X-Ray Polarization Observations of BL Lacertae

Observations of astrophysical jets from supermassive black holes offer unique opportunities to study energetic multiwave band emission processes in the universe (see, e.g., Blandford et al. 2019). Blazars are a subclass of active galactic nuclei (AGNs) whose jets are aligned within a few degrees of the line of sight. They are often characterized by the superluminal motion of bright knots in their jets, and their emission, which is relativistically Doppler boosted, exhibits extreme variability across the electromagnetic spectrum (e.g., Hovatta & Lindfors 2019). Their radio and optical emission is significantly linearly polarized (e.g., Agudo et al. 2018a; Blinov et al. 2021), which is attributed to synchrotron radiation from relativistic electrons in the jet. The origin of the broad keV-to-TeV emission component is a matter of current debate. Most studies interpret the high-energy photons as the result of Compton scattering. The seed photons could originate from either the jet's synchrotron radiation (synchrotron self-Compton; SSC) or from external radiation fields (external Compton; EC). This scenario has been supported by spectral energy distribution (SED, e.g., Abdo et al. 2011) modeling, energetic considerations (Zdziarski & Bottcher 2015; Liodakis & Petropoulou 2020), observations of flux variations that are correlated across the wave bands (e.g., Agudo et al. 2011a, 2011b; Liodakis et al. 2018, 2019b), and low or even undetected radio/optical circular polarization (Wardle et al. 1998; Liodakis et al. 2022a). However, scenarios invoking proton-initiated emission (synchrotron radiation by relativistic protons, and/or emission processes associated with cascades of leptons produced by photohadronic processes, e.g., IceCube Collaboration et al. 2018) have not been definitively excluded. Typically, leptonic models have been more successful in modeling low synchrotron peaked blazars (LBL, ν_syn <10¹⁴ Hz), while hadronic models are often favored for high-synchrotron-peak sources (ν_syn > 10¹⁵ Hz, e.g., Böttcher et al. 2013; Cerrutti et al. 2015, 2017).

Measurements of X-ray polarization can be used to test high-energy emission processes and particle acceleration in jets (e.g., Zhang & Bottcher 2013; Tavecchio et al. 2018; Liodakis et al. 2019a). Starting in 2022 January, the Imaging X-ray Polarimetry Explorer (IXPE; Weisskopf et al. 2010, 2016, 2022) has been carrying out such measurements. Detection by IXPE of high-synchrotron-peak sources like Mrk 501 and Mrk 421 (Di Gesu et al. 2022; Liodakis et al. 2022b) has revealed stronger polarization at X-rays than at longer wavelengths. This is consistent with emission by high-energy electrons that are accelerated at a shock front with partially ordered magnetic fields, after which they are advected to regions with more turbulent fields.

Here we report the first X-ray polarimetric observations of an LBL blazar, the eponymous source BL Lacertae (BL Lac, z = 0.0686, Vermeulen et al. 1995). The X-ray emission of BL Lac is highly variable, with an average flux of F_{2−10 keV} ∼ 1 ×10⁻¹¹ erg cm⁻² s⁻¹ (e.g., Wehrle et al. 2016; Giommi et al. 2021; Middei et al. 2022; Sahakyan & Giommi 2022). Moreover, BL Lac is a very high energy emitting source as it is the 14th brightest AGN at γ-ray energies listed in the Fermi 4LAC catalog (Ajello et al. 2020) and among the few LBL sources detected in TeV γ-rays showing fast, even down to ∼hourly timescales, flux variability (Albert et al. 2007; Arlen et al. 2013). Moreover, BL Lac has been the focus of a large number of multiwavelength and polarization studies (e.g., Raiteri et al. 2013; Blinov et al. 2015, 2018; Weaver et al. 2020; Casadio et al. 2021).

This Letter is organized as follows. We describe the IXPE observations and X-ray data processing and analysis in Section 2 and our contemporaneous observing campaign atoptical circular polarization, infrared, and optical wavelengths in Section 3. In Section 4 we test the interplay among the radio/optical and X-ray bands and we discuss and interpret our results in Section 5. A standard ΛCDM cosmology with H₀ = 70 km s⁻¹ Mpc⁻¹, Ω_m = 0.27, and Ω_λ = 0.73 is adopted throughout this work. Errors quoted in text and in plots correspond to 1σ uncertainties (Δχ² = 1 for 1 parameter of interest). All upper limits related to IXPE observations are quoted at 99% confidence, corresponding to Δχ² = 6.635 for 1 parameter of interest.

