arXiv subjects

Ryan C. Fortenberry

Publications and source records attributed to Ryan C. Fortenberry.

At least 19 recordsLinked to original sources

arXiv2025

SPHEREx: Aromatics, Aliphatics and PAH Size across the Iris Nebula

Observations by the SpectroPhotometer for the History of the Universe, Epoch of Reionization, and Ices Explorer (SPHEREx) are combined with Spitzer spectral map data to study the aromatic, aliphatic, and PAH size evolution across the northwest photo-dissociation region (PDR) of the Iris Nebula (NGC7023). The 3.3-3.4 $μ$m complex (I$_{3.3}$) and 11.2 $μ$m (I$_{11.2}$) PAH band strength are determined through direct integration. In addition, the former is decomposed into a 3.3 (I'$_{3.3}$) and 3.4 $μ$m (I'$_{3.4}$) sub-feature by fitting SPHEREx bandpass-integrated photometry using a modeled, highly sampled, multi-component spectrum. I$_{3.3}$, I$_{11.2}$, I'$_{3.3}$, and I'$_{3.4}$ all peak at the PDR. The NASA Ames PAH IR Spectroscopic Database is used to obtain the average number of carbon atoms ($\overline{\rm N_{C}}$) and small PAH fraction ($f_{\rm small}$) by fitting the isolated PAH component of the Spitzer segment; $70\lesssim\overline{N_{C}}\lesssim76$ and $0.24\lesssim\text{f}_{\rm small}\lesssim0.36$. I'$_{3.4}$/I'$_{3.4}$, I$_{11.2}$/I$_{3.3}$, $\overline{\rm N_{C}}$, and $f_{\rm small}$ all show a demarcation that matches the large-scale morphology of the region. For I'$_{3.3}$ and I'$_{3.4}$ this is reflected by two distinct trends when plotted against each other, one associated with the dense, the other with the diffuse medium; $[N_{\rm H,ali}/N_{\rm H,aro}]_{\rm dense}$ = 0.42$\pm$0.01 and $[N_{\rm H,ali}/N_{\rm H,aro}]_{\rm diffuse}$ = 0.10$\pm$0.01. $\overline{\rm N_{C}}$ and $f_{\rm small}$ are tentatively correlated with I$_{11.2}$/I$_{3.3}$ (R=0.54$\pm$0.05 and -0.45$\pm$0.05, respectively). A wider variety of large(r) extended interstellar medium objects is required to tighten the correlations, turn them into quantitative calibrators for PAH size, and pin down the discrepancy of correlations with I'$_{3.3}$ involved.

astro-ph.GA↗

arXiv2025

Formation of thiocarbonic acid (H$_2$CS$_3$) -- the sulfur counterpart of carbonic acid (H$_2$CO$_3$) - in interstellar analog ices

The first experimental formation of thiocarbonic acid (H$_2$CO$_3$) is presented in this work from low-temperature interstellar ice analogs composed of hydrogen sulfide (H$_2$S) and carbon disulfide (CS$_2$) exposed to electron irradiation simulating the impact of galactic cosmic rays (GCRs) on interstellar ices. The recent attention brought to sulfur-bearing molecules, as well as the recent detection of carbonic acid (H$_2$CO$_3$) in the interstellar medium (ISM), invites the study of the interstellar detection of the sulfur counterpart, thiocarbonic acid. However, the interstellar formation pathways of thiocarbonic acid have remained elusive. In this work, thiocarbonic acid was identified in the gas phase during the temperature programmed desorption (TPD) using isomer-selective single photoionization reflectron time-of-flight mass spectrometry (PI-ReToF-MS), suggesting that the hitherto astronomically unobserved thiocarbonic acid represents a promising candidate for future astronomical searches. The formation of H2CS3 isomers was investigated through additional isotopically labeled experiments and the formation mechanisms through quantum chemical studies. These findings unravel a key reaction pathway to thiocarbonic acid and represent a first step toward its possible formation and detection in the ISM, shedding light on the missing sulfur problem.

astro-ph.GA↗

arXiv2024

The High-Resolution Far- to Near-Infrared Anharmonic Absorption Spectra of Cyano-Substituted Polycyclic Aromatic Hydrocarbons from 300-6200 cm$^{-1}$

