arXiv subjects

Ralf Ballhausen

Publications and source records attributed to Ralf Ballhausen.

At least 37 records · Page 2Linked to original sources

arXiv2025

XRISM insights for interstellar Sulfur

The X-ray Imaging Spectroscopy Mission (XRISM) provides the best spectral resolution with which to study Sulfur (S) K-shell photoabsorption features from the interstellar medium (ISM). For the first time, we demonstrate the high-signal detection of interstellar atomic SII K-beta absorption in the spectrum of X-ray binaries (XRBs) 4U 1630-472 and GX 340+0. The persistence of this feature across multiple instruments, targets, and flux states implies that it is interstellar in nature. We measure the SII Kbeta line centroid at 2470.8 +/- 1.1 eV after including systematic uncertainties. We also find that the most recently published high resolution SII absorption template requires a systematic energy scale shift of +7-8 eV, which is comparable to the level of disagreement among various atomic modeling procedures. The XRISM 300 ks observation of GX 340+0 provides unprecedented signal-to-noise in the S K region, and we find evidence of residual absorption from solid S in the spectra of GX 340+0. Absorption templates from three Fe-S compounds, troilite (FeS), pyrrhotite (Fe_7S_8) and pyrite (FeS_2), provide equally good fits to the residuals. Even though we are not able to distinguish among these three compounds, they provide equal estimates for the abundance of S locked in dust grains. Having accounted for both the gaseous and solid S in the GX 340+0 sightline provides us with a direct measurement of S depletion, which is 40% +/- 15%. Our depletion measurement provides an upper limit to the fraction of interstellar Fe bound in Fe-S compounds of < 25%, which is consistent with prior studies of Fe-S compounds via Fe L-shell absorption. Both XRBs in this study are at a distance of approximately 11 kpc and on the opposite side of the Galactic disk, suggesting that this value could represent the average S depletion of the Milky Way when integrated across all phases of the ISM.

astro-ph.GA↗

arXiv2025

Delving into the depths of NGC 3783 with XRISM. I. Kinematic and ionization structure of the highly ionized outflows

We present our study of the XRISM observation of the Seyfert-1 galaxy NGC 3783. XRISM's Resolve microcalorimeter has enabled, for the first time, a detailed characterization of the highly ionized outflows in this active galactic nucleus. Our analysis constrains their outflow and turbulent velocities, along with their ionization parameter ($ξ$) and column density ($N_{\rm H}$). The high-resolution Resolve spectrum reveals a distinct series of Fe absorption lines between 6.4 and 7.8 keV, ranging from Fe XVIII to Fe XXVI. At lower energies, absorption features from Si, S, and Ar are also detected. Our spectroscopy and photoionization modeling of the time-averaged Resolve spectrum uncovers six outflow components, five of which exhibit relatively narrow absorption lines with outflow velocities ranging from 560 to 1170 km/s. In addition, a broad absorption feature is detected, which is consistent with Fe XXVI outflowing at 14,300 km/s (0.05 $c$). The kinetic luminosity of this component is 0.8-3% of the bolometric luminosity. Our analysis of the Resolve spectrum shows that more highly ionized absorption lines are intrinsically broader than those of lower-ionization species, indicating that the turbulent velocity of the six outflow components (ranging from 0 to 3500 km/s) increases with $ξ$. Furthermore, we find that the $N_{\rm H}$ of the outflows generally declines with $ξ$ up to $\log ξ= 3.2$ but rises beyond this point, suggesting a complex ionization structure. The absorption profile of the Fe XXV resonance line is intriguingly similar to UV absorption lines (Ly$α$ and C IV) observed by the HST, from which we infer that the outflows are clumpy in nature. Our XRISM/Resolve results support a "hybrid wind" scenario in which the observed outflows have multiple origins and driving mechanisms. We explore various interpretations of our findings within AGN wind models.