BL Lac was observed with the three detector units (DUs) of IXPE during 2022 May 6–14 for a net exposure of 390 ks. The second observation was performed 2022 July 9–11 for a net exposure of ∼116 ks. Quasi-simultaneously with the first IXPE observation, BL Lac was observed by the Nuclear Spectroscopic Telescope Array (NuSTAR; Harrison et al. 2013), with a ∼25 ks exposure, and with the EPIC-pn (Struder et al. 2001) camera on board XMM-Newton (Jansen et al. 2001). In addition, another XMM-Newton observation was taken simultaneously with the second IXPE observation of BL Lac. In Appendix A.3, we report the details on the data reduction of the IXPE, XMM-Newton, and NuSTAR data. The X-Ray Telescope (XRT; Burrows et al. 2005) on the Neil Gehrels Swift Observatory (Swift) monitored the blazar from 2022 May until July. The log of the exposures is provided in Table 1 and details on data reduction and the results of these observations are provided in Appendix A.3.

2.1. X-Ray Spectral Analysis

2.2. Spectropolarimetric X-Ray Analysis

We searched for X-ray polarization from BL Lac by performing a spectropolarimetric fit of the I, Q, and U Stokes spectra over the two IXPE exposures. To better constrain the spectral shape of BL Lac we performed the spectropolarimetric analysis also including the XMM-Newton and NuSTAR data. Similarly to the fit to the I Stokes spectra, we fitted simultaneously the Galactic column density and the apec component, while the photon index and the normalization of the power law were computed for each observation. We then accounted for the polarimetric information encoded in the Q and U Stokes parameters multiplying the power law with polconst, i.e., an XSPEC model that assumes the polarization signal to be constant across the IXPE energy range. Thus, the final model consists of ${tbabs}\times {const}\times ({apec}+{polconst}\times {powerlaw}$), in XSPEC notation. The constant accounts for the intercalibration among the different detector units. We first fit separately the two IXPE observations with the polarization degree and angle free to vary between exposures. This procedure leads to a best fit of χ² = 1469 for 1388 dof, and provides two upper limits for the polarization degree: Π_X = < 14.2% and Π_X < 12.6% (at 99% confidence level) for observations 1 and 2, respectively. In Figure 1 we display the fit to the two IXPE exposures and the corresponding confidence regions. In Table 2 we report the best-fit values corresponding to the analysis of the IXPE observations. Then we tested a scenario where both Π_X and ψ_X remained unchanged between observations. Although blazars typically vary on shorter timescales than 2 months, this test is motivated by the fact that the polarization angle in the millimeter/radio energy range ψ_R (see Section 3), i.e., the seed photons in case of synchrotron self-Compton emission, is consistent within uncertainties between the two observations (see Appendix A). Moreover, as found for hadronic models including polarization, X-ray polarization is expected to be less variable than at optical wavelengths (Zhang et al. 2016). This simple test yields a compatible fit (χ²/dof = 1473/1390), with the spectral parameters being consistent with those quoted in Table 2. Also in this case, we obtain only an upper limit to the polarization degree, Π_X < 9.6%, and the polarization angle is unconstrained. We subsequently set the polarization degree to be the same between the observations, but allow the polarization angle to vary. This attempt, which yields only a compatible fit statistic, gives Π_X < 11.1% with no information on the polarization angle. We also tested the opposite scenario in which the polarization angle is constant between the two IXPE exposures and Π_X varies. Such a test, to which corresponds an equivalent fit statistic, led us to an unconstrained X-ray polarization angle and upper limits for the polarization degrees of Π_X < 14.2% and Π_X < 11.7% for the two observations.

