arXiv subjects

L. Stella

Publications and source records attributed to L. Stella.

At least 37 records · Page 2Linked to original sources

arXiv2020

The X-ray outburst of the Galactic Center magnetar over six years of Chandra observations

The magnetar SGR J1745-2900 discovered at parsecs distance from the Milky Way central black hole, Sagittarius A*, represents the closest pulsar to a supermassive black hole ever detected. Furthermore, its intriguing radio emission has been used to study the environment of the black hole, as well as to derive a precise position and proper motion for this object. The discovery of SGR J1745-2900 has opened interesting debates about the number, age and nature of pulsars expected in the Galactic center region. In this work, we present extensive X-ray monitoring of the outburst of SGR J1745-2900 using the Chandra X-ray Observatory, the only instrument with the spatial resolution to distinguish the magnetar from the supermassive black hole (2.4" angular distance). It was monitored from its outburst onset in April 2013 until August 2019, collecting more than fifty Chandra observations for a total of more than 2.3 Ms of data. Soon after the outburst onset, the magnetar emission settled onto a purely thermal emission state that cooled from a temperature of about 0.9 to 0.6 keV over 6 years. The pulsar timing properties showed at least two changes in the period derivative, increasing by a factor of about 4 during the outburst decay. We find that the long-term properties of this outburst challenge current models for the magnetar outbursts.

astro-ph.HE↗

arXiv2020

Search for the optical counterpart of the GW170814 gravitationalwave event with the VLT Survey Telescope

We report on the search for the optical counterpart of the gravitational event GW170814, which was carried out with the VLT Survey Telescope (VST) by the GRAvitational Wave Inaf TeAm (GRAWITA). Observations started 17.5 hours after the LIGO/Virgo alert and we covered an area of 99 deg$^2$ that encloses $\sim 77\%$ and $\sim 59\%$ of the initial and refined localization probability regions, respectively. A total of six epochs were secured over nearly two months. The survey reached an average limiting magnitude of 22 AB mag in the $r-$band. After assuming the model described in Perna et al. 2019 that derives as possible optical counterpart of a BBH event a transient source declining in about one day, we have computed a survey efficiency of about $5\%$. This paper describes the VST observational strategy and the results obtained by our analysis pipelines developed to search for optical transients in multi-epoch images. We report the catalogue of the candidates with possible identifications based on light-curve fitting. We have identified two dozens of SNe, nine AGNs, one QSO. Nineteen transients characterized by a single detection were not classified. We have restricted our analysis only to the candidates that fall into the refined localization map. None out of 39 left candidates could be positively associated with GW170814. This result implies that the possible emission of optical radiation from a BBH merger had to be fainter than r $\sim$ 22 ($L_{optical}$ $\sim$ $1.4 \times 10^{42}$ erg/s) on a time interval ranging from a few hours up to two months after the GW event.

astro-ph.HE↗

arXiv2020

The Ultraluminous X-ray sources population of the galaxy NGC 7456

Ultraluminous X-ray sources (ULXs) are a class of accreting compact objects with X-ray luminosities above 1e39 erg/s. The ULX population counts several hundreds objects but only a minor fraction is well studied. Here we present a detailed analysis of all ULXs hosted in the galaxy NGC 7456. It was observed in X-rays only once in the past (in 2005) by XMM-Newton, but the observation was short and strongly affected by high background. In 2018, we obtained a new, deeper (~90 ks) XMM-Newton observation that allowed us to perform a detailed characterization of the ULXs hosted in the galaxy. ULX-1 and ULX-2, the two brightest objects (Lx~(6-10)e39 erg/s), have spectra that can be described by a two-thermal component model as often found in ULXs. ULX-1 shows also one order of magnitude in flux variability on short-term timescales (hundreds to thousand ks). The other sources (ULX-3 and ULX-4) show flux changes of at least an order of magnitude, and these objects may be candidate transient ULXs although longer X-ray monitoring or further studies are required to ascribe them to the ULX population. In addition, we found a previously undetected source that might be a new candidate ULX (labelled as ULX-5) with a luminosity of ~1e39 erg/s and hard power-law spectral shape, whose nature is still unclear and for which a background Active Galactic Nucleus cannot be excluded. We discuss the properties of all the ULXs in NGC 7456 within the framework of super-Eddington accretion onto stellar mass compact objects. Although no pulsations were detected, we cannot exclude that the sources host neutron stars.

