New high-frequency radio observations of the Cygnus Loop supernova remnant with the Italian radio telescopes
S. Loru, A. Pellizzoni, E. Egron, A. Ingallinera, G. Morlino, S. Celli, G. Umana, C. Trigilio, P. Leto, M.N. Iacolina, S. Righini, P. Reich, S. Mulas, M. Marongiu, M. Pilia, A. Melis, R. Concu, M. Bufano, C. Buemi, F. Cavallaro, S. Riggi, F. Schillirò
MMNRAS , 1–19 () Preprint 22 September 2020 Compiled using MNRAS L A TEX style file v3.0
New high-frequency radio observations of the Cygnus Loopsupernova remnant with the Italian radio telescopes
S. Loru (cid:63) , A. Pellizzoni , E. Egron , A. Ingallinera , G. Morlino , S. Celli , ,G. Umana , C. Trigilio , P. Leto , M.N. Iacolina , S. Righini , P. Reich , S. Mulas ,M. Marongiu , M. Pilia , A. Melis , R. Concu , M. Bufano , C. Buemi ,F. Cavallaro , S. Riggi , F. Schillirò INAF, Osservatorio Astrofisico di Catania, Via Santa Sofia 78, 95123 Catania, IT INAF, Osservatorio Astronomico di Cagliari, Via della Scienza 5, 09047 Selargius, Italy INAF, Osservatorio Astrofisico di Arcetri, L.go E. Fermi 5, I-50125 Firenze, Italy Dipartimento di Fisica dell’Università La Sapienza, P.le Aldo Moro 2, 00185 Roma, Italy INFN - Sezione di Roma, P.le Aldo Moro 2, 00185 Roma, Italy ASI, Osservatorio Astronomico di Cagliari, Via della Scienza 5, 09047 Selargius, Italy INAF, Istituto di Radio Astronomia di Bologna, Via P. Gobetti 101, 40129 Bologna, Italy Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany Dipartimento di Fisica, Università degli Studi di Cagliari, SP Monserrato-Sestu, KM 0.7, 09042 Monserrato, Italy
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
Supernova remnants (SNRs) represent a powerful laboratory to study the Cosmic-Ray acceler-ation processes at the shocks, and their relation to the properties of the circumstellar medium.With the aim of studying the high-frequency radio emission and investigating the energy dis-tribution of accelerated electrons and the magnetic field conditions, we performed single-dishobservations of the large and complex Cygnus Loop SNR from 7.0 to 24.8 GHz with theMedicina and the Sardinia Radio Telescope, focusing on the northern filament (NGC 6992)and the southern shell. Both regions show a spectrum well fitted by a power-law function( S ∝ ν − α ), with spectral index α = . ± . for NGC 6992 and α = . ± . for thesouthern shell and without any indication of a spectral break. The spectra are significantlyflatter than the whole Cygnus Loop spectrum ( α = . ± . ), suggesting a departure fromthe plain shock acceleration mechanisms, which for NGC6992 could be related to the ongo-ing transition towards a radiative shock. We model the integrated spectrum of the whole SNRconsidering the evolution of the maximum energy and magnetic field amplification. Throughthe radio spectral parameters, we infer a magnetic field at the shock of 10 µ G. This value iscompatible with a pure adiabatic compression of the interstellar magnetic field, suggestingthat the amplification process is currently inefficient.
Key words:
ISM: supernova remnants – ISM: individual object: Cygnus Loop – radio con-tinuum: ISM
The Cygnus Loop is a bright SNR that was discovered by WilliamHerschel in 1784. It has an integrated radio flux density of ∼
210 Jy at and an apparent size of ∼ ◦ × ◦ . From the Hubble SpaceTelescope data, the distance of this SNR was estimated by Blairet al. (2005) as
540 pc . More recent studies, which were based onthe distance of two stars located within the remnant, establishedthe distance to the Cygnus Loop’s centre at ∼
735 pc (Fesen et al. (cid:63)
E-mail: [email protected] ∼ − × yr on the basis of X-ray (Hester & Cox 1986, Levenson et al. 1998)and optical measurements (Fesen et al. 2018). Due to its large size,its location well out of the Galactic plane, and its high brightness,the Cygnus Loop is well suited for observations across the entireelectromagnetic spectrum. Furthermore, this SNR presents a com-plex morphology, which deviates largely from its classification oftypical middle-aged shell-type SNR (Aschenbach & Leahy 1999,Leahy et al. 1997, Uyanıker et al. 2004).In the radio band, the Cygnus Loop exhibits a large north-ern circular shell, which is composed of two bright partial shells © The Authors a r X i v : . [ a s t r o - ph . H E ] S e p S. Loru et al. and a central filament, and a bubble-like shell located in the south-ern part. The nature of this very peculiar morphology is still de-bated (Uyanıker et al. 2002). Leahy et al. (1997) derived a stronglydifferent polarisation fraction between the bright northeastern fila-ment (NGC 6992, ∼ . per cent) and the southern shell ( ∼ percent). By exploiting also the comparison with X-ray images, theyattributed the depolarisation of NGC 6992 to high-density, thermalelectrons. Spatially-resolved spectral index studies performed byLeahy & Roger (1998) revealed a flatter spectrum of the north-eastern rim with respect to other Cygnus Loop features. In thesame study, the authors highlighted a spectral curvature: a steep-ening to high frequencies in the bright filaments and a flattening inthe diffuse emission regions. More recent radio studies attributedthe region-dependent variations of spectral indices and polarisa-tion properties between the two main shells of the Cygnus Loopto their nature as two interacting SNRs (Uyanıker et al. 2002). Inparticular, radio spectral index changes and intrinsic variations inthe magnetic field configuration were observed between NGC 6992and the southern shell, suggesting the action of different accelera-tion mechanisms (Uyanıker et al. 2002). Furthermore, the X-rayand infrared emission are strong in NGC 6992, while they are veryfaint or completely absent in the southern shell. Also the H α andO III optical lines appear brighter and more extended in the north-ern filament than in the southern shell, indicating different envi-ronmental conditions (Uyanıker et al. 2002). On the other hand,X-ray observations do not support the two SNRs scenario (Katsudaet al. 2011, Leahy & Hassan 2013), highlighting how the X-rayemission shows a smoothly-gradual change between the northernand the southern shell, which was interpreted as the evidence ofan asymmetry in the whole Cygnus Loop structure (Aschenbach& Leahy 1999). Furthermore, in a recent multi-wavelength investi-gation, Fesen et al. (2018) conclude that there is no morphologicalevidence for two separated SNRs in the Cygnus Loop. In particular,they rely on the lack of X-ray emission at the putative interactinginterface region between the two shells, and on the morphologicalconnection between the main optical filaments of the southern shelland those of the northern part. All these characteristics make thephysical interpretation of the two regions quite controversial. Thischallenging morphology makes the Cygnus Loop an ideal labora-tory to study SNR shock conditions arising from different interact-ing structures in the interstellar medium (ISM; Hester et al. 1994,Leahy 2002, Leahy 2004). Indeed, the investigation of the corre-lation between flux density and spectral radio slope in the specificSNR macro-regions is useful to reach a complete understanding ofcomplex objects like SNRs. This allows us to disentangle possiblemagnetic enhancement processes from spectral variation due to theenergy distribution of the synchrotron emitting particles or to otheremission mechanisms that could become significant at high radiofrequencies.Although the Cygnus Loop represents an interesting scientificcase, high-resolution radio flux density measurements are availableonly up to ∼ , because of the technical difficulties in per-forming radio continuum observations of such a large source. Sunet al. (2006) derived an integrated spectral index of . ± . be-tween 0.408 and . , and ruled out any possible global spec-tral steepening within this frequency range. However, a steepeningin the integrated spectrum, like the one observed for the similarSNR S 147 (Fürst & Reich 1986), could be expected. Spatially-resolved spectral index studies revealed, for both the SNRs, theexistence of a spectral variation between filamentary and diffusestructures, which was ascribed to the compression of the Galacticmagnetic field across the filaments. In the case of S 147, the break observed in the integrated spectrum around 1 GHz was interpretedas a consequence of the spatial differences in the compressed mag-netic field (Uyanıker et al. 2004). It is therefore of interest to firmlyestablish whether there is a spectral break for the Cygnus Loopto better constrain the particle maximum energy and the magneticfield, and compare them with those of SNRs of the same age class.Sensitive maps above ∼ could be crucial in investigate thisaspect. On the basis of this scientific interest, we performed single-dish observations of the Cygnus Loop in order to obtain sensitiveimages of this SNR up to high-radio frequencies.Here, we present the observations performed on the wholeCygnus Loop with the Medicina radio telescope at 8.5 GHz, pro-viding the highest-frequency map of this SNR ever obtained witha single-dish radio telescope. We use the Cygnus Loop radio dataavailable in the literature, including our measurement at 8.5 GHz,and the γ -ray data presented in Katagiri et al. (2011) to model theemission spectrum of the particles accelerated in this SNR. Indeed,the combined study of radio and γ -ray spectra allows us to inves-tigate the cosmic-ray (CR) acceleration mechanisms, taking intoaccount both of the leptonic and the hadronic contributions. Weadopt the model developed by Celli et al. (2019) and Morlino &Celli (2020) to constrain the maximum energy of the particles ac-celerated at the remnant shock and the evolution of magnetic fieldstrength. We also present the observations carried out at 7.0, 18.7and 24.8 GHz with the Sardinia Radio Telescope (SRT) of twoselected regions of the Cygnus Loop: the northern-bright filamentand the southern shell. Our observations allow us to investigate theenergetics of the accelerated particles and on the possible emissionmechanisms that might compete with the synchrotron emission toproduce the radio continuum emission at these frequencies.In Sect. 2, we describe the observations carried out with theMedicina and SRT telescopes and the main steps of the data reduc-tion and analysis. The results in terms of final calibrated images andflux density measurements are presented in Sect. 3. In Sect. 4, wediscuss the spectral analysis performed on the whole Cygnus Loop.Sect. 5 is dedicated to the spectral analysis of the regions NGC6992 and the southern shell. In Sect. 6, we describe the model usedto investigate the Cygnus Loop’s non-thermal emission and relatedresults. We summarise our conclusions in Sect. 7. We observed the Cygnus Loop with the 32-m Medicina radio tele-scope between June and August 2017 . The observations were per-formed at the central frequency of 8.5 GHz ( X -band) using thetotal-power continuum backend. The bandwidth was 680 MHz dur-ing the observing sessions of June, but it was subsequently reducedto 250 MHz due to the observed radio frequency interference (RFI).The observations are summarised in Table 1.The ‘On-the-fly’ (OTF) observing technique was used to mapa ◦ × ◦ area along RA-Dec scan directions. The map size waschosen to be twice the source extension, to properly identify andsubtract the background baseline component. We set the scanningvelocity to 4 arcmin sec − and sampling interval to 20 ms. Twoconsecutive scans were separated by an interleave of 4.8 arcmin, Program code Medicina 14-17, PI: S.Loru. MNRAS , 1–19 () ew radio observations of the Cygnus Loop Table 1.
Summary of the observations of the Cygnus Loop carried out with the Medicina radio telescope and SRT. ‘N.maps’, ‘Obs. time’, ‘Freq.’, ‘BW’,‘HPBW’ and ‘Map size’ indicate the number of maps, the total observation time (including overheads), the central frequency, the bandwidth, the half powerbeam width and the size of the maps in RA and Dec directions, respectively. A single map is intended as a complete scan (RA or Dec) on the source.Radio Observing Target N.maps Obs. time Freq. BW HPBW Map size Map sizetelescope date (h) (GHz) (MHz) (arcmin) (RA) ( ◦ , ◦ ) (Dec) ( ◦ , ◦ )Medicina 2017 June Cygnus Loop 16 25.6 8.5 680 4.77 5 × × × × × × × × × × × × Table 2.
