Polarized blazar X-rays imply particle acceleration in shocks

Most of the light from blazars, active galactic nuclei with jets of magnetized plasma that point nearly along the line of sight, is produced by high-energy particles, up to around 1 TeV. Although the jets are known to be ultimately powered by a supermassive black hole, how the particles are accelerated to such high energies has been an unanswered question. The process must be related to the magnetic field, which can be probed by observations of the polarization of light from the jets. Measurements of the radio to optical polarization—the only range available until now—probe extended regions of the jet containing particles that left the acceleration site days to years earlier1–3, and hence do not directly explore the acceleration mechanism, as could X-ray measurements. Here we report the detection of X-ray polarization from the blazar Markarian 501 (Mrk 501). We measure an X-ray linear polarization degree ΠX of around 10%, which is a factor of around 2 higher than the value at optical wavelengths, with a polarization angle parallel to the radio jet. This points to a shock front as the source of particle acceleration and also implies that the plasma becomes increasingly turbulent with distance from the shock.

Most of the light from blazars, active galactic nuclei with jets of magnetized plasma that point nearly along the line of sight, is produced by high-energy particles, up to ∼ 1 TeV.Although the jets are known to be ultimately powered by a supermassive black hole, how the particles are accelerated to such high energies has been an unanswered question.The process must be related to the magnetic field, which can be probed by observations of the polarization of light from the jets.Measurements of the radio to optical polarization -the only range available until now -probe extended regions of the jet containing particles that left the acceleration site days to years earlier [e.g., 1-3], and hence do not directly explore the acceleration mechanism, as could X-ray measurements.Here we report the detection of X-ray polarization from the blazar Markarian 501 (Mrk 501).We measure an X-ray linear polarization degree Π X ∼ 10%, a factor of ∼ 2 higher than the value at optical wavelengths, with a polarization angle parallel to the radio jet.This points to a shock front as the source of particle acceleration, and also implies that the plasma becomes increasingly turbulent with distance from the shock.
In blazars whose lower-energy emission component peaks in the X-ray band like Mrk 501, synchrotron radiation is the dominant emission process from radio to X-rays.Radiation at longer wavelengths likely arises from larger regions in the jet, hence multiwavelength studies probe spatial variations in the magnetic field structure and other physical properties in different locations [4,5].A particularly important diagnostic is the degree of order of the magnetic field and its mean direction relative to the jet axis, which can be determined by measurements of the linear polarization.For example, particle acceleration at a shock front should result in relatively high levels (tens of percent) of X-ray linear polarization along a position angle that is parallel to the jet [6].In contrast, more stochastic acceleration processes involving turbulence or plasma instabilities are expected to lead to weak polarization with random position angles.The optical, infrared, and radio polarization probe the level of order and mean direction of the magnetic field in regions progressively farther from the site of particle acceleration.Simultaneous multiwavelength polarization from X-ray to radio, now possible with the advent of the Imaging X-ray Polarimetry Explorer (IXPE, [7]), can therefore provide a more complete picture of the emission region of a blazar jet than has been possible until now.
Variations in the flux of blazars at all wavebands, and in the linear polarization at radio to optical wavelengths, is largely stochastic in nature, which can be interpreted as the result of turbulence [5,6,8,9].Multi-zone emission models, often involving a turbulent magnetic field, can reproduce a number of the observed characteristics of the variable linear polarization.In a turbulent region, roughly modeled as N cells, each with a uniform but randomly oriented field, we expect we expect a mean degree of polarization ⟨Π⟩ ∼ 75%/ √ N , with the value of Π exhibiting variability on short time-scales with a standard deviation ∼ 0.5⟨Π⟩ [5], as often observed [10].For a turbulent field in the plasma crossing a shock front, particle acceleration should be most efficient in cells whose magnetic field is nearly parallel to the shock normal; this bias leads to a higher value of Π and more pronounced variability at X-rays compared to lower frequencies [5].The passage of turbulent cells through the emission region would also cause irregular variations, including some apparent rotations, in ψ [8,11].
