The TeV emission of Ap Librae: a hadronic interpretation and prospects for CTA
Maria Petropoulou, Georgios Vasilopoulos, Dimitrios Giannios
aa r X i v : . [ a s t r o - ph . H E ] A ug Mon. Not. R. Astron. Soc. , 1– ?? (2013) Printed 1 August 2018 (MN L A TEX style file v2.2)
The TeV emission of Ap Librae: a hadronic interpretation andprospects for CTA
M. Petropoulou ⋆ † , G. Vasilopoulos ‡ & D. Giannios Department of Physics and Astronomy, Purdue University, 525 Northwestern Avenue, West Lafayette, IN 47907, USA Max-Planck-Institut f¨ur extraterrestrische Physik,Giessenbachstraße, 85748 Garching, Germany
Received / Accepted
ABSTRACT
Ap Librae is one out of a handful of low-frequency peaked blazars to be detected at TeV γ -rays and the only one with an identified X-ray jet. Combined observations of Fermi -LAT athigh energies (HE) and of H.E.S.S. at very high energies (VHE) revealed a striking spectralproperty of Ap Librae; the presence of a broad high-energy component that extends morethan nine orders of magnitude in energy and is, therefore, hard to be explained by the usualsingle-zone synchrotron self-Compton model. We show that the superposition of di ff erentemission components related to photohadronic interactions can explain the γ -ray emission ofAp Librae without invoking external radiation fields. We present two indicative model fits tothe spectral energy distribution of Ap Librae where the VHE emission is assumed to originatefrom a compact, sub-pc scale region of the jet. A robust prediction of our model is VHE fluxvariability on timescales similar to those observed at X-rays and HE γ -rays, which can befurther used to distinguish between a sub-pc or kpc scale origin of the TeV emission. Wethus calculate the expected variability signatures at X-rays, HE and VHE γ -rays and showthat quasi-simultaneous flares are expected, with larger amplitude flares appearing at γ -rays.We assess the detectability of VHE variability from Ap Librae with CTA, next generation ofIACTs. We show that ∼ hr timescale variability at E γ > . Key words: astroparticle physics – galaxies: active – galaxies: BL Lacartae objects: individ-ual: Ap Librae – gamma-rays: galaxies – radiation mechanisms: non-thermal
Blazars with extremely weak optical emission lines or, in manycases, featureless optical spectra, are classified as BL Lac objects.The majority of BL Lac objects that are detected at very highenergies (VHE, E γ >
100 GeV) by ground-based Cherenkovtelescopes belongs to the high-frequency peaked (HBL) subclass(e.g. Wakely & Horan 2008; Hinton & Hofmann 2009) that ischaracterized by a low-energy spectral component peaking at fre-quencies ν p > Hz (Padovani & Giommi 1995). The quiescentemission as well as individual flares from TeV-detected blazarshave been successfully explained by the synchrotron self-Compton(SSC) model (e.g. Maraschi et al. 1992; Bloom & Marscher1996; Mastichiadis & Kirk 1997; Konopelko et al. 2003;Celotti & Ghisellini 2008; Weidinger & Spanier 2010;HESS Collaboration et al. 2013; B¨ottcher et al. 2013). In thisscenario, electron synchrotron radiation is invoked to explainthe low-energy hump of the spectral energy distribution (SED), ⋆ E-mail: [email protected] † Einstein Fellow ‡ E-mail: [email protected] while it serves as the seed photon field for inverse Compton (IC)scattering, which, in turn, results in the observed high-energyemission. Despite its success the SSC model faces di ffi cultiesin explaining the observed emission from certain low-frequencypeaked (LBL; ν p < Hz) and intermediate-frequency peaked(IBL; 10 Hz <ν p < Hz) sources. Examples of VHE emittingLBL that challenge the SSC interpretation are BL Lacartae(Ravasio et al. 2002) and W Comae (Acciari et al. 2009) (see alsoB¨ottcher et al. (2013)). One of the most representative sourcesthough is the LBL Ap Librae (alternative name QSO B1514-24).Ap Librae, lying at a redshift z = . ± .
002 (Disney et al.1974; Jones et al. 2009), belongs to a handful of LBL that havebeen detected at VHE, such as BL Lacartae (Albert et al. 2007)and S5 0716 +
714 (Anderhub et al. 2009), while it is the onlyTeV BL Lac object with a detected X-ray jet (Kaufmann 2011;Kaufmann et al. 2013) . The first detection of Ap Librae at E γ >
100 GeV by H.E.S.S. was reported in 2010 (Hofmann 2010)while the resulting observations have been recently presented in For a review on the extended kpc-scale jets of radio-loud AGN, seeHarris & Krawczynski (2006). © Petropoulou, Vasilopoulos, Giannios
H.E.S.S. Collaboration et al. (2015). These, in combination withthe X-ray and high-energy (HE)
Fermi -LAT observations (100MeV–300 GeV), revealed an unexpected broad high-energy hump,spanning more than nine orders of magnitude in energy (fromX-rays to TeV γ -rays). As first noted by Fortin et al. (2010),Tavecchio et al. (2010) and later by Sanchez et al. (2012), the SEDof Ap Librae cannot be explained by the usual SSC model due tothe extreme broadness of the high-energy component.As the SSC model falls short in explaining the broadbandspectrum of Ap Librae, alternative scenarios have been proposed(Hervet et al. 2015; Sanchez et al. 2015; Zacharias & Wagner2016). In general terms, these models invoke IC scattering of ex-ternal photons fields (EC) in order to fill in the gap between thehard X-rays and VHE γ -rays, caused by the SSC cuto ff at ener-gies below the Fermi -LAT band. In particular, Hervet et al. (2015)showed that photons from the Broad Line Region (BLR) may beup-scattered by electrons in the jet at sub-pc scales (blob) making asignificant contribution to the
Fermi -LAT band, while the externalIC emission from the interaction of the blob electrons with the pc-jet radiation contributes the most at the H.E.S.S. energy band. TheSED of Ap Librae was successfully described from GHz frequen-cies up to VHE γ -rays at the cost, however, of increased complexityand number of free parameters.A second scenario invokes the kpc-scale jet of Ap Librae thathas been observed both in radio and X-rays (Kaufmann et al. 2013).In this case, the VHE emission is explained by IC scattering ofthe cosmic microwave background (CMB) radiation by relativisticelectrons of the kpc jet (Sanchez et al. 2015; Zacharias & Wagner2016). A robust prediction of this model is therefore the lack ofvariability at VHE in Ap Librae. In this scenario the jet is as-sumed to remain highly relativistic, i.e. with bulk Lorentz fac-tors Γ ≫
1, even at kpc scales. It is noteworthy that
