X-Ray Polarization of the Eastern Lobe of SS 433

How astrophysical systems translate the kinetic energy of bulk motion into the acceleration of particles to very high energies is a pressing question. SS 433 is a microquasar that emits TeV γ-rays indicating the presence of high-energy particles. A region of hard X-ray emission in the eastern lobe of SS 433 was recently identified as an acceleration site. We observed this region with the Imaging X-ray Polarimetry Explorer and measured a polarization degree in the range 38%–77%. The high polarization degree indicates the magnetic field has a well-ordered component if the X-rays are due to synchrotron emission. The polarization angle is in the range −12° to +10° (east of north), which indicates that the magnetic field is parallel to the jet. Magnetic fields parallel to the bulk flow have also been found in supernova remnants and the jets of powerful radio galaxies. This may be caused by interaction of the flow with the ambient medium.


INTRODUCTION
A variety of astrophysical systems are capable of translating the kinetic energy of bulk motion into the acceleration of particles to very high energies.Some examples include supernova remnants (Vink 2012), the jets of supermassive black holes and stellar-mass compact objects (Blandford et al. 2019;Mirabel & Rodríguez 1999), and explosive events such as γ-ray bursts (Kumar & Zhang 2015).Understanding the physical conditions within the acceleration regions is key to deciphering the acceleration process.
SS 433 is a stellar binary system exhibiting jets that generate TeV γ-rays revealing the presence of energetic particles (Margon 1984;Abeysekara et al. 2018).SS 433 contains a stellar-mass compact object (likely a black hole) accreting from a supergiant companion (Fabrika 2004) and lies within the Milky Way at a distance of 5.5 kpc (Hjellming & Johnston 1981;Blundell & Bowler 2004).The compact object launches bipolar jets (with a position angle of 100 • and inclined 80 • to our line of sight) containing ionized matter moving at a bulk speed of 0.26c nearly perpendicular to our line of sight (Margon 1984).The jets precess with a period of 162.5 days and an opening angle of 20 • and interact with the surrounding supernova remnant, W50, creating two lobes * Deceased east and west from SS 433 and a unique morphology denoted as the 'Manatee'. 1he jet X-ray emission has a thermal spectrum with prominent line emission within 0.16 pc of SS 433 (Marshall et al. 2002;Migliari et al. 2002).The spectrum is non-thermal in the east ("e1") and west ("w1") lobes starting about 30 pc from SS 433 (Safi-Harb & Ögelman 1997;Yamauchi et al. 1994;Safi-Harb & Petre 1999).Soft thermal emission is seen from the termination shock at the jet end (Safi-Harb & Ögelman 1997;Brinkmann et al. 2007).The X-ray spectra of the e1 and w1 lobes are consistent with synchrotron radiation from energetic electrons (Watson et al. 1983;Safi-Harb & Petre 1999).The High Altitude Water Cherenkov (HAWC) observatory, in Mexico, detected very high-energy (VHE) γ-ray emission from the e1 and w1 lobes extending up to at least 25 TeV indicating the presence of particles with energies of 100's of TeV (Abeysekara et al. 2018).The VHE gammaray emission has been confirmed and more accurately localized with the Large High Altitude Air Shower Observatory (LHAASO) (Cao et al. 2023).Detection of gamma-ray emission from the lobes with the High Energy Stereoscopic System (H.E.S.S.) has also been reported (Olivera-Nieto 2022).The TeV emission and the non-thermal X-ray emission is lo-calized to the lobes which suggests that particle acceleration occurs in the jet at significant distances away from SS 433.
Using XMM-Newton and NuSTAR, Safi-Harb et al. ( 2022) identified a region (the 'Head', see the lower panel of Fig. 1) of nonthermal hard X-ray emission (3-30 keV) at ∼ 18 ′ (29 pc) east of SS 433 coincident with the onset of X-ray emission in the e1 lobe closest to SS 433.Assuming the hard X-rays are synchrotron radiation, the hard spectrum (photon index Γ ≈ 1.6) suggests that this is the site of the acceleration of the high energy particles.This is supported by the morphology of the X-ray emission which shows the hardest X-ray emission closest to SS 433, with lower energy Xrays forming a cometary tail pointed away from SS 433.The 'Head' does not appear to have counterparts at longer wavelengths, thus no polarization information is available.