On the other hand, some of the observed radio and optical patterns of polarization variability (e.g., the aforementioned ψ rotations) have been found to be inconsistent with purely stochastic processes [12,13].This indicates that Polarized X-rays from Mrk 501 there is some coherent ordering of the magnetic field, e.g., by compression or amplification by plasma processes in shocks [e.g., 14] or by the presence of a global, perhaps helical, magnetic field component [e.g., [15][16][17].In the commonly used single zone model, the radiating particles are accelerated by an unspecified process to highly relativistic energies while confined within a plasmoid with a partially ordered or helical magnetic field.The global magnetic field structure is expected to produce similar polarization patterns across frequencies, with little variability over time [18].If the field is helical, ψ should align with the jet direction for most viewing angles [15].In an alternative scenario, which includes shock acceleration, particles become energized over a limited volume -e.g., at a shock front -and then advect or diffuse away from that region [4,6,19].In this process, the electrons lose energy to radiation, and so emit at progressively decreasing frequencies as they travel away from the acceleration site.We refer to this model as "energy-stratified".If the magnetic field is well ordered over the small volume of the acceleration region and becomes increasingly turbulent farther downstream, Π will decrease toward longer wavelengths, while ψ can vary with frequency if the mean direction of the magnetic field changes as the volume increases.In Mrk 501, we expect a progressively higher Π from radio to X-rays.A shock partially orders the magnetic field of the plasma crossing the shock, with the ordered field perpendicular to the shock normal.This causes the net polarization electric vector to be aligned with the jet.In a kink-instability induced magnetic reconnection scenario, where contiguous regions of oppositely-directed magnetic field come into contact, the jet flow is sheared because of transverse velocity gradients [20].Shearing would stretch the magnetic field along the jet boundary, so that ψ is expected to be transverse to the jet direction.3).The two observed ψ X are consistent within 3σ.The radio and optical ψ also lie within 3σ from each other and ψ X .Moreover, the position angle of Mrk 501's jet has been determined through Very Long Baseline Array (VLBA) imaging at 43 GHz to be 120 22].This would suggest that, in both cases, radio-to-X-ray ψ is aligned with the jet axis within uncertainties (Fig. 1).We do not find evidence of polarization variability during either IXPE observation.Compared to the archival multiwavelength observations, we find the flux and polarization of Mrk 501 for both observations to be within one standard deviation of the median of the long-term light curves (Fig. 3).
Blazars like Mrk 501 are known to reach as much as an order of magnitude higher X-ray fluxes during outbursts.For the first IXPE observation the measured X-ray flux indicates an average activity state, while during the second observation we find evidence of a slightly elevated X-ray flux state.Compared to jet axis Observed strongly chromatic slow along the jet axis * There is a slight dependence on the slope of the emission spectrum.† Slow variability = a few days to week, moderate variability = days, high variability ≤ 1 day.
to the historical maximum X-ray flux, during our observations Mrk 501 was a factor of three and a factor of two fainter, respectively.
The polarization measurements reported here reveal an increase in Π toward higher frequencies, with a degree of X-ray polarization that is more than twice the optical value (Fig. 2).This is in tension with the single-zone, turbulent multi-zone, and magnetic reconnection models discussed above.There is no significant variability within the duration of the individual IXPE observations, contrary to the predicted behaviour if turbulent cells moved in and out of the emission region on time-scales of ≲ 2 days.On the other hand, the low (< 10%) optical and X-ray polarization suggests significant disordering of the local magnetic field, possibly due to the presence of stationary turbulence.The wavelength dependence and lack of variability of Π, plus constancy of ψ and its alignment with the jet direction, supports the shock-accelerated energy-stratified electron population scenario [4,19,21]