astro-ph.HE↗

arXiv2025

XRISM Spectroscopy of the Stellar-Mass Black Hole 4U 1630-472 in Outburst

We report on XRISM/Resolve spectroscopy of the recurrent transient and well-known black hole candidate 4U 1630$-$472 during its 2024 outburst. The source was captured at the end of a disk-dominated high/soft state, at an Eddington fraction of $λ_\mathrm{Edd} \sim 0.05~(10 M_{\odot}/M_\mathrm{BH})$. A variable absorption spectrum with unprecedented complexity is revealed with the Resolve calorimeter. This marks one of the lowest Eddington fractions at which highly ionized absorption has been detected in an X-ray binary. The strongest lines are fully resolved, with He-like Fe XXV separated into resonance and intercombination components, and H-like Fe XXVI seen as a spin-orbit doublet. The depth of some absorption lines varied by almost an order of magnitude, far more than expected based on a 10% variation in apparent X-ray flux and ionization parameter. The velocity of some absorption components also changed significantly. Jointly modeling two flux segments with a consistent model including four photoionization zones, the spectrum can be described in terms of highly ionized but likely failed winds that sometimes show red-shifts, variable obscuration that may signal asymmetric structures in the middle and outer accretion disk, and a tentative very fast outflow ($v = 0.026-0.033c$). We discuss the impact of these findings on our understanding of accretion and winds in stellar-mass black holes, and potential consequences for future studies.

astro-ph.HE↗

arXiv2025

XRISM spectroscopy on orbital modulation of Fe Ly$α$ lines in Cygnus X-3

To understand physical processes such as mass transfer and binary evolution in X-ray binaries, the orbital parameters of the system are fundamental and crucial information. Cygnus X-3 is a high-mass X-ray binary composed of a compact object of unknown nature and a Wolf-Rayet star, which is of great interest in the context of wind-fed mass accretion and binary evolution. Here we present XRISM/Resolve high-resolution spectroscopy focusing on the Fe Ly$α$ lines in its hypersoft state. We perform an orbital phase-resolved spectral analysis of the lines to study the orbital modulation of the emission and absorption lines. It is found that the emission lines reflect the orbital motion of the compact object whose estimated velocity amplitude is $430^{~~+150}_{~~-140}~~\mathrm{km\,s^{~-1}}$, while the absorption lines show a variation that can be interpreted as originating from the stellar wind. We discuss possible mass ranges for the binary components using the mass function with the estimated value of the velocity amplitude in this work, combined with the relation between the mass loss rate and the orbital period derivative and the empirical mass and mass loss rate relation for Galactic Wolf-Rayet stars. They are constrained to be $(1.3\text{-}5.1)\,M_\odot$ and $(9.3\text{-}12)\,M_\odot$ for the assumed inclination angle of $i = 25$ deg, which becomes more relaxed to $(1.3\text{-}24)\,M_\odot$ and $(9.3\text{-}16)\,M_\odot$ for $i = 35$ deg, respectively. Thus, it remains unclear whether the system harbors a black hole or a neutron star.

astro-ph.HE↗

arXiv2025

Constraining gas motion and non-thermal pressure beyond the core of the Abell 2029 galaxy cluster with XRISM

We report a detailed spectroscopic study of the gas dynamics and hydrostatic mass bias of the galaxy cluster Abell 2029, utilizing high-resolution observations from XRISM Resolve. Abell 2029, known for its cool core and relaxed X-ray morphology, provides an excellent opportunity to investigate the influence of gas motions beyond the central region. Expanding upon prior studies that revealed low turbulence and bulk motions within the core, our analysis covers regions out to the scale radius $R_{2500}$ (670~kpc) based on three radial pointings extending from the cluster center toward the northern side. We obtain accurate measurements of bulk and turbulent velocities along the line of sight. The results indicate that non-thermal pressure accounts for no more than 2% of the total pressure at all radii, with a gradual decrease outward. The observed radial trend differs from many numerical simulations, which often predict an increase in non-thermal pressure fraction at larger radii. These findings suggest that deviations from hydrostatic equilibrium are small, leading to a hydrostatic mass bias of around 2% across the observed area.