Fermi -LATobservations have recently ruled out the IC / CMB interpretationof the X-ray emission from the kpc jets of other powerful AGN(Meyer & Georganopoulos 2014; Meyer et al. 2015).Recently, Petropoulou & Mastichiadis (2015) (henceforth,PM15) showed that broad HE spectra with significant curvature canbe obtained outside the usual SSC and EC framework, if protons areaccelerated at moderate energies ∼ − eV, i.e. just above the“knee” of the cosmic-ray spectrum (for possible particle accelera-tion mechanisms in blazars, see e.g. Biermann & Strittmatter 1987;Giannios 2010; Sironi et al. 2013, 2015). The broadness of thespectra produced in this scenario can be understood as follows. InBL Lacs, the most important target photon field for photohadronic( p γ ) interactions with the relativistic protons is the synchrotron ra-diation of the co-accelerated (primary) electrons, which emerges asthe low-energy hump of their SED. The p γ interactions are com-prised of two processes of astrophysical interest, namely the Bethe-Heitler pair production ( pe ) and the photopion production ( p π ).Moreover, high-energy photons produced by the decay of neutralpions can be absorbed in the source, thus giving rise to an electro-magnetic cascade which peaks at lower energies (Mannheim et al.1991; Mannheim 1993). Both processes increase the relativisticpair content of the emission region by injecting electron-positronpairs ( e − e + ), which, in turn, undergo synchrotron and IC cooling asprimary electrons. Their radiative signatures will be, in principle,imprinted on the blazar’s SED (see also Petropoulou et al. 2015).PM15 showed, in particular, that the synchrotron emissionfrom pe pairs may have important implications for blazar emis-sion. The broad injection energy distribution of pe pairs (e.g.Kelner & Aharonian 2008) is also reflected at their synchrotronspectrum, which also appears extended and curved. The pe syn- chrotron spectrum might appear as a broad component in the rangeof hard X-rays ( &
40 keV) to soft γ -rays ( .
400 MeV) for cer-tain parameter values (see e.g. Figs. 4 and 5 in PM15). Giventhat the secondary pairs from p π interactions are injected with adi ff erent rate and at di ff erent energies than the Bethe-Heitler sec-ondaries (Kelner & Aharonian 2008; Dimitrakoudis et al. 2012), abroad range of HE spectra is expected (e.g. Petropoulou et al. 2015;Cerruti et al. 2015).In this paper, we show that the superposition of di ff erent emis-sion components related to p γ interactions can explain the HE andVHE γ -ray emission of Ap Librae without invoking external radi-ation fields. Most important is, though, that VHE variability is arobust prediction of our model that can be used to distinguish be-tween a sub-pc or kpc-scale origin of the VHE emission in Ap Li-brae. Being an important diagnostic tool, we calculate first the ex-pected variability signatures at di ff erent energy bands (X-rays, HEand VHE γ -rays) and then focus on VHE γ rays. In this paper weassess the detection of VHE variability from Ap Librae with thefuture TeV Cherenkov Telescope Array (CTA; Actis et al. 2011)which is designed to surpass the sensitivity of current TeV tele-scopes.This paper is structured as follows. In Sec. 2 we present themulti-wavelength data used for the SED compilation and in Sec. 3we outline the adopted model. The results of our model applicationto Ap Librae are presented in Sec. 4. In the same Section we presentthe model predictions on the multi-wavelength variability, while fo-cusing on the VHE γ -rays. The prospects for CTA are presentedin Sec. 5. We continue in Sec. 6 with a discussion of our resultsand conclude in Sec. 7 with a summary. For the required transfor-mations between the reference systems of the blazar and the ob-server, we have adopted a cosmology with Ω m = . Ω Λ = . H =
70 km s − Mpc − . The redshift of Ap Librae z = .
049 corre-sponds to a luminosity distance D L = . γ -ray spectra. The high-energy spectrum of Ap Librae composed by
Fermi -LAT and H.E.S.S. observations has recently been presentedby H.E.S.S. Collaboration et al. (2015). The authors analyzed fiveyears of
Fermi -LAT data (MJD 54682-56508) and divided theiranalysis into a quiescent period (MJD 54682-56305 and MJD56377-56508) and a flaring period (MJD 56306-56376). The VHEobservations by H.E.S.S. were performed during the period MJD55326-55689, i.e. within the quiescent period of
Fermi -LAT obser-vations. No H.E.S.S. data have been presented for the period of the
Fermi -LAT flare and no results regarding the variability at VHEhave been published by the time of writing. We complement ouranalysis and SED modelling with multi-wavelength observationsthat were also temporally coincident with the
Fermi -LAT quiescentperiod. Data from the flaring period of Ap Librae in GeV energiesare therefore exlcuded from the present analysis.We searched the
HEASARC archive for available X-ray obser-vations of Ap Librae during the quiescent period of Fermi -LATobservations (MJD 54682-56305). The source was observed seventimes by
Swift (obs-ids: 00036341005-11, MJD 55247-55783) andfour times by
RXTE (MJD 55387.9-55391.8) during the quiescent http://heasarc.gsfc.nasa.gov/docs/archive.html © , 1– ?? he γ -ray emission of Ap Librae period defined above. Swift / XRT products were downloaded fromthe
HEASARC archive and analysed following the standard pro-cedures described in the
Swift data analysis guide . Swift / XRTproducts were generated with the xrtpipeline and the eventswere extracted using the command line interface xselect . Theauxiliary response files were produced with xrtmkarf . For the
Swift / XRT analysis the latest response matrix was used, as providedby the
Swift calibration database caldb . RXTE publication-gradedata products were downloaded by the
HEAVENS webpage . TheX-ray spectra were analysed with xspec (version 12.8.2, Arnaud1996). The spectra were fitted simultaneously with an absorbedpower-law model with the addition of a scaling factor to accountfor variability and instrumental di ff erences. The X-ray absorptionwas modelled using the tbnew code, a new and improved versionof the X-ray absorption model tbabs (Wilms et al. 2000), whilethe atomic cross sections were adopted from Verner et al. (1996).The column density was fixed based on the value provided by theLeiden / Argentine / Bonn (LAB) Survey of Galactic HI (N H , GAL = × cm − , Kalberla et al. 2005). Swift / XRT spectral fittingshowed evidence of small flux variability ( < Γ = . ± .
