5 (≳500 au), assuming the Baraffe et al. models. The images show a radial gap extending to ∼0.″4 (∼140 au at a distance of 340 pc) that is also evident in the spectral energy distribution. The large gap is a possible signpost of multiple high-mass giant planets at orbital distances (∼60–100 au) that are unusually massive and widely separated compared to those of planet populations previously inferred from protoplanetary disk substructures.

79 ASTRONOMY AND ASTROPHYSICS↗

SCExAO/CHARIS Near-infrared Integral Field Spectroscopy of the HD 15115 Debris Disk

We present new, near-infrared (1.1–2.4 μm) high-contrast imaging of the debris disk around HD 15115 with the Subaru Coronagraphic Extreme Adaptive Optics (SCExAO) system coupled with the Coronagraphic High Angular Resolution Imaging Spectrograph (CHARIS). The SCExAO/CHARIS resolves the disk down to ρ ∼ 0.″2 (r {sub proj} ∼ 10 au), a factor of ∼3–5 smaller than previous recent studies. We derive a disk position angle of PA ∼ 279.°4–280.°5 and an inclination of i ∼ 85.°3–86.2.°. While recent SPHERE/IRDIS imagery of the system could suggest a significantly misaligned two-ring disk geometry, CHARIS imagery does not reveal conclusive evidence for this hypothesis. Moreover, optimizing models of both one- and two-ring geometries using differential evolution, we find that a single ring having a Hong-like scattering phase function matches the data equally well within the CHARIS field of view (ρ ≲ 1″). The disk’s asymmetry, well evidenced at larger separations, is also recovered; the west side of the disk appears, on average, around 0.4 mag brighter across the CHARIS bandpass between 0.″25 and 1″. Comparing Space Telescope Imaging Spectrograph (STIS) 50CCD optical photometry (2000–10500 Å) with CHARIS near-infrared photometry, we find a red (STIS/50CCD−CHARIS broadband) color for both sides of the disk throughout the 0.″4–1″ region of overlap, in contrast to the blue color reported at similar wavelengths for regions exterior to ∼2″. Further, this color may suggest a smaller minimum grain size than previously estimated at larger separations. Finally, we provide constraints on planetary companions and discuss possible mechanisms for the observed inner disk flux asymmetry and color.

79 ASTRONOMY AND ASTROPHYSICS↗

Discovery of a Nearby Young Brown Dwarf Disk

We report the discovery of the youngest brown dwarf with a disk at 102 pc from the Sun, WISEA J120037.79−784508.3 (W1200−7845), via the Disk Detective citizen science project. We establish that W1200−7845 is located in the 3.7{sub −1.4}{sup +4.6} Myr old ε Cha association. Its spectral energy distribution (SED) exhibits clear evidence of an infrared (IR) excess, indicative of the presence of a warm circumstellar disk. Modeling this warm disk, we find the data are best fit using a power-law description with a slope α = −0.94, which suggests that it is a young, Class II type disk. Using a single blackbody disk fit, we find T{sub eff,disk}=521 K and L{sub IR}/L{sub ∗}=0.14. The near-IR spectrum of W1200−7845 matches a spectral type of M6.0 γ ± 0.5, which corresponds to a low surface gravity object, and lacks distinctive signatures of strong Paβ or Brγ accretion. Both our SED fitting and spectral analysis indicate that the source is cool (T {sub eff} = 2784–2850 K), with a mass of 42–58 M {sub Jup}, well within the brown dwarf regime. The proximity of this young brown dwarf disk makes the system an ideal benchmark for investigating the formation and early evolution of brown dwarfs.

