X-ray Polarization of BL Lacertae in Outburst

We report the first $>99\%$ confidence detection of X-ray polarization in BL Lacertae. During a recent X-ray/$\gamma$-ray outburst, a 287 ksec observation (2022 November 27-30) was taken using the Imaging X-ray Polarimetry Explorer ({\it IXPE}), together with contemporaneous multiwavelength observations from the Neil Gehrels {\it Swift} observatory and {\it XMM-Newton} in soft X-rays (0.3--10~keV), {\it NuSTAR} in hard X-rays (3--70~keV), and optical polarization from the Calar Alto, and Perkins Telescope observatories. Our contemporaneous X-ray data suggest that the {\it IXPE} energy band is at the crossover between the low- and high-frequency blazar emission humps. The source displays significant variability during the observation, and we measure polarization in three separate time bins. Contemporaneous X-ray spectra allow us to determine the relative contribution from each emission hump. We find $>99\%$ confidence X-ray polarization $\Pi_{2-4{\rm keV}} = 21.7^{+5.6}_{-7.9}\%$ and electric vector polarization angle $\psi_{2-4{\rm keV}} = -28.7 \pm 8.7^{\circ}$ in the time bin with highest estimated synchrotron flux contribution. We discuss possible implications of our observations, including previous {\it IXPE} BL Lacertae pointings, tentatively concluding that synchrotron self-Compton emission dominates over hadronic emission processes during the observed epochs.


INTRODUCTION
Blazars are active galactic nuclei (AGN) that launch collimated relativistic jets of plasma oriented within a few degrees from the observer's line of sight (Blandford et al. 2019, and references therein). The Dopplerboosted jet emission dominates the observed spectral energy distribution (SED) that extends from radio to γrays and is characterized by two emission components. Blazars are often classified by the peak frequency of the low-energy (electron synchrotron radiation) component as low-synchrotron peaked (LSP, ν syn < 10 14 Hz), intermediate-synchrotron peaked (ISP 10 14 < ν syn < 10 15 Hz), and high-synchrotron peaked (HSP ν syn > 10 15 Hz, Abdo et al. 2010). Here we focus on ISPs and in particular BL Lacertae (BL Lac), whose recent γ-ray outburst (see Appendix C) briefly boosted its characteristic peak energies, moving it from the LSP into the ISP class.
In ISPs the peak of the low-energy component ranges from the near-IR through the UV bands. Thus, the 2-8 keV IXPE band may include substantial emission from the falling high-frequency tail of the leptonic synchrotron (Sy) spectrum emitted by the most efficiently accelerated electrons and positrons, by a related higherfrequency peak hadronic component (synchrotron emission from protons), or by the flatter-spectrum syn-chrotron self-Compton (SSC) leptonic emission. Indeed, in leptonic models the IXPE band may lie in the Ushaped transition region from synchrotron to SSC emission (e.g., Peirson et al. 2022, Fig. 1). Since the polarization is expected to differ between Sy and SSC, IXPE ISP observations can probe both radiation processes, and possibly the jet's composition (Peirson et al. 2022;Zhang & Böttcher 2013). The latter is of particular interest, as blazars have been proposed as candidate sources of TeV neutrinos and ultra-high-energy cosmic-rays (UHECR), which would require a significant hadronic component in some blazar jets (Gao et al. 2019). The possible 3σ association of ISP blazar TXS 0506+056 with the neutrino IceCube-170922A event motivates this connection (Kintscher et al. 2017;ICECUBE COLLABORATION et al. 2018). However, the peculiar γ-ray behavior of TXS 0506+056 and the ∼40% probability of an atmospheric origin of the neutrino challenges the association. Current blazar models that include neutrino emission assume either leptohadronic X-ray emission (e.g., Cerruti et al. 2019) or subdominant hadronic components where the proton emission only dominates the SED in the transition region where the leptonic component is at a minimum level (e.g., Gao et al. 2019). These factors highlight the importance of distinguishing between leptonic and hadronic emission in an ISP blazar when it comes to X-ray polarization measurements with IXPE.