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Table 2. Best-fit Parameters for the Two IXPE Observations

Model	Component	Observation 1	Observation 2
polconst	ΠX	<14.2%	<12.6%
	ψX	⋯	⋯
tbabs	NH†	2.60 ± 0.05
apec	kT (keV)†	0.38 ± 0.04
	Normalization	3.1 ± 0.1
powerlaw	Γ	1.74 ± 0.01	1.87 ± 0.06
	Norm	2.74 ± 0.05	5.5 ± 0.1
F2−8 keV		0.96 ± 0.03(0.05)	1.56 ± 0.06(0.09)

Note. The power-law normalization is in units of ×10⁻³ photons keV⁻¹ cm⁻² s⁻¹, the apec component has a normalization of ×10⁻⁴, and fluxes are ×10⁻¹¹ erg cm⁻² s⁻¹. Errors accounting for the polarimetric information refer to a 99% confidence interval for one parameter of interest.

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During the IXPE observations, a number of telescopes provided multiwavelength polarization coverage: the Atacama Large Millimeter/submillimeter Array (ALMA), AZT-8 (Crimean Astrophysical Observatory, 70 cm diameter), Calar Alto (Spain, 2.2 m), Haleakala T60 (Hawaii, USA), Institut de Radioastronomie Millimétrique (IRAM, 30 m), St. Petersburg University LX-200 (40 cm), Kanata telescope (Japan), Nordic Optical Telescope (NOT, La Palma, Spain, 2.56 m), Palomar Hale telescope (California, USA, 5 m), Boston University Perkins Telescope (1.8 m, Flagstaff, Arizona, USA), the Sierra Nevada Observatory (1.5 and 0.9 m telescopes, Spain), the Skinakas observatory (Crete, Greece, 1.3 m telescope), and the Submillimeter Array (SMA). The observations and data reduction are described in Appendix A. Figures 2, 3, and 4 display the millimiter, optical, and infrared polarized light curves of BL Lac during the IXPE observing windows. During the second IXPE observation, we were unable to obtain infrared polarization data. During both IXPE observations, we find significant variability in polarization degree and angle at millimeter to optical wavelengths.

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For IXPE observation 1, the ALMA observations on May 7 yield a median radio polarization degree Π_R = 3.95% ± 0.3% at 343 GHz along position angle ψ = 23° ± 2°, and, on May 9, Π_R = 3.6% ± 0.3% along ψ_R = 33° ± 1°. The two values of Π_R are consistent between scans within the uncertainties. This is also true for ψ_R during the May 7 observation. However, on May 9 we see a change in ψ_R from the first to the final scan from 19° to 46°. The median uncertainty of each measurement is ±1°. The IRAM 30 m measurements are the same within the uncertainties, which suggests that there is no significant variability. The median value of Π_R at 86 GHz is 4% with a median uncertainty of 0.4% along a median position angle ψ_R = 30° ± 3°. Similarly, at 228.93 GHz, the median Π_R = 4.8% ± 1.2% along median ψ = 35° ± 7°. No circular polarization was detected in any of the observations, with a 95% confidence-interval upper limit of <0.44% and <0.86% for 86 GHz and 228.93 GHz, respectively. We find the optical polarization degree Π_O to vary from 1.6% to 13.7%, with a median of 6.8%. At the same time ψ_O varies from 2° to 172° with a median of 107°, almost perpendicular to the jet axis on the plane of the sky (10° ± 2, Weaver et al. 2022). In the infrared, Π_IR varies from 0.9% to 8.4% with a median of 3.9%. Note that, although the host galaxy has a negligible contribution to the total emission in the optical during the IXPE observation, it is likely that the contribution is much stronger in the infrared. Hence, the Π_IR measurements should be treated as lower limits to the intrinsic polarization degree. The value of ψ_IR varies from 9° to 158° with a median of ∼83°.

During the July IXPE observation, the polarization degree detected by the IRAM 30 m Telescope decreases at 86GHz from 8.5% to 2.2% with a constant median ψ_R of ∼15°; see Figure 2. The SMA observation at 225 GHz yields Π_R = 8.8 ± 1% along ψ_R of 19° ± 2°. The polarization at 228 GHz is consistent within uncertainties at about Π_R = 6% along ψ_R ≈ 20°. At the same time the optical polarization varies from 7% to 23% with a median of Π_O = 14.2%, with ψ_O between 26° and 59° with a median of ψ_O = 42°. A summary of these observations and their polarimetric information is provided in Appendix A.