79 ASTRONOMY AND ASTROPHYSICS↗

The Anatomy of an Unusual Edge-on Protoplanetary Disk. II. Gas Temperature and a Warm Outer Region

We present high-resolution {sup 12}CO and {sup 13}CO 2–1 ALMA observations, as well as optical and near-infrared spectroscopy, of the highly inclined protoplanetary disk around SSTC2D J163131.2–242627. The spectral type we derive for the source is consistent with a 1.2 M {sub ⊙} star inferred from the ALMA observations. Despite its massive circumstellar disk, we find little to no evidence for ongoing accretion on the star. The CO maps reveal a disk that is unusually compact along the vertical direction, consistent with its appearance in scattered light images. The gas disk extends about twice as far away as both the submillimeter continuum and the optical scattered light. CO is detected from two surface layers separated by a midplane region in which CO emission is suppressed, as expected from freeze-out in the cold midplane. We apply a modified version of the tomographically reconstructed distribution method presented by Dutrey et al. to derive the temperature structure of the disk. We find a temperature in the CO-emitting layers and the midplane of ∼33 K and ∼20 K at R < 200 au, respectively. Outside of R > 200 au, the disk’s midplane temperature increases to ∼30 K, with a nearly vertically isothermal profile. The transition in CO temperature coincides with a dramatic reduction in the submicron and submillimeter emission from the disk. We interpret this as interstellar UV radiation providing an additional source of heating to the outer part of the disk.

47 OTHER INSTRUMENTATION↗

A Machine Learning Framework to Predict Images of Edge-on Protoplanetary Disks

The physical structure and properties of protoplanetary disks are typically derived from spatially resolved disk images. Edge-on disks in particular provide an important view point on the vertical structure and degree of settling of disks. Such analyses rely on radiative transfer (RT) calculations that are generally computationally intensive due to the high optical depth of disks. Here we present a machine learning framework that has the potential to dramatically speed up the forward modeling process by approximating the results of RT calculations. This framework, trained on an initial set of RT calculations, utilizes an autoencoder neural network to enable the generation of synthetic scattered light images of edge-on disks directly from a set of physical parameters. We demonstrate that this framework generates synthetic images 2–3 orders of magnitude faster than using RT calculations. These machine learning-generated images appear to approximate the RT images well, in particular preserving their size and shape. We also find a strong correlation between the latent space representations of the generated disk images and several of their associated physical parameters. Finally, we discuss potential changes to the framework, such as methods to further improve the image quality, extending the framework to multiple wavelengths, and inverting the process to infer physical parameters from observed images. Overall, these new tools have the potential to enable a more efficient and uniform analysis of edge-on disk properties and the initial conditions of planet formation.

79 ASTRONOMY AND ASTROPHYSICS↗

Slant, Fan, and Narrow: The Response of Stellar Streams to a Tilting Galactic Disk

Stellar streams are sensitive tracers of the gravitational potential, which is typically assumed to be static in the inner Galaxy. However, massive mergers like Gaia-Sausage-Enceladus can impart torques on the stellar disk of the Milky Way that result in the disk tilting at rates of up to 10°–20° Gyr –1 . Here, we demonstrate the effects of disk tilting on the morphology and kinematics of stellar streams. Through a series of numerical experiments, we find that streams with nearby apocenters (r apo ≲ 20 kpc) are sensitive to disk tilting, with the primary effect being changes to the stream's on-sky track and width. Interestingly, disk tilting can produce both more diffuse streams and more narrow streams, depending on the orbital inclination of the progenitor and the direction in which the disk is tilting. Our model of Pal 5's tidal tails for a tilting rate of 15° Gyr –1 is in excellent agreement with the observed stream's track and width, and reproduces the extreme narrowing of the trailing tail. We also find that failure to account for a tilting disk can bias constraints on shape parameters of the Milky Way's local dark matter distribution at the level of 5%–10%, with the direction of the bias changing for different streams. Disk tilting could therefore explain discrepancies in the Milky Way's dark matter halo shape inferred using different streams.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Vertical Structure of Local Disk Galaxies Revealed by DESI Imaging Data

The vertical structure of galactic disks is an important probe of the disk assembly history. Here we investigate the vertical structure of a sample of 79 local disk galaxies within 50 Mpc using data from the Dark Energy Spectroscopic Instrument Legacy Imaging Surveys. Vertical luminosity profiles as a function of radius in the g, r, and z bands are extracted and fitted using a single-component sech2 model to determine scale height and its radial variation (i.e., flaring). Our measurements indicate local galactic disks are overall thin with negligible flaring. The median scale heights at 1 R e are 0.21, 0.22, and 0.22 kpc in the g, r, and z bands, respectively, while the median radial gradients of scale height are −0.006, 0.003, and 0.001 in these bands. These values are consistent with that of the geometric thin disk of the Milky Way represented by metal-rich, low-[α/Fe] populations, confirming the weak flaring of the geometric thin disk. A clear positive correlation of scale height with stellar mass is observed down to the low-mass end of 10 7 M ⊙ . These results provide a homogeneous benchmark for the vertical structure of nearby disk galaxies and establish the cosmological representativeness of the Milky Way thin disk.

