arXiv subjects

R. Inasaridze

Publications and source records attributed to R. Inasaridze.

17 recordsLinked to original sources

arXiv2026

Earliest simultaneous multi-color optical observations of GRB 230328B: from 41 seconds to the host-galaxy identification

We present a multiwavelength study of the long-duration gamma-ray burst GRB 230328B, combining prompt gamma-ray observations with exceptionally early simultaneous optical photometry and extensive X-ray, radio, and host-galaxy follow-up. NUTTELA- TAO began simultaneous g'r'i' observations only 41 s after the Swift/BAT trigger, corresponding to approximately 16 s in the rest frame for the adopted host-galaxy photometric redshift of z_phot = 1.54+-0.06. Unlike sequential multiband measurements, these observations provide an instantaneous optical spectral slope without temporal-interpolation uncertainties. The early optical continuum remains statistically consistent with a constant slope from approximately 10^2 to 7*10^3 s, providing no evidence for rapid dust destruction. The absence of significant color evolution across the pronounced optical rebrightening at approximately 4*10^3 s demonstrates that it is achromatic and favours a dynamical rather than spectral origin. Broadband modelling shows that the optical, X-ray, and radio evolution can be broadly explained by forward-shock emission with late energy injection, although alternative scenarios cannot be excluded. The red optical continuum is consistent with substantial line-of-sight extinction in a massive, dusty host galaxy. Late-time observations are insufficient to constrain a typical GRB-associated supernova at the adopted redshift. GRB 230328B therefore provides a benchmark for connecting the earliest simultaneous optical colors with afterglow dynamics and the host environment of a representative long GRB.

astro-ph.HE↗

arXiv2026

GRB 241030A: a bright afterglow challenging forward shock emission

Gamma-Ray Burst GRB 241030A (z = 1.411) exhibited a bright afterglow (similar to GRB 221009A), detected across gamma-ray, X-ray, UV, and optical bands, providing a probe of GRB afterglow physics. We compiled multi-wavelength observations spanning from a minute to a week after the prompt emission, processing the data through a unified photometry pipeline. We analysed the observations both analytically and using Bayesian inference with two independent models. Our models assume that the afterglow emission arises from the strong forward shock of a laterally structured jet, with possible contributions from synchrotron self-Compton (SSC) scatterings. Our models reproduce X-ray to optical data, favouring a jet propagating into a constant-density interstellar medium, with a viewing angle within the jet core. However, both analyses require parameter values that are extreme compared to expectations from standard theory. In particular, our results imply extremely energetic jets despite regular prompt energy, leading to a very inefficient prompt emission. Furthermore, the jets are inefficient at accelerating particles, with low electron and magnetic energy fractions, leading to significant SSC emission. Our analyses indicate that the jets have large opening angles and propagate in high-density media. If the afterglow is indeed powered by radiation emitted behind a strong forward shock, our results place GRB 241030A within a sub-class of GRBs characterised by extreme kinetic energies, large jet opening angles, and very low prompt emission efficiencies, with strong SSC radiation. These predictions are difficult to reconcile with typical expectations from other GRBs. We therefore suggest that the afterglow of GRB 241030A is not solely powered by forward shock emission.

astro-ph.HE↗

arXiv2026

Multi-epoch afterglow rebrightenings in GRB 250129A: Evidence for successive shock interactions

Most long gamma-ray bursts (GRBs) exhibit afterglows broadly consistent with external forward-shock emission, typically described by smooth broken power-law decays in the multiband light curve. However, a minority of well-sampled GRBs deviate from this behavior, including GRB 250129A. This object shows multiple late-time rebrightenings at X-ray and optical wavelengths. Rebrightenings are often attributed to energy injection from prolonged central engine activity, refreshed shocks from delayed shell collisions, density jumps in the ambient medium, or angular jet structure and viewing-angle effects. After analysing the prompt emission observed in gamma-rays and the near-infrared, we investigate the origin of X-ray and optical flaring episodes in GRB 250129A. Physical processes in the afterglow light curves were investigated using methods ranging from empirical fitting to Bayesian inference. The well-sampled flares and the connection between the prompt and afterglow emission allow us to test the consistency of the fireball model and alternative scenarios. Conducting the prompt and time-resolved analyses, we obtained an isotropic-equivalent energy of E_iso,gamma = (1.35 +/- 0.12) x 10^53 erg. By modeling the afterglow using an agnostic Bayesian framework (NMMA), we rule out both a single external-shock evolution and a one-time energy-injection scenario. Numerical calculations show that the rebrightening episodes are consistent with refreshed shocks from delayed collisions between relativistic shells. Based on the consistency between our analyses of the prompt and afterglow GRB 250129A data, we find that two statistically significant rebrightening episodes occur within 1.1 days post trigger and can be explained by a sequence of refreshed shocks. Temporally and spectrally rich GRB datasets such as the one presented in this work, provide a powerful means to test current modeling frameworks.

