Searcharxiv⌕ Search

arXiv subjects

A. Udalski

Publications and source records attributed to A. Udalski.

At least 127 records · Page 7Linked to original sources
arXiv2018

Diversity of dynamical phenomena in type II Cepheids of the OGLE collection

We have analysed the photometry of 924 type II Cepheids from the Galactic bulge observed by the Optical Gravitational Lensing Experiment. Our goal was to detect and analyse various dynamical phenomena, including, e.g. multi-mode pulsation, period-doubled pulsation, period-k pulsation, or quasi-periodic modulation of pulsation. First examples of double-mode BL Her-type stars, pulsating simultaneously in the fundamental and first overtone modes are reported. Two double-mode pulsators are not isolated cases however, but form an extension of recently identified class of long-period RRd stars. Period doubling effect was detected in three BL Her-type stars: two were identified previously and one is a new discovery. Through identification of numerous period-doubled W Vir stars we show that the appearance of the period doubling effect, and hence the transition towards RV Tau class, is a smooth process that starts at pulsation periods slightly above 15d. Interchange of the deep and shallow pulsation cycles is identified in tens of RV Tau variables. One RV Tau star is a strong candidate for period-4 pulsation. Quasi-periodic modulation of pulsation in all sub-classes of type II Cepheids is reported for the first time. Modulation was detected in 16 BL Her, 9 W Vir and in 7 RV Tau stars. In the last case, modulation is the most likely scenario, but two other scenarios, excitation of non-radial modes, or period-4 pulsation, can also account for the observed pulsation pattern. Irregular changes of pulsation amplitude and period on various time-scales are common in all subgroups of type II Cepheids.

astro-ph.SR↗
arXiv2018

WFIRST Exoplanet Mass Measurement Method Finds a Planetary Mass of $39\pm 8 M_\oplus$ for OGLE-2012-BLG-0950Lb

We present the analysis of the simultaneous high resolution images from the {\it Hubble Space Telescope} and Keck Adaptive Optics system of the planetary event OGLE-2012-BLG-0950 that determine that the system consists of a $0.58 \pm 0.04 \rm{M}_\odot$ host star orbited by a $39\pm 8 \rm{M}_\oplus$ planet of at projected separation of $2.54 \pm 0.23\,$AU. The planetary system is located at a distance of $2.19\pm 0.23$ kpc from Earth. This is the second microlens planet beyond the snow line with a mass measured to be in the mass range $20$--$80 \rm{M}_\oplus$. The runaway gas accretion process of the core accretion model predicts few planets in this mass range, because giant planets are thought to be growing rapidly at these masses and they rarely complete growth at this mass. So, this result suggests that the core accretion theory may need revision. This analysis also demonstrates the techniques that will be used to measure the masses of planets and their host stars by the WFIRST exoplanet microlensing survey: one-dimensional microlensing parallax combined with the separation and brightness measurement of the unresolved source and host stars to yield multiple redundant constraints on the masses and distance of the planetary system.

astro-ph.EP↗
arXiv2018

An ice giant exoplanet interpretation of the anomaly in microlensing event OGLE-2011-BLG-0173

We analyze the microlensing event OGLE-2011-BLG-0173, which shows a small perturbation at the end of the microlensing event caused by the primary lens. We consider both binary lens and binary source models and we explore their degeneracies, some of which have not previously been recognized. There are two families of binary lens solutions, one with a mass ratio $q\approx4\times10^{-4}$ and a separation s~4.6 and the other with q~0.015 and s~0.22, i.e, both have companions in the planetary regime. We search for solutions by using Bayesian analysis that includes planet frequency as a prior and find that the s~4.6 family is the preferred one with ~4 M_Uranus mass planet on an orbit of ~10 AU. The degeneracies arise from a paucity of information on the anomaly, demonstrating that high-cadence observations are essential for characterizing wide-orbit microlensing planets. Hence, we predict that the planned WFIRST microlensing survey will be less prone to these degeneracies than the ongoing ground-based surveys. We discuss the known low-mass, wide-orbit companions and we notice that for the largest projected separations the mass ratios are either high (consistent with brown dwarf companions) or low (consistent with Uranus analogs), but intermediate mass ratios (Jupiter analogs on wide orbits) have not been detected to date, despite the fact that the sensitivity to such planets should be higher than that of Uranus analogs. This is therefore tentative evidence of the existence of a massive ice giant desert at wide separations. On the other hand, given their low intrinsic detection sensitivity, Uranus analogs may be ubiquitous.

astro-ph.EP↗
arXiv2018

OGLE-2014-BLG-1186: gravitational microlensing providing evidence for a planet orbiting the foreground star or for a close binary source?