09. All the above are consistentwith the findings of Kaufmann et al. (2013). For the SED presenta-tion, we plot the
Swift / XRT spectra with the minimum (4.6 × − erg cm − s − ) and maximum (5.4 × − erg cm − s − ) derivedfluxes from all the available Swift / XRT observations.Ap Librae was observed by the
Swift ultraviolet and opti-cal telescope (UVOT) with all its available filters. We analysedthe
Swift / UVOT images and derived the corresponding magnitudesof Ap Librae. Additional optical observations of the system wereperformed by the FERMI / SMARTS project (Bonning et al. 2012).We used the averaged B, R, J and K magnitudes provided bythe SMARTS database for the quiescent period of Ap Librae.All the observed fluxes were corrected for extinction followingCardelli et al. (1989) where the reddening was set to E ( B − V ) = . Swift / XRT, UVOT and SMARTS fluxeswith the published values reported by Sanchez et al. (2015) andfound that they are compatible.Ap Librae has been monitored at 15 GHz by the Very LongBaseline Array (VLBA) as part of the MOJAVE program . The ra-dio emission originates from the pc-scale jet and shows no signsof variability within the period MJD 53853-55718 covered bythe MOJAVE observations (Sanchez et al. 2015). In our analy-sis we adopt the time-averaged flux at 15 GHz as obtained bySanchez et al. (2015). At higher radio frequencies (30 – 353 GHz)we used the Planck measurements from the Early Release Com-pact Source Catalog (ERCSC, Planck Collaboration et al. (2011))and we included the data at 3.4, 4.6, 12, and 22 µ m from the Wide-field Infrared Survey Explorer (WISE, Wright et al. (2010)).The compilation of the multi-wavelength SED of Ap Li-brae was completed with the inclusion of archival data from theNED database (Dixon 1970; Kuehr et al. 1981; Wright & Otrupcek1990; Wright et al. 1994; Condon et al. 1998; Voges et al. 1999;Healey et al. 2007; Cusumano et al. 2010b,a; Murphy et al. 2010;Bianchi et al. 2011; Giommi et al. 2012; D’Elia et al. 2013; Planck Collaboration et al. 2014; Evans et al. 2014; Boller et al.2016).
In this paper we focus on the emission from the core region ofAp Librae. The contribution of the extended jet to the total X-ray flux is .
10% (Kaufmann et al. 2013; Sanchez et al. 2015)and can be, therefore, safely neglected in our modelling. A multi-wavelength spectrum of the core emission from Ap Librae extend-ing from GHz radio frequencies up to TeV γ -rays was compiled us-ing the data described in the previous section. To explain the SEDwe invoke: i) a compact (sub-pc scale) region for the non-thermalemission from IR wavelengths to VHE γ rays, ii) an extended (pc-scale) region for the radio ( ∼ / UV thermal emission.
We assume that the region responsible for the core emission ofAp Librae (from IR wavelengths up to VHE γ -rays) can be de-scribed as a spherical blob of radius r ′ b , containing a tangled mag-netic field of strength B ′ b and moving towards us with a Dopplerfactor δ D7 . Protons and (primary) electrons are assumed to be ac-celerated to relativistic energies and to be subsequently injectedisotropically in the volume of the blob at a constant rate. The lattertranslates to a particle injection luminosity L ′ i that can be written indimensionless form as ℓ i = σ T L ′ i / π r ′ b m i c , where i = e , p . The ac-celerated particle distributions at injection are modelled generallyas broken power laws, namely N ′ i ( γ ′ ) ∝ A i , γ ′− p i , for γ ′ min , i γ ′ <γ ′ br , i and N ′ i ( γ ′ ) ∝ A i , γ ′− p i , e − (cid:16) γ ′ /γ ′ i , max (cid:17) b for γ ′ br , i < γ ′ < γ ′ max , i , where b is the steepness of the exponential cuto ff (e.g. Lefa et al. 2011)and A i , , are normalization constants.The production of mesons, namely pions ( π ± , π ), muons ( µ ± )and kaons ( K ± , K ), is a natural outcome of p π interactions tak-ing place between the relativistic protons and the internal photons;the latter are predominantly synchrotron photons emitted by rel-ativistic electrons . At any time, the relativistic electron popula-tion is comprised of those that have undergone acceleration (pri-mary) and those that have been produced by other processes (sec-ondary). These include (i) the decay of π ± , i.e. π + → µ + + ν µ , µ + → e + + ¯ ν µ + ν e , (ii) the direct production through the Bethe-Heitler process p γ → p + e − + e + and (iii) the photon-photon ab-sorption ( γγ ) γγ → e + + e − . In addition, π decay into VHE γ -rays(e.g. E γ ∼
10 PeV, for a parent proton with energy E p =
100 PeV),and those are, in turn, susceptible to ( γγ ) absorption and can ini-tiate an electromagnetic cascade (Mannheim et al. 1991). It is thesynchrotron radiationof secondary electrons that has a key role inshapingthehigh-energypartoftheSEDinApLibrae(see Sec. 4).Relativistic neutrons and neutrinos ( ν µ , ν e ) are also producedin p π interactions and together with photons, electrons and protonscomplete the set of the five stable particle populations, that are atwork in the compact emitting region of the blazar. We note thatall particles are assumed to escape from the emitting region in acharacteristic timescale, which is set equal to the photon crossingtime of the source, i.e. t ′ i , esc = r ′ b / c . This energy-independent term Henceforth, quantities measured in the rest frame of the blob are denotedwith a prime. Henceforth, we refer to electrons and positrons commonly as electrons. © , 1–, 1–
100 PeV),and those are, in turn, susceptible to ( γγ ) absorption and can ini-tiate an electromagnetic cascade (Mannheim et al. 1991). It is thesynchrotron radiationof secondary electrons that has a key role inshapingthehigh-energypartoftheSEDinApLibrae(see Sec. 4).Relativistic neutrons and neutrinos ( ν µ , ν e ) are also producedin p π interactions and together with photons, electrons and protonscomplete the set of the five stable particle populations, that are atwork in the compact emitting region of the blazar. We note thatall particles are assumed to escape from the emitting region in acharacteristic timescale, which is set equal to the photon crossingtime of the source, i.e. t ′ i , esc = r ′ b / c . This energy-independent term Henceforth, quantities measured in the rest frame of the blob are denotedwith a prime. Henceforth, we refer to electrons and positrons commonly as electrons. © , 1–, 1– ?? Petropoulou, Vasilopoulos, Giannios mimics the adiabatic expansion of the source, since the steady-stateparticle distributions derived by solving a kinetic equation contain-ing a physical escape term or an adiabatic loss term are similar.The interplay of the processes governing the evolution of theenergy distributions of the five stable particle populations is formu-lated with a set of five time-dependent, energy-conserving kineticequations. To simultaneously solve the coupled kinetic equationsfor all particle types we use the time-dependent code described inDimitrakoudis et al. (2012).
