Searcharxiv⌕ Search

arXiv subjects

F. Hammer

Publications and source records attributed to F. Hammer.

At least 37 records · Page 2Linked to original sources

Solving the conundrum of intervening strong MgII absorbers towards GRBs and quasars

Previous studies have shown that the incidence rate of intervening strong MgII absorbers towards GRBs were a factor of 2 - 4 higher than towards quasars. Exploring the similar sized and uniformly selected legacy data sets XQ-100 and XSGRB, each consisting of 100 quasar and 81 GRB afterglow spectra obtained with a single instrument (VLT/X-shooter), we demonstrate that there is no disagreement in the number density of strong MgII absorbers with rest-frame equivalent widths $W_r^{2796} >$ 1 Å towards GRBs and quasars in the redshift range 0.1 < z < 5. With large and similar sample sizes, and path length coverages of $Δ$z = 57.8 and 254.4 for GRBs and quasars, respectively, the incidences of intervening absorbers are consistent within 1 sigma uncertainty levels at all redshifts. For absorbers at z < 2.3 the incidence towards GRBs is a factor of 1.5$\pm$0.4 higher than the expected number of strong MgII absorbers in SDSS quasar spectra, while for quasar absorbers observed with X-shooter we find an excess factor of 1.4$\pm$0.2 relative to SDSS quasars. Conversely, the incidence rates agree at all redshifts with reported high spectral resolution quasar data, and no excess is found. The only remaining discrepancy in incidences is between SDSS MgII catalogues and high spectral resolution studies. The rest-frame equivalent width distribution also agrees to within 1 sigma uncertainty levels between the GRB and quasar samples. Intervening strong MgII absorbers towards GRBs are therefore neither unusually frequent, nor unusually strong.

astro-ph.GA↗

The properties of GRB 120923A at a spectroscopic redshift of z=7.8

Gamma-ray bursts (GRBs) are powerful probes of early stars and galaxies, during and potentially even before the era of reionization. Although the number of GRBs identified at z>6 remains small, they provide a unique window on typical star-forming galaxies at that time, and thus are complementary to deep field observations. We report the identification of the optical drop-out afterglow of Swift GRB 120923A in near-infrared Gemini-North imaging, and derive a redshift of z=7.84_{-0.12}^{+0.06} from VLT/X-shooter spectroscopy. At this redshift the peak 15-150 keV luminosity of the burst was 3.2x10^52 erg/s, and in fact the burst was close to the Swift/BAT detection threshold. The X-ray and near-infrared afterglow were also faint, and in this sense it was a rather typical long-duration GRB in terms of rest-frame luminosity. We present ground- and space-based follow-up observations spanning from X-ray to radio, and find that a standard external shock model with a constant-density circumburst environment with density, n~4x10^-2 cm^-3 gives a good fit to the data. The near-infrared light curve exhibits a sharp break at t~3.4 days in the observer frame, which if interpreted as being due to a jet corresponds to an opening angle of ~5 degrees. The beaming corrected gamma-ray energy is then E_gamma~2x10^50 erg, while the beaming-corrected kinetic energy is lower, E_K~10^49 erg, suggesting that GRB 120923A was a comparatively low kinetic energy event. We discuss the implications of this event for our understanding of the high-redshift population of GRBs and their identification.

astro-ph.HE↗

Studying distant galaxies: A Handbook of Methods and Analyses

Distant galaxies encapsulate the various stages of galaxy evolution and formation from over 95% of the development of the universe. As early as twenty-five years ago, little was known about them, however since the first systematic survey was completed in the 1990s, increasing amounts of resources have been devoted to their discovery and research. This book summarises for the first time the numerous techniques used for observing, analysing, and understanding the evolution and formation of these distant galaxies. In this rapidly expanding research field, this text is an every-day companion handbook for graduate students and active researchers. It provides guidelines in sample selection, imaging, integrated spectroscopy and 3D spectroscopy, which help to avoid the numerous pitfalls of observational and analysis techniques in use in extragalactic astronomy. It also paves the way for establishing relations between fundamental properties of distant galaxies. At each step, the reader is assisted with numerous practical examples and ready-to-use methodology to help understand and analyse research.