astro-ph.HE↗

arXiv2025

EP240801a/XRF 240801B: An X-ray Flash Detected by the Einstein Probe and Implications of its Multiband Afterglow

We present multiband observations and analysis of EP240801a, a low-energy, extremely soft gamma-ray burst (GRB) discovered on August 1, 2024 by the Einstein Probe (EP) satellite, with a weak contemporaneous signal also detected by Fermi/GBM. Optical spectroscopy of the afterglow, obtained by GTC and Keck, identified the redshift of $z = 1.6734$. EP240801a exhibits a burst duration of 148 s in X-rays and 22.3 s in gamma-rays, with X-rays leading by 80.61 s. Spectral lag analysis indicates the gamma-ray signal arrived 8.3 s earlier than the X-rays. Joint spectral fitting of EP/WXT and Fermi/GBM data yields an isotropic energy $E_{\gamma,\rm{iso}} = (5.57^{+0.54}_{-0.50})\times 10^{51}\,\rm{erg}$, a peak energy $E_{\rm{peak}} = 14.90^{+7.08}_{-4.71}\,\rm{keV}$, a fluence ratio $\rm S(25-50\,\rm{keV})/S(50-100\,\rm{keV}) = 1.67^{+0.74}_{-0.46}$, classifying EP240801a as an X-ray flash (XRF). The host-galaxy continuum spectrum, inferred using Prospector, was used to correct its contribution for the observed outburst optical data. Unusual early $R$-band behavior and EP/FXT observations suggest multiple components in the afterglow. Three models are considered: two-component jet model, forward-reverse shock model and forward-shock model with energy injection. Both three provide reasonable explanations. The two-component jet model and the energy injection model imply a relatively small initial energy and velocity of the jet in the line of sight, while the forward-reverse shock model remains typical. Under the two-component jet model, EP240801a may resemble GRB 221009A (BOAT) if the bright narrow beam is viewed on-axis. Therefore, EP240801a can be interpreted as an off-beam (narrow) jet or an intrinsically weak GRB jet. Our findings provide crucial clues for uncovering the origin of XRFs.

astro-ph.HE↗

arXiv2024

Size, albedo and rotational period of the Hayabusa2# target (98943) 2001 CC21

This study aims to determine the size, albedo and rotational period of (98943) 2001 CC21, target of the Hayabusa2 extended mission, using thermal data from the Spitzer Space telescope and ground based observations. The Spitzer data were acquired with the Infrared Spectrograph in the 6-38 micron range, reduced using the Spitzer pipeline and modeled with the Near Earth Asteroid Thermal Modeling to determine the asteroid size and albedo. The absolute magnitude and the rotational period were determined thanks to new observations carried out at the 3.5m New Technology Telescope, at the 1.2m Observatoire de Haute Provence, and at the 0.7m Abastumani telescope. Three complete lightcurves were obtained in 2023-2024 at the last mentioned telescope. We determine an absolute magnitude of H=18.94$\pm$0.05, and a rotational period of 5.02124$\pm$0.00001 hours, with a large lightcurve amplitude of $\sim$ 0.8 mag. at a phase angle of 22$^o$, indicating a very elongated shape with estimated a/b semiaxis ratio $\geq$ 1.7, or a close-contact binary body. The emissivity of 2001 CC21 is consistent with that of silicates, and its albedo is 21.6$\pm$1.6 %. Finally, the spherical-equivalent diameter of 2001 CC21 is 465$\pm$15 m. The albedo value and emissivity here determined, coupled with results from polarimetry and spectroscopy from the literature, confirm that 2001 CC21 is an S-complex asteroid, and not a L-type, as previously suggested. The size of 2001 CC21 is less than 500 m, which is smaller than its first size estimation ($\sim$ 700 m). These results are relevant in preparation of the observing strategy of 2001 CC21 by Hayabusa2 extended mission.

