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arXiv:1112.2948v1 [astro-ph.HE] 13 Dec 2011
DRAFT VERSION DECEMBER 14, 2011
Preprint typeset using L
A
TEX style emulateapj v. 5/2/11
A GENERAL RELATIVISTIC EXTERNAL COMPTON-SCATTERING MODEL FOR TEV EMISSION FROM M87
YU-DONG CUI1, YE-FEI YUAN1a, YAN-RONG LI2, JIAN-MIN WANG2
1 Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy, University of Sciences and Technology of China, CAS, Hefei, Anhui
230026, China
2 Key Laboratory for Particle Astrophysics, Institute of High Energy Physics, CAS, 19B Yuquan Road, Beijing 100049, China
Draft version December 14, 2011
ABSTRACT
M87 is the first detected non-blazar extragalactic Tera-Electron-Volt (TeV) source with rapid variation and
very flat spectrum in the TeV band. To explain the two-peaks in the spectral energy distribution (SED) of the
nucleus of M87 which is similar to those of blazars, the most commonly adopted models are the synchrotron
self-Compton scattering (SSC) models and the external inverse Compton scattering (EIC) models. Considering
that there is no correlated variation in the soft band (from radio to X-ray) matching the TeV variation, and
the TeV sources should not suffer from the γγ absorption due to the flat TeV spectrum, the EIC models are
advantageous in modeling the TeV emission from M87. In this paper, we propose a self-consistent EIC model
to explain the flat TeV spectrum of M87 within the framework of fully general relativity, where the background
soft photons are from the advection-dominated accretion flow (ADAF) around the central black hole, and the
high energy electrons are from the mini-jets which are powered by the magnetic reconnection in the main jet
(Giannios et al. 2010). In our model, both the TeV flares observed in the years of 2005 and 2008 could be well
explained: the γγ absorption for TeV photons is very low, even inside the region very close to the black hole
20Rg∼50Rg; at the same region, the average EIC cooling time (∼102∼103s) is short, which is consistent with
the observed time scale of TeV variation. Furthermore, we also discuss the possibility that the accompanying
X-ray flare in 2008 is due to the direct synchrotron radiation of the mini-jets.
Subject headings: black hole physics — galaxies: individual (M87)
1. INTRODUCTION
Unlike blazars and the Galactic sources (e.g. SNRs), which composite the most population of TeV sources, M87 is the
first discovered radio galaxy with TeV radiation. Recently three other radio galaxies Centaurus A, 3C66B and IC310 were
also identified as TeV sources (Aharonian et al. 2009; Aliu et al. 2009; Aleksi´
c et al. 2010). Comparing to blazars, M87 has
much milder variations in both optical and X-ray band; most importantly, the prominent kpc-scale jet of M87 has a very large
viewing angle ∼30◦with respect to the line of sight (Bicknell & Begelman 1996; Aharonian et al. 2006). In 2005, rapid TeV
variation (1−2days) was discovered with flat spectrum for the first time, but without correlated X-ray variation from the nuclear
core (Aharonian et al. 2006). While in 2008, the radio, X-ray, TeV joint observation discovered that TeV flares lasts 2 weeks
accompanied with an X-ray flare and a radio flare inside the unresolved nuclear core (30 ×60Rs) as well as with a radio blob
moving out of the unresolved core (Acciari et al. 2009). Here Rsused in the VLBA observations are based on the black hole
(BH) mass of M87 MBH = 6 ×109M⊙(Gebhardt & Thomas 2009). Recently, a TeV flare in 2010 which is very similar to the
previous TeV flares in 2005 and 2008 was reported. Further observations at X-rays and radio find the correlated X-ray flare, but
no enhanced radio flux from the core (Abramowski et al. 2011; Harris et al. 2011). In this paper, we adopt MBH = 3×109M⊙
(Macchetto et al. 1997) to be consistent with the advection-dominated accretion flow (ADAF) models and the mini-jet models in
the previous studies (Li et al. 2009; Giannios et al. 2010).
Although M87 has a large viewing angle, it is very near to the Earth with a distance of ∼16.7Mpc. Owing to its proximity, it
is proposed that M87 might be a misaligned blazar (Tsvetanov et al. 1998). Whereas blazars are believed to have jets beaming
towards us, TeV sources in M87 could be shocks with relativistic bulk velocity inside the jets. Recent observed minute-scale
variation from galaxies like Mrk 421 (Fossati et al. 2008) and PKS 2155-304 (Aharonian et al. 2007) indicates that TeV sources
should be compact and very close to the BH. Comparing to the TeV flares of blazars, the slower variation (1−2 day) detected in
M87 could be the results of too few observed TeV photons (each data point requires integration of photons for the whole night)
or the much lower Doppler factor of the bulk velocity of the TeV sources due to the large inclination. Furthermore, unlike the
steeper TeV spectrum of blazars, the much flatter TeV spectrum of M87 could be mainly due to the lack of γγ absorption. The
large viewing angle may play an important role in avoiding γγ absorption within the jet; thanks to its proximity and the dimness
of its host galaxy, the absorption to TeV photon from M87 caused by the galactic and the intergalactic background soft photons,
as well as the cosmic background photons is rather weak (Neronov & Aharonian 2007).
