Log-parabola Models Research Articles

Detection of the Extended γ-Ray Emission from the New Supernova Remnant G321.3–3.9 with Fermi-LAT

With the 15 yr of Pass 8 data recorded by the Fermi Large Area Telescope, we report the detection of an extended gigaelectronvolt emission component with a 68% containment radius of 0.°85, which is spatially associated with the newly identified supernova remnant (SNR) G321.3–3.9. The γ-ray spectrum is best described by a log-parabola model in the energy range of 100 MeV–1 TeV, which shows a significant spectral curvature at ∼1 GeV. Either a leptonic or a hadronic model could explain the multiwavelength data of G321.3–3.9, while the leptonic model predicts a too-low strength of magnetic field. Also considering the flat radio spectrum of G321.3–3.9 and the γ-ray upper limit in the low energy band, the hadronic model is favored. The spatial coincidence between the γ-ray morphology and the diffuse thermal X-ray emission of G321.3–3.9 and the curved gigaelectronvolt γ-ray spectrum make G321.3–3.9 similar to the typical middle-aged SNRs interacting with molecular clouds (MCs). Such characteristics provide further evidence of the potential hadronic origin for its γ-ray emission. However, there is no MC detected around G321.3–3.9, which challenges the hadronic model.

Probing broadband spectral energy distribution and variability of Mrk 501 in the low flux state

We conducted a multi-wavelength analysis of the blazar Mrk501, utilizing observations from AstroSat (SXT, LAXPC), Swift-UVOT, and Fermi-LAT during the period August 15, 2016 to March 27, 2022. The resulting multi-wavelength light curve revealed relatively low activity of the source across the electromagnetic spectrum. Notably, logparabola and broken power-law models provided a better fit to the joint X-ray spectra from AstroSat-SXT/LAXPC instruments compared to the power-law model. During the low activity state, the source showed the characteristic “harder when brighter” trend at the X-ray energies. To gain insights into underlying physical processes responsible for the broadband emission, we performed a detailed broadband spectral analysis using the convolved one-zone leptonic model with different forms of particle distributions such as logparabola (LP), broken power-law (BPL), power-law model with maximum energy (ξmax), and energy-dependent acceleration (EDA) models. Our analysis revealed similar reduced-χ2 values for the four particle distributions. The LP and EDA models exhibited the lowest jet powers. The correlation analyses conducted for the LP and BPL models revealed that there is a positive correlation between jet power and bulk Lorentz factor. Specifically, in the LP model, jet power proved independent of γmin, whereas in the broken power-law model, jet power decreased with an increase in γmin. The jet power in the LP/EDA particle distribution is nearly 10 percent of the Eddington luminosity of a 107 M⊙ black hole. This result suggests that the jet could potentially be fueled by accretion processes.

Revisiting γ-Ray Emission of the Supernova Remnant RCW 103

We analyze more than 15 yr of γ-ray data obtained with the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope (Fermi) for the region of the young supernova remnant (SNR) RCW 103, since the nearby source 4FGL J1616.2−5054e, counterpart to HESS J1616−518 and ≃13′ away from the SNR, is determined to be extended in the more recent Fermi-LAT source catalog. Different templates for 4FGL J1616.2−5054e and RCW 103 are tested, and we find that a point source (PS) with a power-law (PL) spectrum at the southern limb of the SNR best describes the detected γ-ray emission. The photon index of the PL emission is Γ ≃ 2.31 (or α ≃ 2.4 in a log-parabola model), softer than the previously reported Γ ≃ 2.0 when the counterpart to HESS J1616−518 was considered to be a PS (which likely caused misidentification of extended emission at RCW 103). In order to produce the γ-ray emission in a hadronic scenario, we estimate that protons with an index ∼2.4 PL energy distribution are needed. These results fit with those from multiwavelength observations that have indicated the remnant at the southern limb is interacting with a molecular cloud.

