arXiv subjects

C. Beichman

Publications and source records attributed to C. Beichman.

At least 37 records · Page 2Linked to original sources

arXiv2018

OGLE-2017-BLG-0329L: A Microlensing Binary Characterized with Dramatically Enhanced Precision Using Data from Space-based Observations

Mass measurements of gravitational microlenses require one to determine the microlens parallax $\pie$, but precise $\pie$ measurement, in many cases, is hampered due to the subtlety of the microlens-parallax signal combined with the difficulty of distinguishing the signal from those induced by other higher-order effects. In this work, we present the analysis of the binary-lens event OGLE-2017-BLG-0329, for which $\pie$ is measured with a dramatically improved precision using additional data from space-based $Spitzer$ observations. We find that while the parallax model based on the ground-based data cannot be distinguished from a zero-$\pie$ model at 2$σ$ level, the addition of the $Spitzer$ data enables us to identify 2 classes of solutions, each composed of a pair of solutions according to the well-known ecliptic degeneracy. It is found that the space-based data reduce the measurement uncertainties of the north and east components of the microlens-parallax vector $\pivec_{\rm E}$ by factors $\sim 18$ and $\sim 4$, respectively. With the measured microlens parallax combined with the angular Einstein radius measured from the resolved caustic crossings, we find that the lens is composed of a binary with components masses of either $(M_1,M_2)\sim (1.1,0.8)\ M_\odot$ or $\sim (0.4,0.3)\ M_\odot$ according to the two solution classes. The first solution is significantly favored but the second cannot be securely ruled out based on the microlensing data alone. However, the degeneracy can be resolved from adaptive optics observations taken $\sim 10$ years after the event.

astro-ph.SR↗

arXiv2018

OGLE-2016-BLG-1266: A Probable Brown-Dwarf/Planet Binary at the Deuterium Fusion Limit

We report the discovery, via the microlensing method, of a new very-low-mass binary system. By combining measurements from Earth and from the Spitzer telescope in Earth-trailing orbit, we are able to measure the microlensing parallax of the event, and find that the lens likely consists of an $(12.0 \pm 0.6) M_{\rm J}$ + $(15.7 \pm 1.5) M_{\rm J}$ super-Jupiter / brown-dwarf pair. The binary is located at a distance of $(3.08 \pm 0.18)$ kpc in the Galactic Plane, and the components have a projected separation of $(0.43 \pm 0.03)$ AU. Two alternative solutions with much lower likelihoods are also discussed, an 8- and 6-$M_{\rm J}$ model and a 90- and 70-$M_{\rm J}$ model. Although disfavored at the 3-$σ$ and 5-$σ$ levels, these alternatives cannot be rejected entirely. We show how the more-massive of these models could be tested with future direct imaging.

astro-ph.SR↗

arXiv2018

Spitzer Microlensing Parallax for OGLE-2016-BLG-1067: a sub-Jupiter Orbiting an M-dwarf in the Disk

We report the discovery of a sub-Jupiter mass planet orbiting beyond the snow line of an M-dwarf most likely in the Galactic disk as part of the joint Spitzer and ground-based monitoring of microlensing planetary anomalies toward the Galactic bulge. The microlensing parameters are strongly constrained by the light curve modeling and in particular by the Spitzer-based measurement of the microlens parallax, $π_\mathrm{E}$. However, in contrast to many planetary microlensing events, there are no caustic crossings, so the angular Einstein radius, $θ_\mathrm{E}$ has only an upper limit based on the light curve modeling alone. Additionally, the analysis leads us to identify 8 degenerate configurations: the four-fold microlensing parallax degeneracy being doubled by a degeneracy in the caustic structure present at the level of the ground-based solutions. To pinpoint the physical parameters, and at the same time to break the parallax degeneracy, we make use of a series of arguments: the $χ^2$ hierarchy, the Rich argument, and a prior Galactic model. The preferred configuration is for a host at $D_L=3.73_{-0.67}^{+0.66}~\mathrm{kpc}$ with mass $M_\mathrm{L}=0.30_{-0.12}^{+0.15}~\mathrm{M_\odot}$, orbited by a Saturn-like planet with $M_\mathrm{planet}=0.43_{-0.17}^{+0.21}~\mathrm{M_\mathrm{Jup}}$ at projected separation $a_\perp = 1.70_{-0.39}^{+0.38}~\mathrm{au}$, about 2.1 times beyond the system snow line. Therefore, it adds to the growing population of sub-Jupiter planets orbiting near or beyond the snow line of M-dwarfs discovered by microlensing. Based on the rules of the real-time protocol for the selection of events to be followed up with Spitzer, this planet will not enter the sample for measuring the Galactic distribution of planets.