Methods X-ray polarization observations
IXPE is a joint mission of the U.S. National Aeronautics and Space Administration and the Italian Space Agency (Agenzia Spaziale Italiana).
A description of the spacecraft and of the payload is given by [7]; the detector units are described in [25].Mrk 501 was observed with IXPE over an effective exposure time of 100 ksec from 8 to 10 March 2022 (MJD 59646-59648) and again from 26-28 March 2022 (MJD 59664-59666) for 86 ksec.The exposure times were selected based on [26], which determined that a 100 ksec exposure would be sufficient to measure polarization in Mrk 501 in a blind survey.At the ∼ 30 ′′ angular resolution of IXPE, Mrk 501 is essentially a point source.
The IXPE raw (level-1) data were first reduced and corrected for instrumental polarization artifacts as well as boom and spacecraft motion to create level-2 event files (L2).The L2 data were then corrected for the energy scaling of the detector and bad aspect time intervals following standard procedures within the latest version of the ixpeobssim pipeline [27,28].The IXPE L2 files contain the polarization information in the form of photon-by-photon Stokes parameters.All the quoted results refer to the average of the three identical IXPE detector units (DU).We selected source photons using xpselect and a circular region with a radius of 60 ′′ centered on the source.The polarization degree and angle was determined in the 2-8 keV energy range using three different analysis techniques performed by five independent groups to ensure an unbiased estimation.Those techniques were a model-independent analysis, spectropolarimetric fit in XSPEC, and a maximum likelihood spectropolarimetric (MLS) fit implemented within the MULTINEST algorithm.
Although the effect of the photoelectric absorption is negligible over the 2-8 keV energy range of IXPE, the spectropolarimetric fits included photoelectric absorption based on the measured Galactic neutral hydrogen column density toward Mrk 501 of N H = 1.69 × 10 20 cm −2 [29].
The model-independent analysis applies the [30] formalism to a userdefined subset of photons and determines the total Stokes parameters.
We have performed both a weighted and unweighted analysis.In the model-independent analysis we do not perform background subtraction.
We found that the sky background counts for a 60 ′′ region are only 3% of the total counts.We have verified that for a bright blazar such as Mrk 501, the background has a negligible effect on the polarization analysis.For the spectropolarimetric fits, we simultaneously fit 3× I, Q, U spectra (one set from each IXPE -DU).In XSPEC, following the approach of [31], we used an absorbed single power-law component with constant Π and ψ (CONSTPOL model).For the MLS fit, we used a single power-law spectral component with constant intrinsic Q and U values.Given the exposure time and flux of Mrk 501 at the time of the IXPE observations, the minimum degree of detectable polarization at a 99% confidence level (MDP99) we were able to achieve is 6.6% for the 8-10 March, and 5.2% Data Table 1 for both observations.In both cases, all the measurements through the different analyses are consistent within the uncertainties with the median linear X-ray Π and ψ of Π X = 10 ± 2%, ψ X = 134 and Π X = 11 ± 2%, ψ X = 115 • ± 4 • respectively.Extended Data Figure 1 shows the Stokes Q/I and Stokes U/I of our observation along with the MDP99.Depending on the emission model, variability time scales are expected to range from sub-day to a few days [e.g., 18].A 16-day interval between observations allows us to look for variability on a few days time scale which, however, we do not find.We have also searched for variability within the individual IXPE observations.This was done by splitting the IXPE exposures in two and three equal size time-bins.We again do not find evidence for variability within the uncertainties.

Multiwavelength Observations
Here we report on a subset of our contemporaneous multiwavelength campaign from radio to TeV γ-rays which is summarized in Extended Data Table 2 & 3 and Fig. 2. The complete multiwavelength dataset will be presented in a forthcoming paper.