Curvature in the very-high energy gamma-ray spectrum of M 87

The radio galaxy M 87 is a variable very-high energy (VHE) gamma-ray source, exhibiting three major flares, which were reported in 2005, 2008, and 2010. Despite extensive studies, the origin of the VHE gamma-ray emission is not yet fully understood. In this study, we investigate the VHE gamma-ray spectrum of M 87 during states of high gamma-ray activity, utilizing 20.2 h of H.E.S.S. observations. Our findings indicate a preference for a curved spectrum, characterized by a log-parabola model with extra-galactic background light (EBL) model above 0.3 TeV at the 4σ level, compared to a power-law spectrum with EBL. We investigate the degeneracy between the absorption feature and the EBL normalization and derive upper limits on EBL models that are mainly sensitive in the wavelength range of 12.4 μm–40 μm.

Optimization of performance of the KM2A full array using the Crab Nebula* *Supported by the National Key R & D Program of China (2018YFA0404201, 2018YFA0404202, 2018YFA0404203, 2018YFA0404204), the National Natural Science Foundation of China (12022502, 12205314, 12105301, 12261160362, 12105294, U1931201), the Youth Innovation Promotion Association CAS (2022010) and in Thailand by the National Science and Technology Development Agency (NSTDA), and

The full array of the Large High Altitude Air Shower Observatory (LHAASO) has been in operation since July 2021. For its kilometer-square array (KM2A), we optimized the selection criteria for very high and ultra-high energy γ-rays using data collected from August 2021 to August 2022, resulting in an improvement in significance of the detection in the Crab Nebula of approximately 15%, compared with that of previous cuts. With the implementation of these new selection criteria, the angular resolution was also significantly improved by approximately 10% at tens of TeV. Other aspects of the full KM2A array performance, such as the pointing error, were also calibrated using the Crab Nebula. The resulting energy spectrum of the Crab Nebula in the energy range of 10-1000 TeV are well fitted by a log-parabola model, which is consistent with the previous results from LHAASO and other experiments.

X-Ray Studies of Blazar 1ES 1959+650 Using Swift and XMM-Newton Satellite

High synchrotron energy peaked blazar 1ES 1959+650 was studied with the Swift and XMM-Newton satellites in a total of 127 observations during the period 2018 June–2020 December. We extensively studied its flux and spectral variability on intraday and long-term timescales. Discrete correlation function analysis between soft and hard X-ray bands indicates soft as well as hard lags. The results were used to constrain the magnetic field of the emitting region, which was found to be 0.64 ± 0.05 G. On long-term timescales, the distribution of fluxes shows lognormal behavior, which could be attributed to the minijets-in-a-jet model or might be due to the propagation of relativistic shocks down the jet. The spectral energy distribution around the synchrotron peak is well described by the log-parabola model. Spectral parameters like the peak energy E p , curvature β, and peak luminosity L p were derived from spectral analysis. Their correlations were studied to constrain the acceleration processes of the emitting particles. E p shows strong correlation with L p during the high state of the source, which indicates spectral changes might be caused by the variations of the average electron energy. Low values of the curvature parameter β and a weak correlation between E p and β indicate the coexistence of stochastic/statistical acceleration of electrons in the emitting region. Implications of other results are also discussed.

Analysis of X-Ray Emission From Source TXS 0506+056 Using Xmm-Newton Observations

We report the findings of analysis of X-ray flares in TXS 0506+056 using XMM-Newton data obtained from the maximum likelihood analysis. Two publicly available XMM-Newton X-ray observations for TXS 0506+056 were analyzed to study the spectrum and light curves. The spectrum curves revealed two energy bumps, with the lower energy bump at 0.5 keV and the higher energy bump at 6 keV. For observational IDs 0083960101 and 0083960201, the integrated flux for hard X-ray (2–10 keV) is 1.835 10-12 ergs cm-2 s-1 and 1.813 10-12 ergs cm-2 s-1 with corresponding uncertainty range of (1.754–1.913) 10-12 ergs cm-2 s-1 and (1.490–3.515) 10-12 ergs cm-2 s-1, respectively. The best fit models for X-ray data observations of observational IDs of 0083960101 and 0083960201 were phabs (gaussian+power-law) and Tbabs (gaussian+log-parabola) with reduced chi squared values of 1.56 and 1.05, respectively. A turning point at around 2 keV appeared in the spectrum curve, suggesting that the gaussian model only applies for soft X-ray (0.3–2 keV), while the power law and the log parabola model are the best fit models for hard X-ray (2–10 keV). Observation ID 0850780101 shows that the source TXS 0506+056 has a fractional variability of 1.4 %, while Observation ID 0850780201 shows a higher fractional variability of 3.0 % which indicates brightness varies over time. A greater disparity in the source's rise time suggests a higher degree of variability in its brightness.