To explain the spectral energy distribution (SED) of the nucleus of M87, the one zone synchrotron self-Compton(SSC) models,
which have been applied to the TeV flares in blazars (e.g. Tavecchio et al. 1998; Katarzy´
nski et al. 2001), face difficulties in fitting
the two peaks in the SED, however, in the multi-zone SSC models, the TeV source is separated from the soft ones, therefore the
whole SED could be easily fitted as long as there are enough SSC blobs with specific locations, electron distributions and bulk
velocity (e.g. Tavecchio & Ghisellini 2008; Lenain 2007; Georganopoulos et al. 2005). The multi-zone SSC models could also
provide better explanation for the rapid variation, and the orphan TeV flares (the variations in the soft band can not connect with
acorresponding author: yfyuan@ustc.edu.cn
2
FIG. 1.— The contour of τγγ = 0.1 or 1 in the α,βplane. Where rrepresents the distance to the BH in the Boyer-Lindquist frame. The viewing angle is taken
to be 30◦. The blank region in the lower panels is the region with τγγ ≤1.
the TeV variation). Furthermore, considering the very flat power-law SED of M87 in the TeV band with index p≃−2.2∼−2.6,
the γγ absorption provides crucial constrains on the SSC models. So far, most of the SSC models still have problems in explaining
the very flat TeV spectrum due to the certain γγ absorption, therefore the external inverse Compton (EIC) process could be more
likely responsible for the TeV flare (Begelman et al. 2008; Giannios et al. 2009, 2010). In the EIC models, the TeV source is far
away from the soft one, or has the relativistic bulk velocity with respect to the soft one, thus the γγ absorption can be reduced.
In those models mentioned above, how the very high energy (VHE) particles are produced is still an open question. It is
generally believed that VHE particles are accelerated by the shocks in jets. There are some other possibilities include the mini-
jets powered via the magnetic reconnection in the main jet (Giannios et al. 2010, and references therein); the magnetic centrifugal
acceleration in the vicinity of BH (Neronov & Aharonian 2007; Rieger & Agaronian 2008), and so on. In the mini-jets model
(Giannios et al. 2010), magnetic reconnection within the main jet produces two oppositely directed (in the rest frame of the
main jet) mini-jets, in the laboratory frame, one of them always points within the angle of the main jet and is observable in
blazars because their jets point at us. The other mini-jet (its counterpart) points outside the opening angle of the main jet and is
potentially observable to off-axis observers in case of the misaligned jets, such as those of M87 and Centaurus A. In a word, the
great advantage of the mini-jets model is that even at large inclination, mini-jets with a high bulk speed can still be detected, which
is helpful for explanation of the fast TeV variation from M87. After all, in order to avoid the γγ absorption, the energy density
of the soft synchrotron photons in the TeV source must be limited, therefore, the minimal Lorentz factor of the VHE particles is
generally assumed to be 103−4and the strength of the magnetic field in the TeV source below several Gauss (Giannios et al. 2010).
Beside the direct inverse Compton process of the VHE electrons, there are also some alternative models to produce the SED of
the TeV flares, such as the hadronic models including, among which, the interaction between the VHE protons and soft photons
(Reimer et al. 2004) and the proton-proton collision process when a red giant was passing the base of the jet (Barkov et al. 2010).
In this paper, we develop a fully general relativity EIC model for explaining the TeV emission from M87, in which the soft
photons emanate from the ADAF around the BH. In §2, we investigate the safe zone of TeV photons (the γγ optical depth is
below unity). The technical details of our fully general relativity EIC model can be found in §3. The numerical results and the
discussions are given in §4 and §5, respectively.
2. CONSTRAINTS ON THE LOCATION OF TEV SOURCES
The rapid TeV variation of M87 (tvar <1−2 days) found both in 2005, 2008 and 2010 indicates that the TeV photons should
come from a compact source very close to the black hole (RTeV .ctvarδD, where δDis the Doppler factor of the source). Especially
the TeV flare in 2008, which is accompanied with a radio flare, lies inside the unresolved region and there is a radio blob moving
outwards. Again, this indicates that the TeV source might be near to the BH and its distance might be less than ∼100Rs
(Beilicke et al. 2010).
