arXiv subjects

Philip J. Marshall

Publications and source records attributed to Philip J. Marshall.

At least 37 records · Page 2Linked to original sources

arXiv2019

H0LiCOW XIII. A 2.4% measurement of $H_{0}$ from lensed quasars: $5.3σ$ tension between early and late-Universe probes

We present a measurement of the Hubble constant ($H_{0}$) and other cosmological parameters from a joint analysis of six gravitationally lensed quasars with measured time delays. All lenses except the first are analyzed blindly with respect to the cosmological parameters. In a flat $Λ$CDM cosmology, we find $H_{0} = 73.3_{-1.8}^{+1.7}$, a 2.4% precision measurement, in agreement with local measurements of $H_{0}$ from type Ia supernovae calibrated by the distance ladder, but in $3.1σ$ tension with $Planck$ observations of the cosmic microwave background (CMB). This method is completely independent of both the supernovae and CMB analyses. A combination of time-delay cosmography and the distance ladder results is in $5.3σ$ tension with $Planck$ CMB determinations of $H_{0}$ in flat $Λ$CDM. We compute Bayes factors to verify that all lenses give statistically consistent results, showing that we are not underestimating our uncertainties and are able to control our systematics. We explore extensions to flat $Λ$CDM using constraints from time-delay cosmography alone, as well as combinations with other cosmological probes, including CMB observations from $Planck$, baryon acoustic oscillations, and type Ia supernovae. Time-delay cosmography improves the precision of the other probes, demonstrating the strong complementarity. Allowing for spatial curvature does not resolve the tension with $Planck$. Using the distance constraints from time-delay cosmography to anchor the type Ia supernova distance scale, we reduce the sensitivity of our $H_0$ inference to cosmological model assumptions. For six different cosmological models, our combined inference on $H_{0}$ ranges from $\sim73$-$78~\mathrm{km~s^{-1}~Mpc^{-1}}$, which is consistent with the local distance ladder constraints.

astro-ph.CO↗

arXiv2018

Analyzing interferometric observations of strong gravitational lenses with recurrent and convolutional neural networks

We use convolutional neural networks (CNNs) and recurrent neural networks (RNNs) to estimate the parameters of strong gravitational lenses from interferometric observations. We explore multiple strategies and find that the best results are obtained when the effects of the dirty beam are first removed from the images with a deconvolution performed with an RNN-based structure before estimating the parameters. For this purpose, we use the recurrent inference machine (RIM) introduced in Putzky & Welling (2017). This provides a fast and automated alternative to the traditional CLEAN algorithm. We obtain the uncertainties of the estimated parameters using variational inference with Bernoulli distributions. We test the performance of the networks with a simulated test dataset as well as with five ALMA observations of strong lenses. For the observed ALMA data we compare our estimates with values obtained from a maximum-likelihood lens modeling method which operates in the visibility space and find consistent results. We show that we can estimate the lensing parameters with high accuracy using a combination of an RNN structure performing image deconvolution and a CNN performing lensing analysis, with uncertainties less than a factor of two higher than those achieved with maximum-likelihood methods. Including the deconvolution procedure performed by RIM, a single evaluation can be done in about a second on a single GPU, providing a more than six orders of magnitude increase in analysis speed while using about eight orders of magnitude less computational resources compared to maximum-likelihood lens modeling in the uv-plane. We conclude that this is a promising method for the analysis of mm and cm interferometric data from current facilities (e.g., ALMA, JVLA) and future large interferometric observatories (e.g., SKA), where an analysis in the uv-plane could be difficult or unfeasible.

astro-ph.IM↗

arXiv2018

Integrating human and machine intelligence in galaxy morphology classification tasks