Millimeter-radio observations
Polarimetric millimeter radio measurements at 3.5 mm (86.24GHz) and The NOT observations used the Alhambra Faint Object Spectrograph and Camera (ALFOSC) in four bands (BVRI) in the standard polarimetric mode.The data were then analyzed with the semi-automatic pipeline developed at the Tuorla Observatory using standard photometric procedures [36,37].Both highly-polarized and unpolarized standard stars were observed during the same night for calibration purposes.The T60 polarimetric measurements were performed using the Dipol-2 polarimeter [38].
Dipol-2 is a remotely operated double-image CCD polarimeter, which is capable of recording polarized images in three (BVR) filters simultaneously [39][40][41][42].We obtained 24 individual measurements of the Stokes Q/I and U/I parameters simultaneously in three filters (BVR).Twenty Observations were also obtained with the WIRC+Pol instrument [45] on the 200-inch Palomar Hale telescope in J band.WIRC+Pol uses a polarizing grating to disperse the light into four beams that sense the four different components of linear polarization (0 • , 45 • , 90 • , 135 • ), and a half-wave plate for beam swapping to improve polarimetric sensitivity [46,47].Data reduction made use of the WIRC+Pol Data Reduction Pipeline software (https://github.com/WIRC-Pol/wircdrp, [45]).The pipeline software averages the measurements over the course of the halfwave plate rotation cycles to account for subtle differences in light paths through the instrument, and reports the degree and angle of polarization in each band.The results were verified with the use of both polarized and unpolarized standard stars.For additional details on the data reduction, see [48].
The starlight from the host galaxy (assumed to be unpolarized) of Mrk 501 contributes a significant fraction of the optical flux.For this reason, the observed Π O needs to be corrected for the depolarization effect of the host-galaxy.To achieve this, we need to estimate the contribution of the host galaxy (I host , in mJy) within the aperture used for the analysis of individual observations.The light profile of Mrk 501's host galaxy has been fully characterized in the R-band in [49].This allows us to estimate I host for each observation separately.We then subtract I host from the total intensity I and estimate the intrinsic polarization degree following [36] as Π intr = Π obs × I/(I − I host ).Due to the Dipol-2 instrument layout as well as the lack of a light profile model for the host galaxy in the J-band we are not able to accurately estimate the host-galaxy contribution to the polarization measurements for the T60 and Palomar-Hale telescopes.For this reason, the measurements from T60 and Hale should be treated as lower limits to the intrinsic polarization degree.For the remaining telescopes, we calculate Π intr in the R-band for each observation and then estimate a median.We find the median intrinsic polarization degree and its uncertainty to be Π intr = 4 ± 1% for the 8-10 March observation and Π intr = 5 ± 1% for the 26-28 March observation.Figure 2 shows the multiwavelength polarization degree from radio to X-rays.

X-ray observations
During the IXPE observations we independently measured the X-ray total flux and spectrum with the X-Ray Telescope (XRT, [50]) on the orbiting Neil Gehrels Swift Observatory (Swift) in Window Timing mode (WT, 4×1 ksec exposures -2×1 ksec for each IXPE observation) and with the Nuclear Spectroscopic Telescope Array (NuSTAR, 20 ksec exposure, [51]) during the 8-10 March observation.We extracted the X-ray spectrum from each telescope following standard analysis procedures and the latest calibration data files.For the source regions we used a circular radius of 47 ′′ and 49 ′′ for Swift and NuSTAR, respectively.To estimate the background for the NuSTAR spectra we used a 147 ′′ circular region outside of the region containing significant photon counts from Mrk 501.The background for Swift was extracted using the same Extended Data Table 1 Median polarization degree and angle measurements from the IXPE data analysis performed by independent groups using three analysis techniques.
Extended Data Table 2 Multiwavelenth and polarization observations for the 2022 March 8-10 observation.