Cyano-substituted polycyclic aromatic hydrocarbons (CN-PAHs) may contribute to the emission detected in the 7 - 9 $μ$m (1430 - 1100 cm$^{-1}$) and 11 - 15 $μ$m (900 - 670 cm$^{-1}$) regions of astronomical IR spectra. Anharmonic quantum chemical computations of 17 CN-PAH isomers for 4 small PAHs and Benzene reveal strong, broad absorption features across the entire 300 - 6200 cm$^{-1}$ (33 - 1.6 $μ$m) frequency range. In particular, when a FWHM of 15 cm$^{-1}$ is applied, the composite CN-PAH spectrum is almost indistinguishable from the unsubstituted-PAH spectrum. At high resolution, however, the infrared absorption spectra reveal unique, identifiable features of CN-PAHs in the 700 - 950, 1100 - 1300, 2000 - 2500, and 3400 - 3600 cm$^{-1}$ ranges. The in-plane and out-of-plane CH bending vibrational frequencies of CN-PAHs are shifted when comparing isomers and to their unsubstituted counterparts, making their differentiation in mixed laboratory experiments possible. The overall aromatic CH stretch fundamental (2950 - 3200 cm$^{-1}$) and first overtone (5950 - 6200 cm$^{-1}$) regions are relatively unaffected by the cyano-substitution, with changes only to the breadth and intensity of the bands. Detailed spectroscopic data on the normal mode components of each state reported herein provide the means to directly assign future laboratory spectra and to guide direct IR observations of astronomical regions with, e.g., JWST.

astro-ph.GA↗

arXiv2024

A Possible Additional Formation Pathway for the Interstellar Diatomic SiS

The formation of silicon monosulfide (SiS) in space appears to be a difficult process, but the present work is showing that a previously excluded pathway may contribute to its astronomical abundance. Reaction of the radicals SH + SiH produces SiS with a submerged transition state and generates a stabilizing H$_2$ molecule as a product to dissipate the kinetic energy. Such is a textbook chemical reaction for favorable gas-phase chemistry. While previously proposed mechanisms reacting atomic sulfur and silicon with SiH, SH, and H$_2$S will still be major contributors to the production of SiS, an abundance of SiS in certain regions could be a marker for the presence of SiH where it has previously been unobserved. These quantum chemically-computed reaction profiles imply that the silicon-chalcogen chemistry of molecular clouds, shocked regions, or protoplanetary disks may be richer than previously thought. Quantum chemical spectral data for the intermediate cis- and trans-HSiSH are also provided in order to aid in their potential spectroscopic characterization.

astro-ph.GA↗

arXiv2024

The Infrared Absorption Spectrum of Phenylacetylene and its Deuterated Isotopologue in the Mid- to Far-IR

Anharmonicity strongly influences the absorption and emission spectra of polycyclic aromatic hydrocarbon (PAH) molecules. Here, IR-UV ion-dip spectroscopy experiments together with detailed anharmonic computations reveal the presence of fundamental, overtone, as well as 2- and 3-quanta combination band transitions in the far- and mid-infrared absorption spectrum of phenylacetylene and its singly deuterated isotopologue. Strong absorption features in the 400-900 cm$^{\rm -1}$ range originate from CH(D) in-plane and out-of-plane wags and bends, as well as bending motions including the C$\equiv$C and CH bonds of the acetylene substituent and the aromatic ring. For phenylacetylene, every absorption feature is assigned either directly or indirectly to a single or multiple vibrational mode(s). The measured spectrum is dense, broad, and structureless in many regions but well characterized by computations. Upon deuteration, large isotopic shifts are observed. At frequencies above 1500 cm$^{\rm -1}$ for d$_1$-phenylacetylene, a one-to-one match is seen when comparing computations and experiment with all features assigned to combination bands and overtones. The C$\equiv$C stretch observed in phenylacetylene is not observed in d$_1$-phenylacetylene due to a computed 40-fold drop in intensity. Overall, a careful treatment of anharmonicity that includes 2- and 3-quanta modes is found to be crucial to understand the rich details of the infrared spectrum of phenylacetylene. Based on these results, it can be expected that such an all-inclusive anharmonic treatment will also be key for unraveling the infrared spectra of PAHs in general.

astro-ph.GA↗

arXiv2024

Accurate ab initio spectroscopic studies of promising interstellar ethanolamine iminic precursors