Flux densities of the calibrators at the Medicina and SRT observ-ing frequencies obtained by interpolating the values proposed by Perley &Butler (2013).Calibrator 7.0 GHz 8.5 GHz 18.7 GHz 24.8 GHz3C286 5.8 Jy 5.0 Jy 2.9 Jy 2.3 Jy3C295 4.2 Jy 3.3 Jy 1.2 Jy 0.8 Jy3C147 5.4 Jy 4.4 Jy 2.1 Jy 1.6 Jy3C48 3.8 Jy 3.1 Jy 1.5 Jy 1.1 Jy3C123 11.2 Jy 9.2 Jy 4.0 Jy 2.9 JyNGC 7027 5.6 Jy 5.8 Jy 5.5 Jy 5.4 Jy which implies one passage per beam size at that observing fre-quency. We chose this parameter to minimise the long time nec-essary to complete a map on such a wide source, and to rely onsystem and weather stability during the observation. On the otherhand, oversampling with respect to the beam size is required to per-form a direct evaluation of statistical errors, and to properly rejectthe corrupted data affected by RFI. This leads to the achievement ofimproved accuracy in the final images, as demonstrated by our pre-vious experience in single-dish imaging of Galactic sources (Egronet al. 2016, Egron et al. 2017, Loru et al. 2019). For this reason, weperformed four complete maps for each observing session, whichallowed us to acquire ∼
240 samples per beam once merged. Theoffset between the four maps acquired in each observing session isof . arcmin and assures a proper Nyquist sampling. The afore-mentioned parameters implied a total duration of a target observa-tion (meant as a RA+Dec map) of about 3.2 hours, including slewand dead time. We observed the point-like flux density calibrators(3C286, 3C295, 3C147, 3C48, 3C123 and NGC 7027) through re-peated cross-scans at the beginning and at the end of each observingsession. The observations were carried out in the framework of our SRTobserving program of the 2018B semester, which was focused onthe high-frequency investigation of a wider sample of middle-aged Program code SRT 22-18, PI: A.Pellizzoni. and young SNRs and the precise modelling of the region-dependentcontinuum spectral indices. SRT observations of the Cygnus Loopwere carried out between December 2018 and October 2019 at thecentral frequencies of 7.0 GHz ( C -band), 18.7 GHz and 24.8 GHz( K -band). The data were recorded by using the spectro-polarimetricbackend SARDARA (SArdinia Roach2-based Digital Architecturefor Radio Astronomy, Melis et al. 2018) in full-Stokes mode with1024 spectral channels and the maximum bandwidth available (1.4GHz both for C - and K -band), which maximises the signal-to-noiseratio and increases the spectral coverage. A summary of the observ-ing sessions and parameters with SRT are given in Table 1. We ob-served the target at elevations > ◦ to avoid significantly pointingerrors and beam shape instability effects.The SRT K -band receiver is characterised by a seven-feed sys-tem. The receiver was used in the Best Space Coverage configura-tion (Bolli et al. 2015) that automatically rotates the dewar to op-timally cover the scanned area (scan spacing ∼ (cid:38) − and 20 ms, respectively. Two consec-utive 7.0-GHz scans were separated by an interleave of 0.6 arcmin,which implies four passages per beam size, and about 27 sam-ples beam − scan − were recorded. The same offset was adoptedfor the observations at 18.7 and 24.8 GHz, implying in this caseone passage per beam for each feed of the receiver. We madethis choice in order to minimise the observing time, considering MNRAS000
240 samples per beam once merged. Theoffset between the four maps acquired in each observing session isof . arcmin and assures a proper Nyquist sampling. The afore-mentioned parameters implied a total duration of a target observa-tion (meant as a RA+Dec map) of about 3.2 hours, including slewand dead time. We observed the point-like flux density calibrators(3C286, 3C295, 3C147, 3C48, 3C123 and NGC 7027) through re-peated cross-scans at the beginning and at the end of each observingsession. The observations were carried out in the framework of our SRTobserving program of the 2018B semester, which was focused onthe high-frequency investigation of a wider sample of middle-aged Program code SRT 22-18, PI: A.Pellizzoni. and young SNRs and the precise modelling of the region-dependentcontinuum spectral indices. SRT observations of the Cygnus Loopwere carried out between December 2018 and October 2019 at thecentral frequencies of 7.0 GHz ( C -band), 18.7 GHz and 24.8 GHz( K -band). The data were recorded by using the spectro-polarimetricbackend SARDARA (SArdinia Roach2-based Digital Architecturefor Radio Astronomy, Melis et al. 2018) in full-Stokes mode with1024 spectral channels and the maximum bandwidth available (1.4GHz both for C - and K -band), which maximises the signal-to-noiseratio and increases the spectral coverage. A summary of the observ-ing sessions and parameters with SRT are given in Table 1. We ob-served the target at elevations > ◦ to avoid significantly pointingerrors and beam shape instability effects.The SRT K -band receiver is characterised by a seven-feed sys-tem. The receiver was used in the Best Space Coverage configura-tion (Bolli et al. 2015) that automatically rotates the dewar to op-timally cover the scanned area (scan spacing ∼ (cid:38) − and 20 ms, respectively. Two consec-utive 7.0-GHz scans were separated by an interleave of 0.6 arcmin,which implies four passages per beam size, and about 27 sam-ples beam − scan − were recorded. The same offset was adoptedfor the observations at 18.7 and 24.8 GHz, implying in this caseone passage per beam for each feed of the receiver. We madethis choice in order to minimise the observing time, considering MNRAS000 , 1–19 ()
S. Loru et al. that fast mapping mitigates the effects of time-based atmosphericopacity variations on the image quality, which especially affect thehigh-frequency observations (Navarrini et al. 2016). On the otherhand, the seven-feed K -band receiver configuration significantly in-creased the amount of data acquired for each map, and allowed usto obtain about
140 sample beam − (if we consider the proper op-eration/contribution of all 7 feeds), a proper Nyquist sampling andan exposure time of . − for a full RA or Dec map. The K -band observations were performed on NGC 6992 at the two cen-tral frequencies of 18.7 and 24.8 GHz, while the southern shell wasobserved only at 24.8 GHz due to the strong RFI found at the lower K -band frequency after December 2018. Despite SRT observationswere performed in ‘shared-risk mode’ (for which observations un-der optimal weather conditions are not guaranteed), all the data pre-sented here were acquired in the recommended opacity conditions( τ <0.1 neper), which are necessary to guarantee the good qualityof the K -band observations. We performed the data reduction with the SRT Single-Dish Imager(SDI) software, written in IDL and suitable for all Medicina andSRT receivers/backends (Prandoni et al. 2017, Egron et al. 2016,Marongiu et al. 2020). This tool provides an automatic pipeline(quicklook analysis) and interactive tools for data inspection, base-line removal, RFI rejection and image calibration (standard analy-sis). At the end of these procedures, SDI produces standard FITSimages. All final images were produced in units of mJy beam − ,and using the cubehelix colour scheme (Green 2011).In the case of the Medicina observations, which were carriedout with the total-intensity backend, we adopted the standard datareduction procedure as described in detail in Egron et al. (2017).We performed cross-scan observations on the calibrators and usedthe flux density measurements and the polynomial expressions pro-posed by Perley & Butler (2013) to reconstruct/extrapolate theirflux density at the observed frequency (see Table 2). In order toguarantee the consistency between calibrators and target in termsof the gain stability and observing condition, we chose the calibra-tion factors by requiring that: i) they have same backend attenu-ation parameters; ii) their observations are performed within 12 h(or less in case of changing weather) from each target scan epoch.We noted the presence of persistent RFI that affected the 8.5-GHzband. The decision to reduce the bandwidth from 680 MHz to 250MHz allowed us to mitigate the problem. The data related to theleft polarisation channel were found to be strongly noisy, and wediscarded them in order to avoid their negative impact on the finalimage quality.The SRT observations at 7.0 and 18.7-24.8 GHz used thespectral-polarimetric backend SARDARA. This allowed us to com-plement the ‘spatial’ RFI rejection procedure (as described inEgron et al. 2017) with a ‘spectral’ RFI rejection. A specific SDIroutine is dedicated to the automated search for outliers in eachscan-sample’s spectrum, which are dynamically identified as RFIand rejected. After this procedure, the data are averaged into a sin-gle continuum channel, and they can be processed with the samedata reduction procedure described for the total-intensity Medicinadata. Despite the two different RFI removal processes, the not al-ways ideal weather conditions introduced a background noise con-tribution that could not be deleted in the data reduction phase, es-pecially in the case of a weak target signal. We have accounted forthese effects with the background subtraction procedure describedin Sect. 3. D e c ( J ) NGC 6992 southern shell
Figure 1.
Representation of the regions of the Cygnus Loop (NGC 6992and southern shell) that we observed with SRT at 7.0, 18.7 and 24.8 GHz.The blue and orange boxes indicate the maps in RA and Dec directions,respectively. The grey contours mark the continuum emission detected withMedicina at 8.5 GHz, which correspond to the intensity levels of , and mJy beam − . The multi-feed data at 18.7 and 24.8 GHz were calibrated con-sidering each feed characterised by a specific efficiency (Orfei et al.2010; Loru et al. 2019). For this purpose, we used calibrator mapsof each SRT observing session in order to calculate the ratios be-tween the expected flux of the calibrator and the peak counts relatedto each feed. We then applied these scaling factors to the relatedsingle feed maps of the target.The uncertainties associated with our flux density measure-ments include the statistical errors and the errors related to the cal-ibration procedure, which are added in quadrature. We calculatedthe first term as the product of the standard deviation associatedwith the region used to estimate the background contribution andthe square root of the number of beam solid angles that are con-tained in the extraction area of the target. The calibration errorswere estimated as the standard deviation on the calibration factors.These are strongly related to the gain stability of the receiver andthe observing conditions that characterised each session. We calcu-lated a calibration error of 4 per cent for the 7.0-GHz data, 6 percent for the data at 18.7 GHz and of 14 per cent for those at 24.8GHz.
The map of the whole Cygnus Loop SNR at 8.5 GHz is shownin Fig. 2. It was obtained by merging and averaging all the mapsof the Medicina observing sessions reported in Table 1. This is thehighest-frequency map of the entire Cygnus Loop SNR obtained sofar with a single-dish telescope. The Cygnus Loop results well de-tected, and we can distinguish the two prominent shells (NGC 6960and NGC 6992) and the central filament, which constitutes the
MNRAS , 1–19 () ew radio observations of the Cygnus Loop D e c ( J ) southern shellNGC 6992 central filamentNGC 6960 m J y / b e a m Figure 2.