Table comments:
The millimeter-radio flux density is in Janskys.For the millimeter- Table comments: Same as in Extended Data Table 2.
observation took place 2022 March 26-28 (86 ksec, MJD 59664-59667) yielding Π X = 11 ± 2% along ψ X = 115 • ± 4 • .Simultaneously to the second observation, the optical polarization was measured as Π O = 5 ± 1% along ψ O = 117 • ± 3 • (Extended Data Table . Previous intenselysampled measurements of the polarization of Mrk 501 have found variations in Π O by ±5% and in ψ O by ∼ 50 • from one night to the next [10].These apparently discrepant results can be reconciled if the turbulence of the plasma flowing through shocks in the jet is only intermittent, as has been found previously in other blazars [23].One would also expect deviations of the observed ψ from the jet axis as one moves further away from the shock front into more turbulent regions of the jet.At present, the large ψ uncertainties prevent us from confirming such behavior.Future observations of Mrk 501 or similar blazars will allow us to explore the jet's multiwavelength polarization variability.A prediction of the energy-stratified model is that the X-ray polarization angle of blazars whose synchrotron spectral energy distribution peaks at X-ray frequencies, like Mrk 501, will exhibit rotations [24].Probing the magnetic environment of the radiating particles site of energization has supplied a new method for discriminating among particle acceleration mechanisms in astrophysical jets.The new X-ray polarization observations, in combination with the previously available radio and optical polarization diagnostics, have provided a discriminating set of evidence.Our results demonstrate how multiwavelength polarization uniquely probes the physical conditions in supermassive black-hole systems.Future monitoring of the time variability of multiwavelength polarization with IXPE and other instruments will define better the range of physical conditions that occur in astrophysical jets.Acknowledgments.I.L. thanks the Kavli Institute for the Physics and Mathematics of the Universe for their hospitality while this paper was written.The authors thank A. Veledina for discussions that helped improve this work.I.L. was supported by the JSPS postdoctoral short-term fellowship program.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

Fig. 1
Fig. 1 IXPE observations of Mrk 501.Top left: IXPE image of Mrk 501 during the 8-10 March 2022 observation in the 2-8 keV band.The colorbar denotes the number of X-ray photons per pixel.Top right: Normalized Stokes Q and Stokes U parameters of both IXPE observations.The yellow and cyan shaded regions denote the uncertainty (68% CI) in the polarization angle for the 8-10 March and 26-28 March observations respectively.The dashed black line shows the jet direction and the magenta shaded area its uncertainty (68% CI).The dashed circles mark different levels of polarization degree, as labeled.Error bars denote the 68% CI.

Fig. 2
Fig. 2 Multiwavelength polarization of Mrk 501.Left: Multiwavelength polarization degree of Mrk 501 from radio to X-rays.Black symbols are for the 8-10 March observation, and red for the 26-28 March observation.The open symbols show the host-galaxy correctedintrinsic optical polarization degree.Right: Comparison between the observed logarithm of the X-ray and optical Π ratio and the expectations from single-zone (red dashed line), two turbulent multi-zone jet models (dash-dotted blue and dotted magenta lines), and energystratified models (grey shaded area) for both IXPE observations (black for 8-10 March and red for 26-28 March).The solid errorbars show the ratio uncertainty from the IXPE measurements; the dotted errorbars show the full uncertainty including optical uncertainties.In both panels the error bars denote the 68% CI.

Fig. 3
Fig. 3 Multiwavelength and polarization archival observations of Mrk 501.Optical brightness (R-band, upper panel), observed optical Π in % (second-from-top panel), observed optical ψ in degrees (third-from-top panel), and X-ray flux in ×10 −10 erg/s/cm 2 (lower panel).The black and red dashed line indicate the level of the source during the 8-10 March and 26-28 March IXPE observations respectively.The grey shaded area in the ψ shows the direction of the jet axis.In all panels the error bars denote the 68% CI.
for the26-28 March observation.The source was brighter in X-rays during Springer Nature 2021 L A T E X template Polarized X-rays from Mrk 501 21 the 26-28 March observation (see below), hence the lower MDP99.The derived Π and ψ for the different methods are summarized in Extended