We observed the Head region using the Imaging X-ray Polarimetry Explorer (IXPE) in order to measure the polarization of the X-ray emission and constrain the geometry of the magnetic field.We describe the observations and our analysis in Section 2 and present the X-ray polarization results in Section 3. We discuss the results and the implications for the acceleration mechanism in Section 4.
2. OBSERVATIONS AND DATA REDUCTION IXPE is the first satellite mission dedicated to X-ray polarimetry in the 2-8 keV band (Weisskopf et al. 2022).It contains three X-ray telescopes, each consisting of a Mirror Module Assembly (Ramsey et al. 2022) and a polarizationsensitive gas-pixel detector unit (DU) (Costa et al. 2001;Soffitta et al. 2021;Baldini et al. 2021), that enable imaging Xray polarimetry of extended sources.IXPE provides an angular resolution of ∼ 30 ′′ (half-power diameter).The overlap of the fields of view of the three DUs is circular with a diameter of 12. ′ 9.The DUs record the tracks of photoelectrons produced by X-rays to enable measurement of linear X-ray polarization.
IXPE observed the eastern lobe of SS 433 from 2023 April 19 to 2023 May 9 with a gap on 2023 May 2 due to observations of another target.The target coordinates (RA = 288.• 27799, DEC = 4. • 93573) were selected to cover the region of hard X-ray emission identified by Safi-Harb et al. (2022).The target is 5. ′ 7 from the LHASSO position and within the error circle.
Because our target is extended and relatively faint, the photon event list was processed to reduce the instrumental background that is induced by Earth albedo and primary energetic particles and secondaries produced in their interactions in the detectors or elsewhere on the spacecraft.The rejection algorithm is described in Di Marco et al. (2023) and removes ∼40% of the background events and a negligible fraction (∼1%) of good events.The main components of the residual background are secondary positrons and a few primary protons that cannot be morphologically distinguished from X-ray initiated photoelectron tracks (Xie et al. 2021).We also removed times of high background found following bright solar flares (likely associated with coronal mass ejections) and surrounding intervals when IXPE crosses the South Atlantic Anomaly.These backgrounds appear as short term increases in counting rate and we removed times when the count rate was higher than the mean rate plus three times the rms of the rate (Forsblom et al. 2023).The technique has been important for the study of faint sources such as Galactic Center clouds and supernova remnants with IXPE (Marin et al. 2023;Zhou et al. 2023).After filtering, the total livetime was 800.7, 791.8, and 789.2 ks for DU1, DU2, and DU3, respectively.The background is higher at the field of view edges of each DU, but relatively uniform across the central 10 ′ diameter (Di Marco et al. 2023).We limit our analysis to this central region.
We selected an energy band to optimize the signal from the source versus the background, both instrumental and from the cosmic X-ray background.We extracted a source spectrum using the 'Head' region defined by Safi-Harb et al. ( 2022) and a background spectrum from a nearby region without strong diffuse emission.Scaling for the region sizes, the source spectrum is above the background spectrum in the energy band of 2 to 5 keV, which we use for all subsequent analysis.
The IXPE image in this band is shown in Fig. 1 along with an XMM-Newton mosaic in the 0.3-10 keV band (Safi-Harb et al. 2022).We define an IXPE source region, that we refer to as 'C11', by drawing a contour corresponding to 11 counts per pixel in the IXPE map using the SAOImage DS9 image display tool with the smoothing parameter set to 16 (Smithsonian Astrophysical Observatory 2000).The region covers most of the 'Head' and 'Cone' regions.We define a background region (shown as a dashed line in Fig 1) that avoids areas of strong diffuse emission and is within the central 10 ′ diameter of the image.
We extracted events within the source and background regions using IXPEOBSSIM version 30.5.0 (Baldini et al. 2022).We calculated polarization data cubes in the 2-5 keV energy band using the pcube algorithm in the xpbin tool and spectra of I, Q, and U Stokes parameters with PHA1, PHAQ1, and PHAU1 algorithms in xpbin.We performed spectropolarimetric analysis using XSPEC version 12.13.1.We used version 12 of IXPE instrument response files and performed an unweighted analysis for both pcube and XSPEC.

