Table Of ContentA METHOD FOR LOCALIZING ENERGY DISSIPATION IN BLAZARS USING FERMI VARIABILITY
Amanda Dotson1 [email protected], Markos Georganopoulos1,2, Demosthenes Kazanas 2, Eric S. Perlman 3
Accepted by the Astrophysical Journal Letters
ABSTRACT
The distanceofthe Fermi-detected blazarγ-rayemissionsite fromthe supermassiveblackhole isa
matterofactivedebate. HerewepresentamethodfortestingiftheGeVemissionofpowerfulblazars
2
is produced within the sub-pc scale broad line region (BLR) or farther out in the pc-scale molecular
1
torus (MT) environment. If the GeV emission takes place within the BLR, the inverse Compton
0
(IC) scattering of the BLR ultraviolet (UV) seed photons that produces the γ-raystakes place at the
2
onsetofthe Klein-Nishinaregime. This causesthe electroncoolingtime to becomepracticallyenergy
p independent and the variation of the γ-ray emission to be almost achromatic. If on the other hand
e the γ-ray emission is produced farther out in the pc-scale MT, the IC scattering of the infrared (IR)
S
MT seed photons that produces the γ-rays takes place in the Thomson regime, resulting to energy-
0 dependent electron cooling times, manifested as faster cooling times for higher Fermi energies. We
1 demonstrate these characteristics and discuss the applicability and limitations of our method.
Subject headings: galaxies: active — quasars: general — radiation mechanisms: non-thermal —
] gamma rays: galaxies
E
H
. 1. INTRODUCTION GeV emission well within the BLR (Poutanen & Stern
ph Blazars dominate the extragalactic γ-ray sky 2010). Very short distances (cid:2)1016 cm), however,where
- (Abdo et al. 2011a), exhibiting flares in which the accretion disk photons dominate are not favored, be-
o Fermi γ-ray flux is seen to increase up to several times cause of the high pair production γ-ray opacity (e.g.
r the pre-flare level (e.g. Abdo et al. 2010b). Because the Ghisellini & Tavecchio 2009).
t
s emitting regions are unresolved,the locationof the GeV Gamma-rayflareshavebeenassociatedwithradioand
a emission remains unknown and this constitutes an open opticalflares,placingtheGeVemissionoutsidetheBLR:
[ issue in understanding energy dissipation in blazars. L¨ahteenma¨ki & Valtaoja(2003),usingthetemporalsep-
1 In the leptonic model, the GeV emission of blazars is aration of the radio and γ-ray fluxes, argued that the
v produced by IC scattering of photons off of the same γ-ray emission site is at a distance of ∼ 5 pc from the
3 relativistic electrons in the jet that give rise to syn- central engine. Connections have been also drawn be-
5 chrotronradiation(for areviewseeB¨ottcher2007). The tweenγ-rayoutbursts,opticalflarepolarizationchanges,
0 seed photons for IC scattering are synchrotron photons andejectionsofsuperluminalradioknotsonthepcscale:
2 originating within the relativistic jet (synchrotron - self Marscher et al. (2010) associated short γ-ray variations
9. Compton, SSC scattering) (e.g. Maraschi et al. 1992) or with the passage of disturbances from the radio core,
0 photons originating external to the jet (external Comp- parsecsawayfromthe black hole. Inthe case ofOJ 287,
Agudo et al. (2011) found γ-ray flaring to be simulta-
2 ton, EC scattering), such as UV accretion disk photons
1 (Dermer et al. 1992), UV photons originating from the neous with mm outbursts associated with a VLBA jet
: BLR (Sikora et al. 1994), and IR photons originating component 14 pc downstream from the radio core.
v Here we propose a method to distinguish if the GeV
frommoleculartorus(MT)(e.g.B(cid:3)laz˙ejowski et al.2000).