astro-ph.CO↗

arXiv2025

XRISM forecast for the Coma cluster: stormy, with a steep power spectrum

The XRISM Resolve microcalorimeter array measured the velocities of hot intracluster gas at two positions in the Coma galaxy cluster: 3'x3' squares at the center and at 6' (170 kpc) to the south. We find the line-of-sight velocity dispersions in those regions to be sigma_z=208+-12 km/s and 202+-24 km/s, respectively. The central value corresponds to a 3D Mach number of M=0.24+-0.015 and the ratio of the kinetic pressure of small-scale motions to thermal pressure in the intracluster plasma of only 3.1+-0.4%, at the lower end of predictions from cosmological simulations for merging clusters like Coma, and similar to that observed in the cool core of the relaxed cluster A2029. Meanwhile, the gas in both regions exhibits high line-of-sight velocity differences from the mean velocity of the cluster galaxies, Delta v_z=450+-15 km/s and 730+-30 km/s, respectively. A small contribution from an additional gas velocity component, consistent with the cluster optical mean, is detected along a sightline near the cluster center. The combination of the observed velocity dispersions and bulk velocities is not described by a Kolmogorov velocity power spectrum of steady-state turbulence; instead, the data imply a much steeper effective slope (i.e., relatively more power at larger linear scales). This may indicate either a very large dissipation scale resulting in the suppression of small-scale motions, or a transient dynamic state of the cluster, where large-scale gas flows generated by an ongoing merger have not yet cascaded down to small scales.

astro-ph.HE↗

arXiv2024

Multiwavelength study of 1eRASS J085039.9-421151 with eROSITA NuSTAR and X-shooter

The eROSITA instrument on board Spectrum-Roentgen-Gamma has completed four scans of the X-ray sky, leading to the detection of almost one million X-ray sources in eRASS1 only, including multiple new X-ray binary candidates. We report on analysis of the X-ray binary 1eRASS J085039.9-421151, using a ~55\,ks long NuSTAR observation, following its detection in each eROSITA scan. Analysis of the eROSITA and NuSTAR X-ray spectra in combination with X-shooter data of the optical counterpart provide evidence of an X-ray binary with a red supergiant (RSG) companion, confirming previous results, although we determine a cooler spectral type of M2-3, owing to the presence of TiO bands in the optical and near infrared spectra. The X-ray spectrum is well-described by an absorbed power law with a high energy cutoff typically applied for accreting high mass X-ray binaries. In addition, we detect a strong fluorescent neutral iron line with an equivalent width of ~700\,eV and an absorption edge, the latter indicating strong absorption by a partial covering component. It is unclear if the partial absorber is ionised. There is no significant evidence of a cyclotron resonant scattering feature. We do not detect any pulsations in the NuSTAR lightcurves, possibly on account of a large spin period that goes undetected due to insufficient statistics at low frequencies or potentially large absorption that causes pulsations to be smeared out. Even so, the low persistent luminosity, the spectral parameters observed (photon index, $Γ<1.0$), and the minuscule likelihood of detection of RSG-black hole systems, suggest that the compact object is a neutron star.

astro-ph.HE↗

arXiv2024

Sharp Periodic Flares and Long-Term Variability in the High-Mass X-ray Binary XTE J1829-098 from RXTE PCA, Swift BAT and MAXI Observations

XTE J1829-098 is a transient X-ray pulsar with a period of ~7.8 s. It is a candidate Be star system, although the evidence for this is not yet definitive. We investigated the twenty-year long X-ray light curve using the Rossi X-ray Timing Explorer Proportional Counter Array (PCA), Neil Gehrels Swift Observatory Burst Alert Telescope (BAT), and the Monitor of All-sky X-ray Image (MAXI). We find that all three light curves are clearly modulated on the ~244 day orbital period previously reported from PCA monitoring observations, with outbursts confined to a narrow phase range. The light curves also show that XTE J1829-098 was in an inactive state between approximately December 2008 and April 2018 and no strong outbursts occurred. Such behavior is typical of Be X-ray binary systems, with the absence of outbursts likely related to the dissipation of the Be star's decretion disk. The mean outburst shapes can be approximated with a triangular profile and, from a joint fit of this to all three light curves, we refine the orbital period to 243.95 +/- 0.04 days. The mean outburst profile does not show any asymmetry and has a total phase duration of 0.140 +/- 0.007. However, the PCA light curve shows that there is considerable cycle-to-cycle variability of the individual outbursts. We compare the properties of XTE J1829-098 with other sources that show short phase-duration outbursts, in particular GS 1843-02 (2S 1845-024) which has a very similar orbital period, but longer pulse period, and whose orbit is known to be highly eccentric.

astro-ph.HE↗

arXiv2024

Long term variability of Cygnus X-1. VIII. A spectral-timing look at low energies with NICER