astro-ph.HE↗

arXiv2019

Pulsating in unison at optical and X-ray energies: simultaneous high-time resolution observations of the transitional millisecond pulsar PSR J1023+0038

PSR J1023+0038 is the first millisecond pulsar discovered to pulsate in the visible band; such a detection took place when the pulsar was surrounded by an accretion disk and also showed X-ray pulsations. We report on the first high time resolution observational campaign of this transitional pulsar in the disk state, using simultaneous observations in the optical (TNG, NOT, TJO), X-ray (XMM-Newton, NuSTAR, NICER), infrared (GTC) and UV (Swift) bands. Optical and X-ray pulsations were detected simultaneously in the X-ray high intensity mode in which the source spends $\sim$ 70% of the time, and both disappeared in the low mode, indicating a common underlying physical mechanism. In addition, optical and X-ray pulses were emitted within a few km, had similar pulse shape and distribution of the pulsed flux density compatible with a power-law relation $F_ν \propto ν^{-0.7}$ connecting the optical and the 0.3-45 keV X-ray band. Optical pulses were detected also during flares with a pulsed flux reduced by one third with respect to the high mode; the lack of a simultaneous detection of X-ray pulses is compatible with the lower photon statistics. We show that magnetically channeled accretion of plasma onto the surface of the neutron star cannot account for the optical pulsed luminosity ($\sim 10^{31}$ erg/s). On the other hand, magnetospheric rotation-powered pulsar emission would require an extremely efficient conversion of spin-down power into pulsed optical and X-ray emission. We then propose that optical and X-ray pulses are instead produced by synchrotron emission from the intrabinary shock that forms where a striped pulsar wind meets the accretion disk, within a few light cylinder radii away, $\sim$ 100 km, from the pulsar.

astro-ph.HE↗

arXiv2019

Detailed X-ray spectroscopy of the magnetar 1E 2259+586

Magnetic field geometry is expected to play a fundamental role in magnetar activity. The discovery of a phase-variable absorption feature in the X-ray spectrum of SGR 0418+5729, interpreted as cyclotron resonant scattering, suggests the presence of very strong non-dipolar components in the magnetic fields of magnetars. We performed a deep XMM-Newton observation of pulsar 1E 2259+586, to search for spectral features due to intense local magnetic fields. In the phase-averaged X-ray spectrum, we found evidence for a broad absorption feature at very low energy (0.7 keV). If the feature is intrinsic to the source, it might be due to resonant scattering/absorption by protons close to star surface. The line energy implies a magnetic field of ~ 10^14 G, roughly similar to the spin-down measure, ~ 6x10^13 G. Examination of the X-ray phase-energy diagram shows evidence for a further absorption feature, the energy of which strongly depends on the rotational phase (E >~ 1 keV ). Unlike similar features detected in other magnetar sources, notably SGR 0418+5729, it is too shallow and limited to a small phase interval to be modeled with a narrow phase-variable cyclotron absorption line. A detailed phase-resolved spectral analysis reveals significant phase-dependent variability in the continuum, especially above 2 keV. We conclude that all the variability with phase in 1E 2259+586 can be attributed to changes in the continuum properties which appear consistent with the predictions of the Resonant Compton Scattering model.

astro-ph.HE↗

arXiv2019

The multi-outburst activity of the magnetar in Westerlund I

After two major outbursts in 2006 and 2011, on 2017 May 16 the magnetar CXOU J164710.2-455216, hosted within the massive star cluster Westerlund I, emitted a short (20 ms) burst, which marked the onset of a new active phase. We started a long-term monitoring campaign with Swift (45 observations), Chandra (5 observations) and NuSTAR (4 observations) from the activation until 2018 April. During the campaign, Swift BAT registered the occurrence of multiple bursts, accompanied by two other enhancements of the X-ray persistent flux. The long time span covered by our observations allowed us to study the spectral as well as the timing evolution of the source. After 11 months since the 2017 May outburst onset, the observed flux was about 15 times higher than its historical minimum level and a factor of 3 higher than the level reached after the 2006 outburst. This suggests that the crust has not fully relaxed to the quiescent level, or that the source quiescent level has changed following the multiple outburst activities in the past 10 years or so. This is another case of multiple outbursts from the same source on a yearly time scale, a somehow recently discovered behaviour in magnetars.

