arXiv subjects

Biswajit Banerjee

Publications and source records attributed to Biswajit Banerjee.

At least 19 recordsLinked to original sources

arXiv2026

GRINTA: a new Probe of the Dynamic Universe

Recent observations of the transient sky at all wavelengths are increasingly revealing the importance of the multi-messenger and multi-wavelength approach. The GRINTA (Gamma-Ray INternational Transient Array Observatory) mission, proposed for launch around the middle of the next decade, is conceived as a small mission with good sensitivity, excellent angular resolution and fast follow-up capability for studying transient sources at timescales from ms to hours, at the same time ensuring optimal integration with multi-messenger networks. The GRINTA mission will carry two complementary payloads to cover in total the 5 keV-10 MeV band, that will detect and localise gamma-ray bursts covering $\sim$ half of the sky and will be able to perform imaging surveys with sub-arcmin resolution. GRINTA will operate in synergy with the most powerful electromagnetic, gravitational wave and neutrino observatories foreseen to be operational after 2035.

astro-ph.IM↗

arXiv2026

X-ray Flares in Gamma-Ray Bursts at High and Very-High-Energies

A significant fraction of GRB early afterglows exhibit fast and bright X-ray flares, discovered by Swift X-ray Telescope. Their rapid temporal variability and spectral evolution have suggested an internal shock origin, analogous to prompt MeV emission. However, their physical origin and radiation mechanism remain debated. High-energy (> 100 MeV) and very-high-energy (> 30 GeV) gamma-ray observations provide a powerful probe of flare dissipation region, constraining its size, magnetic field strength, and particle acceleration under the synchrotron self-Compton scenario in optically thin relativistic jets. We present a systematic multi-wavelength study of 66 X-ray flares from 47 GRBs observed by X-ray Telescope over 17 years, all within field of view of Fermi Large Area Telescope. We investigate their GeV counterparts and find that only five flares exhibit significant high-energy emission (> 3 sigma). Broadband spectral modeling indicates that this GeV emission is consistent with standard forward shock afterglow. We further investigate correlations between flare spectral properties and energy fluxes at 1 keV, 10 keV, and 1 GeV. Using a synchrotron self-Compton model, we constrain the physical conditions of the emitting region, including magnetic field strength, bulk Lorentz factor, and emission radius. For the most stringent GeV upper limits, we find a magnetic-to-electron luminosity ratio greater than or equal to 1, implying a highly magnetized emitting region. We predict very-high-energy gamma-ray emission from X-ray flares at early (~500s) and late (~5000s) times and assess their detectability with Cherenkov Telescopes. We find that later X-ray flares provide the most promising targets for follow-up observations owing to improved observational accessibility, sensitivity, and reduced response-time constraints of facilities such as Cherenkov Telescope Array Observatory.

astro-ph.HE↗

arXiv2026

Assessing the Impact of Instrumental Requirements on the Scientific Performance of the Einstein Telescope

We investigate the relationship between instrumental requirements and the scientific performance of the Einstein Telescope (ET), a third-generation (3G) gravitational-wave (GW) observatory. Different technical design choices result in distinct noise budgets, ultimately shaping the detector's scientific capabilities. To systematically assess and compare their impact, we define a comprehensive set of performance metrics spanning compact binary coalescence (CBC) detection and parameter estimation, as well as other sources, including stochastic GW backgrounds, isolated spinning neutron stars, and core-collapse supernovae (CCSNe). We build a comparative reference framework that links degradations in specific noise contributions and frequency bands to losses in scientific capabilities. We consider a representative selection of technical parameters, such as coating and suspension temperatures, the filter cavity length in the low-frequency instrument, and the beam size in the high-frequency instrument. We evaluate how sensitivity variations across specific frequency bands affect different scientific objectives. We quantify how the sensitivity below 30 Hz impacts the detectability of massive and/or high-redshift sources and the reconstruction of long-duration CBC signals, affecting early warning and sky localization for binary neutron stars (BNSs). Sensitivity in the 30-450 Hz range governs most CBC parameter-estimation metrics, while high-frequency sensitivity above ~450 Hz predominantly impacts BNS post-merger studies and CCSN detectability, with modest effects on detection rates. Even with the most significant degradations considered, the ET science case remains robust overall. Our results provide a comprehensive benchmark linking scientific objectives to instrumental requirements, particularly important as the final design and infrastructure of 3G observatories are being defined.