Map of the Cygnus Loop SNR obtained with the Medicina radiotelescope at 8.5 GHz. The image was produced with pixel size of 2.4 ar-cmin (about 1/2 of the HPBW), to which we applied a gaussian smoothresulting in a final map resolution of 5.34 arcmin. The smoothed beam sizeis indicated by the blue circle on the bottom-left corner. The white contourshighlight the major features towards the Cygnus Loop, corresponding to theintensity levels of , and mJy beam − . northern remnant, as well as the southern remnant. These regionsare highlighted by white contours in Fig. 2.Our data analysis procedure ensures a zero-mean flux associ-ated with the regions devoid of unrelated source contamination. De-spite this, we carefully chose the target extraction region in order todiscard possible contributions from near-unrelated sources and RFIfeatures affecting the image. We considered a polygonal region en-compassing the SNR emission in order to carry out the integratedflux density measurement. We obtained a continuum flux densityof 54 ±
24 mJy beam − (calculated in amap area free from source contribution and RFI contamination).We also exploited our 8.5-GHz map to derive the flux densities re-lated to the two region of interest. We calculated a flux density of7.5 ± ± left ) reveals theclumpy emission of the southern part of the filament, probably as-cribed to the interaction of the shock wave with smaller discreteclouds (Fesen et al. 2018). The coincident indented structures ob-served in the X-ray maps are indicative of a blast wave significantlyhampered by dense clumps of gas, which are photoionized by theshock precursor (Levenson et al. 1998). The northern part is insteadmore uniform and bright, resulting from the interaction between theremnant and a more extended cloud (Levenson et al. 1999). TheNGC 6992 radio emission is significantly weaker at the higher fre-quencies. Due to the smaller beam size, in both 18.7- and 24.8-GHzimages (Fig. 3, middle and right ) the filamentary structure appearsthinner, and the highly noisy background makes it difficult to dis-tinguish the morphological features. We overlaid 7.0-GHz contoursto the 24.8-GHz map (Fig. 3, right ) to make the visual identificationof the source easier, and distinguish it from the strong and unrelatednoise and RFI contribution.Despite this, the northern filament is detected at 7.0, 18.7 and24.8 GHz, but the attenuation of the astronomical signal, due tosky conditions (humidity level) not always ideal, and the weaken-ing of the SNR emission with increasing frequency, make the pre-cise baseline subtraction difficult. This implies that the baseline-subtracted pixels in the regions free from source contaminationhave non-zero mean flux density. In this case, we applied the back-ground subtraction to obtain correct flux density measurements. Inorder to estimate the background contribution, we considered theflux density of a region surrounding the filament, excluding theother regions of the Cygnus Loop, and multiplied it by the ratiobetween the extraction area of the source and the background area.We calculated the flux density of NGC 6992 at 7.0, 18.7 and 24.8GHz by considering the same extraction region used for the 8.5-GHz map. In this way, we estimated a flux density of 8.7 ± ± ± left ) re-vealed a non-uniform structure. We detected three bright regions:the western boundary and the two emission knots in the easternside. The SNR shock appears discontinuous between these regions.The eastern feature is most likely attributed to a fully radiativeshock (Levenson et al. 1999). The structure is difficult to be detectin the 24.8-GHz image, because of its lower signal-to-noise ratio. Itis indicated by the white contours in Fig. 4 ( right ). We point out thatthe southern shell region includes the shell-like structure, clearlyvisible in the radio band, and the north-western structure observedboth in radio and X-ray emission (Aschenbach & Leahy 1999).We calculated the 24.8-GHz flux density of the southern shell byconsidering the same extraction region adopted for the maps at 7.0and 8.5 GHz. In the same way as described above for NGC 6992,we estimated the background contribution, obtaining a flux densitymeasurement of 18.2 ± ± Several compact radio sources were detected within the boundaryof the Cygnus Loop or in its immediate vicinity (Keen et al. 1973,Green 2019). In the images at 7.0, 18.7 and 24.8 GHz, we detectfour point sources located in close proximity to the remnant. Thesesources are, instead, confused within the Cygnus Loop emission onthe 8.5-GHz map due to its lower resolution. When possible (de-pending on the variability of the source), we exploited the literature
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S. Loru et al. D e c ( J ) A B m J y / b e a m D e c ( J ) A B m J y / b e a m D e c ( J ) A B m J y / b e a m Figure 3.
Maps of of the bright filament NGC 6992 obtained with SRT at 7.0 GHz ( left ), 18.7 GHz ( middle ) and 24.8 GHz ( right ). The maps were producedwith a beam size of 2.71, 0.99 and 0.75 arcmin, and a pixel size of 1.0, 0.45 and 0.35 arcmin at 7.0, 18.7 and 24.8 GHz, respectively. We applied a gaussiansmooth resulting in a final map resolution of 2.89 arcmin at 7.0 GHz, 1.67 arcmin at 18.7 GHz and 1.29 arcmin at 24.8 GHz. The smoothed beam is indicatedby the blue circle on the bottom-left corner. The dashed circles indicate the point sources NVSS J205800+314231 (A) and NVSS J205458+312614 (B),respectively. The white contours in the 24.8-GHz image correspond to the 7.0-GHz intensity levels of 36 mJy beam − , 72 mJy beam − and 108 mJy beam − . D e c ( J ) DC m J y / b e a m D e c ( J ) DC m J y / b e a m Figure 4.
Maps of of the southern shell obtained with SRT at 7.0 GHz ( left ) and 24.8 GHz ( right ). The maps were produced with a beam size of 2.71 and0.75 arcmin, and a pixel size of 1.0 and 0.35 arcmin at 7.0 and 24.8 GHz, respectively. We applied a gaussian smooth resulting in a final map resolution of2.89 arcmin at 7.0 GHz and 1.29 arcmin at 24.8 GHz. The smoothed beam is indicated by the blue circle on the bottom-left corner. The dashed circles indicatethe point sources NVSS J205122+291140 (C) and NVSS J205109+291629 (D), respectively. The white contours in the 24.8-GHz image correspond to the7.0-GHz intensity levels of 21 mJy beam − and 34 mJy beam − . flux density measurements associated with these sources in order tocross-check our calibration and data analysis procedure.Two point sources are well detected in the 7.0-GHz mapof NGC 6992, and are indicated by the white-dashed circles inFig. 3. These sources are reported in the NVSS catalogue (Con-don et al. 1998) as NVSS J205800+314231 (‘A’ in Fig. 3) andNVSS J205458+312614 (‘B’ in Fig. 3), respectively. The sourceA is also detected at 18.7 and 24.8 GHz, while the weaker sourceB is well-detected only at 18.7 GHz. For both point sources, radioflux density measurements in the range ∼ − along with their spectral energy distribution (SEDs).Although a classification of these sources is not available in the lit-erature, the radio data and their location outside the Galactic planesuggest that they are likely radio galaxies. We coupled the literaturemeasurements with our flux densities of the source A at 7.0, 18.7and 24.8 GHz and those at 7.0 and 18.7 GHz of the source B toassess the quality of our maps. https://vizier.u-strasbg.fr/ MNRAS , 1–19 () ew radio observations of the Cygnus Loop Frequency (GHz) F l u x ( m J y ) Source A power-law model with = 0.84 ± 0.07LiteratureSRT
Frequency (GHz) F l u x ( m J y ) Source B power-law model with = 0.56 ± 0.03LiteratureSRT
Figure 5.
SEDs of the extragalactic point sources ‘A’ (NVSS J205800+314231, left ) and ‘B’ (NVSS J205458+312614, right ) located near NGC 6992. Theblack dots indicate the literature measurements, and the blue triangles indicate the flux densities obtained in this work. The weighted least-squares fit appliedto the source A is related to the 1.4-GHz and 4.85-GHz data, while that applied to the source B is associated with all the literature data.
Frequency (GHz) F l u x ( m J y ) Source C LiteratureSRT
Frequency (GHz) F l u x ( m J y ) Source D power-law model with = 0.28 ± 0.06LiteratureSRT
Figure 6.
SEDs of the extragalactic point sources ‘C’ (NVSS J205122+291140, left ) and ‘D’ (NVSS J205109+291629, right ) located inside the southern shell.The black dots represent the literature measurements, and the blue triangles represent the flux densities obtained in this work.
The SEDs associated with the two sources are shown in Fig. 5,where we also report the extrapolated fit of the spectra referred tothe literature data. In the case of the source A, we excluded fromthe fit the data between 232 and 408 MHz, probably associatedwith a low-frequency spectral turn-over. All the SRT data relatedto this source are perfectly consistent with the fit obtained from theliterature data. In the case of the source B, our flux measurements at7.0 and 18.7 GHz are consistent with the fit derived from the otherdata within 3 σ and 1 σ , respectively.In our 7.0-GHz image of the southern shell, we detected twopoint sources unrelated with the remnant, and indicated with white-dashed circles in Fig. 4. Differently from what was observed forNGC 6992, in the southern shell both point sources are superim-posed on the remnant. The southern source (source ‘C’ in Fig. 4)is listed in the NVSS catalogue as NVSS J205122+291140. Fluxdensity measurements are available on VizieR between 0.325 and4.85 GHz. This source is also included in the ‘Variable 1.4 GHzradio sources from NVSS and FIRST’ catalogue (Ofek & Frail2011). Indeed, as shown in Fig. 6 ( left ), the literature flux density measurements reveal a certain variability of this source, which isparticularly highlighted by the spread of the NVSS flux densitiesat 4.85 GHz. Our measurements at 7.0 and 24.8 GHz also confirmthis variability, which makes this source useless to cross-check ourflux density measurements.The second point source (source ‘D’ in Fig. 4) is namedNVSS J205109+291629 (Condon et al. 1998), and it is indicatedas a blazar candidate in the ‘low-frequency radio catalogue offlat-spectrum sources’ (Massaro et al. 2014). The radio flux den-sity measurements associated with this source are summarised inVollmer et al. (2010), and the related SED is available on VizieR.The spectrum of this point source is shown in Fig. 6 ( right ). Boththe SRT measurements are perfectly consistent with the fit derivedfrom the archive data. The related spectral index is α = . ± . ,in agreement with the flat spectrum expected for this kind of ob-jects. It is worth to note that the flux densities of the source D at 7.0,8.5 (extrapolated from the fit) and 24.8 GHz are within the uncer-tainties associated with the southern shell measurements at these MNRAS000
The SEDs associated with the two sources are shown in Fig. 5,where we also report the extrapolated fit of the spectra referred tothe literature data. In the case of the source A, we excluded fromthe fit the data between 232 and 408 MHz, probably associatedwith a low-frequency spectral turn-over. All the SRT data relatedto this source are perfectly consistent with the fit obtained from theliterature data. In the case of the source B, our flux measurements at7.0 and 18.7 GHz are consistent with the fit derived from the otherdata within 3 σ and 1 σ , respectively.In our 7.0-GHz image of the southern shell, we detected twopoint sources unrelated with the remnant, and indicated with white-dashed circles in Fig. 4. Differently from what was observed forNGC 6992, in the southern shell both point sources are superim-posed on the remnant. The southern source (source ‘C’ in Fig. 4)is listed in the NVSS catalogue as NVSS J205122+291140. Fluxdensity measurements are available on VizieR between 0.325 and4.85 GHz. This source is also included in the ‘Variable 1.4 GHzradio sources from NVSS and FIRST’ catalogue (Ofek & Frail2011). Indeed, as shown in Fig. 6 ( left ), the literature flux density measurements reveal a certain variability of this source, which isparticularly highlighted by the spread of the NVSS flux densitiesat 4.85 GHz. Our measurements at 7.0 and 24.8 GHz also confirmthis variability, which makes this source useless to cross-check ourflux density measurements.The second point source (source ‘D’ in Fig. 4) is namedNVSS J205109+291629 (Condon et al. 1998), and it is indicatedas a blazar candidate in the ‘low-frequency radio catalogue offlat-spectrum sources’ (Massaro et al. 2014). The radio flux den-sity measurements associated with this source are summarised inVollmer et al. (2010), and the related SED is available on VizieR.The spectrum of this point source is shown in Fig. 6 ( right ). Boththe SRT measurements are perfectly consistent with the fit derivedfrom the archive data. The related spectral index is α = . ± . ,in agreement with the flat spectrum expected for this kind of ob-jects. It is worth to note that the flux densities of the source D at 7.0,8.5 (extrapolated from the fit) and 24.8 GHz are within the uncer-tainties associated with the southern shell measurements at these MNRAS000 , 1–19 ()
S. Loru et al.
Table 3.