Quantifying galaxy morphology is a challenging yet scientifically rewarding task. As the scale of data continues to increase with upcoming surveys, traditional classification methods will struggle to handle the load. We present a solution through an integration of visual and automated classifications, preserving the best features of both human and machine. We demonstrate the effectiveness of such a system through a re-analysis of visual galaxy morphology classifications collected during the Galaxy Zoo 2 (GZ2) project. We reprocess the top level question of the GZ2 decision tree with a Bayesian classification aggregation algorithm dubbed SWAP, originally developed for the Space Warps gravitational lens project. Through a simple binary classification scheme we increase the classification rate nearly 5-fold, classifying 226,124 galaxies in 92 days of GZ2 project time while reproducing labels derived from GZ2 classification data with 95.7% accuracy. We next combine this with a Random Forest machine learning algorithm that learns on a suite of nonparametric morphology indicators widely used for automated morphologies. We develop a decision engine that delegates tasks between human and machine, and demonstrate that the combined system provides at least a factor of 8 increase in the classification rate, classifying 210,803 galaxies in just 32 days of GZ2 project time with 93.1% accuracy. As the Random Forest algorithm requires a minimal amount of computation cost, this result has important implications for galaxy morphology identification tasks in the era of Euclid and other large scale surveys.

astro-ph.IM↗

arXiv2018

The Sloan Lens ACS Survey. XIII. Discovery of 40 New Galaxy-Scale Strong Lenses

We present the full sample of 118 galaxy-scale strong-lens candidates in the Sloan Lens ACS (SLACS) Survey for the Masses (S4TM) Survey, which are spectroscopically selected from the final data release of the Sloan Digital Sky Survey. Follow-up Hubble Space Telescope (HST) imaging observations confirm that 40 candidates are definite strong lenses with multiple lensed images. The foreground lens galaxies are found to be early-type galaxies (ETGs) at redshifts 0.06 to 0.44, and background sources are emission-line galaxies at redshifts 0.22 to 1.29. As an extension of the SLACS Survey, the S4TM Survey is the first attempt to preferentially search for strong-lens systems with relatively lower lens masses than those in the pre-existing strong-lens samples. By fitting HST data with a singular isothermal ellipsoid model, we find total projected mass within the Einstein radius of the S4TM strong-lens sample ranges from $3 \times10^{10} M_{\odot}$ to $2 \times10^{11} M_{\odot}$. In [Shu15], we have derived the total stellar mass of the S4TM lenses to be $5 \times10^{10} M_{\odot}$ to $1 \times10^{12} M_{\odot}$. Both total enclosed mass and stellar mass of the S4TM lenses are on average almost a factor of 2 smaller than those of the SLACS lenses, which also represent typical mass scales of the current strong-lens samples. The extended mass coverage provided by the S4TM sample can enable a direct test, with the aid of strong lensing, for transitions in scaling relations, kinematic properties, mass structure, and dark-matter content trends of ETGs at intermediate-mass scales as noted in previous studies.

astro-ph.GA↗

arXiv2017

The broad band SEDs of four 'hypervariable' AGN

We present an optical to X-ray spectral analysis of four 'hypervariable' AGN (HVAs) discovered by comparing Pan-STARRS data to that from SDSS over a 10 year baseline (Lawrence et al 2016). There is some evidence that these objects are X-ray loud for their corresponding UV luminosities, but given that we measured them in a historic high state, it is not clear whether to take the high-state or low-state as typical of the properties of these HVAs. We estimate black hole masses based on MgII and H$α$ emission line profiles, and either the high and low state luminosities, finding mass ranges $\log(M_{\rm BH}/M_{\odot}) = 8.2-8.8$ and $\log(M_{\rm BH}/M_{\odot}) = 7.9-8.3$ respectively. We then fit energy conserving models to the SEDs, obtaining strong constraints on the bolometric luminosity and $α_{\rm OX}$. We compare the SED properties with a larger, X-ray selected AGN sample for both of these scenarios, and observe distinct groupings in spectral shape versus luminosity parameter space. In general, the SED properties are closer to normal if we assume that the low-state is representative. This supports the idea that the large slow outbursts may be due to extrinsic effects (for example microlensing) as opposed to accretion rate changes, but a larger sample of HVAs is needed to be confident of this conclusion.

astro-ph.HE↗

arXiv2017

Fast Automated Analysis of Strong Gravitational Lenses with Convolutional Neural Networks