BL Lac is among the few LSP or ISP blazars detected at ≥ 0.1 TeV (very high-energy, VHE) γ-ray energies, and is the 14th brightest AGN at GeV energies in the Fermi 4LAC catalog (Ajello et al. 2020). It is a rapidly variable VHE source on timescales as short as < 1 hour (Albert et al. 2007;Arlen et al. 2013). Moreover, BL Lac has been the focus of a large number of multi-wavelength and polarization studies (e.g., Blinov et al. 2015;Weaver et al. 2020;Raiteri et al. 2013;Casadio et al. 2021). Because of this blazar's strong variability, the interpretation of its SED requires simultaneous observations.
In §2 we describe the X-ray, optical, and radio polarization observations and data reduction. We discuss our findings in the context of multiwavelength observations in §3. Further analysis details can be found in the appendix §B, §C.
2. DATA ANALYSIS BL Lac was observed by IXPE with an exposure time of 287 ksec on 2022 November 27-30 . IXPE, launched on 2021 December 9, is a joint mission of NASA and the Italian Space Agency (Agenzia Spaziale Italiana, ASI). A description of the instrument is given by Weisskopf et al. (2022). At the ∼ 30 angular resolution of IXPE, BL Lac is a pointlike source. Quasi-simultaneously, BL Lac was observed in the hard and soft X-ray bands with NuSTAR (MJD 59911.87 -59912.31), XMM-Newton (MJD 59910.27 -59910.39) and Swift XRT (MJD 59910.16,59911.89,59912.22,59913.43), in linear polarization at optical BVRI bands with Calar Alto, the Nordic Optical Telescope (NOT), the 1.8m Perkins Telescope of Boston University, and the Sierra Nevada Observatory, and at millimeter wavelengths by the Institut de Radioastronomie Millimétrique 30-m Telescope (IRAM-30m) and SubMillimeter Array (SMA). Additional low-frequency radio observations were performed with the Effelsberg 100m telescope (4.85-10.45 GHz) and . Appendices A, C detail the data reduction of these multi-wavelength observations. The IXPE data were calibrated and reduced following standard procedures within the ixpeobssim pipeline 1 .
To characterize the contribution of the two emission components in the IXPE 2-8 keV band and identify a fiducial spectral model, we first attempt to fit the broadband X-ray spectrum averaged over the full observation, including XMM-Newton 0.3-10 keV and NuSTAR 3-80 keV data. A simple absorbed power-law model is inadequate, with χ 2 /dof = 1898/1087. We find the sum of two absorbed power-laws best reproduces the observations, as measured by χ 2 per degree of freedom, Table 1. XMM-Newton measurements below 1 keV require an additional soft spectral component, probably from a hot diffuse plasma, as noted for BL Lac by Middei et al. (2022); we thus add an unpolarized apec component in XSPEC. The temperature and normalization of this apec component are free parameters in the fit. The bestfit absorption column density, N H = 3.1 ± 0.12 × 10 21 cm −2 , is consistent with values from previous studies (e.g., N H = 2.8 ± 0.05 × 10 21 cm −2 ; Weaver et al. 2020). Figure 1 shows the results of the double power-law fit, including the individual power-law and apec components. We note that the soft power-law component comprises 36.7% (2-4 keV) or 26.1%(2-8 keV) of the total flux.
By extending to a spectro-polarimetric fit and restricting the softer power-law to have constant linear polarization, while assuming that the harder power-law is unpolarized, we find Π X = 27.6% ± 11.6% (with Π X < 57.6% at 99% confidence), ψ X = −34.5 • ± 11.6 • . We do not consider this a significant detection, since it does not meet our 99% confidence of non-zero polarization requirement. We discuss the rationale for assuming an unpolarized high-energy component in §3. Allowing both power-laws to have independent, constant polarization results in high, nearly orthogonal values, which cancel the net polarization over most of the spectrum; these values are poorly constrained owing to the poor statistics.