astro-ph.EP↗

arXiv2018

Searching for Exoplanets Using a Microresonator Astrocomb

Detection of weak radial velocity shifts of host stars induced by orbiting planets is an important technique for discovering and characterizing planets beyond our solar system. Optical frequency combs enable calibration of stellar radial velocity shifts at levels required for detection of Earth analogs. A new chip-based device, the Kerr soliton microcomb, has properties ideal for ubiquitous application outside the lab and even in future space-borne instruments. Moreover, microcomb spectra are ideally suited for astronomical spectrograph calibration and eliminate filtering steps required by conventional mode-locked-laser frequency combs. Here, for the calibration of astronomical spectrographs, we demonstrate an atomic/molecular line-referenced, near-infrared soliton microcomb. Efforts to search for the known exoplanet HD 187123b were conducted at the Keck-II telescope as a first in-the-field demonstration of microcombs.

physics.optics↗

arXiv2018

OGLE-2014-BLG-0289: Precise Characterization of a Quintuple-Peak Gravitational Microlensing Event

We present the analysis of the binary-microlensing event OGLE-2014-BLG-0289. The event light curve exhibits very unusual five peaks where four peaks were produced by caustic crossings and the other peak was produced by a cusp approach. It is found that the quintuple-peak features of the light curve provide tight constraints on the source trajectory, enabling us to precisely and accurately measure the microlensing parallax $π_{\rm E}$. Furthermore, the three resolved caustics allow us to measure the angular Einstein radius $\thetae$. From the combination of $π_{\rm E}$ and $\thetae$, the physical lens parameters are uniquely determined. It is found that the lens is a binary composed of two M dwarfs with masses $M_1 = 0.52 \pm 0.04\ M_\odot$ and $M_2=0.42 \pm 0.03\ M_\odot$ separated in projection by $a_\perp = 6.4 \pm 0.5$ au. The lens is located in the disk with a distance of $D_{\rm L} = 3.3 \pm 0.3$~kpc. It turns out that the reason for the absence of a lensing signal in the {\it Spitzer} data is that the time of observation corresponds to the flat region of the light curve.

astro-ph.SR↗

arXiv2017

OGLE-2016-BLG-1190Lb: First Spitzer Bulge Planet Lies Near the Planet/Brown-Dwarf Boundary

We report the discovery of OGLE-2016-BLG-1190Lb, which is likely to be the first Spitzer microlensing planet in the Galactic bulge/bar, an assignation that can be confirmed by two epochs of high-resolution imaging of the combined source-lens baseline object. The planet's mass M_p= 13.4+-0.9 M_J places it right at the deuterium burning limit, i.e., the conventional boundary between "planets" and "brown dwarfs". Its existence raises the question of whether such objects are really "planets" (formed within the disks of their hosts) or "failed stars" (low mass objects formed by gas fragmentation). This question may ultimately be addressed by comparing disk and bulge/bar planets, which is a goal of the Spitzer microlens program. The host is a G dwarf M_host = 0.89+-0.07 M_sun and the planet has a semi-major axis a~2.0 AU. We use Kepler K2 Campaign 9 microlensing data to break the lens-mass degeneracy that generically impacts parallax solutions from Earth-Spitzer observations alone, which is the first successful application of this approach. The microlensing data, derived primarily from near-continuous, ultra-dense survey observations from OGLE, MOA, and three KMTNet telescopes, contain more orbital information than for any previous microlensing planet, but not quite enough to accurately specify the full orbit. However, these data do permit the first rigorous test of microlensing orbital-motion measurements, which are typically derived from data taken over <1% of an orbital period.