79 ASTRONOMY AND ASTROPHYSICS↗

Zonal Flow and Self-regulating Mechanism in a Hydrodynamic Disk

This study addresses key aspects of momentum transport in hydrodynamic disks, which is critical for understanding zonal flow generation and turbulence in compressible hydrodynamic disks. We find that nonlinear momentum/density transport leads to the formation of zonal flows from the Rossby wave instability in disks. We analytically derive the generation and location of zonal flows and describe a modified Taylor identity applicable to compressible disk flows. We further present a self-regulation model, revealing a dynamic interplay between zonal flow and fluctuations driven by Rossby wave instability that regulates the nonlinear saturation state. This theoretical framework contributes insights into the dynamics of disks such as protoplanetary disks, shedding light on the intricate processes governing momentum/density transport and the emergence of zonal flows in the saturation of protoplanetary disks.

Astrophysical fluid dynamics↗

Fast flavor instability in hypermassive neutron star disk outflows

Here, we examine the effect of neutrino flavor transformation by the fast flavor instability (FFI) on long-term mass ejection from accretion disks formed after neutron star mergers. Neutrino emission and absorption in the disk set the composition of the disk ejecta, which subsequently undergoes r-process nucleosynthesis upon expansion and cooling. Here we perform 28 time-dependent, axisymmetric, viscous-hydrodynamic simulations of accretion disks around hypermassive neutron stars (HMNSs) of variable lifetime, using a 3-species neutrino leakage scheme for emission and an annular-lightbulb scheme for absorption. We include neutrino flavor transformation due the FFI in a parametric way, by modifying the absorbed neutrino fluxes and temperatures, allowing for flavor mixing at various levels of flavor equilibration, and also in a way that aims to respect the lepton-number preserving symmetry of the neutrino self-interaction Hamiltonian. We find that for a promptly-formed black hole (BH), the FFI lowers the average electron fraction of the disk outflow due to a decrease in neutrino absorption, driven primarily by a drop in electron neutrino/antineutrino flux upon flavor mixing. For a long-lived HMNS, the disk emits more heavy lepton neutrinos and reabsorbs more electron neutrinos than for a BH, with a smaller drop in flux compensated by a higher neutrino temperature upon flavor mixing. The resulting outflow has a broader electron fraction distribution, a more proton-rich peak, and undergoes stronger radiative driving. Disks with intermediate HMNS lifetimes show results that fall in between these two limits. In most cases, the impact of the FFI on the outflow is moderate, with changes in mass ejection, average velocity, and average electron fraction of order ~10%, and changes in the lanthanide/actinide mass fraction of up to a factor ~2.

79 ASTRONOMY AND ASTROPHYSICS↗

Global Simulations of Gravitational Instability in Protostellar Disks with Full Radiation Transport. I. Stochastic Fragmentation with Optical-depth-dependent Rate and Universal Fragment Mass

Fragmentation in a gravitationally unstable accretion disk can be an important pathway for forming stellar/planetary companions. To characterize quantitatively the condition for and outcome of fragmentation under realistic thermodynamics, we perform global 3D simulations of gravitationally unstable disks at various cooling rates and cooling types, including the first global simulations of gravitational instability that employ full radiation transport. We find that fragmentation is a stochastic process, with the fragment generation rate per disk area p frag showing an exponential dependence on the parameter β ≡ Ω K t cool , where Ω K is the Keplerian rotation frequency, and t cool is the average cooling timescale. Compared to a prescribed constant β, radiative cooling in the optically thin/thick regime makes p frag decrease slower/faster in β; the critical β corresponding to ∼1 fragment per orbit is ≈3, 5, and 2 for constant β, optically thin, and optically thick cooling, respectively. The distribution function of the initial fragment mass is remarkably insensitive to disk thermodynamics. Regardless of cooling rate and optical depth, the typical initial fragment mass is m frag ≈ 40M tot h 3 , with M tot being the total (star+disk) mass and h = H/R being the disk aspect ratio. Applying this result to typical Class 0/I protostellar disks, we find m frag ∼ 20M J , suggesting that fragmentation more likely forms brown dwarfs. Given the finite width of the m frag distribution, forming massive planets is also possible.