Context. The detection of NH2CH2CH2OH (ethanolamine) in molecular cloud G+0.693-0.027 adds an additional player to the prebiotic molecules discovered so far in the interstellar medium (ISM). As this molecule might be formed through condensed-phase hydrogenation steps, detecting one or more of the molecules involved might help to elucidate the chemical pathway leading to its production. Aims. The chemical path involves the formation of four chemical species. In this work, we study the energies of the isomers involved, indicate the best candidates for detection purposes, and provide the distortion constants of the most energetically favoured isomers undetected so far. Methods. We used highly accurate CCSD(T)-F12/cc-pCVTZ-F12 computations to predict the lowest energy isomers as well as their spectroscopic constants, taking corrections for core electron correlation and scalar relativity into account. Results. We studied 14 isomers. We find that the lowest energy isomer proposed in previous studies is not the actual minimum. We provide a set of rotational and distortion constants of the two new most stable isomers together with their fundamental vibrational frequencies in order to guide the search for these important astrochemical precursors of prebiotic molecules in the ISM.

astro-ph.GA↗

arXiv2024

Towards the IR Detection of Carbonic Acid: Absorption and Emission Spectra

With the recent radioastronomical detection of cis-trans-carbonic acid (H$_2$CO$_3$) in a molecular cloud toward the galactic center, the more stable but currently unobserved cis-cis conformer is shown here to have strong IR features. While the higher-energy cis-trans-carbonic acid was detected at millimeter and centimeter wavelengths, owing to its larger dipole moment, the vibrational structure of cis-cis-carbonic acid is more amenable to its observation at micron wavelengths. Even so, both conformers have relatively large IR intensities, and some of these fall in regions not dominated by polycyclic aromatic hydrocarbons. Water features may inhibit observation near the 2.75 $μ$m hydride stretches, but other vibrational fundamentals and even overtones in the 5.5 $μ$m to 6.0 $μ$m range may be discernible with JWST data. This work has employed high-level, accurately benchmarked quantum chemical anharmonic procedures to compute exceptionally accurate rotational spectroscopic data compared to experiment. Such performance implies that the IR absorption and even cascade emission spectral features computed in this work should be accurate and will provide the needed reference for observation of either carbonic acid conformer in various astronomical environments.

astro-ph.GA↗

arXiv2024

Reaction Pathway and Rovibrational Analysis of Aluminum Nitride Species as Potential Dust Grain Nucleation Agents

A dust nucleating agent may be present in interstellar or circumstellar media that has gone seemingly undetected and unstudied for decades. Some analyses of the Murchison CM2 meteorite suggest that at least some of the aluminum present within condensed as aluminum nitrides instead of the long studied, but heretofore undetected suite of aluminum oxides. The present theoretical study utilizes explicitly correlated coupled cluster theory and density functional theory to provide a pathway of formation from alane (AlH$_3$) and ammonia to the cyclic structure, Al$_2$N$_2$H$_4$ which has the proper Al/N ratio expected of bulk aluminum nitrides. Novel rovibrational spectroscopic constants are computed for alane and the first two formed structures, AlNH$_6$ and AlNH$_4$, along the reaction pathway for use as reference in possible laboratory or observational studies. The $ν_8$ bending frequency for AlNH$_6$ at 755.7 cm$^{-1}$ (13.23 $μ$m) presents a vibrational transition intensity of 515 km mol$^{-1}$, slightly more intense than the anti-symmetric C$-$O stretch of carbon dioxide, and contains a dipole moment of 5.40 D, which is $\sim 3 \times$ larger than that of water. Thus, the present reaction pathway and rovibrational spectroscopic analysis may potentially assist in the astrophysical detection of novel, inorganic species which may be indicative of larger dust grain nucleation.

astro-ph.IM↗

arXiv2023

Rotational spectroscopic characterisation of the [D2,C,S] system: an update from the laboratory and theory

The synergy between high-resolution rotational spectroscopy and quantum-chemical calculations is essential for exploring future detection of molecules, especially when spectroscopy parameters are not available yet. By using highly correlated ab initio quartic force fields (QFFs) from explicitly correlated coupled cluster theory, a complete set of rotational constants and centrifugal distortion constants for D$_2$CS and cis/trans-DCSD isomers have been produced. Comparing our new ab initio results for D$_2$CS with new rotational spectroscopy laboratory data for the same species, the accuracy of the computed B and C rotational constants is within 0.1% while the A constant is only slightly higher. Additionally, quantum chemical vibrational frequencies are also provided, and these spectral reference data and new experimental rotational lines will provide additional references for potential observation of these deuterated sulfur species with either ground-based radio telescopes or space-based infrared observatories.