On the Gamma-Ray Emission of the Andromeda Galaxy M31

Using the γ-ray data obtained with the Large Area Telescope on board the Fermi Gamma-ray Space Telescope (Fermi) for ∼14 yr, we examine the high-energy emission emanating from the center of the Andromeda galaxy M31. Different from previously reported results, which show a seemingly extended source, we instead find two individual point sources, one consistent with being at the center and one 0.°4 southeast of the center. The emission of the former is well described using a log-parabola model, similar to those of previous studies, and that of the latter can be fitted with a power law. We discuss the possible origins for the two sources. M31's central source, now consistent with being a point source, necessitates a revisit of its previously discussed originations with this new property taken into consideration, in particular those cosmic rays or dark matter scenarios involving extended source distributions. The SE source appears to have a projected distance of ∼6 kpc from M31's center, and the investigation is required as to whether it is a source locally associated with M31, or is instead a background extragalactic one.

A Study on the X-Ray Pulse Profile and Spectrum of the Crab Pulsar Using NICER and Insight-HXMT's Observations

Abstract We analyze the energy dependence of the X-ray pulse profile and the phase-resolved spectra (PRS) of the Crab pulsar using observations from the Neutron star Interior Composition Explorer (NICER) and the Hard X-ray Modulation Telescope (Insight-HXMT). We parameterize the pulse profiles and quantify the evolution of these parameters in the broad energy band of 0.4–250 keV. A log-parabola function is used to fit the PRS in 2–250 keV, and the curvature of the spectrum, i.e., the evolution of the photon index with energy, as represented by the parameter β of the log-parabola model, also changes with phase. The relation of β and phase has two turning points slightly later than those of the pulse intensity profile, where the values of β are the lowest, suggesting that the energy-loss rate of the particles is the lowest in the corresponding regions. A three-segment broken-power-law model is also used to fit those PRS. The differences between the hard spectral index and the soft ones have a distribution similar to that of β, confirming the fitting results of the log-parabola model, while the broken energies are generally higher in the region bridging the two pulses. We find anticorrelations between the spectral indices and the curvature of the log-parabola model fitting and a similar anticorrelation between the spectral indices and broken energies of the broken-power-law model fitting, suggesting a scenario where the highest-energy particles are produced in regions where radiation energy loss is strongest.

Improved Characterization of the Astrophysical Muon–neutrino Flux with 9.5 Years of IceCube Data

Abstract We present a measurement of the high-energy astrophysical muon–neutrino flux with the IceCube Neutrino Observatory. The measurement uses a high-purity selection of 650k neutrino-induced muon tracks from the northern celestial hemisphere, corresponding to 9.5 yr of experimental data. With respect to previous publications, the measurement is improved by the increased size of the event sample and the extended model testing beyond simple power-law hypotheses. An updated treatment of systematic uncertainties and atmospheric background fluxes has been implemented based on recent models. The best-fit single power-law parameterization for the astrophysical energy spectrum results in a normalization of ϕ @ 100 TeV ν μ + ν ¯ μ = 1.44 − 0.26 + 0.25 × 10 − 18 GeV − 1 cm − 2 s − 1 sr − 1 and a spectral index γ SPL = 2.37 − 0.09 + 0.09 , constrained in the energy range from 15 TeV to 5 PeV. The model tests include a single power law with a spectral cutoff at high energies, a log-parabola model, several source-class-specific flux predictions from the literature, and a model-independent spectral unfolding. The data are consistent with a single power-law hypothesis, however, spectra with softening above one PeV are statistically more favorable at a two-sigma level.