As mentioned above, beside the constrains from the VLBA radio image and the variation time scale of the TeV emission, the
background soft photons could also lay strong constrains on the location of the TeV sources, in consideration of the γγ absorption.
Both the TeV flares in 2005, 2008 and 2010 had shown very flat power-law spectrum (0.1∼10 TeV) strongly suggesting quite
weak γγ absorption. Therefore, the EIC process seems to be a more plausible mechanism to produce the flat TeV spectrum, while
the SSC models suffer from certain γγ absorption (Giannios et al. 2010). Even in the EIC models, if the source of soft photons
is from a homogeneously isotropic blob whose size is about 50Rgand infrared luminosity is about LIR ∼1041erg/s, the location
of the TeV sources could be still limited to be no deeper than ∼5Rginside that blob.
The observed soft photons from M87 could be mainly either from the disk or from the outflow/jet. According to the VLBI
observations of M87, its jet is well known with a large inclination. However, the base of the jet seems to havea large opening angle
(θopen ∼30◦inside the region ∼70Rs, Junor et al. 1999; Ly et al. 2007; Acciari et al. 2009), therefore the jet might contribute
to the observed soft emission. Due to the slight variation of the observed flux of soft photons (from radio to X-ray) from M87
nucleus, here we suggest that the observed soft photons are mainly from the accretion disk around the central black hole as in Li
et al. (2009).
3
By applying the ADAF model to the nuclear emission of M87, Li et al. (2009) obtained the accretion rate of ADAF in M87,
generally consistent with the previous estimate of the Bondi accretion rate from the Chandra X-ray observation (Di Matteo et
al. 2003). They then calculated optical depth of the radiation fields from the ADAF to TeV photons due to γγ absorption. The
resultant optical depth suggests that the location of TeV sources should be larger than ∼10Rg, in order to avoid the significant
γγ absorption to a 10 TeV photon (Wang et al. 2008; Li et al. 2009). Here we try to map a more detailed safe zone (τγγ ≤1)
for TeV photons in the vicinity of BH. As in Li et al. (2009). For this purpose, we calculate the optical depth (τγ γ ) to 10 TeV
photons emanating from vicinity of the central BH in the Kerr spacetime. The TeV photons move outwards along their geodesic
trajectories and reach the observer’s sky at points described by the impact parameters αand β. Here αand βrespectively represent
the displacement of the image perpendicular to the projection of the rotation of the black hole on the sky and the displacement
parallel to the projection of the axis (see e.g. Fig. 1 of Li et al. 2009). The resultant contour of τγ γ as a function of the location
of the TeV sources for τγγ = 1 and 0.1 in the αβ plane can be obtained (see Fig. 1).
As shown in Fig. 1, it is obvious that the larger the spin a, the deeper the safe zone. For instance, for a= 0.998, the safe zone
can reach even to 10Rgalong some trajectories of 10TeV photons, the reason is that for larger BH spin, the infrared-UV radiation
is concentrated in the inner disk. Therefore, the colliding angle between the soft photons and the TeV photons in the mini-jets is
smaller, significantly reducing the γ γ absorption. Besides, in the panels of a= 0,0.8, the asymmetricity is caused by the rotation
of the disk and the viewing angle(30◦) of the observer. While in the panels of a= 0.998, since the disk become a more compact
source of soft photons, the asymmetricity caused by the disk become weaker.
3. FULLY GENERAL RELATIVITY EXTERNAL-INVERSE COMPTON MODEL
3.1. The TeV source
In our EIC model, following Giannios et al. (2010), the mini-jets powered by magnetic energy in the jet correspond to be the
TeV sources. For a clarity, we present the details of the model in what follows.
The strength of the magnetic field in the main jet is estimated as,
B2
j
4π= Lj,iso
4πr2
jcΓ2
j!σ
1+σ,(1)
where Bjis the magnetic strength, Lj,iso (∼1045 erg/s) is the observed isotropic power of the jet of M87 (Bicknell & Begelman
1996; Reynolds et al. 1996; Owen et al. 2000; Stawarz et al. 2006; Bromberg & Levinson 2009), Aj(πrj2) is the cross sectional
area of the jet, σis the ratio of the magnetization energy to the kinetic energy of the main jet, Γjis the Lorentz factor of the main
jet, and cis the light speed.