Time variability
The null result is based on the assumption of constant polarization with time of both power-law spectral components. However, the source is clearly variable during the present IXPE epoch, which may affect the derived polarizations. To assess this, we split the observation into three equal time bins based on the IXPE count spectrum and optical observations. We also analyze the data over two energy bins, measuring separately the low-(2-4 keV) and full-energy (2-8 keV) ranges. To check whether the polarization degree and electric vector position angles (EVPA) vary with energy, supporting a multi-component interpretation, we make modelindependent measurements of constant polarization in each time and energy bin, Fig. 2.
XMM-Newton and NuSTAR observations straddle the first time bin, and three short ∼ 1 ksec Swift XRT exposures are available, two within the second time bin and the other in the final time bin. To assess the contribution of the individual power-law components to each time bin, we fit the absorbed sum of a double powerlaw model (Table 1) separately to each appropriate set of IXPE plus Swift XRT time-binned spectra, fixing the photon indices Γ 1 and Γ 2 to their NuSTAR plus XMM-Newton fitted values. This allows the power-law normalizations to vary in time while their slopes remain fixed. Estimated fractions of the soft power-law (synchrotron) contribution for each time and energy bin are displayed in Fig. 2. While the similar variation of the fluxes in the two energy bins (Fig. 2) shows that both power-laws vary together (as expected for synchrotron and Compton components), we find that the soft-component contribution is largest in the first time bin, as might be expected from observations at the high-energy tail of a cooling synchrotron flare.
Interestingly, in the low energy channel within the first time bin, where our spectral fits indicate that the soft component contributes the maximum flux, we detect linear polarization exceeding minimum detectable polarization at 99% confidence (MDP99), Fig. 3. When considered as a single measurement, we find 99.3% confidence in non-zero polarization. Considering all three binned 2-4 keV polarization measurements jointly we find a 98.4% confidence in non-zero polarization. As noted previously, we do not exceed the 99% threshold over the full time interval.
We have attempted full spectro-polarimetric double power-law fits to each time bin as in Fig. 1, but none produced a high-significance detection for the soft powerlaw component. Instead, we have used these fits to estimate the lower-energy power-law (synchrotron) contri- bution fractions in Fig. 2. The results for all such fits are detailed in Appendix B.

DISCUSSION & CONCLUSIONS
In order to fit our XMM-Newton and NuSTAR spectra, (Fig. 1), we find that a two-component spectrum is required for BL Lac. A power-law fit with lowenergy photon index Γ 1 = 3.28 and high-energy value Γ 2 = 1.62, with equal flux at 2 keV, is statistically preferred over a simple power-law. Our polarization results thus probe the cross-over region.
Pure leptonic models predict a significant decrement in polarization of the hard (Compton) component relative to the optical synchrotron value, with Π SSC /Π Sy ≈ 0.3 (Krawczynski 2012;Peirson & Romani 2019). When the high-energy tail of the synchrotron emission reaches into the IXPE band, we might expect the soft-component polarization even to exceed the optical value if the X-ray emission arises from a region of more highly-ordered magnetic field.
One possibility is that the X-ray synchrotron emission occurs mainly in the acceleration and collimation zone of the jet, where the magnetic field is expected to have a well-ordered helical geometry (e.g., Vlahakis & Königl 2004), as inferred previously in BL Lac (Marscher et al. 2008). Alternatively, the emission could take place in a region of the jet with a turbulent magnetic field, with acceleration of particles occurring only within a small volume, for example by magnetic reconnection. Since X-ray synchrotron radiation requires extremely highenergy electrons that are subject to strong radiative energy losses, the X-ray emission would be confined to locations close to the site of particle acceleration, while lower-frequency emission from lower-energy electrons, which can travel farther from the acceleration site before their fractional energy loss becomes high, would occur over a larger volume. In a turbulent magnetic field, the net field is more ordered (but randomly oriented) over smaller volumes, hence the polarization is higher (see, e.g., Marscher 2014; Peirson & Romani 2018, for discussions and estimates). The random value of ψ agrees with our finding that the observed EVPA does not appear related to the direction of the jet.