Quantifying image distortions caused by strong gravitational lensing and estimating the corresponding matter distribution in lensing galaxies has been primarily performed by maximum likelihood modeling of observations. This is typically a time and resource-consuming procedure, requiring sophisticated lensing codes, several data preparation steps, and finding the maximum likelihood model parameters in a computationally expensive process with downhill optimizers. Accurate analysis of a single lens can take up to a few weeks and requires the attention of dedicated experts. Tens of thousands of new lenses are expected to be discovered with the upcoming generation of ground and space surveys, the analysis of which can be a challenging task. Here we report the use of deep convolutional neural networks to accurately estimate lensing parameters in an extremely fast and automated way, circumventing the difficulties faced by maximum likelihood methods. We also show that lens removal can be made fast and automated using Independent Component Analysis of multi-filter imaging data. Our networks can recover the parameters of the Singular Isothermal Ellipsoid density profile, commonly used to model strong lensing systems, with an accuracy comparable to the uncertainties of sophisticated models, but about ten million times faster: 100 systems in approximately 1s on a single graphics processing unit. These networks can provide a way for non-experts to obtain lensing parameter estimates for large samples of data. Our results suggest that neural networks can be a powerful and fast alternative to maximum likelihood procedures commonly used in astrophysics, radically transforming the traditional methods of data reduction and analysis.

astro-ph.IM↗

arXiv2016

H0LiCOW IV. Lens mass model of HE 0435-1223 and blind measurement of its time-delay distance for cosmology

Strong gravitational lenses with measured time delays between the multiple images allow a direct measurement of the time-delay distance to the lens, and thus a measure of cosmological parameters, particularly the Hubble constant, $H_{0}$. We present a blind lens model analysis of the quadruply-imaged quasar lens HE 0435-1223 using deep Hubble Space Telescope imaging, updated time-delay measurements from the COSmological MOnitoring of GRAvItational Lenses (COSMOGRAIL), a measurement of the velocity dispersion of the lens galaxy based on Keck data, and a characterization of the mass distribution along the line of sight. HE 0435-1223 is the third lens analyzed as a part of the $H_{0}$ Lenses in COSMOGRAIL's Wellspring (H0LiCOW) project. We account for various sources of systematic uncertainty, including the detailed treatment of nearby perturbers, the parameterization of the galaxy light and mass profile, and the regions used for lens modeling. We constrain the effective time-delay distance to be $D_{Δt} = 2612_{-191}^{+208}~\mathrm{Mpc}$, a precision of 7.6%. From HE 0435-1223 alone, we infer a Hubble constant of $H_{0} = 73.1_{-6.0}^{+5.7}~\mathrm{km~s^{-1}~Mpc^{-1}}$ assuming a flat $Λ$CDM cosmology. The cosmographic inference based on the three lenses analyzed by H0LiCOW to date is presented in a companion paper (H0LiCOW Paper V).

astro-ph.CO↗

arXiv2016

EmpiriciSN: Re-sampling Observed Supernova/Host Galaxy Populations using an XD Gaussian Mixture Model

We describe two new open source tools written in Python for performing extreme deconvolution Gaussian mixture modeling (XDGMM) and using a conditioned model to re-sample observed supernova and host galaxy populations. XDGMM is new program for using Gaussian mixtures to do density estimation of noisy data using extreme deconvolution (XD) algorithms that has functionality not available in other XD tools. It allows the user to select between the AstroML (Vanderplas et al. 2012; Ivezic et al. 2015) and Bovy et al. (2011) fitting methods and is compatible with scikit-learn machine learning algorithms (Pedregosa et al. 2011). Most crucially, it allows the user to condition a model based on the known values of a subset of parameters. This gives the user the ability to produce a tool that can predict unknown parameters based on a model conditioned on known values of other parameters. EmpiriciSN is an example application of this functionality that can be used for fitting an XDGMM model to observed supernova/host datasets and predicting likely supernova parameters using on a model conditioned on observed host properties. It is primarily intended for simulating realistic supernovae for LSST data simulations based on empirical galaxy properties.