gravitational instability↗

Toward accurate measurement of electromagnetic field by retrieving and refining the center position of non-uniform diffraction disks in Lorentz 4D-STEM

Recent advancement in scanning transmission electron microscopy (STEM) allows the use of 4D-STEM, a technique that captures an electron diffraction pattern at each scan point in STEM, to measure electrostatic and magnetic potential and field in materials. However, accurate measurement, separation of the magnetic and electric signals, and removal of artifacts remain challenging, especially in the presence of complex non-uniform diffraction contrast within the disks. In this work, based on dynamic simulations of 4D-STEM patterns built upon superstructures consisting of millions of atoms to account for different sample thickness and edge geometries, we show how the shape and intensity distribution of the central disk are affected by multiple scattering. We propose a robust refinement procedure through iteration of the spin-sensitive peak position of the disk-center in the circular Hough transform filtered images from experimental Lorentz 4D-STEM dataset after minimizing the possible artifacts, such as those due to the change of thickness, dynamic scattering, and scanning process. We verify that caution must be taken as in practice the rigid-disk-shift model used to reconstruct induction maps can easily break down due to disk-protrusion when there exists a nonconstant phase gradient or thickness within the width of the probe. Through quantitative analysis and comparing experiment with calculation the effect of the non-spin-related intensity distribution inside the disk as well as that causes the disk shift due to the intensity-protrusion can be removed, and high-quality magnetic field mapping is possible.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Mo-100 Disk Structural Integrity Tests II

This report is a continuation of the work performed in the report, Mo-100 Disk Structural Integrity Tests I [1]. The NorthStar pressed and sintered 29 mm diameter, 0.5 mm thick Mo-100 disks will be subjected to large temperature gradients when in-beam during production. These large temperature gradients cause high stress and deformation within the disks that could prove detrimental to the target assembly’s cooling performance. Disk fracture is also a possibility that must be understood. Therefore, disk structural integrity tests were performed to understand the thermal induced behavior of these disks. In order to replicate the in-beam conditions, the Mo-100 disks were subjected to large temperature gradients using a 30kW induction heater and coil. A series of transient tests were conducted in a similar fashion as the previous work, as well as an attempt to create steady state conditions for more accurate temperature gradients. The transient thermal test setup and results are described in this report.

36 MATERIALS SCIENCE↗

On the Diversity of Asymmetries in Gapped Protoplanetary Disks

Protoplanetary disks with large inner dust cavities are thought to host massive planetary or substellar companions. These disks show asymmetries and rings in the millimeter continuum caused by dust trapping in pressure bumps and potentially vortices or horseshoes. The origin of the asymmetries and their diversity remains unclear. We present a comprehensive study of 16 disks for which the gas surface density profile has been constrained by CO isotopologue data. First, we compare the azimuthal extents of the dust continuum profiles with the local gas surface density in each disk and find that the asymmetries correspond to higher Stokes numbers or low gas surface density. We discuss which asymmetric structures can be explained by a horseshoe, a vortex, or spiral density waves. Second, we reassess the gas gap radii from the {sup 13}CO maps, which are about a factor of 2 smaller than the dust ring radii, suggesting that the companions in these disks are in the brown dwarf (∼15–50 M {sub Jup}) or super-Jovian (∼3–15 M {sub Jup}) mass regime on eccentric orbits. This is consistent with the estimates from contrast curves on companion mass limits. These curves rule out (sub)stellar companions (q > 0.05) for the majority of the sample at the gap location, but it remains possible at even smaller radii. Third, we find that spiral arms in scattered-light images are primarily detected around high-luminosity stars with disks with wide gaps, which can be understood by the dependence of the spiral arm pitch angle on disk temperature and companion mass.

47 OTHER INSTRUMENTATION↗