γ-ray Flux and Spectral Variability of Blazar Ton 599 during Its 2021 Flare

Blazars are known to emit exceptionally variable non-thermal emission over the wide range (from radio to γ-rays) of electromagnetic spectrum. We present here the results of our γ-ray flux and spectral variability study of the blazar Ton 599, which has been recently observed in the γ-ray flaring state. Using 0.1–300 GeV γ-ray data from the Fermi Gamma-ray Space Telescope (hereinafter Fermi), we generated one-day binned light curve of Ton 599 for a period of about one-year from MJD 59,093 to MJD 59,457. During this one year period, the maximum γ-ray flux detected was 2.24 ± 0.25 × 10−6 ph cm−2 s−1 at MJD 59,399.50. We identified three different flux states, namely, epoch A (quiescent), epoch B (pre-flare) and epoch C (main-flare). For each epoch, we calculated the γ-ray flux variability amplitude (Fvar) and found that the source showed largest flux variations in epoch C with Fvar∼ 35%. We modelled the γ-ray spectra for each epoch and found that the Log-parabola model adequately describes the γ-ray spectra for all the three epochs. We estimated the size of the γ-ray emitting region as 1.03 × 1016 cm and determined that the origin of γ-ray radiation, during the main-flare, could be outside of the broad line region.

An XMM–Newton catalogue of BL Lacs

Aims. We present an XMM–Newton catalogue of BL Lac X-ray, optical, and UV properties based on cross-correlation with the 1151 BL Lacs listed in the fifth edition of the Roma–BZCAT. Methods. We searched for the X-ray counterparts to these objects in the field of view of all pointed observations in the XMM–Newton archive over nearly 20 years of mission. The cross-correlation yields a total of 310 XMM–Newton fields which correspond to 103 different BL Lacs. We homogeneously analysed data from the three EPIC cameras (X-ray) and OM (optical/UV) using the XMM–Newton SAS software, and produced images, light curves, and spectral products for BL Lacs detected in any of the three EPIC cameras. We tested two different phenomenological models, log parabola and power law, with different variations of the absorbing column density and extracted their parameters. We derived time-variability information from the light curves following well-established statistical methods and quantified variability through statistical indicators. OM magnitudes and fluxes were computed wherever possible. Results. We see that the log parabola model is preferred over the power law model for sources showing higher fluxes, which might indicate that curvature is intrinsic to BL Lacs and is only seen when the flux is high. We present the results of our analysis as a catalogue of X-ray spectral properties of the sample in the 0.2–10 keV energy band as well as in the optical/UV band. We complete the catalogue with multi-wavelength information at radio and γ-ray energies.

Blazar OJ 287 after First VHE Activity: Tracking the Reemergence of the HBL-like Component in 2020

Abstract We report the reemergence of a new broadband emission through a detailed and systematic study of the multiwavelength spectral and temporal behavior of OJ 287 after its first-ever reported very high energy activity in 2017 to date, which includes the second-highest X-ray flux of the source. The source shows high optical to X-ray flux variations, accompanied mainly by strong spectral changes. The optical to X-ray flux variations are correlated and simultaneous except for two durations when they are anticorrelated. The flux variations, however, are anticorrelated with the X-ray spectral state while correlated with optical–UV (ultraviolet). Weekly binned Fermi-LAT data around the duration of the highest X-ray activity show a few detections with a log-parabola model but none with a power law, yet the extracted LAT spectral energy distribution of the high-activity duration for both the models is similar and shows a hardening above 1 GeV. Further, near-infrared data indicate strong spectral change, resembling a thermal component. Overall, the combined optical to gamma-ray broadband spectrum establishes the observed variations to a new high-energy-peaked broadband emission component, similar to the one seen during the highest reported X-ray flux state of the source in 2017. The observed activities indicate some peculiar features that seem to be characteristic of this emission component, while its appearance a few years around the claimed ∼12 yr optical outbursts strongly indicates a connection between the two.

Understanding the X-ray spectral curvature of Mkn 421 using broad-band AstroSat observations

ABSTRACT We present a time-resolved X-ray spectral study of the high energy peaked blazar Mkn 421 using simultaneous broad-band observations from the LAXPC and SXT instruments on-board AstroSat. The ∼400 ksec long observation taken during 2017 January 3–8 was divided into segments of 10 ksecs. Each segment was fitted using synchrotron emission from particles whose energy distribution was represented by a log-parabola model. We also considered particle energy distribution models where (i) the radiative cooling leads to a maximum energy (ξmax model), (ii) the system has energy-dependent diffusion (EDD) and (iii) has energy-dependent acceleration (EDA). We found that all these models describe the spectra, although the EDD and EDA models were marginally better. Time-resolved spectral analysis allowed for studying the correlation between the spectral parameters for different models. In the simplest and direct approach, the observed correlations are not compatible with the predictions of the ξmax model. While the EDD and EDA models do predict the correlations, the values of the inferred physical parameters are not compatible with the model assumptions. Thus, we show that spectrally degenerate models, can be distinguished based on spectral parameter correlations (especially those between the model normalization and spectral shape ones) making time-resolved spectroscopy a powerful tool to probe the nature of these systems.