As we show in Sec. 4 the emission from the compact emittingregion of Ap Librae cannot explain the Planck and MOJAVE ra-dio observations, as the synchrotron spectrum is self-absorbed at ν . Hz; this is a common feature of single-zone models forblazar emission (see e.g. Figs. 7-10 in Celotti & Ghisellini (2008)for leptonic models and B¨ottcher et al. (2013); Petropoulou et al.(2015) for hadronic models). Radio emission at GHz frequenciescan be more naturally explained as synchrotron radiation producedfrom a larger and less compact region, such as the base of the pc-scale jet, i.e. the radio core (Lister et al. 2013). The pc-scale jet canbe modeled using a series of a (large ∼
50) number of slices, wherethe magnetic field strength and particle distributions are assumed toevolve self-similarly along the jet (see e.g. Hervet et al. 2015). Asour focus is the broad HE spectrum of Ap Librae, we do not adopt asophisticated jet model for the radio emission (e.g. Potter & Cotter2012, 2013). Instead, we assume that the radio emission is pro-duced by a spherical region of pc-scale size, further away from thecentral engine. Our choice and a possible physical interpretation arediscussed in Sec. 6. We have also verified that the external Comptonscattering of the synchrotron radiation field from the extended ra-dio blob by the electrons in the sub-pc blob can be neglected for theadopted parameters (see Tables 1-2 and Appendix in Petropoulou(2014)). On the other way around, the radiation produced by thesub-pc blob is negligible for EC by the electrons in the pc-scaleregion, as long as their separation distance is & . The host galaxy of Ap Librae has been clearly detected in the(near-infrared) H-band (Kotilainen et al. 1998) and in the (blue) B-band (Hyv¨onen et al. 2007). The multi-colour imaging results sug-gest that the host galaxy of Ap Librae, as for most low-redshiftBL Lac objects, is a luminous and massive elliptical galaxy; itsmass has been estimated to be 10 . ± . M ⊙ (Woo et al. 2005).Hyv¨onen et al. (2007) showed that the luminosity ratio between thenuclear region and the host galaxy is 1.7 and 0.58 in the U andB bands. Since the contribution of the host galaxy cannot be ne-glected we will model it based on an appropriate galaxy template.In particular, we use the template of an elliptical galaxy producedby a single episode of star formation with age 13 Gyr, total mass6 × M ⊙ , and solar metallicity (Silva et al. 1998). The normal-ization of the spectrum has been ajusted to fit the data. In particular,the fluxes of the template were multiplied by a factor of 2 . / ff erence between the real and simulated hostgalaxy. Table 1.
Model parameters describing the sub-pc scale region producingthe non-thermal IR-TeV emission of Ap Librae. The parameters describingthe particle distributions refer to those at injection.Parameters model A model B B ′ (G) 2.5 5 r ′ b (cm) 10 × δ D θ (°) † Γ † ℓ e × − . × − γ ′ e , min
10 10 γ ′ e , br . × . × γ ′ e , max . × . × p e , p e , b e‡ ℓ p × − × − γ ′ p , min γ ′ p , br − − γ ′ p , max . × × p p , p p , − − b p † Assuming that the apparent speed deter-mined for the pc-scale jet, β app = . ± . c (Lister et al. 2016), applies also to the sub-pcjet, we solve for the bulk Lorentz factor Γ andangle θ , given the Doppler factor δ D derivedfrom the SED fitting. ‡ This parameter cannot be constrained; theexact value does not a ff ect the fit, because ofthe steep electron distribution. We thus adopt b e = b p . The accretion disk can illuminate the gas in close proximity of theblack hole, thus giving rise to the emission from the BLR. Thesetwo external radiation fields can serve as target photons for inverseCompton scattering by the electrons of the sub-pc scale region. Dif-ferent analyses of the faint H α emission lines result in di ff erent es-timates of the BLR luminosity, ranging between L BLR = . × erg s − (Stickel et al. 1993) and 9 . × erg s − (Morris & Ward1988). Nevertheless, both estimates suggest a low-luminosity BLR.Assuming a BLR covering factor of ξ =
1% as inferred for otherBL Lac objects (Stocke et al. 2011; Fang et al. 2014), the accre-tion disk luminosity is given by L disk . L BLR , ξ − − erg s − .The inner radius of the BLR can be also estimated as R BLR ≃ × L / , cm (Ghisellini & Tavecchio 2008). Being conserva-tive, we do not include in our modelling any external photon fields.In fact, as we detail in Sec. 4 the HE and VHE γ -ray emission ofAp Librae can be explained alone with radiation produced inter-nally. Inclusion of the accretion disk and BLR radiation fields inthe fitting procedure might result in di ff erent parameter values butit would not alter our main conclusions. Aim of this paper is to demonstrate the possibility of producingbroad HE non-thermal spectra from a single compact emitting re- © , 1– ?? he γ -ray emission of Ap Librae -14-13-12-11-10 8 10 12 14 16 18 20 22 24 26 28 30 32 34-6 -3 0 3 6 9 12 15 18 l og ν F ν ( e r g s - c m - ) log ν (Hz)log E (eV)MODEL A Fermi/LATHESSNED archivalSwift/XRTSwift/XRTRXTESwift/UVOTSMARTSWISEPlanckMOJAVEno EBLpc-scalehost galaxye-syn+sscp-synp π +pe+ γ γ total -14-13-12-11-10 8 10 12 14 16 18 20 22 24 26 28 30 32 34-6 -3 0 3 6 9 12 15 18 l og ν F ν ( e r g s - c m - ) log ν (Hz)log E (eV)MODEL BMODEL BMODEL BMODEL B Fermi/LATHESSNED archivalSwift/XRTSwift/XRTRXTESwift/UVOTSMARTSWISEPlanckMOJAVEno EBLpc-scalehost galaxye-syn+sscp-synp π +pe+ γ γ total Figure 1.
