Optical circular polarization of blazar S4 0954+65 during high linear polarized states

Optical circular polarization observations can directly test the particle composition in black holes jets. Here we report on the first observations of the BL Lac type object S4 0954+65 in high linear polarized states. While no circular polarization was detected, we were able to place upper limits of<0.5% at the 99.7% confidence. Using a simple model and our novel optical circular polarization observations we can constrain the allowed parameter space for the magnetic field strength and composition of the emitting particles. Our results favor models that require magnetic field strengths of only a few Gauss and models where the jet composition is dominated by electron-positron pairs. We discuss our findings in the context of typical magnetic field strength requirements for blazar emission models.


Introduction 1
The origin of the high-energy (keV -TeV) emission in blazar 2 jets is a highly debated open question since the discovery of 3 these jets (Blandford et al. 2019;Hovatta & Lindfors 2019).In 4 the past few years, this debate has intensified since the poten-5 tial association of TXS 0506+06 with a high-energy neutrino 6 (IceCube Collaboration et al. 2018).The standard approach to 7 the problem has been to model the (quasi-)simultaneous spectral 8 energy distribution (SED) of flaring blazars (e.g., Raiteri et al. 9 2017; Acciari et al. 2022;MAGIC Collaboration et al. 2023).10 However, the incomplete wavelength coverage, the complexity 11 of even the simplest models, and the uncertainty introduced by 12 relativistic effects and degenerate parameters leads to multiple 13 and often drastically different models to provide equally good 14 fits to the data.yannis.liodakis@gmail.comX-ray polarization has recently provided a new path forward with the launch of the Imaging X-ray Polarimetry Explorer (IXPE; Weisskopf et al. 2022).The first observations of IXPE clearly demonstrated two things.First, the most commonly used single-zone models to describe the SEDs are not consistent with the observed behavior (Liodakis et al. 2022b;Di Gesu et al. 2023;Middei et al. 2023b).Second, the X-ray polarization observations of low-synchrotron peaked sources (LSP; i.e., sources in which the X-ray emission is dominated by the highenergy emission component) favor a scenario in which inverse-Compton scattering from relativistic electrons likely causes at least the keV emission in LSP blazars (Middei et al. 2023a;Peirson et al. 2023).However, LSPs are typically at or below the detection capabilities of IXPE, and it is therefore likely that future missions such as e-XTP are required to solve this puzzle (Peirson et al. 2022).
All of the above demonstrates that new and complementary approaches are necessary.Optical circular polarization (OCP) to this day because fewer optical polarimeters are available with 35 CP capabilities.There are only a handful of OCP measurements 36 for blazars and for quasars in general (Valtaoja et al. 1993;Wagner & Mannheim 2001;Hutsemékers et al. 2010;Liodakis et where Π l and Π c are the OLP and OCP, respectively, f is the frac- ).f is defined as the fraction of positrons to the total num-86 ber of leptons, that is, f = N e + /(N e + + N e − ).Hence, f = 0 is for a pure proton-electron plasma (or normal plasma), and f = 0.5 is 88 for a pure electron-positron plasma (or pair plasma).The model 89 assumes a power-law distribution of emitting particles, an intrin-90 sic magnetic field perpendicular to the jet axis, and that the jet is 91 viewed at the critical angle (θ obs ≈ 1/Γ), which implies that the 92 Lorentz factor (Γ) is approximately equal to the Doppler factor 93 (Γ ≈ δ).We estimated the Doppler factor of the source follow-94 ing Liodakis et al. (2018) and using the most recent data release 95 from the Owens Valley Radio Observatory (up to August 2023; 96 Richards et al. 2011).In brief, we used the Bayesian hierarchical 97 models implemented in Magnetron3 (Huppenkothen et al. 2015) 98 to model the radio light curve at 15 GHz as a series of flares 99 superimposed on stochastic backgrounds.We used the results of 100 Magnetron to compute the maximum observed brightness tem-101 perature distribution, which we compared to the intrinsic maxi-102 mum brightness temperature of T int,max = 2.78×10 11 K (Liodakis 103 et al. 2018).We find a Doppler factor of δ = 11.6 +11.1 −5.5 , which 104 is consistent with previous estimates in the literature (Liodakis 105 et al. 2017(Liodakis 105 et al. , 2021)).The uncertainties on δ are not statistical, but 106 rather express the range of possible values over the ∼15 years of 107 radio observations.In addition, the imperfectly ordered magnetic 108 field will reduce OCP and OLP similarly from the maximum po-109 larization (Jones & O'Dell 1977; hence the [0.71/Π l ] term).The 110 OLP observations are made in the R band, but the polarization 111 degree of S4 0954+65 is fairly achromatic (e.g., Raiteri et al. 112 2021), with any differences far below the observational uncer-113 tainties, which we have taken into account in our simulations 114 below.