astro-ph.IM↗

arXiv2022

The mid-infrared molecular inventory towards Orion IRc2

We present the first high spectral resolution mid-infrared survey in the Orion BN/KL region, covering 7.2 to 28.3 micron. With SOFIA/EXES we target the enigmatic source Orion IRc2. While this is in the most prolifically studied massive star-forming region, longer wavelengths and molecular emission lines dominated previous spectral surveys. The mid-infrared observations in this work access different components and molecular species in unprecedented detail. We unambiguously identify two new kinematic components, both chemically rich with multiple molecular absorption lines. The "blue clump" has vLSR = -7.1 \pm 0.7 km/s and the "red clump" 1.4 \pm 0.5 km/s. While the blue and red clumps have similar temperatures and line widths, molecular species in the blue clump have higher column densities. They are both likely linked to pure rotational H2 emission also covered by this survey. This work provides evidence for the scenario that the blue and red clumps are distinct components unrelated to the classic components in the Orion BN/KL region. Comparison to spectroscopic surveys towards other infrared targets in the region show that the blue clump is clearly extended. We analyze, compare, and present in depth findings on the physical conditions of C2H2, 13CCH2, CH4, CS, H2O, HCN, H13CN, HNC, NH3, and SO2 absorption lines and an H2 emission line associated with the blue and red clumps. We also provide limited analysis of H2O and SiO molecular emission lines towards Orion IRc2 and the atomic forbidden transitions [FeII], [SI], [SIII], and [NeII].

astro-ph.GA↗

arXiv2021

Vibrational and Rotational Spectral Data for Possible Interstellar Detection of AlH$_3$OH$_2$, SiH$_3$OH, and SiH$_3$NH$_2$

This work provides the first full set of vibrational and rotational spectral data needed to aid in the detection of AlH$_3$OH$_2$, SiH$_3$OH, and SiH$_3$NH$_2$ in astrophysical or simulated laboratory environments through the use of quantum chemical computations at the CCSD(T)-F12b level of theory employing quartic force fields for the three molecules of interest. Previous work has shown that SiH$_3$OH and SiH$_3$NH$_2$ contain some of the strongest bonds of the most abundant elements in space. AlH$_3$OH$_2$ also contains highly abundant atoms and represents an intermediate along the reaction pathway from H$_2$O and AlH$_3$ to AlH$_2$OH. All three of these molecules are also polar with AlH$_3$OH$_2$ having the largest dipole of 4.58 D and the other two having dipole moments in the 1.10-1.30 D range, large enough to allow for the detection of these molecules in space through rotational spectroscopy. The molecules also have substantial infrared intensities with many of the frequencies being over 90 km mol$^{-1}$ and falling within the currently uncertain 12-17 $μ$m region of the spectrum. The most intense frequency for AlH$_3$OH$_2$ is $ν_9$ which has an intensity of 412 km mol$^{-1}$ at 777.0 cm$^{-1}$ (12.87 $μ$m). SiH$-3$OH has an intensity of 183 km mol$^{-1}$ at 1007.8 cm$^{-1}$ (9.92 $μ$m) for $ν_5$, and SiH$_3$NH$_2$ has an intensity of 215 km mol$^{-1}$ at 1000.0 cm$^{-1}$ (10.00 $μ$m) for $ν_7$.

astro-ph.IM↗

arXiv2020

The First Mid-Infrared Detection of HNC in the Interstellar Medium: Probing the Extreme Environment Towards the Orion Hot Core