astro-ph.EP↗

arXiv2023

Ready for O4 II: GRANDMA Observations of Swift GRBs during eight-weeks of Spring 2022

We present a campaign designed to train the GRANDMA network and its infrastructure to follow up on transient alerts and detect their early afterglows. In preparation for O4 II campaign, we focused on GRB alerts as they are expected to be an electromagnetic counterpart of gravitational-wave events. Our goal was to improve our response to the alerts and start prompt observations as soon as possible to better prepare the GRANDMA network for the fourth observational run of LIGO-Virgo-Kagra (which started at the end of May 2023), and future missions such as SM. To receive, manage and send out observational plans to our partner telescopes we set up dedicated infrastructure and a rota of follow-up adcates were organized to guarantee round-the-clock assistance to our telescope teams. To ensure a great number of observations, we focused on Swift GRBs whose localization errors were generally smaller than the GRANDMA telescopes' field of view. This allowed us to bypass the transient identification process and focus on the reaction time and efficiency of the network. During 'Ready for O4 II', 11 Swift/INTEGRAL GRB triggers were selected, nine fields had been observed, and three afterglows were detected (GRB 220403B, GRB 220427A, GRB 220514A), with 17 GRANDMA telescopes and 17 amateur astronomers from the citizen science project Kilonova-Catcher. Here we highlight the GRB 220427A analysis where our long-term follow-up of the host galaxy allowed us to obtain a photometric redshift of $z=0.82\pm0.09$, its lightcurve elution, fit the decay slope of the afterglows, and study the properties of the host galaxy.

astro-ph.HE↗

arXiv2023

Multi-band analyses of the bright GRB 230812B and the associated SN2023pel

GRB~230812B is a bright and relatively nearby ($z =0.36$) long gamma-ray burst (GRB) that has generated significant interest in the community and has thus been observed over the entire electromagnetic spectrum. We report over 80 observations in X-ray, ultraviolet, optical, infrared, and sub-millimeter bands from the GRANDMA (Global Rapid Advanced Network for Multi-messenger Addicts) network of observatories and from observational partners. Adding complementary data from the literature, we then derive essential physical parameters associated with the ejecta and external properties (i.e. the geometry and environment) of the GRB and compare with other analyses of this event. We spectroscopically confirm the presence of an associated supernova, SN2023pel, and we derive a photospheric expansion velocity of v $\sim$ 17$\times10^3$ km s$^{-1}$. We analyze the photometric data first using empirical fits of the flux and then with full Bayesian Inference. We again strongly establish the presence of a supernova in the data, with a maximum (pseudo-)bolometric luminosity of $5.75 \times 10^{42}$ erg/s, at $15.76^{+0.81}_{-1.21}$ days (in the observer frame) after the trigger, with a half-max time width of 22.0 days. We compare these values with those of SN1998bw, SN2006aj, and SN2013dx. Our best-fit model favours a very low density environment ($\log_{10}({n_{\rm ISM}/{\rm cm}^{-3}}) = -2.38^{+1.45}_{-1.60}$) and small values for the jet's core angle $\theta_{\rm core} = 1.54^{+1.02}_{-0.81} \ \rm{deg}$ and viewing angle $\theta_{\rm obs} = 0.76^{+1.29}_{-0.76} \ \rm{deg}$. GRB 230812B is thus one of the best observed afterglows with a distinctive supernova bump.

astro-ph.HE↗

arXiv2023

GRANDMA and HXMT Observations of GRB 221009A -- the Standard-Luminosity Afterglow of a Hyper-Luminous Gamma-Ray Burst