astro-ph.HE↗

arXiv2018

Optical pulsations from a transitional millisecond pulsar

Weakly magnetic, millisecond spinning neutron stars attain their very fast rotation through a 1E8-1E9 yr long phase during which they undergo disk-accretion of matter from a low mass companion star. They can be detected as accretion-powered millisecond X-ray pulsars if towards the end of this phase their magnetic field is still strong enough to channel the accreting matter towards the magnetic poles. When mass transfer is much reduced or ceases altogether, pulsed emission generated by particle acceleration in the magnetosphere and powered by the rotation of the neutron star is observed, preferentially in the radio and gamma-ray bands. A few transitional millisecond pulsars that swing between an accretion-powered X-ray pulsar regime and a rotationally-powered radio pulsar regime in response to variations of the mass in-flow rate have been recently identified. Here we report the detection of optical pulsations from a transitional pulsar, the first ever from a millisecond spinning neutron star. The pulsations were observed when the pulsar was surrounded by an accretion disk and originated inside the magnetosphere or within a few hundreds of kilometres from it. Energy arguments rule out reprocessing of accretion-powered X-ray emission and argue against a process related to accretion onto the pulsar polar caps; synchrotron emission of electrons in a rotation-powered pulsar magnetosphere seems more likely.

astro-ph.HE↗

arXiv2018

Unveiling the enigma of ATLAS17aeu

Aim. The unusual transient ATLAS17aeu was serendipitously detected within the sky localisation of the gravitational wave trigger GW170104. The importance of a possible association with gravitational waves coming from a binary black hole merger led to an extensive follow-up campaign, with the aim of assessing a possible connection with GW170104. Methods. With several telescopes, we carried out both photometric and spectroscopic observations of ATLAS17aeu, for several epochs, between $\sim 3$ and $\sim 230$ days after the first detection. Results. We studied in detail the temporal and spectroscopic properties of ATLAS17aeu and its host galaxy. We detected spectral features similar to those of a broad lined supernova superposed to an otherwise typical long-GRB afterglow. Based on analysis of the optical light curve, spectrum and host galaxy SED, we conclude that the redshift of the source is probably $z \simeq 0.5 \pm 0.2$. Conclusions. While the redshift range we have determined is marginally compatible with that of the gravitational wave event, the presence of a supernova component and the consistency of this transient with the E$_{\rm p}$-E$_{\rm iso}$ correlation support the conclusion that ATLAS17aeu was associated with the long gamma-ray burst GRB170105A. This rules out the association of the GRB170105A/ATLAS17aeu transient with the gravitational wave event GW170104, which was due to a binary black hole merger.

astro-ph.HE↗

arXiv2018

The magnetospheric radius of an inclined rotator in the magnetically threaded disk model

The estimate of the magnetospheric radius in a disk-fed neutron star X-ray binary is a long standing problem in high energy Astrophysics. We review the magnetospheric radius calculations in the so-called magnetically threaded disk model, comparing the simplified approach originally proposed by Ghosh & Lamb (1979) with the revised version proposed by Wang (1987), Wang (1995), and Wang (1997). We show that for a given set of fixed parameters (assuming also a comparable screening factor of the neutron star magnetic field by the currents induced on the disk surface) the revised magnetically threaded disk model predicts a magnetospheric radius that is significantly smaller than that derived from the Ghosh & Lamb (1979) treatment. For a fixed value of the neutron star magnetic field and a wide range of mass accretion rates, the inclusion of a large inclination angle between the neutron star rotation and magnetic field axes ($χ$$\gtrsim$60 deg) leads to a further decrease of the magnetospheric radius. To illustrate the relevance of these calculations, we consider, as an example, the case of the transitional pulsars. During the so-called "high mode" of their sub-luminous accretion disk state, these sources have shown X-ray pulsations interpreted as due to accretion at an unprecedented low luminosity level compared to other neutron stars in X-ray binaries. In the context of the magnetic threaded disk model, we show that accretion at luminosities of $\sim$10$^{33}$ erg s$^{-1}$ (and thus accretion-driven X-ray pulsations) can be more easily explained when the prescription of the magnetospheric radius provided by Wang (1997) is used. This avoids the need of invoking very strong propeller outflows in the transitional pulsars, as proposed in other literature works.