Although the inclination of the jet is about 300, the mini-jets (blobs of plasma with characteristic Lorentz factor Γco at angle
θmini with respect to the jet in the jet rest frame) are capable of beaming towards us with a high bulk velocity Γem =ΓjΓco(1 +
βjβco cosθmini) in the laboratory frame. The bulk Lorentz factor of the mini-jets in the jet rest frame is about Γco ∼σ1/2, which
corresponds to the Alfvén speed of the plasma in the jet. The characteristic thermal Lorenz factor of the electrons in the mini-jets
rest frame is about γ′
ch ∼fσ1/2mp/me. The energy distribution of the high energy electrons is assumed to be
N′
e(γ′) = Ne(γ)/δ3
D=N0γ′p,(2)
where 104.γ′=γ/δD<∞,p.−3.2. In our canonical model, Γjis taken to be 5, and Γem = 12 (δD= 23, if the mini-jets are
beaming toward us). These parameters are consistent with the original mini-jets model of Giannios et al. (2010).
3.2. The Local Soft Radiation Field
In our EIC model, we assume that the soft photons are from the accretion disk and the TeV source (mini-jets) is located along
the major axis of jet with a height HTeV above the central black hole. To investigatethe EIC process, we apply the same ray-tracing
technique as discussed in Li et al. (2009). In Li et al. (2009), the authors discussed the optical depth of the TeV photons due to
colliding with the soft photons from the accretion disk. In this work, we investigate the Compton scattering of the soft photons
from the disk by the VHE electrons in the mini-jets (as shown in Fig. 2), therefore, we just simply replace the TeV photons in the
model of Li et al. (2009) with the VHE electrons.
To obtain the flux density of the soft photons from the disk, the global dynamical structure of the ADAF, such as the four
velocity of the fluid in the disk, the temperature of ions and electrons, should be determined first; then the local emergent spectra
Iνd(rd) at the radius rdin the rest frame of the fluid can be calculated. Using the ray-tracing technique, the observed SED can be
obtained to fit the multi-wavelength observations of M87. The fitting parameters of the ADAF are obtained by Li et al. (2009).
In what follows, we summarize the procedure to obtain the radiation energy density of the soft photons from the direction (θs, φs)
at the colliding location (rc, θc,φc).
In the locally non-rotating frame (LNRF), at the interacting place (rc,θc,φc) , the two motion constants of the soft photons (λs,
Qs) are related with their traveling direction (θs, φs) as follows:
λs=A
1+ωA,Qs=B2−(acosθc)2+(λscotθc)2.(3)
where,
A=sinθssinφssinθcA
Σ∆1/2,B=sinθscosφsA1/2(1 −ωλs)
∆1/2,(4)
4
FIG. 2.— A schematic picture for the disk dominating external Compton-scattering model. A mini-jet is beaming toward the infinity observer, and the soft
photons are from the disk.
where A,Σ,∆, and ωare the metric functions defined in Bardeen et al. (1972).
After knowing the constants of motion λsand Qs, the soft photons can be traced back to the disk at certain radius rdby solving
the geodesic equations (e.g. Bardeen et al. 1972; Yuan et al. 2009)
T=±Zrd
rc
dr
√R(r)=±Zθd
θc
dθ
√Θ(θ)(5)
where Tis the affine parameter and the ±signs represent the increment (+) or decrement (−) of rand θcoordinates along the
trajectory, respectively.
Along these trajectories, the redshift factor gsfor a soft photon travels from disk to the IC interaction location can be obtained
by
gs=νs
νd=eµ
(t)(LNRF)Ps
µrc
eµ
(t)(LRF)Ps
µrd
=e−ν(1−ωλs)|rc
γrγφe−ν1−Ωλs∓βrR(r)1/2
γφA1/2rd
.(6)
where νsand νdare the frequency of the soft photon at the colliding place and the disk, and γr= (1 −β2
r)−1/2and γφ= (1 −β2
φ)−1/2
are the Lorentz factors of the radial and azimuthal velocity of the fluid in the accretion disk, respectively.
According to the Liouvell theorem, the final radiation energy density of the soft photons at the IC location (rc,θc, φc) can be
written as
Us(hνs,θs,φs,rc,θc, φc) = Iνd(hνd,rd)g3
s
c,(7)
where his the Planck’s constant.
3.3. The VHE electrons
After determining the radiation energy density of the soft photons Usat the colliding points, the direction of motion of the
VHE electrons which produce the observed TeV photons is needed to calculate the TeV spectra. Due to the effects of special
relativity, it is a reasonable assumption that both the direction of the relativistic electrons and that of the TeV photons are the
same. Denoting the two constants of the motion of the TeV photons as λIC and QIC, the beaming direction of the TeV photons is
as follows:
cosθIC =eµ
(r)PIC
µrc
−eµ
(t)PIC
µrc
=±R(r)1/2
A1/2(1−ωλIC),(8)
sinθIC cosφIC =eµ
(θ)PIC
µrc
−eµ
(t)PIC
µrc
=±Θ(θ)1/2∆1/2
A1/2(1−ωλIC),(9)
5
sinθIC sinφIC =eµ
(φ)PIC
µrc
−eµ
(t)PIC
µrc
=λIC
sinθc
Σ∆1/2
A(1−ωλIC),(10)
where the trajectory of the TeV photons determined by λIC and QIC can be found by tracing the observed TeV photons from the
infinity (r=∞,θobs = 30◦) to the interacting location (r=rc, θ =θc). As assumed above, the TeV source is located inside the jet,
therefore, θc= 0 and subsequently λIC = 0.