Flux density measurements of the point sources observed close toNGC 6992 (sources A and B) and the southern shell (sources C and D) withSRT between 7.0 GHz and 24.8 GHz. Flux density (mJy)Source ID 7.0 GHz 18.7 GHz 24.8 GHzNVSS J205800+314231 A 150.0 ±
23 72 ±
32 71 ± ± ±
12 -NVSS J205122+291140 C 201 ±
15 - 194 ± ±
20 - 41 ± frequencies (Sect. 5.2). For this reason, we did not remove theircontribution to the integrated flux density of the southern shell.Our flux density measurements of the four point sources at7.0, 18.7 and 24.8 GHz are given in Table 3. The derived spectraof the point sources A, B and D provide a useful verification of thereliability of our flux density measurements. We analysed the radio spectrum of the entire Cygnus Loop SNR bycoupling our measurement at 8.5 GHz and all the flux density mea-surements available in the literature. We also included the
Planck measurement at 30 GHz, the only one reported by Planck Collab-oration et al. (2016) in Table 3 for this SNR. All the values andrelated references are reported in Table 4.It is worth noting that our measurement is the most sensi-tive obtained so far at these frequencies, if we exclude the lower-resolution
Planck data. The overall radio spectrum is displayed inFig. 7. The Medicina value at 8.5 GHz is represented with a filledred triangle, and perfectly matches the tendency suggested by theother data without any apparent spectral variation. We modelledthe integrated spectrum of the Cygnus Loop using a simple syn-chrotron power-law function. From the weighted least-squares fit( χ / do f = . ), we obtained a spectral index of α = . ± . and a normalisation constant at 1 GHz of ± Jy. Our result isconsistent within σ with the spectral index α = . ± . derivedby Uyanıker et al. (2004) by considering all the flux density mea-surements available in the literature between 0.022 and 4.94 GHz,and within σ with the spectral index of α = . ± . calculatedby Uyanıker et al. (2004) by considering the data from the Effels-berg 100-m telescope and the DRAO Synthesis telescope between0.408 and 2.675 GHz, and that calculated by Sun et al. (2006), α = . ± . , by adding the Urumqi telescope data at 4.8 GHz.We also fit the data reported in Table 4 with a simple synchrotronmodel with an exponential cutoff: S ν = K (cid:18) νν (cid:19) − α e − νν where K is the normalisation constant and ν is the cutoff fre-quency. The weighted least-squares fit ( χ / do f = . ) gives aspectral index α = . ± . , K = ± Jy (representingthe flux density at 1 GHz) and a cutoff frequency ν = ± GHz. Although the data are well-fitted by both the simple syn-chrotron power-law and the cutoff-frequency model, the high valueof the obtained cutoff frequency suggests that the non-thermal syn-
Frequency (GHz) F l u x ( J y ) power-law model with = 0.53 ± 0.01LiteratureMedicinaPlanck Figure 7.
Weighted least-squares fit applied to the Cygnus Loop spectrumfor the synchrotron power-law model. The red and black filled trianglescorrespond respectively to the Medicina point at 8.5 GHz and the
Planck data at 30 GHz. All the flux density values and related references are givenin Table 4. chrotron emission, without any steepening, is dominant in the con-sidered frequency range.Furthermore, our measurement rules out any spectral steepen-ing up to high radio frequencies, and it confirms the tendency sug-gested by the
Planck data at 30 GHz. Although the Cygnus Loop isconsidered approximately at the same evolutionary phase of otherSNRs that showed a synchrotron spectral break, as in the case ofS 147 (Fürst & Reich 1986) and W44 (Loru et al. 2019), or charac-teristic spectral features, as the spectral bump observed in the IC443between 20 and 70 GHz (Oni´c et al. 2017, Loru et al. 2019), its inte-grated spectrum appears dominated by the non-thermal synchrotronemission without any noticeable deviation. This result could indi-cate an earlier evolutionary phase of this SNR, for which a spectralsteepening is expected at higher frequencies, or the global effect ofdifferent electron populations across the remnant undergoing pecu-liar shocks conditions.On the other hand, the presence of a synchrotron spectralsteepening above ∼
20 GHz could be hidden by other processes,like thermal Bremsstrahlung or thermal dust-emission, which maybecome dominant depending on environmental conditions. On thisbase, we considered an upper cutoff frequency of 25 GHz and alower cutoff frequency of 22 MHz, the latter corresponding to thelower-frequency flux density measurement available in the litera-ture, to estimate the minimum total energy contents U min in theCygnus Loop and the related magnetic field strength B (U min ). Wehere estimate these quantities under the assumption of the equipar-tition between particles and magnetic energy (Condon & Ransom2016): U min = . ( η AL ) / V / erg (1) B ( U min ) = (cid:18) πη ALV (cid:19) / G (2)where V and L are the volume and the total luminosity of the sourceexpressed in cm and erg s − , respectively; η is a factor that ac-counts for the contribution to the total energy of protons and heav-ier ions with respect to electrons; A is a physical parameter that MNRAS , 1–19 () ew radio observations of the Cygnus Loop Table 4.
Integrated flux density measurements towards the whole Cygnus Loop SNR.Freq. Flux density Reference Freq. Flux density Reference(GHz) (Jy) (GHz) (Jy)0.022 1378 ±
400 Roger et al. (1999) 0.863 184 ±
18 Uyanıker et al. (2004)0.0345 1245 ±
195 Sastry et al. (1981) 0.960 190 ±
50 Kenderdine (1963)0.038 956 ±
150 Kenderdine (1963) 1.420 143 ±
14 Uyanıker et al. (2004)0.041 770 ±
140 Kundu & Velusamy (1967) 2.675 115 ±
12 Uyanıker et al. (2004)0.158 350 ±
70 Mathewson et al. (1960) 2.695 125 ±
16 Green (1990)0.195 382 ±
60 Kundu & Velusamy (1967) 2.7 88 ± ±
50 Kenderdine (1963) 4.940 73 ± ±
50 Mathewson et al. (1960) 4.8 90 ± ±
24 Uyanıker et al. (2004) 8.5 54 ± ±
50 Kundu & Velusamy (1967) 30 24.9 ± Table 5.
Summary of the parameters used to estimate the minimum energy ( U min ) and related magnetic field ( B ( U min ) ) under the equipartition condition. Weindicated with ‘sphere’ and ‘shell’ the source geometry assumed as a roughly uniform sphere or a spherical shell, respectively. V , L and α are the volume, thetotal luminosity and the spectral index, respectively. parameters ResultsSource geometry V L α U min B ( U min ) (cm ) (erg s − ) (erg) ( µ G)Cygnus Loop sphere . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × depends on the lower ( ν ) and upper ( ν ) cutoff frequencies andthe spectral index ( α ): A = C / C ( − α )( − α ) ν / − α − ν / − α ν − α − ν − α ( for α (cid:44) . ) where C and C are constants with value C = . × and C = . × − in cgs units (Dubner & Giacani 2015). We as-sumed an isotropic emission in the frequency range from 22 MHzto 25 GHz and η ∼ , as it was usually done in previous workson SNRs (Castelletti et al. 2007). We assumed these values also inthe case of NGC 6992 (Sect. 5.1) and the southern shell (Sect. 5.2).The other parameters are summarised in Table 5 together with theresults. We performed the analysis for two geometrical models: i)by approximating the Cygnus Loop to an uniform sphere of radius . deg; ii) by considering the CR electrons confined within theCygnus Loop shell, with a thickness of approximately 5 per centof the SNR radius. The assumption of the energy equipartition be-tween particles and magnetic field provides a first estimation ofthe minimum value of the energy and magnetic field strength in aSNR. However, it is very difficult to decide whether synchrotronsources are in equipartition, especially in the case of extended andcomplex object like SNRs (Dubner & Giacani 2015). Observationalconstraints from radio and γ -ray data are then needed to firmly con-strain the particle energetics and the magnetic field strength, andto investigate on a possible SNR departure from the equipartitioncondition. Indeed, the maximum energy achieved by an electron population with cutoff frequency ν c is (Reynolds 2008): E = . (cid:18) ν c / GHz B / µ G (cid:19) GeV (3)Considering a tentative lower limit on the radio cutoff frequency of25 GHz and the maximum particle energy between 1 and 10 GeV,as derived from the γ -ray observations by Katagiri et al. (2011),we obtained a minimum value of the magnetic field ranging from54 µ G to 5.4 mG from Eq. (3).On the other hand, a stringent upper limit on the magnetic fieldcan be obtained from the condition that the synchrotron coolingtime has to be larger than the remnant’s age, otherwise a coolingbreak should be visible in the radio spectrum. The cooling time isgiven by (Ohira et al. 2012): t sync = m e r cB E = . × (cid:18) B µ G (cid:19) − / (cid:16) ν c GHz (cid:17) − / yr , (4)where m e and r are the electron mass and the classical elec-tron radius, respectively. In the second equality, we substituted ν c from Eq. (3), Hence, imposing t sync > t age with the condition ν c > GHz, we get B < µ G.A more constraining investigation on the particle energeticsand magnetic field strength can be achieved through a model of theradio and γ -ray emission from the Cygnus Loop, which accountsfor the electron radiative losses and the evolution of the magneticfield, coupled to the SNR dynamics. A detailed description of thismethod is provided in Sect. 6. MNRAS000
Summary of the parameters used to estimate the minimum energy ( U min ) and related magnetic field ( B ( U min ) ) under the equipartition condition. Weindicated with ‘sphere’ and ‘shell’ the source geometry assumed as a roughly uniform sphere or a spherical shell, respectively. V , L and α are the volume, thetotal luminosity and the spectral index, respectively. parameters ResultsSource geometry V L α U min B ( U min ) (cm ) (erg s − ) (erg) ( µ G)Cygnus Loop sphere . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × depends on the lower ( ν ) and upper ( ν ) cutoff frequencies andthe spectral index ( α ): A = C / C ( − α )( − α ) ν / − α − ν / − α ν − α − ν − α ( for α (cid:44) . ) where C and C are constants with value C = . × and C = . × − in cgs units (Dubner & Giacani 2015). We as-sumed an isotropic emission in the frequency range from 22 MHzto 25 GHz and η ∼ , as it was usually done in previous workson SNRs (Castelletti et al. 2007). We assumed these values also inthe case of NGC 6992 (Sect. 5.1) and the southern shell (Sect. 5.2).The other parameters are summarised in Table 5 together with theresults. We performed the analysis for two geometrical models: i)by approximating the Cygnus Loop to an uniform sphere of radius . deg; ii) by considering the CR electrons confined within theCygnus Loop shell, with a thickness of approximately 5 per centof the SNR radius. The assumption of the energy equipartition be-tween particles and magnetic field provides a first estimation ofthe minimum value of the energy and magnetic field strength in aSNR. However, it is very difficult to decide whether synchrotronsources are in equipartition, especially in the case of extended andcomplex object like SNRs (Dubner & Giacani 2015). Observationalconstraints from radio and γ -ray data are then needed to firmly con-strain the particle energetics and the magnetic field strength, andto investigate on a possible SNR departure from the equipartitioncondition. Indeed, the maximum energy achieved by an electron population with cutoff frequency ν c is (Reynolds 2008): E = . (cid:18) ν c / GHz B / µ G (cid:19) GeV (3)Considering a tentative lower limit on the radio cutoff frequency of25 GHz and the maximum particle energy between 1 and 10 GeV,as derived from the γ -ray observations by Katagiri et al. (2011),we obtained a minimum value of the magnetic field ranging from54 µ G to 5.4 mG from Eq. (3).On the other hand, a stringent upper limit on the magnetic fieldcan be obtained from the condition that the synchrotron coolingtime has to be larger than the remnant’s age, otherwise a coolingbreak should be visible in the radio spectrum. The cooling time isgiven by (Ohira et al. 2012): t sync = m e r cB E = . × (cid:18) B µ G (cid:19) − / (cid:16) ν c GHz (cid:17) − / yr , (4)where m e and r are the electron mass and the classical elec-tron radius, respectively. In the second equality, we substituted ν c from Eq. (3), Hence, imposing t sync > t age with the condition ν c > GHz, we get B < µ G.A more constraining investigation on the particle energeticsand magnetic field strength can be achieved through a model of theradio and γ -ray emission from the Cygnus Loop, which accountsfor the electron radiative losses and the evolution of the magneticfield, coupled to the SNR dynamics. A detailed description of thismethod is provided in Sect. 6. MNRAS000 , 1–19 () S. Loru et al.