The Neutron Star Interior Composition Explorer (NICER) monitoring campaign of Cyg X-1 allows us to study its spectral-timing behavior at energies ${<}1$ keV across all states. The hard state power spectrum can be decomposed into two main broad Lorentzians with a transition at around 1 Hz. The lower-frequency Lorentzian is the dominant component at low energies. The higher-frequency Lorentzian begins to contribute significantly to the variability above 1.5 keV and dominates at high energies. We show that the low- and high-frequency Lorentzians likely represent individual physical processes. The lower-frequency Lorentzian can be associated with a (possibly Comptonized) disk component, while the higher-frequency Lorentzian is clearly associated with the Comptonizing plasma. At the transition of these components, we discover a low-energy timing phenomenon characterized by an abrupt lag change of hard (${\gtrsim}2$ keV) with respect to soft (${\lesssim}1.5$ keV) photons, accompanied by a drop in coherence, and a reduction in amplitude of the second broad Lorentzian. The frequency of the phenomenon increases with the frequencies of the Lorentzians as the source softens and cannot be seen when the power spectrum is single-humped. A comparison to transient low-mass X-ray binaries shows that this feature does not only appear in Cyg X-1, but that it is a general property of accreting black hole binaries. In Cyg X-1, we find that the variability at low and high energies is overall highly coherent in the hard and intermediate states. The high coherence shows that there is a process at work which links the variability, suggesting a physical connection between the accretion disk and Comptonizing plasma. This process fundamentally changes in the soft state, where strong red noise at high energies is incoherent to the variability at low energies.

astro-ph.HE↗

arXiv2024

An in-depth analysis of the variable cyclotron lines in GX 301$-$2

Context. The High-Mass X-ray Binary (HMXB) system GX 301$-$2 is a persistent source with a well-known variable cyclotron line centered at 35 keV. Recently, a second cyclotron line at 50 keV has been reported with a presumably different behavior than the 35 keV line. Aims. We investigate the presence of the newly discovered cyclotron line in the phase-averaged and phase-resolved spectra at higher luminosities than before. We further aim to determine the pulse-phase variability of both lines. Methods. We analyze a NuSTAR observation of GX 301$-$2 covering the pre-periastron flare, where the source luminosity reached its peak of ${\sim} 4 \times 10^{37}\,\mathrm{erg}\,\mathrm{s}^{-1}$ in the 5-50 keV range. We analyze the phase-averaged spectra in the NuSTAR energy range from 3.5-79 keV for both the complete observation and three time segments of it. We further analyze the phase-resolved spectra and the pulse-phase variability of continuum and cyclotron line parameters. Results. We confirm that the description of the phase-averaged spectrum requires a second absorption feature at $51.5^{+1.1}_{-1.0}$ keV besides the established line at 35 keV. The statistical significance of this feature in the phase-averaged spectrum is $>99.999\%$. We further find that the 50 keV cyclotron line is present in three of eight phase bins. Conclusions. Based on the results of our analysis, we confirm that the detected absorption feature is very likely to be a cyclotron line. We discuss a variety of physical scenarios which could explain the proposed anharmonicity, but also outline circumstances under which the lines are harmonically related. We further present the cyclotron line history of GX 301$-$2 and evaluate concordance among each other. We also discuss an alternative spectral model including cyclotron line emission wings.

astro-ph.HE↗

arXiv2023

Stellar wind variability in Cygnus X-1 from high-resolution excess variance spectroscopy with Chandra

Stellar winds of massive stars are known to be driven by line absorption of UV photons, a mechanism which is prone to instabilities, causing the wind to be clumpy. The clumpy structure hampers wind mass-loss estimates, limiting our understanding of massive star evolution. The wind structure also impacts accretion in high-mass X-ray binary (HMXB) systems. We analyse the wavelength-dependent variability of X-ray absorption in the wind to study its structure. Such an approach is possible in HMXBs, where the compact object serves as an X-ray backlight. We probe different parts of the wind by analysing data taken at superior and inferior conjunction. We apply excess variance spectroscopy to study the wavelength-dependent soft X-ray variability of the HMXB Cygnus X-1 in the low/hard spectral state. Excess variance spectroscopy quantifies the variability of an object above the statistical noise as a function of wavelength, which allows us to study the variability of individual spectral lines. As one of the first studies, we apply this technique to high-resolution gratings spectra provided by Chandra, accounting for various systematic effects. The frequency dependence is investigated by changing the time binning. The strong orbital phase dependence we observe in the excess variance is consistent with column density variations predicted by a simple model for a clumpy wind. We identify spikes of increased variability with spectral features found by previous spectroscopic analyses of the same data set, most notably from silicon in over-dense clumps in the wind. In the silicon line region, the variability power is redistributed towards lower frequencies, hinting at increased line variability in large clumps. In prospect of the microcalorimetry missions that are scheduled to launch within the next decade, excess variance spectra present a promising approach to constrain the wind structure.