astro-ph.IM↗

arXiv2026

The ultra-fast afterglow of GRB 260226A

Long-duration gamma-ray bursts are typically powered by relativistic jets launched after the core collapse of some rapidly rotating massive stars. Internal dissipation releases part of the jet energy as highly variable MeV prompt emission, while the remaining kinetic energy drives an external shock into the surrounding medium and produces the so-called afterglow. During the first minutes of the afterglow, the unsteady jet transfers energy to the external shock. The early afterglow emission in MeV-GeV energies is rarely observed because the emergence of afterglow can be overshined by the prompt emission. Here we report exceptional observations of GRB 260226A with the Fermi Large Area Telescope, which recorded the largest number of photons above 100 MeV from a gamma-ray burst. These data allow us to reconstruct the evolution of the bolometric flux of the afterglow from its emergence during the prompt emission phase with unprecedented detail. The afterglow component peaks near 50 MeV and fades rapidly, first as t$^{-1.5}$ and then transiting to an ultra-fast t$^{-2.8}$ decay after about one minute. This behavior cannot be explained by standard synchrotron emission from a blast wave propagating into a cold medium. We interpret it as external inverse Compton radiation from freshly heated electrons cooling on prompt photons in a dense, pair-loaded stellar wind. GRB 260226A therefore shows that MeV-GeV observations can directly reveal the formation of the external shock and the massive-star environment is significantly reshaped by the prompt emission.

astro-ph.HE↗

arXiv2026

Detectability of Gravitational-wave counterparts of EP-FXTs observed during the O4b LIGO-Virgo-KAGRA Observing Run

Fast X-ray transients (FXTs) detected by the Einstein Probe mission have emerged as a rapidly growing class of extragalactic transients, whose physical origin remains uncertain. Compact binary coalescence (CBC) systems have been proposed as one possible progenitor for at least a subset of these events, making FXTs promising targets for multi-messenger studies with gravitational-wave (GW) observations. This work presents the first systematic investigation of GW counterparts to FXTs observed by Einstein Probe and assesses the detectability of associated CBC. We focus on FXTs detected during the second half of the fourth observing run (O4b) of the Advanced LIGO-Virgo-KAGRA detector network by searching for temporal coincidences with GW candidates from the fifth Gravitational-Wave Transient Catalog (GWTC-5). We analyze a sample of 47 FXTs, including 11 with measured redshifts, and assess the significance of the association between FXTs and GW candidates using a ranking statistic. We find no significant GW counterpart associated with any FXT in our sample. In the absence of a detection, we place 90% exclusion-distance constraints under the assumptions of binary neutron star and neutron star-black hole progenitor scenarios. For observations with the full LIGO and Virgo detector network, the typical median exclusion distances are $\sim$178 Mpc and $\sim$349 Mpc, respectively. These constraints disfavor a nearby compact-binary merger origin. Longer periods of joint observations by the LVK and Einstein Probe, combined with improved GW detector sensitivity, will enhance the prospects for identifying genuine GW-FXT associations and place tighter constraints on the progenitor scenarios of these events.

astro-ph.HE↗

arXiv2026

Thermal Electrons in an Ultra-Relativistic Shock Shape the Optical Afterglow of GRB 250702F

Observing early optical emission from gamma-ray bursts (GRBs) contemporaneous with the MeV prompt emission phase remains rare, requiring rapid-response robotic facilities. The Ond\v{r}ejov D50 telescope detected the optical counterpart of GRB 250702F at z = 1.520 only 27.8 s after trigger, enabling high-cadence monitoring during the brightest prompt emission pulses. The optical light curve reveals two distinct flares. The first (30 - 100 s) is spectrally consistent with the MeV prompt emission. The second flare (100 - 1400 s) exhibits an unusual morphology (F_nu ~ t^-alpha): a rapid rise to a plateau, followed by a steep decay (alpha ~ 1.6) before transitioning to a standard power-law afterglow (alpha = 0.79). This steep decay phase cannot be explained by nonthermal electrons accelerated at the forward shock, and reverse-shock scenario is disfavored due to the long duration of the flare and the temporal offset from the underlying deceleration time. We interpret the steep decay as the synchrotron frequency of a thermal (Maxwellian) electron population sweeping through the optical band. Modeling yields a non-thermal energy fraction delta ~ 0.8 with the remaining energy heating electrons at characteristic Lorentz factor gamma_th ~ 900. These observations provide evidence for thermal electron signatures in GRB afterglows, consistent with predictions from particle-in-cell simulations of ultra-relativistic collisionless shocks.

