A new lepto-hadronic model applied to the first simultaneous multiwavelength data set for Cygnus X--1
D. Kantzas, S. Markoff, T. Beuchert, M. Lucchini, A. Chhotray, C. Ceccobello, A. J. Tetarenko, J. C. A. Miller-Jones, M. Bremer, J. A. Garcia, V. Grinberg, P. Uttley, J. Wilms
MMNRAS , 1–16 (2020) Preprint 19 October 2020 Compiled using MNRAS L A TEX style file v3.0
A new lepto-hadronic model applied to the first simultaneousmultiwavelength data set for Cygnus X–1
D. Kantzas , ★ , S. Markoff , , T. Beuchert , , M. Lucchini , A. Chhotray ,C. Ceccobello , A. J. Tetarenko , J. C. A. Miller-Jones , M. Bremer , J. A. Garcia , ,V. Grinberg , P. Uttley & J. Wilms Anton Pannekoek Institute for Astronomy (API), University of Amsterdam, Science Park 904, 1098 XH Amsterdam, the Netherlands GRavitational AstroParticle Physics Amsterdam (GRAPPA), University of Amsterdam, Science Park 904, 1098 XH Amsterdam, the Netherlands European Southern Observatory, Karl-Schwarzschild-Straße 2, 85748 Garching bei München, Germany Department of Space, Earth and Environment, Chalmers University of Technology, Onsala Space Observatory, 439 92 Onsala, Sweden East Asian Observatory, 660 N. A’oh¯ok¯u Place, University Park, Hilo, Hawaii 96720, USA International Centre for Radio Astronomy Research - Curtin University, GPO Box U1987, Perth, WA 6845, Australia Institut de Radio Astronomie Millimétrique (IRAM), 300 rue de la Piscine, 38406 Saint Martin d’Hères, France Cahill Center for Astronomy and Astrophysics, Caltech, 1200 East California Boulevard, Pasadena, CA 91125, the USA Dr. Karl Remeis-Observatory and Erlangen Centre for Astroparticle Physics, Sternwartstr. 7, 96049 Bamberg, Germany Institute for Astronomy und Astrophysics, University of Tübingen, Sand 1, 72076 Tübingen, Germany
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Cygnus X–1 is the first Galactic source confirmed to host an accreting black hole. It has beendetected across the entire electromagnetic spectrum from radio to GeV 𝛾 -rays. The source’sradio through mid-infrared radiation is thought to originate from the relativistic jets. Theobserved high degree of linear polarisation in the MeV X-rays suggests that the relativistic jetsdominate in this regime as well, whereas a hot accretion flow dominates the soft X-ray band.The origin of the GeV non-thermal emission is still debated, with both leptonic and hadronicscenarios deemed to be viable. In this work, we present results from a new semi-analytical,multi-zone jet model applied to the broad-band spectral energy distribution of Cygnus X–1 forboth leptonic and hadronic scenarios. We try to break this degeneracy by fitting the first-everhigh-quality, simultaneous multiwavelength data set obtained from the CHOCBOX campaign(Cygnus X–1 Hard state Observations of a Complete Binary Orbit in X-rays). Our modelparameterises dynamical properties, such as the jet velocity profile, the magnetic field, andthe energy density. Moreover, the model combines these dynamical properties with a self-consistent radiative transfer calculation including secondary cascades, both of leptonic andhadronic origin. We conclude that sensitive TeV 𝛾 -ray telescopes like Cherenkov TelescopeArray (CTA) will definitively answer the question of whether hadronic processes occur insidethe relativistic jets of Cygnus X–1. Key words:
X-rays: individual: Cyg X–1, radiation mechanisms: non-thermal, accelerationof particles
Throughout the Universe, a significant fraction of accreting blackholes are known to launch relativistic and collimated jets. Funda-mental properties, such as the extent and power of these jets, scaleessentially with the mass of the central black hole. While super-massive black holes (SMBHs) with M BH ∼ –10 M (cid:12) located atthe center of Active Galactic Nuclei (AGN) are able to power jets ★ E-mail: [email protected] up to Mpc scales (e.g., Waggett et al. 1977), Galactic black holes(M BH ∼ tens of M (cid:12) ) hosted by X-ray binaries (XRBs) typicallylaunch jets that remain collimated up to sub-pc scales (e.g., Mirabel& Rodriguez 1994; Hjellming & Rupen 1995; Mioduszewski et al.2001; Gallo et al. 2005; Fender et al. 2006; Rushton et al. 2017;Russell et al. 2019).AGN jets carry enough power to accelerate particles up toultra-high energies of 10 eV and above (Aharonian 2000), whichwe detect as cosmic rays (CRs) on Earth. The exact accelerationmechanism is not known, but is likely related to diffusive shock © a r X i v : . [ a s t r o - ph . H E ] O c t D. Kantzas et al. acceleration (Axford 1969; Blandford & Ostriker 1978; Ellison et al.1990; Rieger et al. 2007), magnetic re-connection (Spruit et al. 2001;Giannios 2010; Sironi et al. 2015), or shearing and instabilities atboundary layers between different velocities (Rieger & Duffy 2004;Liu et al. 2017).The CR spectrum detected on Earth covers more than ten or-ders of magnitude in particle energy, from 10 to ∼ eV. Twowell-known characteristic spectral features of that spectrum are theso-called ’knee’ at 10 eV and the ’ankle’ at 10 eV (Kulikov &Khristiansen 1959; Bird et al. 1993, respectively). As shown byHillas (1984), the maximum energy of the accelerated particles at agiven magnetic field is limited by the size of the source due to con-finement arguments. Accordingly, CRs above the ankle are likely ofextragalactic origin whereas CRs below the knee are of Galactic ori-gin. AGN jets are considered the most likely source of extragalacticCRs (e.g., Hillas 1984; Gaisser et al. 2016; Eichmann et al. 2018,and references therein). Supernovae and supernova remnants havebeen considered the dominant source of Galactic CRs for decadesalthough questioned quite recently due to lack of ≥
100 TeV obser-vations (Aharonian et al. 2019). Hence, new candidate sources areneeded.Large AGN jets and small-scale XRB jets are (self-)similar inmany regards. For example, they display similar non-thermal emis-sion processes, suggesting that both classes are capable of acceler-ating particles to high energies regardless of their physical scales(e.g., Markoff et al. 2001; Bosch-Ramon et al. 2006; Zdziarski et al.2012). Recent observations of hydrogen and helium emission linesfrom the jets of the accreting compact object SS 433 (Fabrika 2004),as well as the iron emission lines from the stellar-mass black holecandidate 4U 1630-47 (Díaz Trigo et al. 2013), provide indirectevidence of hadronic content their jets. It is still not clear whetherXRB jets can efficiently accelerate hadrons to high energy, but if so,they could also be potential Galactic CRs sources (see e.g., Heinz& Sunyaev 2002; Fender et al. 2005; Cooper et al. 2020).The most striking evidence for particle acceleration insideGalactic jets comes from the non-thermal GeV radiation detectedby the XRBs Cygnus X–1 (Cyg X–1) and Cygnus X-3 (Malyshevet al. 2013; Bodaghee et al. 2013; Zanin et al. 2016; Tavani et al.2009). The jet-origin of the GeV emission is further favored by theorbital modulation predicted, e.g., by Böttcher & Dermer (2005).Zdziarski et al. (2017) in fact detected an MeV–GeV modulationthat likely originates from synchrotron self-Compton upscatteringby particles accelerated in the compact black-hole-jet system ofCyg X–1 orbiting its companion star.The exact nature of the non-thermal radiation is still unclear,with both leptonic and hadronic processes deemed to be viable.In the former case, a leptonic population is responsible for theoverall electromagnetic spectrum from radio to 𝛾 -rays (e.g., Bosch-Ramon et al. 2006). In the latter case, the hadronic populationreaches relativistic speeds as well and contributes equally, or evendominates, in the high energy regime of the spectrum. According tothe Hillas criterion, particles can attain high-enough energy only ifa strong magnetic field confines them in the acceleration region andprovides enough power for particle acceleration. The power carriedby accelerated protons has been claimed to exceed the Eddingtonluminosity in several cases making the hadronic model controversial(Zdziarski & Böttcher 2015). The hadronic channel, however, is theonly possible way to explain the observed high and ultra-high energyCRs, as well as neutrinos through particle cascades (e.g., Mannheim& Schlickeiser 1994; Aharonian 2002).The modeling of either of these radiative processes requiresknowledge of the geometrical structure of the emitting region. Ob- servations show jets that remain collimated up to large distances,following cylindrical or conical structures (e.g., Lister et al. 2013;Hada et al. 2016). However, for simplicity, spectral models oftenconsider localized and spherical single-zone accelerating regionsbecause they provide a good first-order approximation (e.g., Tavec-chio et al. 1998; Mastichiadis & Kirk 2002; Marscher et al. 2008). Inorder to correctly factor in the observed jet geometry, we need to de-scribe an accelerating and expanding outflow, and properly connectits physical properties with those of the accretion flow. Such inho-mogeneous multi-zone jet models are able to self-consistently pro-duce both the characteristic flat-to-inverted radio spectra observedin many compact jet systems, and the upscattered high-energy con-tinuum (Blandford & Königl 1979; Hjellming & Johnston 1988).Multiple groups have considered such multi-zone models inthe past. For instance, Falcke & Biermann (1995) derived a simplemodel for the dynamical properties of a hydrodynamically driven,self-collimating jet, assumed to be powered by the accretion flow.This model was further developed with jet-intrinsic particle distri-butions and more detailed radiative calculations, and extended toXRBs by Markoff et al. (2001) and Markoff et al. (2005). The semi-analytical nature of this model has the great advantage that one candirectly fit its physical parameters to data. Numerical simulationsof the detailed magnetohydrodynamics of the jet flow, combinedwith radiative transfer calculations, would be very computationalexpensive and time consuming for such a task.In this work, we adopt the multi-zone leptonic model ofMarkoff et al. (2005) in its most recent version (Maitra et al. 2009;Crumley et al. 2017; Lucchini et al. 2018; Lucchini et al. submitted)and we further develop it by including hadronic interactions. Thisis the first hadronic multi-zone jet model for Galactic sources thatadditionally includes further improvements to the already imple-mented leptonic ones, such as pair cascades (Coppi & Blandford1990; Böttcher & Schlickeiser 1997).An ideal source to test our newly developed model, is one ofthe brightest and well-studied black-hole high-mass XRB, Cyg X–1and its persistent jets (Stirling et al. 2001; Rushton et al. 2012).Along with the model, we present a new data set obtained by theCHOCBOX campaign (Cyg X-1 Hard state Observations of a Com-plete Binary Orbit in X-rays: Uttley 2017). This campaign per-formed simultaneous observations with the satellite observatories XMM-Newton , NuSTAR , and
INTEGRAL , which, together with theground-based interferometers (NOEMA, VLA, and VLBA) providethe first multi-wavelength data set of that kind for Cyg X–1.We also include the most recent X-ray polarisation informa-tion for Cyg X–1. Linear polarisation has been reported in the en-ergy band below 200 keV but the polarisation fraction is stronglyenergy-dependent and does not exceed 10 per cent (Chauvin et al.2018a,b). In contrast, the hard X-ray emission in the 0.4–2 MeVband is linearly polarised at a level of ∼
70 per cent (Laurent et al.2011; Jourdain et al. 2012; Rodriguez et al. 2015). Such a highpolarisation fraction can only be explained as synchrotron emissionfrom an ordered magnetic field, and places strong constraints on themodelling. In this work, we assume that the synchrotron radiationoriginates in the compact jets of Cyg X–1.For this work, we adopt the updated distance and black-holemass for Cyg X–1 of 2 .