After determining the trajectory (λIC,QIC ) of the TeV photons, the corresponding redshift factor gIC for the γ-ray photons
traveling from the IC interaction location to the infinity is given by
gIC =νIC
∞
νIC
rc
=eµ
(t)PIC
µ∞
eµ
(t)PIC
µrc
=Σ1/2∆1/2
A1/21
1−ωλIC rc
.(11)
3.4. Spectrum of Compton-scattered external radiation fields
Given the radiation energy of the soft photons and the energy distribution of the high energy electrons, the Compton spectral
luminosity is given by (see Finke et al. 2008 and Dermer et al. 2009 for more details):
fEC
local(ǫIC) = ǫICLC(ǫIC,ΩIC)
d2
L=cπr2
e
4πd2
Lǫ2
ICδ3
DZ2π
0dφsZ1
−1dµsZǫs,hi
0dǫsIνdg3
s
ǫ2
sZ∞
γlow
dγN′
e(γ′)
γ2Ξ,(12)
where ǫsis the energy of the soft photons, ǫIC is the energy of the γ-ray photons created via the IC process, µs= cos(θs), and
µIC = cos(θIC). With the approximation that scattered photons travel in the same direction as the VHE electrons, the Compton
cross section can be drawn as (Dermer et al. 1993 ; Dermer et al. 2006)
dσIC(ǫs, ǫIC, γ, ψIC)
dǫIC ∼
=πr2
e
γ¯ǫΞ,¯ǫ
2γ< ǫIC <2γ¯ǫ
1+2¯ǫ(13)
¯ǫ≡γǫs(1 −q1−1/γ2cosψIC)∼
=γǫs(1 −cosψIC),(14)
where
Ξ≡y+y−1−2ǫIC
γ¯ǫy+ǫIC
γ¯ǫy2
,(15)
y≡1−ǫIC
γ,(16)
and ψIC is the interaction angle between the VHE electron and the soft photon during the IC process.
cosψIC =µICµs+q1−µ2
ICq1−µ2
scos(φIC −φs),(17)
The optical depth τ(ǫIC,HTeV,a) of these γ-ray photons (ǫIC) can be integrated along their trajectories as in Li et al. (2009),
τγγ (λIC,QIC, ǫIC) = ZZZ (1 −cosψγγ )σγ γ (ǫs,ǫIC,ψγγ )Iνd
cǫsg3
sdΩsdǫsdl,(18)
where dl=eνΣdTis the proper length differential with dTdefined to be differential of the affine parameter Talong the
trajectory of the TeV photons, and ψγ γ is the interacting angle between the TeV photon (ǫIC) and the soft photon (ǫs).
Consequently, the final observed SED in the infinity would be,
fEC
Earth ǫIC gIC
1+z=e−τ(ǫIC)gIC
1+z4fEC
local (ǫIC).(19)
4. NUMERICAL RESULTS
4.1. HTeV,a dependence
In this paper, we choose the BH spin as a= 0,0.8,0.998 to be consistent with the ADAF model used in fitting the SED (from
radio to X-ray) of M87 in Li et al. (2009). The location of the TeV source is set to be very close to the BH as HTeV = 5,10,20,50,
and 100Rg, respectively. The distribution of the VHE electrons is described by N0= 0.4×1050,γ′
min = 104, and p=−3.2, where
the maximal index pis chosen to fit the very flat TeV flare spectrum observed in 2005 and 2008 (Giannios et al. 2010).
