arXiv subjects

L. D. Anderson

Publications and source records attributed to L. D. Anderson.

At least 91 records · Page 5Linked to original sources

arXiv2015

Finding Distant Galactic HII Regions

The WISE Catalog of Galactic HII Regions contains $\sim2000$ HII region candidates lacking ionized gas spectroscopic observations. All candidates have the characteristic HII region mid-infrared morphology of WISE $12\,\,μ\,m$ emission surrounding $22\,μ\,m$ emission, and additionally have detected radio continuum emission. We here report Green Bank Telescope (GBT) hydrogen radio recombination line (RRL) and radio continuum detections at X-band (9GHz; 3cm) of 302 WISE HII region candidates (out of 324 targets observed) in the zone $225^{\circ} > l > -20^{\circ}$, $|b| \le 6^{\circ}$. Here we extend the sky coverage of our HII region Discovery Survey (HRDS), which now contains nearly 800 HII regions distributed across the entire northern sky. We provide LSR velocities for the 302 detections and kinematic distances for 131 of these. Of the 302 new detections, five have ($l, b, v$) coordinates consistent with the Outer Scutum-Centaurus Arm (OSC), the most distant molecular spiral arm of the Milky Way. Due to the Galactic warp, these nebulae are found at Galactic latitudes $>1^{\circ}$ in the first Galactic quadrant, and therefore were missed in previous surveys of the Galactic plane. One additional region has a longitude and velocity consistent with the OSC but lies at a negative Galactic latitude (G039.183$-$01.422; $-$54.9 kms). With Heliocentric distances >22 kpc and Galactocentric distances >16 kpc, the OSC HII regions are the most distant known in the Galaxy. We detect an additional three HII regions near $l \simeq 150^{\circ}$ whose LSR velocities place them at Galactocentric radii >19 kpc. If their distances are correct, these nebulae may represent the limit to Galactic massive star formation.

astro-ph.GA↗

arXiv2015

Untangling the Recombination Line Emission from HII Regions with Multiple Velocity Components

HII regions are the ionized spheres surrounding high-mass stars. They are ideal targets for tracing Galactic structure because they are predominantly found in spiral arms and have high luminosities at infrared and radio wavelengths. In the Green Bank Telescope HII Region Discovery Survey (GBT HRDS) we found that >30% of first Galactic quadrant HII regions have multiple hydrogen radio recombination line (RRL) velocities, which makes determining their Galactic locations and physical properties impossible. Here we make additional GBT RRL observations to determine the discrete HII region velocity for all 117 multiple-velocity sources within 18deg. < l < 65deg. The multiple-velocity sources are concentrated in the zone 22deg. < l < 32deg., coinciding with the largest regions of massive star formation, which implies that the diffuse emission is caused by leaked ionizing photons. We combine our observations with analyses of the electron temperature, molecular gas, and carbon recombination lines to determine the source velocities for 103 discrete H II regions (88% of the sample). With the source velocities known, we resolve the kinematic distance ambiguity for 47 regions, and thus determine their heliocentric distances.

astro-ph.GA↗

arXiv2015

Bipolar HII regions - Morphology and star formation in their vicinity - I - G319.88$+$00.79 and G010.32$-$00.15

Our goal is to identify bipolar HII regions and to understand their morphology, their evolution, and the role they play in the formation of new generations of stars. We use the Spitzer and Herschel Hi-GAL surveys to identify bipolar HII regions. We search for their exciting star(s) and estimate their distances using near-IR data. Dense clumps are detected using Herschel-SPIRE data. MALT90 observations allow us to ascertain their association with the central HII region. We identify Class 0/I YSOs using their Spitzer and Herschel-PACS emissions. These methods will be applied to the entire sample of candidate bipolar HII regions. This paper focuses on two bipolar HII regions, one interesting in terms of its morphology, G319.88$+$00.79, and one in terms of its star formation, G010.32$-$00.15. Their exciting clusters are identified and their photometric distances estimated to be 2.6 kpc and 1.75 kpc, respectively. We suggest that these regions formed in dense and flat structures that contain filaments. They have a central ionized region and ionized lobes perpendicular to the parental cloud. The remains of the parental cloud appear as dense (more than 10^4 per cm^3) and cold (14-17 K) condensations. The dust in the PDR is warm (19-25 K). Dense massive clumps are present around the central ionized region. G010.32-00.14 is especially remarkable because five clumps of several hundred solar masses surround the central HII region; their peak column density is a few 10^23 per cm^2, and the mean density in their central regions reaches several 10^5 per cm^3. Four of them contain at least one massive YSO; these clumps also contain extended green objects and Class II methanol masers. This morphology suggests that the formation of a second generation of massive stars has been triggered by the central bipolar HII region. It occurs in the compressed material of the parental cloud.

