BL Lac Objects Research Articles

The Detection of Possible Quasiperiodic Oscillations in the BL Lac 4FGL J2139.4−4235

We present periodicity search analyses on the long-term γ-ray light curve of the BL Lacertae object 4FGL J2139.4−4235 observed by the Fermi Large Area Telescope, over a period of more than 15 yr, from 2008 August 4 to 2023 December 10. To determine the quasiperiodic oscillation (QPO) behavior of 4FGL J2139.4−4235 in the 0.3–300 GeV energy range, we used four methods, namely the Lomb–Scargle periodogram, the weighted wavelet z-transform, the phase dispersion minimization, and the autoregressive integrated moving average model. A Monte Carlo simulation technique is used to evaluate the significance level of the QPO signal. Significant levels above 3.5σ were detected in the γ-ray light curve at about 650 days QPO, which is presented throughout the observation period. Interestingly, there was some correlation between the three bands in the discrete correlation function method calculations, which may be an indication that the variability trends between the three bands are similar. We explore the possible physical models and show that a supermassive binary black hole system or a jet helical motion model seem to be reasonable explanations for the potential QPO behavior.

A multiwavelength study of the most distant gamma-ray detected BL Lacertae object 4FGL J1219.0+3653 (z = 3.59)

BL Lac objects are a class of jetted active galactic nuclei that do not exhibit or have weak emission lines in their optical spectra. Recently, the first γ-ray emitting BL Lac beyond z=3, 4FGL J1219.0 +3653 (hereafter J1219), was identified, i.e., within the first two billion years of the age of the universe. Here we report the results obtained from a detailed broadband study of this peculiar source by analyzing the new ∼58 ksec XMM-Newton and archival observations and reproducing the multiwavelength spectral energy distribution with the conventional one-zone leptonic radiative model. The XMM-Newton data revealed that J1219 is a faint X-ray emitter (F0.3−10 keV=1.02−0.24+0.47×10−15ergcm−2s−1) and exhibits a soft spectrum (0.3−10 keV photon index=2.28−0.46+0.58). By comparing the broadband physical properties of J1219 with z>3γ-ray detected flat spectrum radio quasars (FSRQs), we have found that it has a relatively low jet power and, similar to FSRQs, the jet power is larger than the accretion disk luminosity. We conclude that deeper multiwavelength observations will be needed to fully explore the physical properties of this unique high-redshift BL Lac object.

Optical and γ-ray variability analysis of BL Lacertae object TXS 1902+556

ABSTRACT The variability data for the BL Lacertae object TXS 1902+556 in the optical and $\gamma$-ray wavebands were obtained from the 0.76-m Katzman Automatic Imaging Telescope and the Fermi Large Area Telescope (Fermi-LAT), covering periods of 14.4 and 14.7 yr, respectively. The variability properties were systematically analysed, with particular emphasis on the first comprehensive investigation of radiation variation in the optical waveband. Four well-established techniques were employed for this purpose: the Lomb–Scargle periodogram, REDFIT program, Jurkevich method, and discrete correlation function (DCF) approach. The optical waveband exhibits quasi-periodic oscillations (QPO) with a time-scale of $P_{\rm O}=276.8\pm 6.1$ d at a significance level $3.87\sigma$, while the $\gamma$-ray waveband does not exhibit any significant periodicity. However, it should be noted that the QPO time-scale is consistent with the Sun-gaps in the optical light curve within 2$\sigma$ uncertainties. The optical QPO behaviour is most likely attributed to the helical motion of the jet driven by the orbital motion in a supermassive black hole binary system. Moreover, we have provided an explanation for the absence of QPO in the $\gamma$-ray light curves. Furthermore, utilizing the DCF method, a weak correlation between the variability in the optical and $\gamma$-ray wavebands was observed, suggesting that the emission of TXS 1902+556 may be generated through a combination of synchrotron self-Compton (SSC) and external Compton (EC) processes, or a leptonic–hadronic hybrid process.