GRB 221009A is the brightest Gamma-Ray Burst (GRB) detected in more than 50 years of study. In this paper, we present observations in the X-ray and optical domains after the GRB obtained by the GRANDMA Collaboration (which includes observations from more than 30 professional and amateur telescopes) and the Insight-HXMT Collaboration. We study the optical afterglow with empirical fitting from GRANDMA+HXMT data, augmented with data from the literature up to 60 days. We then model numerically, using a Bayesian approach, the GRANDMA and HXMT-LE afterglow observations, that we augment with Swift-XRT and additional optical/NIR observations reported in the literature. We find that the GRB afterglow, extinguished by a large dust column, is most likely behind a combination of a large Milky-Way dust column combined with moderate low-metallicity dust in the host galaxy. Using the GRANDMA+HXMT-LE+XRT dataset, we find that the simplest model, where the observed afterglow is produced by synchrotron radiation at the forward external shock during the deceleration of a top-hat relativistic jet by a uniform medium, fits the multi-wavelength observations only moderately well, with a tension between the observed temporal and spectral evolution. This tension is confirmed when using the extended dataset. We find that the consideration of a jet structure (Gaussian or power-law), the inclusion of synchrotron self-Compton emission, or the presence of an underlying supernova do not improve the predictions, showing that the modelling of GRB22109A will require going beyond the most standard GRB afterglow model. Placed in the global context of GRB optical afterglows, we find the afterglow of GRB 221009A is luminous but not extraordinarily so, highlighting that some aspects of this GRB do not deviate from the global known sample despite its extreme energetics and the peculiar afterglow evolution.

astro-ph.HE↗

arXiv2022

GRANDMA Observations of ZTF/Fink Transients during Summer 2021

We present our follow-up observations with GRANDMA of transient sources revealed by the Zwicky Transient Facility (ZTF). Over a period of six months, all ZTF triggers were examined in real time by a dedicated science module implemented in the Fink broker, which will be used for the data processing of the Vera C. Rubin Observatory. In this article, we present three selection methods to identify kilonova candidates. Out of more than 35 million candidates, a hundred sources have passed our selection criteria. Six were then followed-up by GRANDMA (by both professional and amateur astronomers). The majority were finally classified either as asteroids or as supernovae events. We mobilized 37 telescopes, bringing together a large sample of images, taken under various conditions and quality. To complement the orphan kilonova candidates (those without associated gamma-ray bursts, which were all), we included three additional supernovae alerts to conduct further observations of during summer 2021. We demonstrate the importance of the amateur astronomer community that contributed images for scientific analyzes of new sources discovered in a magnitude range r'=17-19 mag. We based our rapid kilonova classification on the decay rate of the optical source that should exceed 0.3 mag/day. GRANDMA's follow-up determined the fading rate within 1.5+/-1.2 days post-discovery, without waiting for further observations from ZTF. No confirmed kilonovae were discovered during our observing campaign. This work will be continued in the coming months in the view of preparing for kilonova searches in the next gravitational-wave observing run O4.

astro-ph.HE↗

arXiv2022

The GRANDMA network in preparation for the fourth gravitational-wave observing run

GRANDMA is a world-wide collaboration with the primary scientific goal of studying gravitational-wave sources, discovering their electromagnetic counterparts and characterizing their emission. GRANDMA involves astronomers, astrophysicists, gravitational-wave physicists, and theorists. GRANDMA is now a truly global network of telescopes, with (so far) 30 telescopes in both hemispheres. It incorporates a citizen science programme (Kilonova-Catcher) which constitutes an opportunity to spread the interest in time-domain astronomy. The telescope network is an heterogeneous set of already-existing observing facilities that operate coordinated as a single observatory. Within the network there are wide-field imagers that can observe large areas of the sky to search for optical counterparts, narrow-field instruments that do targeted searches within a predefined list of host-galaxy candidates, and larger telescopes that are devoted to characterization and follow-up of the identified counterparts. Here we present an overview of GRANDMA after the third observing run of the LIGO/VIRGO gravitational-wave observatories in $2019-2020$ and its ongoing preparation for the forthcoming fourth observational campaign (O4). Additionally, we review the potential of GRANDMA for the discovery and follow-up of other types of astronomical transients.

