TIME RESOLVED SPECTRA OF GRBs SIMULTANEOUSLY DETECTED WITH BATSE andBeppoSAX WFCs

We will discuss preliminary results of a systematic investigation devoted to study the time resolved broad-band spectra of the prompt emission of a sample of GRBs. These events were simultaneously detected with the BeppoSAX WFCs and the BATSE instrument aboard CGRO. We will discuss the fit of these spectra with the Band function, with a blackbody plus a power–law model, and with a Comptonization model developed by Titarchuk & Farinelli (2011, to be submitted).

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Extremely Bright GRB160625B with Short-Soft Precursor and long-hard extended emission: Hints for long-term evolution of the GRB Ejecta

Proceedings of the International Astronomical Union ◽

10.1017/s1743921317003295 ◽

2016 ◽

Vol 12 (S324) ◽

pp. 74-77

Author(s):

Shu-Qing Zhong ◽

Jing Lü ◽

Hou-Jun Lü ◽

Hai-Ming Zhang ◽

Xiao-Li Huang ◽

...

Keyword(s):

Power Law ◽

Optical Emission ◽

High Energy ◽

Power Law Model ◽

Term Evolution ◽

Internal Shock ◽

High Energy Emission ◽

Prompt Emission ◽

Extended Emission

AbstractIn this paper, we focus on studying the high energy emission of GRB 160625B. The lightcurve of prompt emission is composed of three episodes: short-soft precursor, hard main burst, and possible long extended emission. The spectra of first and third episode can be fitted by a multi-color blackbody and cutoff power-law model, respectively. However, the spectrum of second episode was contributed by both multi-color blackbody and cutoff power-law. One can estimate the Lorenz factor of jet of first two episodes by invoking photosphere model as Γ0 ~ 175 and 1694, respectively. It suggests that the ejecta of this case evolved from photosphere dominated initially to internal shock later. On the other hand, the optical emission is very bright during the second episode, which is likely a prompt optical emission. Finally, a more shallower normal decay segment appeared, which is consistent with standard external shock model.

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A NuSTAR view of GRS 1716−249 in the hard and intermediate states

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa017 ◽

2020 ◽

Vol 492 (2) ◽

pp. 1947-1956

Author(s):

Jiachen Jiang ◽

Felix Fürst ◽

Dominic J Walton ◽

Michael L Parker ◽

Andrew C Fabian

Keyword(s):

Power Law ◽

Broad Band ◽

High Density ◽

Density Parameter ◽

Reflection Spectroscopy ◽

Reflection Model ◽

Hard State ◽

Band Spectra ◽

Reflection Component ◽

Emission Line Feature

ABSTRACT We present a detailed analysis of the spectral properties of the black hole transient GRS 1716−249, based on the archival Swift and NuSTAR observations taken during the outburst of this source in 2016–2017. The first six NuSTAR observations show that the source is in a canonical hard state, where the spectrum is dominated by a power-law continuum. The seventh NuSTAR observation is taken during the intermediate state where both a disc thermal component and a power-law continuum are shown. All of our observations show a broad emission-line feature in the iron band and a Compton hump above 10 keV. We model the broad-band spectra using a high-density disc reflection model, where the soft X-ray emission in the hard state is interpreted as part of the disc reflection component. This model enables us to constrain the disc density parameter of GRS 1716−249 in the range of 1019–1020 cm−3. We only obtain an upper limit of the inner disc radius using high-density disc reflection spectroscopy and the results indicate either a non-truncated disc or a slightly truncated disc with Rin ≲ 20 rg.

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NUSTAR and Swift observations of AMXP Swift J1756.9−2508 during its 2018 outburst

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz2510 ◽

2019 ◽

Vol 489 (4) ◽

pp. 5858-5865

Author(s):

Binay Rai ◽

Bikash Chandra Paul

Keyword(s):

Spectral Analysis ◽

Power Law ◽

Power Law Model ◽

Pulse Profile ◽

Spectral Parameters ◽

Time Resolved ◽

Pulse Phase ◽

Photon Index ◽

Hard State ◽

Orbital Phase

ABSTRACT We present here the timing and spectral analysis of the accreting millisecond pulsar (AMXP) SwiftJ1756.9−2508 during its recent outburst in 2018 using Swift and NUSTAR observations. The simultaneous fitting of the Swift and NUSTAR spectra indicates that the source was in the hard state with a cut-off energy of about 74.58 keV. We also study in detail the pulse profile of the AMXP and its dependence on energy. The colour–colour diagram of the source is different from those previously reported. We performed phase- and time-resolved spectral analysis using NUSTAR data. Pulse phase-resolved spectra were fitted with a power-law model and significant changes in the spectral parameters with pulse phase were observed. The orbital phase and time-resolved spectra were fitted with a cut-off power-law model. The column density and photon index obtained from orbital phase spectral analysis were found to show some anticorrelation with the flux. Through time-resolved spectral analysis, we observed that the spectral parameters show positive correlation with each other and with the flux. We do not observe a softening of the spectrum with time. No emission lines or Compton bump were observed in the spectrum of the AMXP.