(abridged) Using the particularly long gravitational microlensing event OGLE-2014-BLG-1186 with a time-scale $t_\mathrm{E}$ ~ 300 d, we present a methodology for identifying the nature of localised deviations from single-lens point-source light curves, which ensures that 1) the claimed signal is substantially above the noise floor, 2) the inferred properties are robustly determined and their estimation not subject to confusion with systematic noise in the photometry, 3) there are no alternative viable solutions within the model framework that might have been missed. Annual parallax and binarity could be separated and robustly measured from the wing and the peak data, respectively. We find matching model light curves that involve either a binary lens or a binary source. Our binary-lens models indicate a planet of mass $M_2$ = (45 $\pm$ 9) $M_\oplus$, orbiting a star of mass $M_1$ = (0.35 $\pm$ 0.06) $M_\odot$, located at a distance $D_\mathrm{L}$ = (1.7 $\pm$ 0.3) kpc from Earth, whereas our binary-source models suggest a brown-dwarf lens of $M$ = (0.046 $\pm$ 0.007) $M_\odot$, located at a distance $D_\mathrm{L}$ = (5.7 $\pm$ 0.9) kpc, with the source potentially being a (partially) eclipsing binary involving stars predicted to be of similar colour given the ratios between the luminosities and radii. The ambiguity in the interpretation would be resolved in favour of a lens binary by observing the luminous lens star separating from the source at the predicted proper motion of $μ$ = (1.6 $\pm$ 0.3) mas yr$^{-1}$, whereas it would be resolved in favour of a source binary if the source could be shown to be a (partially) eclipsing binary matching the obtained model parameters. We experienced that close binary source stars pose a challenge for claiming the detection of planets by microlensing in events where the source passes very close to the lens star hosting the planet.

astro-ph.EP↗
arXiv2018

MOA-2015-BLG-337: A Planetary System with a Low-mass Brown Dwarf/Planetary Boundary Host, or a Brown Dwarf Binary

We report the discovery and the analysis of the short timescale binary-lens microlensing event, MOA-2015-BLG-337. The lens system could be a planetary system with a very low mass host, around the brown dwarf/planetary mass boundary, or a brown dwarf binary. We found two competing models that explain the observed light curves with companion/host mass ratios of q~0.01 and ~0.17, respectively. From the measurement of finite source effects in the best-fit planetary model, we find a relatively small angular Einstein radius of theta_E ~ 0.03 mas which favors a low mass lens. We conduct a Bayesian analysis to obtain the probability distribution of the lens properties. The results for the planetary models strongly depend on the minimum mass, M_min, in the assumed mass function. In summary, there are two solutions of the lens system: (1) a brown dwarf/planetary mass boundary object orbited by a super-Neptune (the planetary model with M_min=0.001 M_sun) and (2) a brown dwarf binary (the binary model). If the planetary models is correct, this system can be one of a new class of planetary system, having a low host mass and also a planetary mass ratio (q <0.03) between the host and its companion. The discovery of the event is important for the study of planetary formation in very low mass objects. In addition, it is important to consider all viable solutions in these kinds of ambiguous events in order for the future comprehensive statistical analyses of planetary/binary microlensing events.

astro-ph.EP↗
arXiv2018

The OGLE Collection of Variable Stars. Type II Cepheids in the Magellanic System

We present a nearly complete collection of type II Cepheids in the Magellanic System. The sample consists of 338 objects: 285 and 53 variables in the Large and Small Magellanic Clouds, respectively. Based on the pulsation periods and light-curve morphology, we classified 118 of our type II Cepheids as BL Herculis, 120 as W Virginis, 34 as peculiar W Virginis, and 66 as RV Tauri stars. For all objects, we publish time-series VI photometry obtained during the OGLE-IV survey, from 2010 to the end of 2017. We present the most interesting individual objects in our collection: 16 type II Cepheids showing additional eclipsing or ellipsoidal variability, two RV Tau variables more than 2.5 mag fainter than other stars of this type in the LMC, an RVb star that drastically decreased the amplitude of the long-period modulation, type II Cepheids exhibiting significant amplitude and period changes, and an RV Tau star which experiences interchanges of deep and shallow minima. We show that peculiar W Vir stars have markedly different spatial distribution than other subclasses of type II Cepheids, which indicates different evolutionary histories of these objects.

astro-ph.SR↗
arXiv2018

OGLE-2017-BLG-0537: Microlensing Event with a Resolvable Lens in $\lesssim 5$ years from High-resolution Follow-up Observations

