SearcharxivSearch

arXiv subjects

Debanjan Bose

Publications and source records attributed to Debanjan Bose.

At least 19 recordsLinked to original sources

Revisiting neutrino event epochs for the blazar PKS 0735+178 with TESS

We present here the results of the optical light curve variability analysis of the blazars PKS 0735+178, in weeks-scale flare state, observed in three sectors with the Transiting Exoplanet Survey Satellite (TESS). The TESS observations in this study coincide with a well-known neutrino emission phase detected with four different neutrino observatories at multiple epochs in a narrow time window. We segmented the rising and decaying parts of the flare and individually analyzed their flux distribution, excess variance, variability timescale, and the power spectral density (PSD). The source displayed an elevated excess variance of ~25%, with a multi-modal flux distribution (coherent in the rising and distorted in the decaying phase). The variability timescale analysis highlights a much faster decay than the rising scale, and the PSDs depict a nominal change in the power spectral slope. We discuss a likely connection in the optical variations and the neutrino events, and briefly explain a possible physical scenario for the observed optical flux behavior in view of previously discovered radio-band results.

astro-ph.HE

Observation of Wobbling and Precessing Jet Signatures in Gamma-Ray Emission from Blazar PKS 1424-41

We report a clear observational evidence for jet precession and nutation manifested in the gamma-ray emissions of the blazar PKS 1424$-$41. An analysis of $\sim$16 yr of \emph{Fermi}-LAT observations reveals three distinct and superimposed quasi-periodic oscillations (QPOs), with characteristic timescales of $\sim$5.26 yr, $\sim$0.96 yr and $\sim$1.3 yr. The longer timescale is detected with a local significance of $\sim 4.1\sigma$ ($99.9958\%$ confidence) and a global significance of $\sim 2.45\sigma$ ($98.5714\%$ confidence). The shorter timescales ($\sim 0.96$ yr and $\sim 1.3$ yr) both show local significances exceeding $3\sigma$. To interpret the origin of these modulations, we examine two physically motivated scenarios: Lense-Thirring precession of a misaligned accretion disk and orbital-driven jet precession in a binary supermassive black hole (BSBH) system. We model the gamma-ray variability using a compound framework that incorporates jet precession together with intrinsic jet rotation (nutation), which successfully reproduces the observed year-like QPOs. Our results indicate that the long-term, persistent $\sim$5.26 yr oscillation is most consistent with a BSBH origin, while the shorter year-like QPO modulation can be naturally attributed to rotation or wobbling of the jet axis. If PKS 1424$-$41 hosts a supermassive black hole binary, it represents a promising target for future space-borne gravitational-wave observatories such as the Laser Interferometer Space Antenna (LISA), providing an independent probe of supermassive black hole binaries.

astro-ph.HE

Neutrino mass ordering from the next Galactic supernova at DUNE, HK, and JUNO

The next Galactic core-collapse supernova (CCSN) will offer a unique opportunity to determine the neutrino mass ordering. We focus on two observables: the electron neutrino ($\nu_e$) neutronization burst and the rise-time of the electron antineutrino ($\bar{\nu}_e$) flux during the accretion phase. The neutronization burst, a sharp $\nu_e$ peak within $\sim 20$-$30$ ms, provides a clean and robust signature of mass ordering through its appearance or disappearance. During the accretion phase, the faster rise of heavy lepton flavor neutrinos ($\nu_x$) leads to a distinct faster rise-time behavior of the oscillated $\bar{\nu}_e$ signal, resulting in mass ordering discrimination. Using realistic CCSN simulations for multiple progenitor masses, we compute event rates and perform a statistical analysis for a Galactic ($10$~kpc) CCSN event at DUNE, Hyper-Kamiokande (HK), and JUNO detectors. The neutronization burst remains largely independent of SN hydrodynamic simulation models, with DUNE and HK achieving $\gtrsim 6\sigma$ and $\gtrsim 4\sigma$ sensitivity for normal (NO) to inverted ordering (IO) discrimination, respectively. However, the rise-time observable is prone to progenitor degeneracies. To mitigate this cumulative and ratio-based observables constructed at characteristic timescales ($20$ ms & $100$ ms) are used. The resulting confidence levels from the rise-time analysis to discriminate IO/NO in HK and JUNO are $\sim 5\sigma$ and $\sim 3\sigma$, respectively. Our results highlight the complementarity of detectors and observables, and demonstrate that combining neutronization burst and accretion phase information will be crucial for a definitive determination of the neutrino mass ordering in the next Galactic supernova.