astro-ph.HE↗

arXiv2018

The first continuous optical monitoring of the transitional millisecond pulsar PSR J1023+0038 with Kepler

We report on the first continuous, 80 day optical monitoring of the transitional millisecond pulsar PSR J1023+0038 carried out in mid-2017 with Kepler in the K2 configuration, when an X-ray subluminous accretion disk was present in the binary. Flares lasting from minutes to 14 hr were observed for 15.6% of the time, which is a larger fraction than previously reported on the basis of X-ray and past optical observations, and more frequently when the companion was at the superior conjunction of the orbit. A sinusoidal modulation at the binary orbital period was also present with an amplitude of ~16%, which varied by a few percent over timescales of days, and with a maximum that took place 890 +/- 85 s earlier than the superior conjunction of the donor. We interpret these phenomena in terms of reprocessing of the X-ray emission by an asymmetrically heated companion star surface and/or a non-axisymmetric outflow possibly launched close to the inner Lagrangian point. Furthermore, the non-flaring average emission varied by up to ~ 40% over a time scale of days in the absence of correspondingly large variations of the irradiating X-ray flux. The latter suggests that the observed changes in the average optical luminosity might be due to variations of the geometry, size, and/or mass accretion rate in the outer regions of the accretion disk.

astro-ph.HE↗

arXiv2018

Characterization of the Infrared/X-ray sub-second variability for the black-hole transient GX 339-4

We present a detailed analysis of the X-ray/IR fast variability of the Black-Hole Transient GX 339-4 during its low/hard state in August 2008. Thanks to simultaneous high time-resolution observations made with the VLT and RXTE, we performed the first characterisation of the sub-second variability in the near-infrared band - and of its correlation with the X-rays - for a low-mass X-ray binary, using both time and frequency-domain techniques. We found a power-law correlation between the X-ray and infrared fluxes when measured on timescales of 16 seconds, with a marginally variable slope, steeper than the one found on timescales of days at similar flux levels. We suggest the variable slope - if confirmed - could be due to the infrared flux being a non-constant combination of both optically thin and optically thick synchrotron emission from the jet, as a result of a variable self-absorption break. From cross spectral analysis we found an approximately constant infrared time lag of $\approx$ 0.1s, and a very high coherence of $\approx$ 90 per cent on timescales of tens of seconds, slowly decreasing toward higher frequencies. Finally, we report on the first detection of a linear rms-flux relation in the emission from a low-mass X-ray binary jet, on timescales where little correlation is found between the X-rays and the jet emission itself. This suggests that either the inflow variations and jet IR emission are coupled by a non-linear or time-variable transform, or that the IR rms-flux relation is not transferred from the inflow to the jet, but is an intrinsic property of emission processes in the jet.

astro-ph.HE↗

arXiv2017

Spectroscopic identification of r-process nucleosynthesis in a double neutron star merger

The merger of two neutron stars is predicted to give rise to three major detectable phenomena: a short burst of gamma-rays, a gravitational wave signal, and a transient optical/near-infrared source powered by the synthesis of large amounts of very heavy elements via rapid neutron capture (the r-process). Such transients, named "macronovae" or "kilonovae", are believed to be centres of production of rare elements such as gold and platinum. The most compelling evidence so far for a kilonova was a very faint near-infrared rebrightening in the afterglow of a short gamma-ray burst at z = 0.356, although findings indicating bluer events have been reported. Here we report the spectral identification and describe the physical properties of a bright kilonova associated with the gravitational wave source GW 170817 and gamma-ray burst GRB 170817A associated with a galaxy at a distance of 40 Mpc from Earth. Using a series of spectra from ground-based observatories covering the wavelength range from the ultraviolet to the near-infrared, we find that the kilonova is characterized by rapidly expanding ejecta with spectral features similar to those predicted by current models. The ejecta is optically thick early on, with a velocity of about 0.2 times light speed, and reaches a radius of about 50 astronomical units in only 1.5 days. As the ejecta expands, broad absorption-like lines appear on the spectral continuum indicating atomic species produced by nucleosynthesis that occurs in the post-merger fast-moving dynamical ejecta and in two slower (0.05 times light speed) wind regions. Comparison with spectral models suggests that the merger ejected 0.03-0.05 solar masses of material, including high-opacity lanthanides.