astro-ph.EP↗

arXiv2017

OGLE-2017-BLG-0173Lb: Low Mass-Ratio Planet in a "Hollywood" Microlensing Event

We present microlensing planet OGLE-2017-BLG-0173Lb, with planet-host mass ratio either $q\simeq 2.5\times 10^{-5}$ or $q\simeq 6.5\times 10^{-5}$, the lowest or among the lowest ever detected. The planetary perturbation is strongly detected, $Δχ^2\sim 10,000$, because it arises from a bright (therefore, large) source passing over and enveloping the planetary caustic: a so-called "Hollywood" event. The factor $\sim 2.5$ offset in $q$ arises because of a previously unrecognized discrete degeneracy between Hollywood events in which the caustic is fully enveloped and those in which only one flank is enveloped, which we dub "Cannae" and "von Schlieffen", respectively. This degeneracy is "accidental" in that it arises from gaps in the data. Nevertheless, the fact that it appears in a $Δχ^2=10,000$ planetary anomaly is striking. We present a simple formalism to estimate the sensitivity of other Hollywood events to planets and show that they can lead to detections close to, but perhaps not quite reaching, the Earth/Sun mass ratio of $3\times 10^{-6}$. This formalism also enables an analytic understanding of the factor $\sim 2.5$ offset in $q$ between the Cannae and von Schlieffen solutions. The Bayesian estimates for the host-mass, system distance, and planet-host projected separation are $M=0.39^{+0.40}_{-0.24}\,M_\odot$, $D_L=4.8^{+1.5}_{-1.8}\,\kpc$, and $a_\perp=3.8\pm 1.6\,\au$. The two estimates of the planet mass are $m_p=3.3^{+3.8}_{-2.1}\,M_\oplus$ and $m_p=8^{+11}_{-6}\,M_\oplus$. The measured lens-source relative proper motion $μ=6\,\masyr$ will permit imaging of the lens in about 15 years or at first light on adaptive-optics imagers on next-generation telescopes. These will allow to measure the host mass but probably cannot resolve the planet-host mass-ratio degeneracy.

astro-ph.EP↗

arXiv2017

Toward a Galactic Distribution of Planets. I. Methodology & Planet Sensitivities of the 2015 High-Cadence Spitzer Microlens Sample

We analyze an ensemble of microlensing events from the 2015 Spitzer microlensing campaign, all of which were densely monitored by ground-based high-cadence survey teams. The simultaneous observations from Spitzer and the ground yield measurements of the microlensing parallax vector $π_{\rm E}$, from which compact constraints on the microlens properties are derived, including $\lesssim$25\% uncertainties on the lens mass and distance. With the current sample, we demonstrate that the majority of microlenses are indeed in the mass range of M dwarfs. The planet sensitivities of all 41 events in the sample are calculated, from which we provide constraints on the planet distribution function. In particular, assuming a planet distribution function that is uniform in $\log{q}$, where $q$ is the planet-to-star mass ratio, we find a $95\%$ upper limit on the fraction of stars that host typical microlensing planets of 49\%, which is consistent with previous studies. Based on this planet-free sample, we develop the methodology to statistically study the Galactic distribution of planets using microlensing parallax measurements. Under the assumption that the planet distributions are the same in the bulge as in the disk, we predict that $\sim$1/3 of all planet detections from the microlensing campaigns with Spitzer should be in the bulge. This prediction will be tested with a much larger sample, and deviations from it can be used to constrain the abundance of planets in the bulge relative to the disk.

astro-ph.EP↗

arXiv2017

Combining Spitzer parallax and Keck II adaptive optics imaging to measure the mass of a solar-like star orbited by a cold gaseous planet discovered by microlensing

To obtain accurate mass measurements for cold planets discovered by microlensing, it is usually necessary to combine light curve modeling with at least two lens mass-distance relations. Often, a constraint on the Einstein ring radius measurement is obtained from the caustic crossing time: This is supplemented by secondary constraints such as precise parallax measurements and/or measures of the lens luminosity using high angular resolution observations. We resolved the source+lens star from sub-arcsecond blends in H band using adaptive optics (AO) observations with NIRC2 mounted on Keck II telescope. We identify additional flux, coincident with the source to within 160 mas. We estimate the potential contributions to this blended light (chance-aligned star, additional companion to the lens or to the source) and find that 85 % of of the NIR flux is due to the lens star at H_L=16.63 +- 0.06 and K_L=16.46 +- 0.06. We combined the parallax constraint and the AO constraint to derive the physical parameters of the system. The lensing system is composed of a mid-late type G main sequence star of M_L=0.89 +- 0.05 Mo located at D_L = 3.6 +- 0.3 kpc in the Galactic disk. Taking the mass ratio and projected separation from the original study leads to a planet of M_p= 0.64 +- 0.044 M_Jupiter at 3.48 +- 0.22 AU. Excellent parallax measurement from simultaneous ground-space observations have been obtained on the microlensing event OGLE-2014-BLG-0124, but it is only when they are combined with ~ 30 min of Keck II AO observations that the physical parameters of the host star are well measured.