22 kpc and 21 . (cid:12) , respectively (Miller-Jones et al. subm). The distance is in good agreement with the Gaia
DR2 distance of 2 . + . − . (Brown et al. 2018), which isabout 30 per cent more distant than previously thought (Reid et al.2011). The mass of the black hole was historically estimated to bebetween 14 . (cid:12) (Orosz et al. 2011) and 16 M (cid:12) (Ziółkowski 2014;Mastroserio et al. 2019), significantly lower than the updated value. MNRAS , 1–16 (2020) adronic processes in Cygnus X–1 The impact of the updated value of the mass of the black hole can besignificant making the revision of modeling the source necessary.The jet inclination angle is 27.5 ◦ . The companion is a ∼ (cid:12) star(Miller-Jones et al. subm), which is about twice as massive as theforegoing estimate by Orosz et al. (2011). The spectral type of thecompanion star is O9.7 Iab (Bolton 1972). The binary separation isestimated to be ∼ . × cm (Miller et al. 2005) and the systemorbital period is around 5.6 days (Webster & Murdin 1972).This paper is organized as follows. We discuss the new obser-vational data set of Cyg X–1 in Section 2 and our new lepto-hadronicmodel in Section 3. In Section 4 we present the results of our mod-elling. Finally, we outline in Section 5 the significance of the resultsand summarize our work in Section 6. The bulk of the data we use to constrain the physical parameters ofour model resulted from the CHOCBOX campaign (Uttley 2017).In particular, we select data within the time interval 2016 May 3105:15:01.5 – 07:07:04.5 UTC, which provides simultaneous cover-age by NOEMA,
XMM-Newton , NuSTAR , and
INTEGRAL .In addition, we consider some supplemental, non-simultaneous, long-term averaged archival data. We use the mid-infrared data (Rahoui et al. 2011) to constrain physical propertiesof the donor star. We take into account a long-term 15-year aver-age MeV spectrum by
INTEGRAL (Cangemi et al. 2020) as wellas the publicly available GeV 𝛾 -ray spectrum from the Fermi/LAT collaboration (Zanin et al. 2016). The low flux and challenging de-tection techniques require averaging the data over longer timescales.Cangemi et al. (2020) are the first to average over all existing
IN-TEGRAL data of Cyg X–1 in its hard state. The 𝛾 -ray spectrum weuse here comprises data averaged over 7.5 years, only during thehard state of Cyg X–1. Averaging thus provides the best-possibleconstraints to the MeV and GeV emission at the moment. Whilemodeling, we do take into account the systematics arising from in-tegrating over flux variations. We list all the data we use in this workin Table 1. We observed Cyg X–1 with the Karl G. Jansky Very Large Array(VLA) on 2016 May 31, from 04:29–08:28 UT, under project codeVLA/15B-236. The VLA observed in two subarrays, of 14 and 13antennas spread approximately evenly over each of the three arms ofthe array, which was in its moderately-extended B configuration. Thefirst subarray observed primarily in the Q-band, with two 1024-MHzbasebands centred at 40.5 and 46.0 GHz, and the second observedprimarily in the K-band, with the two 1024-MHz basebands centredat 20.9 and 25.8 GHz. Each subarray observed a single two-minutescan at a lower frequency (two 1024-MHz basebands centred at 5.25and 7.45 GHz, and a single 1024-MHz baseband centred at 1.5 GHz,respectively) to characterise the broadband spectral behaviour. Weused 3C 286 as the bandpass and delay calibrator, and to set the fluxdensity scale, and we derived the complex gain solutions using thenearby extragalactic source J2015+3710.We processed the data using the Common Astronomy SoftwareApplication (CASA; McMullin et al. 2007). The data were initiallycalibrated using the VLA CASA Calibration Pipeline (v4.5.3), andafter some additional flagging to excise radio frequency interfer-ence, we imaged the target data using CASA version 4.5.2. The low elevation at the beginning of the run caused significant phase decor-relation and an increased system temperature. Although we wereable to self-calibrate the data in phase down to a solution timescaleof 2 minutes, the flux densities were still found to be biased low.We therefore restricted our images to the final 90 min of the run.Cygnus X–1 was significantly detected in all images, which weremade with Briggs weighting, with a robust parameter of 1.
The NOEMA observations of Cyg X–1 (project code: W15BQ, PI:Tetarenko) took place on 2016 May 31 (05:15:01-07:52:53.0 UT,MJD 57539.2188 - 57539.3284), in the 2 mm (tuning frequencyof 140 GHz) band. These observations were made with the WideXcorrelator, to yield 1 base-band, with a total bandwidth of 3.6 GHzper polarisation. The array was in the 6ant-Special configuration(N02W12E04N11E10N07), with 6 antennas, spending 1.9 hrs onsource during our observations. We used J2013+370 as a phasecalibrator, 3C454.3 as a bandpass calibrator, and MWC349 as a fluxcalibrator. We performed phase only self-calibration on the data,with a solution interval of 45 seconds. The weather significantlydegraded after 07:07 UT at NOEMA, therefore we do not includedata after that time in our analysis. As CASA is unable to handleNOEMA data in its original format, flagging and calibration of thedata were first performed in gildas using standard procedures,then the data were exported to CASA for imaging (with naturalweighting to maximize sensitivity). The flux density of the sourcewas measured by fitting a point source in the image plane (using the imfit task). XMM-Newton
We consider the
XMM-Newton observation ID 0745250501, whichobserved Cyg X–1 in timing mode using its EPIC-pn camera(Strüder et al. 2001) for a total of about 145 ks. First, we createcalibrated and filtered event lists using the
SAS v.16.1.0 , whichwe further correct for X-ray loading and flag soft flare events. Weconsider only counts strictly simultaneous to the NOEMA obser-vation time period resulting in a net exposure time of 3.5 ks. Weuse the filtered event lists to extract 0.3–10 keV spectra accordingto standard procedures.
NuSTAR
NuSTAR (Harrison et al. 2013) measures photons up to ∼
80 keVby focusing hard X-rays on two focal-plane modules FPM A andFPM B. We extract data from within 3–78 keV with the standard
NuSTAR
Data Analysis Software
NuSTARDAS-v.1.8.0 as part of
HEASOFT-v.6.22.1 . Due to the high flux of Cyg X–1, we extractsource counts from within a relatively large region of 150 (cid:48)(cid:48) radiuson both chips FPM A and FPM B, and background counts froma region of 100 (cid:48)(cid:48) located off-source but close enough not preventbias due to the spatial background dependence (Wik et al. 2014).To make sure to have simultaneous coverage with the observationaltime window of NOEMA, we define appropriate good-time intervals , 1–16 (2020) D. Kantzas et al. for the observation ID 30002150004, which results in a net exposuretime of 1.9 ks each for FPM A and FPM B.
INTEGRAL
We extract the
INTEGRAL
Soft Gamma-Ray Imager (ISGRI; Le-brun et al. 2003) data with the
Off-line Scientific Analysis(OSA) software v10.2 to match the simultaneous time interval asmuch as possible, resulting in the use of three science windows,168500020010, 168500030010 and 168500040010 and 6.5 ks ef-fective exposure time.The state-resolved scientific products (images, light curves,and spectra) of the coded-mask instrument ISGRI were obtainedwith standard procedures. We extract spectra and images of CygX-1 on a single-science-window (scw) basis. For each scw, weconstruct a sky model including the brightest sources active in thefield at the time of observation as found from the analysis of the fullCHOCBOX
INTEGRAL exposure, i.e. Cyg X–1, Cyg X–3, Cyg A,GRO J2058 +
42, KS 1947 +
300 and SAX J2103.5+4545.
We describe the multi-zone jet model based on Markoff et al. (2005)and its extensions referenced above. In this section we summarizethe major properties of the model and focus on our new extension ofincluding the effect of hadronic particle acceleration and secondaryproduction.A fully self-consistent jet model should solve the force bal-ance equations along the streamlines and perpendicular to them.This calculation would yield the radial profile and the accelerationprofile describing a given jet configuration starting from a set ofinitial conditions. For simplicity we assume a fixed shape for thejet radial profile, based on observational evidence in AGN, whichtogether with the longitudinal velocity profile then determines theprofiles along the jet of the number density, and global magneticfield strength. Specifically, the cross-sectional radius 𝑅 at any height 𝑧 along the jet is given by 𝑅 ( 𝑧 ) = 𝑅 + ( 𝑧 − 𝑧 ) Γ 𝛽 Γ 𝑗 𝛽 𝑗 , (1)where 𝑅 is the radius of the jet base, 𝑧 is the height of the jetbase above the black hole, 𝛽 , 𝑗 and 𝛽 𝑗 are the bulk velocity of theplasma at the jet base and at height 𝑧 respectively, and Γ is thecorresponding Lorentz factor.The solution of the Euler equation (Crumley et al. 2017) (cid:26) Γ 𝑗 𝛽 𝑗 Γ ad + 𝜉 Γ ad − − Γ ad Γ 𝑗 𝛽 𝑗 − Γ ad Γ 𝑗 𝛽 𝑗 + ( 𝑧 − 𝑧 ) Γ 𝛽 /( Γ 𝑗 𝛽 𝑗 ) 𝑅 Γ 𝑗 𝛽 𝑗 + Γ 𝛽 ( 𝑧 − 𝑧 ) (cid:27) × 𝜕 Γ 𝑗 𝛽 𝑗 𝜕𝑧 = Γ 𝛽 𝑅 Γ 𝑗 𝛽 𝑗 + Γ 𝛽 ( 𝑧 − 𝑧 ) (2)gives the velocity profile along the jet Γ 𝑗 ( 𝑧 ) . In the above equation, Γ ad is the adiabatic index of the flow (5/3 for a non-relativistic and4/3 for a relativistic flow), 𝜉 = (cid:18) Γ 𝑗 𝛽 𝑗 Γ 𝛽 (cid:19) Γ ad − ; Γ 𝛽 = √︄ Γ ad ( Γ ad − ) + Γ ad − Γ . (3) Conservation of the particle number density results in; 𝑛 ( 𝑧 ) = 𝑛 (cid:18) Γ 𝑗 𝛽 𝑗 Γ 𝛽 (cid:19) − (cid:18) 𝑅𝑅 (cid:19) − , (4)where 𝑛 is the differential number density at the jet base incm − erg − . For a quasi-isothermal jet, which seems to be necessaryto explain the flat/inverted spectrum, the internal energy density isgiven by (see Crumley et al. 2017): 𝑈 𝑗 ( 𝑧 ) = 𝑛 m p c (cid:18) Γ j 𝛽 j Γ 𝛽 (cid:19) − Γ ad (cid:18) RR (cid:19) − , (5)where m p c is the rest-frame energy of the protons that carry mostof the kinetic energy. By assuming a fixed plasma beta parameter 𝛽 = 𝑈 e / 𝑈 B , where 𝑈 e is the internal energy density of the electrons,and 𝑈 B the magnetic energy density, we can determine the profileof the magnetic field along the jet to be 𝐵 ( 𝑧 ) = √︄ 𝜋𝑈 e ( 𝑧 ) 𝛽 , (6)where the energy density of the magnetic field is 𝑈 B = 𝐵 / 𝜋 . Forsimplicity, we do not distinguish between toroidal and poloidal com-ponents but we assume that the field is tangled with a characteristicstrength.In addition to the jets, which include a thermal-dominated,corona-like region at their base, we incorporate a simple descriptionfor an additional thermal compact corona located around the blackhole. We assume that a hot electron plasma of temperature 𝑇 cor is covering a radius 𝑅 cor and has an optical depth 𝜏 cor . These hotelectrons inverse Compton upscatter the black body photons emittedby the accretion disc, while the thermal population in the jet basecan upscatter both disc photons as well as synchrotron photons. Thermal electrons are assumed to be directly injected into thejet base from the accreting inflow with a thermal Maxwell-Jüttnerdistribution, which reduces to the standard Maxwellian form in thenon-relativistic case. Protons can be found in the jet base as wellbut they are entirely cold, and only carry the kinetic energy of thejet. The initial number density of the protons carried by the jet isdefined as 𝑛 = 𝐿 jet 𝛽 ,𝑠 Γ ,𝑠 𝑐 m p c 𝜋 R , (7)where half of the injected power 𝐿 jet goes into cold protons, whilethe other half is shared by the magnetic field and leptons, thusthe factor 1/4. We assume equal number density of electrons andprotons. Further, 𝛽 ,𝑠 Γ ,𝑠 𝑐 is the sound speed of a relativistic fluidwith adiabatic index 4/3. The total injected power 𝐿 jet is a freeparameter of the model and is assumed to be proportional to theaccretion energy (cid:164) 𝑀𝑐 .Once the particles propagate out some distance 𝑧 diss along thejet, a fitted parameter, we assume that a fixed fraction (10 per cent)of both leptons and hadrons are accelerated into a power-law withindex 𝑝 from this point onwards. We do not invoke any particularacceleration mechanism nor distinguish between acceleration or re-acceleration. We thus allow the power-law index 𝑝 to be a free We do not distinguish between electrons and positrons. The results in thiswork do not depend on the charge of the lepton. MNRAS000
