Interstellar Polarization Research Articles

Polarimetric and Photometric Investigation of the Dark Globule LDN 1225: Distance, Extinction Law, and Magnetic Fields

Abstract We present results based on the optical R-band observations of the polarization of 280 stars distributed toward the dark globule LDN 1225. Parallaxes from Gaia data release 2 along with the polarization data of ∼200 stars have been used to (a) constrain the distance of LDN 1225 as 830 ± 83 pc, (b) determine the contribution of interstellar polarization, and (c) characterize the dust properties and delineate the magnetic field (B-field) morphology of LDN 1225. We find that B-fields are more organized and exhibit a small dispersion of 12°. Using the 12CO molecular line data from the Purple Mountain Observatory, along with the column density and dispersion in B-fields, we estimate the B-field strength to be ∼56 ± 10 μG, the ratio of magnetic to turbulent pressure to be ∼3 ± 2, and the ratio of mass to magnetic flux (in units of the critical value) to be <1. These results indicate the dominant role of B-fields in comparison to turbulence and gravity in rendering the cloud support. B-fields are aligned parallel to the low-density parts (traced by a 12CO map) of the cloud; in contrast, they are neither parallel nor perpendicular to the high-density core structures (traced by 13CO and C18O maps). LDN 1225 hosts two 70 μm sources, which seem to be low-mass Class 0 sources. The ratio of total to selective extinction derived using optical and near-infrared photometric data is found to be anomalous (R V = 3.4), suggesting the growth of dust grains in LDN 1225. The polarization efficiency of dust grains follows a power law with an index of −0.7, implying that optical polarimetry traces B-fields in the outer parts of the cloud.

Laboratory experiments on cosmic dust and ices

AbstractThe existence of cosmic dust is attested by the interstellar extinction and polarization, IR emission and absorption spectra, and elemental depletion patterns. Dust grains are efficiently processed or even destroyed in shocks, molecular clouds, or protoplanetary disks. A considerable amount of dust has to be re-formed in the ISM. In various astrophysical environments, dust grains are covered by molecular ices and therefore contribute or catalytically influence the chemical reactions in these layers. Laboratory experiments are desperately required to understand the evolution of grains and grain/ice mixtures in molecular clouds and early planetary disks. This review considers recent progress in laboratory approaches to dust/ice experiments.

Evolving optical polarisation of the black hole X-ray binary MAXI J1820+070

Aims. The optical emission of black hole transients increases by several magnitudes during the X-ray outbursts. Whether the extra light arises from the X-ray heated outer disc, from the inner hot accretion flow, or from the jet is currently debated. Optical polarisation measurements are able to distinguish the relative contributions of these components. Methods. We present the results of BVR polarisation measurements of the black hole X-ray binary MAXI J1820+070 during the period of March-April 2018. Results. We detect small, ∼0.7%, but statistically significant polarisation, part of which is of interstellar origin. Depending on the interstellar polarisation estimate, the intrinsic polarisation degree of the source is between ∼0.3% and 0.7%, and the polarisation position angle is between ∼10 ° −30°. We show that the polarisation increases after MJD 58222 (2018 April 14). The change is of the order of 0.1% and is most pronounced in the R band. The change of the source Stokes parameters occurs simultaneously with the drop of the observed V-band flux and a slow softening of the X-ray spectrum. The Stokes vectors of intrinsic polarisation before and after the drop are parallel, at least in the V and R filters. Conclusions. We suggest that the increased polarisation is due to the decreasing contribution of the non-polarized component, which we associate with the the hot flow or jet emission. The low polarisation can result from the tangled geometry of the magnetic field or from the Faraday rotation in the dense, ionised, and magnetised medium close to the black hole. The polarized optical emission is likely produced by the irradiated disc or by scattering of its radiation in the optically thin outflow.