We present the first mid-infrared (MIR) detections of HNC and H13CN in the interstellar medium, and numerous, resolved HCN rovibrational transitions. Our observations span 12.8 to 22.9 micron towards the hot core Orion IRc2, obtained with the Echelon-Cross-Echelle Spectrograph aboard the Stratospheric Observatory for Infrared Astronomy (SOFIA). Exceptional, ~5 km/s, resolution distinguishes individual rovibrational transitions of the HNC and HCN P, Q, and R branches; and the H13CN R branch. This allows direct measurement of the species' excitation temperatures, column densities, and relative abundances. HNC and H13CN exhibit a local standard rest velocity of -7 km/s that may be associated with an outflow from nearby radio source I and an excitation temperature of about 100 K. We resolve two velocity components for HCN, the primary component also being at -7 km/s with temperature 165 K. The hottest component, which had never before been observed, is at 1 km/s with temperature 309 K. This is the closest component to the hot core's centre measured to date. The derived 12C/13C=13 is below expectation for Orion's Galactocentric distance, but the derived HCN/HNC=72 is expected for this extreme environment. Compared to previous sub-mm and mm observations, our SOFIA line survey of this region shows that the resolved MIR molecular transitions are probing a distinct physical component and isolating the chemistry closest to the hot core.

astro-ph.GA↗

arXiv2017

Gas-Phase Spectra of MgO Molecules: A Possible Connection from Gas-Phase Molecules to Planet Formation

A more fine-tuned method for probing planet-forming regions, such as protoplanetary discs, could be rovibrational molecular spectroscopy observation of particular premineral molecules instead of more common but ultimately less related volatile organic compounds. Planets are created when grains aggregate, but how molecules form grains is an ongoing topic of discussion in astrophysics and planetary science. Using the spectroscopic data of molecules specifically involved in mineral formation could help to map regions where planet formation is believed to be occurring in order to examine the interplay between gas and dust. Four atoms are frequently associated with planetary formation: Fe, Si, Mg, and O. Magnesium, in particular, has been shown to be in higher relative abundance in planet-hosting stars. Magnesium oxide crystals comprise the mineral periclase making it the chemically simplest magnesium-bearing mineral and a natural choice for analysis. The monomer, dimer, and trimer forms of (MgO)_n with n = 1 - 3 are analyzed in this work using high-level quantum chemical computations known to produce accurate results. Strong vibrational transitions at 12.5 μm, 15.0 μm, and 16.5 μm are indicative of magnesium oxide monomer, dimer, and trimer making these wavelengths of particular interest for the observation of protoplanetary discs and even potentially planet-forming regions around stars. If such transitions are observed in emission from the accretion discs or absorptions from stellar spectra, the beginning stages of mineral and, subsequently, rocky body formation could be indicated.

astro-ph.EP↗

arXiv2017

The Interstellar Formation and Spectra of the Noble Gas, Proton-Bound HeHHe+, HeHNe+, & HeHAr+ Complexes

The sheer interstellar abundance of helium makes any bound molecules or complexes containing it of potential interest for astrophysical observation. This work utilizes high-level and trusted quantum chemical techniques to predict the rotational, vibrational, and rovibrational traits of HeHHe+, HeHNe+, and HeHAr+. The first two are shown to be strongly bound, while HeHAr+ is shown to be more of a van der Waals complex of argonium with a helium atom. In any case, the formation of HeHHe+ through reactions of HeH+ with HeH3+ is exothermic. HeHHe+ exhibits the quintessentially bright proton-shuttle motion present in all proton-bound complexes in the 7.4 micron range making it a possible target for telescopic observation at the mid-IR/far-IR crossover point and a possible tracer for the as-of-yet unobserved helium hydride cation. Furthermore, a similar mode in HeHNe+ can be observed to the blue of this close to 6.9 microns. The brightest mode of HeHAr+ is dimmed due the reduced interaction of the helium atom with the central proton, but this fundamental frequency can be found slightly to the red of the Ar-H stretch in the astrophysically detected argonium cation.

physics.space-ph↗

arXiv2015

Electronic and Rovibrational Quantum Chemical Analysis of C$_3$P$^-$: The Next Interstellar Anion?