astro-ph.HE↗

arXiv2026

MeV absorption in gamma-ray bursts as a probe of their progenitor environments

A small fraction of X-ray photons from $\gamma$-ray bursts (GRBs), after escaping the relativistic jet, are scattered by electrons in the circumburst medium. Subsequent photon-photon absorption between the incoming MeV $\gamma$-rays and the back-scattered X-rays generate electron-positron pairs, enriching the surrounding medium with leptons. We investigate how these back-scattered photons modify the prompt GRB spectrum through $\gamma-\gamma$ absorption. In a dense and pair-loaded environment, the emerging spectra exhibit a broad absorption feature, whose profile is sensitive to the low-energy spectral index $\alpha$. In particular, spectra with $\alpha > -1$ develop a pronounced, saddle-shaped absorption between 1 and 100 MeV (rest frame). Such external MeV absorption could account for the spectral curvature seen in some bright GRBs, and may point to a dense circum-stellar medium (CSM) around their progenitor stars - consistent with early observations of core-collapse supernovae. In this scenario, the blastwave caused by the GRB is expected to start off with a relatively low Lorentz factor, and undergo an acceleration phase when traversing the large density drop at the interface between the dense CSM and the surrounding medium. The impact of these non-trivial dynamics on the afterglow emission is yet to be explored.

astro-ph.HE↗

arXiv2025

Early X-ray emission of short Gamma-Ray Bursts: insights into physics and multi-messenger prospects

Early X-ray emission of Gamma-Ray Bursts (GRBs) traces the transition between the prompt emission and the afterglow radiation, and its rapid flux decline is often interpreted as the tail of the prompt emission. As such, it can offer insights into the emission mechanisms active during the prompt emission and the physics of GRB jets. In this work, we focus on merger-driven GRBs, which are sources of gravitational waves (GWs) detectable by ground-based interferometers, such as LIGO, Virgo, and KAGRA. We present a systematic analysis of the early X-ray emission ($t < 10^3 \ \mathrm{s}$) of a sample of 16 merger-driven GRB candidates detected by the Neil Gehrels Swift Observatory (hereafter, Swift). We performed a time-resolved spectral analysis of soft and hard X-ray data (0.3-150 keV) by fitting two curved spectral models to the spectra: a physical synchrotron model and an empirical smoothly broken power law model. We characterized the evolution of the peak energy and bolometric flux, and derived the intrinsic properties of the 10 bursts with measured redshift. We discovered a tight correlation between the rest-frame peak energy of the spectra and the isotropic-equivalent luminosity. Specifically, we obtained $ν_{c,z} \propto L_{\rm iso}^{(0.64 \pm 0.03)}$ when adopting the synchrotron model, and $E_{p,z} \propto L_{\rm iso}^{(0.58 \pm 0.04)}$ when adopting the smoothly broken power law. Both relations were extrapolated to the typical prompt emission energies and well describe the properties of short GRBs detected in the MeV gamma-rays. These results suggest a common origin for the prompt and steep-decay emissions in merger-driven GRBs, and rule out high-latitude emission as the dominant process shaping the early X-ray tails. Finally, we assessed the detectability of these sources with the Wide-field X-ray Telescope onboard the Einstein Probe mission.

astro-ph.HE↗

arXiv2025

Ultra-long MeV transient from a relativistic jet: a tidal disruption event candidate