astro-ph.GA↗

arXiv2015

THOR - The HI, OH, Recombination Line Survey of the Milky Way - The pilot study: HI observations of the giant molecular cloud W43

To study the atomic, molecular and ionized emission of Giant Molecular Clouds (GMCs), we have initiated a Large Program with the VLA: 'THOR - The HI, OH, Recombination Line survey of the Milky Way'. We map the 21cm HI line, 4 OH lines, 19 H_alpha recombination lines and the continuum from 1 to 2 GHz of a significant fraction of the Milky Way (l=15-67deg, |b|<1deg) at ~20" resolution. In this paper, we focus on the HI emission from the W43 star-formation complex. Classically, the HI 21cm line is treated as optically thin with column densities calculated under this assumption. This might give reasonable results for regions of low-mass star-formation, however, it is not sufficient to describe GMCs. We analyzed strong continuum sources to measure the optical depth, and thus correct the HI 21cm emission for optical depth effects and weak diffuse continuum emission. Hence, we are able to measure the HI mass of W43 more accurately and our analysis reveals a lower limit of M=6.6x10^6 M_sun, which is a factor of 2.4 larger than the mass estimated with the assumption of optically thin emission. The HI column densities are as high as N(HI)~150 M_sun/pc^2 ~ 1.9x10^22 cm^-2, which is an order of magnitude higher than for low mass star formation regions. This result challenges theoretical models that predict a threshold for the HI column density of ~10 M_sun/pc^2, at which the formation of molecular hydrogen should set in. By assuming an elliptical layered structure for W43, we estimate the particle density profiles. While at the cloud edge atomic and molecular hydrogen are well mixed, the center of the cloud is strongly dominated by molecular hydrogen. We do not identify a sharp transition between hydrogen in atomic and molecular form. Our results are an important characterization of the atomic to molecular hydrogen transition in an extreme environment and challenges current theoretical models.

astro-ph.SR↗

arXiv2015

Azimuthal Metallicity Structure in the Milky Way Disk

Elemental abundance patterns in the Galactic disk constrain theories of the formation and evolution of the Milky Way. HII region abundances are the result of billions of years of chemical evolution. We made radio recombination line and continuum measurements of 21 HII regions located between Galactic azimuth Az = 90-130 degree, a previously unexplored region. We derive the plasma electron temperatures using the line-to-continuum ratios and use them as proxies for the nebular [O/H] abundances, because in thermal equilibrium the abundance of the coolants (O, N, and other heavy elements) in the ionized gas sets the electron temperature, with high abundances producing low temperatures. Combining these data with our previous work produces a sample of 90 HII regions with high quality electron temperature determinations. We derive kinematic distances in a self-consistent way for the entire sample. The radial gradient in [O/H] is -0.082 +/- 0.014 dex/kpc for Az = 90-130 degree, about a factor of two higher than the average value between Az = 0-60 degree. Monte Carlo simulations show that the azimuthal structure we reported for Az = 0-60 degree is not significant because kinematic distance uncertainties can be as high as 50% in this region. Nonetheless, the flatter radial gradients between Az = 0-60 degree compared with Az = 90-130 degree, are significant within the uncertainty. We suggest that this may be due to radial mixing from the Galactic Bar whose major axis is aligned toward Az ~30 degree.

astro-ph.GA↗

arXiv2015

Results from the Wide-field Infrared Survey Explorer (WISE) Future Uses Session at the WISE at 5 Meeting