astro-ph.IM↗

arXiv2021

Photometry of selected outer main belt asteroids

We present new photometric observations for twelve asteroids ((122) Gerda, (152) Atala, (260) Huberta, (665) Sabine, (692) Hippodamia, (723) Hammonia, (745) Mauritia, (768) Struveana, (863) Benkoela, (1113) Katja, (1175) Margo, (2057) Rosemary) from the outer part of the main belt aimed to obtain the magnitude-phase curves and to verify geometric albedo and taxonomic class based on their magnitude-phase behaviors. The measured magnitude-phase relations confirm previously determined composition types of (260) Huberta (C-type), (692) Hippodamia (S-type) and (1175) Margo (S-type). Asteroids (665) Sabine and (768) Struveana previously classified as X-type show phase-curve behavior typical for moderate-albedo asteroids and may belong to the M-type. The phase-curve of (723) Hammonia is typical for the S-type which contradicts the previously determined C-type. We confirmed the moderate-albedo of asteroids (122) Gerda and (152) Atala, but their phase-curves are different from typical for the S-type and may indicate more rare compositional types. Based on magnitude-phase behaviors and V-R colors, (2057) Rosemary most probably belongs to M-type, while asteroids (745) Mauritia and (1113) Katja belong to S-complex. The phase curve of the A-type asteroid (863) Benkoela does not cover the opposition effect range and further observations are needed to understand typical features of the phase-curves of A-type asteroids in comparison with other types. We have also determined lightcurve amplitudes of the observed asteroids and obtained new or improved values of the rotation periods for most of them.

astro-ph.EP↗

arXiv2020

Potential asteroid discoveries by the ESA Gaia mission: Results from follow-up observations

Since July 2014, the ESA Gaia mission has been surveying the entire sky down to magnitude 20.7 in the visible. In addition to the millions of stars, thousands of Solar System Objects (SSOs) are observed daily. By comparing their positions to those of known objects, a daily processing pipeline filters known objects from potential discoveries. However, owing to Gaia's specific scanning law designed for stars, potential newly discovered moving objects are characterized by very few observations, acquired over a limited time. This aspect was recognized early in the design of the Gaia data processing. A daily processing pipeline dedicated to these candidate discoveries was set up to release calls for observations to a network of ground-based telescopes. Their aim is to acquire follow-up astrometry and to characterize these objects. From the astrometry measured by Gaia, preliminary orbital solutions are determined, allowing to predict the position of these potentially new discovered objects in the sky accounting for the large parallax between Gaia and the Earth (separated by 0.01 au). A specific task within the Gaia Consortium has been responsible for the distribution of requests for follow-up observations of potential Gaia SSO discoveries. Since late 2016, these calls for observations (called alerts) are published daily via a Web interface, freely available to anyone world-wide. Between November 2016 and July 2020, over 1700 alerts have been published, leading to the successful recovery of more than 200 objects. Among those, six have provisional designation assigned with the Gaia observations, the others being previously known objects with poorly characterized orbits, precluding identification at the time of Gaia observations. There is a clear trend for objects with a high inclination to be unidentified, revealing a clear bias in the current census of SSOs against high inclination populations.

astro-ph.EP↗

arXiv2019

The first six months of the Advanced LIGO's and Advanced Virgo's third observing run with GRANDMA

We present the Global Rapid Advanced Network Devoted to the Multi-messenger Addicts (GRANDMA). The network consists of 21 telescopes with both photometric and spectroscopic facilities. They are connected together thanks to a dedicated infrastructure. The network aims at coordinating the observations of large sky position estimates of transient events to enhance their follow-up and reduce the delay between the initial detection and the optical confirmation. The GRANDMA program mainly focuses on follow-up of gravitational-wave alerts to find and characterise the electromagnetic counterpart during the third observational campaign of the Advanced LIGO and Advanced Virgo detectors. But it allows for any follow-up of transient alerts involving neutrinos or gamma-ray bursts, even with poor spatial localisation. We present the different facilities, tools, and methods we developed for this network, and show its efficiency using observations of LIGO/Virgo S190425z, a binary neutron star merger candidate. We furthermore report on all GRANDMA follow-up observations performed during the first six months of the LIGO-Virgo observational campaign, and we derive constraints on the kilonova properties assuming that the events' locations were imaged by our telescopes.

astro-ph.HE↗

arXiv2017

Transition from Fireball to Poynting-flux-dominated Outflow in Three-Episode GRB 160625B