Xi Because the γ-ray emission of blazars can vary sig- emission of powerful blazars takes place within the sub-
nificantly on short times, down to the instrument lim- pc BLR or further out within the pc-scale MT. In §2
r we discuss our understanding of the BLR,MT, and SSC
a its, ranging from a few minutes (in the TeV range)
(Aharonian et al. 2009) to a few hours (in the GeV photon fields and where each one dominates. We show
range)(Foschini et al.2011),light-timetravelarguments that cooling on the UV BLR photons results in achro-
matic cooling times in the Fermi band, while cooling
constrain the size of the emitting region and it has been
argued(e.g. Tavecchio et al. 2010) that this requires the on the MT IR photons results to faster cooling times at
emission to take place at the sub-pc scale. Explain- higher γ-rayenergies. In §3 we present our method, dis-
cussingthe dilutionofanenergy-dependentcoolingtime
ing the Fermi GeV spectral breaks seen in powerful
blazars (Abdo et al. 2010c) as a result of pair absorp- fromlighttraveltimeeffectsanddiscusstheapplicability
tion on the He Lyman recombination continuum and ofourmethod. Finally,in§4wepresentourconclusions.
lines, produced in the inner part of the BLR, places the 2. COOLINGOFGEVEMITTINGELECTRONS
2.1. Characterizing the BLR and the MT
1Department of Physics, University of Maryland Baltimore Reverberation mapping of the BLR points to a typi-
County, 1000HilltopCircle,Baltimore,MD21250, USA
2NASA Goddard Space Flight Center, Code 660, Greenbelt, cal size of RBLR ≈1017Ld1/,425 cm (e.g. Kaspi et al. 2007;
MD3D2e0p7a7r1t,mUeSnAt ofPhysicsandSpace Sciences, FloridaInsitute Bentz et al. 2009), where Ld,45 is the accretion disk lu-
of Technology, 150 West University Boulevard, Melbourne, FL minosityinunitsof1045 ergs−1. Becauseofthisscaling,
32901, USA and assuming that LBLR = ξBLRLd, where ξBLR ∼ 0.1
2 Dotson, Georganopoulos,Kazanas,Pearlman
is the BLRcoveringfactor,the energydensity inside the in days. Setting δ =Γ the condition U(cid:2) <U(cid:2) requires
s ext
w2B0Lid0R9e)ly.(UAfBrsoLmwRa∼sobs1hje0oc−wt2netrbogycoTmbaj−ve3ce)tccih(sGionho(it2se0el0lxi8np)ie,c&wtehTdeantvoetrcvacahnrisyo- Γ(cid:3)(cid:2)3Ls(1+z)2(cid:3)18 =8.6(cid:4)Ls,46(1+z)2(cid:5)18 . (1)
16πc3t2U(cid:2) t2 U(cid:2)
formed to the jet frame, the BLR spectrum, dominated v ext v,1d ext,−4
by H Lyα photons, is broadened and boosted in lu-
minosity due to relativistic effects and can be well- This translates to Γ (cid:3) 4.8×Ls1,/486(1+z)1/4tv−,11/d4 for
baνBpuplLkrRoLx=oimr1ea.n5ttezΓdνfabLcyytαoar((cid:6)baBlnaLdcRk(cid:6)b≈oisd3yt×hes1p0pe−chto5rtΓuom)n, wetnhheaertrgeypΓeianikssmthcae2t zth)1e/e4mt−v,i11s/ds4iofnorstitheeaetmRisBsiLoRnssictaeleastaRnMdTΓs(cid:3)ca8le.s6.×InLg1se,/48n6e(1ra+l,
units. powerfulquasarsexhibitsuperluminalmotionsrequiring
In the MT the dust temperature ranges from T ∼300 Γ∼10−40 (Jorstad et al. 2005; Kharb et al. 2010) and
K (Landt et al. 2010) ( to T ∼ 1200 K (Cleary et al. therefore, the dominant source of seed photons for these
2007; Malmrose et al. 2011), with hotter emitting ma- sources should be the BLR or the MT, provided the γ-
terial expected to be closer to the central engine (e.g. ray emission site is at a distance not significantly larger
Nenkova et al. 2008). Because of the larger size of thanthesizeoftheMT.ArecentfindingbyMeyer et al.
the MT, it has been probed by reverberation mapping (2012) that the ratio of γ-ray to synchrotron luminos-
only for Seyfert galaxies (e.g. Suganuma et al. 2006) ity increases with increasing radio core, as expected for
which have lower luminosities and therefore smaller MT ECemission(Dermer1995;Georganopouloset al.2001),
sizes. These studies, along with near-IR interferomet- supportsfurtherthepossibilitythatpowerfulblazarsare
ric studies (e.g. Kishimoto et al. 2011) also support an EC emitters.