astro-ph.HE↗

arXiv2022

Accreting on the edge: a luminosity-dependent cyclotron line in the Be/X-ray Binary 2S 1553-542 accompanied by accretion regimes transition

Accreting X-ray pulsars (XRPs) undergo luminous X-ray outbursts during which the luminosity-dependent spectral and timing features of the neutron star's emission can be analyzed in detail, thus shedding light on the accretion regime at work. We took advantage of a monitoring campaign performed with NuSTAR, Swift/XRT, AstroSat and NICER, to follow the Be/X-ray Binary 2S 1553-542 along one of its rare outbursts and trace its spectral and timing evolution. We report the discovery of a luminosity-dependent cyclotron line energy for the first time in this source. The pulse profiles and pulsed fraction also show variability along the outburst, consistently with the interpretation that the source transitions from the sub-critical to the super-critical accretion regime, separated by a critical luminosity of L$_{crit}\approx4\times10^{37}$ erg/s.

astro-ph.HE↗

arXiv2021

Fitting strategies of accretion column models and application to the broadband spectrum of Cen X-3

Due to the complexity of modeling the radiative transfer inside the accretion columns of neutron star binaries, their X-ray spectra are still commonly described with phenomenological models, for example, a cutoff power law. While the behavior of these models is well understood and they allow for a comparison of different sources and studying source behavior, the extent to which the underlying physics can be derived from the model parameters is very limited. During recent years, several physically motivated spectral models have been developed to overcome these limitations. Their application, however, is generally computationally much more expensive and they require a high number of parameters which are difficult to constrain. Previous works have presented an analytical solution to the radiative transfer equation inside the accretion column assuming a velocity profile that is linear in the optical depth. An implementation of this solution that is both fast and accurate enough to be fitted to observed spectra is available as a model in XSPEC. The main difficulty of this implementation is that some solutions violate energy conservation and therefore have to be rejected by the user. We propose a novel fitting strategy that ensures energy conservation during the $χ^2$-minimization which simplifies the application of the model considerably. We demonstrate this approach as well a study of possible parameter degeneracies with a comprehensive Markov-chain Monte Carlo analysis of the complete parameter space for a combined NuSTAR and Swift/XRT dataset of Cen X-3. The derived accretion-flow structure features a small column radius of $\sim$63 m and a spectrum dominated by bulk-Comptonization of bremsstrahlung seed photons, in agreement with previous studies.

astro-ph.HE↗

arXiv2020

Observation of strong two-electron--one-photon transitions in few-electron ion

We resonantly excite the $K$ series of O$^{5+}$ and O$^{6+}$ up to principal quantum number $n=11$ with monochromatic x rays, producing $K$-shell holes, and observe their relaxation by soft-x-ray emission. Some photoabsorption resonances of O$^{5+}$ reveal strong two-electron--one-photon (TEOP) transitions. We find that for the $[(1s\,2s)_1\,5p_{3/2}]_{3/2;1/2}$ states, TEOP relaxation is by far stronger than the radiative decay and competes with the usually much faster Auger decay path. This enhanced TEOP decay arises from a strong correlation with the near-degenerate upper states $[(1s\,2p_{3/2})_1\,4s]_{3/2;1/2}$ of a Li-like satellite blend of the He-like $Kα$ transition. Even in three-electron systems, TEOP transitions can play a dominant role, and the present results should guide further research on the ubiquitous and abundant many-electron ions where electronic energy degeneracies are far more common and configuration mixing is stronger.

physics.atom-ph↗

arXiv2020

High Resolution Photoexcitation Measurements Exacerbate the Long-Standing Fe XVII Oscillator Strength Problem