SED of Ap Librae compiled using multi-wavelength data (filled colored symbols) collected by various instruments as noted in the legend (for details,see Sec. 2). The grey open circles depict archival data obtained from the NED database. The multi-wavelength spectrum (thick gold line) is composed of theemission from the pc-scale radio emitting region (grey solid line), the host galaxy (magenta solid line), and the emission from the sub-pc region. This isdecomposed into the following components: SSC radiation from primary electrons (orange dashed line), proton synchrotron radiation (dark cyan dotted line),and synchrotron radiation from secondary electrons produced by p γ and γγ processes (red dash-dotted line). The spectrum without taking the EBL absorptioninto account is overplotted with a black dashed line. The results for models A and B are displayed in the left and right panels, respectively. For interpretationof the references to colour in this figure legend, the reader is referred to the web version of this article. Table 2.
Model parameters of the extended (pc-scale) region used for mod-elling radio emission of Ap Librae.Parameter Value B ′ (G) 0.01 r ′ (cm) 1 . × δ D θ (°) † Γ ℓ e . × − γ ′ e , min × γ ′ e , br × γ ′ e , max × p e , p e , b e ≫ † Same as in Table 1. gion instead of deriving a unique parameter set as determined bythe best χ fit to the data. We, therefore, present two indicativemodel fits to the SED of Ap Librae that di ff er only in the prop-erties of the compact component. We will refer to these as modelsA and B (see Table 1). The parameter values that describe the radio-emitting region are summarized in Table 2.Our results for models A and B are presented, respectively,in the left and right panels of Fig. 1. The total multi-wavelengthspectrum (thick gold line) is composed of the emission from thepc-scale radio emitting region (grey solid line), the host galaxy(magenta solid line), and the emission from the sub-pc region. Thelatter is decomposed into the following emission components: theSSC radiation from primary electrons (orange dashed line), the proton synchrotron radiation (dark cyan dotted line), and the syn-chrotron radiation from secondary electrons produced by the p γ and γγ processes (red dash-dotted line). The black dashed curveshows the spectrum before the attenuation on the EBL and indicatesthe degree of the internal to the source γγ absorption. Both modelsprovide a satisfactory representation of the source’s SED withoutthe need of external photon sources to account for the Fermi -LATand H.E.S.S. data. The broad and curved γ -ray spectra obtained inboth models are a natural outcome of the leptohadronic scenario,despite the fact that the radiative processes responsible for the X-ray and γ -ray emission are di ff erent. This can be understood byinspection of the various emission components that comprise thetotal emission from the sub-pc scale region.The X-ray emission in model A is mainly produced by theSSC emission of primary electrons (orange dashed line) and, in thisregard, it resembles the pure leptonic SSC models (see e.g. Fig. 3in Sanchez et al. (2015)). Note, however, that at 10 − Hz( ∼ . − p π and γγ processes dominates the γ -ray emission in the Fermi -LAT andH.E.S.S. energy bands, similarly to what have been shown for sev-eral other HBL (e.g. Petropoulou et al. 2015, 2016). While in HBLthe target photons for p π interactions belong to the low-energycomponent of the SED, in the case of Ap Librae, which is an LBL,the photons of the low-energy hump are less energetic and typi-cally cannot satisfy the energy threshold condition for pion pro-duction. In particular, for protons with Lorentz factors γ ′ p , the en-ergy threshold condition for pion production is satisfied by pho-tons with observed energies ǫ & δ D ¯ ǫ th /γ ′ p ≃ . δ D , /γ ′ , where¯ ǫ th =
145 MeV. Given that the maximum energy of the protons is γ ′ p , max ∼ (10 ) in model A (model B), hard X-ray photons ( ≫ © , 1–, 1–
145 MeV. Given that the maximum energy of the protons is γ ′ p , max ∼ (10 ) in model A (model B), hard X-ray photons ( ≫ © , 1–, 1– ?? Petropoulou, Vasilopoulos, Giannios -13.5-13-12.5-12-11.5-11-10.5-10-9.5 8 10 12 14 16 18 20 22 24 26 28 30 32 34-6 -3 0 3 6 9 12 15 18 l og ν F ν ( e r g s - c m - ) log ν (Hz)log E (eV)MODEL A shapshotsaverage (15 hr)Fermi/LATFermi/LAT flareHESSNED archivalSwift/XRTSwift/XRTRXTESwift/UVOTSMARTSWISEPlanckMOJAVE -13.5-13-12.5-12-11.5-11-10.5-10-9.5 8 10 12 14 16 18 20 22 24 26 28 30 32 34-6 -3 0 3 6 9 12 15 18 l og ν F ν ( e r g s - c m - ) log ν (Hz)log E (eV)MODEL B shapshotsaverage (41 hr)Fermi/LATFermi/LAT flareHESSNED archivalSwift/XRTSwift/XRTRXTESwift/UVOTSMARTSWISEPlanckMOJAVE Figure 2.