Table 6.
Flux density measurements and rms related to the maps of NGC6962 and the southern shell carried out with the Medicina radio telescopeand SRT. Source Freq. Flux density σ name (GHz) (Jy) (mJy/beam) NGC 6962 ± ± ± ± Southern shell ± ± ± Table 7.
Flux density measurements of the regions NGC 6962 and thesouthern shell related to the
Planck maps of the Cygnus Loop at 30 and44 GHz. Source Freq. Flux densityname (GHz) (Jy)
NGC 6962
30 4.32 ± ± Southern shell
30 9.49 ± ± In this Section, we use the Medicina and SRT data and the fluxdensity measurements at 30 and 40 GHz, derived from the public
Planck maps, in order to investigate the integrated spectrum of thetwo regions of the Cygnus Loop: NGC 6992 and the southern shell.Due to the lack of separated γ -ray flux measurements for these tworegions, we cannot use the Eq. (3) or the model described in Sect.6 to constrain the magnetic field strength and the particle spectrum.We will estimate, instead, the magnetic field using only radio dataunder the assumption of energy equipartition between non-thermalparticles and magnetic field. The morphology of NGC 6992 is governed by the interaction of theSNR blast wave with smaller discrete clouds (Fesen et al. 2018).The correlation between X-ray and optical emission reflects thenon-homogeneous interaction of the blast wave with the clouds:in the low-density inter-cloud medium, the shock wave propagatesunimpeded and emits X-ray radiation, while it decelerates where itencounters dense clumps of gas with a resultant optical emission(Levenson et al. 1998). Local changes in shock velocity and in thepreshock density were also pointed out by optical studies of the H α filaments observed in NGC 6992 (Blair et al. 2005). These resultin isolated regions where the non-radiative shock is becoming ra-diative. NGC 6992 corresponds to the brightest sector of the γ -rayCygnus Loop emission observed with Fermi-LAT between 1 and100 GeV (Katagiri et al. 2011), suggesting the interaction of high-energy particles with the circumstellar medium (CSM) regions.We used the flux densities calculated from our maps at 7.0, 8.5 and 18.7 GHz to investigate the integrated spectrum associatedwith NGC 6992. These values are listed in Table 6. We performeda weighted fit of our data by using a simple power-law model, asshown in Fig. 8. We calculated for this region α = . ± . ,which is significantly lower ( > σ ) than the value that we obtainedfor the whole Cygnus Loop SNR ( α = 0.53 ± α (cid:39) . ) revealed for this region by the spatially-resolvedspectral index studies performed by Uyanıker et al. (2002) in thefrequency range from 0.408 to 2.675 GHz.There are several explanations for flat radio spectra of SNRsin the current literature (see Oni´c 2013, for an overview). Most ofthe models involve a significant contribution of the second-orderFermi mechanism, but some of them also discuss high compressionratio, contribution of secondary electrons produced in hadronic col-lisions, as well as the possibility of thermal contamination. Giventhe relatively low density in the region of NGC 6992 ( ∼ cm − ),contributions from secondary electrons and thermal emission aredisfavoured.Concerning the second-order Fermi acceleration, we haveconsidered the model developed by Ostrowski (1999), which in-cludes this mechanism in the shock acceleration and predicts hardspectra when the ratio v A / u sh (cid:38) . (where v A is the Alfvén ve-locity and u sh is the shock velocity) and/or the particle diffusion ismuch flatter, in energy, than the Bohm-like diffusion. However, inthe case of NGC 6992, a spectrum with α = . requires eitheran upstream magnetic field B ≈ µ G, a value which we willexclude in our next analysis (see the last part of this Section andSect. 6), or a diffusion coefficient D ∝ E . . The latter conditionis also at odds with the idea that diffusion results form the self-generated turbulence. In such a case, particle spectra harder than E − would produce self-generated diffusion harder than E , con-tradicting the premise. Hence a different turbulence origin shouldbe invoked.We are left with the possibility of large compression. Sucha condition is naturally realised in radiative shocks because thedownstream plasma loses energy through radiation and becomesmore compressible. Blair et al. (2005) found that some portionsof the shock in NGC 6992 are close to become radiative. The sameconclusion was reached by Szentgyorgyi et al. (2000) for the regionNGC 6995. Then it is possible that the compression ratio ( r ) is justslightly larger than 4. Remembering that the radio spectral indexis connected to the shock compression ratio as α = /( ( r − )) ,we need r = . to produce α = . . Such an interpretation isvery attractive, but comes with some caveats. First of all, radiativeshocks are not thought to be efficient accelerators even though it isnot very clear when the transition from efficient to inefficient ac-celeration occurs. Indeed, the Cygnus Loop may represent a rareexample where such a transition may be studied. Secondly, whena shock becomes radiative, its velocity structure is more complexthan the simple step function used to describe high-velocity shocks.Therefore, the final particle spectrum should be computed using thecorrect velocity profile but this is beyond the aim of the presentwork.We used the Planck public maps of the Cygnus Loop availableon the NASA/IPAC Infrared Science Archive to compute the fluxdensity of NGC 6992 at 30 and 44 GHz. We considered the sameextraction region as shown in Fig. 9. The background-corrected re- https://irsa.ipac.caltech.edu/Missions/planck.html MNRAS , 1–19 () ew radio observations of the Cygnus Loop
105 6 7 8 9 20 30 40 50
Frequency (GHz) F l u x ( J y ) power-law model with = 0.45 ± 0.05Medicina & SRTPlanck
105 6 7 8 9 20 30 40 50
Frequency (GHz) F l u x ( J y ) power-law model with = 0.49 ± 0.01NLDSA modelMedicina & SRTPlanck Figure 8.
Left : weighted least-squares fit applied to our measurements at 7.0, 8.5, 18.7 and 24.8 GHz, indicated with black circles, of NGC 6992 by using thesynchrotron power-law model. The red triangles correspond to the
Planck data at 30 and 44 GHz.
Right : spectral energy distribution related to the southern shell.The black solid line shows the weighted least-squares fit applied to our flux density measurements at 7.0, 8.5 and 24.8 GHz for a simple synchrotron power-lawmodel. The non-linear diffusive shock acceleration model is represented by a black dotted line and it is obtained tacking also the
Planck measurements at 30GHz and 44 GHz (red triangles) into account G a l a c t i c L a t i t u d e NGC 6992 Southern shell m J y / b e a m G a l a c t i c L a t i t u d e NGC 6992 Southern shell m J y / b e a m Figure 9.
The Cygnus Loop images from
Planck at 30 GHz ( left ) and 44 GHz ( right ). The beam size of 32.3 arcmin at 30 GHz and 27.1 arcmin at 44 GHz isindicated by the blue-filled circle on the bottom left corner of the maps. The white contours indicate the extraction regions that we used to calculate the fluxdensity. sults are listed in Table 7. We calculated the errors associated withthe
Planck measurements adding in quadrature the statistical un-certainty and the flux calibration uncertainty. For the latter, we as-sumed the values of the mission calibration uncertainty reportedin the Table 1 of Planck Collaboration et al. (2016). The
Planck flux density at 30 GHz is consistent with the tendency suggestedby our data. This represents a further confirmation that no spectralsteepening takes place in this region up to high radio frequencies.The value at 44 GHz indicates, instead, a significant flux densityincrease, suggesting that the dust emission contribution becomesimportant. On the other hand, we cannot exclude a possible contri- bution of the dust emission also at lower frequencies, in particularon the flux density at 30 GHz. This could compete with the syn-chrotron emission, hiding a possible spectral cutoff. However, wenote that our high-frequency maps, especially that at 24.8 GHz, areaffected by artefacts and high noise, which together with the weak-ness of the source emission make a precise flux density estimationdifficult. More K -band SRT observations are needed to firmly es-tablish the NGC 6992 spectral behaviour at high radio frequencies.As in the case of the whole Cygnus Loop, we established alower limit for a possible spectral break in the NGC 6992 regionat ∼
25 GHz and used it for estimating the minimum energy and
MNRAS000
MNRAS000 , 1–19 () S. Loru et al. related magnetic field by assuming that this region satisfies theequipartition condition. The used parameters and results are sum-marised in Table 5. The magnetic field value (46 µ G) is in perfectagreement with the estimation performed by Sun et al. (2006) forthe same region considered in the energy equipartition condition.On the other hand, the magnetic field obtained for NGC 6992 ishigher than that obtained for the entire Cygnus Loop SNR bothmodelling it as an uniform sphere (19 µ G) or a shell (27 µ G), sug-gesting a possible magnetic field amplification process in this re-gion like the turbulent dynamo.