In both leptonic and hadronic models, the X-ray polarimetric properties are tightly related to those at the millimeter-radio and optical bands, respectively. Motivated by that close connection, we performed additional tests, fixing ψ_X to the corresponding values of ψ_R and ψ_O and computing Π_X for the IXPE observations. In an SSC scenario, we expect the polarization angle to be similar to the one of the millimeter-radio seed photons. On the other hand, in hadronic scenarios, the optical polarization degree is expected to be similar to Π_X . Motivated by these expectations, we proceed to restrict the polarization parameters. We therefore first restrict ψ_X to the value of the millimeter-radio observations. This seems to improve the Π_X < upper limits when fitting the observations separately (Π_X < 6.2% and Π_X < 12.9% for observations 1 and 2, respectively). We repeat the exercise, but this time we restrict ψ_X to the average value of the optical observations. We see a marginal improvement for the second observation with Π_X < 14.2% and Π_X < 11.9% for observations 1 and 2, respectively. Since ψ_O change by more than 70° from the first to the second IXPE observation we do not attempt a joined fit. The derived upper limits from these tests are also summarized in Table 3. Although improved upper limits as low as <6.2% can be obtained for the first IXPE observation, none of these attempts significantly enhanced or degraded the fit to the data presented in Section 2.2. In Table 3 we report the corresponding upper limits from our tests.

Table 3. The Upper Limits for the X-Ray Polarization Degree Π_X Derived Assuming the X-Ray Polarization Angle to Be the Same as the Average Values for ψ_O and ψ_R

Optical Angle	${{\rm{\Pi }}}_{X}^{\mathrm{Obs}1}$	${{\rm{\Pi }}}_{X}^{\mathrm{Obs}2}$
${\psi }_{O}^{\mathrm{Obs}1}$=112°	<14.2%
${\psi }_{O}^{\mathrm{Obs}2}$=38°		<11.9%
Radio angle
${\psi }_{R}^{\mathrm{Obs}1}$=30°	< 6.2%
${\psi }_{R}^{\mathrm{Obs}2}$=18°		<12.9%

Note. Upper limits were computed for both the IXPE observations.

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We have presented the first X-ray polarization observations of an LBL blazar, BL Lac. The analysis of the IXPE data only provides upper limits (corresponding to the 99% confidence level) to the polarization degree: Π_X < 14.2% and Π_X < 12.6% for the first and second exposure, respectively. As a consequence, the polarization angle ψ_X is unconstrained for both of the observations. The upper limit to Π_X can be decreased to as low as <6% by making assumptions for the Π_X and ψ_X only for the first IXPE observation. The upper limits can then be compared with the polarization at longer wavelengths (whose properties are quoted in Tables 4 and 5 in Appendix A). In the optical, we measure a median Π_O = 6.8% at a median angle of ψ_O = 107° for the May observation and medians Π_O = 14.2% and ψ_O = 42° for the July observation. We find evidence of significant millimeter-radio to optical polarization variability during both IXPE observations. Moreover, the variability in the polarization angle is stronger in the optical. Changes in the ψ due to perhaps turbulence or multiple emission regions would reduce the observed polarization degree by $1/\sqrt{N}$, where N is the number of emission regions or turbulent cells (Marscher 2014). Considering the IXPE upper limits derived over the observing period, the median Π_O during the May observation was a factor of ∼2.5 lower, whereas for the July observation Π_O was higher than the Π_X limit.