Rapid optical flare in the extreme teraelectronvolt blazar 1ES 0229+200 on intraday timescales with the Transiting Exoplanet Survey Satellite

Context. The extreme teraelectronvolt (TeV) blazar 1ES 0229+200 is a high-frequency-peaked BL Lacertae object. It has not shown intraday variability in extensive optical and X-ray observations, nor has it shown any significant variability on any measurable timescale in the 1–100 GeV energy range over a 14-year span; however, variations in the source flux around its average are present in the energy range above 200 GeV. Aims. We aim to search for intraday optical variability in 1ES 0229+200 as part of an ongoing project to search for variability and quasi-periodic oscillations in the high-cadence (2 min), nearly uniformly sampled optical light curves of blazars provided by the Transiting Exoplanet Survey Satellite (TESS). Methods. 1ES 0229+200 was monitored by TESS in its Sectors 42, 43, and 44. We analysed the data of all these three sectors both with the TESS-provided lightkurve software and the eleanor reduction pipeline. We detected a strong, essentially symmetric flare that lasted about 6 h in Sector 42. We fitted the flare’s rising and declining phases to exponential functions. We also analysed the light curve of Sector 42 using the Lomb-Scargle periodogram (LSP) and continuous auto-regressive moving average (CARMA) methods. Results. The optical light curve of Sector 42 of the TESS observations displayed in the present work provides the first evidence of a strong, rapid, short-lived optical flare on the intraday timescale in the TeV blazar 1ES 0229+200. The variability timescale of the flare provides the upper limit for the size of the emission region to be within (3.3 ± 0.2–8.3 ± 0.5)×1015 cm. Away from the flare, the slope of the periodogram’s power spectrum is fairly typical of many blazars (α < 2), but the nominal slopes for the flaring regions are very steep (α ∼ 4.3), which may indicate that the electron distribution undergoes a sudden change. We discuss possible emission mechanisms that could explain this substantial and rapid flare.

SPRITEly: Time-domain Millimeter Interferometry at the Owens Valley Radio Observatory

Though the time-domain millimeter sky is yet to be well characterized, the scarcity of millimeter observing resources in the world at present hampers progress toward it. In efforts to bolster the exploration of millimeter transients, we present the Stokes Polarization Radio Interferometer for Time-Domain Experiments (SPRITEly). Located at the Owens Valley Radio Observatory, SPRITEly is currently deployed as a two-element short-baseline 90 GHz interferometer uniquely focused on monitoring bright variable millimeter-continuum sources. We leverage two existing 10.4 m antennas and their existing receiver systems to begin, but we make significant upgrades to the back-end system during the commissioning process. With the ability to achieve rms noise of a few mJy, we plan to monitor known variable sources along with new nearby transients detected from optical surveys at high cadence, with the goal of producing well-sampled light curves. Interpreting these data in conjunction with multiwavelength observations stands to provide insight into the physical properties of the sources that produce transient millimeter emission. We present commissioning and early-science observations that demonstrate the performance of the instrument, including observations of the flaring BL Lac object S2 0109+22 and a periastron passage of the binary T Tauri system DQ Tau.

Distance estimation of gamma-ray-emitting BL Lac objects from imaging observations

The direct redshift determination of BL Lac objects is highly challenging as the emission in the optical and near-infrared bands is largely dominated by the non-thermal emission from the relativistic jet, which points very close to our line of sight. Therefore, the optical spectra of BL Lac objects often show no spectral lines from the host galaxy. In this work, we aim to overcome this difficulty by attempting to detect the host galaxy and derive redshift constraints based on assumptions on the galaxy magnitude (`imaging redshifts'). Imaging redshifts were derived by obtaining deep optical images under good seeing conditions, making it possible to detect the host galaxy as a weak extension of the point-like source. We then derived the imaging redshift by using the host galaxy as a standard candle, employing two different methods. We determine the imaging redshift for 9 out of 17 blazars that we observed as part of this programme. The redshift range of these targets is 0.28-0.60, and the two methods used to derive the redshift give very consistent results within the uncertainties. We also performed a detailed comparison of the imaging redshifts with those obtained using other methods, such as direct spectroscopic constraints or looking for groups of galaxies close to the blazar. We show that the constraints from the different methods are consistent and that combining the three constraints narrows down the redshift. For example, in the case of J2156.0+1818, which is the most distant source for which we detect the host galaxy, the redshift range is narrowed to $0.63<z<0.71$. This makes the source interesting for future studies of extragalactic background light in the Cherenkov Telescope Array Observatory era.