We describe the multi-zone jet model based on Markoff et al. (2005)and its extensions referenced above. In this section we summarizethe major properties of the model and focus on our new extension ofincluding the effect of hadronic particle acceleration and secondaryproduction.A fully self-consistent jet model should solve the force bal-ance equations along the streamlines and perpendicular to them.This calculation would yield the radial profile and the accelerationprofile describing a given jet configuration starting from a set ofinitial conditions. For simplicity we assume a fixed shape for thejet radial profile, based on observational evidence in AGN, whichtogether with the longitudinal velocity profile then determines theprofiles along the jet of the number density, and global magneticfield strength. Specifically, the cross-sectional radius 𝑅 at any height 𝑧 along the jet is given by 𝑅 ( 𝑧 ) = 𝑅 + ( 𝑧 − 𝑧 ) Γ 𝛽 Γ 𝑗 𝛽 𝑗 , (1)where 𝑅 is the radius of the jet base, 𝑧 is the height of the jetbase above the black hole, 𝛽 , 𝑗 and 𝛽 𝑗 are the bulk velocity of theplasma at the jet base and at height 𝑧 respectively, and Γ is thecorresponding Lorentz factor.The solution of the Euler equation (Crumley et al. 2017) (cid:26) Γ 𝑗 𝛽 𝑗 Γ ad + 𝜉 Γ ad − − Γ ad Γ 𝑗 𝛽 𝑗 − Γ ad Γ 𝑗 𝛽 𝑗 + ( 𝑧 − 𝑧 ) Γ 𝛽 /( Γ 𝑗 𝛽 𝑗 ) 𝑅 Γ 𝑗 𝛽 𝑗 + Γ 𝛽 ( 𝑧 − 𝑧 ) (cid:27) × 𝜕 Γ 𝑗 𝛽 𝑗 𝜕𝑧 = Γ 𝛽 𝑅 Γ 𝑗 𝛽 𝑗 + Γ 𝛽 ( 𝑧 − 𝑧 ) (2)gives the velocity profile along the jet Γ 𝑗 ( 𝑧 ) . In the above equation, Γ ad is the adiabatic index of the flow (5/3 for a non-relativistic and4/3 for a relativistic flow), 𝜉 = (cid:18) Γ 𝑗 𝛽 𝑗 Γ 𝛽 (cid:19) Γ ad − ; Γ 𝛽 = √︄ Γ ad ( Γ ad − ) + Γ ad − Γ . (3) Conservation of the particle number density results in; 𝑛 ( 𝑧 ) = 𝑛 (cid:18) Γ 𝑗 𝛽 𝑗 Γ 𝛽 (cid:19) − (cid:18) 𝑅𝑅 (cid:19) − , (4)where 𝑛 is the differential number density at the jet base incm − erg − . For a quasi-isothermal jet, which seems to be necessaryto explain the flat/inverted spectrum, the internal energy density isgiven by (see Crumley et al. 2017): 𝑈 𝑗 ( 𝑧 ) = 𝑛 m p c (cid:18) Γ j 𝛽 j Γ 𝛽 (cid:19) − Γ ad (cid:18) RR (cid:19) − , (5)where m p c is the rest-frame energy of the protons that carry mostof the kinetic energy. By assuming a fixed plasma beta parameter 𝛽 = 𝑈 e / 𝑈 B , where 𝑈 e is the internal energy density of the electrons,and 𝑈 B the magnetic energy density, we can determine the profileof the magnetic field along the jet to be 𝐵 ( 𝑧 ) = √︄ 𝜋𝑈 e ( 𝑧 ) 𝛽 , (6)where the energy density of the magnetic field is 𝑈 B = 𝐵 / 𝜋 . Forsimplicity, we do not distinguish between toroidal and poloidal com-ponents but we assume that the field is tangled with a characteristicstrength.In addition to the jets, which include a thermal-dominated,corona-like region at their base, we incorporate a simple descriptionfor an additional thermal compact corona located around the blackhole. We assume that a hot electron plasma of temperature 𝑇 cor is covering a radius 𝑅 cor and has an optical depth 𝜏 cor . These hotelectrons inverse Compton upscatter the black body photons emittedby the accretion disc, while the thermal population in the jet basecan upscatter both disc photons as well as synchrotron photons. Thermal electrons are assumed to be directly injected into thejet base from the accreting inflow with a thermal Maxwell-Jüttnerdistribution, which reduces to the standard Maxwellian form in thenon-relativistic case. Protons can be found in the jet base as wellbut they are entirely cold, and only carry the kinetic energy of thejet. The initial number density of the protons carried by the jet isdefined as 𝑛 = 𝐿 jet 𝛽 ,𝑠 Γ ,𝑠 𝑐 m p c 𝜋 R , (7)where half of the injected power 𝐿 jet goes into cold protons, whilethe other half is shared by the magnetic field and leptons, thusthe factor 1/4. We assume equal number density of electrons andprotons. Further, 𝛽 ,𝑠 Γ ,𝑠 𝑐 is the sound speed of a relativistic fluidwith adiabatic index 4/3. The total injected power 𝐿 jet is a freeparameter of the model and is assumed to be proportional to theaccretion energy (cid:164) 𝑀𝑐 .Once the particles propagate out some distance 𝑧 diss along thejet, a fitted parameter, we assume that a fixed fraction (10 per cent)of both leptons and hadrons are accelerated into a power-law withindex 𝑝 from this point onwards. We do not invoke any particularacceleration mechanism nor distinguish between acceleration or re-acceleration. We thus allow the power-law index 𝑝 to be a free We do not distinguish between electrons and positrons. The results in thiswork do not depend on the charge of the lepton. MNRAS000 , 1–16 (2020) adronic processes in Cygnus X–1 Observatory log Frequency (Hz) log Energy (eV) Flux Density (mJy a ) ReferencesVLA 10 .
32 10 . .
61 10 . − . − . − . − .
72 8 . ± .
03 8 . ± . . ± .
10 8 . ± .
15 This workNOEMA 11.15 − .
24 6 . ± .
27 This work
Spitzer − . − .
61 54 .
57 at 10 Hz Rahoui et al. (2011)
XMM-Newton .
07 at 3 keV0 .
32 at 10 keV This work
NuSTAR .
54 at 3 keV0 .
18 at 78 keV This work
INTEGRAL − at 3.3 MeV Cangemi et al. (2020) Fermi/LAT × − at 0 . × − at 10 GeV Zanin et al. (2016) Table 1.
The observational multiwavelength data used in this work. a mJy = − erg cm − s − Hz − . parameter in our model. Moreover, we assume constant particleacceleration beyond the particle acceleration region 𝑧 diss . Anotherfree parameter is the acceleration efficiency 𝑓 sc (see e.g., Jokipii1987; Aharonian 2004). Given this efficiency, the maximum energyachieved by the particles is calculated self-consistently along thejet by considering the main physical processes that limit the furtheracceleration of particles. The dominant cooling mechanisms aresynchrotron radiation and inverse Compton scattering (ICS) forleptons, and escape from the source for hadrons. Adiabatic coolingis not relevant because the jets are actively collimated.In order to calculate the particle distributions along the jets,we solve the continuity equation, which in energy phase space canbe written in the general form: 𝜕𝑁 𝑖 ( 𝐸 𝑖 , 𝑡, 𝑧 ) 𝜕𝑡 + 𝜕 (cid:0) Γ 𝑗 𝑣 𝑗 𝑁 ( 𝐸 𝑖 , 𝑡, 𝑧 ) (cid:1) 𝜕𝑧 + 𝜕 ( 𝑏 ( 𝐸 𝑖 , 𝑡, 𝑧 ) 𝑁 𝑖 ( 𝐸 𝑖 , 𝑡, 𝑧 )) 𝜕𝐸 𝑖 − 𝑁 𝑖 ( 𝐸 𝑖 , 𝑡, 𝑧 ) 𝜏 esc ( 𝐸 𝑖 , 𝑡, 𝑧 ) = 𝑄 ( 𝐸 𝑖 , 𝑡, 𝑧 ) . (8)The above equation describes the temporal evolution of the numberdensity of the particle population 𝑖 , i.e. electrons or protons. Sincewe assume a steady-state source, we neglect the first term on theleft-hand side, making every quantity time-independent. We alsoneglect the effects of spallation and diffusion.The second term on the left-hand side describes the propaga-tion of particles along the jet. The third term expresses the radiativecooling of the particles, i.e. synchrotron radiation and ICS for lep-tons, as well as inelastic collisions for hadrons. The particles mayescape the source within the timescale 𝜏 esc ( 𝐸 𝑖 , 𝑡, 𝑧 ) , which in ourtreatment is only energy-dependent. Finally, the right-hand side de-scribes the injection term, which is the sum of a Maxwell-Jüttnerthermal distribution at low energies and a non-thermal power-lawwith an exponential cutoff at the self-consistently derived maximumenergy. The non-thermal power-law is included only starting at thedissipation region 𝑧 diss where particle acceleration initiates.Losses will dominate over acceleration above some particularenergy 𝐸 max which can be self-consistently calculated – here forthe leptonic case – by setting 𝜏 − (cid:0) 𝐸 𝑒, max (cid:1) = 𝜏 − (cid:0) 𝐸 𝑒, max (cid:1) + 𝜏 − (cid:0) 𝐸 𝑒, max (cid:1) + 𝜏 − (cid:0) 𝐸 𝑒, max (cid:1) , (9)with the timescales for acceleration, synchrotron cooling, ICS cool-ing in the Thomson regime, and the escape of leptons, i.e. • 𝜏 acc = 𝐸 𝑒 𝑓 sc ecB • 𝜏 syn = 𝜋 m e2 c 𝜎 T 𝐵 𝐸 𝑒 𝛽 𝑒 • 𝜏 ICS = 𝜏 syn 𝑈 𝐵 𝑢 rad • 𝜏 esc = 𝑅𝛽 𝑒 c ,respectively. Here, e is the electron charge, 𝐵 the magnetic field ofthe jet at height 𝑧 with radius 𝑅 , m e the rest mass of the electron,c the speed of light, 𝜎 T the Thomson cross-section, 𝛽 𝑒 the speedof the particle in units of c, 𝑈 B = 𝐵 / 𝜋 the energy density ofthe magnetic field, 𝑢 rad the energy density of the radiation fieldupscattered by the electrons.Following the same approach, we calculate the maximum en-ergy of protons in case of hadronic acceleration by setting 𝜏 − (cid:0) 𝐸 𝑝, max (cid:1) = 𝜏 − (cid:0) 𝐸 𝑝, max (cid:1) + 𝜏 − (cid:0) 𝐸 𝑝, max (cid:1) + 𝜏 − 𝛾 (cid:0) 𝐸 𝑝, max (cid:1) + 𝜏 − (cid:0) 𝐸 𝑝, max (cid:1) , (10)with the timescales for acceleration, synchrotron cooling, proton-proton collisions, proton-photon collisions, and the escape of pro-tons, i.e. • 𝜏 acc = 𝐸 𝑝 𝑓 sc ecB • 𝜏 syn = 𝜋 m p2 c 𝜎 T 𝐵 𝐸 𝑝 𝛽 𝑝 × (cid:18) m p m e (cid:19) • 𝜏 pp = (cid:0) 𝐾 pp 𝜎 pp 𝑛 th 𝑐 (cid:1) − • 𝜏 𝑝𝛾 = (cid:0) 𝐾 p 𝛾 𝜎 p 𝛾 𝑛 𝛾 𝑐 (cid:1) − • 𝜏 esc = 𝑅𝛽 𝑝 𝑐 Here, 𝐾 pp corresponds to the multiplicity (average number of sec-ondary particles), 𝜎 pp to the cross-section of this interaction, and 𝑛 th to the number density of the target particles (see Section 3.3.2).For proton-photon interactions between the accelerated protons anda photon field with number density 𝑛 𝛾 , we consider the multiplicity 𝐾 p 𝛾 (Mannheim & Schlickeiser 1994). One can see that the proton-synchrotron timescale is approximately (cid:0) m p / m e (cid:1) times longer thanthe electron one. MNRAS , 1–16 (2020)