A strong synchrotron X-ray component from ultra-high-energy electrons can also occur in BL Lac, but in this case the X-ray spectrum would be much steeper than that of our model fits (Marscher et al. 2008). In a leptonic scenario, under which X-ray and γ-ray emission arises from Compton scattering, the X-ray polarization degree is expected to be substantially lower than that of the seed photons (Bonometto & Saggion 1973; Nagirner & Poutanen 1993; Poutanen 1994; Liodakis et al. 2019a; Peirson & Romani 2019). In the case of EC scattering, depending on the scattering geometry and isotropy of the seed photon field, the outgoing radiation could be either unpolarized or polarized. However, based on previous SED modeling (Böttcher & Bloom 2000; Böttcher et al. 2013; MAGIC Collaboration et al. 2019; Morris et al. 2019; Sahakyan & Giommi 2022) we expect SSC emission to be dominated over the EC one in the IXPE energy band. In an SSC model, the seed photons are expected to come from millimeter-radio synchrotron radiation. The millimeter-radio observations give Π_R ∼ 4% for the first observation and Π_R ∼ 6% for the second. This would suggest an expected Π_X of <3% (Peirson & Romani 2019). Therefore, our upper limits for any X-ray polarization signal are consistent with a leptonic scenario. On the other hand, in the case of hadronic processes, X-ray polarization should be less variable, or even stable, compared to the optical, with negligible depolarization (Zhang et al. 2016). The contribution from synchrotron radiation by protons and secondary particles from collisions involving hadrons is expected to yield a similar, or higher (in the case of a pure proton-synchrotron model) value of Π_X compared to optical wavelengths (Zhang & Bottcher 2013; Paliya et al. 2018; Zhang et al. 2019). Alternative emission models involving scattering from relativistic cold electrons are also expected to produce much higher Π_X than Π_O (Begelman et al. 1987). During both IXPE observations, Π_O exceeded the 99% upper limits of Π_X on several occasions. Even considering the median Π_O estimates during the IXPE observations, the optical still exceeds the X-ray upper limit for the July observation. This difference between the optical and X-ray polarization degrees is in strong tension with the relativistic cold electron scattering model as well as a pure proton-synchrotron model. Although we cannot definitively exclude contribution from hadronic processes to the overall emission, the multiwavelength polarization observations provide evidence against the hadronic interpretation. Instead, our findings favor leptonic emission, and particularly Compton scattering as the dominant mechanism for the X-ray emission in BL Lac.

We thank the anonymous referee for their bright comments. The Imaging X-ray Polarimetry Explorer (IXPE) is a joint US and Italian mission. The US contribution is supported by the National Aeronautics and Space Administration (NASA) and led and managed by its Marshall Space Flight Center (MSFC), with industry partner Ball Aerospace (contract NNM15AA18C). The Italian contribution is supported by the Italian Space Agency (Agenzia Spaziale Italiana, ASI) through contract ASI-OHBI-2017-12-I.0, agreements ASI-INAF-2017-12-H0 and ASI-INFN-2017.13-H0, and its Space Science Data Center (SSDC), and by the Istituto Nazionale di Astrofisica (INAF) and the Istituto Nazionale di Fisica Nucleare (INFN) in Italy. This research used data products provided by the IXPE Team (MSFC, SSDC, INAF, and INFN) and distributed with additional software tools by the High-Energy Astrophysics Science Archive Research Center (HEASARC), at NASA Goddard Space Flight Center (GSFC). We acknowledge financial support from ASI-INAF agreement n. 2022-14-HH.0. The research at Boston University was supported in part by National Science Foundation grant AST-2108622 and NASA Swift Guest Investigator grant 80NSSC22K0537. This research has made use of data from the RoboPol program, a collaboration between Caltech, the University of Crete, IA-FORTH, IUCAA, the MPIfR, and the Nicolaus Copernicus University, which was conducted at Skinakas Observatory in Crete, Greece. The IAA-CSIC coauthors acknowledge financial support from the Spanish "Ministerio de Ciencia e Innovacion" (MCINN) through the "Center of Excellence Severo Ochoa" award for the Instituto de Astrofísica de Andalucía-CSIC (SEV-2017-0709). Acquisition and reduction of the POLAMI, TOP-MAPCAR, and OSN data was supported in part by MICINN through grants AYA2016-80889-P and PID2019-107847RB-C44. The POLAMI observations were carried out at the IRAM 30 m Telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany), and IGN (Spain). This Letter makes use of the following ALMA director's discretionary time data under proposal ESO#2021.A.00016.T. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada), MOST, and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ. Some of the data reported here are based on observations obtained at the Hale Telescope, Palomar Observatory as part of a continuing collaboration between the California Institute of Technology, NASA/JPL, Yale University, and the National Astronomical Observatories of China. This research made use of Photutils, an Astropy package for detection and photometry of astronomical sources (Bradley et al. 2019). G.V.P. acknowledges support by NASA through the NASA Hubble Fellowship grant #HST-HF2-51444.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. 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. Part of the French contribution is supported by the Scientific Research National Center (CNRS) and the French Spatial Agency (CNES). 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). D.B., S.K., R.S., and N. M. acknowledge support from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation program under grant agreement No. 771282. C.C. acknowledges support by the European Research Council (ERC) under the HORIZON ERC Grants 2021 program under grant agreement No. 101040021. The Dipol-2 polarimeter was built in cooperation by the University of Turku, Finland, and the Leibniz Institut für Sonnenphysik, Germany, with support from the Leibniz Association grant SAW-2011-KIS-7. We are grateful to the Institute for Astronomy, University of Hawaii, for the allocated observing time. A.H. acknowledges The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This work was supported by JST, the establishment of university fellowships toward the creation of science technology innovation; grant No. JPMJFS2129. This work was supported by Japan Society for the Promotion of Science (JSPS) KAKENHI grant Nos. JP21H01137. This work was also partially supported by Optical and Near-Infrared Astronomy Inter-University Cooperation Program from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan. We are grateful to the observation and operating members of Kanata Telescope. The Submillimeter 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. Maunakea, 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.