Multi-Wavelength Study of 4C+28.07

Abstract 4C+28.07 is a γ-ray flat-spectrum-radio-quasar-type source. It is often monitored at different frequencies, though long-term multi-wavelength data of this source have not been modeled in detail before. We have analyzed ∼12 yr (2008 August–2020 May) of Fermi-LAT data with a binning of 10 day timescale and observed three distinctive flaring states. Each flaring state consists of different phases of activity, namely, pre-flare, flare, and post-flare regions. γ-ray spectral analysis of these different activity phases has been performed and the best-fit model for its spectra is found to be a log-parabola model. We have also studied the correlation of simultaneous γ-ray light curves with the optical & radio counterparts in these flaring states and report the DCF with 95% significance level. A large time delay is found between radio and gamma-ray data for two flares, indicating two zones of emission. We have fitted the multi-wavelength data with a two-zone leptonic model. In our two-zone leptonic model the maximum required power in the jet is 9.64 × 1046 erg s−1, which is lower than its Eddington luminosity 2.29 × 1047 erg s−1.

Spatiotemporal Contrast Sensitivity of Brown-Norway Rats under Scotopic and Photopic Illumination

Rats are a popular animal model for vision research and for investigating disorders of the visual system. The study aimed to quantify the spatiotemporal contrast sensitivity function (CSF) of healthy adult Brown-Norway rats under scotopic and photopic illumination. Animals were trained to jump onto the one of two adjacent platforms behind which was displayed a sinewave grating pattern. Contrast thresholds of light- and dark-adapted rats were determined using a staircase method of adjustment for gratings that varied in spatial frequency (sf) and temporal frequency (tf) and ranged several log-units in mean luminance. Photopic CSFs showed strong bandpass spatial tuning, consistent with prior measurements, and weak bandpass temporal tuning. CSFs were parameterized by a truncated log-parabola model, yielding a peak contrast sensitivity of 52 ± 9, peak sf of 0.17 ± 0.05 cycles/degree, sf limit of 1.6 ± 0.3 cycles/degree, low sf attenuation of 85 ± 9%, peak tf of 1.7 ± 1.1 Hz, extrapolated tf limit of 166 ± 44 Hz, and low tf attenuation of 55 ± 12%. CSFs became more lowpass and decreased systematically in contrast sensitivity and spatiotemporal acuity as mean luminance was reduced. CSFs were also measured via the visual head-tracking reflex. Photopic contrast sensitivity, spatial acuity, and temporal acuity were all markedly below that of the grating detection task and optomotor findings for other rat strains. The CSF data provide a comprehensive and quantitative description of rat spatial and temporal vision and a benchmark for evaluating effects of ocular diseases on their ability to see.

NuSTAR View of TeV Blazar Mrk 501

We report the results of flux and spectral variability studies of all seven Nuclear Spectroscopic Telescope Array (NuSTAR) observations of TeV γ-ray emitting blazar Markarian (or Mrk) 501. We found strong evidence of intraday variability in 3–79 keV X-ray light curves (LCs) of Mrk 501 during four out of these seven observations. We examined spectral variability using a model-independent hardness-ratio analysis and found a general “harder-when-brighter” behaviour in two observations. We also investigated the nature of 3–79 keV X-ray spectra of TeV blazar Mrk 501 and found that five out of seven spectra are well described by the curved log-parabola models with photon indices (at 10 keV) α∼ 2.12–2.32 and a curvature β∼ 0.15–0.28. The two other spectra are somewhat better represented by simple power-law models with photon indices 2.70 and 2.75. We briefly discuss available physical models to explain our results.