R ∝ L1/2 scaling, suggesting that U is similar for
d 2.3. Cooling in the BLR vs Cooling in the MT
sources of different luminosities. Adopting the scaling
ofGhisellini & Tavecchio(2009),RMT =2.5×1018L1d/,425 isTthhee ecnrietricgayl odfifftehreensceeedbeptwhoeteonntsh:etBheLRBLaRndptrhoeduMceTs
cm and assuming a covering factor ξMT ∼ 0.1 − 0.5, UV photons while the MT produces IR photons. This
the MT photon energy density is UMT ∼ 10−4 erg difference by a factor of ∼ 100 in typical photon energy
cm−3. We also adopta temperature TMT ≈1000,corre- iscriticalinthatitaffectstheenergyregimeinwhichthe
sponding to a blackbody peak at νMT ≈ 6.0×1013 Hz GeV-emitting electron IC-cooling takes place, and thus
((cid:6)MT ≈5×10−7). the energy dependence of the electron cooling time.
For this consideration to be relevant, IC cooling must
dominateoversynchrotroncooling. Thisconditionissat-
isfied,sinceinpowerfulblazarsthe IC luminosityclearly
dominates over the synchrotron luminosity, reaching in
2.2. Which seed photons dominate where? highstatesanICluminosityhigherthatthesynchrotron
Foranisotropicphotonfield,theco-moving(jetframe) one by a factor of up to ∼ 100 (e.g. Abdo et al. 2010a;
energy density U(cid:2) is U(cid:2) ≈ (4/3)Γ2U, while for pho- Meyer et al. 2012).
tons entering the emitting region from behind, U(cid:2) ≈ For electrons cooling in the Thomson regime (γ(cid:6)0 <<
(3/4)Γ−2U (Dermer & Schlickeiser 1994). If the emis- 1,where boththe electronLorentzfactorγ andthe seed
sion site is located at R (cid:2) RBLR, the BLR photon photon energy (cid:6)0 are measured in the same frame) the
field can be considered isotropic in the galaxy frame cooling rate γ˙ ∝ γ2. For electrons with γ(cid:6)0 >> 1 cool-
and, using the BLR energy density discussed in §2.1, ing takes place in the Klein-Nishina (KN) regime with
U(cid:2) ∼ 1.3× Γ2 erg cm−3. Similarly, the MT pho- γ˙ ∝ lnγ (Blumenthal & Gould 1970). For the broad in-
toBnLfiReld is isotrop1i0c inside the BLR and its co-moving termediate regime, 10−2 (cid:2) γ(cid:6)0 (cid:2) 102, a parametric ap-
seed photon energy density is U(cid:2) ∼ 1.3 × 10−2 Γ2 proximation has been suggested (Moderski et al. 2005).
MT 10
oervgercmU(cid:2)−3. bCyleaarflayc,toart oRfB∼LR10s0ca.leIsf, tUhB(cid:2)eLeRmdisosmioinnastitees Ienrgwyhlaotssforlalotwesγ˙w, ewchaiclchulfaotremnuonmoeernicearglleytitcheseeeldecptrhoontoenns-
is locatMedT at R ∼ RMT, then the BLR photons en- of number density n0 and dimensionless energy (cid:6)0 is
ter the emitting region practically from behind, so that (cid:6)
tUaB(cid:2)inLRth∼e 7sa.5m×e 1c0o−-m7Γov−10i2ngeregncemrg−y3.deTnhsietyMaTs bphefootroensanrde-, γ˙ =n0 0∞ 34σ(cid:6)T0cf(x)((cid:6)−(cid:6)0)d(cid:6), (2)
in this case, the MT dominates the co-moving photon
where, following Jones (1968),
energy density.
Theseexternalphotonfieldco-movingenergydensities (4(cid:6) γx)2
need to be compared to the synchrotron one. If Rblob is f(x)=2xlogx+x+1−2x2+ 1+04(cid:6) γx(1−x) (3)
the size of the emitting region, then the co-moving syn- 0
wchhreorteroδnpishotthoenuensuearglyDdoepnpsilteyrisfaUctS(cid:2)or≈aLnsd/(L4πscRthb2elobsδy4n)-, wiTthhexe=ffe(cid:6)c/t[s4oγf2(cid:6)th0e(1tr−an(cid:6)s/iγti)o].nbetweenThomsonandKN
chrotron luminosity. An upper limit to Rblob is set by regimes on the electron energy distribution (EED) and
the variability timescale tv: Rblob (cid:2) ctvδ/(1+z), where the resultant spectrum of the synchrotron and IC emis-
z is the source redshift. We then obtain a lower limit sion have been studied before (e.g. Blumenthal 1971;
Us(cid:2) ≈Ls(1+z)2/(4πc3t2vδ6) or Us(cid:2) ∼6.3×10−2Ls,46(1+ Zdziarski 1989; Dermer & Atoyan 2002; Sokolov et al.