Facilities: ALMA - Atacama Large Millimeter Array, CAO:2.2m - Calar Alto Observatory's 2.2 meter Telescope, CrAO:0.7m - , Hale - Palomar Observatory's 5.1m Hale Telescope, IRAM:30m - Institute de Radioastronomie Millimetrique 30 meter telescope, IXPE - , Kanata - , LX-200 - , NOT - Nordic Optical Telescope, NuSTAR - The NuSTAR (Nuclear Spectroscopic Telescope Array) mission, OSN:0.9m - IAA-CSIC Observatorio de Sierra Nevada's 0.9m Telescope, OSN:1.5m - IAA-CSIC Observatorio de Sierra Nevada's 1.5m Telescope, Perkins - Lowell Observatory's 72in Perkins Telescope, Skinakas:1.3m - Skinakas Observatory 1.3 meter Telescope, SMA - SubMillimeter Array, Swift - Swift Gamma-Ray Burst Mission, TU:0.6m - , XMM-Newton. -

A.1. Millimeter-radio Observations

A.2. Optical and Infrared Observations

A.3. X-Ray Observations

Wehere report on a list of the Swift-XRT exposures that were obtained in the context of a monitoring campaign aimed at tracking the flux level of BL Lac. Scientific products from the Swift-XRT exposures were derived using the facilities provided by the Space Science Data Center (SSDC ⁸⁴ ) of the Italian Space Agency (ASI). In particular, the source spectra were extracted with a circular region of radius ∼47'', with a concentric annulus for determination of the background with inner (outer) radii of 120 (150) arcseconds. The spectra were then binned in order to include at least 25 counts in each bin. We modeled each of the obtained 21 XRT spectra as a simple power law with Galactic photoelectric absorption. This model was found to adequately reproduce the data, based on the χ² statistic. We report the 2–8 keV fluxes and the inferred photon indices in Table 6. We then used Swift light curve to study the variability properties of BL Lac over ∼3 months preceding and including the dates in which IXPE was observing BL Lac. The photon index as well as the 2–8 keV flux of BL Lac was derived for each of the XRT exposures fitting a simple power law observed for the Galaxy. Our results, quoted in Table 6, are in agreement with a harder when brighter behavior as the 2–8 flux and Γ are moderately anticorrelated with a Pearson cross-correlation coefficient of P_cc = −0.6 and an accompanying null probability P(<r) = 0.004. This behavior has been already observed in blazars and BL Lac itself (e.g., Prince 2021) and is suggestive of a nonflaring activity of the source. Interestingly, this anticorrelation is moderately stronger if we consider the 2–10 keV flux (P_cc = –0.64 and P(<r) = 0.002), while no relation between the photon index and 0.5–2 keV flux is found in this data set. Finally, in Figure 5, we report the flux variability and compare it with the two IXPE and XMM-Newton light curves.

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