D. Kantzas et al.
The injection term becomes a power-law with an exponentialcutoff beyond the particle acceleration region 𝑧 diss , i.e. 𝑄 ( 𝐸 𝑖 ) = 𝑄 𝐸 − 𝑝𝑖 × exp (cid:0) − 𝐸 𝑖 / 𝐸 𝑖, max (cid:1) , (11)where 𝑄 is a normalisation factor and 𝑝 > 𝑄 . Electrons throughout the jet lose energy due to synchrotron and ICradiation. Before the particle acceleration region, even thermal elec-trons emit synchrotron radiation due to the relatively strong mag-netic field. Beyond the particle acceleration region, the non-thermalleptonic process that dominates is the synchrotron radiation. Forelectron ICS we include photon fields from synchrotron radiation(synchrotron-self Compton – SSC), the disc around the black hole,and the companion star. We take into account the geometry of thecompanion star because, for high-mass XRBs like Cyg X–1, the sizeof the star is comparable to the size of the jet, especially for regionsclose to the compact object where the majority of the high energyradiation is likely to originate. In particular, we calculate the photonfield of the companion star as seen in the jet frame accounting forthe Doppler boosting (each jet segment travels at a different Lorentzfactor). All expressions for synchrotron radiation and ICS are takenfrom Blumenthal & Gould (1970) and Rybicki & Lightman (2008).Furthermore, we include the full treatment of photon-photonannihilation and electromagnetic cascades (Coppi & Blandford1990; Böttcher & Schlickeiser 1997). Depending on the numberdensity of produced pairs, additional interactions between electronsand positrons can cause pair-annihilation leading to the productionof 𝛾 -rays. This process can occur until the lepton energy budget be-comes insufficient for further photon production. The photon fieldswe take into account are the same as for ICS. Finally, we add theproduced pairs to the leptonic population, which are then cooled asdescribed above. In the case where protons and/or ions are accelerated to relativisticenergies in the jet, they can inelastically collide with thermal pro-tons and photons inside the jet flow and produce secondary particles(Mannheim & Schlickeiser 1994). In the extension of our model,we therefore implement both proton-proton and proton-photon in-teractions. We use the full semi-analytical treatment of Kelner et al.(2006) and Kelner & Aharonian (2008) based on Monte-Carlo sim-ulations (see below for more details).
Collisions of non-thermal protons with thermal jet protons andstellar-wind protons (proton-proton collisions, pp, henceforth) lead to the production of 𝛾 -rays, secondary electrons, and neutrinos. Theinteractions responsible for the production of these particles can bedescribed as p + p → p + p + 𝛼𝜋 + 𝛽 (cid:0) 𝜋 + + 𝜋 − (cid:1) , where 𝛼 and 𝛽 are the collision energy-dependent multiplicity of therelated products (see e.g., Romero et al. 2017). The charged pionsdecay as 𝜋 + → 𝜇 + + 𝜈 𝜇 , 𝜇 + → e + + 𝜈 e + ¯ 𝜈 𝜇 ,𝜋 − → 𝜇 − + ¯ 𝜈 𝜇 , 𝜇 − → e − + ¯ 𝜈 e + 𝜈 𝜇 , and the neutral pions decay into two gamma-rays, i.e. 𝜋 → 𝛾 + 𝛾. In order for these interactions to occur, the energy of the ac-celerated proton has to exceed the threshold of 𝐸 th (cid:39) .
22 GeV(Mannheim & Schlickeiser 1994).The lifetime of the produced mesons is well measured by labo-ratory experiments and short compared to the dynamical timescalesof the jet. We can therefore assume instant decays. Consequently,the charged products do not radiatively lose energy as they would inextreme environments of either very strong magnetic fields or veryhigh energies (e.g., Mücke et al. 2003). The above statement can beparametrized as follows (e.g., Böttcher et al. 2013)B 𝛾 p (cid:28) (cid:40) . × G for pions5 . × G for muons , (12)where B is the strength of the magnetic field in the jet rest frameand 𝛾 p the Lorentz factor of the proton. Given that the highest valueof the magnetic field is in the jet base (10 G) and that hadronicinteractions do not occur yet because particle acceleration occurslater, one can see that the above inequality is always satisfied.In order to produce the distributions of stable products, wefollow the semi-analytical approximation of Kelner et al. (2006). Inparticular, the differential number density of the 𝛾 -rays is given bythe expression: 𝑑𝑛 𝛾 (cid:0) 𝑧, 𝐸 𝛾 (cid:1) 𝑑𝐸 𝛾 = 𝑐𝑛 targ ∫ 𝜎 pp (cid:18) 𝐸 𝛾 𝑥 (cid:19) 𝑛 𝑝 (cid:18) 𝑧, 𝐸 𝛾 𝑥 (cid:19) 𝐹 𝛾 (cid:18) 𝑥, 𝐸 𝛾 𝑥 (cid:19) 𝑑𝑥𝑥 , (13)where 𝐸 𝛾 is the energy of the 𝛾 -ray, 𝑛 targ is the number density ofthe thermal target protons, 𝜎 pp is the cross section for pp collisions,n p is the number density of the non-thermal protons, x = E 𝛾 / E p isthe normalized photon energy with respect to initial proton energyand F 𝛾 (cid:0) x , E 𝛾 / x (cid:1) is the spectrum of 𝛾 -rays.The cross section for pp interactions can be given by the semi-analytical expression 𝜎 pp (cid:0) 𝑇 𝑝 (cid:1) = (cid:20) . − .
96 log (cid:18) 𝑇 𝑝 𝑇 thr (cid:19) + .
18 log (cid:18) 𝑇 𝑝 𝑇 thr (cid:19)(cid:21) × (cid:34) − (cid:18) 𝑇 thr 𝑇 𝑝 (cid:19) . (cid:35) mb , (14)where 𝑇 𝑝 is the proton kinetic energy in the laboratory frame and 𝑇 thr = 𝑚 𝜋 + 𝑚 𝜋 / 𝑚 𝑝 (cid:39) . 𝛾 -ray spectrumas well as the other secondary particles.For this work the target protons are the cold protons of the jetand protons emitted by the heavy companion star in the form of MNRAS000
18 log (cid:18) 𝑇 𝑝 𝑇 thr (cid:19)(cid:21) × (cid:34) − (cid:18) 𝑇 thr 𝑇 𝑝 (cid:19) . (cid:35) mb , (14)where 𝑇 𝑝 is the proton kinetic energy in the laboratory frame and 𝑇 thr = 𝑚 𝜋 + 𝑚 𝜋 / 𝑚 𝑝 (cid:39) . 𝛾 -ray spectrumas well as the other secondary particles.For this work the target protons are the cold protons of the jetand protons emitted by the heavy companion star in the form of MNRAS000 , 1–16 (2020) adronic processes in Cygnus X–1 a homogeneous stellar wind. In particular, the companion star ofCyg X–1 is a blue supergiant that loses ∼ − M (cid:12) /yr in the formof stellar wind (Gies et al. 2008). We use the following expressionto calculate the proton number density emitted by the companion 𝑛 wind ( 𝑧 ) = (cid:164) 𝑀 ★ 𝜋 (cid:16) 𝛼 ★ + 𝑧 (cid:17) 𝑣 wind m p × − 𝑅 ★ √︃ 𝛼 ★ + 𝑧 − 𝛽 wind (15)(Grinberg et al. 2015), where (cid:164) 𝑀 ★ = 𝜋𝜌 ( 𝑟 ) 𝑣 ( 𝑟 ) is the mass-loss rate based on the radially-dependent mass density profile 𝜌 ( 𝑧 ) , 𝑣 wind is the terminal velocity of the wind on the jet wall, 𝛼 ★ is thedistance of the massive star from the black hole, 𝑅 ★ is the radiusof the massive star, 𝑧 is the distance from the central black holealong the jet axis and 𝛽 wind is a free parameter used to improve thevelocity profile of the wind found to be 1.6 (see e.g., Grinberg et al.2015). From geometrical, filling-factor considerations, we assumethat only 10 per cent of the wind protons take part in the pp process(see e.g., Pepe et al. 2015). Therefore, the total target number density(in cm − ) is given by: 𝑛 targ ( 𝑧 ) = . 𝑛 wind ( 𝑧 ) + 𝑛 p , cold ( 𝑧 ) . (16) In addition to the pp interaction, inelastic collisions between non-thermal protons and photons occur in the jet (p 𝛾 henceforth). For thisprocess we take into account the same photons fields as describedabove for leptonic ICS.Depending on the centre-of-mass energy of the inelastic colli-sion, we consider two processes: photopair and photomeson inter-actions. The photopair interaction is a p 𝛾 collision resulting in theproduction of an electron-positron pairp + 𝛾 → p + e + + e − , also called the Bethe-Heitler process. Alternatively, a p 𝛾 collisioncan result in the production of mesons, similarly to the pp interactiondiscussed above. The photomeson process can be written asp + 𝛾 → p + p + 𝛼𝜋 + 𝛽 (cid:0) 𝜋 + + 𝜋 − (cid:1) . The energy thresholds for photopair and photomeson processesto occur are: 𝐸 𝑝, thres = . × / 𝜖 eV eV for photopair , (17) 𝐸 𝑝, thres = . × / 𝜖 eV eV for photomeson , (18)where 𝜖 eV is the energy of the target photon in eV. The photopairprocess has a lower energy threshold to occur. However, if theenergy threshold for the photomeson process is met, then the energyloss of the proton is more significant compared to the photopairprocess, making the photomeson process dominant (Mannheim &Schlickeiser 1994).Semi-analytical expressions for the distributions of stable sec-ondary particles are provided by Kelner & Aharonian (2008). Sec-ondary particles produced in the above processes can further in-teract within the jet before escaping. In this paper we do not addthe secondary leptons to the primary leptonic population, but rathercalculate their radiative processes and their relative contribution tothe electromagnetic spectrum separately, for comparison. Along with the jet, we include an additional component in the formof a simple spherical corona surrounding the accretion disc. As parameter value description 𝑀 BH ( M (cid:12) ) † 𝜃 incl ◦ viewing angle † 𝐷 ( kpc ) † 𝑁 𝐻 ( cm − ) ℎ = 𝑧 / 𝑅 𝑧 max (cid:0) 𝑟 g (cid:1) maximum jet height ∗ 𝑇 ★ ( 𝐾 ) . × temperature of the companion star † 𝐿 ★ (cid:16) erg s − (cid:17) . × luminosity of the companion star † 𝑎 ★ ( cm ) . × orbital separation distance † (cid:164) 𝑀 ★ (cid:16) M (cid:12) yr − (cid:17) . × − mass loss rate of the companion star ‡ 𝑣 wind (cid:16) cm s − (cid:17) . × velocity of the stellar wind ‡ Table 2.