If the turbulent plasma encounters a shock, the magnetic field becomes partially aligned with the shock front (e.g., Hughes et al. 1985;Marscher 2014;Tavecchio et al. 2018), at which X-ray emitting particles can be accelerated. By the same argument as above, the synchrotron X-ray polarization should then be higher than at longer wavelengths, but instead of a random orientation of the EVPA, ψ should be oriented along the jet direction, contrary to the observations of BL Lac presented here.
During a synchrotron X-ray flare, the more highly polarized synchrotron component contributes more to the X-ray spectrum at lower X-ray energies than does the flatter-spectrum Compton component. As this steepspectrum component fades across the IXPE band, the lower Compton polarization should dominate at higher energies. Although the EVPAs measured at the synchrotron peak and SSC peak frequencies are expected to be correlated (Peirson & Romani 2019), turbulence and energy-dependent emission volumes can cause differences.
To best constrain the soft component polarization we assume that the high energy power-law component is negligibly polarized, as the logical approximation of the expected polarization decrease noted above. The polarization Π X = 27.6% ± 11.6% measured over all IXPE times and energies, while a > 2σ detection, does not reach the threshold for high significance. However, noting that the soft component varies in strength, we find that a time and energy bin analysis allows a significant Π X = 21.7 +5.6 −7.9 % detection at low energies in the first time bin, when the spectral analysis indicates that the soft component accounts for the largest fraction of the total flux. Note that this polarization is substantially higher than the simultaneous optical polarization Π O = 13.1% ± 2.4% for the same time bin. Both the optical and X-ray EVPA are at ∼ 40 • to the projection of BL Lac's jet axis on the plane of the sky at 43GHz (Weaver et al. 2022).
Even the first time/energy bin is diluted by the high energy component. Under the assumption of relatively constant photon indices at the XMM-Newton and NuS-TAR values, the high-energy component still comprises 56% of the flux in this 2-4 keV time bin (Fig. 2). If the component is unpolarized, correction for this flux implies Π Sy = 21.7%/(1 − 0.56) ≈ 49% for the soft component; if the high-energy component corresponds to Compton scattering, polarized at ∼ 0.3× the synchrotron value with approximately the same EVPA, the polarization of the low energy component is Π Sy = 21.7%/((1 − 0.56) + 0.3 × 0.56) ≈ 36%. These polarization degrees are consistent with the upper limit provided by the double power-law spectral fit in Table 4 of the appendix. These large values dramatically exceed the optical polarization, arguing that we are probing the high-frequency end of the synchrotron component, which fades during our observation window.
Two previous IXPE observations of BL Lac (Middei et al. 2023), which occurred during a low state, where the X-ray spectrum was apparently dominated by SSC, produced upper limits on Π X that were significantly below the simultaneous optical polarization. However, in the data from the third epoch presented here, even the total (time and energy) averaged IXPE polarization signal is comparable to the optical values. After correction for hard-component contamination, the soft component substantially exceeds the optical polarization degree.
Other scenarios have different polarization signatures. In simple single-zone lepto-hadronic models, the polarization should be similar across the transition region ( fig. 1). Synchrotron emission from primary leptons producing the low-energy hump yields to higher-energy synchrotron radiation from protons and secondary leptons produced in pγ cascades (Zhang & Böttcher 2013), all in the same magnetic field environment. As noted above, in more realistic jet models, turbulent magnetic fields, differential cooling times (Marscher et al. 2010) and relativistic boosting (Peirson & Romani 2019) cause a significant increase in polarization and changes in EVPA as one approaches the quasi-exponential cutoff of the low-energy peak, where only the highest energy electrons from the most efficient particle acceleration zones contribute synchrotron emission. If a hadronic emission component becomes dominant above this energy, it should be averaged over the lower-energy particle population typical of particle acceleration in the jet, and thus should display polarization similar to that of the primary (optical) synchrotron peak. In models including hadronic synchrotron emission, we expect the polarization fraction at the upper end of the transition region to meet or exceed the optical value.