astro-ph.EP↗

arXiv2017

Ground-based parallax confirmed by Spitzer: binary microlensing event MOA-2015-BLG-020

We present the analysis of the binary gravitational microlensing event MOA-2015-BLG-020. The event has a fairly long timescale (about 63 days) and thus the light curve deviates significantly from the lensing model that is based on the rectilinear lens-source relative motion. This enables us to measure the microlensing parallax through the annual parallax effect. The microlensing parallax parameters constrained by the ground-based data are confirmed by the Spitzer observations through the satellite parallax method. By additionally measuring the angular Einstein radius from the analysis of the resolved caustic crossing, the physical parameters of the lens are determined. It is found that the binary lens is composed of two dwarf stars with masses $M_1 = 0.606 \pm 0.028M_\odot$ and $M_2 = 0.125 \pm 0.006M_\odot$ in the Galactic disk. Assuming the source star is at the same distance as the bulge red clump stars, we find the lens is at a distance $D_L = 2.44 \pm 0.10 kpc$. In the end, we provide a summary and short discussion of all published microlensing events in which the annual parallax effect is confirmed by other independent observations.

astro-ph.SR↗

arXiv2017

OGLE-2016-BLG-0168 Binary Microlensing Event: Prediction and Confirmation of the Micorlens Parallax Effect from Space-based Observation

The microlens parallax is a crucial observable for conclusively identifying the nature of lens systems in microlensing events containing or composed of faint (even dark) astronomical objects such as planets, neutron stars, brown dwarfs, and black holes. With the commencement of a new era of microlensing in collaboration with space-based observations, the microlens parallax can be routinely measured. In addition, space-based observations can provide opportunities to verify the microlens parallax measured from ground-only observations and to find a unique solution of the lensing lightcurve analysis. However, since most space-based observations cannot cover the full lightcurves of lensing events, it is also necessary to verify the reliability of the information extracted from fragmentary space-based lightcurves. We conduct a test based on the microlensing event OGLE-2016-BLG-0168 created by a binary lens system consisting of almost equal mass M-dwarf stars to demonstrate that it is possible to verify the microlens parallax and to resolve degeneracies by using the space-based lightcurve even though the observations are fragmentary. Since space-based observatories will frequently produce fragmentary lightcurves due to their short observing windows, the methodology of this test will be useful for next-generation microlensing experiments that combine space-based and ground-based collaboration.

astro-ph.SR↗

arXiv2017

Project 1640 Observations of the White Dwarf HD 114174 B

We present the first near infra-red spectrum of the faint white dwarf companion HD 114174 B, obtained with Project 1640. Our spectrum, covering the Y, J and H bands, combined with previous TRENDS photometry measurements, allows us to place further constraints on this companion. We suggest two possible scenarios; either this object is an old, low mass, cool H atmosphere white dwarf with Teff ~ 3800 K or a high mass white dwarf with Teff > 6000 K, potentially with an associated cool (Teff ~ 700 K) brown dwarf or debris disk resulting in an infra-red excess in the L band. We also provide an additional astrometry point for 2014 June 12 and use the modelled companion mass combined with the RV and direct imaging data to place constraints on the orbital parameters for this companion.

astro-ph.SR↗

arXiv2017

An Earth-mass Planet in a 1-AU Orbit around an Ultracool Dwarf

We combine $Spitzer$ and ground-based KMTNet microlensing observations to identify and precisely measure an Earth-mass ($1.43^{+0.45}_{-0.32} M_\oplus$) planet OGLE-2016-BLG-1195Lb at $1.16^{+0.16}_{-0.13}$ AU orbiting a $0.078^{+0.016}_{-0.012} M_\odot$ ultracool dwarf. This is the lowest-mass microlensing planet to date. At $3.91^{+0.42}_{-0.46}$ kpc, it is the third consecutive case among the $Spitzer$ "Galactic distribution" planets toward the Galactic bulge that lies in the Galactic disk as opposed to the bulge itself, hinting at a skewed distribution of planets. Together with previous microlensing discoveries, the seven Earth-size planets orbiting the ultracool dwarf TRAPPIST-1, and the detection of disks around young brown dwarfs, OGLE-2016-BLG-1195Lb suggests that such planets might be common around ultracool dwarfs. It therefore sheds light on the formation of both ultracool dwarfs and planetary systems at the limit of low-mass protoplanetary disks.