hep-ph

Hadronic Emissions from the Microquasar V4641 Sgr, SS433, and its implications in the Diffuse Galactic Emission

Microquasars (MQs) are Galactic binary systems, consisting of a star and a compact object, a neutron star or a stellar mass black hole, which accretes matter from its companion star and gives rise to relativistic jets. Recent detection of very-high-energy (VHE; $E \gtrsim 100,\text{GeV}$) and ultra-high-energy (UHE; $E \gtrsim 100,\text{TeV}$) gamma-rays by LHAASO, HAWC and HESS from the MQ V4641 Sgr and SS 433 suggests them as Galactic PeVatrons. In this work, we studied a hadronic origin of the observed TeV-PeV gamma-ray emission from these MQs. We considered the hadronic scenario where the gamma-rays are produced by the interaction of relativistic protons in the MQ jet with the stellar wind. We fitted our model with observed data and constrained physical parameters like the hadronic jet power fraction, the proton spectral index, the maximum proton energy and the jet bulk Lorentz factor. Our best-fit model shows hard proton spectra ($1.84-2.44$) and maximum proton energies between 1 and 5 PeV. We also estimated the all-flavor neutrino fluxes corresponding to the gamma-ray fluxes from the hadronic model and found that V4641 sgr can be detected by next-generation neutrino telescopes like KM3NeT-ARCA and TRIDENT. Furthermore, we modeled a synthetic population of Galactic MQs and estimated their contribution to the diffuse TeV-PeV gamma-ray flux. For the inner Galaxy PSR contribution dominates in the range 10-100 TeV, and above 100 TeV diffused cosmic ray interactions with the molecular clouds is most dominant. We find that a population $\sim 14$ MQs is required to explain the LHAASO data above 100 TeV. For the outer Galaxy, we show that MQs are the dominant class of sources, and we constrain their population $\sim$14. Our findings strongly suggest that MQs are efficient particle accelerators, contributing to Galactic PeVatrons and potential multimessenger sources in our Galaxy.

astro-ph.HE

Broadband Spectral Modeling of Blazars: Constraining the Lorentz Factor and Gamma-Ray Emission Site

We present a comprehensive temporal and spectral analysis of a few blazars using multi-wavelength observations. Rapid flux variations are quantified via the doubling/halving timescale method, revealing the shortest variability timescales of a few hours in $\gamma$-ray emissions. The broadband fractional variability is systematically computed and examined as a function of frequency, displaying a characteristic double-hump structure akin to the typical spectral energy distribution (SED) of blazars. To distinguish between different emission states, we utilize the Bayesian block algorithm, which effectively identifies distinct flux states for targeted spectral modeling. A one-zone leptonic emission framework is employed to model the broadband emission during these states. The minimum Doppler factors are estimated based on the shortest variability timescales observed in the $\gamma$-ray emissions. Under the external Compton scenario, we constrain the location of the gamma-ray emitting region and the Lorentz factor using three physical conditions: the upper limit on the jet collimation parameter, $\Gamma \theta < 1$; the upper limit on the synchrotron self-Compton contribution, $L_{\mathrm{SSC}} \lesssim L_X$; and the observational constraint on the cooling break energy, $E_{\mathrm{cool, obs}} \lesssim 100$ MeV.

astro-ph.HE

A White Paper on The Multi-Messenger Science Landscape in India

The multi-messenger science using different observational windows to the Universe such as Gravitational Waves (GWs), Electromagnetic Waves (EMs), Cosmic Rays (CRs), and Neutrinos offer an opportunity to study from the scale of a neutron star to cosmological scales over a large cosmic time. At the smallest scales, we can explore the structure of the neutron star and the different energetics involved in the transition of a pre-merger neutron star to a post-merger neutron star. This will open up a window to study the properties of matter in extreme conditions and a guaranteed discovery space. On the other hand, at the largest cosmological scales, multi-messenger observations allow us to study the long-standing problems in physical cosmology related to the Hubble constant, dark matter, and dark energy by mapping the expansion history of the Universe using GW sources. Moreover, the multi-messenger studies of astrophysical systems such as white dwarfs, neutron stars, and black holes of different masses, all the way up to a high redshift Universe, will bring insightful understanding into the physical processes associated with them that are inaccessible otherwise. This white paper discusses the key cases in the domain of multi-messenger astronomy and the role of observatories in India which can explore uncharted territories and open discovery spaces in different branches of physics ranging from nuclear physics to astrophysics.