astro-ph.GA↗

Morpho-kinematics of z~1 galaxies probe the hierarchical scenario

We have studied a representative sample of intermediate-mass galaxies at z~1, observed by the kinematic survey KMOS3D. We have re-estimated the kinematical parameters from the published kinematic maps and analysed photometric data from HST to measure optical disk inclinations and PAs. We find that only half of the z~1 galaxies show kinematic properties consistent with rotating disks, using the same classification scheme than that adopted by the KMOS3D team. Because merger orbital motions can also brought rotation, we have also analysed galaxy morphologies from the available HST imagery. Combining these results to those from kinematics, it leads to a full morpho-kinematic classification. To test the robustness of the latter for disentangling isolated disks from mergers, we confronted the results with an analysis of pairs from the open-grism redshift survey 3D-HST. All galaxies found in pairs are affected by either kinematic and/or morphological perturbations. Conversely, all galaxies classified as virialized spirals are found to be isolated. A significant fraction (one fourth) of rotating disks classified from kinematics by the KMOS3D team are found in pairs, which further supports the need for a morpho-kinematic classification. It results that only one third of z~1 galaxies are isolated and virialized spirals, while 58% of them are likely involved in a merger sequence, from first approach to disk rebuilding. The later fraction is in good agreement with the results of semi-empirical ΛCDM models, supporting a merger-dominated hierarchical scenario as being the main driver of galaxy formation at least during the last 8 billion years.

astro-ph.GA↗

The E-ELT Multi-Object Spectrograph: latest news from MOSAIC

There are 8000 galaxies, including 1600 at z larger than 1.6, which could be simultaneously observed in an E-ELT field of view of 40 sq. arcmin. A considerable fraction of astrophysical discoveries require large statistical samples, which can only be obtained with multi-object spectrographs (MOS). MOSAIC will provide a vast discovery space, enabled by a multiplex of 200 and spectral resolving powers of R=5000 and 20000. MOSAIC will also offer the unique capability of more than 10 "high-definition" (multi-object adaptive optics, MOAO) integral-field units, optimised to investigate the physics of the sources of reionization. The combination of these modes will make MOSAIC the world-leading MOS facility, contributing to all fields of contemporary astronomy, from extra-solar planets, to the study of the halo of the Milky Way and its satellites, and from resolved stellar populations in nearby galaxies out to observations of the earliest "first-light" structures in the Universe. It will also study the distribution of the dark and ordinary matter at all scales and epochs of the Universe. Recent studies of critical technical issues such as sky-background subtraction and MOAO have demonstrated that such a MOS is feasible with state-of-the-art technology and techniques. Current studies of the MOSAIC team include further trade-offs on the wavelength coverage, a solution for compensating for the non-telecentric new design of the telescope, and tests of the saturation of skylines especially in the near-IR bands. In the 2020s the E-ELT will become the world's largest optical/IR telescope, and we argue that it has to be equipped as soon as possible with a MOS to provide the most efficient, and likely the best way to follow-up on James Webb Space Telescope (JWST) observations.

astro-ph.IM↗

Science Requirements and Trade-offs for the MOSAIC Instrument for the European ELT

Building on the comprehensive White Paper on the scientific case for multi-object spectroscopy on the European ELT, we present the top-level instrument requirements that are being used in the Phase A design study of the MOSAIC concept. The assembled cases span the full range of E-ELT science and generally require either 'high multiplex' or 'high definition' observations to best exploit the excellent sensitivity and spatial performance of the telescope. We highlight some of the science studies that are now being used in trade-off studies to inform the capabilities of MOSAIC and its technical design.

astro-ph.IM↗

Are LGRBs biased tracers of star formation? Clues from the host galaxies of the Swift/BAT6 complete sample of bright LGRBs. II: star formation rates and metallicities at z < 1