The fixed parameters of our models. † Miller-Jones et al. (subm), ∗ Tetarenko et al. (2019), ‡ similar to Grinberg et al. (2015). discussed in section 4.2, this is necessary in order to match theX-ray emission of the source.We assume that the electrons in the corona are thermal witha temperature 𝑇 cor , and that the entire corona is described by anoptical depth 𝜏 cor and a radius 𝑅 cor . We define the number densityof the injected electrons as: 𝑛 e , cor = 𝜏 cor / 𝜎 T 𝑅 cor , where 𝜎 T is theThomson cross section. For the emission related to the corona, weonly consider the disc photons as the source of seed photons for ICS,and we calculate the radiation energy density of the seed photonsat the centre of the system. This means that the coronal radius 𝑅 cor effectively acts as a normalisation constant, rather than representingthe exact physical radius of the X-ray emitting region. We perform simultaneous spectral fits of all data presented in Sec-tion 2 using the Interactive Spectral Interpretation System (
ISIS ;Houck & Denicola 2000). We explore the parameter space using aMarkov Chain Monte Carlo (MCMC) method and its implementa-tion via the emcee algorithm. In particular, we initiate 20 walkersper free parameter and perform ∼ loops. The chains require asignificant number of loops before they successfully converge, sowe exclude the 50 per cent of the initial loops. We use the rest ofthe loops to derive the uncertainties of each free parameter (shownin Table 3. The fixed parameters including those of the donor staras assumed by Grinberg et al. (2015) are given in Table 2. The freeparameters we allow to vary during the fitting are shown in Table 3.These are the injected power to the jet base 𝐿 jet , the radius of the jetbase 𝑅 , the location where the particle acceleration initiates 𝑧 diss ,the plasma beta parameter 𝛽 , the parameters for the disc, namely theinnermost radius 𝑅 in , disc and the mass accretion rate in Eddingtonunits ( (cid:164) 𝑚 = (cid:164) 𝑀 c / 𝐿 Edd ), and the parameters of the corona, namelythe temperature 𝑇 cor , the normalisation radius 𝑅 cor and the opticaldepth 𝜏 cor .We present here the results of the best fits of our models.We choose one lepto-hadronic and one purely leptonic model toreproduce the MeV X-rays as jet synchrotron radiation, so as toexplain the high degree of linear polarization (Laurent et al. 2011;Jourdain et al. 2012; Rodriguez et al. 2015; Cangemi et al. 2020). Weachieve this by assuming that the non-thermal electrons acceleratein a hard power-law. We find that an index of 𝑝 = . MNRAS , 1–16 (2020)
D. Kantzas et al. sufficient results. We show two more models for comparison. Onepurely leptonic and one lepto-hadronic, with softer power-laws of 𝑝 = .
2. With such an assumption we fail to reproduce the MeVpolarization as we show below.
The four different models presented here lead to different jet dy-namical quantities, as we show in Table 3. The jet base radius variesbetween 2–27 𝑟 g and the region where the energy dissipates into par-ticle acceleration varies between 15–125 𝑟 g . The two models witha hard injected particle distribution require a small value of plasma 𝛽 compared to the softer models.The best-fitting values for the injected power 𝐿 jet for the modelswith the hard power law ( 𝑝 = . 𝑅 and the plasma 𝛽 , we calculate the strength of themagnetic field along the jet. For all our models, we find relativelyhigh magnetic field strengths at the jet base on the order of 10 G.In Fig. 1 we plot the energy density of various quantities alongthe jet axis for models the two models with 𝑝 = .
7. In particular,our fits are driven towards particle-dominated jets with the energydensity of the protons dominating along the jet. Moreover, the en-ergy density of the magnetic field is higher than the energy densityof the (primary) electrons. We also show the energy density of thesecondary pairs due to photon annihilation. We see that this pro-cess has its peak but still insignificant contribution in jet segmentsof high compactness, i.e. high photon number density at the jetbase and in the particle acceleration region. The number density ofthe target photons drops significantly after the jet base, which sup-presses the pair production. At the particle acceleration region thecompactness increases due to the non-thermal synchrotron and SSCphotons. For the case of the lepto-hadronic model, we also show theenergy density of secondary electrons from pp interactions, eventhough their energy density is more than five orders of magnitudelower than the rest.
The combined data of Cyg X–1 presented in Section 2 result ina broad-band spectrum covering almost 15 orders of magnitude inphoton frequency. We are able to reasonably fit all wavebands si-multaneously with our model. Figures 2 and 3 show all four differentmodel scenarios. The residuals are not always negligible, especiallyfor the X-ray spectrum between 10 and 10 Hz. This is a naturalconsequence of our broad-band fit. The superb data coverage of theX-rays suggests a number of specific spectral features, e.g., due torelativistic reflection off the inner accretion disc, which our over-simplified model for the corona is not able to describe in detail.Such an in-depth treatment of all X-ray features is outside the scopeof this work (see e.g., Tomsick et al. 2013; Duro et al. 2016; Parkeret al. 2015; Basak et al. 2017).We also take into account synchrotron-self absorption in theradio band and photoabsorption of X-ray photons with the columndensity 𝑁 𝐻 = . × cm − (Grinberg et al. 2015). The wind ofthe companion star could in principle attenuate the radio band evenat inferior conjunction (when the companion star is behind the jeton the line of sight) examined here. Nevertheless, the 20 GHz radioemission originates from a region much further out in the jets than10 times the separation of the system so this attenuation should beinsignificant (see e.g., Szostek & Zdziarski 2007). The lepto-hadronic model with 𝑝 = . ∼ . Hz) is dominatedby the 𝛾 -rays produced via neutral pion decay from the hadronic col-lisions. The dominant process at the highest photon energies is thep 𝛾 interaction, between accelerated jet protons and the synchrotronMeV photons. The number density of other target photon fields isnegligible compared to this MeV band in the jet rest frame. The fluxlevels predicted by our model are overall higher than the sensitivitylimits of next-generation 𝛾 -ray telescopes. HAWC, LHAASO, andCTA will therefore be key for breaking further degeneracies withinour model, and constraining important processes such as the p 𝛾 interactions in astrophysical jets.For our discussion of the highest energies, we only consider thehard lepto-hadronic model ( 𝑝 = . 𝑝 = . A key open issue regarding Cyg X–1 is the polarised 0.4–2 MeV taildetected by
INTEGRAL while the source is in the hard state (Laurentet al. 2011; Jourdain et al. 2012; Rodriguez et al. 2015; Cangemiet al. 2020). The above studies all independently conclude that thelinear polarisation degree of the MeV emission is of the order of50–70 per cent. While there is an overall agreement on the degreeof polarisation,
INTEGRAL does not have the spatial resolutionto resolve the source, thus the integrated polarisation angle overthe entire system does not provide constraining information on thedetailed magnetic field geometry of the source.Such high degree of polarisation, requires a structured andwell-ordered magnetic field. High-resolution numerical simulationssuggest that the wind of the accretion disc, which is associated to thecorona, is very turbulent and could not explain such structured mag-netic field (Chatterjee et al. 2019; Liska et al. 2017, 2020). Hence,jet-synchrotron is more likely to explain the MeV polarisation.In this work, we take advantage of the new and unprecedented(in broadband simultaneity) CHOCBOX multi-wavelength data setto revisit the question of leptonic vs. hadronic processes, using amore sophisticated multi-zone approach. In particular we explorethe consequences of taking the MeV polarisation as a ‘hard’ con-straint, and the consequences for potential TeV 𝛾 -ray emission. We MNRAS000
INTEGRAL does not have the spatial resolutionto resolve the source, thus the integrated polarisation angle overthe entire system does not provide constraining information on thedetailed magnetic field geometry of the source.Such high degree of polarisation, requires a structured andwell-ordered magnetic field. High-resolution numerical simulationssuggest that the wind of the accretion disc, which is associated to thecorona, is very turbulent and could not explain such structured mag-netic field (Chatterjee et al. 2019; Liska et al. 2017, 2020). Hence,jet-synchrotron is more likely to explain the MeV polarisation.In this work, we take advantage of the new and unprecedented(in broadband simultaneity) CHOCBOX multi-wavelength data setto revisit the question of leptonic vs. hadronic processes, using amore sophisticated multi-zone approach. In particular we explorethe consequences of taking the MeV polarisation as a ‘hard’ con-straint, and the consequences for potential TeV 𝛾 -ray emission. We MNRAS000 , 1–16 (2020) adronic processes in Cygnus X–1 parameter lepto-hadronic models leptonic models description 𝑝 𝐿 jet (cid:16) − 𝐿 Edd (cid:17)(cid:16) erg s − (cid:17) + − + − . + . − . . + . − . jet base injected power2 . + . − . × . + . − . × . + . − . × . + . − . × 𝑅 (cid:0) 𝑟 g (cid:1) + − + . + . − . . + . − . jet base radius 𝑧 diss (cid:0) 𝑟 g (cid:1) + − + − + − + − particle acceleration region 𝑇 e ( keV ) + − + − + − + − jet base thermal electron temperature 𝛽 . + . − . . + . − . . + . − . . + . − . plasma beta (cid:164) 𝑚 ( − ) . + . − . . + . − . . + . − . . + . − . mass accretion rate 𝑅 in , disc (cid:0) 𝑟 g (cid:1) + − . + . − . . + . − . . + . − . disc innermost radius 𝑇 cor ( keV ) + − + − + − + − corona temperature 𝑅 cor (cid:0) 𝑟 g (cid:1) + − + − + − + − corona normalisation radius 𝜏 cor . + . − . . + . − . . + . − . . + . − . corona optical depth 𝐵 ( G ) . × . × . × . × magnetic field at jet base 𝐵 ( G ) @ 𝑧 diss . × . × . × . × magnetic field at particle acceleration region 𝐿 𝑝 (cid:16) erg s − (cid:17) . × . × - - accelerated proton power 𝐿 𝑒 (cid:16) erg s − (cid:17) . × . × . × . × accelerated electron power 𝐸 𝑝, max ( eV ) . × . × - - proton maximum energy 𝐸 𝑒, max ( eV ) . × . × . × . × (primary) electron maximum energy 𝜒 / 𝐷𝑜𝐹 𝜒 / degrees of freedom Table 3.