astro-ph.HE

Comprehensive Variability Analysis of Blazars Using Fermi Light Curves Across Multiple Timescales

In this study, we conducted a systematic analysis of long-term Fermi-LAT \gamma-ray data for a sample of blazars, including FSRQs, BL\,Lacs, and BCUs, to investigate their $\gamma$-ray variability. We focused on light curves binned in 3-, 7-, and 30-day intervals to assess the impact of binning, using data with TS >4 as a detection threshold. We calculated fractional variability ($F_{\rm var}$) for each category and found that FSRQs exhibit higher mean variability compared to BL\,Lacs and BCUs, with BCUs displaying intermediate variability closer to BL\,Lacs. The KS test on the variability distributions indicates that FSRQs differ from both BL Lacs and BCUs, whereas BCUs are more similar to BL Lacs. The higher variability in FSRQs is likely linked to more powerful jets and accretion. The correlation between \gamma-ray flux and spectral index suggests a moderate positive correlation for BL Lacs and BCUs, indicating a "softer when brighter" behavior. FSRQs displayed a mild anticorrelation, suggesting these sources tend to become harder as their flux increases. Analysis of flux distributions revealed log-normal behavior in many sources, consistent with multiplicative variability in blazar jets. Some sources show bimodal distributions, implying transitions between emission states. Binning affects the observed variability, with longer bins smoothing short-term fluctuations. Power spectral density analysis suggests FSRQs exhibit steeper slopes, reflecting structured variability, while BL Lacs display shallower slopes, dominated by stochastic processes. The absence of PSD breaks suggests no dominant timescale within the Fermi window. Spectral index distributions further highlight complexity, often requiring multi-component models.

astro-ph.HE

Exploring Year-timescale Gamma-ray Quasi-Periodic Oscillations in Blazars: Evidence for Supermassive Binary Black Holes Scenario

A comprehensive analysis of quasi-periodic oscillations (QPOs) in the gamma-ray emissions of blazars. Utilizing 15 years of Fermi-LAT observations of seven blazars in our sample, we identify both long-term and transient quasi-periodic oscillations in the gamma-ray light curves, with timescales ranging from a few months to years. These periodicities were detected using the Lomb-Scargle periodogram and REDFIT techniques. To robustly evaluate the statistical significance of the quasi-periodic signals observed in the Lomb-Scargle Periodograms, 30,000 synthetic $\gamma$-ray light curves were generated for each source using a stochastic model known as the Damped Random Walk (DRW) process. To investigate the physical origin of the observed gamma-ray QPOs with different timescales, we explore several plausible scenarios, with particular emphasis on a relativistic jet hosted by one of the black holes in a supermassive binary black hole system, jet precession, and helical motion of magnetized plasma blob within the jet. The $\gamma$-ray light curves exhibiting long-timescale quasi-periodic oscillations (QPOs) are analyzed within the framework of a supermassive binary black hole (SMBBH) model, employing a Markov Chain Monte Carlo (MCMC) approach, allowing us to constrain key physical parameters such as the jet Lorentz factor ($\Gamma$) and the viewing angle between the observer's line of sight ($\psi$) relative to the spin axis of SMBH.

astro-ph.HE

Searching for quasi periodic oscillations in optical and $\gamma$-ray emissions $\&$ black hole mass estimation of blazar ON 246