Long gamma-ray bursts (LGRBs) are associated with the deaths of massive stars and could thus be a potentially powerful tool to trace cosmic star formation. However, especially at low redshifts (z < 1.5) LGRBs seem to prefer particular types of environment. Our aim is to study the host galaxies of a complete sample of bright LGRBs to investigate the impact of the environment on GRB formation. We study host galaxy spectra of the Swift/BAT6 complete sample of 14 z < 1 bright LGRBs. We use the detected nebular emission lines to measure the dust extinction, star formation rate (SFR) and nebular metallicity (Z) of the hosts and supplement the data set with previously measured stellar masses M$_{\star}$. The distributions of the obtained properties and their interrelations (e.g. mass-metallicity and SFR-M$_{\star}$ relations) are compared to samples of field star-forming galaxies.We find that LGRB hosts at z < 1 have on average lower SFRs than if they were direct star-formation tracers. By directly comparing metallicity distributions of LGRB hosts and star-forming galaxies, we find a good match between the two populations up to Z $\sim 8.4-8.5$, after which the paucity of metal-rich LGRB hosts becomes apparent. The LGRB host galaxies of our complete sample are not inconsistent with the mass-metallicity relation at similar mean redshift and stellar masses. The cutoff against high metallicities (and high masses) can explain the low SFR values of LGRB hosts. We find a hint of increased incidence of starburst galaxies in the Swift/BAT6 z < 1 sample with respect to that of a field star-forming population. Given that the SFRs are low on average, the latter is ascribed to low stellar masses. Nevertheless the limits on the completeness and metallicity availability of current surveys, coupled with the limited number of LGRB host galaxies, prevent us from reaching more quantitative conclusions.

astro-ph.HE↗

The Magellanic Stream System: I. Ram-pressure tails and the relics of the collision between the Magellanic Clouds

We have analyzed the Magellanic Stream (MS) using the deepest and the most resolved H I survey of the Southern Hemisphere (the Galactic All-Sky Survey). The overall Stream is structured into two filaments, suggesting two ram-pressure tails lagging behind the Magellanic Clouds (MCs), and resembling two close, transonic, von Karman vortex streets. The past motions of the Clouds appear imprinted in them, implying almost parallel initial orbits, and then a radical change after their passage near the N(H I) peak of the MS. This is consistent with a recent collision between the MCs, $200-300$ Myr ago, which has stripped their gas further into small clouds, spreading them out along a gigantic bow shock, perpendicular to the MS. The Stream is formed by the interplay between stellar feedback and the ram pressure exerted by hot gas in the Milky Way (MW) halo with $ρ_{hot}$= $10^{-4}$ $cm^{-3}$ at 50-70 kpc, a value necessary to explain the MS multiphase high-velocity clouds. The corresponding hydrodynamic modeling provides the currently most accurate reproduction of the whole H I Stream morphology, of its velocity, and column density profiles along $L_{MS}$. The 'ram pressure plus collision' scenario requires tidal dwarf galaxies, which are assumed to be the Cloud and dSph progenitors, to have left imprints in the MS and the Leading Arm, respectively. The simulated LMC and SMC have baryonic mass, kinematics and proper motions consistent with observations. This supports a novel paradigm for the MS System, which could have its origin in material expelled toward the MW by the ancient gas-rich merger that formed M31.

astro-ph.GA↗

Young tidal dwarf galaxies cannot be used to probe dark matter in galaxies

The location of dark-matter free, tidal dwarf galaxies (TDGs) in the baryonic Tully Fisher (bTF) diagram has been used to test cosmological scenarios, leading to various and controversial results. Using new high-resolution 3D spectroscopic data, we re-investigate the morpho-kinematics of these galaxies to verify whether or not they can be used for such a purpose. We find that the three observed TDGs are kinematically not virialized and show complex morphologies and kinematics, leading to considerable uncertainties about their intrinsic rotation velocities and their locations on the bTF. Only one TDG can be identify as a (perturbed) rotation disk that it is indeed a sub-component of NGC5291N and that lies at $<$1$σ$ from the local bTF relation. It results that the presently studied TDGs are young, dynamically forming objects, which are not enough virialized to robustly challenge cosmological scenarios.

astro-ph.GA↗

GRB hosts through cosmic time - VLT/X-Shooter emission-line spectroscopy of 96 GRB-selected galaxies at 0.1 < z < 3.6