During the "WISE at 5: Legacy and Prospects" conference in Pasadena, CA -- which ran from February 10 - 12, 2015 -- attendees were invited to engage in an interactive session exploring the future uses of the Wide-field Infrared Survey Explorer (WISE) data. The 65 participants -- many of whom are extensive users of the data -- brainstormed the top questions still to be answered by the mission, as well as the complementary current and future datasets and additional processing of WISE/NEOWISE data that would aid in addressing these most important scientific questions. The results were mainly bifurcated between topics related to extragalactic studies (e.g. AGN, QSOs) and substellar mass objects. In summary, participants found that complementing WISE/NEOWISE data with cross-correlated multiwavelength surveys (e.g. SDSS, Pan-STARRS, LSST, Gaia, Euclid, etc.) would be highly beneficial for all future mission goals. Moreover, developing or implementing machine-learning tools to comb through and understand cross-correlated data was often mentioned for future uses. Finally, attendees agreed that additional processing of the data such as co-adding WISE and NEOWISE and extracting a multi-epoch photometric database and parallax and proper motion catalog would greatly improve the scientific results of the most important projects identified. In that respect, a project such as MaxWISE which would execute the most important additional processing and extraction as well as make the data and catalogs easily accessible via a public portal was deemed extremely important.

astro-ph.IM↗

arXiv2015

Mopra CO Observations of the Bubble HII Region RCW120

We use the Mopra radio telescope to test for expansion of the molecular gas associated with the bubble HII region RCW120. A ring, or bubble, morphology is common for Galactic HII regions, but the three-dimensional geometry of such objects is still unclear. Detected near- and far-side expansion of the associated molecular material would be consistent with a three-dimensional spherical object. We map the $J = 1\rightarrow 0$ transitions of $^{12}$CO, $^{13}$CO, C$^{18}$O, and C$^{17}$O, and detect emission from all isotopologues. We do not detect the $0_0\rightarrow 1_{-1} E$ masing lines of CH$_3$OH at 108.8939 GHz. The strongest CO emission is from the photodissociation region (PDR), and there is a deficit of emission toward the bubble interior. We find no evidence for expansion of the molecular material associated with RCW120 and therefore can make no claims about its geometry. The lack of detected expansion is roughly in agreement with models for the time-evolution of an HII region like RCW120, and is consistent with an expansion speed of $< 1.5\, {\rm km\, s^{-1}}$. Single-position CO spectra show signatures of expansion, which underscores the importance of mapped spectra for such work. Dust temperature enhancements outside the PDR of RCW120 coincide with a deficit of emission in CO, confirming that these temperature enhancements are due to holes in the RCW120 PDR. H$α$ emission shows that RCW120 is leaking $\sim5\%$ of the ionizing photons into the interstellar medium (ISM) through PDR holes at the locations of the temperature enhancements. H-alpha emission also shows a diffuse "halo" from leaked photons not associated with discrete holes in the PDR. Overall $25\pm10\%$ of all ionizing photons are leaking into the nearby ISM.

astro-ph.GA↗

arXiv2014

Age, size, and position of H ii regions in the Galaxy. Expansion of ionized gas in turbulent molecular clouds

This work aims at improving the current understanding of the interaction between H ii regions and turbulent molecular clouds. We propose a new method to determine the age of a large sample of OB associations by investigating the development of their associated H ii regions in the surrounding turbulent medium. Using analytical solutions, one-dimensional (1D), and three-dimensional (3D) simulations, we constrained the expansion of the ionized bubble depending on the turbulent level of the parent molecular cloud. A grid of 1D simulations was then computed in order to build isochrone curves for H ii regions in a pressure-size diagram. This grid of models allowed to date large sample of OB associations and was used on the H ii Region Discovery Survey (HRDS). Analytical solutions and numerical simulations showed that the expansion of H ii regions is slowed down by the turbulence up to the point where the pressure of the ionized gas is in a quasi-equilibrium with the turbulent ram pressure. Based on this result, we built a grid of 1D models of the expansion of H ii regions in a profile based on Larson laws. The 3D turbulence is taken into account by an effective 1D temperature profile. The ages estimated by the isochrones of this grid agree well with literature values of well-known regions such as Rosette, RCW 36, RCW 79, and M16. We thus propose that this method can be used to give ages of young OB associations through the Galaxy such as the HRDS survey and also in nearby extra-galactic sources.

astro-ph.SR↗

arXiv2014

Ionization compression impact on dense gas distribution and star formation, Probability density functions around H ii regions as seen by Herschel