z)2t−v,21dδ1−06 erg cm−3, where tv,1d is the variability time 2004; Moderski et al. 2005; Kusunose & Takahara 2005;
Localizing energy dissipation in blazars 3
chrotron or external photons). For these reasons their
use in understanding where the GeV emission takes
106 place is problematic.
Thomson Cooling
Klein−Nishina Cooling
Synchrotron Cooling 3. LOCATINGTHEGEVEMISSIONSITE
R) 105 Total Cooling There is however another observable aspect of the
L
B Thomson - KN transition that is free of the issues faced
τ (s) (cool 104 bofytrheelyeinlegctornonspceocotrlianlgsitginmaetucraens:bteheuseendertgoyedveaplueantdeenthcee
regimeatwhichtheelectronsthatproducetheGeVradi-
ationcool,andthroughthis evaluatewherethe emission
takes place.
103 In the Thomson regime, the electron cooling time
102 103 104 tc = γ/γ˙ scales as γ−1, while in the KN regime the
electron cooling time scales as as γ/lnγ. These two
regimes connect smoothly forming a wide valley around
106 γ(cid:6)0 ∼ 1 in which the cooling time is practically energy-
independent. Theenergyoftheseedphotonsoriginating
inthe BLRis greaterthan thatof photonsfromthe MT
by a factor of ∼ 100. As a result, (see Fig. 1) the lo-
T) 105 cation of the energy-independent valley of the BLR case
M is manifested at electron energies lower by a factor of
s) ( ∼ 100 than that of the MT case. In turn, the energy
τ (cool 104 dtheepeonbdseenrvceedoffatllcincgautismeseatfreolfatthede flenareer.gyTdheepfeanlldinegncteimine
tf of Fermi light curvescan be used, therefore,to deter-
mine whether a flare occurs within the BLR or within
103 the MT.
102 103 104
γ 3.1. Flare decay in the BLR vs flare decay in the MT
We utilize an one-zone code to demonstrate the ef-
fect of a flare occurring within the BLR versus a flare
Fig. 1.—Electroncoolingtimeinthegalaxyframeasafunction
ofγ. Toppanel: BlazaremissionsitelocatedintheBLR.Bottom occurring within the MT. The code assumes the injec-
panel: BlazarlocatedintheMT.Brokenlinesrepresentthevarious tion of a power law electron distribution and follows
cooling mechanisms and the solid black line is the total cooling its evolution taking into account the KN cross section,
time. Plots were calculated for seed photon energies (cid:3)0,BLR = SSC losses, and assuming a black body external photon
3×10−5 and (cid:3)0,MT = 5×10−7, seed photon energy densities field. The implicit numerical scheme is similar to that
UBLR = 10−2 erg cm−3, UMT = 10−4 erg cm−3 and magnetic used by Chiaberge & Ghisellini (1999) and Graff et al.
fieldenergyUB =100UEC.
(2008). After the code reaches a steady-state, an in-
crease in the injection rate is introduced that lasts for
Georganopoulos et al. 2006; Manolakou et al. 2007;
a short time before it returns to its initial value. The
Sikora et al. 2009).
codewasinitializedtosimulatetheflareoccurringwithin
In short, the transition from Thomson to KN cool-
the BLR and the MT respective, described by the val-
ing in t(cid:7)he EED can be seen for the steady state
ues discussed in §2. We assumed a Compton dominance
n(γ) ∝ Q(γ)dγ/γ˙: for a power law injection Q(γ) ∝
γ−p, the cooled EED hardens from n(γ) ∝ γ−(p+1) bLuIClk,mLaxo/reLnstyzncfha,mctaoxr≈Γ5=0, s1o0u.rceDseiezpe Rin=th3e×T1h0o1m6csmon,
in the Thomson regime to n(γ) ∝ γ−(p−1) in the KN regime (MT case) the Compton dominance corresponds
regime. The transition takes place gradually at γ ∼ to UEC/UB, where UEC is the external energy density
(cid:6)−01. A second transition back to n(γ) ∝ γ−(p+1) is and UB is the magnetic energy density. However, as
expected at higher γ, as synchrotron losses (assumed cooling transitions from the Thomson to the KN regime
to be less significant than Thomson EC losses) be- (BLR case), the ratio UEC/UB over-estimates the ob-
come larger than KN losses. The imprint of these con- served Compton dominance by a factor of ∼2.