astro-ph.EP↗

arXiv2017

OGLE-2015-BLG-1482L: the first isolated low-mass microlens in the Galactic bulge

We analyze the single microlensing event OGLE-2015-BLG-1482 simultaneously observed from two ground-based surveys and from \textit{Spitzer}. The \textit{Spitzer} data exhibit finite-source effects due to the passage of the lens close to or directly over the surface of the source star as seen from \textit{Spitzer}. Such finite-source effects generally yield measurements of the angular Einstein radius, which when combined with the microlens parallax derived from a comparison between the ground-based and the \textit{Spitzer} light curves, yields the lens mass and lens-source relative parallax. From this analysis, we find that the lens of OGLE-2015-BLG-1482 is a very low-mass star with the mass $0.10 \pm 0.02 \ M_\odot$ or a brown dwarf with the mass $55\pm 9 \ M_{J}$, which are respectively located at $D_{\rm LS} = 0.80 \pm 0.19\ \textrm{kpc}$ and $ D_{\rm LS} = 0.54 \pm 0.08\ \textrm{kpc}$, and thus it is the first isolated low-mass microlens that has been decisively located in the Galactic bulge. The fundamental reason for the degeneracy is that the finite-source effect is seen only in a single data point from \textit{Spitzer} and this single data point gives rise to two solutions for $ρ$. Because the $ρ$ degeneracy can be resolved only by relatively high cadence observations around the peak, while the \textit{Spitzer} cadence is typically $\sim 1\,{\rm day}^{-1}$, we expect that events for which the finite-source effect is seen only in the \textit{Spitzer} data may frequently exhibit this $ρ$ degeneracy. For OGLE-2015-BLG-1482, the relative proper motion of the lens and source for the low-mass star is $μ_{\rm rel} = 9.0 \pm 1.9\ \textrm{mas yr$^{-1}$}$, while for the brown dwarf it is $5.5 \pm 0.5\ \textrm{mas yr$^{-1}$}$. Hence, the degeneracy can be resolved within $\sim 10\ \rm yrs$ from direct lens imaging by using next-generation instruments with high spatial resolution.

astro-ph.SR↗

arXiv2017

Project 1640 Observations of Brown Dwarf GJ 758 B: Near-Infrared Spectrum and Atmospheric Modeling

The nearby Sun-like star GJ 758 hosts a cold substellar companion, GJ 758 B, at a projected separation of $\lesssim$30 AU, previously detected in high-contrast multi-band photometric observations. In order to better constrain the companion's physical characteristics, we acquired the first low-resolution ($R \sim 50$) near-infrared spectrum of it using the high-contrast hyperspectral imaging instrument Project 1640 on Palomar Observatory's 5-m Hale telescope. We obtained simultaneous images in 32 wavelength channels covering the $Y$, $J$, and $H$ bands ($\sim$952-1770 nm), and used data processing techniques based on principal component analysis to efficiently subtract chromatic background speckle-noise. GJ 758 B was detected in four epochs during 2013 and 2014. Basic astrometric measurements confirm its apparent northwest trajectory relative to the primary star, with no clear signs of orbital curvature. Spectra of SpeX/IRTF observed T dwarfs were compared to the combined spectrum of GJ 758 B, with $χ^2$ minimization suggesting a best fit for spectral type T7.0$\pm$1.0, but with a shallow minimum over T5-T8. Fitting of synthetic spectra from the BT-Settl13 model atmospheres gives an effective temperature $T_{\text{eff}}=741 \pm 25$ K and surface gravity $\log g = 4.3 \pm 0.5$ dex (cgs). Our derived best-fit spectral type and effective temperature from modeling of the low-resolution spectrum suggest a slightly earlier and hotter companion than previous findings from photometric data, but do not rule out current results, and confirm GJ 758 B as one of the coolest sub-stellar companions to a Sun-like star to date.