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With this model, we explored a parameter space for 116 f =[0,0.5]and for B=[0.1,20]Gauss.For each pair of (B, f ), 117 we drew a random value for the Doppler factor and the OLP 118 given the uncertainties.We marginalized over all potential val-119 ues by repeating the process 20,000 times.For each simula-120 tion, we evaluated whether the produced OCP was below the 121 observed 3σ upper limit.Figure 1 shows the results of the simu-122 lations.It is evident for both observations that models with mag-123 netic field strengths B > 10 Gauss and a low positron fraction 124 ( f < 0.2) are disfavored.It is also evident that the observation on 125 JD 2459738.3737provides more stringent constraints on [B, f ]. 126

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We presented the first optical circular polarization observations 128 of S4 0954+65 in high linear polarized states.Our observations 129 provide strict upper limits below < 0.5% at the 3σ level.).We re-estimated the Doppler factor for the source using 135 ∼15 years of radio observations at 15 GHz from OVRO, which 136 we used to constrain its magnetic field strength and jet composi-137 tion.Throughout our modeling, we assumed that the optical and 138 radio emission regions have the same Doppler factor and that 139 the entire potential OCP signal is intrinsic to the source.If the 140 interstellar dust contributes to the OCP, then our limits will de-141 crease, tightening the constraints on (B, f ).Similarly, if the op-142 tical emission region has a higher Doppler factor, as is typically 143 assumed to resolve the Doppler crisis in high-synchrotron peak 144 blazars4 (e.g., Georganopoulos & Kazanas 2003), our constraints 145

Liodakis et al.,: Optical Circular polarization of S4 0954+65
Table 1.Summary of the observations for S4 0954+65.The columns are (1) Julian date, (2) Gregorian date, (3) linear polarization degree (%), (4) polarization angle (degrees), and ( 5) upper limit on the circular polarization degree (%) at the 99.7% confidence interval.The linear polarization observations are made in the R band and the circular polarization observations in the z-SDSS band.The radio polarization angle in S4 0954+65 has been found to be  direction is estimated using the brightest knot that is well re-172 solved from the radio core (i.e., the brightest feature in the radio 173 image).Hence, our estimates might not be representative of the true direction of the magnetic field with respect to the jet axis.175 While our quantitative estimates might be affected because our 176 observations encompass different conditions, it is unlikely that 177 our conclusions will be altered. 178 We find that high magnetic field values (> 10 Gauss) and pre-179 dominately proton-electron jets overproduce the observed level 180 of OCP.This is important in the context of leptonic versus 181 hadronic models because the latter typically require much larger 182 magnetic field strengths (> 30 Gauss; e.g., Cerruti 2020).Lio-183 dakis & Petropoulou (2020) estimated the minimum magnetic 184 field strength required for proton synchrotron models to pro-185 duce the observed SED for 145 blazars.While S4 0954+65 was 186 not included in their sample, we can use the distribution of the 187 population.For all subclasses of blazars, we find a median of 188 238 Gauss, and the lowest estimate is 2.85 Gauss.When the sam-189 ple is restricted to the LSP sources (the subclass of S4 0954+65), 190 the median and lowest value are 243.2Gauss and 5.34 Gauss, re-191 spectively.For high values close to the median, we can exclude 192 the pure electron-proton models at > 4σ significance.For any 193 value above 70 Gauss, we can exclude the pure electron-proton 194 models at > 3σ significance.At 5.34 Gauss, as the minimum 195 found for LSPs, only 3% of the simulations can produce con-196 sistent OCP values.For 2.85 Gauss, 4.4% of the simulations are 197 consistent with the observations.198 Estimates of the magnetic field strength of S4 0954+65 199 through leptonic SED modeling (Tanaka et al. 2016;MAGIC 200 Collaboration et al. 2018) suggest values at 1 Gauss or lower.In 201 this case, > 9% of the simulations can produce consistent OCP 202 values.Therefore, we cannot exclude a significant fraction of rel-203 suggest that proton emission, and the potential high-energy neu-211 trino emission, is rare or takes place under certain conditions, 212 for example, compression from a shock that would amplify the 213 magnetic field strength, shock-shock interactions, or rotations

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tion of positrons, ν obs is the observing frequency set to the cen-83 tral wavelength of the z-SDSS band (3.28×10 14 Hz), and B is the 84 intrinsic magnetic field strength in Gauss (Rieger & Mannheim 85 2005

Fig. 1 .
Fig. 1.Constraints on the magnetic field strength and positron fraction for the two observations of S4 0954+65.The left panel shows JD 2459738.3737, and the right panel shows JD 2460084.4184.The color bar shows the fraction of successful simulations for each (B, f ) pair.The contours have been added to guide the eye. 160

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roughly parallel to the jet during the first observation and perpen-169 dicular during the second.The OLP angle traces the integrated 170 magnetic field direction along the line of sight, and the inner jet171

data were reduced following the standard steps 73 of bias and flat-field subtraction, as well as the correction of the 74 polarization channel transmission performed using two stars in 75 3 field of view (FoV) around the source. The processing of the 76 SCORPIO-2 polarimetric data is described in detail in Afanasiev
al.