For more than 40 years, most astrophysical observations and laboratory studies of two key soft x-ray diagnostic $2p-3d$ transitions, $3C$ and $3D$, in Fe XVII ions found oscillator strength ratios $f(3C)/f(3D)$ disagreeing with theory, but uncertainties had precluded definitive statements on this much studied conundrum. Here, we resonantly excite these lines using synchrotron radiation at PETRA III, and reach, at a millionfold lower photon intensities, a 10 times higher spectral resolution, and 3 times smaller uncertainty than earlier work. Our final result of $f(3C)/f(3D) = 3.09(8)(6)$ supports many of the earlier clean astrophysical and laboratory observations, while departing by five sigmas from our own newest large-scale ab initio calculations, and excluding all proposed explanations, including those invoking nonlinear effects and population transfers.

physics.atom-ph↗

arXiv2019

The giant outburst of 4U 0115+634 in 2011 with Suzaku and RXTE

We present an analysis of X-ray spectra of the high mass X-ray binary 4U 0115+634 as observed with Suzaku and RXTE in 2011 July, during the fading phase of a giant X-ray outburst. We used a continuum model consisting of an absorbed cutoff power-law and an ad-hoc Gaussian emission feature centered around 8.5 keV, which we discuss to be due to cyclotron emission. Our results are consistent with a fundamental cyclotron absorption line centered at ${\sim}10.2$ keV for all observed flux ranges. At the same time we rule out significant influence of the 8.5 kev Gaussian on the CRSF parameters, which are not consistent with the cyclotron line energies and depths of previously reported flux-dependent descriptions. We also show that some continuum models can lead to artificial line-like residuals in the analyzed spectra, which are then misinterpreted as unphysically strong cyclotron lines. Specifically, our results do not support the existence of a previously claimed additional cyclotron feature at ${\sim}15$ keV. Apart from these features, we find for the first time evidence for a He-like Fe XXV emission line at ${\sim}6.7$ keV and weak H-like Fe XXVI emission close to ${\sim}7.0$ keV.

astro-ph.HE↗

arXiv2019

Chandra X-ray spectroscopy of the focused wind in the Cygnus X-1 system III. Dipping in the low/hard state

We present an analysis of three Chandra High Energy Transmission Gratings observations of the black hole binary Cyg X-1/HDE 226868 at different orbital phases. The stellar wind that is powering the accretion in this system is characterized by temperature and density inhomogeneities including structures, or "clumps", of colder, more dense material embedded in the photoionized gas. As these clumps pass our line of sight, absorption dips appear in the light curve. We characterize the properties of the clumps through spectral changes during various dip stages. Comparing the silicon and sulfur absorption line regions (1.6-2.7 keV $\equiv$ 7.7-4.6 Å) in four levels of varying column depth reveals the presence of lower ionization stages, i.e., colder or denser material, in the deeper dip phases. The Doppler velocities of the lines are roughly consistent within each observation, varying with the respective orbital phase. This is consistent with the picture of a structure that consists of differently ionized material, in which shells of material facing the black hole shield the inner and back shells from the ionizing radiation. The variation of the Doppler velocities compared to a toy model of the stellar wind, however, does not allow us to pin down an exact location of the clump region in the system. This result, as well as the asymmetric shape of the observed lines, point at a picture of a complex wind structure.

astro-ph.HE↗

arXiv2018

Explaining the asymmetric line profile in Cepheus X-4 with spectral variation across pulse phase

The high mass X-ray binary Cep X-4, during its 2014 outburst, showed evidence for an asymmetric cyclotron line in its hard X-ray spectrum. The 2014 spectrum provides one of the clearest cases of an asymmetric line profile among all studied sources with Cyclotron Resonance Scattering Features (CRSF). We present a phase-resolved analysis of NuSTAR and Suzaku data taken at the peak and during the decline phases of this outburst. We find that the pulse-phased resolved spectra are well-fit by a single, symmetric cyclotron feature. The fit parameters vary strongly with pulse phase: most notably the central energy and depth of the cyclotron feature, the slope of the power-law component, and the absorbing column density. We synthesise a phase averaged spectrum using the best-fit parameters for these individual pulse phases, and find that this combined model spectrum has a similar asymmetry in the cyclotron features as discovered in phase-averaged data. We conclude that the pulse phase resolved analysis with simple symmetric line profiles when combined can explain the asymmetry detected in the phase-averaged data.

astro-ph.HE↗