The southern shell is the brightest region of the Cygnus Loop inthe radio domain. It is a typical shell centred at about ( α , δ ) =(20 h m , 29 ◦ (cid:48) ) with a size of ∼ . ◦ × . ◦ (Uyanıker et al.2002). Radio polarimetric studies revealed a tangential configura-tion of the magnetic field along the whole southern shell, as typi-cally expected for a middle-aged SNR in its adiabatic phase (Sunet al. 2006). Spatially-resolved spectral index studies performed onthe whole Cygnus Loop by Leahy & Roger (1998) between 0.408and 1.420 GHz revealed region-dependent spectral indices, rangingfrom flat spectra corresponding to the north and northeast rims, tosteep spectra in the southern shell and in the faint region on thewest of the central bright filament of the northern shell. By includ-ing also the radio data at 2.695 GHz, the authors also pointed outregion-dependent spectral shapes with a negative curvature (spec-tral steepening) associated with NGC 6992 and a positive curvature(concave-up) in the central faint regions of the northern shell andin the southern shell. More recent observations by Uyanıker et al.(2004) between 0.408 and 2.675 GHz showed slight variations ofthe southern shell spectral index compared to the integrated valueof the whole Cygnus Loop SNR ( α ∼ . ). In particular a steeperspectrum was observed in the central fainter region ( α ∼ . ), whilelower spectral indices are found in the brightest filaments ( α ∼ . ).The authors attributed these variations to a weak compression be-tween the shock wave and the ISM in the southern shell, where theshock acceleration appears as the dominant mechanism.Optical observations revealed a fully radiative region on theeast side of the shell. However, the filamentary structures are lessextended than those observed in the northern shell, suggestingsmaller clouds or a more recent interaction of the SNR shock withthem (Levenson et al. 1998). The southern shell is very faint inthe X-ray images, with an extremely smooth shell detected in thesoft X-ray band (Levenson et al. 1999). The radio continuum andthe γ -ray emission do not appear correlated in this region (Katagiriet al. 2011). Only the bright southern γ -ray spot (centred at ∼ α , δ = h m , + ◦ (cid:48) ) is coincident with the brightest radio regionof the shell.We investigated the high-frequency spectrum of the southernshell by using the flux densities at 7.0, 8.5 and 24.8 GHz. The re-sulting spectrum is shown in Fig. 8 ( ri g ht ), where we also includedthe Planck measurements at 30 GHz and 44 GHz (see Table 7). Be-tween 7.0 and 24.8 GHz, the spectrum results perfectly fitted by asimple power-law function with α = . ± . , ruling out anyspectral steepening. Our fit underestimates the Planck data. If weinclude them in our analysis, the spectrum results well fitted by asynchrotron power-law function with α = . ± . . The uncer-tainties related to our flux density at 24.8 GHz make it compatiblewith this fit. Nevertheless, both Planck values seem to suggest aconcave-up deviation from the simple synchrotron-emission model.We tried to investigate the emission processes and the theoretical models that could be at the basis of this spectral tendency.‘Concave-up’ radio spectra, flattening to high frequencies, were ob-served both in evolved (composite, mixed-morphology) and youngshell-like SNRs. In the first case, the curvature of the spectrum isrelated to other emission mechanisms that become significant athigh frequencies, especially for SNR evolving in complex environ-mental conditions (Uroševi´c 2014). The most accredited models in-clude bremsstrahlung emission in presence of dense ISM environ-ment, thermal dust emission linked to cold dust in molecular cloudsand spinning dust emission from very small grains usually foundin nearby Galactic molecular and dust clouds interacting with theSNR shocks. The density in the southern shell is even lower thanthe one in NGC 6992 (Fesen et al. 2018), hence a possible signifi-cant contribution from these processes is not expected. In particu-lar, the thermal dust contribution, expected at these frequencies, isnot strongly evident at 30 and 44 GHz. It could become significantat higher frequencies. In some young SNRs, in the free-expansionand in the early adiabatic-expansion phases of their evolution (Dub-ner & Giacani 2015), a curved concave-up shape is observed as apossible result of the dynamical reaction of accelerated particlesthat modify the shock structure. Under the modified shock con-figuration, the low-energy electrons are confined in the subshockregion where they undergo a compression factor r < . This re-sults in a steepening of the radio spectra at low frequencies. On thecontrary, because the high-energy electrons can sample a more ex-tended space region ( r > far from the shock) the related energyspectrum results harder (flat radio spectrum). The overall effect isa concave-up radio spectrum due to a significant CR productionand confinement (Amato & Blasi 2005, Uroševi´c 2014). The mag-netic field configuration of the southern shell is consistent with thatof a shell-like SNR in the adiabatic phase, and it results differentfrom that of the northern shell, where the magnetic field shell struc-ture appears more irregularly (Sun et al. 2006). The nature of thesouthern shell is still debated. On the basis of neutral Hydrogenline observations, Leahy (2005) interpreted this region as a resultof a southern cavity arising from the Cygnus Loop expansion ona wall of neutral gas with consequent acceleration of smaller in-terstellar clouds adjacent to the northern rim of this region towardthe center of the Cygnus Loop. On the other hand, in the scenarioof two SNRs composing the Cygnus Loop, the radio and magneticfield characteristics are attributed to an early evolutionary stage ofthe southern SNR, which would have formed after the northern one(Uyanıker et al. 2004). The absence of a spectral steepening, dueto a still very efficient acceleration mechanism up to high radio fre-quencies, could be a confirmation of this hypothesis. In this context,the indication of a concave-up spectrum could be associated withan efficient CR production at the shock.In order to investigate this possibility, we fitted our data andthe Planck measurements at 30 GHz and 44 GHz by a model thatincludes non-linear diffusive shock acceleration (NLDSA) effects.We represented this model with a varying power-law of the form S ν ∝ ν − α − c log ν , where c is a curvature parameter. The resultingfit for the varying spectral-index model is represented by the dottedline in Fig. 8 ( right ). We obtained a spectral index α = . ± . , aspectral curvature parameter c = . ± . and a normalisationconstant of 61 ± c = . ± . ) for thecase of the young SNR Cas A, which they ascribed to an efficientnon-linear diffusive shock accelerator. Furthermore, the spectral in- MNRAS , 1–19 () ew radio observations of the Cygnus Loop dex obtained for the southern shell is consistent within σ with thatobtained for Cas A ( α = . ± . ). We point out that our fluxdensity measurements, including the Planck ones, perfectly agreewith both the simple synchrotron emission and the non-linear syn-chrotron model due to the large uncertainties, and do not allow usto constrain the spectral tendency in the frequency range between20 and 50 GHz. Therefore, we cannot completely exclude a possi-ble dust emission contribution, although not dominant. More flux-density measurements with higher sensitivity between ∼ GHz and ∼ GHz could be crucial to constrain the particle-accelerationmechanisms in the southern shell.Assuming the southern shell in the energy-equipartition con-dition, we calculated the minimum energy and associated mag-netic field strength by using Eqs. 1 and 2. In Table 5, we list theused parameters and related results. We assumed two shell mod-els with a thickness of: i) ∼ ∼ B ( U min ) = G ), is very close to that ob-tained for the whole Cygnus Loop, suggesting very similar con-ditions ( B ( U min ) = G ). On the other hand, the estimation per-formed by considering the southern shell as an independent SNR(shell-II) provides a higher magnetic field ( B ( U min ) = G ) com-pared to that obtained for the entire Cygnus Loop. This couldbe consistent with an amplification of the magnetic field as ob-served in SNRs with a concave-up radio spectrum and resultingfrom an efficient shock acceleration that modifies the shock struc-ture (Reynolds 2011). However, only a detailed modelling of thenon-thermal emission from the radio to the γ -ray band will firmlyconstrain the magnetic field strength in this region. In this Section, we model the non-thermal emission from the wholeCygnus Loop, combining radio and γ -ray observations, to investi-gate the properties of particle acceleration at the forward shock andtheir time-dependent escape from the source.One of the main issues in the shock acceleration theory is iden-tifying the maximum energy that particles can reach and under-standing how it evolves in time. This is also intimately connectedwith the magnetic field amplification, a process thought to occur inthe shock region by means of the same accelerated particles and anecessary requirement to reach energies much larger than a few tensof GeV (for recent reviews see Blasi 2013; Amato 2014). To thisrespect, middle-aged SNRs can be very helpful given that severalamong these remnants show a γ -ray spectrum with a cutoff, or aspectral softening above ∼ − GeV, and the Cygnus Loop makesno exception (Katagiri et al. 2011). Such a feature could be relatedto the maximum energy of the particles accelerated at the presenttime (Celli et al. 2019; Brose et al. 2020). In fact, the break, or soft-ening, could be produced by particles accelerated in the past that areno more confined by the acceleration mechanism and start diffusingaway from the source in such a way that a fraction of escaped parti-cles are still located inside the source. If this were indeed the case,a spectral break is expected in the radio band at a frequency givenby Eq. (3), namely ν br (cid:39) . ( E max , e /
10 GeV ) ( B / µ G ) GHz. Inturn, if the γ -ray emission is due to hadronic processes, the max-imum energy inferred from the high-energy cutoff rather refers toprotons, such that the magnetic field remains generally poorly con-strained and ν br cannot be determined. Hence, it is fundamentalto describe both contributions from accelerated hadrons and lep- tons, and related radiative emissions, to obtain a clear understand-ing about the relative importance of the many ongoing physical pro-cesses. For this reason, we will use a self-consistent model, wherethe magnetic field at the shock is estimated from the maximum en-ergy of particles through the amplification process. Here, the tem-poral evolution of the SNR is taken into account to calculate adi-abatic losses for both particles and magnetic field, in order to cor-rectly determine the whole synchrotron spectrum.With such a time-dependent model, we can constrain severalquantities like particle maximum energy, acceleration efficiency,ratio between accelerated electrons and protons, and magnetic fieldstrength at different stages of the remnant evolution. In order tokeep the calculations as simple as possible, we will use a spheri-cally symmetric model, which in turn will not allow to account forthe different radio slopes observed in different parts of the CygnusLoop. The model that we adopt here is developed by Celli et al. (2019)and Morlino & Celli (2020), hence the reader is referred to thosepapers for further details. For simplicity, we assume that the rem-nant is expanding into a uniform CSM, with numerical density n .The SNR properties (namely SN explosion kinetic energy E SN , cir-cumstellar density n , SNR age t age and distance from us d ) arefixed to the best values obtained by Fesen et al. (2018), and sum-marised in Table 8. We then follow Truelove & McKee (1999) todescribe the SNR evolution assuming an ejecta power-law indexequal to 0 (see Table 5 in Truelove & McKee 1999). The ejectamass is then fixed to M (cid:12) to match the measured shock propermotion of 0.1 arcsec yr − , which at d = pc, corresponds to ashock velocity u sh =
367 km s − (Fesen et al. 2018). At the sametime, the predicted shock radius, R sh = pc, well matches withthe E-W semi-axis of 18.5 pc.We account for particle acceleration at the forward shock as-suming that a fixed fraction of the shock kinetic energy is trans-ferred to non-thermal particles. The instantaneous proton spectrumaccelerated at the shock is f p , ( p , t ) = ξ CR u ( t ) ρ π c ( m p c ) Λ ( p max ( t )) (cid:18) pm p c (cid:19) − s e − p / p max ( t ) , (5)where ρ = n m p ( m p being the proton’s mass), Λ ( p max ( t )) is anormalisation constant such that the CR pressure at the shock is P CR = ξ CR ρ u . The factor ξ CR represents the instantaneous ac-celeration efficiency, and it is kept constant during the whole evo-lution of the SNR until now. We also remember that the linear dif-fusive shock acceleration process (DSA) predicts the particle spec-tral slope to be s = for strong shocks. p max ( t ) represents theinstantaneous maximum momentum (and E max is the correspond-ing maximum energy) achieved at the time t . Simple considerationson particle confinement suggest that it increases during the ejectadominated (ED) phase and decreases during the Sedov-Taylor (ST)phase, following a simple power-law: p max ( t ) = (cid:40) p M ( t / t Sed ) if t (cid:54) t Sed p M ( t / t Sed ) − δ if t > t Sed (6)where t Sed (cid:39) yr is the beginning of the ST age. Both the abso-lute maximum momentum p M and the slope δ are free parameters,that will be constrained from data. We also stress that the final re-sult is not very sensitive to the behaviour of p max for t < t Sed , as
MNRAS000