Our past measurements of Π X < Π O (Middei et al. 2023) and the persistent low polarization at the upper end of the IXPE band therefore argues against a leptohadronic emission model. Furthermore, the detection of total polarization at low energies, with Π 2−4keV Π O , indicates that we are sampling the upper cut-off of the synchrotron spectrum. This is even more striking after correction for dilution by the hard, weakly polarized component. The decreasing relative flux of the soft component and the resulting loss of detection of polarization are consistent with the tail end of a jet flare, as suggested by the γ-ray and X-ray light curves. While these results provide tentative evidence for a fully leptonic emission model in BL Lac at our IXPE observation epoch, variability allows significant hadronic emission at other times. Blazars are particularly variable in polarization (Blinov et al. 2018), and broadband or long-exposure measurements can make polarization results difficult to interpret properly (Kiehlmann et al. 2021;Peirson et al. 2022). Thus, repeated polarization measurements of blazars, with attendant contemporaneous multiwavelength intensity and polarization observations, are needed to fully explore blazar emission. Most interesting would be measurements during flares associated with neutrino events. With the plausible neutrino connection, and the ability to probe the critical Sy/SSC transition regions, BL Lac and other ISPs will be prime targets for such studies. . Funding for this work was provided in part by contract 80MSFC17C0012 from the MSFC to MIT in support of the IXPE project. Support for this work was provided in part by the NASA through the Smithsonian Astrophysical Observatory (SAO) contract SV3-73016 to MIT for support of the Chandra X-Ray Center (CXC), which is operated by SAO for and on behalf of NASA under contract NAS8-03060. The IAA-CSIC co-authors acknowledge financial support from the Spanish "Ministerio de Ciencia e Innovación" (MCIN/AEI/ 10.13039/501100011033) through the Center of Excellence Severo Ochoa award for the Instituto de Astrofíisica de Andalucía-CSIC (CEX2021-001131-S), and through grants PID2019-107847RB-C44 and PID2022-139117NB-C44. Some of the data are based on observations collected at the Observatorio de Sierra Nevada, owned and operated by the Instituto de Astrofísica de Andalucía (IAA-CSIC). Further data are based on observations collected at the Centro Astronómico Hispano-Alemán(CAHA), operated jointly by Junta de Andalucía and Consejo Superior de Investigaciones Científicas (IAA-CSIC). The POLAMI observations were carried out at the IRAM 30m Telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain). The Submillimetre Array is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics and is funded by the Smithsonian Institution and the Academia Sinica. Mauna Kea, the location of the SMA, is a culturally important site for the indigenous Hawaiian people; we are privileged to study the cosmos from its summit. The data in this study include observations made with the Nordic Optical Telescope, owned in collaboration by the University of Turku and Aarhus University, and operated jointly by Aarhus University, the University of Turku and the University of Oslo, representing Denmark, Finland and Norway, the University of Iceland and Stockholm University at the Observatorio del Roque de los Muchachos, La Palma, Spain, of the Instituto de Astrofisica de Canarias. The data presented here were obtained in part with ALFOSC, which is provided by the Instituto de Astrofísica de Andalucía (IAA) under a joint agreement with the University of Copenhagen and NOT. E. L. was supported by Academy of Finland projects 317636 and 320045. We acknowledge funding to support our NOT observations from the Finnish Centre for Astronomy with ESO (FINCA), University of Turku, Finland (Academy of Finland grant nr 306531). The research at Boston University was supported in part by National Science Foundation grant AST-2108622, NASA Fermi Guest Investigator grants 80NSSC21K1917 and 80NSSC22K1571, and NASA Swift Guest Investigator grant 80NSSC22K0537. This study used observations conducted with the 1.8 m Perkins Telescope Observatory (PTO) in Arizona (USA), which is owned and op-erated by Boston University. The above study is based in part on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. We are grateful to the NuSTAR team for approving our DDT request. This work was supported under NASA contract No. NNG08FD60C, and made use of data from the NuSTAR mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory, and funded by the NASA. This research has made use of the NuSTAR Data Analysis Software (NuSTARDAS) jointly developed by the ASI Science Data Center (ASDC, Italy) and the California Institute of Technology (USA). This work was supported by JST, the establishment of university fellowships towards the creation of science technology innovation, Grant Number JPMJFS2129. This work was supported by Japan Society for the Promotion of Science  Table 2. For the IXPE data, the cleaned event files and the associated science products were obtained using a dedicated pipeline relying on the Ftools software package and adopting the latest calibration data files from IXPE (CALDB 20211118). The source regions for each of the three detector units (DUs) were then selected via an iterative process aimed at maximizing the signal-to-noise ratio (SNR) over the IXPE standard energy range of 2--8 keV. In particular, we used circular regions with radius 50 for all three DUs and annulus regions of size 100-300 for the background spectra in Stokes parameters I, Q, and U .