We report the detection of a potential quasi-periodic signal with a period of $\sim2$ years in the blazar ON 246, based on Fermi-LAT ($\gamma$-rays) and ASAS-SN (optical) observations spanning 11.5 years (MJD 55932-60081). We applied various techniques to investigate periodic signatures in the light curves, including the Lomb-Scargle periodogram (LSP), Weighted Wavelet Z-transform (WWZ), and REDFIT. The significance of the signals detected in LSP and WWZ was assessed using two independent approaches: Monte Carlo simulations and red noise modeling. Our analysis revealed a dominant peak in the $\gamma$-ray and optical light curves, with a significance level exceeding 3$\sigma$ in both LSP and WWZ, consistently persisting throughout the observation period. Additionally, the REDFIT analysis confirmed the presence of a quasi-periodic signal at $\sim$0.00134 $day^{-1}$ with a 99% confidence threshold. To explain the observed quasi-periodic variations in $\gamma$-ray and optical emissions, we explored various potential physical mechanisms. Our analysis suggests that the detected periodicity could originate from a supermassive binary black hole (SMBBH) system or the jet-induced orbital motion within such a system. Based on variability characteristics, we estimated the black hole mass of ON 246. The study suggests that the mass lies within the range of approximately $(0.142 - 8.22) \times 10^9 \ M_{\odot}$.

astro-ph.HE

Study of Multi-Wavelength Variability, Emission Mechanism and Quasi-Periodic Oscillation for Transition Blazar S5 1803+784

This work present the results of a multi-epoch observational study of the blazar S5\,1803+784, carried out from 2019 to 2023. The analysis is based on simultaneous data obtained from the Swift/UVOT/XRT, ASAS-SN, and Fermi-LAT instruments. A historically high $\gamma$-ray flux observed for this source on march 2022 ($\mathrm{2.26\pm0.062)\times10^{-6}~phcm^{-2}s^{-1}}$. This study investigates the $\gamma$-ray emission from a blazar, revealing a dynamic light curve with four distinct flux states: quiescent and high-flux by using the Bayesian Blocks (BB) algorithm. A potential transient quasi-periodic signal with an oscillation timescale of $\sim$411 days was identified, showing a local significance level surpassing 99.7$\%$ from the Lomb-Scargle Periodogram (LSP) and Damped Random Walk (DRW) analysis and exceeds 99.5$\%$ from the Weighted Wavelet Z-Transform (WWZ) analysis. The observed QPO was confirmed through an autoregressive process (AR(1)), with a significance level exceeding 99$\%$, suggesting a potential physical mechanism for such oscillations involves a helical motion of a magnetic plasma blob within the relativistic jet. Log parabola modeling of the $\gamma$-ray spectrum revealed a photon index ($\alpha_\gamma$) variation of 1.65$\pm$0.41 to 2.48$\pm$0.09 with a steepening slope, potentially indicative of particle cooling, changes in radiative processes, or modifications in the physical parameters. The $\alpha_\gamma$ of 2.48$\pm$0.09 may hint at an evolutionary transition state from BL\,Lac to FSRQ. A comparative analysis of variability across different energy bands reveals that Optical/UV and GeV emissions display greater variability compared to X-rays. Broadband SED modeling shows that within a one-zone leptonic framework, the SSC model accurately reproduces flux states without external Compton contributions, highlighting magnetic fields crucial role.

astro-ph.HE

Signature of hadronic emission in gamma-ray spectrum of B2 1308+326

The Flat Spectrum Radio Quasar (FSRQ) B2\,1308+326 was in its highest $\gamma$-ray flaring state during 60260-60310\,MJD. During this period, the source was detected in very high energy (VHE) by the large-sized telescope (LST-1). We conducted a detailed broadband spectral study of this source using the simultaneous data available in optical/UV, X-ray, and $\gamma$-ray bands. For the broadband spectral study, we select two gamma-ray high flux states (59750-59800\,MJD, 60260-60310\,MJD) and one low flux state (59250-59320\,MJD). During the epochs, 59750-59800\,MJD (high flux state) and 59250-59320\,MJD (low flux state), the broadband spectral energy distribution (SED) is well fitted using one zone leptonic emission model involving synchrotron, synchrotron self Compton (SSC) and external Compton (EC) processes. However, the flaring state (60260-60310\,MJD) during which the source showed VHE emission requires an additional component. We show that the inclusion of the photo-meson process can successfully explain this excess $\gamma$-ray emission. Further the estimated parameters, also suggest the source is transparent to VHE gamma-rays against pair production process.