The 3D shape of Type IIb SN 2011hs

We observed seven epochs of spectropolarimetry in optical wavelengths for the Type IIb SN 2011hs, ranging from -3 to +40 days with respect to V -band maximum. A high degree of interstellar polarization was detected (up to ~3 percent), with a peak lying blueward of 4500A. Similar behaviours have been seen in some Type Ia SNe, but had never been observed in a Type IIb. We find that it is most likely the result of a relative enhancement of small silicate grains in the vicinity of the SN. Significant intrinsic continuum polarization was recovered at -3 and +2 days (p = 0.55 +\- 0.12 percent and p = 0.75 +\- 0.11 percent, respectively). We discuss the change of the polarization angle across spectral lines and in the continuum as diagnostics for the 3D structure of the ejecta. We see a gradual rotation by about -50 degree in the continuum polarization angle between -2 and +18 days after V - band maximum. A similar rotation in He I {\lambda}5876, H{\alpha} and the Ca II infrared triplet seems to indicate a strong influence of the global geometry on the line polarization features. The differences in the evolution of their respective loops on the Stokes q - u plane suggest that line specific geometries are also being probed. Possible interpretations are discussed and placed in the context of literature. We find that the spectropolarimetry of SN 2011hs is most similar to that of SN 2011dh, albeit with notable differences.

The wavelength dependence of interstellar polarization in the Local Hot Bubble

The properties of dust in the interstellar medium (ISM) nearest the Sun are poorly understood because the low column densities of dust toward nearby stars induce little photometric reddening, rendering the grains largely undetectable. Stellar polarimetry offers one pathway to deducing the properties of this diffuse material. Here we present multi-wavelength aperture polarimetry measurements of seven bright stars chosen to probe interstellar polarization near the edge of the Local Hot Bubble (LHB) - an amorphous region of relatively low density interstellar gas and dust extending ~70-150 pc from the Sun. The measurements were taken using the HIgh Precision Polarimetric Instrument (HIPPI) on the 3.9-m Anglo-Australian Telescope. HIPPI is an aperture stellar polarimeter with a demonstrated sensitivity of 4.3 parts-per-million (ppm). Of the stars observed two are polarized to a much greater degree than the others; they have a wavelength of maximum polarization ($\lambda_{max}$) of ~550 $\pm$ 20 nm - similar to that of stars beyond the LHB - and we conclude that they are in the wall of the LHB. The remaining five stars have polarizations of ~70 to 160 ppm, of these four have a much bluer $\lambda_{max}$, ~350 $\pm$ 50 nm. Bluer values of $\lambda_{max}$ may indicate grains shocked during the evolution of the Loop I Superbubble. The remaining star, HD 4150 is not well fit by a Serkowski curve, and may be intrinsically polarized.

Interstellar polarization and extinction in the Local Bubble and the Gould Belt

We analyse an all-sky compilation of thirteen data sources with optical interstellar linear polarisation for 3871 {\it Gaia} DR2 and {\it Hipparcos} stars within 500 pc, which do not exhibit a considerable intrinsic polarisation. These data are analysed together with five 3D maps and models of the reddening $E(B-V)$. We consider variations of the polarisation degree $P$, position angle $\theta$, and polarisation efficiency $P/E(B-V)$ with Galactic coordinates, distance $R$, and dereddened colour. $P$ shows a maximum at the Gould Belt mid-plane. $P/R$ drops in the Local Bubble by several times defining a boundary of the Bubble at $P=0.1$ per cent. All the data sources of the reddening, except Lallement et al., show a drop of $P/E(B-V)$ in the Bubble. A significant number of stars with a too high $P/E(B-V)$, where the reddening is taken from Arenou et al., Drimmel et al. or Lallement et al., either reject the Serkowski's limit $P/E(B-V)<9.3$ per cent per mag or manifest a systematic underestimation of the reddening by these data sources. The spatial and colour dependent variations of $P$ and $E(B-V)$ outside the Bubble compensate each other, resulting in a nearly constant $P/E(B-V)$. A giant envelope of aligned dust dominates at middle and high latitudes outside the Bubble. The Markkanen's cloud, the North Polar Spur, and some other filaments are parts of this envelope.

Local measurements of the mean interstellar polarization at high Galactic latitudes