A Comprehensive Study on the Mid-Infrared Variability of Blazars

We present a comprehensive investigation of mid-infrared (MIR) flux variability at 3.4 μm (W1 band) for a large sample of 3816 blazars, using Wide-field Infrared Survey Explorer (WISE) data through December 2022. The sample consists of 1740 flat-spectrum radio quasars (FSRQs), 1281 BL Lac objects (BL Lacs), and 795 blazars of uncertain type (BCUs). Considering Fermi Large Area Telescope detection, we classify 2331 as Fermi blazars and 1485 as non-Fermi blazars. Additionally, based on synchrotron peak frequency, the sample includes 2264 low-synchrotron peaked (LSP), 512 intermediate-synchrotron peaked (ISP), and 655 high-synchrotron peaked (HSP) sources. We conduct a comparative analysis of short- and long-term intrinsic variability amplitude (σm), duty cycle (DC), and ensemble structure function (ESF) across blazar subclasses. The median short-term σm values were 0.181−0.106+0.153, 0.104−0.054+0.101, 0.135−0.076+0.154, 0.173−0.097+0.158, 0.177−0.100+0.156, 0.096−0.050+0.109, and 0.106−0.058+0.100 mag for FSRQs, BL Lacs, Fermi blazars, non-Fermi blazars, LSPs, ISPs, and HSPs, respectively. The median DC values were 71.03−22.48+14.17, 64.02−22.86+16.97, 68.96−25.52+15.66, 69.40−22.17+14.42, 71.24−21.36+14.25, 63.03−33.19+16.93, and 64.63−24.26+15.88 percent for the same subclasses. The median long-term σm values were 0.137−0.105+0.408, 0.171−0.132+0.206, 0.282−0.184+0.332, 0.071−0.062+0.143, 0.218−0.174+0.386, 0.173−0.132+0.208, and 0.101−0.077+0.161 mag for the same subclasses, respectively. Our results reveal significant differences in 3.4 μm flux variability among these subclasses. FSRQs (LSPs) exhibit larger σm and DC values compared to BL Lacs (ISPs and HSPs). Fermi blazars display higher long-term σm but lower short-term σm relative to non-Fermi blazars, while DC distributions between the two groups are similar. ESF analysis further confirms the greater variability of FSRQs, LSPs, and Fermi blazars across a wide range of time scales compared to BL Lacs, ISPs/HSPs, and non-Fermi blazars. These findings highlight a close correlation between MIR variability and blazar properties, providing valuable insights into the underlying physical mechanisms responsible for their emission.

Optical Variability Properties of Southern TESS Blazars

We present a study of high-cadence, high-precision optical light curves from the TESS satellite of 67 blazars in the southern sky. We provide descriptive flux statistics, power spectral density (PSD) model parameters, and characteristic variability timescales. We find that only 15 BL Lacertae objects (BLLs) and 18 flat spectrum radio quasars (FSRQs) from the initial 26 and 41, respectively, exhibit statistically significant variability. We employ an adapted power spectral response method to test the goodness of fit for the PSD function to three power-law variant models. From our best-fitting description of the PSD, we extract the high-frequency power-spectral slopes, and if present, determine the significant bend or break in the model to identify characteristic timescales. We find no significant difference in the excess variance or rms scatter between blazar subpopulations. We identify a linear rms–flux relation in ∼69% of our sample, in which ∼20% show a strong correlation. We find that both subpopulations of blazars show power spectral slopes of α ∼ 2 in which a broken power-law best fits five BLLs and six FSRQs and a bending power-law best fits one BLL and five FSRQs. The shortest timescales of variability in each light-curve range widely from minutes to weeks. Additionally, these objects’ characteristic timescales range from ∼0.8 to 8 days, consistent with optical variability originating in the jet.