astro-ph.IM↗

arXiv2016

H0LiCOW VI. Testing the fidelity of lensed quasar host galaxy reconstruction

The empirical correlation between the mass of a super-massive black hole (MBH) and its host galaxy properties is widely considered to be evidence of their co-evolution. A powerful way to test the co-evolution scenario and learn about the feedback processes linking galaxies and nuclear activity is to measure these correlations as a function of redshift. Unfortunately, currently MBH can only be estimated in active galaxies at cosmological distances. At these distances, bright active galactic nuclei (AGN) can outshine the host galaxy, making it extremely difficult to measure the host's luminosity. Strongly lensed AGNs provide in principle a great opportunity to improve the sensitivity and accuracy of the host galaxy luminosity measurements as the host galaxy is magnified and more easily separated from the point source, provided the lens model is sufficiently accurate. In order to measure the MBH-L correlation with strong lensing, it is necessary to ensure that the lens modelling is accurate, and that the host galaxy luminosity can be recovered to at least a precision and accuracy better than that of the typical MBH measurement. We carry out extensive and realistic simulations of deep Hubble Space Telescope observations of lensed AGNs obtained by our collaboration. We show that the host galaxy luminosity can be recovered with better accuracy and precision than the typical uncertainty on MBH(~ 0.5 dex) for hosts as faint as 2-4 magnitudes dimmer than the AGN itself. Our simulations will be used to estimate bias and uncertainties on the actual measurements to be presented in a future paper.

astro-ph.GA↗

arXiv2016

Probabilistic Cosmological Mass Mapping from Weak Lensing Shear

We infer gravitational lensing shear and convergence fields from galaxy ellipticity catalogs under a spatial process prior for the lensing potential. We demonstrate the performance of our algorithm with simulated Gaussian-distributed cosmological lensing shear maps and a reconstruction of the mass distribution of the merging galaxy cluster Abell 781 using galaxy ellipticities measured with the Deep Lens Survey. Given interim posterior samples of lensing shear or convergence fields on the sky, we describe an algorithm to infer cosmological parameters via lens field marginalization. In the most general formulation of our algorithm we make no assumptions about weak shear or Gaussian distributed shape noise or shears. Because we require solutions and matrix determinants of a linear system of dimension that scales with the number of galaxies, we expect our algorithm to require parallel high-performance computing resources for application to ongoing wide field lensing surveys.

astro-ph.CO↗

arXiv2016

H0LiCOW III. Quantifying the effect of mass along the line of sight to the gravitational lens HE 0435-1223 through weighted galaxy counts

Based on spectroscopy and multiband wide-field observations of the gravitationally lensed quasar HE 0435-1223, we determine the probability distribution function of the external convergence $κ_\mathrm{ext}$ for this system. We measure the under/overdensity of the line of sight towards the lens system and compare it to the average line of sight throughout the universe, determined by using the CFHTLenS as a control field. Aiming to constrain $κ_\mathrm{ext}$ as tightly as possible, we determine under/overdensities using various combinations of relevant informative weighing schemes for the galaxy counts, such as projected distance to the lens, redshift, and stellar mass. We then convert the measured under/overdensities into a $κ_\mathrm{ext}$ distribution, using ray-tracing through the Millennium Simulation. We explore several limiting magnitudes and apertures, and account for systematic and statistical uncertainties relevant to the quality of the observational data, which we further test through simulations. Our most robust estimate of $κ_\mathrm{ext}$ has a median value $κ^\mathrm{med}_\mathrm{ext} = 0.004$ and a standard deviation of $σ_κ= 0.025$. The measured $σ_κ$ corresponds to $2.5\%$ uncertainty on the time delay distance, and hence the Hubble constant $H_0$ inference from this system. The median $κ^\mathrm{med}_\mathrm{ext}$ value is robust to $\sim0.005$ (i.e. $\sim0.5\%$ on $H_0$) regardless of the adopted aperture radius, limiting magnitude and weighting scheme, as long as the latter incorporates galaxy number counts, the projected distance to the main lens, and a prior on the external shear obtained from mass modeling. The availability of a well-constrained $κ_\mathrm{ext}$ makes \hequad\ a valuable system for measuring cosmological parameters using strong gravitational lens time delays.

astro-ph.GA↗

arXiv2016

Time Delay Cosmography

Gravitational time delays, observed in strong lens systems where the variable background source is multiply-imaged by a massive galaxy in the foreground, provide direct measurements of cosmological distance that are very complementary to other cosmographic probes. The success of the technique depends on the availability and size of a suitable sample of lensed quasars or supernovae, precise measurements of the time delays, accurate modeling of the gravitational potential of the main deflector, and our ability to characterize the distribution of mass along the line of sight to the source. We review the progress made during the last 15 years, during which the first competitive cosmological inferences with time delays were made, and look ahead to the potential of significantly larger lens samples in the near future.

astro-ph.CO↗

arXiv2016

Detection of lensing substructure using ALMA observations of the dusty galaxy SDP.81