Very little information exists concerning the properties of the interstellar medium (ISM)-induced starlight polarization at high Galactic latitudes. Future optopolarimetric surveys promise to fill this gap. We conduct a small-scale pathfinding survey designed to identify the average polarization properties of the diffuse ISM locally, at regions with the lowest dust content. We perform deep optopolarimetric surveys within three ~15′× 15′ regions located atb&gt; 48° using the RoboPol polarimeter. The observed samples of stars are photometrically complete to ~16 mag in theR-band. The selected regions exhibit low total reddening compared to the majority of high-latitude sightlines. We measure the level of systematic uncertainty for all observing epochs and find it to be 0.1% in fractional linear polarization,p. The majority of individual stellar measurements have low signal-to-noise ratios. However, our survey strategy enables us to locate the mean fractional linear polarizationpmeanin each of the three regions. The region with lowest dust content yieldspmean= (0.054 ± 0.038)%, not significantly different from zero. We find significant detections for the remaining two regions of:pmean= (0.113 ± 0.036)% andpmean= (0.208 ± 0.044)%. Using a Bayesian approach, we provide upper limits on the intrinsic spread of the small-scale distributions ofqandu. At the detectedpmeanlevels, the determination of the systematic uncertainty is critical for the reliability of the measurements. We verify the significance of our detections with statistical tests, accounting for all sources of uncertainty. Using publicly available HI emission data, we identify the velocity components that most likely account for the observedpmeanand find their morphologies to be misaligned with the orientation of the mean polarization at a spatial resolution of 10′. We find indications that the standard upper envelope ofpwith reddening underestimates the maximumpat very lowE(B–V) (≤0.01 mag).

Polarization as a Probe of Thick Dust Disks in Edge-on Galaxies: Application to NGC 891

Abstract Radiative transfer models were developed to understand the optical polarizations in edge-on galaxies, which are observed to occur even outside the geometrically thin dust disk, with a scale height of ≈0.2 kpc. In order to reproduce the vertically extended polarization structure, we find that it is essential to include a geometrically thick dust layer in the radiative transfer model, in addition to the commonly known thin dust layer. The models include polarizations due to both dust scattering and dichroic extinction, which are responsible for the observed interstellar polarization in the Milky Way. We also find that the polarization level is enhanced if the clumpiness of the interstellar medium, and the dichroic extinction by vertical magnetic fields in the outer regions of the dust lane are included in the radiative transfer model. The predicted degree of polarization outside the dust lane was found to be consistent with that (ranging from 1% to 4%) observed in NGC 891.

Modeling optical and UV polarization of AGNs

Context. One of the main challenges for polarimetric observations of active galactic nuclei (AGN) is to properly estimate the amount of parasitic light that contaminates the polarization signal. Removing this unpolarized flux is a complex task that has only been achieved in a couple of objects.Aims. In this fifth paper of the series, we present a new version of the Monte Carlo code STOKES that accounts for dilution by interstellar polarization and host starlight in radiative transfer modeling.Methods. We upgraded our code by including spectral energy distribution (SED) templates for a set of representative host galaxies. The unpolarized light emitted by those hosts alters the observer polarization while being coherently radiatively coupled to the AGN structure. We also included in our analysis tool a routine that may add, depending on the user’s objectives, an interstellar component.Results. Using a generic AGN model, we illustrate how interstellar polarization and starlight dilution impact the observed polarimetric signal of AGN. We applied our code to NGC 1068, an archetypal edge-on AGN and demonstrate that STOKES can reproduce its SED, the expected wavelength-dependent polarimetric signatures, and the observed high-angular resolution polarimetric maps. Using the flexibility of the code, we derived several intrinsic parameters such as the system inclination and the torus opening angle.Conclusions. The new version of our publicly available code now allows observers to better prepare their observations, interpret their data and simulate the three-dimensional geometry and physics of AGN in order to probe unresolved structures. Additionally, the radiative interaction between the host and the AGN can be used to probe the co-evolution of the system.

Interstellar polarization and extinction towards the young open cluster NGC 1502

Aims.NGC 1502 is located at the periphery of the Cam OB1 association and probably within the Orion Spur, with published distance estimates varying between 0.7 and 1.5 kpc. We combine new polarimetric observations and existinguvbyβandUBVphotometries to provide new estimates of the cluster’s parameters.Methods.We present new multi-wavelength polarization observations of 22 stars in the direction of the cluster and, using the wavelength of maximum polarization, calculate the total-to-selective extinction ratio for each of these stars. These are combined with homogenizeduvbyβandUBVphotometries to obtain the individual stellar distances and study the structure of the field.Results.We found no evidence of significant extinction variation across the cluster and obtained an average color excessE(b−y) = 0.56 ± 0.02 mag, corresponding toE(B−V) = 0.76 mag. Given the uniformity of bothpmaxandλmaxtoward the cluster and the distribution of the color excess with distance, it seems likely that the polarization in this region arises from aligned dust grains in the foreground of the cluster, not farther than 500–600 pc. Based on 20 stars located beyond 500 pc within the studied field of view, we obtained an average polarization-based total-to-selective extinction ratioR= 2.83 ± 0.14 yielding visual absorptionAV= 2.14 ± 0.16 mag. Using 11 stars withuvbyβdata that represent the main sequence of the cluster, we calculated a photometric distance of 1117−89+96pc. This estimate is fully supported by theUBV-based analysis and the new individual membership probabilities that we derive. Assuming a solar metallicity yields an age of 5 Myr. Our analysis yields controversial results regarding the membership of the stars associated with the SZ Cam system (HD 25638 and HD 25639) to the cluster.