The Spectra of IceCube Neutrino (SIN) candidate sources

Context. A correlation has been reported between the arrival directions of high-energy IceCube events and γ-ray blazars classified as intermediate- and high-synchrotron-peaked BL Lacs. Subsequent studies have investigated the optical properties of these sources, compiled and analyzed public multiwavelength data, and constrained their individual neutrino emission based on public IceCube point-source data. Aims. We provide a theoretical interpretation of public multiwavelength and neutrino point source data for the 32 BL Lac objects in the sample previously associated with an IceCube alert event. We combined the individual source results to draw conclusions regarding the multimesssenger properties of the sample and the required power in relativistic protons. Methods. We performed particle interaction modeling using open-source numerical simulation software. We constrained the model parameters using a novel and unique approach that simultaneously describes the host galaxy contribution, the observed synchrotron peak properties, the average multiwavelength fluxes, and, where possible, the IceCube point source constraints. Results. We show that a single-zone leptohadronic model can describe the multiwavelength broadband fluxes from all 32 IceCube candidates. In some cases, the model suggests that hadronic emission may contribute a considerable fraction of the γ-ray flux. The required power in relativistic protons ranges from a few percent to a factor of ten of the Eddington luminosity, which is energetically less demanding compared to other leptohadronic blazar models in recent literature. The model can describe the 68% confidence level IceCube flux for a large fraction of the masquerading BL Lacs in the sample, including TXS 0506+056; whereas, for true BL Lacs, the model predicts a low neutrino flux in the IceCube sensitivity range. Physically, this distinction is due to the presence of photons from broad line emission in masquerading BL Lacs, which increase the efficiency of hadronic interactions. The predicted neutrino flux peaks between a few petaelectronvolt and 100 PeV and scales positively with the flux in the gigaelectronvolt, megaelectronvolt, X-ray, and optical bands. Based on these results, we provide a list of the brightest neutrino emitters, which can be used for future searches targeting the 10–100 PeV regime.

Integrated Study of X-Ray Spectrum and Time Lags for HBL Mrk 421 within the Framework of the Multiple-zone Leptonic Model

We present the timing analysis of 10 archived XMM-Newton observations with an exposure of >40 ks of Markarian 421. Mrk 421 is the brightest high-frequency-peaked BL Lac object emitting in X-rays produced by electrons accelerated in the innermost regions of a relativistic jet pointing toward us. For each observation, we construct averaged X-ray spectra in 0.5–10 keV band, as well as 100 s binned light curves (LCs) in various subbands. During these observations, the source exhibited various intensity states differing by close to an order of magnitude in flux, with the fractional variability amplitude increasing with energy through the X-ray band. Bayesian power spectral density analysis reveals that the X-ray variability can be characterized by a colored noise, with an index ranging from ∼ −1.9 to −3.0. Moreover, both the standard cross-correlation function and cross-spectral methods indicate that the amount of time lags increases with the energy difference between two compared LCs. A time-dependent two-zone jet model is developed to extract physical information from the X-ray emission of Mrk 421. In the model, we assume that the jet emission mostly comprises a quasi-stationary component and a highly variable one. Our results show that the two-zone model can simultaneously provide a satisfactory description for both the X-ray spectra and time lags observed in different epochs, with the model parameters constrained in a fully acceptable interval. We suggest that shocks within the jets may be the primary energy dissipation process responsible for triggering the rapid variability, although magnetic reconnection cannot be excluded.