SED snapshots (grey thin lines) as obtained in models A and B for the fiducial flare discussed in text. The time-averaged spectrum is overplotted(black dashed line). In addition to the observations shown in Fig. 1, we include the time-averaged
Fermi -LAT spectrum during the period MJD 56306-56376(red symbols) for comparison reasons. For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article. keV) will serve as targets for photopion interactions with the lessenergetic protons. As the energy threshold for Bethe-Heitler pairproduction is lower, protons with γ ′ p = (10 ) will interact with ∼ keV (eV) photons. These simple estimates indicate that the result-ing γ -ray emission is a non-linear combination of various radiativeprocesses.In model B, because of the larger γ ′ p , max and stronger magneticfield, the proton synchrotron component dominates the soft-to-hardX-ray band (right panel in Fig. 1), while the synchrotron radia-tion from Bethe-Heitler and γγ produced pairs contributes the mostto the observed photohadronic emission (red dash-dotted line).Electrons produced by Bethe-Heitler interactions much above thethreshold, attain a maximum Lorentz factor γ ′ e , pe ≃ γ ′ ǫ ′ t , where ǫ ′ t is the energy of the target photon (e.g. Kelner & Aharonian 2008).Thus, the characteristic synchrotron photon energy is ∝ B γ ′ (seealso Petropoulou & Mastichiadis (2015)). Based on the parametervalues listed in Table 1 and Fig. 1 (right panel), the peak energy ofthe Bethe-Heitler component in model B is expected to be ∼ ∼ . ff er significantly in the relativeimportance of the various emission processes, despite the small dif-ferences in the adopted parameter values of models A and B. Ourresults reflect the non-linearity of the radiative processes that haveto be present in a system that contains relativistic electrons and pro-tons. The decomposition of the SED obtained in models A and B re-vealed their di ff erences in the origin of the X-ray and γ -ray emis-sion. Di ff erent X-ray and γ -ray variability signatures are, therefore,expected. Regardless, both models predict variable VHE emissionontimescalessimilartothoseinX-rays,incontrasttothescenariosthatattributetheTeVemissiontothekpc-scalejetofApLibrae.To illustrate the model predictions on the variability and the broadband spectral evolution we present an indicative example ofa flaring event. An increase of the observed flux (i.e., flare) can beattributed, in general, to a higher injection rate of radiating particlesat the dissipation region, which, in turn, may be caused by temporalmodulations of the jet power. In the following, we model a fiducialflare caused by an increase in the injection compactness (or, equiv-alently luminosity) of primary electrons and protons given by: ℓ i ( τ ) ℓ (0)i = + ( A / ( τ − τ pk ) + ( A / , (1)where τ ≡ t ′ / t ′ dyn = ct ′ / r ′ b , τ pk = A = ℓ (0)i is the valuederived from fitting the SED (see Table 1). Here, the starting time τ = τ pk is the peak time where ℓ i ( τ pk ) = ℓ (0)i . We define ∆ τ inj75% = A , i.e. the time interval where ℓ i > . ℓ i , pk , to be the measure of the injection’s duration. Thiscorrespond to ∆ t inj75% = At ′ dyn (1 + z ) /δ D ≃ . r ′ b , /δ D , .Fig. 2 shows, in total, 20 snapshots (grey thin lines) of thebroadband emission during the flaring episode described above.Left and right panels correspond to models A and B, respectively.The time-averaged spectrum is also plotted (black dashed line),while no attempt in fitting the Fermi -LAT flare (red points) hasbeen made. We find that changes in the luminosity of radiating par-ticles alone do not a ff ect the spectral shape either in the X-ray orthe γ -ray bands. Interestingly, no significant spectral change wasdetected during the Fermi -LAT flare of 2013 (MJD 56306-56376)(H.E.S.S. Collaboration et al. 2015). The flux variations in the op-tical / UV energy bands are less pronounced than these at higher en-ergies, although the radiating primary electrons are more energeticthan those emitting at ∼ . − / UV emission has a significant contribution fromthe host galaxy itself, while the primary synchrotron component issub-dominant (see Fig. 1).The integrated flux in di ff erent energy bands, normalized toits pre-flare value ( F min ), is presented as a function of time in © , 1– ?? he γ -ray emission of Ap Librae F / F m i n Time (hr)Model A Model B 2-10 keV0.1-300 GeV0.1-6 TeVInjection
Figure 3.
Model-derived light curves for the fiducial flare described in text.The results obtained in models A and B are shown with solid and dashedlines, respectively. Here, F is the integrated flux at di ff erent energy bandsmarked on the plot and F min is the respective value prior to the flare. Theinjection luminosity of particles (normalized to its minimum value) is alsoshown as a function of time (blue coloured lines). Fig. 3. For comparison reasons, the ratio ℓ i /ℓ (0)i is also shown (bluecoloured lines). In both models, we find no time-lag between the X-ray and γ -ray energy bands. Unless there is a time-lag in the injec-tion of accelerated electrons and protons, the flares predicted by themodels are (quasi)-simultaneous. The properties of the light curvesobtained in models A and B, namely peak flux F pk and durationare summarized in Table 3. The amplitude of the flare is larger athigher energies and its shape becomes more symmetric, i.e. the riseand decay timescales are similar. In both models, the rise timescaleof the flares in X-rays and γ -rays are similar. On the contrary, the γ -ray flares appear to be shorter in duration compared to those inX-rays. In particular, we find that the X-ray flare is twice as long asthe injection episode, namely ∆ t ∼ t dyn , where t dyn ≃ .
75 hr(2.11 hr) is the crossing time of the source in the observer’s framefor Model A (Model B). The γ -ray flare is shorter than the X-rayflare by one t dyn in both models. Because of the superposition ofvarious emitting components at di ff erent energy bands, it is notstraigthforward to provide an explicit expression for the expectedflare duration. This can be, however, qualitatively understood; thefaster decay timescale of the γ -ray flares reflects the shorter cool-ing timescale of the radiating (secondary) electrons, which are typ-ically more energetic than those emitting in X-rays (see Section 3.1in Petropoulou & Mastichiadis 2015).Although the injection luminosity function for primary elec-trons and protons is the same in models A and B, the obtained peakfluxes are lower in the latter. The di ff erences are related to the un-derlying physical process responsible for the X-ray and γ -ray emis-sion. For example, the X-ray emission in model B is expected to be ∝ ℓ p , since it is dominated by the proton synchrotron radiation. Onthe contrary, the X-ray variability amplitude in model A is expectedto be larger than in model B, since the X-ray emission is a superpo-sition of the SSC and Bethe-Heitler components that respectivelydependent on the varying ℓ e and ℓ p .An interesting point to be considered is the detectability ofthe X-ray flux variability with Swift / XRT during a fiducial γ -rayflare, as shown in Fig. 3. The source has been so far observed with Swift / XRT for a few ks, with single observations being usually splitto several (two to four) snapshots with exposure times less than 1ks. Based on the count rate of the existing
Swift / XRT observations,
Table 3.