POLARIZATION RESULTS
Figure 2 shows the polarization of the events from the C11 region as measured using the model-independent pcube algorithm.The observed polarization degree (PD) is 17.3% ± 4.3% and the electric vector position angle (EVPA) is −0.• 2± 7. • 0 (all uncertainties are 68% confidence).Position angles are measured anticlockwise from north in the equatorial coordinate system as per the convention of the International Astronomical Union.The probability that the signal is a random fluctuation from an unpolarized source is 2.4 × 10 −4 .This is equivalent to a 3.7σ confidence level.We note that the energy band and source region selection were based on the intensity data alone, thus there is only one trial for calculation of the significance of the polarization detection.The events include the X-ray emission from the lobe of SS 433, the cosmic Xray background, and the residual instrumental background.
All are expected to be unpolarized except for the emission from the lobe.Thus, the result indicates a highly probable detection of polarization in the X-ray emission of the lobe.Scaling from the background region, we estimate that 30% of the counts are from the lobe and 70% are from instrumental or astrophysical backgrounds.Utilizing the additive nature of the Stokes parameters, we calculated the Stokes I, Q, and U for the source and background regions then subtracted the background from the source after scaling for the different region areas.After background subtraction, we estimate the PD of the lobe emission as 62% ± 15% and the EVPA as 2. • 8 ± 7. • 0. As expected for unpolarized backgrounds, the EVPA is consistent with the results before background subtraction.The PD is consistent with that calculated using the polarization dilution equation (eq.2) in Di Marco et al. (2023).
We also divided the C11 region into two parts, see Fig. 1, and performed a background-subtracted polarization analysis.The circular region covering the forward region has PD = 59% ± 17%, EVPA = 6 • ± 8 • , and a chance probability of 0.0044.While the polygon covering the trailing region does not provide a significant detection, yielding a chance probability of 0.033, the PD (48% ± 18%) and EVPA (4 • ± 10 • ) are consistent with those of C11.The lower detection significance of the forward region relative to C11 suggests that the polarization signal is not concentrated in the forward region.
We measured the polarization of the events from the background region and found that it is consistent with zero.The same background region is used for the spectropolarimetic analysis described below.We also investigated three rectangular background regions placed to the North, West, and South of C11 with an area equal to that of C11.The inferred PD and EVPA for the C11 emission are consistent within the statistical uncertainties regardless of the background region used.We also investigated other procedures for the removal of intervals of high background.While the statistical significance of the polarization signal varies, the PD and EVPA after background subtraction remain consistent.
Figure 3 shows the IXPE background-subtracted X-ray spectra for the C11 region.We performed spectropolarimetric analysis using Xspec.This differs from the pcube analysis in that it fully takes into account the response of the instrument including the non-diagonal portion of the energy response.The Stokes I spectra have 80 eV bins below 3 keV and 120 eV above.The Stokes Q and U spectra have 400 eV bins.We modeled the spectrum using an absorbed power law with constant polarization multiplied by a constant allowed to vary between the three DUs.The column density for the tbabs absorption model using the Wilms et al. (2000) abundances was fixed to 1.18 × 10 22 cm −2 as for the 'Cone' region in Safi-Harb et al. (2022).The normalization for DU1 was fixed to unity and those for the other DUs were allowed to vary.We find a good spectropolarimetric fit (χ 2 /dof = 137.0/123)with a photon index of Γ = 1.57± 0.14, consistent with that found by Safi-Harb et al. (2022).The observed flux is 5.8 × 10 −13 erg cm −2 s −1 in the 2-5 keV band.This corresponds to a luminosity of 1.3 × 10 34 erg s −1 in the 0.3-30 keV band.The EVPA is −3.• 7 ± 7. • 8, which is consistent with the pcube results.The PD is 52% ± 14%, which is consistent with the backgroundsubtracted pcube result.The allowed range for PD considering the two analyses is 38% to 77%.

DISCUSSION
The high polarization degree found from the C11 region suggests the magnetic field has a well-ordered component, assuming that the X-rays are produced via synchrotron radiation.The maximum polarization for synchrotron radiation is Π = (p + 1)/(p + 7/3) where the electron spectral index is p = 2Γ − 1.For the C11 region, Γ = 1.57thus p = 2.14 and Π = 0.70.The ratio of the PD after background correction to the maximum polarization is approximately equal to the ratio of the energy in the magnetic field component with uniform direction to that in the total field (Burn 1966).For the C11 region, the lower bound on the PD of 38% indicates at least ≈ 50% of the field is in the uniform component.