To improve the polarimetric sensitivity, we applied a background rejection strategy (Xie et al. 2021;Di Marco et al. 2023). The method refines the sensitivity by applying energy-dependent cuts on photo-electron tracks from the level 1 data. This method substantially decreases the background event rate, which are triggered by electrons, positrons, muons, or protons either directly impinging upon the detector or created by high energy interactions in the surrounding satellite structures. The cuts employ (1) the number of pixels: the size of the track region of interest (NUM PIX); (2) energy fraction: the fraction of the event energy in the track (EVT FRA); and (3) border pixels: the number of activated pixels along the boundary of the detector (NUM TRK). Here we eliminated the events that do not satisfy the X-ray photon criteria of Di Marco et al. (2021, submitted). Using the point source as a monitor, we rejected ∼ 30% of the diffuse background, with little impact on the source events. For IXPE spectro-polarization analysis, a constant energy binning of 4×0.05keV PI channels per bin was used for Q and U ; we required 30 counts per bin for the intensity spectra.
The XMM-Newton spectra were produced with standard SAS routines and the latest calibration files. The source spectrum was extracted from a circular (radius= 40 ) aperture, while the background spectrum was extracted from a blank region on the Epic-pn CCD camera from a circular region of the same size. The resulting spectrum was re-grouped to include at least 30 counts in each bin and to avoid > 3× oversampling of the spectral resolution. The NuSTAR data were calibrated and cleaned with the NuSTAR Data Analysis Software (NuSTARDAS7), and employed the nuproducts pipeline using the latest calibration database (v. 20220302). The source spectrum was extracted from a circular radius of 70 aperture; a surrounding 270 -370 annulus provided the background. Swift-XRT exposures were obtained in the context of a monitoring campaign tracking the BL Lac flux level before, during, and after the IXPE pointing. Scientific products from the Swift-XRT exposures were derived by using the facilities provided by the Space Science Data Center (SSDC8) of the Italian Space Agency (ASI). In particular, the source spectra were extracted from a source-centered 47 radius aperture, with a 120 -150 concentric annulus providing a background spectrum. The events were grouped to include at least 25 counts in each spectral bin. We modeled each of the four XRT spectra as a simple power-law with Galactic photo-electric absorption. We report the 2-8 keV fluxes and the inferred photon indices in Table 3. The softest spectrum corresponds to the first IXPE time bin, Fig. 2, for which the highest polarization is measured. As discussed in §3, softer spectra represent a higher synchrotron fraction.
We use XSPEC to perform spectro-polarimetric analyses on the entire IXPE observation, including NuSTAR and XMM-Newton spectra, and each of the three IXPE time bins defined in the main text, Fig. 2. Analysis of the entire Note observation is discussed in the main text (Fig. 1, Table 1), where we find that an absorbed sum of two power-laws with an apec component, constant * tbAbs * (polconst * powerlaw + polconst * (apec + powerlaw)) is preferred according to XSPEC model fitting. Here we fix polarization degree of both the high-energy power-law (PL) and apec to zero. Figure 5 displays a contour plot with the polarization measurement of the low-energy PL for the full IXPE observation fit, as displayed in Fig. 1. We note that fixing the polarization degree of the high-energy power-law (PL) to 0.3× the synchrotron, as expected in a leptonic model, does not improve the significance of the fit.