siderations on the observed synchrotron and IC spec- In the BLR case (Fig. 2, blue curve) IC cooling oc-
tra has been considered for the case of the X-ray curs at the onset on the KN regime, resulting in a near-
emission of large scale jets (Dermer & Atoyan 2002) flattening of tf within the Fermi band, where a change
and in the case of blazars (Kusunose & Takahara 2005; in energy by a factor of 100 (from 200 MeV to 20 GeV)
Georganopoulos et al. 2006; Sikora et al. 2009). results in a change in cooling time of less than an hour,
Spectral signatures, however, are not unique and can with all the Fermi energies having practically indistin-
be diluted or altered by extraneous causes (e.g. the guishable decay times (between ∼ 2−3 hours). In the
accelerated electron distribution has intrinsic features MT case (Fig. 2, red curve) cooling occurs mostly in
thatdeviate froma powerlaw,the synchrotronemission theThomsonregimeandtf isheavilyenergy-dependent;
is contaminated by the big blue bump, the IC emission the same change in energy by a factor of 100 results in
is modified by pair production absorption from syn- a change in cooling time by ∼ 10 hours. This is also
4 Dotson, Georganopoulos,Kazanas,Pearlman
20
1
MT hν= 200 MeV
18 BLR hν = 2 GeV
0.8 hν = 20 GeV
16
R)0.6
L
B
14 L (0.4
12
0.2
hr) 10
t (f 00 5 10 15
8
6 1
4 0.8
2 0.6
T)
M
−01.5 −1 −0.5 0 0.5 1 1.5 L (0.4
Log(hν) (GeV)
0.2
Fig.2.— 1/e falling time in the galaxy frame versus observing
energy(GeV)forMTseedphotons(red),BLRseedphotons(blue) 0
0 5 10 15
t (hr)
apparent in the light curves shown in Fig 3. A flare
occurringwithin the BLR (Fig 3, top panel) has compa-
rablevalues oftf within the Fermienergyrange. Aflare Fig.3.—Lightcurvesat200MeV,2GeV,and20GeVforBLR
occurring within the MT exhibits distinct falling times seed photons (upper panel) and MT seed photons (lower panel),
that decrease with observing energy (3, lower panel). normalizedforasteadystateL=0andmaximumL=1(inarbitrary
units). Times are in the galaxy frame. The dashed black line is
For sufficiently bright flares with short decay times the1/edecaytime. Timesareinthegalaxyframe.
(comparable to the cooling times of few to severalhours
anticipated), Fermi light curves can be generated at
multiple energies, and the energy dependence (or lack
thereof) of tf can be used to reveal the location of the
GeV emitting site.
3.2. Light Travel Time Effects
1
HE,t =0
BecausetheGeVemittingregionisnotapointsource, lc
0.9 LE,t =0
the observed 1/e decay time tobs of the light curve is HE,tlc=0.1 t
a convolution of tf and the blob light-crossing time tlc. 0.8 LE,tlc=0.1 tfall,HE
Anyothervariations(e.g. agradualdecreaseofthe elec- lc fall,HE
tron density) will have a similar effect. For BLR achro- 0.7 HE,tlc=1.0 tfall,HE
LE,t =1.0 t
maticcooling,weexpectthelightcurvestoremainachro- 0.6 HE,tlc=10 tfall,HE
lc fall,HE
matic after considering light crossing time effects. To LE,t =10 t
see the effects of tlc in the case of MT cooling, where, L0.5 lc fall,HE
tf ∝ (cid:6)−1/2, we consider a source with exponentially de- 0.4
cayingemissioncoefficient,j(t)=j exp−t/tf,andcalcu-
0 0.3
late the expected light curves for two energies differing
by 10 and for a range of tlc. As can be seen in Fig 3.2, 0.2
althoughtobs increases with increasing tlc, the difference
of tobs between (cid:6)LE and (cid:6)HE is practically preserved for 0.1
all tlc. Moreover,because for given(cid:6)LE and (cid:6)HE the ra- 0
tiooftf isalsogiven,observationsofthe1/edecaytimes 0 2 4 6 8 1t0 12 14 16 18 20
for (cid:6)LE and (cid:6)HE can be used to find both tlc and tf for
each energy. Fig.4.— Exponentially decaying light curves of a flare in the
MT.Highandlowenergyluminosities((cid:3)HE/(cid:3)LE =10)areplotted
3.3. The feasibility of the diagnostic (normalizedto1)forincreasingtlc. Solidlinesrepresent(cid:3)HE and
dashed lines (cid:3)LE. Colors represent tlc at differing factors of tf,
Very bright flares, such as the November 2010 flare of where tf,HE is normalized to 1. The dashed black line is the 1/e
3C454.3(Abdo et al.2011b)haveenoughphotonstatis- decaytime.