In Fig. 3, we show the dependence of the SED of the EIC scattering on the height of the TeV source and BH spins. We can find
that the efficiency of the Compton-scattering increases dramatically if the TeV source is closer to the disk. Furthermore, if the
location of the TeV source HTeV is below 20Rg, the Compton-scattered luminosity of the soft radiation fields from the the disk
6
FIG. 3.— SED of the external Compton-scattering model with the different spins of the black hole (a= 0,0.8,0.998) and the location of the mini-jets is above
the black hole (Left panel: HTeV = 5,50Rg,right panel: HTeV = 10,20,100Rg). The energy distribution of the VHE electrons are determined by three parameters:
N0= 0.4×1050,γmin = 104and p=−3.2. The Lorentz factor of the mini-jets in the laboratory frame is taken to be Γem = 12. MAGIC observation in 2008 is
shown in the symbol of butterfly (Albert et al. 2008).
around the black hole with spin a= 0.998 is higher than that from the black hole with spin a= 0; meanwhile, if the location of
the TeV source is higher than 20Rg, for a= 0, the Compton-scattered luminosity is higher than that for a= 0.998. This is because
for a= 0.998, the soft radiation field from the disk is more compact, i.e., the soft radiation field is strong in the vicinity of the
BH, however,at the distance far away from the disk, the region of the soft radiation field looks like a point source. Therefore, the
colliding angle between the soft photons and the VHE electrons in the mini-jets is smaller, which reduces the rate of the inverse
Compton scattering significantly.
It is also clearly shown in Fig. 3 that each spectrum has an exponential cut off beyond Ecut ∼108∼9mec2which is caused by the
γγ absorption. If the location of the TeV source is nearer to the BH (HTeV <20Rg), the spectrum will also suffer from the severe
γγ absorption in the observable band 0.1−10TeV. In each of those reduced spectrums of HTeV = 5,10, there is always a warp up
trend at EIC ∼108mec2which is caused by the relatively low optical depth τγ γ at that band, since the spectrum of the disk has a
relatively low luminosity at Es∼10−2mec2.
4.2. TeV flares and The X-ray companion
In 2008, observations had shown that the TeV, X-ray, and radio flares are well correlated (Acciari et al. 2009), though no X-ray
correlation was found in 2005. We propose that the accompanying X-ray flare in 2008 results from the synchrotron radiation of
the VHE electrons in the mini-jets, in other words, the X-ray flare could be a byproduct of the TeV flare, which just happens
to be above the background X-ray flux. While in 2005, it is more likely the X-ray flaring flux is below the more stable X-ray
background which is attributed to the disk and/or the corona. It is notified that the TeV flare in 2008 is stronger than that in 2005,
and the corresponding X-ray flare is rather mild: during the flaring, the X-ray flux only increased about two times above the
average.
In Fig. 4, both the SED of the direct synchrotron radiation and the Compton-scattered radiation are shown. We choose HTeV =
20,50 to be as close to the BH as possible while avoid severe γγ absorption. Owing to the weak γ γ absorption, all the EIC
spectra have inherited the original power-law index of the VHE electrons, which is p=−3.2,−3.5. As expected, the corresponding
synchrotron spectrum fitting the X-ray flares in 2008 is comparable with or exceeds the average X-ray flux, while the X-ray flux
in 2005 is buried beneath the background flux.
The magnetic field in the mini-jets is taken to be B= 1.6,4,2.6,8G, respectively, which is used to calculate the direct syn-
chrotron radiation. The strength of the magnetic field used in this work is consistent with that in the original mini-jet model
Bem (Giannios et al. 2010, and references therein), that is, .0.8(Lj,iso/1045 erg/s)1/2(100Rg/rjet)(5/Γj)2G. We propose that the
base of jet is cone shaped as rjet ∼0.5Hsinθopen, where the full opening angle θopen ∼30◦(Acciari et al. 2009), which leads to
B(50Rg).6.4G, B(20Rg).16G. The more detailed parameters are shown in Table 1.
There are four main parameters N0,p,HTeV,ain our models. Where the spin ais fixed because it only slightly influence the
SED for HTeV = 20,50 as shown in Fig. 3; the electron power-law index pis fixed to follow the observed TeV spectrum index
7
FIG. 4.— Synchrotron (dashed lines and dash-dotted lines) and the external Compton-scattered (solid lines and dotted lines) emission from a Mini-jet which are
modeled to fit the observed emission from M87, the detailed model parameters are shown in Table one. The observed emission include: (1). MAGIC observation
in 2008 which is shown in the symbol of butterfly (Albert et al. 2008); (2). HESS observation in 2005 which is indicated by the black square with long error-bars
; (3). HESS observation in 2004 which is labeled as the black triangle with long error-bar (Aharonian et al. 2006); (4). FERMI observation in 2009 which is
labeled as the black solid circle with error-bars (Abdo et al.2009); (5). The approximate data from Chandra is shown in the hollow triangles. With 5% uncertainty,
the one on the top represent the flux of nucleus in 2008 Feb 16 (data are provided by Dr. D. E. Harris), the other three represent the flux in 2005 Apr 22, Apr
28, May 04 separately (Harris et al. 2006, 2009); (6). Typical nucleus emission is shown in the asterisk.(Harms et al. 1994; Maoz et al. 2005; Reynolds et al.
1996; Sparks et al. 1996). The synchrotron-self Compton emission is too weak to be shown in this figure.