Distortion of Magnetic Fields in a Starless Core. III. Polarization–Extinction Relationship in FeSt 1-457

Abstract The relationship between dust polarization and extinction was determined for the cold dense starless molecular cloud core FeSt 1-457 based on the background star polarimetry of dichroic extinction at near-infrared wavelengths. Owing to the known (three-dimensional) magnetic field structure, the observed polarizations from the core were corrected by considering (a) the subtraction of the ambient polarization component, (b) the depolarization effect of inclined distorted magnetic fields, and (c) the magnetic inclination angle of the core. After these corrections, a linear relationship between polarization and extinction was obtained for the core in the range up to A V ≈ 20 mag. The initial polarization versus extinction diagram changed dramatically after the corrections of (a) to (c), with the correlation coefficient being refined from 0.71 to 0.79. These corrections should affect the theoretical interpretation of the observational data. The slope of the finally obtained polarization–extinction relationship is , which is close to the statistically estimated upper limit of the interstellar polarization efficiency. This consistency suggests that the upper limit of interstellar polarization efficiency might be determined by the observational viewing angle toward polarized astronomical objects.

Polarization as a probe of dusty environments around Type Ia supernovae: radiative transfer models for SN 2012dn

Geometry of circumstellar (CS) medium around supernovae (SNe) provides important diagnostics to understand the nature of their progenitors. In this paper, properties of CS dust around SN 2012dn, a super-Chandrasekhar candidate Type Ia supernova (SC-SN), have been studied through detailed three dimensional radiation transfer simulations. With the detected near-infrared excess from SN 2012dn, we show that it has a disk-like dusty CS environment whose mass is roughly consistent with a branch of an accreting white dwarf system (the single degenerate scenario). We show that a similar system should produce polarization signals up to $\sim 8$ \% in the $B$ band, depending on the viewing direction if polarimetric observation is performed. We predict that the maximum polarization is reached around $\sim 60$ days after the $B$-band maximum. We show that the temporal and wavelength dependence of the polarization signals, together with other unique features, can be easily distinguished from the interstellar polarization and intrinsic SN polarization. Indeed, the small polarization degree observed for normal Type Ia SNe (SNe Ia) can constrain a parameter space in the CS dust mass and distribution. We thus encourage multi-band polarimetric observations for SNe Ia, especially for outliers including SC-SNe for which some arguments for the single degenerate scenario exist but the polarization data are very rare so far.

Large Interstellar Polarisation Survey

It is well known that the dust properties of the diffuse interstellar medium exhibit variations towards different sight-lines on a large scale. We have investigated the variability of the dust characteristics on a small scale, and from cloud-to-cloud. We use low-resolution spectro-polarimetric data obtained in the context of the Large Interstellar Polarisation Survey (LIPS) towards 59 sight-lines in the Southern Hemisphere, and we fit these data using a dust model composed of silicate and carbon particles with sizes from the molecular to the sub-micrometre domain. Large (≥6 nm) silicates of prolate shape account for the observed polarisation. For 32 sight-lines we complement our data set with UVES archive high-resolution spectra, which enable us to establish the presence of single-cloud or multiple-clouds towards individual sight-lines. We find that the majority of these 35 sight-lines intersect two or more clouds, while eight of them are dominated by a single absorbing cloud. We confirm several correlations between extinction and parameters of the Serkowski law with dust parameters, but we also find previously undetected correlations between these parameters that are valid only in single-cloud sight-lines. We find that interstellar polarisation from multiple-clouds is smaller than from single-cloud sight-lines, showing that the presence of a second or more clouds depolarises the incoming radiation. We find large variations of the dust characteristics from cloud-to-cloud. However, when we average a sufficiently large number of clouds in single-cloud or multiple-cloud sight-lines, we always retrieve similar mean dust parameters. The typical dust abundances of the single-cloud cases are [C]/[H] = 92 ppm and [Si]/[H] = 20 ppm.