C$_3$P$^-$ is analogous to the known interstellar anion C$_3$N$^-$ with phosphorus replacing the nitrogen in a simple step down the periodic table. In this work, it is shown that C$_3$P$^-$ is likely to possess a dipole-bound excited state. It has been hypothesized and observationally supported that dipole-bound excited states are an avenue through which anions could be formed in the interstellar medium. Additionally, C$_3$P$^-$ has a valence excited state that may lead to further stabilization of this molecule, and C$_3$P$^-$ has a larger dipole moment than neutral C$_3$P ($\sim 6$ D vs. $\sim 4$ D). As such, C$_3$P$^-$ is probably a more detectable astromolecule than even its corresponding neutral radical. Highly-accurate quantum chemical quartic force fields are also applied to C$_3$P$^-$ and its singly $^{13}$C substituted isotopologues in order to provide structures, vibrational frequencies, and spectroscopic constants that may aid in its detection.

physics.chem-ph↗

arXiv2014

ArH2+ and NeH2+ as Global Minima in the Ar+/Ne+ + H2 Reactions: Energetic, Spectroscopic, and Structural Data

In light of the recent discovery of ArH+ in the Crab nebula, it is shown through high-level quantum chemical comptuations that the global minima on the Ar+/Ne+ + H2 potential energy surfaces are ArH2+ and NeH2+. Hence, ArH2+ may be a necessary intermediate in the Ar+ + H2 -> ArH+ + H formation reaction proposed in the same work where ArH+ is first reported in the Crab nebula. ArH2+ is also probably an intermediate in the alternative Ar + H+2 -> ArH+ + H reaction. Additionally, it is shown that Ne+ + H2 -> NeH+2 will subsequently most likely yield Ne + H+2 and not NeH+ + H offering a possible rationale as to the absence of NeH+ in spectra obtained from the interstellar medium (ISM). Following from this, spectroscopic data (both rotational and vibrational) are provided for NeH2+ and ArH2+ through the use of highly-accurate quantum chemical quartic and cubic force fields. All possible isotopologues are also included for 20Ne, 22Ne, 36Ar, 38Ar, 40Ar, 1H, and D. The dipole moments for these systems are quite large at 5.61 D for NeH2+ and 4.37 D for ArH2+. The spectroscopic constants provided will aid in the potential detection of these open-shell noble gas dihydride cations in the ISM.

astro-ph.SR↗

arXiv2013

Theoretical Electronic and Rovibrational Studies for Anions of Interest to the DIBs

The dipole-bound excited state of the methylene nitrile anion (CH2CN-) has been suggested as a candidate carrier for a diffuse interstellar band (DIB) at 803.8 nm. Its corresponding radical has been detected in the interstellar medium (ISM), making the existence for the anion possible. This work applies state-of-the-art ab initio methods such as coupled cluster theory to reproduce accurately the electronic excitations for CH2CN- and the similar methylene enolate anion, CH2CHO-. This same approach has been employed to indicate that 19 other anions may possess electronically excited states, five of which are valence in nature. Concurrently, in order to assist in the detection of these anions in the ISM, work has also been directed towards predicting vibrational frequencies and spectroscopic constants for these anions through the use of quartic force fields (QFFs). Theoretical rovibrational work on anions has thus far included studies of CH2CN-, C3H-, and is currently ongoing for similar systems.

physics.chem-ph↗

arXiv2013

Singlet Excited States of Anions with Higher Main Group Elements

Previous studies have shown that dipole-bound excited states exist for certain small anions. However, valence excited states have been reported for some closed-shell anions, but those with singlet valence excited states have, thus far, contained a single silicon atom. This work utilizes high-level coupled cluster theory previously shown to reproduce excited state energies to better than 0.1 eV compared with experiment in order to examine the electronic excited state properties of anions containing silicon and other higher main group atoms as well as their first row analogues. Of the fourteen anions involved in this study, nine possess bound excited states of some kind: CH$_2$SN$^-$, C$_3$H$^-$, CCSiH$^-$, CCSH$^-$, CCNH$_2^-$, CCPH$_2^-$, BH$_3$PH$_2^-$, AlH$_3$NH$_2^-$, and AlH$_3$PH$_2^-$. Two possess clear valence states: CCSiH$^-$ and its first row analogue C$_3$H$^-$. Substantial mixing appears to be present in the valence and dipole-bound characters for the first excited state wavefunctions of many of the systems reporting excited states, but the mixing is most pronounced with the ammonia borane-like AlH$_3$NH$_2^-$, and AlH$_3$PH$_2^-$ anions. Inclusion of second row atoms in anions whose corresponding radical is strongly dipolar increases the likelihood for the existence of excited states of any kind, but among the systems considered to date with this methodology, only the nature of group 14 atoms in small, closed-shell anions has yet been shown to allow valence singlet excited states.

physics.chem-ph↗