On July 2, 2025, the Gamma-ray Burst Monitor (GBM) onboard the Fermi Gamma-ray space telescope detected three short-duration MeV transients with overlapping sky locations. These events, named as GRB 250702D, B, and E (collectively referred to as DBE), triggered the detector with delays of approximately 1-2 hours between each burst. Follow-up observations of this unusually long MeV transient (lasting >3 hours) by the Neil Gehrels Swift Observatory and the Nuclear Spectroscopic Telescope Array over a period of 10 days revealed a steep temporal decline in soft X-rays ($\propto t^{-1.9 \pm 0.1}$). The time-averaged spectra during the outbursts are well described by a single power law $dN_γ/dE \propto E^{-1.5}$, while upper limits above 100 MeV imply a spectral cutoff between 10 MeV and 100 MeV. Using standard gamma-ray transparency arguments, we derive a lower limit on the bulk Lorentz factor. Combined with the steep decline in X-rays, these constraints point to a relativistic jet origin. The properties of DBE are inconsistent with established GRB spectral-energy correlations, disfavoring classical long GRB progenitors. Instead, the basic characteristics of DBE resemble those of previously reported jetted tidal disruption events (TDEs), though alternative progenitor channels cannot be excluded. In the relativistic TDE scenario, DBE is the first one with detected MeV gamma-ray emission. We argue that the observed emission is most likely produced by synchrotron radiation from sub-TeV electrons.

astro-ph.HE↗

arXiv2025

Binary black holes in magnetized AGN disks

Stellar-mass binary black hole (BBH) mergers occurring within the disks of active galactic nuclei (AGN) are promising sources for gravitational waves detectable by the LIGO, Virgo, and KAGRA (LVK) interferometers. Some of these events have also been potentially associated with transient electromagnetic flares, indicating that BBH mergers in dense environments may be promising sources of multi-messenger signals. To investigate the prospects for electromagnetic emission from these systems, we study the dynamics of accretion flows onto BBHs embedded in AGN disks using numerical simulations. Although recent studies have explored this scenario, they often employ simplified disk models that neglect magnetic fields. In this work, we examine how strong magnetic fields influence and regulate the accretion onto such binary systems. In this context, we conduct three-dimensional magnetohydrodynamical local shearing-box simulations of a binary black hole system embedded within a magnetized disk of an AGN. We observe that the dynamically important magnetic fields can drive the formation of well-collimated outflows capable of penetrating the vertical extent of the AGN disk. However, outflow generation is not ubiquitous and strongly depends on the radial distance of the binary from the supermassive black hole (SMBH). In particular, binaries placed at a larger distance from the central SMBH show relatively more transient accretion and the formation of stronger spiral shocks. Furthermore, accretion behavior onto the binary system via individual circum-singular disks (CSDs) is also modulated by local AGN disk properties. Our simulations highlight the importance of shear velocity in the amplification of the toroidal magnetic field component, which plays a crucial role in governing the outflow strength.

astro-ph.HE↗

arXiv2025

Crystal Eye: all sky MeV monitor with high precision real-time localization

Crystal Eye is a space-based all-sky monitor optimized for the autonomous detection and localization of transients in the 10 keV to 30 MeV energy range, a region where extensive observations and monitoring of various astrophysical phenomena are required. By focusing on the operating environment and its impact on the observation process, we optimized the detector design and assessed its scientific potential. We explored the use of novel techniques to achieve the science goals of the experiment. We assumed the orbit of a potential future mission at approximately 550 km altitude near the equatorial region with a 20° inclination. In such an orbit, the main background contributions for this kind of detector are from different particles and radiation of cosmic origin and secondaries produced by their interaction in the Earth's atmospheric and geomagnetic environment. We studied the response of the detector in this background environment, using the Geant4 Monte Carlo simulation toolkit. We also calculated other detector performance parameters to estimate its scientific capabilities. The detector effective area and efficiency are calculated for low energy gamma-ray sources and used to estimate its sensitivity to short-duration transient sources. The calculation shows a better effective area and sensitivity by several factors compared to existing instruments of similar type. A method is also developed and discussed to estimate the online transient-localization performance of the detector, suggesting a better localization precision by about an order of magnitude than those typically reported by existing gamma-ray monitors. We present here the simulation study and results of an innovative detector design concept that can make a significant contribution in the multi-messenger era. Moreover, this study can be useful as a technical reference for similar future experiments.