astro-ph.SR↗

arXiv2016

OGLE-2015-BLG-0196: Ground-based Gravitational Microlens Parallax Confirmed By Space-Based Observation

In this paper, we present the analysis of the binary gravitational microlensing event OGLE-2015-BLG-0196. The event lasted for almost a year and the light curve exhibited significant deviations from the lensing model based on the rectilinear lens-source relative motion, enabling us to measure the microlens parallax. The ground-based microlens parallax is confirmed by the data obtained from space-based microlens observations using the {\it Spitzer} telescope. By additionally measuring the angular Einstein radius from the analysis of the resolved caustic crossing, the physical parameters of the lens are determined up to the two-fold degeneracy: $u_0<0$ and $u_0>0$ solutions caused by the well-known "ecliptic" degeneracy. It is found that the binary lens is composed of two M dwarf stars with similar masses $M_1=0.38\pm 0.04\ M_\odot$ ($0.50\pm 0.05\ M_\odot)$ and $M_2=0.38\pm 0.04\ M_\odot$ ($0.55\pm 0.06\ M_\odot$) and the distance to the lens is $D_{\rm L}=2.77\pm 0.23$ kpc ($3.30\pm 0.29$ kpc). Here the physical parameters out and in the parenthesis are for the $u_0<0$ and $u_0>0$ solutions, respectively.

astro-ph.EP↗

arXiv2016

UKIRT microlensing surveys as a pathfinder for $WFIRST$: The detection of five highly extinguished low-$|b|$ events

Optical microlensing surveys are restricted from detecting events near the Galactic plane and center, where the event rate is thought to be the highest, due to the high optical extinction of these fields. In the near-infrared (NIR), however, the lower extinction leads to a corresponding increase in event detections and is a primary driver for the wavelength coverage of the $WFIRST$ microlensing survey. During the 2015 and 2016 bulge observing seasons we conducted NIR microlensing surveys with UKIRT in conjunction with and in support of the $Spitzer$ and $Kepler$ microlensing campaigns. Here we report on five highly extinguished ($A_H=0.81-1.97$), low-Galactic latitude ($-0.98\le b\le -0.36$) microlensing events discovered from our 2016 survey. Four of them were monitored with an hourly cadence by optical surveys but were not reported as discoveries, likely due to the high extinction. Our UKIRT surveys and suggested future NIR surveys enable the first measurement of the microlensing event rate in the NIR. This wavelength regime overlaps with the bandpass of the filter in which the $WFIRST$ microlensing survey will conduct its highest-cadence observations, making this event rate derivation critically important for optimizing its yield.

astro-ph.EP↗

arXiv2016

OGLE-2015-BLG-0479LA,B: Binary Gravitational Microlens Characterized by Simultaneous Ground-based and Space-based Observation

We present a combined analysis of the observations of the gravitational microlensing event OGLE-2015-BLG-0479 taken both from the ground and by the {\it Spitzer Space Telescope}. The light curves seen from the ground and from space exhibit a time offset of $\sim 13$ days between the caustic spikes, indicating that the relative lens-source positions seen from the two places are displaced by parallax effects. From modeling the light curves, we measure the space-based microlens parallax. Combined with the angular Einstein radius measured by analyzing the caustic crossings, we determine the mass and distance of the lens. We find that the lens is a binary composed of two G-type stars with masses $\sim 1.0\ M_\odot$ and $\sim 0.9\ M_\odot$ located at a distance $\sim 3$ kpc. In addition, we are able to constrain the complete orbital parameters of the lens thanks to the precise measurement of the microlens parallax derived from the joint analysis. In contrast to the binary event OGLE-2014-BLG-1050, which was also observed by {\it Spitzer}, we find that the interpretation of OGLE-2015-BLG-0479 does not suffer from the degeneracy between $(\pm,\pm)$ and $(\pm,\mp)$ solutions, confirming that the four-fold parallax degeneracy in single-lens events collapses into the two-fold degeneracy for the general case of binary-lens events. The location of the blend in the color-magnitude diagram is consistent with the lens properties, suggesting that the blend is the lens itself. The blend is bright enough for spectroscopy and thus this possibility can be checked from future follow-up observations.

astro-ph.SR↗