MNRAS000 , 1–19 () S. Loru et al. a consequence of the fact that t Sed (cid:28) t age . Hence the behaviour ofthe maximum energy during the ED phase cannot be constrained.Differently from protons, electrons are affected by radiativelosses, so that we need to estimate the magnetic field strength inorder to determine their distribution at the shock. To be conser-vative, we only evaluate the magnetic field at the shock requiredto reach the maximum energy. The common assumption is thatthis field is self generated by the same particles through resonant(Skilling 1975) or non-resonant instabilities (Bell 2004) (see alsoAmato & Blasi 2009). Here, we do not specify the precise mech-anism, but we make the assumption that the magnetic turbulencehas a flat power distribution to produce a Bohm-like diffusion co-efficient in the upstream of the shock, i.e. D = r L ( p ) c /( F ( k res )) where r L = pc /( eB ) is the particle’s Larmor radius and F ( k ) isthe logarithmic power spectrum of magnetic turbulence related toparticle momentum through the resonant condition k res = / r L ( p ) .In the following, B refers to the unperturbed circumstellar mag-netic field, while δ B represents the turbulent component, so that thetotal magnetic field upstream reads as B = (cid:113) B + δ B . In addi-tion, subscript 1 (2) refers to quantities evaluated upstream (down-stream) of the shock. When the magnetic field is amplified beyondthe linear regime ( δ B (cid:29) B ), the diffusion becomes Bohm-likein the amplified magnetic field (Blasi 2013). In other words, thefunction F should have the following limits: F ∼ ( δ B / B ) for δ B (cid:28) B and F ∼ ( δ B / B ) for δ B (cid:29) B . A minimal formula thatreproduces these limits is F = (cid:2) ( B / δ B ) + ( B / δ B ) (cid:3) − , which,once inverted, gives δ B ( t ) = B (cid:18) F ( t ) + (cid:113) F ( t ) + F ( t ) (cid:19) . (7)The relation between the maximum energy and the turbulent mag-netic field upstream, δ B , is obtained by imposing that the max-imum energy is determined by the age of the SNR, i.e. t acc = t age . Using the acceleration time from quasi-linear theory, namely t acc (cid:39) D ( p max )/ u sh ( t ) (Morlino 2017), we have F ( t ) = r L ( p max ( t )) c /( u sh ( t ) t ) . This equation allows us to compute themagnetic turbulence self-generated by accelerated particles at theshock, once a receipt is given for the maximum momentum andthe shock speed temporal evolution. The magnetic field upstreamis then compressed at the shock and expands adiabatically duringthe SNR evolution.The electron spectrum is similar to that of protons, but themaximum energy and the cutoff shape are different. In the loss-dominated case, i.e. for t sync < t age , a super-exponential cutoff isexpected (Zirakashvili & Aharonian 2007; Blasi 2010). In particu-lar, when energy losses are proportional to E , like in synchrotronand inverse Compton (IC) processes, the spectral cutoff is propor-tional to exp [−( p / p max , e ) ] . A good approximation to the spec-trum is provided by Zirakashvili & Aharonian (2007): f e , ( p ) = K ep f p , ( p ) (cid:104) + . (cid:0) p / p max , e (cid:1) (cid:105) e − (cid:16) pp max , e (cid:17) , (8)where the constant K ep accounts for the different injection effi-ciency of electrons with respect to protons. The electron maximummomentum, p max , e is determined (as a function of time) either bylosses or by the acceleration time, i.e. t acc = min [ t loss , t age ] wherelosses include both synchrotron emission and IC scattering. The lat-ter is evaluated adopting the average Galactic background photonsdue to the cosmic microwave background (CMB), plus infrared,optical and UV radiation produced by dust emission and star-light.Once proton and electron spectra are known at the shock, their evolution inside the SNR is calculated assuming that all particleswith energies E < E max , p ( t ) remain confined into their plasmaelements, suffering adiabatic and radiative losses (for electrons).On the contrary, when E > E max , p ( t ) , particles (both protons andelectrons) start escaping from the shock with a rate determined bythe properties of the local CSM. Inferring such properties is quitedifficult, hence we assume that particles diffuse with a local diffu-sion coefficient given by D csm = χ D Gal , where D Gal is the averageGalactic diffusion coefficient as estimated from direct CR measure-ments (see e.g. Evoli et al. 2019) and χ is a free parameter that canbe estimated from observations. The model outlined in the previous Section has seven free parame-ters, listed in the right side of Table 8, which can all be constrainedwith a reasonable accuracy using radio and γ -ray observations. Fig-ures 10 and 11 show the γ -ray and the radio emission, respec-tively, resulting from our best model, as compared with availabledata. The modelling result accounts for the radiation emerging fromseveral mechanisms, including proton collisions on target gas den-sity (pp interaction), electron IC scattering on the background pho-tons and synchrotron emission from electrons in the SNR magneticfield. The γ -ray emission from pp interaction is calculated usingthe parametrization provided by Kafexhiu et al. (2014). Each radia-tion process contains two different contributions, one produced byconfined particles and one from escaping particles.To better understand the shape of the non-thermal radiation,it is useful to have a closer look at the particles spectra. Figure 12shows both electron and proton spectra spatially integrated in theremnant interior at the present time. The maximum energy reachedat t age is 65 GeV for both electrons and protons: below this energy,particles are all confined and their spectrum is proportional to p − ,as set through Eq. (5), while above the spectra steepen as a conse-quence of the escaping process. We highlight that the flattening ob-served towards the largest energies is due to the contribution of theshock precursor, where particles do not suffer adiabatic losses. Thecutoffs observed at the highest energies are due to the absolute max-imum energy reached at the beginning of the ST phase, which forprotons is E M , p (cid:39) TeV while, for electrons is a factor 10 lowerdue to severe synchrotron losses, resulting in E M , e (cid:39) TeV. Wenote that the maximum energy we derived here is much larger thanthe interval − GeV obtained by Katagiri et al. (2011).In the following, we outline how data constrain each singleparameter of the model. First of all, the radio spectral index fixesthe particle spectral slope through the relation s = α + , hence α (cid:39) . ⇒ s (cid:39) , in good agreement with linear DSA prediction.As the observed γ -ray spectrum is expected to arise entirely thoughpp collisions, its normalisation allows us to fix the acceleration ef-ficiency ξ CR , once the target density is fixed, while the spectralshape beyond few GeV simultaneously constraints p M , p , δ and χ .Unfortunately, the lacks data beyond a few 10 GeV results in somedegeneracy between those three parameters. Hence, we decided tomake the conservative assumption D csm = D Gal , which allows usto constrain p M , p (cid:39) TeV and δ (cid:39) in order to reproduce the γ -ray data as shown in Figure 10. It is worth stressing that the ICemission spectrum from escaping electrons is quite flat and domi-nates the emission above ∼ GeV. Even if those electrons havebeen accelerated in the past, a fraction of them is still located in-side the SNR and its amount depends on the diffusion coefficientlike N e ∝ D − / . As a consequence, our choice of χ = should MNRAS , 1–19 () ew radio observations of the Cygnus Loop Table 8.
Value of parameters used to model the Cygnus Loop spectrum. The left block refers to the SN explosion kinetic energy ( E SN ), the SNR age ( t age )and distance ( d ), and the circumstellar density ( n ) as inferred by Fesen et al. (2018). The ejecta mass ( M ej ) is, instead, chosen to match the present values ofthe shock radius ( R sh ) and the shock velocity ( u sh ). The right block refers to the parameters used in the acceleration model described in Sect. 6, where: ξ CR isthe acceleration efficiency; s is the particle spectral slope; E M is the absolute maximum proton energy; δ is the maximum momentum spectral slope; K ep is aconstant that accounts for the different injection efficiency of electrons with respect to protons; B is the unperturbed circumstellar magnetic field; χ is a freeparameter related to the local diffusion coefficient.Cygnus Loop properties Acceleration model parametersAssumed Derived E SN M ej t age d n R sh u sh ξ CR s E M δ K ep B χ × erg 5 M (cid:12) . × yr 735 pc 0.4 cm −
20 pc 380 km s − µ G 1 -14 -13 -12 -11 -10 -9 -3 -2 -1 E φ ( E ) ( e r g c m - s - ) E (GeV) δ = 3, p M = 200 TeV/c, D = 1x10 cm /s, n = 0.4 cm -3 , ξ CR = 7%, K ep = 0.15, pp+ICIC totalIC confinedIC escapedpp totalpp confinedpp escaped Figure 10. γ -ray emission estimated from the model compared with Fermi-LAT observations (Katagiri et al. 2011). Hadronic (pp) and leptonic (IC)components are shown respectively with blue and yellow lines, while theirsum is given in red. For each process, dashed and dotted lines show thecontribution from confined and escaped particles, respectively. -13 -12 -11 -6 -4 -2 E φ ( E ) ( e r g c m - s - ) E (eV) δ = 3, p M = 200 TeV/c, D = 1x10 cm /sB = 3 µ GConfinedEscapedB = 1 µ GConfinedEscaped
Figure 11.
Synchrotron emission as derived from the model compared withradio data from the whole SNR. Yellow lines show our best model, whichassumes B = µ G, while the magenta lines show the case with B = µ G. Dashed and dotted lines show the contribution from confined andescaped electrons, respectively. -14 -13 -12 -11 -10 -9 -8 π p ∫ R s h ( t ) d r f ( t, r , p ) ( G e V / c c m - ) p (GeV/c)Spatially integrated spectrum ( δ = 3, p M = 200 TeV/c, D = 1x10 cm /ElectronsProtons Figure 12.
Accelerated proton and electron spectra located inside the SNRat the present age, integrated inside the whole SNR and multiplied by π p .The break located at GeV corresponds to the maximum energy reachedat the present time hence, particles above this energy are escaping. -2 -1 B ( t, r) ( µ G ) r/R sh (t)Magnetic field in Cygnus Loop (T SNR = 21 kyr, t
Sed = 1.5 kyr, δ = 3, p M = 200 TeV/c)B = 3 µ G, t = t age B = 3 µ G, t = t
Sed B = 1 µ G, t = t age B = 1 µ G, t = t
Sed
Figure 13.
Total magnetic field strength inside and outside the SNR as pre-dicted by the model presented in Sect. 6.1, assuming B = µ G (upper-yellow lines) and µ G (bottom-magenta lines). Solid and dashed curvesrefer to t = t age and t = t Sed , respectively. The radial coordinate is dividedby R sh ( t ) , which increases with time. be considered as a lower limit, in that χ (cid:28) would result in over-shooting the Fermi-LAT upper limits above 10 GeV.An interesting test for our model would be to look for the TeVemission produced through IC by escaping electrons. The differen-tial flux at 1 TeV is ∼ − erg s − cm − , well within the sensi- MNRAS000
Total magnetic field strength inside and outside the SNR as pre-dicted by the model presented in Sect. 6.1, assuming B = µ G (upper-yellow lines) and µ G (bottom-magenta lines). Solid and dashed curvesrefer to t = t age and t = t Sed , respectively. The radial coordinate is dividedby R sh ( t ) , which increases with time. be considered as a lower limit, in that χ (cid:28) would result in over-shooting the Fermi-LAT upper limits above 10 GeV.An interesting test for our model would be to look for the TeVemission produced through IC by escaping electrons. The differen-tial flux at 1 TeV is ∼ − erg s − cm − , well within the sensi- MNRAS000 , 1–19 () S. Loru et al. tivity range of current imaging atmospheric Cherenkov telescopes(IACTs). Unfortunately, the Cygnus Loop is very extended, whatmakes the observation very challenging for the small field of view(FoV) of IACTs. An attempt was made by the MAGIC collabora-tion (Reichardt Candel 2012), resulting only in upper limits (com-patible with our predictions). The large IC flux produced by theescaping electrons in the γ -ray band results from the large electrondensity as inferred from the radio data. In fact, radio data allow toestimate the remaining parameters, K ep and B , which are 0.15 and µ G, respectively, for our fiducial model shown in Figure 11. Inparticular, the magnetic field is determined by the absence of anyspectral break up to the highest frequency point detected by
Planck at 30 GHz. For our fiducial model the breaking frequency is locatedat ∼ GHz and below such energy the emission behaves like asingle power-law. Values of B much smaller than µ G are incom-patible with the radio data as shown in Figure 11, where we alsodisplay the synchrotron emission from a model with B = µ G,keeping all the other parameters unchanged. Such a low magneticfield implies ν br (cid:39) GHz and underestimates the synchrotronemission as measured by