astro-ph.IM↗

arXiv2025

The Science of the Einstein Telescope

Einstein Telescope (ET) is the European project for a gravitational-wave (GW) observatory of third-generation. In this paper we present a comprehensive discussion of its science objectives, providing state-of-the-art predictions for the capabilities of ET in both geometries currently under consideration, a single-site triangular configuration or two L-shaped detectors. We discuss the impact that ET will have on domains as broad and diverse as fundamental physics, cosmology, early Universe, astrophysics of compact objects, physics of matter in extreme conditions, and dynamics of stellar collapse. We discuss how the study of extreme astrophysical events will be enhanced by multi-messenger observations. We highlight the ET synergies with ground-based and space-borne GW observatories, including multi-band investigations of the same sources, improved parameter estimation, and complementary information on astrophysical or cosmological mechanisms obtained combining observations from different frequency bands. We present advancements in waveform modeling dedicated to third-generation observatories, along with open tools developed within the ET Collaboration for assessing the scientific potentials of different detector configurations. We finally discuss the data analysis challenges posed by third-generation observatories, which will enable access to large populations of sources and provide unprecedented precision.

gr-qc↗

arXiv2025

Broadband Modelling of GRB 230812B Afterglow: Implications for VHE $γ$-ray Detection with IACTs

A significant fraction of the energy from the $γ$-ray burst (GRB) jets, after powering the keV-MeV emission, forms an ultra-relativistic shock propagating into the circumburst medium. The particles in the medium accelerate through the shock and produce afterglow emission. Recently, a few GRB afterglows have been observed in TeV $γ$-rays by Cherenkov Telescopes. This provides access to broadband spectra of GRB afterglows containing rich information about the microphysics of relativistic shocks and the profile of the circumburst medium. Since the transition from synchrotron to inverse Compton regime in afterglow spectra occurs between hard X-rays and the very-high-energy (VHE) $γ$-rays, detection in one of these bands is required to identify the two spectral components. The early afterglow data in the hard X-rays, along with the GeV emission, could accurately constrain the spectral shape and help in capturing the spectral turnover to distinguish the two components. We present the multiwavelength spectral and temporal study, focused on the keV-VHE domain, of GRB 230812B, one of the brightest GRBs detected by Fermi Gamma Ray Burst Monitor (GBM), along with the detection of a 72 GeV photon in Large Area Telescope (LAT) during the early afterglow phase. Through a detailed modelling of the emission within the afterglow external forward shock in a wind-like scenario, we predict optical to high-energy observations up to ~1 day. We emphasize the importance of following up poorly localised GRBs by demonstrating that even without prompt sub-degree localisation, such as in GRB 230812B, it is possible to recover the emission using imaging atmospheric Cherenkov telescopes, thanks to their relatively wider field of view. Moreover, we show that the low energy threshold of Large-Sized Telescope is essential in discovering the VHE component at much higher redshifts, typical of long GRBs.

astro-ph.HE↗

arXiv2025

GeV emission from a compact binary merger

An energetic $\rm γ$-ray burst (GRB), GRB 211211A, was observed on 2021 December 11 by the Neil Gehrels Swift Observatory. Despite its long duration, typically associated with bursts produced by the collapse of massive stars, the discovery of an optical-infrared kilonova and a quasi-periodic oscillation during a gamma-ray precursor points to a compact object binary merger origin. The complete understanding of this nearby ($\sim$ 1 billion light-years) burst will significantly impact our knowledge of GRB progenitors and the physical processes that lead to electromagnetic emission in compact binary mergers. Here, we report the discovery of a significant ($\rm >5 σ$) transient-like emission in the high-energy $\rm γ$-rays (HE; E$>0.1$ GeV) observed by Fermi/LAT starting at $10^3$ s after the burst. After an initial phase with a roughly constant flux ($\rm \sim 5\times 10^{-10}\ erg\ s^{-1}\ cm^{-2}$) lasting $\sim 2\times 10^4$ s, the flux started decreasing and soon went undetected. The multi-wavelength afterglow emission observed at such late times is usually in good agreement with synchrotron emission from a relativistic shock wave that arises as the GRB jet decelerates in the interstellar medium. However, our detailed modelling of a rich dataset comprising public and dedicated multi-wavelength observations demonstrates that GeV emission from GRB 211211A is in excess with respect to the expectation of this scenario. We explore the possibility that the GeV excess is inverse Compton emission due to the interaction of a long-lived, low-power jet with an external source of photons. We discover that the kilonova emission can provide the necessary seed photons for GeV emission in binary neutron star mergers.