astro-ph.HE

Microquasars to AGNs: An uniform Jet variability

The long-term variability study over a range of black hole (BH) mass systems from the microquasars of stellar-mass black holes to the Active Galactic Nuclei (AGNs) of supermassive black holes, in $\gamma$-rays offers new insights into the physics of relativistic jets. In this work, we investigate the $\gamma$-ray variability of 11 AGNs--including 7 blazars, 2 unclassified blazar candidates (BCUs), 1 radio galaxy (RG), and 1 narrow-line Seyfert 1 galaxy (NLS1) as well as 2 microquasars. We apply a stochastic process known as the Damped Random Walk (DRW) to model the $\sim$15 years of Fermi-LAT light curves. The characteristic timescales observed for AGNs are comparable to those in the accretion disc. Interestingly, the timescales observed in the jet emission of microquasars are similar to those of AGNs, suggesting uniform jet properties across the black hole masses. The observed rest-frame timescales of AGNs overlap with both thermal and non-thermal timescales associated with the jet and accretion disk, respectively, suggesting a scaled relationship between $\tau_{DRW}^{rest}$ and black hole mass ($\rm{M_{BH}}$). While the timescales observed for microquasars deviate significantly from this relationship, nonetheless exhibit a scaled $\tau_{DRW}^{rest}-\rm{M_{BH}}$ relationship using $\gamma$-rays specifically. These findings offer new insights into the origin of jets and the processes driving the emission within them. Additionally, this study hints at a new perspective that the relativistic jets' properties or their production mechanisms may be independent of the black hole mass.

astro-ph.HE

Detection of a Transient Quasi-periodic Oscillation in $\gamma$-Rays from Blazar PKS 2255-282

We conducted a comprehensive variability analysis of the blazar PKS 2255-282 using Fermi-LAT observations spanning over four years, from MJD 57783.5 to 59358.5. Our analysis revealed a transient quasi-periodic oscillation (QPO) with a period of 93$\pm$2.6 days. We employed a variety of Fourier-based methods, including the Lomb-Scargle Periodogram (LSP) and Weighted Wavelet Z-Transform (WWZ), as well as time domain analysis techniques such as Seasonal and Non-Seasonal Autoregressive Integrated Moving Average (ARIMA) models and the Stochastic modeling with Stochastically Driven Damped Harmonic Oscillator (SHO) models. Consistently, the QPO with a period of 93 days was detected across all methods used. The observed peak in LSP and time-averaged WWZ plots has a significance level of 4.06$\sigma$ and 3.96$\sigma$, respectively. To understand the source of flux modulations in the light curve, we explored various physical models. A plausible scenario involves the precession of the jet with a high Lorentz factor or the movement of a plasma blob along a helical trajectory within the relativistic jet.

astro-ph.HE

Detection of gamma-ray quasi-periodic oscillations in non-blazar AGN PKS 0521-36

Quasi-periodic oscillations (QPOs) have been detected in many Fermi-detected bright blazars. In this letter, we report multiple QPOs detected in a non-blazar AGN PKS 0521-36 searched over the entire 15 years of Fermi-LAT data. QPOs are detected at 268 days, at 295 days, and at 806 days timescales with more than 3$\sigma$ significance. The QPO detected at 806 days happens to be the third harmonic of QPO at 268 days. The time scales are consistent in both Lomb-Scargle and Wavelet analysis. Furthermore, the Gaussian Process modeling of the light curve is performed with stochastically driven damped harmonic oscillator (SHO) and damped random walk (DRW) modeling to uncover the presence of QPOs. The constructed power spectral density (PSD) exhibits two QPOs, with observed timescales of approximately 283 days and 886 days. This is the first non-blazar AGN where the long-term QPO is detected. Earlier studies show this source has a weak beamed jet. The exact cause for these QPOs remains unclear. We also assembled the $\gamma$-ray QPO detected in various blazar and tested the QPO time scale dependent on the black hole mass. No significant correlation is found.

astro-ph.HE

Gravitational memory signal from neutrino self-interactions in supernova

Neutrinos with large self-interactions, arising from exchange of light scalars or vectors with mass $M_\phi\simeq 10{\rm MeV}$, can play a useful role in cosmology for structure formation and solving the Hubble tension. It has been proposed that large self-interactions of neutrinos may change the observed properties of supernova like the neutrino luminosity or the duration of the neutrino burst. In this paper, we study the gravitational wave memory signal arising from supernova neutrinos. Our results reveal that memory signal for self-interacting neutrinos are weaker than free-streaming neutrinos in the high frequency range. Implications for detecting and differentiating between such signals for planned space-borne detectors, DECIGO and BBO, are also discussed.