Amplitude and duration of the fiducial flare described in text atX-rays (2-10 keV), HE (0.1-300 GeV) and VHE (0.1-6 TeV) γ rays. Therespective fluxes prior to the flare ( F min ) are also listed.2 −
10 keV 0 . −
300 GeV 0 . − F min (erg cm − s − )model A 6 . × − . × − . × − model B 3 . × − . × − . × − Amplitude: F pk / F min model A 2.4 3.2 3.6model B 1.8 2.5 2.6Duration: ∆ t (hr)model A 3.0 2.3 2.3model B 8.6 6.6 6.5 a one ks exposure would deliver approximately 100 counts. A fluxincrease by a factor of two, as shown in Fig. 3, would be detectablewith Swift / XRT above a 3 σ level. This could be achieved with mul-tiple observations (of at least one ks exposure time) spanning overthe duration of the fiducial flare. The detectability of a TeV flarewith the next generation of IACTs is discussed in the followingsection. Ap Librae has been one of the few VHE emitting LBL ob-jects and it was first discovered by H.E.S.S. (Hofmann 2010;H.E.S.S. Collaboration et al. 2015). As discussed by the authors,H.E.S.S. was able to detect the system with a significance of6.6 σ during an integrated exposure time of 14 h. The CherenkovTelescope Array (CTA, Actis et al. 2011; Acharya et al. 2013) is anext-generation observatory of Imaging Air Cherenkov Telescopes(IACT). It is planned to cover more than 1 km area and will becomposed of an array of large, middle, and small-sized telescopes.When completed, CTA is expected to reach an e ff ective area largerthan the Cherenkov light pool size, and deliver a sensitivity aboutan order of magnitude better than that of current Cherenkov tele-scopes. In principle, CTA will be therefore able to detect Ap Libraeat a fraction of the time needed by H.E.S.S.In order to test this we created simulated light curves of theVHE flares (0.1-6 TeV) predicted by the models A and B (Fig. 3)using the software package ctools (Kn¨odlseder et al. 2016). Oursimulated events are drawn from three components i) a point sourcewith the spectral properties of Ap Librae, ii) an isotropic CR back-ground that was modeled as a di ff use isotropic source with a spec-tral shape and flux adopted by Silverwood et al. (2015) (see Fig. 2therein), and iii) an instrumental background of the detector (seeCTAI rf B ackground of ctools ). We used the task ctobssim to sim-ulate the event files, and the ctlike tool to perform a maximumlikelihood fitting of a power-law model (photon index 2.65) to theunbinned simulated data. Finally the cttsmap tool was used to con-firm the significance of the detection. The procedure was repeatedfor various flux levels of the models shown in Fig. 3. The simu-lated data were binned in intervals of 0.5 h for model A and 5 hfor model B. In both cases, the adopted bin size is less than themaximum visibility of the system during a single day. http: // cta.irap.omp.eu / ctools / © , 1–, 1–
300 GeV 0 . − F min (erg cm − s − )model A 6 . × − . × − . × − model B 3 . × − . × − . × − Amplitude: F pk / F min model A 2.4 3.2 3.6model B 1.8 2.5 2.6Duration: ∆ t (hr)model A 3.0 2.3 2.3model B 8.6 6.6 6.5 a one ks exposure would deliver approximately 100 counts. A fluxincrease by a factor of two, as shown in Fig. 3, would be detectablewith Swift / XRT above a 3 σ level. This could be achieved with mul-tiple observations (of at least one ks exposure time) spanning overthe duration of the fiducial flare. The detectability of a TeV flarewith the next generation of IACTs is discussed in the followingsection. Ap Librae has been one of the few VHE emitting LBL ob-jects and it was first discovered by H.E.S.S. (Hofmann 2010;H.E.S.S. Collaboration et al. 2015). As discussed by the authors,H.E.S.S. was able to detect the system with a significance of6.6 σ during an integrated exposure time of 14 h. The CherenkovTelescope Array (CTA, Actis et al. 2011; Acharya et al. 2013) is anext-generation observatory of Imaging Air Cherenkov Telescopes(IACT). It is planned to cover more than 1 km area and will becomposed of an array of large, middle, and small-sized telescopes.When completed, CTA is expected to reach an e ff ective area largerthan the Cherenkov light pool size, and deliver a sensitivity aboutan order of magnitude better than that of current Cherenkov tele-scopes. In principle, CTA will be therefore able to detect Ap Libraeat a fraction of the time needed by H.E.S.S.In order to test this we created simulated light curves of theVHE flares (0.1-6 TeV) predicted by the models A and B (Fig. 3)using the software package ctools (Kn¨odlseder et al. 2016). Oursimulated events are drawn from three components i) a point sourcewith the spectral properties of Ap Librae, ii) an isotropic CR back-ground that was modeled as a di ff use isotropic source with a spec-tral shape and flux adopted by Silverwood et al. (2015) (see Fig. 2therein), and iii) an instrumental background of the detector (seeCTAI rf B ackground of ctools ). We used the task ctobssim to sim-ulate the event files, and the ctlike tool to perform a maximumlikelihood fitting of a power-law model (photon index 2.65) to theunbinned simulated data. Finally the cttsmap tool was used to con-firm the significance of the detection. The procedure was repeatedfor various flux levels of the models shown in Fig. 3. The simu-lated data were binned in intervals of 0.5 h for model A and 5 hfor model B. In both cases, the adopted bin size is less than themaximum visibility of the system during a single day. http: // cta.irap.omp.eu / ctools / © , 1–, 1– ?? Petropoulou, Vasilopoulos, Giannios F l u x ( × − e r g s − c m − ) MODEL A c oun t s σ F l u x ( × − e r g s − c m − ) MODEL B c oun t s
10 15 20 25 30 35 40 σ Figure 4.