tics to produce light curves in two Fermi energy bands.
The practical application of our diagnostic requires that
Localizing energy dissipation in blazars 5
the decay times in different energy bands have statis- and 1 GeV, R (cid:2) 2.3 × 1018 Γ10(Δtmax,hLMT,45/(1 +
tically meaningful differences if the flare occurs within z)1/2)1/2cm. The Lorentz factor can be estimated from
the MT. To evaluate if this is the case for a flare as VLBIstudies(e.g.Jorstad et al.2005)andtheMTlumi-
bright as that of 3C 454.3, we adopted the maximum nosity can be taken to be a fraction ξ ∼0.1−0.5 of the
observed errors in the 0.1−1 GeV range and > 1 GeV accretiondiskluminosityorinsomecasescanbedirectly
range (Abdo et al. 2011b) and produced simulated data measured(e.g. Landt et al. 2010; Malmrose et al.2011).
assuming energy-dependent cooling in the form of expo-
nentially decaying light curves. We fitted an exponen- 4. CONCLUSIONS
tialdecayfunctiontothe simulateddataforeachenergy
We presented a diagnostic test for determining if the
band, with the characteristic decay time as a free pa-
GeVemissioninpowerfullblazarsoriginatesfromwithin
rameter. Thedecaytimeswerecoveredwerestatistically
or outside the BLR. Our method utilizes the fact that if
distinguishable, suggesting that our diagnostic is appli-
electronscoolviaICscatteringonBLRphotons,cooling
cable, at least for the brightest flares observed.
occurs at the onset of the KN regime and the resulting
cooling times (and thus light curves) should be achro-
3.4. Constraints from upper limits of the decay time matic. IfcoolingoccursviaICscatteringoflessenergetic
difference MT photons, the electron cooling times, and thus light-
curves,shouldexhibitsignificantenergy-dependenceand
For flares from which no statistically significantdiffer-
decrease as photon energy increases. The energy depen-
ence in the decay time can be established, constraints
dence of the cooling time difference perseveres in the
can still be imposed on the location of the Fermi de-
presence of energy independent timescales such as the
tectedemissionbyconsideringΔtmax,themaximumde- light crossing time. The method is applicable for the
cay time difference allowed by the data, between a high brightest Fermi γ-ray flares, and can provide upper lim-
energy(cid:6)HE andalowenergy(cid:6)LE. Therequirementthat its on the flare location even when the decay times in
Δtmax ≥tf((cid:6)LE)−tf((cid:6)HE) canbe castedasupper limit different energies are statistically indistinguishable.
for the location R of the Fermi emission
(cid:8) (cid:9)
R(cid:2) √ 2σTLMTΓ2Δtmax 1/2, coWmme ethnatsnkantdhesurgefgeerseteioLnus.igi Foschini for his thoughtful
3 3πmec2(1+z)1/2(cid:6)M1/2T((cid:6)L−E1/2−(cid:6)H−1E/2) We acknowledge support from NASA ATFP grant
(4) NNX08AG77G, Fermi grant NNX12AF01G. E.P.
where LMT is the MT luminosity. In terms ofquantities and M. G. acknowledge support from LTSA grant
usedin§2.1andfor(cid:6)LE, (cid:6)LE correspondingto100MeV NNX07AM17G.
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