Redshift constrain of BL Lac PKS 1424+240

ABSTRACT In the period between 2009 and 2015, several very high-energy (VHE $> 100$ GeV) gamma-ray flaring events from the BL Lac object PKS 1424+240 were observed by the Cerenkov telescopes VERITAS and MAGIC. It had uncertain redshift (z) and using spectroscopical measurement, Paiano et al. (2017) found it to be $z=0.604$. Using four different extragalactic background light (EBL) models and the photohadronic model, nine independently observed VHE gamma-ray spectra of PKS 1424+240 are analysed and a global $\chi ^2$ fit is performed on all observations to estimate the best-fitting value for the redshift for each EBL model. Confidence levels (CL) intervals for the redshift are also estimated using all the EBL models. This method is tested by comparing our analysis with the observed value. It is shown that the photohadronic scenario provides an excellent description of all the observed spectra. It is found that the EBL model of Dominguez et al. (2011) is the one that provides the most restrictive limits on the redshift of PKS 1424+240, but in our analysis, $z=0.604$ lies within the $3\sigma$ CL interval of the EBL model of Saldana-Lopez et al. (2021).

Optical spectroscopic classification of a selection of Southern Hemisphere 3FHL blazar candidates

ABSTRACT The Fermi-LAT has detected more than 7000 $\gamma$-ray sources which show emission above 50 MeV of which more than half are associated with blazars. However, the Fourth Fermi-LAT catalogue (4FGL-DR4) lists 1625 of these as blazar candidates of uncertain type. Increasing the number of classified Fermi-LAT sources is important for improving our understanding of extragalactic $\gamma$-ray sources and can be used to search for new classes of very high energy sources. We report on the optical spectroscopy of twelve blazar candidates with hard photon indices included in the Third Catalogue of Hard Fermi-LAT Sources during 2016 and 2017 using the SAAO 1.9-m telescope. We classify all the sources observed as BL Lac objects, and determine the potential spectroscopic redshift for seven of them.

X-ray flux and spectral variability of the blazar OJ 287 with Suzaku

ABSTRACT We present analyses of Suzaku XIS light curves and spectra of the BL Lac object OJ 287 with observations positioned primarily around proposed recurrent optical outbursts. The first two observations were performed in 2007 April 10–13 (epoch 1) and 2007 November 7–9 (epoch 2) that, respectively, correspond to a low and a high optical state and which, within the binary supermassive black hole model for OJ 287, precede and follow the impact flare. The last three observations, made consecutively during 2015 May 3–9 (epoch 3), were during the post-impact state of the 2013 disc impact and are the longest continuous X-ray observation of OJ 287 taken before the optical outburst in 2015 December. Intraday variability is found in both the soft (0.5–2 keV) and hard (2–10 keV) bands. The discrete correction function analysis of the light curves in both bands peaks at zero lag during epochs 2 and 3, indicating that the emission in both bands was cospatial and emitted from the same population of leptons. Power spectral densities of all three light curves are red noise dominated, with a rather wide range of power spectrum slopes. These X-ray spectra are overall consistent with power laws but with significantly different spectral indices. In the 2015 observations the X-ray spectrum softens during the flare, showing an obvious soft X-ray excess that was not evident in the 2007 observations. We discuss the implications of these observations on the jet, the possible accretion disc, and the binary supermassive black hole model proposed for the nearly periodic optical flaring of OJ 287.