The free parameters of the four models discussed in this paper that differ in the power-law index 𝑝 of the accelerated particles. Before the double line,we show the fitted parameters and their uncertainties. Below, we show the evaluated quantities of the magnetic field, the total luminosity of the acceleratedproton/electron population and the maximum energy of the protons/electrons at the particle acceleration region. Figure 1.
Contributions to the total energy density as a function of the distance along the jet for the model with a power-law index 𝑝 = .
7, for the thelepto-hadronic case ( left ) and the purely leptonic case ( right ). The particle acceleration initiates at the vertical dot-dashed grey line. The jump in the protonenergy density on the left plot is due to proton acceleration. We do not assume extraction of energy from other components to accelerate the particles. Theproton and the jet kinetic energy density of the right plot coincide because no proton acceleration is taken into account. We stop to calculate the pair productionafter some distance because it has insignificant contribution. find that the only way to produce sufficient synchrotron flux to fitthe MeV data is by assuming a hard power-law distribution of accel-erated electrons with 𝑝 = .
7. If we assume a soft power-law with 𝑝 = . 𝑝 = .
7) suggests second-order Fermiacceleration (e.g., Rieger et al. 2007) or magnetic reconnection(e.g., Biskamp 1996; Sironi & Spitkovsky 2014; Petropoulou &Sironi 2018 or Khiali et al. 2015 for the case of Cyg X–1 specifi-cally). The softer injection value of 𝑝 = . MNRAS , 1–16 (2020) D. Kantzas et al. pp corona disk starjet SSCjet base ICSjet synchjet base synch total -6 -8 -10 -12 -14 -4 -5 ν F ν ( e r g s − c m − ) E (eV) ν (Hz) χ pp corona disk starjet SSCjet base ICSjet synchjet base synch total -6 -8 -10 -12 -14 -4 -5 ν F ν ( e r g s − c m − ) E (eV) ν (Hz) χ Figure 2.
The best-fit multiwavelength spectrum of Cyg X–1 for the two lepto-hadronic scenarios with 𝑝 = . top ) and 𝑝 = . bottom ) and their 𝜒 residuals. The solid black line shows the total unabsorbed spectrum. The absorbed spectrum that we fitted to the data in detector space is shown as solid red line.We also show some individual unabsorbed model components, i.e. the broad-band radio-to- 𝛾 -ray synchrotron spectrum from primary electrons (thick solidgreen line), the ICS spectrum ranging from eV to GeV (dashed dark blue line), the pp spectral component arising from the neutral pion decay (solid red line),disc photons upscattered in the thermal corona (dotted-dashed purple line), the black-body component emitted by the companion star (double-dotted-dashedorange line), and the multi-temperature thermal spectrum arising from the accretion disk (dotted magenta line). The dotted-dashed light green line shows thesynchrotron radiation from thermal electrons and the triple-dotted-dashed light blue line shows the ICS from regions before the particle acceleration region. Inthe case where 𝑝 = . 𝑝 = .000
The best-fit multiwavelength spectrum of Cyg X–1 for the two lepto-hadronic scenarios with 𝑝 = . top ) and 𝑝 = . bottom ) and their 𝜒 residuals. The solid black line shows the total unabsorbed spectrum. The absorbed spectrum that we fitted to the data in detector space is shown as solid red line.We also show some individual unabsorbed model components, i.e. the broad-band radio-to- 𝛾 -ray synchrotron spectrum from primary electrons (thick solidgreen line), the ICS spectrum ranging from eV to GeV (dashed dark blue line), the pp spectral component arising from the neutral pion decay (solid red line),disc photons upscattered in the thermal corona (dotted-dashed purple line), the black-body component emitted by the companion star (double-dotted-dashedorange line), and the multi-temperature thermal spectrum arising from the accretion disk (dotted magenta line). The dotted-dashed light green line shows thesynchrotron radiation from thermal electrons and the triple-dotted-dashed light blue line shows the ICS from regions before the particle acceleration region. Inthe case where 𝑝 = . 𝑝 = .000 , 1–16 (2020) adronic processes in Cygnus X–1 corona disk starjet SSCjet base ICSjet synchjet base synch total -6 -8 -10 -12 -14 -4 -5 ν F ν ( e r g s − c m − ) E (eV) ν (Hz) χ corona disk starjet SSCjet base ICSjet synchjet base synch total -6 -8 -10 -12 -14 -4 -5 ν F ν ( e r g s − c m − ) E (eV) ν (Hz) χ Figure 3.
Similar to Fig. 2 but for the two leptonic scenarios with 𝑝 = . top ) and 𝑝 = . bottom ).MNRAS , 1–16 (2020) D. Kantzas et al. ν (Hz) − − − ν F ν ( e r g s − c m − ) E (eV)
ICS CTA (North 50h) HAWC (3yr)HAWC (5yr)LHAASO (1yr) p γ pp Figure 4.
The GeV-to-TeV regime of the multiwavelength spectrum of Cyg X–1 for the lepto-hadronic scenario with 𝑝 = .
7. The black line shows the totalspectrum. The ICS (solid dark blue) explains the
Fermi /LAT (purple) data points in the GeV band. The neutral pion decay from p 𝛾 & Drury 2001; Caprioli 2012), but we show that the high degreeof MeV polarisation cannot be attained. We find that the best fitsto the data require a more efficient acceleration mechanism to bethe dominant source of non-thermal particles. We note however thatwhen we define the acceleration timescale to derive the maximumenergy of the particles (see Equations 10 and 9), we use a simplifiedexpression that is commonly used to describe first-order Fermi ac-celeration. In future work, we will include energy dependence to theacceleration timescale to explore in detail the different accelerationmechanisms.Taking as a constraint the explanation of both the observedMeV spectrum and the GeV 𝛾 -rays, we require a generally highparticle acceleration efficiency 𝑓 sc . For the models with a soft par-ticle spectrum, we require a higher efficiency (0.1) as opposed tothe models with the hard particle spectrum, where an accelera-tion efficiency of 0.01 is sufficient. This parameter also drives themaximum achievable energy of the particles. We find a maximumelectron energy of 10–100 GeV (see Table 3) and proton energy of ∼ eV. The high particle energies we find for both electronsand protons translate to a required high total power in particles, i.e. ∼ erg s − for electrons and ∼ erg s − for protons.Independent measurements of the total kinetic jet power areuseful to benchmark our fitted values for the total injected energy.One can estimate the jet power from the bubble-like structure lo- cated 5 pc from Cyg X–1 caused by the apparent interaction betweenthe jet and the ISM. The mechanical power required to inflate suchbubble has been calculated to be of the order of 10 erg s − (Galloet al. 2005). It is, however, still debated whether the jet is solelyevacuating this bubble, or whether other feedback channels, such asthe companion star’s stellar wind, play a role. In that case, the jetpower estimated by Gallo et al. (2005) would have to be consideredas an upper limit (Sell et al. 2014). This estimate would lead tothe exclusion of the lepto-hadronic model because of its exceedingjet power, while the purely leptonic model requires merely 10 per-cent of the estimated power. This large discrepancy (up to 3 orderof magnitude) driven by the inclusion/exclusion of hadronic pro-cesses is a well-known issue in the field (e.g., Bosch-Ramon et al.2008; Zdziarski et al. 2012; Malyshev et al. 2013; Zdziarski et al.2014; Zhang et al. 2014; Pepe et al. 2015; Zdziarski et al. 2017;Beloborodov 2017; Fernández-Barral et al. 2017).Most hadronic models show jet powers close to Eddingtonlimit either for Galactic or extragalactic sources (Böttcher et al.2013; Zdziarski & Böttcher 2015). However, there are a few possi-ble ways of extracting further power from the system to the particleswithout violating other constraints. One possibility is a much moreefficient dissipation of either magnetic or kinetic energy via particleacceleration, i.e. greater than 10 per cent. Another, perhaps morelikely scenario is the one where the jets are launched by a magneti- MNRAS000
Fermi /LAT (purple) data points in the GeV band. The neutral pion decay from p 𝛾 & Drury 2001; Caprioli 2012), but we show that the high degreeof MeV polarisation cannot be attained. We find that the best fitsto the data require a more efficient acceleration mechanism to bethe dominant source of non-thermal particles. We note however thatwhen we define the acceleration timescale to derive the maximumenergy of the particles (see Equations 10 and 9), we use a simplifiedexpression that is commonly used to describe first-order Fermi ac-celeration. In future work, we will include energy dependence to theacceleration timescale to explore in detail the different accelerationmechanisms.Taking as a constraint the explanation of both the observedMeV spectrum and the GeV 𝛾 -rays, we require a generally highparticle acceleration efficiency 𝑓 sc . For the models with a soft par-ticle spectrum, we require a higher efficiency (0.1) as opposed tothe models with the hard particle spectrum, where an accelera-tion efficiency of 0.01 is sufficient. This parameter also drives themaximum achievable energy of the particles. We find a maximumelectron energy of 10–100 GeV (see Table 3) and proton energy of ∼ eV. The high particle energies we find for both electronsand protons translate to a required high total power in particles, i.e. ∼ erg s − for electrons and ∼ erg s − for protons.Independent measurements of the total kinetic jet power areuseful to benchmark our fitted values for the total injected energy.One can estimate the jet power from the bubble-like structure lo- cated 5 pc from Cyg X–1 caused by the apparent interaction betweenthe jet and the ISM. The mechanical power required to inflate suchbubble has been calculated to be of the order of 10 erg s − (Galloet al. 2005). It is, however, still debated whether the jet is solelyevacuating this bubble, or whether other feedback channels, such asthe companion star’s stellar wind, play a role. In that case, the jetpower estimated by Gallo et al. (2005) would have to be consideredas an upper limit (Sell et al. 2014). This estimate would lead tothe exclusion of the lepto-hadronic model because of its exceedingjet power, while the purely leptonic model requires merely 10 per-cent of the estimated power. This large discrepancy (up to 3 orderof magnitude) driven by the inclusion/exclusion of hadronic pro-cesses is a well-known issue in the field (e.g., Bosch-Ramon et al.2008; Zdziarski et al. 2012; Malyshev et al. 2013; Zdziarski et al.2014; Zhang et al. 2014; Pepe et al. 2015; Zdziarski et al. 2017;Beloborodov 2017; Fernández-Barral et al. 2017).Most hadronic models show jet powers close to Eddingtonlimit either for Galactic or extragalactic sources (Böttcher et al.2013; Zdziarski & Böttcher 2015). However, there are a few possi-ble ways of extracting further power from the system to the particleswithout violating other constraints. One possibility is a much moreefficient dissipation of either magnetic or kinetic energy via particleacceleration, i.e. greater than 10 per cent. Another, perhaps morelikely scenario is the one where the jets are launched by a magneti- MNRAS000 , 1–16 (2020) adronic processes in Cygnus X–1 cally dominated (MAD) accretion flow and a spinning black hole. Insuch systems, the jet can benefit from an efficient extraction of powerboth from the accretion disc and the black hole rotation (Blandford& Znajek 1977; Narayan et al. 2003; Tchekhovskoy et al. 2011). Al-ternatively, the total proton power can be reduced. One possibilityis that the jets are predominantly leptonic up to when the bulk flowis accelerated to maximum velocity. The majority of protons arethen mass-loaded further away from the launching point either bythe wind of the accretion disc or of the companion star (Chatterjeeet al. 2019; Perucho 2020). To calculate the total proton power inthis work, we sum the proton power per segment along the jet. If weassume that protons accelerate only within a small part of the jet,then the total power could be significantly reduced (Pepe et al. 2015;Khiali et al. 2015; Abeysekara et al. 2018). Such assumptions wouldhowever only increase the free parameters of our model. Therefore,we decided to restrict ourselves to ’standard’ assumptions for fittingthe data, and to ease comparison with prior approaches. In Table 4 we present a schematic comparison between the mainfeatures of our new model and of a sample of similar works usedto explain the multiwavelength spectrum of Cyg X–1. The modelsthat we consider here are the following: Romero et al. 2014 (R14),Zdziarski et al. 2014 (Z14), Khiali et al. 2015 (K15), Pepe et al.2015 (P15), and Zdziarski et al. 2017 (Z17).It is generally agreed that the radio-to-FIR spectrum of Cyg X–1 is produced by its relativistic jets, and likely the GeV emissionas well. Numerous studies dedicated to fitting high signal-to-noiseX-ray spectra of Cyg X–1 invoke the presence of a corona withhot, thermal electrons to upscatter soft disc photons up to ∼ 𝛾 -rays. Many of the prior works did not consider the MeVpolarisation as a hard constraint. For those that did, R14 suggest thatthe synchrotron radiation from secondary electrons in the coronacould explain the MeV tail. As we discussed above though, jet syn-chrotron is a more likely origin. Z14 explain the MeV flux as a resultof jet synchrotron from primary electrons. They presented only apurely leptonic model and thus no TeV detection can be predicted.This choice thus places them in a regime with reasonable total jetpowers. P15 manage to reproduce the MeV tail in a lepto-hadronicscenario with primary electron synchrotron radiation. This is simi-lar to our lepto-hadronic model with 𝑝 = . 𝛾 𝑝, min =
100 and second, the particle acceleration terminates atsome distance from the jet base. None of these works though at-tempted to fit their free parameters to simultaneous data and performstatistical analysis, which may affect their conclusions.