[Abridged] We present data and initial results from VLT/X-Shooter emission-line spectroscopy of 96 GRB-selected galaxies at 0.1<z<3.6, the largest sample of GRB host spectroscopy available to date. Most of our GRBs were detected by Swift and 76% are at 0.5<z<2.5 with a median z~1.6. Based on Balmer and/or forbidden lines of oxygen, nitrogen, and neon, we measure systemic redshifts, star formation rates (SFRs), visual attenuations, oxygen abundances (12+log(O/H)), and emission-line widths. We find a strong change of the typical physical properties of GRB hosts with redshift. The median SFR, for example, increases from ~0.6 M_sun/yr at z~0.6 up to ~15 M_sun/yr at z~2. A higher ratio of [OIII]/[OII] at higher redshifts leads to an increasing distance of GRB-selected galaxies to the locus of local galaxies in the BPT diagram. Oxygen abundances of the galaxies are distributed between 12+log(O/H)=7.9 and 12+log(O/H)=9.0 with a median of 12+log(O/H)~8.5. The fraction of GRB-selected galaxies with super-solar metallicities is around 20% at z<1 in the adopted metallicity scale. This is significantly less than the fraction of star formation in similar galaxies, illustrating that GRBs are scarce in high-metallicity environments. At z~3, sensitivity limits us to probing only the most luminous GRB hosts for which we derive metallicities of Z ~< 0.5 Z_sun. Together with a high incidence of galaxies with similar metallicity in our sample at z~1.5, this indicates that the metallicity dependence observed at low redshift will not be dominant at z~3.

astro-ph.GA↗

Are LGRBs biased tracers of star formation? Clues from the host galaxies of the Swift/BAT6 complete sample of LGRBs. I: Stellar mass at z<1

LGRBs are associated with massive stars and are therefore linked to star formation. The conditions necessary to produce LGRBs can affect the relation between the LGRB rate and star formation. By using the power of a complete LGRB sample, our aim is to understand whether such a bias exists and, if it does, what is its origin. In this first paper, we build the SED of the z<1 host galaxies of the BAT6 LGRB sample, and determine their stellar masses from SED fitting. We compare the resulting stellar mass distribution (i) with star-forming galaxies observed in deep surveys (UltraVISTA); (ii) with semi-analitical models of the z<1 star forming galaxy population and (iii) with numerical simulations of LGRB hosts having different metallicity thresholds for the progenitor star environment. We find that at z<1 LGRBs tend to avoid massive galaxies and are powerful in selecting faint low-mass star-forming galaxies. The stellar mass distribution of the hosts is not consistent with that of the UltraVISTA star-forming galaxies weighted for their SFR. This implies that, at least at z<1, LGRBs are not unbiased tracers of star formation. To make the two distributions consistent, a much steeper faint-end of the mass function would be required, or a very shallow SFR-Mass relation for the low mass galaxy population. GRB host galaxy simulations indicates that, to reproduce the stellar mass distribution, a metallicity threshold of the order of Z_th=0.3-0.5Z_sun is necessary. Models without a metallicity threshold or with an extreme threshold of Z_th = 0.1Z_sun are excluded at z<1. The use of the BAT6 complete sample makes this result not affected by possible biases which could have influenced past results based on incomplete samples. The preference for low metallicities (Z<~0.5Z_sun) can be a consequence of the particular conditions needed for the progenitor star to produce a GRB. (Abridged)

astro-ph.HE↗

GRB host galaxies with VLT/X-Shooter: properties at 0.8 < z < 1.3

Long gamma-ray bursts (LGRBs) are associated with the death of massive stars. Their host galaxies therefore represent a unique class of objects tracing star formation across the observable Universe. Indeed, recently accumulated evidence shows that GRB hosts do not differ substantially from general population of galaxies at high (z > 2) redshifts. However, it has been long recognised that the properties of z < 1.5 hosts, compared to general star-forming population, are unusual. To better understand the reasons for the supposed difference in LGRB hosts properties at z < 1.5, we obtained VLT/X- Shooter spectra of six hosts lying in the redshift range of 0.8 < z < 1.3. Some of these hosts have been observed before, yet we still lack well constrained information on their characteristics such as metallicity, dust extinction and star formation rate. We search for emission lines in the VLT/X-Shooter spectra of the hosts and measure their fluxes. We perform a detailed analysis, estimating host average extinction, star-formation rates, metallicities and electron densities where possible. Measured quantities of our hosts are compared to a larger sample of previously observed GRB hosts at z < 2. Star-formation rates and metallicities are measured for all the hosts analyzed in this paper and metallicities are well determined for 4 hosts. The mass-metallicity relation, the fundamental metallicity relation and SFRs derived from our hosts occupy similar parameter space as other host galaxies investigated so-far at the same redshift. We therefore conclude that GRB hosts in our sample support the found discrepancy between the properties of low-redshift GRB hosts and the general population of star- forming galaxies.