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Power law model. Goodness-of-fit tests and estimation methods

10.3403/30249080 ◽

2013 ◽

Keyword(s):

Power Law ◽

Goodness Of Fit ◽

Estimation Methods ◽

Power Law Model ◽

Goodness Of Fit Tests

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Polyconvex hyperelastic modeling of rubberlike materials

Journal of the Brazilian Society of Mechanical Sciences and Engineering ◽

10.1007/s40430-021-03062-w ◽

2021 ◽

Vol 43 (7) ◽

Author(s):

Cyprian Suchocki ◽

Stanisław Jemioło

Keyword(s):

Experimental Data ◽

Power Law ◽

Curve Fitting ◽

Constitutive Relations ◽

Data Sets ◽

Power Law Model ◽

Stored Energy ◽

Data Approximation ◽

Exponential Power ◽

Hyperelastic Models

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

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Unsteady thermal Maxwell power law nanofluid flow subject to forced thermal Marangoni Convection

Scientific Reports ◽

10.1038/s41598-021-86865-0 ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Muhammad Jawad ◽

Anwar Saeed ◽

Taza Gul ◽

Zahir Shah ◽

Poom Kumam

Keyword(s):

Relaxation Time ◽

Power Law ◽

Marangoni Convection ◽

Power Law Model ◽

Analysis Method ◽

Stretching Surface ◽

Nanofluid Flow ◽

Welan Gum ◽

Homotopy Analysis ◽

Power Law Nanofluid

AbstractIn the current work, the unsteady thermal flow of Maxwell power-law nanofluid with Welan gum solution on a stretching surface has been considered. The flow is also exposed to Joule heating and magnetic effects. The Marangoni convection equation is also proposed for current investigation in light of the constitutive equations for the Maxwell power law model. For non-dimensionalization, a group of similar variables has been employed to obtain a set of ordinary differential equations. This set of dimensionless equations is then solved with the help of the homotopy analysis method (HAM). It has been established in this work that, the effects of momentum relaxation time upon the thickness of the film is quite obvious in comparison to heat relaxation time. It is also noticed in this work that improvement in the Marangoni convection process leads to a decline in the thickness of the fluid’s film.

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Searching for energy-resolved quasi-periodic oscillations in AGN

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa4024 ◽

2021 ◽

Author(s):

Dominic I Ashton ◽

Matthew J Middleton

Keyword(s):

Power Law ◽

Spectral Component ◽

Broad Band ◽

Initial Study ◽

Periodic Oscillations ◽

Single Observation ◽

Curved Space ◽

Multiple Observations ◽

Band Noise ◽

The Impact

Abstract X-ray quasi-periodic oscillations (QPOs) in AGN allow us to probe and understand the nature of accretion in highly curved space-time, yet the most robust form of detection (i.e. repeat detections over multiple observations) has been limited to a single source to-date, with only tentative claims of single observation detections in several others. The association of those established AGN QPOs with a specific spectral component has motivated us to search the XMM-Newton archive and analyse the energy-resolved lightcurves of 38 bright AGN. We apply a conservative false alarm testing routine folding in the uncertainty and covariance of the underlying broad-band noise. We also explore the impact of red-noise leak and the assumption of various different forms (power-law, broken power-law and lorentzians) for the underlying broad-band noise. In this initial study, we report QPO candidates in 6 AGN (7 including one tentative detection in MRK 766) from our sample of 38, which tend to be found at characteristic energies and, in four cases, at the same frequency across at least two observations, indicating they are highly unlikely to be spurious in nature.

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X-ray Properties of 3C 111: Separation of Primary Nuclear Emission and Jet Continuum

Universe ◽

10.3390/universe6110219 ◽

2020 ◽

Vol 6 (11) ◽

pp. 219

Author(s):

Elena Fedorova ◽

B.I. Hnatyk ◽

V.I. Zhdanov ◽

A. Del Popolo

Keyword(s):

Accretion Disk ◽

Power Law ◽

Line Emission ◽

High Energy ◽

Power Law Model ◽

X Ray ◽

Additional Information ◽

Observational Dataset ◽

Simple Power ◽

Photon Index

3C111 is BLRG with signatures of both FSRQ and Sy1 in X-ray spectrum. The significant X-ray observational dataset was collected for it by INTEGRAL, XMM-Newton, SWIFT, Suzaku and others. The overall X-ray spectrum of 3C 111 shows signs of a peculiarity with the large value of the high-energy cut-off typical rather for RQ AGN, probably due to the jet contamination. Separating the jet counterpart in the X-ray spectrum of 3C 111 from the primary nuclear counterpart can answer the question is this nucleus truly peculiar or this is a fake “peculiarity” due to a significant jet contribution. In view of this question, our aim is to estimate separately the accretion disk/corona and non-thermal jet emission in the 3C 111 X-ray spectra within different observational periods. To separate the disk/corona and jet contributions in total continuum, we use the idea that radio and X-ray spectra of jet emission can be described by a simple power-law model with the same photon index. This additional information allows us to derive rather accurate values of these contributions. In order to test these results, we also consider relations between the nuclear continuum and the line emission.

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Dynamics of Developing Laminar Non-Newtonian Falling Liquid Films With Free Surface

Journal of Applied Mechanics ◽

10.1115/1.3424229 ◽

1978 ◽

Vol 45 (1) ◽

pp. 19-24 ◽

Cited By ~ 20

Author(s):

V. Narayanamurthy ◽

P. K. Sarma

Keyword(s):

Liquid Film ◽

Power Law ◽

Mathematical Formulation ◽

Liquid Films ◽

Interfacial Shear ◽

Newtonian Liquid ◽

Power Law Model ◽

Falling Liquid Film ◽

Falling Liquid Films ◽

Special Case

The dynamics of accelerating, laminar non-Newtonian falling liquid film is analytically solved taking into account the interfacial shear offered by the quiescent gas adjacent to the liquid film under adiabatic conditions of both the phases. The results indicate that the thickness of the liquid film for the assumed power law model of the shear deformation versus the shear stress is influenced by the index n, the modified form of (Fr/Re). The mathematical formulation of the present analysis enables to treat the problem as a general type from which the special case for Newtonian liquid films can be derived by equating the index in the power law to unity.

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