We study the abundance of substructure in the matter density near galaxies using ALMA Science Verification observations of the strong lensing system SDP.81. We present a method to measure the abundance of subhalos around galaxies using interferometric observations of gravitational lenses. Using simulated ALMA observations, we explore the effects of various systematics, including antenna phase errors and source priors, and show how such errors may be measured or marginalized. We apply our formalism to ALMA observations of SDP.81. We find evidence for the presence of a $M=10^{8.96\pm 0.12} M_{\odot}$ subhalo near one of the images, with a significance of $6.9σ$ in a joint fit to data from bands 6 and 7; the effect of the subhalo is also detected in both bands individually. We also derive constraints on the abundance of dark matter subhalos down to $M\sim 2\times 10^7 M_{\odot}$, pushing down to the mass regime of the smallest detected satellites in the Local Group, where there are significant discrepancies between the observed population of luminous galaxies and predicted dark matter subhalos. We find hints of additional substructure, warranting further study using the full SDP.81 dataset (including, for example, the spectroscopic imaging of the lensed carbon monoxide emission). We compare the results of this search to the predictions of $Λ$CDM halos, and find that given current uncertainties in the host halo properties of SDP.81, our measurements of substructure are consistent with theoretical expectations. Observations of larger samples of gravitational lenses with ALMA should be able to improve the constraints on the abundance of galactic substructure.

astro-ph.CO↗

arXiv2015

Precision cosmology with time delay lenses: high resolution imaging requirements

Lens time delays are a powerful probe of cosmology, provided that the gravitational potential of the main deflector can be modeled with sufficient precision. Recent work has shown that this can be achieved by detailed modeling of the host galaxies of lensed quasars, which appear as "Einstein Rings" in high resolution images. We carry out a systematic exploration of the high resolution imaging required to exploit the thousands of lensed quasars that will be discovered by current and upcoming surveys with the next decade. Specifically, we simulate realistic lens systems as imaged by the Hubble Space Telescope (HST), James Webb Space Telescope (JWST), and ground based adaptive optics images taken with Keck or the Thirty Meter Telescope (TMT). We compare the performance of these pointed observations with that of images taken by the Euclid (VIS), Wide-Field Infrared Survey Telescope (WFIRST) and Large Synoptic Survey Telescope (LSST) surveys. We use as our metric the precision with which the slope $γ'$ of the total mass density profile $ρ_{tot}\propto r^{-γ'}$ for the main deflector can be measured. Ideally, we require that the statistical error on $γ'$ be less than 0.02, such that it is subdominant to other sources of random and systematic uncertainties. We find that survey data will likely have sufficient depth and resolution to meet the target only for the brighter gravitational lens systems, comparable to those discovered by the SDSS survey. For fainter systems, that will be discovered by current and future surveys, targeted follow-up will be required. However, the exposure time required with upcoming facilitites such as JWST, the Keck Next Generation Adaptive Optics System, and TMT, will only be of order a few minutes per system, thus making the follow-up of hundreds of systems a practical and efficient cosmological probe.

astro-ph.CO↗

arXiv2015

Space Warps II. New Gravitational Lens Candidates from the CFHTLS Discovered through Citizen Science

We report the discovery of 29 promising (and 59 total) new lens candidates from the CFHT Legacy Survey (CFHTLS) based on about 11 million classifications performed by citizen scientists as part of the first Space Warps lens search. The goal of the blind lens search was to identify lens candidates missed by robots (the RingFinder on galaxy scales and ArcFinder on group/cluster scales) which had been previously used to mine the CFHTLS for lenses. We compare some properties of the samples detected by these algorithms to the Space Warps sample and find them to be broadly similar. The image separation distribution calculated from the Space Warps sample shows that previous constraints on the average density profile of lens galaxies are robust. SpaceWarps recovers about 65% of known lenses, while the new candidates show a richer variety compared to those found by the two robots. This detection rate could be increased to 80% by only using classifications performed by expert volunteers (albeit at the cost of a lower purity), indicating that the training and performance calibration of the citizen scientists is very important for the success of Space Warps. In this work we present the SIMCT pipeline, used for generating in situ a sample of realistic simulated lensed images. This training sample, along with the false positives identified during the search, has a legacy value for testing future lens finding algorithms. We make the pipeline and the training set publicly available.