Planck . In addition B = µ G implies K ep = . , a very large value that has never been inferred in otherSNRs.On the contrary, B (cid:29) µ G is still compatible with the radiodata, but it would violate the pressure equilibrium. In fact, the de-tection of H α emission from several regions of the forward shock(Blair et al. 2005) implies that the temperature of the CSM has tobe ≈ K, hence the ratio between magnetic and thermal pres-sures is P mag / P gas ≈ . ( B / µ G ) /( n / . − ) implying that B cannot be much larger than the value adopted here.In Figure 13, we show the profile of magnetic field strength in-side and outside the SNR at t = t Sed and at t = t age . In the first case,the amplification is very efficient, giving δ B / B = . , which af-ter the compression at the shock rises up to B = √ B (cid:39) µ G,while for r < R sh decreases due to adiabatic losses. In addi-tion, a precursor upstream of the shock develops with a thickness L pr (cid:39) . R sh ( t Sed ) . On the contrary, the amplification is inefficientat the present age, resulting in δ B / B = . and B (cid:39) µ G.A precursor is still present with L pr (cid:39) . R sh ( t age ) but is notvisible in the plotted scale. The peak observed at r / R sh = . corresponds, instead, to the plasma that has been shocked at the t = t Sed , namely when the magnetic field amplification was muchmore efficient. Nevertheless, the contribution of this region to theoverall radio emission today is negligible. The same profile is alsoshown for the case with B = µ G. Interestingly, the peak value at r / R sh = . is very close to the case with B = µ G, confirmingthat the magnetic field there was dominated by the amplificationprocess.In the Appendix A, we demonstrate how the inferred levelof turbulence in the precursor is compatible with that being de-termined by the competition between the CR amplification and thedamping due to ion-neutral friction. At the same time, this damp-ing can explain the temperature of the shock precursor as measuredthrough Balmer emission.Concerning the energy budget, the total content in the non-thermal particles located inside the SNR is . × erg and . × erg for electrons and protons, respectively. The total en-ergy in magnetic field instead is . × erg. Hence, it is clearthat the equipartition argument illustrated in Sect. 4 does not hold.This is not surprising, given that a SNR is a transient system wherenon-thermal particles do not have enough time to equilibrate withthe magnetic field which is, instead, a byproduct of instabilities in-volving mainly ions. Figure 11 shows that Cygnus Loop is still producing non-thermal X-ray emission thanks to the residual component of nonconfined electrons. Such flux is much smaller than the detected X-ray emission, estimated to be . × − erg s − cm − in the [0.7-1.85] keV interval (Tomida et al. 2016) which is, however, com-patible with being of purely thermal origin. In this work we do notattempt to model the thermal emission because it requires to ac-count for the different chemical abundances to fit the X-ray lines,and goes beyond our aims. Nevertheless, as a consistency check, wecan compare the electron temperature inferred from X-ray data withthe proton temperature estimated from our model. X-ray emissiondetected with ROSAT from the whole SNR allow to infer an elec-tron temperature of + − eV (Levenson et al. 1999). In our model,the post shock proton temperature is k B T p = /( ) m p u = eV, which implies that the electron to proton temperature ratiois T e / T p = . + . − . . Such a result is compatible with the findingthat for shock speed below ∼ km s − the equilibration betweenelectron and proton is quite efficient, resulting in T e / T p > . (see,eg. Ghavamian et al. 2001).A final comment concerns the value of K ep which is foundto be 0.15, quite larger than typical values estimated for youngSNRs (like Tycho or SN 1006), which are in the range − − − (Berezhko et al. 2013; Morlino & Caprioli 2012; Morlino et al.2009). This finding may be a peculiarity of the Cygnus Loop ormay indicate that the electron/proton ratio is larger for middle-agedSNRs, suggesting that K ep increases for decreasing shock speed.Indeed, the mechanism allowing electrons to be injected into theDSA is still far from being understood. Given the small Larmorradius, thermal electrons need to be pre-accelerated before to en-ter the DSA. Such pre-acceleration is probably due to kinetic in-stabilities that develop in the shock foot, as shown by particle-in-cell (PIC) simulations (Amano & Hoshino 2010; Riquelme &Spitkovsky 2011), which suggest that electron injection increasesfor increasing shock speed (Xu et al. 2019), contrary to our sug-gestion. Nevertheless, at the moment, PIC simulations are limitedto explore 1D systems, and cannot catch the complex phenomenol-ogy of 3D reality. It is also important that K ep may be lower thanwhat estimated here if additional mechanisms able to amplify themagnetic field are present downstream of the shock, like turbulentdynamo processes (Giacalone & Jokipii 2007). In such a case, thedownstream magnetic field increases without modifying the pro-ton maximum energy (which is mainly determined by the upstreammagnetic field). Hence, the hadronic γ -ray emission would remainunaltered but the number of electrons required to match the radiodata would be reduced because the product B n e is fixed by theradio flux. A systematic study of SNRs showing possible corre-lation between the electron/proton ratio with SNR properties canshed light on this difficult problem. We presented the spectral analysis performed on the whole CygnusLoop SNR and on its two peculiar regions, NGC 6992 and thesouthern shell, by using the Medicina and SRT data between 7.0and 24.8 GHz and the
Planck data at 30 and 40 GHz.Our observations at 8.5 GHz of the entire Cygnus Loop SNRconfirm the tendency suggested by the
Planck data, ruling out anyspectral curvature up to high radio frequencies. By modelling theradio and γ -ray emission, we constrained the maximum particleenergy (for both electrons and protons) at 65 GeV, and the mag-netic field strength at the shock at 10 µ G. The model description
MNRAS , 1–19 () ew radio observations of the Cygnus Loop of the radio data also constrains the electron density, revealing adominant IC emission from escaping electrons in the γ -ray spec-trum above ∼
10 GeV. This result sheds new light on the electroncontribution to the SNR spectral features at high energies. In thisrespect, new γ -ray observations with the next IACT generation, likethe Cherenkov Telescope Array (CTA), could be crucial to inves-tigate the emission produced through IC by escaping electrons atenergies ∼ TeV and place observing constraints on this spectraltendency. On the other hand, high-frequency radio data are also re-quired to better constrain the electron density and the backgroundmagnetic field B . The new multi-feed Q -band (33-50 GHz) re-ceiver (Navarrini et al. 2016), that is currently being implementedfor SRT, will allow us to explore this range.We investigated the integrated spectrum of NGC 6992 andthe southern shell between 7.0 and 44 GHz, by using our single-dish data and the Planck flux density measurements. Both regionspresent a spectrum flatter than the one associated with the wholeCygnus Loop SNR, showing no indication of a spectral cutoff. The
Planck data indicated a flux density rising at 44 GHz in the NGC6992 spectrum that we attributed to a significant dust-emission con-tribution. In the case of the southern shell,
Planck measurementssuggested a concave-up spectral shape that we tentatively ascribedto an efficient production of CRs, which could modify the shockstructure. For both regions, further sensitive flux density measure-ments in the range between ∼ and ∼ GHz are needed to firmlycharacterise their spectral tendency.Unlike the case of the whole Cygnus Loop SNR, we could notmodel the non-thermal emission from NGC 6992 and the south-ern shell, because no separated γ -ray measurements are availablefor these regions. Nevertheless, we exploited the fact that the ra-dio spectrum of both regions showed no indications for a spec-tral steepening to establish a lower limit on the break frequencyof ∼
25 GHz and estimate the magnetic field strength under the as-sumption of equipartition between the particle and magnetic fieldenergy. For the southern shell, we obtained a value very similar tothat estimated in the same way for the whole SNR, suggesting thatthis region is a good approximation for the properties of the wholeSNR. In the case of NGC 6992, we obtained a higher magnetic fieldwith respect to the average Cygnus Loop value. In addition, this re-gion presents a harder radio spectrum with respect to the wholeSNR. Both these findings may be a consequence of the fact that theshock is currently transiting to a radiative phase. However, thesehypotheses can be tested only through a proper modelling of thenon-thermal emission associated with this region possibly account-ing for the presence of thermal Hydrogen which can significantlymodify the shock dynamics (Morlino et al. 2013). In this regard,high spatial resolution γ -ray observations, which will be possiblewith CTA, will be crucial to achieve spatially-resolved images ofthe Cygnus Loop and constrain the maximum particle energy andmagnetic field strength of its peculiar regions through refined mod-els, like the one used in this work for the whole SNR. ACKNOWLEDGEMENTS
The Sardinia Radio Telescope is funded by the Department of Uni-versity and Research (MIUR), the Italian Space Agency (ASI), andthe Autonomous Region of Sardinia (RAS), and is operated as aNational Facility by the National Institute for Astrophysics (INAF). We deeply thank W. Reich for assistance and the very useful sug-gestions. We are very grateful to H. Katagiri for the useful discus-sion about the
Fermi -LAT data. SL acknowledge contribution fromthe grant INAF CTA-SKA "Probing particle acceleration and γ -ray propagation with CTA and its precursors". GM acknowledgessupport from Grants ASI/INAF n. 2017-14-H.O, SKA- CTA-INAF2016 and INAF-Mainstream 2018. DATA AVAILABILITY
The data underlying this article are all reported in the tables of thepaper.
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APPENDIX A: THE SHOCK PRECURSOR
One of the main finding of our acceleration model is the fact thatthe particle maximum energy in the ST stage decreases in time like ∼ t − . This is quite remarkable because the streaming instability(resonant and non resonant) predicts a less pronounced decrease,with δ (cid:54) . One possible explanation for our finding is connectedto the presence of neutral Hydrogen in the CSM, which in the caseof Cygnus Loop is firmly established by the detection of H α emis-sion (see, e.g. Blair et al. 2005). In fact, neutral atoms can dampthe amplified magnetic waves, making the particle escape from thesource easier. Here, we show that this assumption is compatible with the level of magnetic turbulence that we have found and abovewhich, quite remarkably, can also account for the temperature in-crease observed in the precursor ahead of the shock (Katsuda et al.2016).We start from the common assumption that the magnetic tur-bulence upstream consists of Alfvén waves excited by streaming in-stability with a rate (integrated over all momenta) given by (Skilling1975) Γ cr = π v A δ B ∂ P cr ∂ x , (A1)where v A = B /√ πρ i is the Alfvén speed, ρ i is the ion massdensity and P cr the CR pressure at the shock. At the same time, theturbulence is damped by the ion-neutral friction with a dampingrate (Kulsrud & Cesarsky 1971): Γ in = ν in = . × − n n cm − (cid:18) T K (cid:19) . s − , (A2)where ν in = n n (cid:104) σ v (cid:105) is the ion neutral collision frequency, n n isthe neutral Hydrogen density and T the plasma temperature. Forreasonable values of n n and T , the damping timescale τ in = Γ − ranges between few years to few tens of years, hence it is muchsmaller than the advection time in the precursor, given by t adv = D ( p max )/ u (cid:39) yr. In such a situation, the level of magneticturbulence is given by the equilibrium condition between dampingand growth, i.e. Γ in = Γ cr . Approximating ∂ x P cr ≈ P cr / L pr , where L pr = D ( p max )/ u sh (cid:39) pc is the CR precursor length, the equilib-rium condition gives: (cid:18) δ B B (cid:19) = P cr B /( π ) v A u sh τ in t adv . (A3)Using the parameter values in Table 8 and assuming a neutral frac-tion of 0.5, we found δ B / B = . , namely 3 times larger thanthe value found in Sect. 6.2. Given the uncertainties in several pa-rameters, we consider this result in fair agreement with our model.An interesting method to test the level of magnetic turbu-lence in the shock precursor is through the measurement of itstemperature. Blair et al. (2005) and Katsuda et al. (2016) detectedBalmer emission from non-radiative shocks in the northeastern partof the Cygnus Loop, reporting a clear detection also in the re-gion upstream of the shock. Measuring the H α line width, theyinferred a temperature of ∼ , K in an extended region of ∼ . ( d / ) pc attributed to a photo-ionization precursor plusa smaller region close to the shock with T ∼ , K and size ∼ . × ( d / ) cm, which they attribute to a tiny CR pre-cursor. However, temperatures T > , K lead to complete ion-ization of neutral hydrogen in equilibrium, so that H α emissionfrom the filament would not be detected. Thus, the reported ob-servation implies that the pre-shock gas is heated in a thin precur-sor. Katsuda et al. (2016) argued that the damping of Alfvén wavescould account for at least a fraction of this heating, and here wewant to investigate this scenario. The total energy density releasedby the turbulent damping into a plasma element that crosses thewhole precursor is ∆ U = δ B /( π ) Γ in t adv . This energy is com-pletely converted into heating, hence, neglecting radiation losses,the final plasma temperature just ahead of the shock is given bythe relation ∆ U = . n k B ( T pr − T ) , where k B is the Boltzmannconstant and T ≈ K is the far upstream temperature. Using thesame values as above, we have T pr = T + ξ cr u sh v A k B (cid:39) T + . × K (A4) MNRAS , 1–19 () ew radio observations of the Cygnus Loop a value in between the extended and the small precursors’ temper-atures. This is a quite remarkable result, in that we have not tunedany parameter of the model to get it, and demonstrates that Alfvénwave damping can be the main process to heat the shock precur-sor. One should note, however, that the CR precursor length thatwe estimated is ∼ times larger than the extended precursor and ∼ times larger than the smaller and hotter precursor. Hence theextended precursor could be mainly heated by CRs rather than byionizing photons. On the other hand, the thinner precursor requiresan additional heating which may be provided either by very low en-ergy CRs ( E (cid:46) MeV) or by fast neutrals (Katsuda et al. 2016).A proper answer can be provided by using a model for particle ac-celeration in presence of neutral plasma (Morlino et al. 2013).
This paper has been typeset from a TEX/L A TEX file prepared by the author.MNRAS000