Ionization feedback should impact the probability distribution function (PDF) of the column density around the ionized gas. We aim to quantify this effect and discuss its potential link to the Core and Initial Mass Function (CMF/IMF). We used in a systematic way Herschel column density maps of several regions observed within the HOBYS key program: M16, the Rosette and Vela C molecular cloud, and the RCW 120 H ii region. We fitted the column density PDFs of all clouds with two lognormal distributions, since they present a double-peak or enlarged shape in the PDF. Our interpretation is that the lowest part of the column density distribution describes the turbulent molecular gas while the second peak corresponds to a compression zone induced by the expansion of the ionized gas into the turbulent molecular cloud. The condensations at the edge of the ionized gas have a steep compressed radial profile, sometimes recognizable in the flattening of the power-law tail. This could lead to an unambiguous criterion able to disentangle triggered from pre-existing star formation. In the context of the gravo-turbulent scenario for the origin of the CMF/IMF, the double peaked/enlarged shape of the PDF may impact the formation of objects at both the low-mass and the high-mass end of the CMF/IMF. In particular a broader PDF is required by the gravo-turbulent scenario to fit properly the IMF with a reasonable initial Mach number for the molecular cloud. Since other physical processes (e.g. the equation of state and the variations among the core properties) have already been suggested to broaden the PDF, the relative importance of the different effects remains an open question.

astro-ph.GA↗

arXiv2013

The WISE Catalog of Galactic HII Regions

Using data from the all-sky Wide-Field Infrared Survey Explorer (WISE) satellite, we made a catalog of over 8000 Galactic HII regions and HII region candidates by searching for their characteristic mid-infrared (MIR) morphology. WISE has sufficient sensitivity to detect the MIR emission from HII regions located anywhere in the Galactic disk. We believe this is the most complete catalog yet of regions forming massive stars in the Milky Way. Of the ~8000 cataloged sources, ~1500 have measured radio recombination line (RRL) or H$α$ emission, and are thus known to be HII regions. This sample improves on previous efforts by resolving HII region complexes into multiple sources and by removing duplicate entries. There are ~2500 candidate HII regions in the catalog that are spatially coincident with radio continuum emission. Our group's previous RRL studies show that ~95% of such targets are HII regions. We find that ~500 of these candidates are also positionally associated with known HII region complexes, so the probability of their being bona fide HII regions is even higher. At the sensitivity limits of existing surveys, ~4000 catalog sources show no radio continuum emission. Using data from the literature, we find distances for ~1500 catalog sources, and molecular velocities for ~1500 HII region candidates.

astro-ph.GA↗

arXiv2013

Pillars and globules at the edges of H ii regions, Confronting Herschel observations and numerical simulations

Pillars and globules are present in many high-mass star-forming regions, such as the Eagle nebula (M16) and the Rosette molecular cloud, and understanding their origin will help characterize triggered star formation. The formation mechanisms of these structures are still being debated. Recent numerical simulations have shown how pillars can arise from the collapse of the shell in on itself and how globules can be formed from the interplay of the turbulent molecular cloud and the ionization from massive stars. The goal here is to test this scenario through recent observations of two massive star-forming regions, M16 and Rosette. The column density structure of the interface between molecular clouds and H ii regions was characterized using column density maps obtained from far-infrared imaging of the Herschel HOBYS key programme. Then, the DisPerSe algorithm was used on these maps to detect the compressed layers around the ionized gas and pillars in different evolutionary states. Finally, their velocity structure was investigated using CO data, and all observational signatures were tested against some distinct diagnostics established from simulations. The column density profiles have revealed the importance of compression at the edge of the ionized gas. The velocity properties of the structures, i.e. pillars and globules, are very close to what we predict from the numerical simulations. We have identified a good candidate of a nascent pillar in the Rosette molecular cloud that presents the velocity pattern of the shell collapsing on itself, induced by a high local curvature. Globules have a bulk velocity dispersion that indicates the importance of the initial turbulence in their formation, as proposed from numerical simulations. Altogether, this study re-enforces the picture of pillar formation by shell collapse and globule formation by the ionization of highly turbulent clouds.

astro-ph.GA↗

arXiv2013

HI Absorption Toward HII Regions at Small Galactic Longitudes

We make a comprehensive study of HI absorption toward HII regions located within Galactic longitudes less than 10 degrees. Structures in the extreme inner Galaxy are traced using the longitude-velocity space distribution of this absorption. We find significant HI absorption associated with the Near and Far 3kpc Arms, the Connecting Arm, Banias Clump 1 and the H I Tilted Disk. We also constrain the line of sight distances to HII regions, by using HI absorption spectra together with the HII region velocities measured by radio recombination lines.