The energy of the electrons producing the emission can be calculated given the magnetic field strength.Assuming equipartition between the energies of the relativistic electrons and the magnetic field, the latter can be estimated from the X-ray luminosity and volume as B ≈ 10 µG (Safi-Harb et al. 2022).To produce X-rays of energy E γ , the electron energy needed is E e ≈ (50 TeV)(B/10 µG) −1/2 (E γ /1 keV) 1/2 .For E γ = 4 keV and B = 10 µG, electrons must be accelerated to 100 TeV.The same electrons also produce γ-rays near 25 TeV via inverse-Compton scattering on cosmic microwave background photons.Thus, IXPE probes the magnetic field configuration in the same region producing the VHE emission.The gyroradius for 100 TeV electrons in a 10 µG magnetic field is 0.011 pc which is much smaller than the transverse diameter of the C11 region of 3 pc.The synchrotron lifetime is 1200 yr (Reynolds 1998).Thus, either the magnetic field is significantly higher than the equipartition estimate or some other loss mechanism dominates over the length of the region.
For synchrotron radiation, the EVPA is perpendicular to the magnetic field.Thus, the magnetic field lies along the direction of the main bulk motion of the jet.The key result of the IXPE observations is that the magnetic field near the acceleration region contains a significant component that is well-ordered and parallel to the flow direction.This result places constraints on models of the acceleration process and raises questions on the origin of the magnetic field.
The magnetic field could be intrinsic to the jet.However, while radio polarization measurements show the magnetic field is aligned with the ridge line of the precessing jet near SS 433 (Stirling et al. 2004), at larger distances, the field is instead parallel to the motion of individual knots (Miller-Jones et al. 2008).Thus, the field appears to be determined by the interaction between the individual knots and the ambient medium (Blundell et al. 2018).
The powerful jets in Fanaroff-Riley Class II (FR II) radio galaxies have magnetic fields that are predominantly parallel to the jet axis all across the jet (Bridle & Perley 1984;Asseo & Sol 1987).The radio PDs are high, typically 20%-40% and reaching 50%, e.g., in a knot in the jet of 4C 32.69 that may be analogous to the knot considered here (Potash & Wardle 1980).Velocity shear due to the interaction of the jet with the ambient medium is a natural means to produce a magnetic field aligned with the direction of bulk motion (Blandford 1983).
Young, shell-type supernova remnants show radio EVPAs perpendicular to the flow near the shocks in the outer rims.Recent IXPE observations show similar EVPAs, typically with higher PDs, in the X-ray band (Vink et al. 2022;Ferrazzoli et al. 2023;Zhou et al. 2023).These results indicate magnetic fields parallel to the flow, as seen here.Giacalone & Jokipii (2007) and Inoue et al. (2013) suggest that the magnetic field may stretch as the shock propagates around density fluctuations in the interstellar medium.This stretching can both amplify and align the field with the flow.Again, velocity shear is key to aligning the magnetic field with the flow.Alternatively, West et al. (2017) suggest that the overall field is disordered and that the mean EVPA represents the magnetic field only in localized regions where electrons are most efficiently accelerated because the magnetic field is parallel to the flow.
We consider several scenarios for acceleration and subsequent propagation and radiation of the energetic particles in the eastern lobe of SS 433.We note that the jet speed of 0.26c implies a bulk Lorentz factor of 1.036.The magnetic field of 10 µG estimated above and a jet density of 0.05 cm −3 (Panferov 2017) implies an Alfvén Mach number of ∼ 900 and a magnetization of σ ∼ 2 × 10 −4 .Thus, the interaction is non-relativistic with a very high Mach number and the jet is hydrodynamical.
One possible scenario is stochastic acceleration in a shock (see, e.g., Caprioli & Spitkovsky 2014;Park et al. 2015) at the leading edge of the e1 lobe followed by synchrotron emission from gradually cooling electrons flowing eastward (Sudoh et al. 2020).In this scenario, acceleration would be localized; Safi-Harb et al. (2022) show a compact region at the leading edge that is bright in the 10-20 keV band and could be the acceleration region.Ordering of the parallel magnetic field would occur downstream of the turbulent shock region.The energetic electrons would suffer radiative loss while propagating downstream from the shock.Thus, the photon index of the nonthermal X-ray emission should gradually steepen eastward as is observed.