Strong Soft X-Ray Excess in 2015 XMM-Newton Observations of BL Lac OJ 287

Abstract We report a strong soft X-ray excess in the BL Lacartae γ-ray blazar OJ 287 during long exposure in 2015 May, among two of the latest XMM-Newton observations performed in 2015 and 2018 May. In the case of the 2015 May observation, a log parabola model fits the EPIC-pn data well, while a log parabola plus a power law describes the overall simultaneous optical to X-ray spectra, suggesting the excess as the synchrotron tail. This interpretation, however, is inconsistent with the observed spectral break between near-infrared (NIR) and optical spectra, attributed to a standard disk around a supermassive black hole (SMBH). Based on this, we considered two commonly invoked accretion-disk-based models in active galactic nuclei (AGNs) to explain the soft excess: the cool Comptonization component in the accretion disk and the blurred reflection from the partially ionized accretion disk. We found that both cool Comptonization and blurred reflection models provide an equally good fit to the data, and favor a super-heavy SMBH of mass ∼1010 M ⊙. Further investigation of about a month-long simultaneous X-ray and ultraviolet (UV) pointing observations revealed a delayed UV emission with respect to the 1.5–10 keV band, favoring X-ray reprocessing phenomenon as the dominant mechanism. The results suggest that the soft excess is probably caused by strong light bending close to the SMBH. The detected soft excess in the 2015 data and its disappearance in the 2018 data is also consistent with the presence of accretion-disk emission, inferred from the NIR–optical spectral break between 2013 May and 2016 March.

Hard X-ray properties of NuSTAR blazars

Context. Investigation of the hard X-ray emission properties of blazars is key to the understanding of the central engine of the sources and associated jet process. In particular, simultaneous spectral and timing analyses of the intraday hard X-ray observations provide us a means to peer into the compact innermost blazar regions that are not accessible to our current instruments. Aims. The primary objective of the work is to associate the observed hard X-ray variability properties in blazars with their flux and spectral states, thereby, based on the correlation among these states, extract the details about the emission regions and processes occurring near the central engine. Methods. We carried out timing, spectral, and cross-correlation analysis of 31 NuSTAR observations of 13 blazars. We investigated the spectral shapes of the sources using single power-law, broken power-law, and log-parabola models. We also studied the co-relation between the soft and hard emission using z-transformed discrete correlation function. In addition, we attempted to constrain the smallest emission regions using minimum variability timescales derived from the light curves. Results. We found that, for most of the sources, the hard X-ray emission can be well represented by the log-parabola model and that the spectral slopes for different blazar subclasses are consistent with the so-called blazar sequence. We also report the steepest spectra (Γ ∼ 3) in the BL Lacertae PKS 2155–304 and the hardest spectra (Γ ∼ 1.4) in the flat-spectrum radio quasar PKS 2149–306. In addition, we noted a close connection between the flux and spectral slope within the source subclass in the sense that high flux and/or flux states tend to be harder in spectra. In BL Lacertae objects, assuming particle acceleration by diffusive shocks and synchrotron cooling as the dominant processes governing the observed flux variability, we constrain the magnetic field of the emission region to be a few Gauss; whereas in flat-spectrum radio quasars, using external Compton models, we estimate the energy of the lower end of the injected electrons to be a few Lorentz factors.

Gamma-ray emission from high Galactic latitude globular clusters

We analyse 8 years of PASS 8 Fermi-LAT data, in the 60 MeV - 300 GeV energy range, from 30 high Galactic latitude globular clusters. Six of these globular clusters are detected with a TS > 25, with NGC 6254 being detected as gamma-ray bright for the first time. The most significant detection is of the well-known globular cluster 47 Tuc, and we produce a refined spectral fit for this object with a log parabola model. NGC 6093, NGC 6752 and NGC 6254 are fitted with hard, flat power law models, NGC 7078 is best fitted with a soft power law and NGC 6218 is best fitted with a hard, broken power law. This variety of spectral models suggests that there is a variety of gamma-ray source types within globular clusters, in addition to the traditional millisecond pulsar interpretation. We identify a correspondence between diffuse X-ray emission in globular cluster cores and gamma-ray emission. This connection suggests that gamma-ray emission in globular clusters could also arise from unresolved X-ray sources or a relativistic electron population, perhaps generated by the millisecond pulsars. X-ray observations of further gamma-ray bright globular clusters would allow a functional relationship to be determined between diffuse X-ray and gamma-ray emission.