1. 3
mm (230 GHz) were obtained with the 30 m Telescope of the Institut de Radioastronomie Millimétrique (IRAM), located at the Pico Veleta Observatory (Sierra Nevada, Granada, Spain), on 9-10 March 2022 (MJD 59647-59649), within the Polarimetric Monitoring of AGN at Millimeter Wavelengths (POLAMI) program (http://polami.iaa.es/,[32][33][34]).Polarized X-rays from Mrk 501Weather related reasons prevented us from obtaining radio observations during the second IXPE exposure.Under the POLAMI observing setup, the four Stokes parameters (I, Q, U, and V) are recorded simultaneously using the XPOL procedure[35].The data reduction, calibration, and managing and flagging procedures used in POLAMI are thoroughly described in[32].The source was relatively stable in flux during the observations at both 1.3 and 3.5 mm with total flux densities of 0.71±0.04Jy and 0.73±0.04Jy at 3.5 mm, and 0.41±0.02Jy and 0.39±0.02Jy at 1.3 mm, on 9 and 10 of March respectively.Also, the polarized flux at 3.5 mm remained stable both in linear polarization degree and angle between the two dates.No polarization above 3.46% (95% confidence upper limit) was detected at 1.3 mm.Optical and infrared observationsOptical polarization observations were performed using several telescopes across the world: the Nordic Optical Telescope (NOT) on the night of 8-9 March (MJD 59647); the Tohoku 60 cm (T60) telescope at the Haleakala Observatory on 10 March (MJD 59649) and on 28 March (MJD 59667); the 2.2m Calar Alto Observatory and 1.5m Sierra Nevada Observatory telescopes on 8-10 March; the AZT-8 telescope of the Crimean Astrophysical Observatory and the St. Petersburg State University LX-200 telescope during 8-10 March and 25-28 March.
unpolarized and two highly-polarized (HD204827 and HD25443) nearby standard stars were observed for calibration and determination of the polarization angle zero point.The individual measurements were used to compute nightly average values using the "2 × sigma-weighting algorithm".The algorithm iteratively filters out outliers, assigning smaller weights to these measurements.The errors on the Stokes Q/I and U/I parameters were computed as standard errors of the weighted means.These errors were then used to estimate uncertainties on the polarization degree and angle[42,43].The Calar Alto Observatory observations were performed in the Johnson Cousins R c optical band by the Calar Alto Faint Object Spectrograph (CAFOS) in imaging polarimetric mode on the 2.2m Telescope.The data were reduced following standard analysis procedures using both unpolarized and polarized standard stars for calibration purposes.Similarly, Mrk 501 was observed by the 1.5 m telescope at Sierra Nevada Observatory using polarized R c filters during the three nights.The 70cm AZT-8 telescope and the 40cm LX-200 telescope observations were carried out in the Cousins R band.Both telescopes are equipped with nearly identical imaging photometers-polarimeters based on a ST-7 camera.Two Savart plates rotated by 45 deg relative to each other are swapped to measure the relative Stokes q and u parameters from Polarized X-rays from Mrk 501 the two split images of each source in the field.The polarization parameters for each observation are produced by the sum of 15×30s consecutive exposures.The data are then corrected for bias, flat field, background level, and calibrated for instrumental and interstellar polarization using the (assumed) unpolarized comparison stars 1, 4, and 6 from [44].The same stars were used to perform differential photometry.During both IXPE observations, all the optical polarization observations are within uncertainties, which suggests no significant variability.
radio and optical observations we report the median estimate of the observations during the IXPE observation.The listed uncertainty is either the standard deviation of the measurements or the median uncertainty, whichever is larger.For the NOT and T60 analysis we used a circular 1.5 ′′ radius aperture.For the data analysis of remaining optical telescopes we used a 7.5 ′′ aperture.The Palomar observations are in the J-band.ψ is given in degrees.The X-ray fluxes are estimated in the 2-8 keV range, and given in units of 10 −11 erg/s/cm 2 .

Extended Data Figure 1
Stokes Q/I and Stokes U/I parameters of our IXPE observations during 8-10 March 2022 (left) and 26-28 March 2022 (right).The measurements are shown for the three detectors (DU1 [red x], DU2 [blue star], DU3 [magenta circle]) separately and combined (black triangle).In both panels error bars denote the 68% CI

Table 1
Summary of model properties.We find increasing Π towards higher frequencies, no significant variability during the 2-3 day long IXPE observations, and rough alignment of ψ with the jet axis from radio to X-rays.Therefore, a shock-accelerated, energy-stratified electron population model satisfies all our multiwavelength polarization observations.