We present the analysis of the binary-lens microlensing event OGLE-2017-BLG-0537. The light curve of the event exhibits two strong caustic-crossing spikes among which the second caustic crossing was resolved by high-cadence surveys. It is found that the lens components with a mass ratio $\sim 0.5$ are separated in projection by $\sim 1.3\thetae$, where $\thetae$ is the angular Einstein radius. Analysis of the caustic-crossing part yields $\thetae=1.77\pm 0.16$~mas and a lens-source relative proper motion of $μ=12.4\pm 1.1~{\rm mas}~{\rm yr}^{-1}$. The measured $μ$ is the third highest value among the events with measured proper motions and $\sim 3$ times higher than the value of typical Galactic bulge events, making the event a strong candidate for follow-up observations to directly image the lens by separating it from the source. From the angular Einstein radius combined with the microlens parallax, it is estimated that the lens is composed of two main-sequence stars with masses $M_1\sim 0.4~M_\odot$ and $M_2\sim 0.2~M_\odot$ located at a distance of $D_{\rm L}\sim 1.2$~kpc. However, the physical lens parameters are not very secure due to the weak microlens-parallax signal, and thus we cross check the parameters by conducting a Bayesian analysis based on the measured Einstein radius and event timescale combined with the blending constraint. From this, we find that the physical parameters estimated from the Bayesian analysis are consistent with those based on the measured microlens parallax. Resolving the lens from the source can be done in about 5 years from high-resolution follow-up observations and this will provide a rare opportunity to test and refine the microlensing model.

astro-ph.SR↗
arXiv2018

OGLE-2016-BLG-1045: A Test of Cheap Space-Based Microlens Parallaxes

Microlensing is a powerful and unique technique to probe isolated objects in the Galaxy. To study the characteristics of these interesting objects based on the microlensing method, measurement of the microlens parallax is required to determine the properties of the lens. Of the various methods to measure microlens parallax, the most robust way is to make simultaneous ground- and space-based observations, i.e., by measuring the space-based microlens parallax. However, space-based campaigns usually require "expensive" resources. Gould & Yee (2012) proposed an idea called the "cheap space-based microlens parallax" that can measure the lens-parallax using only $2$ or $3$ space-based observations of high-magnification events. This cost-effective observation strategy to measure microlens parallaxes could be used by space-borne telescopes to build a complete sample for studying isolated objects. This would enable a direct measurement of the mass function including both extremely low-mass objects and high-mass stellar remnants. However, to adopt this idea requires a test to check how it would work in actual situations. Thus, we present the first practical test of the idea using the high-magnification microlensing event OGLE-2016-BLG-1045, for which a subset of Spitzer observations fortuitously duplicate the prescription of Gould & Yee (2012). From the test, we confirm that the measurement of the lens-parallax adopting this idea has sufficient accuracy to determine the physical properties of the isolated lens.

astro-ph.SR↗
arXiv2018

OGLE-2015-BLG-1459L: The Challenges of Exo-Moon Microlensing

We show that dense OGLE and KMTNet $I$-band survey data require four bodies (sources plus lenses) to explain the microlensing light curve of OGLE-2015-BLG-1459. However, these can equally well consist of three lenses and one source (3L1S), two lenses and two sources (2L2S) or one lens and three sources (1L3S). In the 3L1S and 2L2S interpretations, the host is a brown dwarf and the dominant companion is a Neptune-class planet, with the third body (in the 3L1S case) being a Mars-class object that could have been a moon of the planet. In the 1L3S solution, the light curve anomalies are explained by a tight (five stellar radii) low-luminosity binary source that is offset from the principal source of the event by $\sim 0.17\,\au$. These degeneracies are resolved in favor of the 1L3S solution by color effects derived from comparison to MOA data, which are taken in a slightly different ($R/I$) passband. To enable current and future ($WFIRST$) surveys to routinely characterize exomoons and distinguish among such exotic systems requires an observing strategy that includes both a cadence faster than 9 min$^{-1}$ and observations in a second band on a similar timescale.

astro-ph.EP↗
arXiv2018

Spitzer Opens New Path to Break Classic Degeneracy for Jupiter-Mass Microlensing Planet OGLE-2017-BLG-1140Lb