TABL E 1
MODEL PARAMETERS USED IN FITTING THE OBSERVATIONS SHOWN IN FIG.4.
EIC lines in Fig.4 HTeV(Rg)γmin N0(counts) p B(G)
Fitting 2008MAGICawith two lines on the top
dash-3doted line 50 1041.0×1051 -3.2 2.6
dotted line 20 1041.0×1050 -3.2 8
Fitting 2005HESSbwith two lines in the middle
dashed line 50 1040.6×1051 -3.2 1.6
dash-dotted line 20 1040.4×1050 -3.2 4
Fitting 2004HESSc+2009FERMIdwith two lines at the bottom
solid line 50 1041.6×1052 -3.5 –
solid line 20 1040.5×1051 -3.5 –
NOTE. — The bulk speed of the mini-jets in local lab frame is taken as Γmini = 12 and the viewing angle is set as θobs = 30◦.
The parameter spin of the BH is chosen as a= 0.8 , because the changing of the spin barely influence the shape of the spectrum,
it just slightly boost the entire SED up or down when applying HTeV = 20,50Rg.
aMAGIC observation of M87 in 2008, as a flaring state
bHESS observation of M87 in 2005, as a flaring state
cHESS observation of M87 in 2004, as a quiet state
dFERMI observation of M87 in 2009, as a quiet state
and the γγ absorption is too low to soften the spectrum; the other two parameters N0and HTeV are degenerated, making it hard
to draw any solid constrains by fitting the SED. To be more specific, the final TeV flux should be roughly FIC ∼N0/H2
TeV. As
shown in Table 1, to fit the same observationdata, when the HTeV changes from 20Rgto 50Rg, we need about 10 times more VHE
electrons. Therefore, considering that both the TeV flares in 2005 and 2008 have the same aand p(−2.2∼−2.6), we suggest that
the TeV source in 2008 may be more powerful or/and be closer to the BH.
Being closer to the BH, the TeV source will suffer more γγ absorption, which would soften the spectrum. But no obvious
changes of the spectrum index can be drawn from the observations in 2005 and 2008 due to the long error-bars. It is noticed that,
as shown in Fig. 3, the γγ absorption barely influences the γ-ray spectrum below 0.1 TeV, therefore the Fermi telescope should
be able to provide better constrains on the power-law index of the VHE electrons.
As shown in Fig. 4, we also fit the quiet state (2004HESS+2009FERMI) spectrum of M87 with the mini-jets model. In
other words, the quiet TeV flux could be attributed from some mini-jets which are weaker, misaligned, or heavily absorbed by
synchrotron or/and γγ pair production (lower Ne,p,δD). Where the misaligned Mini-jets could be considered as weaker mini-
jets consisted of much fewer VHE electrons beaming towards us with lower bulk velocity, see details in (Giannios et al. 2010).
8
Therefor we could not exclude the possibility that weaker flares are due to misaligned mini-jets, which are supposed to have
lower δD. It should be noticed that lower δDcould not explain the steeper spectrum.
As mentioned above, the soft photons field are demanded to satisfy both the low γγ absorption rate and the high IC cooling
efficiency. In models as shown in Fig. 4, apparently, the synchrotron cooling effect is not dominating since the EIC flux is much
higher. The IC cooling time is short enough so that there is no influence on the observed rapid variation (1 ∼2days):
Ee∼LGeV−TeVtcool/(4Γ2
em),Ee∼Γem Z∞
104γ′N′
e(γ′)dγ′,tcool <tvar,(20)
where LGeV−TeV is the isotropic total EIC flux and Eeis the total energy of VHE electrons in the lab frame. With the parameters
listed in Table 1, as expected, one can find tcool ∼102−3s. During this cooling time, the mini-jets can only travel less than ∼0.5Rg,
which is consistent with the above assumption that the location of the TeV source keeps unchanged during a flare event.
5. CONCLUSIONS AND DISCUSSIONS
In this paper, by taking into account the fully general relativity effects, we propose a disk-dominating external Compton-
scattering model for explaining the flat TeV radiation from M87. The external Compton-scattering model suffers much less self-
γγ absorption, comparing to the one-zone self-synchrotron Compton model, in which the soft photons and the VHE electrons
are from the same blobs. The advantage of the EIC model in which the soft radiation is from the accretion disk is that the
soft radiation source could be more compact and further away from the TeV source than ones in the SSC models, in which
the γγ absorption can be reduced significantly. Besides, our EIC model is also supported by the observed mild IR-UV-X flux
variations of the nucleus and the large viewing angle of the jet of M87 (the nuclei flux with viewing angle 30◦is unlikely to be
contaminated by the jet, neither to be blocked by the disk itself). It should be noticed that the VHE electrons and TeV photons
may be influenced by some outflows with the anisotropic radiation at the soft band which are not beaming towards us, such as
the jet itself. Unfortunately, the base of the jet of M87 appears to be quite chaotic, thus it is hard to draw any conclusions about
the detailed structure of jet/outflows (Perlman et al. 2011). In our model, the TeV sources are the mini-jets which are easily able
to beam towards us with high Doppler factor and give rise to the observed VHE radiation.