On interstellar light polarization by diamagnetic silicate and carbon dust in the infrared

The motion of diamagnetic dust particles in interstellar magnetic fields is studied numerically with several different sets of parameters. Two types of behavior are observed, depending on the value of the critical number $R$, which is a function of the grain inertia, the magnetic susceptibility of the material and of the strength of rotation braking. If $R\leq10$, the grain ends up in a static state and perfectly aligned with the magnetic field, after a few braking times. If not, it goes on precessing and nutating about the field vector for a much longer time. Usual parameters are such that the first situation can hardly be observed. Fortunately, in the second and more likely situation, there remains a persistent partial alignment which is far from negligible, although it decreases as the field decreases and as $R$ increases. The solution of the complete equations of motion of grains in a field helps understanding the details of this behavior. One particular case of an ellipsoidal forsterite silicate grain is studied in detail and shown to polarize light in agreement with astronomical measurements of absolute polarization in the infrared. Phonons are shown to contribute to the progressive flattening of extinction and polarization towards long wavelengths. The measured dielectric properties of forsterite qualitatively fit the Serkowski peak in the visible.

Large Interstellar Polarisation Survey (LIPS)

Polarimetric studies of light transmitted through interstellar clouds may give constraints on the properties of the interstellar dust grains. Traditionally, broadband linear polarisation (BBLP) measurements have been considered an important diagnostic tool for the study of the interstellar dust, while comparatively less attention has been paid to spectropolarimetric measurements. However, spectropolarimetry may offer stronger constraints than BBLP, for example by revealing narrowband features, and by allowing us to distinguish the contribution of dust from the contribution of interstellar gas. Therefore, we have decided to carry out a Large Interstellar Polarisation Survey (LIPS) using spectropolarimetric facilities in both hemispheres. Here we present the results obtained in the Southern Hemisphere with the FORS2 instrument of the ESO Very Large Telescope. Our spectra cover the wavelength range 380--950\,nm at a spectral resolving power of about 880. We have produced a publicly available catalogue of 127 linear polarisation spectra of 101 targets. We also provide the Serkowski-curve parameters, as well as the wavelength gradient of the polarisation position angle for the interstellar polarisation along 76 different lines of sight. In agreement with previous literature, we found that the best-fit parameters of the Serkowski-curve are not independent of each other. However, the relationships that we obtained are not always consistent with what was found in previous studies.

Interstellar Polarization and Extinction towards the Open Cluster NGC 457

NGC 457 is a moderately reddened and relatively young open cluster very rich in variable stars, particularly Be stars, but not associated with any prominent star-forming field. We combine new multi-wavelength polarization measurements with existing UBV and uvby photometries to obtain precise estimates of the total-to-selective extinction in the field of the cluster and re-evaluate its distance and age. The polarization measurements show a tight alignment of the polarization vectors with the Galactic plane and yield an average value of the total-to-selective extinction of 3.05 ± 0.17 for the cluster’s field. Using this value and the confirmed color excess mag, we obtain a distance modulus of 12.20 ± 0.39, corresponding to 2.75 ± 0.49 kpc and, assuming slightly sub-solar metallicity, an age of 15.8 Myr.

Constraints on interstellar dust models from extinction and spectro-polarimetry

We present polarisation spectra of seven stars in the lines-of-sight towards the Sco OB1 association. Our spectra were obtained within the framework of the Large Interstellar Polarization Survey carried out with the FORS instrument of the ESO VLT. We have modelled the wavelength-dependence of extinction and linear polarisation with a dust model for the diffuse interstellar medium which consists of a mixture of particles with size ranging from the molecular domain of 0.5 nm up to 350 nm. We have included stochastically heated small dust grains with radii between 0.5 and 6 nm made of graphite and silicate, as well as polycyclic aromatic hydrocarbon molecules (PAHs), and we have assumed that larger particles are prolate spheroids made of amorphous carbon and silicate. Overall, a dust model with eight free parameters best reproduces the observations, and is in agreement with cosmic abundance constraints. Reducing the number of free parameters leads to results that are inconsistent with the cosmic abundances of silicate and carbon. We found that aligned silicates are the dominant contributor to the observed polarisation, and that the polarisation spectra are best-fit by a lower limit of the equivolume sphere radius of aligned grains of 70–200 nm.