We analyze the combined Spitzer and ground-based data for OGLE-2017-BLG-1140 and show that the event was generated by a Jupiter-class $(m_p\simeq 1.6\,M_{\rm jup})$ planet orbiting a mid-late M dwarf $(M\simeq 0.2\,M_\odot)$ that lies $D_{LS}\simeq 1.0\,\mathrm{kpc}$ in the foreground of the microlensed, Galactic-bar, source star. The planet-host projected separation is $a_\perp \simeq 1.0\,\mathrm{au}$, i.e., well-beyond the snow line. By measuring the source proper motion ${\mathbfμ}_s$ from ongoing, long-term OGLE imaging, and combining this with the lens-source relative proper motion ${\mathbfμ}_\mathrm{rel}$ derived from the microlensing solution, we show that the lens proper motion ${\mathbfμ}_l={\mathbfμ}_\mathrm{rel} + {\mathbfμ}_s$ is consistent with the lens lying in the Galactic disk, although a bulge lens is not ruled out. We show that while the Spitzer and ground-based data are comparably well fitted by planetary (i.e., binary-lens, 2L1S) models and by binary-source (1L2S) models, the combination of Spitzer and ground-based data decisively favor the planetary model. This is a new channel to resolve the 2L1S/1L2S degeneracy, which can be difficult to break in some cases.

astro-ph.EP↗
arXiv2018

OGLE-2017-BLG-0373Lb: A Jovian Mass-Ratio Planet Exposes A New Accidental Microlensing Degeneracy

We report the discovery of microlensing planet OGLE-2017-BLG-0373Lb. We show that while the planet-host system has an unambiguous microlens topology, there are two geometries within this topology that fit the data equally well, which leads to a factor 2.5 difference in planet-host mass ratio, i.e., $q=1.5\times 10^{-3}$ vs. $q=0.6\times 10^{-3}$. We show that this is an "accidental degeneracy" in the sense that it is due to a gap in the data. We dub it "the caustic-chirality degeneracy". We trace the mathematical origins of this degeneracy, which should enable similar degenerate solutions to be easily located in the future. A Bayesian estimate, based on a Galactic model, yields a host mass $M=0.25^{+0.30}_{-0.15} M_\odot$ at a distance $D_L=5.9^{+1.3}_{-1.95}$ kpc. The lens-source relative proper motion is relatively fast, $μ=9$ mas/yr, which implies that the host mass and distance can be determined by high-resolution imaging after about 10 years. The same observations could in principle resolve the discrete degeneracy in $q$, but this will be more challenging.

astro-ph.EP↗
arXiv2018

OGLE-2017-BLG-0482Lb: A Microlensing Super-Earth Orbiting a Low-mass Host Star

We report the discovery of a planetary system in which a super-earth orbits a late M-dwarf host. The planetary system was found from the analysis of the microlensing event OGLE-2017-BLG-0482, wherein the planet signal appears as a short-term anomaly to the smooth lensing light curve produced by the host. Despite its weak signal and short duration, the planetary signal was firmly detected from the dense and continuous coverage by three microlensing surveys. We find a planet/host mass ratio of $q\sim 1.4\times 10^{-4}$. We measure the microlens parallax $π_{\rm E}$ from the long-term deviation in the observed lensing light curve, but the angular Einstein radius $θ_{\rm E}$ cannot be measured because the source trajectory did not cross the planet-induced caustic. Using the measured event timescale and the microlens parallax, we find that the masses of the planet and the host are $M_{\rm p}=9.0_{-4.5}^{+9.0}\ M_\oplus$ and $M_{\rm host}=0.20_{-0.10}^{+0.20}\ M_\odot$, respectively, and the projected separation between them is $a_\perp=1.8_{-0.7}^{+0.6}$ au. The estimated distance to the lens is $D_{\rm L}=5.8_{-2.1}^{+1.8}$ kpc. The discovery of the planetary system demonstrates that microlensing provides an important method to detect low-mass planets orbiting low-mass stars.

astro-ph.EP↗
arXiv2018

The First Planetary Microlensing Event with Two Microlensed Source Stars

We present the analysis of microlensing event MOA-2010-BLG-117, and show that the light curve can only be explained by the gravitational lensing of a binary source star system by a star with a Jupiter mass ratio planet. It was necessary to modify standard microlensing modeling methods to find the correct light curve solution for this binary-source, binary-lens event. We are able to measure a strong microlensing parallax signal, which yields the masses of the host star, $M_* = 0.58\pm 0.11 M_\odot$, and planet $m_p = 0.54\pm 0.10 M_{\rm Jup}$ at a projected star-planet separation of $a_\perp = 2.42\pm 0.26\,$AU, corresponding to a semi-major axis of $a = 2.9{+1.6\atop -0.6}\,$AU. Thus, the system resembles a half-scale model of the Sun-Jupiter system with a half-Jupiter mass planet orbiting a half-solar mass star at very roughly half of Jupiter's orbital distance from the Sun. The source stars are slightly evolved, and by requiring them to lie on the same isochrone, we can constrain the source to lie in the near side of the bulge at a distance of $D_S = 6.9 \pm 0.7\,$kpc, which implies a distance to the planetary lens system of $D_L = 3.5\pm 0.4\,$kpc. The ability to model unusual planetary microlensing events, like this one, will be necessary to extract precise statistical information from the planned large exoplanet microlensing surveys, such as the WFIRST microlensing survey.