astro-ph.GA↗

arXiv2013

Herschel Reveals Massive Cold Clumps in NGC 7538

We present the first overview of the Herschel observations of the nearby high-mass star-forming region NGC 7538, taken as part of the Herschel imaging study of OB Young Stellar objects (HOBYS) Key Programme. These PACS and SPIRE maps cover an approximate area of one square degree at five submillimeter and far-infrared wavebands. We have identified 780 dense sources and classified 224 of those. With the intention of investigating the existence of cold massive starless or class 0-like clumps that would have the potential to form intermediate- to high-mass stars, we further isolate 13 clumps as the most likely candidates for followup studies. These 13 clumps have masses in excess of 40 M_sun and temperatures below 15 K. They range in size from 0.4 pc to 2.5 pc and have densities between 3x10^3 cm^-3 to 4x10^4 cm^-3. Spectral energy distributions are then used to characterize their energetics and evolutionary state through a luminosity-mass diagram. NGC 7538 has a highly filamentary structure, previously unseen in the dust continuum of existing submillimeter surveys. We report the most complete imaging to date of a large, evacuated ring of material in NGC 7538 which is bordered by many cool sources.

astro-ph.SR↗

arXiv2012

The Green Bank Telescope H II Region Discovery Survey: IV. Helium and Carbon Recombination Lines

The Green Bank Telescope H II Region Discovery Survey (GBT HRDS) found hundreds of previously unknown Galactic regions of massive star formation by detecting hydrogen radio recombination line (RRL) emission from candidate H II region targets. Since the HRDS nebulae lie at large distances from the Sun, they are located in previously unprobed zones of the Galactic disk. Here we derive the properties of helium and carbon RRL emission from HRDS nebulae. Our target sample is the subset of the HRDS that has visible helium or carbon RRLs. This criterion gives a total of 84 velocity components (14% of the HRDS) with helium emission and 52 (9%) with carbon emission. For our highest quality sources, the average ionic He-4+/H+ abundance ratio by number, , is 0.068 +/- 0.023 (1-sigma). This is the same ratio as that measured for the sample of previously known Galactic H II regions. Nebulae without detected helium emission give robust y+ upper limits. There are 5 RRL emission components with y+ less than 0.04 and another 12 with upper limits below this value. These H II regions must have either a very low He-4 abundance or contain a significant amount of neutral helium. The HRDS has 20 nebulae with carbon RRL emission but no helium emission at its sensitivity level. There is no correlation between the carbon RRL parameters and the 8 microns mid-infrared morphology of these nebulae.

astro-ph.GA↗

arXiv2012

Spitzer and Herschel multiwavelength characterization of the dust content of evolved HII regions

We have analyzed a uniform sample of 16 evolved HII regions located in a 2 deg X 2 deg Galactic field centered at (l,b) = (30 deg, 0 deg) and observed as part of the Herschel Hi-GAL survey. The evolutionary stage of these HII regions was established using ancillary radio continuum data. By combining Hi-GAL PACS (70 micron, 160 micron) and SPIRE (250 micron, 350 micron and 500 micron) measurements with MIPSGAL 24 micron data, we built Spectral Energy Distributions (SEDs) of the sources and showed that a 2-component grey-body model is a good representation of the data. In particular, wavelengths > 70 micron appear to trace a cold dust component, for which we estimated an equilibrium temperature of the Big Grains (BGs) in the range 20 - 30 K, while for lambda < 70 micron, the data indicated the presence of a warm dust component at temperatures of the order of 50 - 90 K. This analysis also revealed that dust is present in the interior of HII regions, although likely not in a large amount. In addition, the data appear to corroborate the hypothesis that the main mechanism responsible for the (partial) depletion of dust in HII regions is radiation-pressure-driven drift. In this framework, we speculated that the 24 micron emission which spatially correlates with ionized gas might be associated with either Very Small Grain (VSG) or BG replenishment, as recently proposed for the case of Wind-Blown Bubbles (WBB). Finally, we found that evolved HII regions are characterized by distinctive far-IR and sub-mm colors, which can be used as diagnostics for their identification in unresolved Galactic and extragalactic regions.