astro-ph.CO↗

arXiv2015

Space Warps: I. Crowd-sourcing the Discovery of Gravitational Lenses

We describe Space Warps, a novel gravitational lens discovery service that yields samples of high purity and completeness through crowd-sourced visual inspection. Carefully produced colour composite images are displayed to volunteers via a web- based classification interface, which records their estimates of the positions of candidate lensed features. Images of simulated lenses, as well as real images which lack lenses, are inserted into the image stream at random intervals; this training set is used to give the volunteers instantaneous feedback on their performance, as well as to calibrate a model of the system that provides dynamical updates to the probability that a classified image contains a lens. Low probability systems are retired from the site periodically, concentrating the sample towards a set of lens candidates. Having divided 160 square degrees of Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) imaging into some 430,000 overlapping 82 by 82 arcsecond tiles and displaying them on the site, we were joined by around 37,000 volunteers who contributed 11 million image classifications over the course of 8 months. This Stage 1 search reduced the sample to 3381 images containing candidates; these were then refined in Stage 2 to yield a sample that we expect to be over 90% complete and 30% pure, based on our analysis of the volunteers performance on training images. We comment on the scalability of the SpaceWarps system to the wide field survey era, based on our projection that searches of 10$^5$ images could be performed by a crowd of 10$^5$ volunteers in 6 days.

astro-ph.IM↗

arXiv2015

Discovery of two gravitationally lensed quasars in the Dark Energy Survey

We present spectroscopic confirmation of two new lensed quasars via data obtained at the 6.5m Magellan/Baade Telescope. The lens candidates have been selected from the Dark Energy Survey (DES) and WISE based on their multi-band photometry and extended morphology in DES images. Images of DES J0115-5244 show two blue point sources at either side of a red galaxy. Our long-slit data confirm that both point sources are images of the same quasar at $z_{s}=1.64.$ The Einstein Radius estimated from the DES images is $0.51$". DES J2200+0110 is in the area of overlap between DES and the Sloan Digital Sky Survey (SDSS). Two blue components are visible in the DES and SDSS images. The SDSS fiber spectrum shows a quasar component at $z_{s}=2.38$ and absorption compatible with Mg II and Fe II at $z_{l}=0.799$, which we tentatively associate with the foreground lens galaxy. The long-slit Magellan spectra show that the blue components are resolved images of the same quasar. The Einstein Radius is $0.68$" corresponding to an enclosed mass of $1.6\times10^{11}\,M_{\odot}.$ Three other candidates were observed and rejected, two being low-redshift pairs of starburst galaxies, and one being a quasar behind a blue star. These first confirmation results provide an important empirical validation of the data-mining and model-based selection that is being applied to the entire DES dataset.

astro-ph.GA↗

arXiv2015

CHITAH: Strong-gravitational-lens hunter in imaging surveys

Strong gravitationally lensed quasars provide powerful means to study galaxy evolution and cosmology. Current and upcoming imaging surveys will contain thousands of new lensed quasars, augmenting the existing sample by at least two orders of magnitude. To find such lens systems, we built a robot, CHITAH, that hunts for lensed quasars by modeling the configuration of the multiple quasar images. Specifically, given an image of an object that might be a lensed quasar, CHITAH first disentangles the light from the supposed lens galaxy and the light from the multiple quasar images based on color information. A simple rule is designed to categorize the given object as a potential four-image (quad) or two-image (double) lensed quasar system. The configuration of the identified quasar images is subsequently modeled to classify whether the object is a lensed quasar system. We test the performance of CHITAH using simulated lens systems based on the Canada-France-Hawaii Telescope Legacy Survey. For bright quads with large image separations (with Einstein radius $r_{\rm ein}>1.1"$) simulated using Gaussian point-spread functions, a high true-positive rate (TPR) of $\sim$90% and a low false-positive rate of $\sim$$3\%$ show that this is a promising approach to search for new lens systems. We obtain high TPR for lens systems with $r_{\rm ein}\gtrsim0.5"$, so the performance of CHITAH is set by the seeing. We further feed a known gravitational lens system, COSMOS 5921$+$0638, to CHITAH, and demonstrate that CHITAH is able to classify this real gravitational lens system successfully. Our newly built CHITAH is omnivorous and can hunt in any ground-based imaging surveys.

astro-ph.GA↗