In the case of the three IXPE time bins, we use the same model as above, but with photon indices and apec temperature (Γ 1 , Γ 2 , kT ) fixed to the values found in the full observation fit, Table 1. Hence, only the PL normalization constants and low-energy PL polarization are determined by the fits. We fit this model to the time-binned IXPE spectra along with the appropriate XRT observation(s); see Fig. 2. The first time bin does not have a simultaneous XRT observation, and the second time bin has two (XRT2, XRT3). Table 4 and Fig. 6 give the results of these fits. We are able to determine the relative flux contribution of the low-energy PL in Fig. 2, which correspond to the PL normalization constants at 1 keV.  n/a n/a n/a Note-Π -polarization fraction, ψ -EVPA. Relative power-law normalizations in each time bin dictate the soft power-law fractions in Fig. 2. and 3.5 mm (86.24 GHz), and by the Submillimeter Array (SMA) at 1.3 mm (225.538 GHz) on the 2022 December 1 (MJD 59914.0). The QUIVER observations are performed at several radio bands (depending on receiver availability and weather conditions) from 2.6 GHz to 44 GHz (11 cm to 7 mm wavelength). The receivers are equipped with two orthogonally polarized feeds (either circular or linear) that can deliver polarimetric observables using either native polarimeters or by connecting the SpecPol spectropolarimetric backend. Instrumental polarization is calibrated using observations of both polarized and unpolarized calibrators performed in each session and removed from the data (e.g., Kraus et al. 2003;Myserlis et al. 2018). The polarized intensity, position angle, and polarization percentage were derived from the Stokes I, Q, and U cross-scans. For frequencies <10 GHz), we find a polarization degree Π R ∼ 5% with a polarization angle ψ R between 148 • and 188 • . The radio spectrum obtained between 2.6-43 GHz shows a smooth increase in flux towards higher frequencies, corresponding to a (hard) radio spectrum with spectral index of a = +0.25 (S ∝ ν a ). We find a continuous rotation of the polarization angle between 4.85 GHz and 10.45 GHz that suggests the presence of a Faraday screen with rotation measure of RM ∼ −230 rad/m 2 .
Optical polarization coverage was provided by the Calar Alto (Calar Alto Faint Object Spectrograph -CAFOS, R-band), Higashi-Hiroshima Observatory (Kanata telescope) with the Hiroshima Optical and Near-InfraRed camera (HONIR -R, J-band), the Nordic Optical Telescope (NOT) with the Alhambra Faint Object Spectrograph and Camera (ALFOSC, BVRI), the 1.8m Perkins Telescope (BVRI), and the Sierra Nevada Observatory (SNO, R-band). A detailed description of the observing strategy and data reduction of the aforementioned telescopes can be found in Kawabata et al. (1999) Middei et al. (2023), respectively, and references therein. The observations cover the entire duration of the IXPE observation, revealing high variability of the polarization degree, from ∼3% to ∼17%, with EVPA fluctuating about the direction of the jet axis, 10 • ± 2 • (Weaver et al. 2022). Figure 7 displays the optical observations, while Table 5 summarizes the radio and optical polarization results for the individual telescopes.
The 3-day binned Fermi -LAT γ ray light curve of BL Lac is given in Fig. 8, extracted from the Fermi -LAT Light Curve Repository (Soheila et al. 2023), with IXPE observation times highlighted. The third IXPE observation of BL Lac, reported here, occurred during an outburst.  10.23 ± 0.2 3.33 168 ± 1 8.08 Note-The uncertainties in Π and ψ are either the uncertainty of the measurement or, in the case of multiple measurements, the median uncertainty. σΠ and σ ψ show the standard deviation of the observations.