astro-ph.HE↗

arXiv2017

GRAWITA: VLT Survey Telescope observations of the gravitational wave sources GW150914 and GW151226

We report the results of deep optical follow-up surveys of the first two gravitational-wave sources, GW150914 and GW151226, done by the GRAvitational Wave Inaf TeAm Collaboration (GRAWITA). The VLT Survey Telescope (VST) responded promptly to the gravitational-wave alerts sent by the LIGO and Virgo Collaborations, monitoring a region of $90$ deg$^2$ and $72$ deg$^2$ for GW150914 and GW151226, respectively, and repeated the observations over nearly two months. Both surveys reached an average limiting magnitude of about 21 in the $r-$band. The paper describes the VST observational strategy and two independent procedures developed to search for transient counterpart candidates in multi-epoch VST images. Several transients have been discovered but no candidates are recognized to be related to the gravitational-wave events. Interestingly, among many contaminant supernovae, we find a possible correlation between the supernova VSTJ57.77559-59.13990 and GRB150827A detected by {\it Fermi}-GBM. The detection efficiency of VST observations for different types of electromagnetic counterparts of gravitational-wave events are evaluated for the present and future follow-up surveys.

astro-ph.HE↗

arXiv2017

The transitional millisecond pulsar IGR J18245-2452 during its 2013 outburst at X-rays and soft gamma-rays

IGR~J18245--2452/PSR J1824--2452I is one of the rare transitional accreting millisecond X-ray pulsars, showing direct evidence of switches between states of rotation powered radio pulsations and accretion powered X-ray pulsations, dubbed transitional pulsars. IGR~J18245--2452 is the only transitional pulsar so far to have shown a full accretion episode, reaching an X-ray luminosity of $\sim10^{37}$~erg~s$^{-1}$ permitting its discovery with INTEGRAL in 2013. In this paper, we report on a detailed analysis of the data collected with the IBIS/ISGRI and the two JEM-X monitors on-board INTEGRAL at the time of the 2013 outburst. We make use of some complementary data obtained with the instruments on-board XMM-Newton and Swift in order to perform the averaged broad-band spectral analysis of the source in the energy range 0.4 -- 250~keV. We have found that this spectrum is the hardest among the accreting millisecond X-ray pulsars. We improved the ephemeris, now valid across its full outburst, and report the detection of pulsed emission up to $\sim60$ keV in both the ISGRI ($10.9 σ$) and Fermi/GBM ($5.9 σ$) bandpass. The alignment of the ISGRI and Fermi GBM 20 -- 60 keV pulse profiles are consistent at a $\sim25\ μ$s level. We compared the pulse profiles obtained at soft X-rays with \xmm\ with the soft \gr-ray ones, and derived the pulsed fractions of the fundamental and first harmonic, as well as the time lag of the fundamental harmonic, up to $150\ μ$s, as a function of energy. We report on a thermonuclear X-ray burst detected with \Integ, and using the properties of the previously type-I X-ray burst, we show that all these events are powered primarily by helium ignited at a depth of $y_{\rm ign} \approx 2.7\times10^8$ g cm${}^{-2}$. For such a helium burst the estimated recurrence time of $Δt_{\rm rec}\approx5.6$ d is in agreement with the observations.

astro-ph.HE↗

arXiv2017

Modelling a Bistable System Strongly Coupled to a Debye Bath: A Quasiclassical Approach Based on the Generalised Langevin Equation

Bistable systems present two degenerate metastable configurations separated by an energy barrier. Thermal or quantum fluctuations can promote the transition between the configurations at a rate which depends on the dynamical properties of the local environment (i.e., a thermal bath). In the case of classical systems, strong system-bath interaction has been successfully modelled by the Generalised Langevin Equation (GLE) formalism. Here we show that the efficient GLE algorithm introduced in Phys. Rev. B 89, 134303 (2014) can be extended to include some crucial aspects of the quantum fluctuations. In particular, the expected isotopic effect is observed along with the convergence of the quantum and classical transition rates in the strong coupling limit. Saturation of the transition rates at low temperature is also retrieved, in qualitative, yet not quantitative, agreement with the analytic predictions. The discrepancies in the tunnelling regime are due to an incorrect sampling close to the barrier top. The domain of applicability of the quasiclassical GLE is also discussed.