How to distinguish between SSC and EIC models by the future observations? The main difference between these two models
is that the IR-UV variation and TeV flares are not necessarily correlated in the EIC models, but they are in the SSC models,
especially the multi-zone SSC model. Therefore, we can distinguish between the SSC and EIC models by the simultaneous
observations of the IR-UV emission during the TeV flare. Unfortunately, during the 2005 TeV flares, there is no accompanied
HST observation of M87. With the better sensitivity of CTA (it is about >10 times better than those of the present Cerenkov
telescopes), we will be able to detect the fainter flares and obtain the minimal variation time scale of the TeV flares, which
increases the opportunity of finding the correlated variation between IR-UV and TeV emission.
In our models, with little γγ absorption, all the EIC spectra at the observational band have inherited the original power-law
index of the VHE electrons. After fitting those spectra, we calculate the cooling time of the VHE electrons in the mini-jets (see
section 4) to make sure that they would not travel longer than ctvarδD. It turns out when TeV source is located at HTeV <50Rg,
the IC cooling time is very much shorter than the upper-limits of the observed TeV variation of 1-2 days. Therefore, if possibly,
the TeV source is located further away from the disk (HTeV >50Rg), the cooling efficiency of the VHE electrons in the mini-jets
is much lower, the mini-jets could move out of the main jet. As a result, the variation of the soft radiation background at the
different locations above the disk should be considered.
We also discuss the probability that the direct synchrotron radiation from the mini-jets may cause the correlated X-ray flare in
2008. As expected, according to our model, if the magnetic field is about several Gauss, the direct synchrotron flux from these
mini-jets which lies at the X-ray band can explain the X-ray flare very well but has no influence on the observed radiation at the
GeV-TeV band. However, the magnetic field Bcan not be constrained by any direct observation, as discussed above, and we only
have a rough estimate of the strength of the magnetic field supposed to be consistent with the mini-jets model. Considering that
the synchrotron flux is roughly about Fsyn ∼N0B2, it is obvious that the N0and Bare degenerated. If the TeV source is confined
inside the region 20Rg<HTeV <50Rg, the corresponding strength of the magnetic field is required to be about 2G<B<8G, in
order to produce the X-ray flare in 2008.
Dealing with the two weeks data of the 2008 flare from MAGIC, Albert et al. (2008) had separated the high state data ( ∼
1 day time scale) from the low state data and they found that during the high states, the spectra are harder: the spectrum index
of the high state is about 2.2, while that of the low state is about 2.6. Because the IC cooling time and the synchrotron cooling
time of VHE particles is short, the observed fastest variation should be dominated by the time of the acceleration, or even the
shifting of the beaming angle of the mini-jets. If there is no continuous acceleration of the relativistic electrons, the spectra
of the TeV flares will become steeper. In the year of 2008, VERITAS captured the TeV flare (Feb 9-13, 2008) which is close
to the date of the X-ray flare (Feb 16, 2008). VERITAS observation shows that the spectrum index of the TeV flare is about
2.4, which is softer than the earlier flares captured by MAGIC (Acciari et al. 2010). We suggest that the TeV flare captured by
VERITAS is happening during the rapid synchrotron cooling of the relativistic electrons in the mini-jet, and the X-ray flare could
be a byproduct of that TeV flare, as the X-ray flares in 2008. Our suggestion could naturally explain the X-ray excess and the
softer spectrum of TeV emission. There are two ways to check above suggestion: first, the flux of the X-ray via synchrotron
radiation should be anti-correlated with the TeV flux via EIC, which could be tested by the future observations with the higher
time resolution (less than 1 day); second, and the TeV flare should share the similar spectrum index with that of the X-ray flare.
Unfortunately, due to the pile up effect of X-ray observation (Harris et al. 2009), we can not obtain the correct spectrum index of
the X-ray flare.
9
We would like to thank the anonymous referee for her/his constructive suggestions and comments, and Dr. Daniel Harris
for providing his preliminary results on Chandra observations of M87. This work is partially supported by National Basic
Research Program of China (2009CB824800), the National Natural Science Foundation (11073020,10733010,11133005), and
the Fundamental Research Funds for the Central Universities (WK2030220004).
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