astro-ph.GA↗

arXiv2012

The Arecibo HII Region Discovery Survey

We report the detection of radio recombination line emission (RRL) using the Arecibo Observatory at X-band (9GHz, 3cm) from 37 previously unknown HII regions in the Galactic zone 66 deg. > l > 31 deg. and |b| < 1 deg. This Arecibo HII Region Discovery Survey (Arecibo HRDS) is a continuation of the Green Bank Telescope (GBT) HRDS. The targets for the Arecibo HRDS have spatially coincident 24 micron and 20 cm emission of a similar angular morphology and extent. To take advantage of Arecibo's sensitivity and small beam size, sources in this sample are fainter, smaller in angle, or in more crowded fields compared to those of the GBT HRDS. These Arecibo nebulae are some of the faintest HII regions ever detected in RRL emission. Our detection rate is 58%, which is low compared to the 95% detection rate for GBT HRDS targets. We derive kinematic distances to 23 of the Arecibo HRDS detections. Four nebulae have negative LSR velocities and are thus unambiguously in the outer Galaxy. The remaining sources are at the tangent point distance or farther. We identify a large, diffuse HII region complex that has an associated HI and 13CO shell. The ~90 pc diameter of the G52L nebula in this complex may be the largest Galactic HII region known, and yet it has escaped previous detection.

astro-ph.GA↗

arXiv2012

Interstellar matter and star formation in W5-E - A Herschel view

W5-E has been observed with the Herschel-PACS and -SPIRE photometers, at 100, 160, 250, 350, and 500 microns. The dust temperature map shows a rather uniform temperature, in the range 17.5-20 K in the dense condensations or filaments, 21-22 K in the photodissociation regions, and 24-31 K in the direction of the ionized regions. The column densities are rather low, everywhere lower than 10^23 cm-2, and of the order of a few 10^21 cm-2 in the PDRs. About 8000 solar masses of neutral material surrounds the ionized region, which is low with respect to the volume of this HII region; we suggest that the exciting stars of the W5-E, W5-W, Sh~201, A and B HII regions formed along a dense filament or sheet rather than inside a more spherical cloud. Fifty point sources have been detected at 100 microns. Most of them are Class 0/I YSOs. The SEDs of their envelopes have been fitted using a modified blackbody model. These envelopes are cold, with a mean temperature of 15.7+-1.8K. Their masses are in the range 1.3-47 solar masses. Eleven of these point sources are candidate Class 0 YSOs. Twelve of these point sources are possibly at the origin of bipolar outflows detected in this region. None of the YSOs contain a massive central object, but a few may form a massive star as they have both a massive envelope and also a high envelope accretion rate. Most of the Class 0/I YSOs are observed in the direction of high column density material, for example in the direction of the massive condensations present at the waist of the bipolar Sh 201 HII region or enclosed by the bright-rimmed cloud BRC14. The overdensity of Class 0/I YSOs on the borders of the HII regions strongly suggests that triggered star formation is at work in this region but, due to insufficient resolution, the exact processes at the origin of the triggering are difficult to determine.

astro-ph.GA↗

arXiv2012

The spine of the swan: A Herschel study of the DR21 ridge and filaments in Cygnus X

In order to characterise the cloud structures responsible for the formation of high-mass stars, we present Herschel observations of the DR21 environment. Maps of the column density and dust temperature unveil the structure of the DR21 ridge and several connected filaments. The ridge has column densities larger than 1e23/cm^2 over a region of 2.3 pc^2. It shows substructured column density profiles and branching into two major filaments in the north. The masses in the studied filaments range between 130 and 1400 Msun whereas the mass in the ridge is 15000 Msun. The accretion of these filaments onto the DR21 ridge, suggested by a previous molecular line study, could provide a continuous mass inflow to the ridge. In contrast to the striations seen in e.g., the Taurus region, these filaments are gravitationally unstable and form cores and protostars. These cores formed in the filaments potentially fall into the ridge. Both inflow and collisions of cores could be important to drive the observed high-mass star formation. The evolutionary gradient of star formation running from DR21 in the south to the northern branching is traced by decreasing dust temperature. This evolution and the ridge structure can be explained by two main filamentary components of the ridge that merged first in the south.

astro-ph.GA↗