gr-qc

Probing the disc-jet coupling in S4 0954+65, PKS 0903-57, & 4C +01.02 with $γ$-rays

We present a comprehensive variability study on three blazars, S4 0954+65, PKS 0903-57, and 4C +01.02 covering a mass range of log(M/M$_{\odot}$) = 8--9, by using $\sim$15 years-long $γ$-ray light curves from \textit{Fermi}-LAT. The variability level is characterized by the fractional variability amplitude which is higher for $γ$-rays compared to optical/UV and X-rays emissions. A power spectral density (PSD) study and damped random walk (DRW) modeling are done to probe the characteristic timescale. The PSD is fitted with a single power-law (PL) and bending power-law models and the corresponding success fraction was estimated. In the case of PKS 0903-57, We observed a break in the $γ$-ray PSD at 256 days which is comparable to the viscous timescale in the accretion disc suggesting a possible disk-jet coupling. The non-thermal damping timescale from the DRW modeling is compared with the thermal damping timescale for AGNs including our three sources. Our sources lie on the best-fit of the $\mathrm{τ^{rest}_{damping}} - M_{BH}$ plot derived for AGN suggesting a possible accretion disc-jet connection. If the jet's variability is linked to the disc's variability, we expect a log-normal flux distribution, often connected to the accretion disc's multiplicative processes. Our study observed a double log-normal flux distribution, possibly linked to long and short-term variability from the accretion disk and the jet. In summary, PSD and DRW modeling results for these three sources combined with blazars and AGNs studied in literature favor a disc-jet coupling scenario. However, more such studies are needed to refine this understanding.

astro-ph.HE

Quasi-periodic oscillation detected in $γ$-rays in blazar PKS 0346-27

We present a variability study of the blazar PKS 0346-27 from December 2018 to January 2022 in its archival $γ$-ray observation by Fermi-LAT. We use the Lomb-Scargle periodogram and the weighted wavelet transform methods in order to detect the presence of periodicity/quasi-periodicity and localize this feature in time and frequency space. The significance of the periodicity feature has been estimated using the Monte-Carlo simulation approach. We have also determined the global significance of the periodicity to test the robustness of our claim. To explore the most probable scenario, we modeled the light curve with both a straight jet and a curved jet model. We detect a periodicity feature of $\sim$ 100 days duration for the entire period of observation with a statistical significance of $3σ$, which amounts to a 99.7\% confidence level. The global significance of this feature is found to be 96.96\%. Based on the Akaike Information Criteria, the most probable explanation is that the observed emission is enhanced due to the helical motion of a blob within a curved jet. The origin of this QPO is very likely a region of enhanced emission moving helically inside a curved jet. This work presents strong evidence for jet curvature in the source and an independent (albeit a little serendipitous) procedure to estimate the curvature in blazar jets.

astro-ph.HE

Multi-wavelength study of TeV blazar 1ES 1218+304 using gamma-ray, X-ray and optical observations

We report the multi-wavelength study for a high-synchrotron-peaked BL Lac 1ES 1218+304 using near-simultaneous data obtained during the period from January 1, 2018, to May 31, 2021 (MJD 58119-59365) from various instruments including Fermi-LAT, Swift-XRT, AstroSat, and optical from Swift-UVOT $\&$ TUBITAK observatory in Turkey. The source was reported to be flaring in TeV $γ$-ray band during 2019, but no significant variation is observed with Fermi-LAT. A sub-hour variability is seen in the SXT light curve, suggesting a compact emission region for their variability. However, hour scale variability is observed in the $γ$-ray light curve. A "softer-when-brighter" trend is observed in $γ$-rays, and an opposite trend is seen in X-rays suggesting both emissions are produced via two different processes as expected from an HBL source. We have chosen the two epochs in January 2019 to study and compare their physical parameters. A joint fit of SXT and LAXPC provides a constraint on the synchrotron peak, roughly estimated to be $\sim$1.6 keV. A clear shift in the synchrotron peak is observed from $\sim$1 keV to above 10 keV revealing its extreme nature or behaving like an EHBL-type source. The optical observation provides color-index variation as "blue-when-brighter". The broadband SED is fitted with a single-zone SSC model, and their parameters are discussed in the context of a TeV blazar and the possible mechanism behind the broadband emission.

astro-ph.HE