Comparing Submillimeter Polarized Emission with Near-infrared Polarization of Background Stars for the Vela C Molecular Cloud

Abstract We present a large-scale combination of near-infrared (near-IR) interstellar polarization data from background starlight with polarized emission data at submillimeter wavelengths for the Vela C molecular cloud. The near-IR data consist of more than 6700 detections probing a range of visual extinctions between 2 and in and around the cloud. The submillimeter data were collected in Antarctica by the Balloon-borne Large Aperture Submillimeter Telescope for Polarimetry. This is the first direct combination of near-IR and submillimeter polarization data for a molecular cloud aimed at measuring the “polarization efficiency ratio” ( ), a quantity that is expected to depend only on grain-intrinsic physical properties. It is defined as , where p 500 and p I are polarization fractions at and the I band, respectively, and is the optical depth. To ensure that the same column density of material is producing both polarization from emission and from extinction, we conducted a careful selection of near-background stars using 2MASS, Herschel, and Planck data. This selection excludes objects contaminated by the Galactic diffuse background material as well as objects located in the foreground. Accounting for statistical and systematic uncertainties, we estimate an average value of 2.4 ± 0.8, which can be used to test the predictions of dust grain models designed for molecular clouds when such predictions become available. The ratio appears to be relatively flat as a function of the cloud depth for the range of visual extinctions probed.

Time-resolved Polarimetry of the Superluminous SN 2015bn with the Nordic Optical Telescope

Abstract We present imaging polarimetry of the superluminous supernova SN 2015bn, obtained over nine epochs between −20 and +46 days with the Nordic Optical Telescope. This was a nearby, slowly evolving Type I superluminous supernova that has been studied extensively and for which two epochs of spectropolarimetry are also available. Based on field stars, we determine the interstellar polarization in the Galaxy to be negligible. The polarization of SN 2015bn shows a statistically significant increase during the last epochs, confirming previous findings. Our well-sampled imaging polarimetry series allows us to determine that this increase (from ∼0.54% to ≳1.10%) coincides in time with rapid changes that took place in the optical spectrum. We conclude that the supernova underwent a “phase transition” at around +20 days, when the photospheric emission shifted from an outer layer, dominated by natal C and O, to a more aspherical inner core, dominated by freshly nucleosynthesized material. This two-layered model might account for the characteristic appearance and properties of Type I superluminous supernovae.

A measurement of interstellar polarization and an estimation of Galactic extinction for the direction of the X-ray black hole binary V404 Cygni

Abstract V404 Cygni is a well-known candidate for the black hole binary thought to have relativistic jets. It showed extreme outbursts in 2015 June, characterized by a large amplitude and short time variation of flux in the radio, optical, and X-ray bands. Not only disk emission but also synchrotron radiation from the relativistic jets was suggested by radio observations. However, it is difficult to measure the accurate spectral shape in the optical/near-infrared band because there are uncertainties of interstellar extinction. To estimate the extinction value for V404 Cygni, we performed photopolarimetric and spectroscopic observations of V404 Cygni and nearby field stars. Here, we estimate the Galactic extinction using interstellar polarization based on the observation that the origin of the optical polarization is the interstellar medium, and investigate the properties of interstellar polarization around V404 Cygni. We found a good correlation between the color excess and polarization degree in the field stars. We also confirmed that the wavelength dependence of the polarization degree in the highly polarized field stars was similar to that of V404 Cygni. Using the highly polarized field stars, we estimated the color excess for the (B − V) color and the extinction in the V band to be E(B − V) = 1.2 ± 0.2 and 3.0 &amp;lt; A(V) &amp;lt; 3.6, respectively. A tendency for a bluer peak of polarization (λmax &amp;lt; 5500 Å) was commonly seen in the highly polarized field stars, suggesting that the dust grains toward this region are generally smaller than the Galactic average. The corrected spectral energy distribution of V404 Cygni in the near-infrared and optical bands in our results indicated a spectral break between 2.5 × 1014 Hz and 3.7 × 1014 Hz, which might originate in the synchrotron self-absorption.