astro-ph.HE↗

arXiv2025

Gamma-ray burst prompt emission spectra at high energies

Despite more than fifty years of gamma-ray burst (GRB) observations, several questions regarding the origin of the prompt emission, particularly at high energies, remain unresolved. We present a comprehensive analysis of 35 GRBs observed by \textit{Fermi}/GBM and \textit{Fermi}/LAT over the past 15 years, focusing on the nature of high-energy (HE, E$>$100 MeV) emission during the prompt emission phase. Our study combines temporal and spectral analyses to investigate the synchrotron origin of the observed emission spanning the energy range from 10 keV to 100 GeV and explore the possible contribution of additional spectral components. Temporal modeling of \textit{Fermi}/LAT light curves for 12 GRBs in our sample reveals deviations from standard afterglow scenarios during the early phases, suggesting a significant contamination from prompt emission. We find that most GRB spectra align with synchrotron emission extending to GeV energies, with the slope $p$ of the non-thermal electron distribution clustering around $p\sim2.7$, consistently with theoretical predictions. For three GRBs, an additional power law component is required to explain the high-energy emission, but the nature and temporal evolution of this component remain unclear due to the limited quality of \textit{Fermi}/LAT data. When the power law component is needed, the synchrotron spectrum shows a sharp MeV suppression. It could be explained by the pair loading effects in the early afterglow. These findings emphasize the importance of multi-wavelength observations in unveiling the mechanisms driving early HE prompt emission in GRBs. We briefly discuss the implications of our findings for future very-high-energy (VHE, E$>$100 GeV) gamma-ray observatories, such as the Cherenkov Telescope Array, and address the detection prospects of additional non-thermal components in GRB spectra.

astro-ph.HE↗

arXiv2025

Imprint of "Local Opacity" Effect in Gamma-Ray Spectrum of Blazar Jet

Relativistic jets from accreting supermassive black holes at cosmological distances can be powerful emitters of $γ$-rays. However, the precise mechanisms and locations responsible for the dissipation of energy within these jets, leading to observable $γ$-ray radiation, remain elusive. We detect evidence for an intrinsic absorption feature in the $γ$-ray spectrum at energies exceeding $10\,$GeV, presumably due to the photon-photon pair production of $γ$-rays with low ionization lines at the outer edge of Broad-line region (BLR), during the high-flux state of the flat-spectrum radio quasar PKS 1424$-$418. The feature can be discriminated from the turnover at higher energies resulting from $γ$-ray absorption in the extragalactic background light. It is absent in the low-flux states supporting the interpretation that powerful dissipation events within or at the edge of the BLR evolve into fainter $γ$-ray emitting zones outside the BLR, possibly associated with the moving VLBI radio knots. The inferred location of $γ$-ray emission zone is consistent with the observed variability time scale of the brightest flare, provided that the flare is attributed to external Compton scattering with BLR photons.

astro-ph.HE↗

arXiv2024

The Lunar Gravitational-wave Antenna: Mission Studies and Science Case

The Lunar Gravitational-wave Antenna (LGWA) is a proposed array of next-generation inertial sensors to monitor the response of the Moon to gravitational waves (GWs). Given the size of the Moon and the expected noise produced by the lunar seismic background, the LGWA would be able to observe GWs from about 1 mHz to 1 Hz. This would make the LGWA the missing link between space-borne detectors like LISA with peak sensitivities around a few millihertz and proposed future terrestrial detectors like Einstein Telescope or Cosmic Explorer. In this article, we provide a first comprehensive analysis of the LGWA science case including its multi-messenger aspects and lunar science with LGWA data. We also describe the scientific analyses of the Moon required to plan the LGWA mission.

gr-qc↗

arXiv2024

GWFish: A simulation software to evaluate parameter-estimation capabilities of gravitational-wave detector networks

An important step in the planning of future gravitational-wave (GW) detectors and of the networks they will form is the estimation of their detection and parameter-estimation capabilities, which is the basis of science-case studies. Several future GW detectors have been proposed or are under development, which might also operate and observe in parallel. These detectors include terrestrial, lunar, and space-borne detectors. In this paper, we present GWFish, a new software to simulate GW detector networks and to calculate measurement uncertainties based on the Fisher-matrix approximation. GWFish models the impact of detector motion on PE and makes it possible to analyze multiband scenarios, i.e., observation of a GW signal by different detectors in different frequency bands. We showcase a few examples for the Einstein Telescope (ET) including the sky-localization of binary neutron stars, and ET's capability to measure the polarization of GWs.

gr-qc↗