In Fig. 4 we compare the results of the lepto-hadronic model with 𝑝 = . 𝛾 -rays,as well as the sensitivity of LHAASO (Bai et al. 2019), whichmostly focuses on ∼
100 TeV. In the hadronic model with 𝑝 = . 𝛾 inelastic collisions be-tween accelerated protons and synchrotron photons of the jet. Thepeak is at 20 TeV and the corresponding flux is expected to be2 × − erg cm − s − , significantly above the predicted CTA sen-sitivity for 50 hours of observation from the north site. Moreover,the spectral index of this TeV emission is predicted to be positiveand ∼ . 𝐹 𝜈 ∝ 𝜈 . ).An interesting aspect of our model is that the photomesoninteractions dominate the pp collisions. The energy threshold of ppinelastic collisions, in general, is lower than p 𝛾 . Nevertheless, thenumber density of the target protons from the thermal wind of thecompanion star within the jet is constant up to 𝑧 (cid:39) 𝑎 ★ regardlessof the physics of the jets (see equation 15). On the other hand,the number density of the target photons of p 𝛾 are highly model-dependent. For the hadronic models presented here the dominanttarget photons are the synchrotron photons of each jet segment.Consequently, in the case of the hard particle distribution ( 𝑝 = . 𝛾 processdominates the TeV band.A detection of TeV photons and a measurement of the spec-tral index of this emission by forthcoming very high-energy fa-cilities could therefore give further insights into the accelerationmechanism. Finally, regardless of the spectral shape, the detectionof Cyg X–1 from HAWC, and especially from CTA or LHAASOwould exclude the possibility of purely leptonic jets for this source. In this work, we present a new multi-zone jet model, based onthe initial work of Markoff et al. (2005) and references above.We implement proton acceleration and inelastic hadronic collisions(proton-proton and proton-photon, Kelner et al. 2006; Kelner &Aharonian 2008, respectively). We include the distributions of sec-ondary electrons and 𝛾 − rays produced through pion decay. We fur-ther improve the existing leptonic processes with more sophisticatedpair-production calculations (Coppi & Blandford 1990; Böttcher &Schlickeiser 1997), as well as take into account the proper geome-try of the companion star as seen in the jet rest frame. With suchenhancements, we can make more accurate predictions of the highenergy phenomena related to astrophysical jets, particularly the non-thermal emitted radiation.Along with this new model, we present the first broadband,simultaneous data set obtained by the CHOCBOX campaign forCyg X–1 (Uttley 2017). This data set covers ten orders of mag-nitude in photon energy, from radio wavelengths to MeV X-rays.These bands are most susceptible to faster variability and hence si- MNRAS , 1–16 (2020) D. Kantzas et al. other works this workfeatures \model R14 Z14 K15 P15 Z17 hadronic leptonicpower-law index † . / . . / . . / . . / . (cid:51) (cid:51) (cid:55) (cid:51) (cid:51) (cid:51) (cid:51) hadronic processes (cid:51) (cid:55) (cid:51) (cid:51) (cid:55) (cid:51) (cid:55) simultaneous data (cid:55) (cid:55) (cid:55) (cid:55) (cid:55) (cid:51) (cid:51) statistical modelling / MCMC (cid:55) (cid:55) (cid:55) (cid:55) (cid:55) (cid:51) (cid:51) MeV X-rays origin cor-SYN SYN/COM SYN SYN/COM COM SYN/COM SYN/COMexplain MeV polarisation (cid:51) (cid:51) / (cid:55) (cid:55) (cid:51) / (cid:55) (cid:55) (cid:51) / (cid:55) (cid:51) / (cid:55) CTA @ TeV prediction (cid:55) (cid:55) (cid:51) (cid:51) / (cid:55) (cid:55) (cid:51) (cid:55) LHAASO @ 100 TeV prediction (cid:55) (cid:55) ( (cid:51) ) ( (cid:51) )/ (cid:55) (cid:55) (cid:51) (cid:55) Table 4.
Comparison between our results and previous works on reproducing the (multiwavelength) spectrum of Cyg X–1. When two models are discussedin a specific work, we separate them with a slash. cor-SYN stands for synchrotron radiation from a non-thermal corona, SYN for jet (primary) synchrotronradiation and ( (cid:51) ) stands for a marginal detection. References included are: Romero et al. 2014 (R14), Zdziarski et al. 2014 (Z14), Khiali et al. 2015 (K15),Pepe et al. 2015 (P15) and Zdziarski et al. 2017 (Z17). † accelerated particle power-law index 𝑝 : 𝑁 ( 𝐸 ) ∝ 𝐸 − 𝑝 . multaneous high-quality observations are beneficial to break modeldegeneracies.The keV-to-MeV spectrum of Cyg X–1 exhibits significantevidence of linear polarisation. The keV spectrum shows low degreeof linear polarisation (Chauvin et al. 2018b,b) but the 0.4–2 MeVis highly polarised at a level of 50–70 per cent (Laurent et al.2011; Jourdain et al. 2012; Rodriguez et al. 2015; Cangemi et al.2020). We interpret this high degree of linear polarisation in theMeV band as synchrotron radiation emitted by (primary) electronsaccelerated inside the jets of Cyg X–1 in the presence of a highlyordered magnetic field. Such non-turbulent, dynamically dominantmagnetic fields are most likely associated with astrophysical jets. Toachieve the required MeV synchrotron flux, we must inject a hardpower-law of accelerated electrons with index of 𝑝 = . 𝛾 -ray telescopes of HAWC, LHAASO and CTA. Inter-estingly, we find that the dominant hadronic process is the proton-photon interaction. This scenario however requires near-Eddingtonpower in the accelerated protons, using the most basic assump-tions. We discuss ways around this issue but leave that for futurework, in the case of a TeV detection. Such a detection would be agame-changer for the field of XRBs, and support the possibility thatGalactic CRs originate in more sources than only supernovae. ACKNOWLEDGEMENTS
We would like to thank the reviewer for the very helpful com-ments on improving the original manuscript. DK would like to thank Maria Petropoulou for fruitful discussions, and Ping Zhouand Thomas Russell for useful comments on the manuscript. DK,SM, ML, and AC were supported by the Netherlands Organisa-tion for Scientific Research (NWO) VICI grant (no. 639.043.513).VG is supported through the Margarete von Wrangell fellowshipby the ESF and the Ministry of Science, Research and the ArtsBaden-Württemberg. JCAM-J is the recipient of an AustralianResearch Council Future Fellowship (FT140101082), funded bythe Australian government. This work is based on observationscarried out under the project number W15BQ with the IRAMNOEMA Interferometer. IRAM is supported by INSU/CNRS(France), MPG (Germany) and IGN (Spain). This research madeuse of
ASTROPY
PYTHON package for Astronomy (Astropy Collaboration et al.2013; Price-Whelan et al. 2018),
MATPLOTLIB (Hunter 2007),
NUMPY (Oliphant 2006),
SCIPY
DATA AVAILABILITY
The data underlying this article are available in Zenodo, athttps://dx.doi.org/[doi]
REFERENCES
Abeysekara A., et al., 2013, Astroparticle Physics, 50-52, 26Abeysekara A., et al., 2017, ApJ, 843, 40Abeysekara A., et al., 2018, Nature, 562, 82Abeysekara A., et al., 2019, arXiv preprint arXiv:1909.08609Aharonian F., 2000, New Astronomy, 5, 377Aharonian F., 2002, MNRAS, 332, 215Aharonian F. A., 2004, Very high energy cosmic gamma radiation: a crucialwindow on the extreme Universe. World ScientificAharonian F., Yang R., de Oña Wilhelmi E., 2019, Nature astronomy, 3, 561MNRAS000