The ejecta composition is an open question in gamma-ray bursts (GRB) physics. Some GRBs possess a quasi-thermal spectral component in the time-resolved spectral analysis, suggesting a hot fireball origin. Others show a featureless non-thermal spectrum known as the "Band" function, consistent with a synchrotron radiation origin and suggesting that the jet is Poynting-flux-dominated at the central engine and likely in the emission region as well. There are also bursts showing a sub-dominant thermal component and a dominant synchrotron component suggesting a likely hybrid jet composition. Here we report an extraordinarily bright GRB 160625B, simultaneously observed in gamma-rays and optical wavelengths, whose prompt emission consists of three isolated episodes separated by long quiescent intervals, with the durations of each "sub-burst" being $\sim$ 0.8 s, 35 s, and 212 s, respectively. Its high brightness (with isotropic peak luminosity L$_{\rm p, iso}\sim 4\times 10^{53}$ erg/s) allows us to conduct detailed time-resolved spectral analysis in each episode, from precursor to main burst and to extended emission. The spectral properties of the first two sub-bursts are distinctly different, allowing us to observe the transition from thermal to non-thermal radiation between well-separated emission episodes within a single GRB. Such a transition is a clear indication of the change of jet composition from a fireball to a Poynting-flux-dominated jet.

astro-ph.HE↗

arXiv2016

Multicolour modelling of SN 2013dx associated with GRB 130702A

We present optical observations of SN 2013dx, related to the Fermi burst GRB 130702A occurred at a redshift z = 0.145. It is the second-best sampled GRB-SN after SN~1998bw: the observational light curves contain more than 280 data points in uBgrRiz filters until 88 day after the burst, and the data were collected from our observational collaboration (Maidanak Observatory, Abastumani Observatory, Crimean Astrophysical Observatory, Mondy Observatory, National Observatory of Turkey, Observatorio del Roque de los Muchachos) and from the literature. We model numerically the multicolour light curves using the one-dimensional radiation hydrodynamical code STELLA, previously widely implemented for the modelling of typical non-GRB SNe. The best-fitted model has the following parameters: pre-supernova star mass M = 25 M_Sun, mass of a compact remnant M_CR = 6 M_Sun, total energy of the outburst E_oburst = 3.5 x 10^(52) erg, pre-supernova star radius R = 100 R_Sun, M_56Ni = 0.2 M_Sun which is totally mixed through the ejecta; M_O = 16.6 M_Sun, M_Si = 1.2 M_Sun, and M_Fe = 1.2 M_Sun, and the radiative efficiency of the SN is 0.1 per cent.

astro-ph.HE↗

arXiv2013

GRB 130606A within a sub-DLA at redshift 5.91

Events such as GRB130606A at z=5.91, offer an exciting new window into pre-galactic metal enrichment in these very high redshift host galaxies. We study the environment and host galaxy of GRB 130606A, a high-z event, in the context of a high redshift population of GRBs. We have obtained multiwavelength observations from radio to gamma-ray, concentrating particularly on the X-ray evolution as well as the optical photometric and spectroscopic data analysis. With an initial Lorentz bulk factor in the range Γ_0 ~ 65-220, the X-ray afterglow evolution can be explained by a time-dependent photoionization of the local circumburst medium, within a compact and dense environment. The host galaxy is a sub-DLA (log N (HI) = 19.85+/-0.15), with a metallicity content in the range from ~1/7 to ~1/60 of solar. Highly ionized species (N V and Si IV) are also detected. This is the second highest redshift burst with a measured GRB-DLA metallicity and only the third GRB absorber with sub-DLA HI column density. GRB ' lighthouses' therefore offer enormous potential as backlighting sources to probe the ionization and metal enrichment state of the IGM at very high redshifts for the chemical signature of the first generation of stars.

astro-ph.HE↗

arXiv2007

A method of open cluster membership determination

A new method for the determination of open cluster membership based on a cumulative effect is proposed. In the field of a plate the relative x and y coordinate positions of each star with respect to all the other stars are added. The procedure is carried out for two epochs t_1 and t_2 separately, then one sum is subtracted from another. For a field star the differences in its relative coordinate positions of two epochs will be accumulated. For a cluster star, on the contrary, the changes in relative positions of cluster members at t_1 and t_2 will be very small. On the histogram of sums the cluster stars will gather to the left of the diagram, while the field stars will form a tail to the right. The procedure allows us to efficiently discriminate one group from another. The greater the distance between t_1 and t_2 and the more cluster stars present, the greater is the effect. The accumulation method does not require reference stars, determination of centroids and modelling the distribution of field stars, necessary in traditional methods. By the proposed method 240 open clusters have been processed, including stars up to m<13. The membership probabilities have been calculated and compared to those obtained by the most commonly used Vasilevskis-Sanders method. The similarity of the results acquired the two different approaches is satisfactory for the majority of clusters.

astro-ph↗