astro-ph.HE↗

Environment, morphology and stellar populations of bulgeless low surface brightness galaxies

Based on the Sloan Digital Sky Survey DR 7, we investigate the environment, morphology and stellar population of bulgeless low surface brightness (LSB) galaxies in a volume-limited sample with redshift ranging from 0.024 to 0.04 and $M_r$ $\leq$ $-18.8$. The local density parameter $Σ_5$ is used to trace their environments. We find that, for bulgeless galaxies, the surface brightness does not depend on the environment. The stellar populations are compared for bulgeless LSB galaxies in different environments and for bulgeless LSB galaxies with different morphologies. The stellar populations of LSB galaxies in low density regions are similar to those of LSB galaxies in high density regions. Irregular LSB galaxies have more young stars and are more metal-poor than regular LSB galaxies. These results suggest that the evolution of LSB galaxies may be driven by their dynamics including mergers rather than by their large scale environment.

astro-ph.GA↗

TOPoS: II. On the bimodality of carbon abundance in CEMP stars. Implications on the early chemical evolution of galaxies

In the course of the TOPoS (Turn Off Primordial Stars) survey, aimed at discovering the lowest metallicity stars, we have found several carbon-enhanced metal-poor (CEMP) stars. We here present our analysis of six CEMP stars. Calcium and carbon are the only elements that can be measured in all six stars. The range is -5.0<=[Ca/H]< -2.1 and 7.12<=A(C)<=8.65. For star SDSS J1742+2531 we were able to detect three FeI lines from which we deduced [Fe/H]=-4.80, from four CaII lines we derived [Ca/H]=-4.56, and from synthesis of the G-band we derived A(C)=7.26. For SDSS J1035+0641 we were not able to detect any iron lines, yet we could place a robust (3sigma) upper limit of [Fe/H]< -5.0 and measure the Ca abundance, with [Ca/H]=-5.0, and carbon, A(C)=6.90. No lithium is detected in the spectrum of SDSS J1742+2531 or SDSS J1035+0641, which implies a robust upper limit of A(Li)<1.8 for both stars. Our measured carbon abundances confirm the bimodal distribution of carbon in CEMP stars, identifying a high-carbon band and a low-carbon band. We propose an interpretation of this bimodality according to which the stars on the high-carbon band are the result of mass transfer from an AGB companion, while the stars on the low-carbon band are genuine fossil records of a gas cloud that has also been enriched by a faint supernova (SN) providing carbon and the lighter elements. (Abridged)

astro-ph.GA↗

Spectrophotometric analysis of GRB afterglow extinction curves with X-shooter

In this work we use gamma-ray burst (GRB) afterglow spectra observed with the VLT/X-shooter spectrograph to measure rest-frame extinction in GRB lines-of-sight by modeling the broadband near-infrared (NIR) to X-ray afterglow spectral energy distributions (SEDs). Our sample consists of nine Swift GRBs, eight of them belonging to the long-duration and one to the short-duration class. Dust is modeled using the average extinction curves of the Milky Way and the two Magellanic Clouds. We derive the rest-frame extinction of the entire sample, which fall in the range $0 \lesssim {\it A}_{\rm V} \lesssim 1.2$. Moreover, the SMC extinction curve is the preferred extinction curve template for the majority of our sample, a result which is in agreement with those commonly observed in GRB lines-of-sights. In one analysed case (GRB 120119A), the common extinction curve templates fail to reproduce the observed extinction. To illustrate the advantage of using the high-quality X-shooter afterglow SEDs over the photometric SEDs, we repeat the modeling using the broadband SEDs with the NIR-to-UV photometric measurements instead of the spectra. The main result is that the spectroscopic data, thanks to a combination of excellent resolution and coverage of the blue part of the SED, are more successful in constraining the extinction curves and therefore the dust properties in GRB hosts with respect to photometric measurements. In all cases but one the extinction curve of one template is preferred over the others. We show that the modeled values of the extinction and the spectral slope, obtained through spectroscopic and photometric SED analysis, can differ significantly for individual events. Finally we stress that, regardless of the resolution of the optical-to-NIR data, the SED modeling gives reliable results only when the fit is performed on a SED covering a broader spectral region.