Abeysekara A., et al., 2013, Astroparticle Physics, 50-52, 26Abeysekara A., et al., 2017, ApJ, 843, 40Abeysekara A., et al., 2018, Nature, 562, 82Abeysekara A., et al., 2019, arXiv preprint arXiv:1909.08609Aharonian F., 2000, New Astronomy, 5, 377Aharonian F., 2002, MNRAS, 332, 215Aharonian F. A., 2004, Very high energy cosmic gamma radiation: a crucialwindow on the extreme Universe. World ScientificAharonian F., Yang R., de Oña Wilhelmi E., 2019, Nature astronomy, 3, 561MNRAS000 , 1–16 (2020) adronic processes in Cygnus X–1 Ahnen M. L., et al., 2017, MNRAS, 472, 3474Astropy Collaboration et al., 2013, A&A, 558, A33Axford W., 1969, in , Invited Papers. Springer, pp 155–203Bai X., et al., 2019, arXiv preprint arXiv:1905.02773Basak R., Zdziarski A. A., Parker M., Islam N., 2017, MNRAS, 472, 4220Beloborodov A. M., 2017, ApJ, 850, 141Bird D., et al., 1993, Physical Review Letters, 71, 3401Biskamp D., 1996, Astrophysics and Space Science, 242, 165Blandford R., Königl A., 1979, ApJ, 232, 34Blandford R. D., Ostriker J. P., 1978, ApJ, 221, L29Blandford R. D., Znajek R. L., 1977, MNRAS, 179, 433Blumenthal G. R., Gould R. J., 1970, Reviews of Modern Physics, 42, 237Bodaghee A., Tomsick J. A., Pottschmidt K., Rodriguez J., Wilms J., PooleyG. G., 2013, ApJ, 775, 98Bolton C. T., 1972, Nature, 235, 271Bosch-Ramon V., Romero G. E., Paredes J. M., 2006, A&A, 447, 263Bosch-Ramon V., Khangulyan D., Aharonian F., 2008, A&A, 489, L21Böttcher M., Dermer C. D., 2005, ApJ Letters, 634, L81Böttcher M., Schlickeiser R., 1997, arXiv preprint astro-ph/9703069Böttcher M., Reimer A., Sweeney K., Prakash A., 2013, ApJ, 768, 54Brown A., et al., 2018, A&A, 616, A1Cangemi F., et al., 2020, submittedCaprioli D., 2012, JCAP, 07, 038Chatterjee K., Liska M., Tchekhovskoy A., Markoff S. B., 2019, MNRAS,490, 2200Chauvin M., et al., 2018a, Nature Astronomy, 2, 652Chauvin M., et al., 2018b, MNRAS: Letters, 483, L138Cooper A. J., Gaggero D., Markoff S., Zhang S., 2020, MNRAS, 493, 3212Coppi P., Blandford R., 1990, MNRAS, 245, 453Crumley P., Ceccobello C., Connors R. M. T., Cavecchi Y., 2017, A&A,601, A87Crumley P., Caprioli D., Markoff S., Spitkovsky A., 2019, MNRAS, 485,5105Díaz Trigo M., Miller-Jones J. C., Migliari S., Broderick J. W., Tzioumis T.,2013, Nature, 504, 260Drury L. O., 1983, Reports on Progress in Physics, 46, 973Duro R., et al., 2016, A&A, 589, A14Eichmann B., Rachen J., Merten L., van Vliet A., Tjus J. B., 2018, Journalof Cosmology and Astroparticle Physics, 2018, 036Ellison D. C., Jones F. C., Reynolds S. P., 1990, ApJ, 360, 702Fabrika S., 2004, Astrophysics and Space Physics Reviews, 12, 1Falcke H., Biermann P. L., 1995, A&A, 293, 665Fender R. P., Maccarone T. J., van Kesteren Z., 2005, MNRAS, 360, 1085Fender R. P., Stirling A., Spencer R., Brown I., Pooley G., Muxlow T.,Miller-Jones J., 2006, MNRAS, 369, 603Fernández-Barral A., et al., 2017, arXiv preprint arXiv:1709.01725Gaisser T. K., Engel R., Resconi E., 2016, Cosmic rays and particle physics.Cambridge University Press, doi:10.1017/CBO9781139192194, https://cds.cern.ch/record/2126960
Gallo E., Fender R., Kaiser C., Russell D., Morganti R., Oosterloo T., HeinzS., 2005, Nature, 436, 819Giannios D., 2010, MNRAS: Letters, 408Gies D. R., et al., 2008, ApJ, 678, 1237Grinberg et al., 2015, A&A, 576, A117Hada K., et al., 2016, ApJ, 817, 131Harrison F. A., et al., 2013, ApJ, 770, 103Heinz S., Sunyaev R., 2002, A&A, 390, 751Hillas A. M., 1984, Annual review of A&A, 22, 425Hjellming R., Johnston K., 1988, ApJ, 328, 600Hjellming R., Rupen M., 1995, Nature, 375, 464Houck J. C., Denicola L. A., 2000, in Manset N., Veillet C., Crabtree D.,eds, ASP Conf. Ser. Vol. 216, Astronomical Data Analysis Software andSystems IX. Astron. Soc. Pac., San Francisco, p. 591Hunter J. D., 2007, Computing in Science & Engineering, 9, 90Jokipii J., 1987, ApJ, 313, 842Jourdain E., Roques J., Chauvin M., Clark D., 2012, ApJ, 761, 27Kafexhiu E., Aharonian F., Taylor A. M., Vila G. S., 2014, Physical ReviewD, 90, 123014 Kelner S., Aharonian F., 2008, Physical Review D, 78, 034013Kelner S., Aharonian F. A., Bugayov V., 2006, Physical Review D, 74,034018Khiali B., de Gouveia Dal Pino E. d., del Valle M. V., 2015, MNRAS, 449,34Kulikov G., Khristiansen G., 1959, Sov. Phys. JETP, 35, 441Laurent P., Rodriguez J., Wilms J., Cadolle Bel M., Pottschmidt K., GrinbergV., 2011, Science, 332, 438Lebrun F., et al., 2003, A&A, 411, L141Liska M., Hesp C., Tchekhovskoy A., Ingram A., van der Klis M., MarkoffS., 2017, MNRAS: Letters, 474, L81Liska M., Tchekhovskoy A., Quataert E., 2020, MNRAS, 494, 3656Lister M. L., et al., 2013, The Astronomical Journal, 146, 120Liu R.-Y., Rieger F., Aharonian F., 2017, ApJ, 842, 39Lucchini M., Markoff S., Crumley P., Krauß F., Connors R. M. T., 2018,MNRAS, 482, 4798Maitra D., Markoff S., Brocksopp C., Noble M., Nowak M., Wilms J., 2009,MNRAS, 398, 1638Malkov M., Drury L. O., 2001, Reports on Progress in Physics, 64, 429Malyshev D., Zdziarski A. A., Chernyakova M., 2013, MNRAS, 434, 2380Mannheim K., Schlickeiser R., 1994, A&A, 286, 983Markoff S., Falcke H., Fender R., 2001, A&A, 372, L25Markoff S., Nowak M. A., Wilms J., 2005, ApJ, 635, 1203Marscher A. P., et al., 2008, Nature, 452, 966Mastichiadis A., Kirk J. G., 2002, Publications of the Astronomical Societyof Australia, 19, 138Mastroserio G., Ingram A., van der Klis M., 2019, MNRAS, 488, 348McMullin J. P., Waters B., Schiebel D., Young W., Golap K., 2007, inShaw R. A., Hill F., Bell D. J., eds, Astronomical Society of the PacificConference Series Vol. 376, Astronomical Data Analysis Software andSystems XVI. p. 127Miller J. M., Wojdowski P., Schulz N., Marshall H., Fabian A., RemillardR., Wijnands R., Lewin W., 2005, ApJ, 620, 398Mioduszewski A. J., Rupen M. P., Hjellming R. M., Pooley G. G., WaltmanE. B., 2001, ApJ, 553, 766Mirabel I., Rodriguez L., 1994, Nature, 371, 46Mücke A., Protheroe R., Engel R., Rachen J., Stanev T., 2003, AstroparticlePhysics, 18, 593Narayan R., Igumenshchev I. V., Abramowicz M. A., 2003, Publications ofthe Astronomical Society of Japan, 55, L69Oliphant T. E., 2006, A guide to NumPy. Vol. 1, Trelgol Publishing USAOrosz J. A., McClintock J. E., Aufdenberg J. P., Remillard R. A., Reid M. J.,Narayan R., Gou L., 2011, ApJ, 742, 84Parker M. L., et al., 2015, ApJ, 808, 9Pepe C., Vila G. S., Romero G. E., 2015, A&A, 584, A95Perucho M., 2020, MNRAS, 494, L22Petropoulou M., Sironi L., 2018, MNRAS, 481, 5687Price-Whelan A. M., et al., 2018, AJ, 156, 123Rahoui F., Lee J. C., Heinz S., Hines D. C., Pottschmidt K., Wilms J.,Grinberg V., 2011, ApJ, 736, 63Reid M. J., McClintock J. E., Narayan R., Gou L., Remillard R. A., OroszJ. A., 2011, ApJ, 742, 83Rieger F. M., Duffy P., 2004, ApJ, 617, 155Rieger F. M., Bosch-Ramon V., Duffy P., 2007, in Paredes J. M., ReimerO., Torres D. F., eds, The Multi-Messenger Approach to High-EnergyGamma-Ray Sources. Springer Netherlands, Dordrecht, pp 119–125Rodriguez J., et al., 2015, ApJ, 807, 17Romero Vieyro, F. L. Chaty, S. 2014, A&A, 562, L7Romero G. E., Boettcher M., Markoff S., Tavecchio F., 2017, Space ScienceReviews, 207, 5Rushton A., et al., 2012, MNRAS, 419, 3194Rushton A. P., et al., 2017, MNRAS, 468, 2788Russell T. D., et al., 2019, ApJ, 883, 198Rybicki G. B., Lightman A. P., 2008, Radiative processes in astrophysics.John Wiley & Sons, doi:10.1002/9783527618170Sell P. H., et al., 2014, MNRAS, 446, 3579Sironi L., Spitkovsky A., 2009, ApJ, 698, 1523Sironi L., Spitkovsky A., 2014, ApJ, 783, L21MNRAS , 1–16 (2020) D. Kantzas et al.
Sironi L., Petropoulou M., Giannios D., 2015, MNRAS, 450, 183Spruit H., Daigne F., Drenkhahn G., 2001, A&A, 369, 694Stirling A. M., Spencer R., De La Force C., Garrett M., Fender R. P., OgleyR. N., 2001, MNRAS, 327, 1273Strüder L., et al., 2001, A&A, 365, L18Szostek A., Zdziarski A. A., 2007, MNRAS, 375, 793Tavani M., et al., 2009, Nature, 462, 620Tavecchio F., Maraschi L., Ghisellini G., 1998, ApJ, 509, 608Tchekhovskoy A., Narayan R., McKinney J. C., 2011, MNRAS: Letters,418, L79Tetarenko A., Casella P., Miller-Jones J., Sivakoff G., Tetarenko B., Mac-carone T., Gandhi P., Eikenberry S., 2019, MNRAS, 484, 2987Tomsick J. A., et al., 2013, ApJ, 780, 78Uttley P., 2017, in Ness J.-U., Migliari S., eds, The X-ray Universe 2017.p. 230Virtanen P., et al., 2020, Nature Methods, 17, 261Waggett P., Warner P., Baldwin J., 1977, MNRAS, 181, 465Walter R., Xu M., 2017, A&A, 603, A8Webster B. L., Murdin P., 1972, Nature, 235, 37Wik D. R., et al., 2014, ApJ, 792, 48Zanin R., Fernández-Barral A., de Oña Wilhelmi E., Aharonian F., BlanchO., Bosch-Ramon V., Galindo D., 2016, A&A, 596, A55Zdziarski A. A., Böttcher M., 2015, MNRAS: Letters, 450, L21Zdziarski A. A., Lubiński P., Sikora M., 2012, MNRAS, 423, 663Zdziarski A. A., Pjanka P., Sikora M., Stawarz Ł., 2014, MNRAS, 442, 3243Zdziarski A. A., Malyshev D., Chernyakova M., Pooley G. G., 2017, MN-RAS, 471, 3657Zhang J., Xu B., Lu J., 2014, ApJ, 788, 143Ziółkowski J., 2014, MNRAS, 440, L61This paper has been typeset from a TEX/L A TEX file prepared by the author. MNRAS000