astro-ph.EP↗
arXiv2018

OGLE-2017-BLG-1522: A giant planet around a brown dwarf located in the Galactic bulge

We report the discovery of a giant planet in the OGLE-2017-BLG-1522 microlensing event. The planetary perturbations were clearly identified by high-cadence survey experiments despite the relatively short event timescale of $t_{\rm E} \sim 7.5$ days. The Einstein radius is unusually small, $θ_{\rm E} = 0.065\,$mas, implying that the lens system either has very low mass or lies much closer to the microlensed source than the Sun, or both. A Bayesian analysis yields component masses $(M_{\rm host}, M_{\rm planet})=(46_{-25}^{+79}, 0.75_{-0.40}^{+1.26})~M_{\rm J}$ and source-lens distance $D_{\rm LS} = 0.99_{-0.54}^{+0.91}~{\rm kpc}$, implying that this is a brown-dwarf/Jupiter system that probably lies in the Galactic bulge, a location that is also consistent with the relatively low lens-source relative proper motion $μ= 3.2 \pm 0.5~{\rm mas}~{\rm yr^{-1}}$. The projected companion-host separation is $0.59_{-0.11}^{+0.12}~{\rm AU}$, indicating that the planet is placed beyond the snow line of the host, i.e., $a_{sl} \sim 0.12~{\rm AU}$. Planet formation scenarios combined with the small companion-host mass ratio $q \sim 0.016$ and separation suggest that the companion could be the first discovery of a giant planet that formed in a protoplanetary disk around a brown dwarf host.

astro-ph.EP↗
arXiv2018

A Likely Detection of a Two-Planet System in a Low Magnification Microlensing Event

We report on the analysis of a microlensing event OGLE-2014-BLG-1722 that showed two distinct short term anomalies. The best fit model to the observed light curves shows that the two anomalies are explained with two planetary mass ratio companions to the primary lens. Although a binary source model is also able to explain the second anomaly, it is marginally ruled out by 3.1 $σ$. The 2-planet model indicates that the first anomaly was caused by planet "b" with a mass ratio of $q = (4.5_{-0.6}^{+0.7}) \times 10^{-4}$ and projected separation in unit of the Einstein radius, $s = 0.753 \pm 0.004$. The second anomaly reveals planet "c" with a mass ratio of $q_{2} = (7.0_{-1.7}^{+2.3}) \times 10^{-4}$ with $Δχ^{2} \sim 170$ compared to the single planet model. Its separation has a so-called close-wide degeneracy. We estimated the physical parameters of the lens system from Bayesian analysis. This gives that the masses of planet b and c are $m_{\rm b} = 56_{-33}^{+51}\,M_{\oplus}$ and $m_{\rm c} = 85_{-51}^{+86}\,M_{\oplus}$, respectively, and they orbit a late type star with a mass of $M_{\rm host} = 0.40_{-0.24}^{+0.36}\,M_{\odot}$ located at $D_{\rm L} = 6.4_{-1.8}^{+1.3}\,\rm kpc$ from us. If the 2-planet model is true, this is the third multiple planet system detected by using the microlensing method, and the first multiple planet system detected in the low magnification events, which are dominant in the microlensing survey data. The occurrence rate of multiple cold gas giant systems is estimated using the two such detections and a simple extrapolation of the survey sensitivity of 6 year MOA microlensing survey (Suzuki et al. 2016) combined with the 4 year $μ$FUN detection efficiency (Gould et al. 2010). It is estimated that $6 \pm 2\,\%$ of stars host two cold giant planets.

astro-ph.EP↗
arXiv2018

OGLE-2017-BLG-1130: The First Binary Gravitational Microlens Detected From Spitzer Only

We analyze the binary gravitational microlensing event OGLE-2017-BLG-1130 (mass ratio q~0.45), the first published case in which the binary anomaly was only detected by the Spitzer Space Telescope. This event provides strong evidence that some binary signals can be missed by observations from the ground alone but detected by Spitzer. We therefore invert the normal procedure, first finding the lens parameters by fitting the space-based data and then measuring the microlensing parallax using ground-based observations. We also show that the normal four-fold space-based degeneracy in the single-lens case can become a weak eight-fold degeneracy in binary-lens events. Although this degeneracy is resolved in event OGLE-2017-BLG-1130, it might persist in other events.

astro-ph.EP↗
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↗