The First VHE Activity of OJ 287 and the Extragalactic Background Light

The BL Lacertae (BL Lac) object OJ 287 underwent an intense X-ray activity phase, exhibiting its brightest recorded X-ray flare in 2016-2017, characterized by much softer X-ray spectra and, concurrently, its first-ever recorded very-high-energy (VHE) emission (100–560 GeV), reported by the VERITAS observatory. Broadband spectral energy distribution reveals a new jet emission component similar to high-synchrotron-peaked BL Lac objects, thereby implying the soft X-ray spectrum for the synchrotron emission. Using the advantage of simultaneous X-ray and VHE spectral information, as well as the source being a low-synchrotron-peaked BL Lac object, we systematically explored the extragalactic background light (EBL) spectrum by demanding that the VHE spectrum cannot be harder than the X-ray spectrum. We used three different phenomenological forms of the EBL spectral shape (power-law, parabola, and polynomial) motivated by current constraints on the EBL with the Bayesian Monte Carlo approach to infer the credible EBL range. Our study favors an almost flat power-law spectral shape and is consistent with previous studies. The other spectral forms capable of capturing curvature though result in a better statistics value; the improvement is statistically insignificant given the additional parameters.

Statistical Tests of the Relativistic Beaming Indicators of jetted AGNs and Implication for the Revised Blazar Sequence

The latest detection by the Fermi Large Area Telescope (Fermi-LAT) of strong relativistic jets of very high-energy (VHE, above 100 GeV) from the Narrow-Line Seyfert 1 Galaxies (NLS1s) has opened a new unified scheme of active galactic nuclei (AGN) in which jetted Seyfert galaxies are viewed as counterparts to a subclass of AGNs. In this paper, we report a systematic investigation of the revised blazar sequence using the γ-ray Doppler factor () and the radio core-dominance parameter (R) of AGN samples of NLS1s and blazar subtypes of flat-spectrum radio quasars (FSRQs) and BL Lac objects (BLs). Furthermore, we explore the γ-ray properties of NLS1s and blazar subtypes in the context of the blazar unification scheme at different scales. The main results are as follows: (a) The average values of R and γ-ray luminosity () of our sample agree with the sequence BLs – FSRQs – NLS1s and provide quantitative explanations for the observed relativistic beaming effects in these objects. (b) Through a parameter t-test and non-parametric K-S test with chance probability p <10-3, we find that the distributions of R and Lγ for NLS1s and the blazar subtypes are not significantly different. (c) There is a regular positive trend (r > +0.79) in the variation of Lγ – data from BLs to NLS1s through FSRQs which is consistent with the prediction of the revised blazar sequence. These results imply that NLS1s could fit very well into the conventional blazar sequence.

Correction to: The physical properties of Fermi-4LAC low-synchrotron-peaked BL Lac objects

Correction to: The physical properties of <i>Fermi</i>-4LAC low-synchrotron-peaked BL Lac objects

Changing Look of the Optical Spectrum of the MeV Blazar PKS 0446+112 (4FGL J0449.1+1121)

Following the high activity of the γ-ray Fermi source 4FGL J0449.1+1121 (PKS 0446+112), possibly associated with a IceCube neutrino event IC-240105A, we obtained optical spectroscopy with the Gran Telescopio Canarias of the counterpart. We detect a clear emission line at 3830 Å identified as Lyα that confirms the redshift of source at z = 2.153. Comparing with previous spectroscopy, we find an increase of the continuum by a factor ∼10, and a significant decrease of the C iv 1550 emission line flux by a factor ∼5. This produces a dramatic drop of the equivalent width from ∼20 to 0.8 Å, which is suggestive of a very high jet activity. The full width half maximum of the emission lines are midway (1000–2000 km s −1) between those typical of the broad and narrow regions of quasars. Based on this, the source classification is intermediate between flat spectrum radio quasar and BL Lac object.