Simulated CTA light curves for models A (left panel) and B (right panel). The event files were generated according to the 0.1-6 TeV light curvesshown in Fig. 3. A time binning of 0.5 h and 5 h was used for the simulated light curves of models A and B, respectively. The expected number of sourcecounts is shown in the top panel of both plots. Colour coding is used for the significance of the detection (in Gaussian σ ) as obtained by the analysis of thesimulated event files. The results of our simulations are presented in Fig. 4. For aTeV flare with ∼ . σ (see left panelin Fig.4). A detection significance similar to that of H.E.S.S. ( ∼ σ ) would be achieved for the quiescent flux levels but at a fractionof the integrated exposure time of H.E.S.S. A longer exposure time(5 hr) was adopted for the longer duration flare predicted by modelB. Despite the lower peak flux of the flare (see also Table 3), theexpected number of counts at the peak time of the flare is six timeslarger than that of flare A due to the larger exposure time. For a5 hr exposure time, the lowest significance that can be reached isstill above 15 σ . We have presented two indicative models for explaining the broadhigh-energy spectrum of Ap Librae with their parameters listedin Table 1. Both models are viable alternatives, when only con-sidering their ability of reproducing the observed SED. However,they di ff er in terms of energetic requirements. The power of atwo-sided jet can be written as (e.g. Ghisellini et al. 2014) P j = π r ′ Γ c P i u ′ i + (8 / Γ /δ ) L ph , where u ′ i ( i = e , p , B ) is the en-ergy density as measured in the respective rest frame, L ph is theapparent photon luminosity and the last term in the right handside of the equation is the bolometric absolute photon power (e.g.Dermer et al. 2012). The inferred jet power for models A and B isrespectively 10 erg s − and 10 erg s − to be compared to thejet radiation power P r ∼ × erg s − and the Eddington lu-minosity of Ap Librae L Edd ∼ × erg s − , for a black holemass M BH = . ± . M ⊙ (Woo et al. 2005). It is interesting to notethat even in scenarios that invoke the presence of relativistic elec-trons alone, the jet power may be as high as ∼ erg s − (see e.g.Hervet et al. 2015).If the accretion operates in the magnetically arrested (MAD) regime (Narayan et al. 2003), the jet power may be related tothe accretion power, ˙ Mc , as P j = η j ˙ Mc , where η j ∼ . − η j values obtained for faster spinning black holes and thickerdisks. Adopting η j =
2, the accretion power for models A and B is,respectively, 5 × erg s − and 5 × erg s − . The luminosityof the accretion flow can be estimated from the BLR luminosityassuming a covering fraction ξ , i.e., L disk . L BLR , ξ − − erg s − and the radiative e ffi ciency is given by ǫ = L disk / ˙ Mc = × − (2 × − ) for model A (model B). The low radiative e ffi ciencyin this source is not a feature unique to our model (see alsoHervet et al. 2015).Assuming that the magnetic field is mostly toroidal at pcscales it can be written as B ′ = (4 P B / c ) / ( R Γ θ j ) − , where P B isthe jet power carried by the magnetic field, R ≃ r ′ b /θ j is the dis-tance from the black hole, and θ j is the opening angle of the jet.At sub-pc scales we found that most of the contribution to the jetpower comes from the relativistic proton component, i.e., P j ≃ P p .Assuming that the ratio P B / P p remains constant from the sub-pcto the pc scales and equal to ∼ − (10 − ) for model B (modelA), the magnetic field at R = Γ θ j ∼ Γ θ ∼ . P B . P j at the pc scales of the jet. However, theestimated magnetic field would be then close to 1 G, i.e. larger thanthe adopted value at Table 2 (see also Pushkarev et al. (2012)).In general, the energetic comparison of the two models sug-gests that solutions with higher magnetic field strengths in the (sub-pc) emitting region are favoured. Here, we did not aim at findingthe most “economic model” that describes the SED of Ap Librae,so we cannot exclude models with sub-Eddington accretion andjet powers (see e.g. Petropoulou & Dermer 2016). Other solutionscharacterized by lower jet powers, higher magnetic field strengthsand larger blobs are also expected to be closer to equipartition( P B ∼ P p ). We plan to search for the model that minimizes thejet power by scanning the available parameter space in the future. © , 1– ?? he γ -ray emission of Ap Librae In summary, our results outline a physical picture where the jet isinitially Poynting-flux dominated, it dissipates a significant frac-tion of its magnetic energy to relativistic protons at sub-pc scaledistances, and extends to pc scale distances with a constant ratio ofmagnetic-to-(relativistic) particle powers.The low-energy spectrum from the compact, high-energyemitting blob cuts o ff at ∼ GHz, being unable to explain theradio observations at lower frequencies. To account for the radioemission in Ap Librae, we assumed that this originates from a moreextended region of the jet, which we approximated by a sphericalblob with characteristic radius r ′ ∼ ∼ − times smaller than those inferred for the compact re-gion (see Table 3). Since r ′ / r ′ b ∼ , this is compatible with ascenario of a conical jet where the energy densities are expectedto decrease as ∼ / r ′ . On the other hand, without new injectionof electrons, it is di ffi cult for a blob that produces a high-energyflare (in X-rays and γ -rays) to also produce a radio flare later, afterit has su ffi ciently expanded. The reason is that the electrons thatare responsible for the radio emission are typically very energeticand not the result of excessive adiabatic cooling. However, if theelectron injection continues from the sub-pc to the pc-scale jet, adelayed radio flare with respect to the γ -ray one may be expectedon a timescale of 3 × s r ′ /δ D , (see Table 2). In this scenario,therefore, fast ( ∼ hr) X-ray and γ -ray flares caused by a strong jetepisode may be followed by radio flares a few months later (seeHovatta et al. 2015, for Mrk 421). We have shown that the superposition of di ff erent emission compo-nents related to photohadronic interactions can explain the HE andVHE γ -ray emission of Ap Librae without invoking external radi-ation fields. This was exemplified with two indicative model fitsto the SED of Ap Librae where the VHE emission was assumedto originate from the core of the jet, i.e. from a compact, sub-pcscale region. Our model for the non-thermal emission of Ap Li-brae predicts (quasi)-simultaneous flares at X-rays, HE, and VHE γ -rays. The flare duration in the aforementioned energy bands isof the same order of magnitude, with shorter durations and largervariability amplitudes obtained at higher energies. In addition, nospectral changes during the flares are expected, unless the slopeof the radiating particles changes. We showed that CTA would beable to detect ∼ hr timescale variability at E γ > . γ -rays and / or X-rays could be therefore used to trigger pointing observations ofAp Librae with CTA. The detection of VHE variability on simi-lar timescales as those observed in X-rays and GeV γ -rays wouldpoint towards a common emitting region of sub-pc scale. Althoughit could not rule out a kpc-jet origin of the quiescent VHE emis-sion, as the latter could still be explained by an additional emittingcomponent, a model of a sub-pc scale origin would be preferred inthe spirit of Ockham’s razor. ACKNOWLEDGMENTS
We thank Dr. Tullia Sbarrato for useful discussions. M. P. acknowl-edges support from NASA through the Einstein Postdoctoral Fel-lowship grant number PF3 140113 awarded by the Chandra X-rayCenter, which is operated by the Smithsonian Astrophysical Obser-vatory for NASA under contract NAS8-03060. G. V. acknowledgessupport from the BMWi / DLR grants FKZ 50 OR 1208. D. G. ac-knowledges support from NASA through grant NNX16AB32G is-sued through the Astrophysics Theory Program. This research hasmade use of the RXTE / PCA python script pca.py developed byJ.-C. Leyder and J. Wilms, freely available from the HEAVENSwebpage.
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