cond-mat.stat-mech↗

arXiv2017

Nonequilibrium Generalised Langevin Equation for the calculation of heat transport properties in model 1D atomic chains coupled to two 3D thermal baths

We use a Generalised Langevin Equation (GLE) scheme to study the thermal transport of low dimensional systems. In this approach, the central classical region is connected to two realistic thermal baths kept at two different temperatures [H. Ness et al., Phys. Rev. B {\bf 93}, 174303 (2016)]. We consider model Al systems, i.e. one-dimensional atomic chains connected to three-dimensional baths. The thermal transport properties are studied as a function of the chain length $N$ and the temperature difference $ΔT$ between the baths. We calculate the transport properties both in the linear response regime and in the non-linear regime. Two different laws are obtained for the linear conductance versus the length of the chains. For large temperatures ($T \gtrsim 500$ K) and temperature differences ($ΔT \gtrsim 500$ K), the chains, with $N > 18$ atoms, present a diffusive transport regime with the presence of a temperature gradient across the system. For lower temperatures($T \lesssim 500$ K) and temperature differences ($ΔT \lesssim 400$ K), a regime similar to the ballistic regime is observed. Such a ballistic-like regime is also obtained for shorter chains ($N \le 15 $). Our detailed analysis suggests that the behaviour at higher temperatures and temperature differences is mainly due to anharmonic effects within the long chains.

cond-mat.mes-hall↗

arXiv2017

An XMM-Newton and INTEGRAL view on the hard state of EXO 1745-248 during its 2015 outburst

CONTEXT - Transient low-mass X-ray binaries (LMXBs) often show outbursts lasting typically a few-weeks and characterized by a high X-ray luminosity ($L_{x} \approx 10^{36}-10^{38}$ erg/sec), while for most of the time they are found in X-ray quiescence ($L_X\approx10^{31} -10^{33}$ erg/sec). EXO 1745-248 is one of them. AIMS - The broad-band coverage, and the sensitivity of instrument on board of {\xmm} and {\igr}, offers the opportunity to characterize the hard X-ray spectrum during {\exo} outburst. METHODS - In this paper we report on quasi-simultaneous {\xmm} and {\igr} observations of the X-ray transient {\exo} located in the globular cluster Terzan 5, performed ten days after the beginning of the outburst (on 2015 March 16th) shown by the source between March and June 2015. The source was caught in a hard state, emitting a 0.8-100 keV luminosity of $\simeq10^{37}$~{\lumcgs}. RESULTS - The spectral continuum was dominated by thermal Comptonization of seed photons with temperature $kT_{in}\simeq1.3$ keV, by a cloud with moderate optical depth $τ\simeq2$ and electron temperature $kT_e\simeq 40$ keV. A weaker soft thermal component at temperature $kT_{th}\simeq0.6$--0.7 keV and compatible with a fraction of the neutron star radius was also detected. A rich emission line spectrum was observed by the EPIC-pn on-board {\xmm}; features at energies compatible with K-$α$ transitions of ionized sulfur, argon, calcium and iron were detected, with a broadness compatible with either thermal Compton broadening or Doppler broadening in the inner parts of an accretion disk truncated at $20\pm6$ gravitational radii from the neutron star. Strikingly, at least one narrow emission line ascribed to neutral or mildly ionized iron is needed to model the prominent emission complex detected between 5.5 and 7.5 keV. (Abridged)

astro-ph.HE↗

arXiv2017

An accreting pulsar with extreme properties drives an ultraluminous x-ray source in NGC 5907

Ultraluminous x-ray sources (ULXs) in nearby galaxies shine brighter than any X-ray source in our Galaxy. ULXs are usually modeled as stellar-mass black holes (BHs) accreting at very high rates or intermediate-mass BHs. We present observations showing that NGC5907 ULX is instead an x-ray accreting neutron star (NS) with a spin period evolving from 1.43~s in 2003 to 1.13~s in 2014. It has an isotropic peak luminosity of about 1000 times the Eddington limit for a NS at 17.1~Mpc. Standard accretion models fail to explain its luminosity, even assuming beamed emission, but a strong multipolar magnetic field can describe its properties. These findings suggest that other extreme ULXs (x-ray luminosity > 10^{41} erg/s) might harbor NSs.

astro-ph.HE↗