The Energy Budget in the Jet of High-frequency Peaked BL Lacertae Objects

Energy equipartition and the energy budget in the jet are important issues for the radiation mechanism of blazars. Early work predominantly concentrated on flat-spectrum radio quasars and a limited number of BL Lacertae (BL Lac) objects. In this paper, we compile 348 high-frequency peaked BL Lac objects (HBLs) based on the catalog of active galactic nuclei (4LAC-DR3) from Fermi-LAT, and employ JetSet to fit the spectral energy distributions (SEDs) of these HBLs in the framework of the one-zone lepton model. We aim to determine whether the energy budget is reasonable and whether energy equipartition is satisfied in HBLs. The results of the statistical analysis suggest that: (1) SEDs of HBLs can be reproduced well by using the one-zone lepton model; however, it cannot achieve energy equalization, and the relativistic electron energy density is far greater than the magnetic field energy density, U e ≳ 100U B ; (2) the majority of HBLs are located in the t cool < t dyn region (where the horizontal coordinate represents the jet power of electrons, while the ordinate indicates the ratio of the dynamic timescale to the cooling timescale), and the jet kinetic power of HBLs is greater than the jet power of radiation; there is a very low radiation efficiency, we deduce that HBLs may have optically thin advection-dominated accretion flows; (3) logϵB of HBLs is less than zero, which indicates that the jet kinetic power of HBLs is not affected by Poynting flux; (4) the relationships U e > U Syn ∼ U B , L e ∼ L p > L B ∼ L rad, and logϵe>0.5 are established. These relations indicate that most of the energy of HBLs is stored in the population of low-energy electrons.

Systematic Search for and Study of Short-timescale Flare Structures in BL Lac Object Gamma-Ray Emission

We present here the first systematic search of short-timescale γ-ray flares from 29 high Galactic latitude BL Lac objects over 14 yr of Fermi Large Area Telescope data. Using a combined Bayesian Blocks and HOP algorithm, we identified seven high-quality orbital timescale flare segments from three sources and quantified 24 short-timescale flare structures. We then performed a comprehensive analysis of flare symmetry, power spectral density (PSD) of variability, and flux–photon index relation. The main results are as follows. (1) The flare symmetry parameter A shows a “U-shaped” distribution. Short-timescale flares are symmetric while long-timescale flares are asymmetric. The number of fast-rise, slow-decay and slow-rise, fast-decay type flares are equal. No correlation is found between A and peak/integral flux. No parameter evolution is seen between consecutive flares, either. The observations support a scenario where longer-timescale flares originate from the superposition of short, symmetric subhour flares. (2) PSD from yearly to hourly timescales is modeled using the CARMA process. At lower frequencies, the PSD follows the typical broken power-law form. The high-frequency region of the PSD exhibits a continuous power-law shape, indicating that γ-ray variability originates from a single physical process across all probed timescales. (3) The flux–photon index distribution shows a pattern of “harder-when-brighter” or “softer-when-brighter,” but becomes flat above a certain critical flux, with Γ ≈ 2. This behavior cannot be simply explained by a two-component or blazar sequence model, and we speculate it may be related to complex interplay between electron acceleration and cooling.

Revealing the Variation Mechanism of ON 231 via the Two-component Shock-in-jet Model

The variation mechanism of blazars is a long-standing unresolved problem. In this work, we present a scenario to explain diverse variation phenomena for ON 231, where the jet emissions are composed of the flaring and the less variable components (most probably from the post-flaring blobs), and the variation is dominated by shock-in-jet instead of the Doppler effect. We perform correlation analysis for the multiwavelength light curves and find no significant correlations. For the optical band, ON 231 exhibits a harder when brighter (HWB) trend, and the trend seems to shift at different periods. Correspondingly, the correlation between the degree of polarization and flux exhibits a V-shaped behavior, and a similar translation relation during different periods is also found. These phenomena could be understood via the superposition of the flaring component and slowly varying background component. We also find that the slopes of the HWB trend become smaller at higher flux levels, which indicates the energy-dependent acceleration processes of the radiative particles. For the X-ray band, we discover a trend transition from HWB to softer when brighter (SWB) to HWB. We consider that the X-ray emission is composed of both the synchrotron tail and the synchrotron self-Compton components, which could be described by two log-parabolic functions. By varying the peak frequency, we reproduce the observed trend transition in a quantitative manner. For the γ-ray band, we find the SWB trend, which could be explained naturally if a very-high-energy γ-ray background component exists. Our study elucidates the variation mechanism of intermediate synchrotron-peaked BL Lac objects.