A second scenario is stochastic acceleration by turbulence (Petrosian 2012) in the shear interfaces between the jet and ambient medium.Such models have been proposed for FR II radio galaxies and predict hard particle spectra consistent with those observed (Stawarz & Ostrowski 2002;Rieger & Duffy 2004).The acceleration is stochastic, hence the electron energy spectrum would be a power law with an index similar to that observed.Acceleration is not localized and can occur along the extent of the lobe where there is strong shear, thus steepening of the spectrum would not be expected over that region.The polarized emission would be predominantly from particles diffused out from the turbulent acceleration shear layer into the interior region with parallel magnetic field (Tavecchio 2021).
A third scenario is acceleration through plasma processes (see, e.g., Melrose 1990) associated with magnetic field reconnection.This may occur at magnetic loops produced by shear (Romanova & Lovelace 1992;Sironi et al. 2021) or at quasi-separatrix layers of adjacent magnetic flux ropes (see Aulanier et al. 2006).The overall field reconfiguration process should be continual and gradual to maintain a quasiequilibrium between particle acceleration, escape and radiative loss in order to produce a power-law spectrum with a relatively stable spectral index.While acceleration can occur wherever there is strong shear, the electron spectral index may vary due to local variations in the intensity of reconnection.
We note that Thomson scattering of radiation from the binary system, as alternative to synchrotron emission, would naturally produce highly polarized X-rays with an EVPA perpendicular to jet axis.Such a scenario requires an X-ray bright central source and SS 433 may be an ultraluminous Xray source with the X-ray beam along the jet axis.Waisberg et al. (2019) place an upper bound on the X-ray luminosity of ≲ 5 × 10 36 erg s −1 in a beam with a 1 • opening angle assuming the X-ray spectrum of a hard ultraluminous source (Kaaret et al. 2017).C11 viewed from SS 433 has an opening angle of 3. • 2, so the illuminating beam would have a luminosity of ≲ 5 × 10 37 erg s −1 .An optical depth of 3 × 10 −4 within C11 would be required to produce the observed lumi-nosity, which is much larger than the expected optical depth of 3 × 10 −7 given the density estimate of Panferov (2017).We note that the differing morphology in different energy bands seen with NuSTAR (Safi-Harb et al. 2022) may also present issues with the scattering interpretation.
It may be possible to distinguish between these various models with future IXPE and other X-ray and multiwavelength observations.Deeper observations of the e1 lobe could enable spatially-resolved polarization measurements while observations of the e2 lobe could provide information on downstream evolution of the magnetic field.IXPE observation of the w1 lobe would be of great interest to determine if it also shows an EVPA perpendicular to the jet.Facilities: IXPE, XMM-Newton, NuSTAR Software: IXPEOBSSIM (Baldini et al. 2022), XSPEC (Arnaud 1996), DS9 (Smithsonian Astrophysical Observatory 2000), ASTROPY (Astropy Collaboration et al. 2013)

Figure 1 .Figure 2 .
Figure 1.X-ray images of the eastern lobe of SS 433.(Top) Mosaic of XMM-Newton data in the 0.3-10 keV band.The × marks the location of the binary.The dashed line indicates the jet axis (Hjellming & Johnston 1981) and the dashed rectangle marks the jet termination shock.The blue contour is 25 counts pixel −1 in the XMM-Newton image.The black contour is the IXPE source region.The black circle is the HAWC error circle and has a radius of 15 ′ .(Bottom) X-ray image from IXPE in the 2-5 keV band.C11 marks the black contour used as the IXPE source region.The partially-overlapping magneta contours indicate the forward region (overlapping the Head) and trailing region (overlapping the Cone) used for spatially-resolved polarization analysis.The blue, dashed contour marks the background region.The blue circle is the Head region and the blue quadrilateral is the Cone region from Safi-Harb et al. (2022).The black arrows have a length of 2 ′ (3.2 pc).

Figure 3 .
Figure 3. IXPE X-ray spectra of the C11 region.(Top) Intensity (Stokes I) spectra.Data from the three IXPE DUs are shown as crosses: DU1 (black), DU2 (orange), and DU3 (blue).The fitted models, identical except for the normalization, are in the corresponding color.The lower panel shows the fit residuals.(Bottom) Stokes Q (black) and U (orange) spectra.Points are shifted on the x-axis by ±20 eV for clarity.Data from the three DUs are added.The fitted model is shown as a solid line in the same color.
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.A.V. acknowledges support from the Academy of Finland grant 355672.