astro-ph.HE↗

Galaxy Mass Assembly with VLT & HST and lessons for E-ELT/MOSAIC

The fraction of distant disks and mergers is still debated, while 3D-spectroscopy is revolutionizing the field. However its limited spatial resolution imposes a complimentary HST imagery and a robust analysis procedure. When applied to observations of IMAGES galaxies at z=0.4-0.8, it reveals that half of the spiral progenitors were in a merger phase, 6 billion year ago. The excellent correspondence between methodologically-based classifications of morphologies and kinematics definitively probes a violent origin of disk galaxies as proposed by Hammer et al. (2005). Examination of nearby galaxy outskirts reveals fossil imprints of such ancient merger events, under the form of well organized stellar streams. Perhaps our neighbor, M31, is the best illustration of an ancient merger, which modeling in 2010 leads to predict the gigantic plane of satellites discovered by Ibata et al. (2013). There are still a lot of discoveries to be done until the ELT era, which will open an avenue for detailed and accurate 3D-spectroscopy of galaxies from the earliest epochs to the present.

astro-ph.GA↗

The mysterious optical afterglow spectrum of GRB140506A at z=0.889

Context. Gamma-ray burst (GRBs) afterglows probe sightlines to star-forming regions in distant star-forming galaxies. Here we present a study of the peculiar afterglow spectrum of the z = 0.889 Swift GRB 140506A. Aims. Our aim is to understand the origin of the very unusual properties of the absorption along the line-of-sight. Methods. We analyse spectroscopic observations obtained with the X-shooter spectrograph mounted on the ESO/VLT at two epochs 8.8 h and 33 h after the burst as well as imaging from the GROND instrument. We also present imaging and spectroscopy of the host galaxy obtained with the Magellan telescope. Results. The underlying afterglow appears to be a typical afterglow of a long-duration GRB. However, the material along the line-of- sight has imprinted very unusual features on the spectrum. Firstly, there is a very broad and strong flux drop below 8000 AA (4000 AA in the rest frame), which seems to be variable between the two spectroscopic epochs. We can reproduce the flux-drops both as a giant 2175 AA extinction bump and as an effect of multiple scattering on dust grains in a dense environment. Secondly, we detect absorption lines from excited H i and He i. We also detect molecular absorption from CH+ . Conclusions. We interpret the unusual properties of these spectra as reflecting the presence of three distinct regions along the line-of-sight: the excited He i absorption originates from an H ii-region, whereas the Balmer absorption must originate from an associated photodissociation region. The strong metal line and molecular absorption and the dust extinction must originate from a third, cooler region along the line-of-sight. The presence of (at least) three separate regions is reflected in the fact that the different absorption components have different velocities relative to the systemic redshift of the host galaxy.

astro-ph.GA↗

Comparing the Host Galaxies of Type Ia, Type II and Type Ibc Supernovae

We compare the host galaxies of 902 supernovae, including SNe Ia, SNe II and SNe Ibc, which are selected by cross-matching the Asiago Supernova Catalog with the SDSS Data Release 7. We further selected 213 galaxies by requiring the light fraction of spectral observations $>$15%, which could represent well the global properties of the galaxies. Among them, 135 galaxies appear on the Baldwin-Phillips-Terlevich diagram, which allows us to compare the hosts in terms of star-forming, AGNs (including composites, LINERs and Seyfert 2s) and "Absorp" (their related emission-lines are weak or non-existence) galaxies. The diagrams related to parameters D$_n$(4000), H$δ_A$, stellar masses, SFRs and specific SFRs for the SNe hosts show that almost all SNe II and most of SNe Ibc occur in SF galaxies, which have a wide range of stellar mass and low D$_n$(4000). The SNe Ia hosts as SF galaxies follow similar trends. A significant fraction of SNe Ia occurs in AGNs and Absorp galaxies, which are massive and have high D$_n$(4000). The stellar population analysis from spectral synthesis fitting shows that the hosts of SNe II have a younger stellar population than hosts of SNe Ia. These results are compared with those of the 689 comparison galaxies where the SDSS fiber captures less than 15% of the total light. These comparison galaxies appear biased towards higher 12+log(O/H) ($\sim$0.1dex) at a given stellar mass. Therefore, we believe the aperture effect should be kept in mind when the properties of the hosts for different types of SNe are discussed.

astro-ph.GA↗