DTIC ADA465052: Is the High-Energy Emission from Centaurus A Compton-Scattered Jet Radiation?

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by  Defense Technical Information Center

Is the High-Energy Emission from Centaurus A
Compton-Scattered Jet Radiation?
1
J. G. Skibo , C. D. Dermer and R. L. Kinzer
E. O. Hulburt Center for Space Research
Naval Research Laboratory
Code 7650, Washington, DC 20375
ABSTRACT
We consider whether the hard X-ray and soft gamma-ray emission from Centaurus
A is beamed radiation from the active nucleus which is Compton-scattered into our line-
of-sight. We derive the spectrum and degree of polarization of scattered radiation when
2
incident beamed radiation is scattered from a cold (kT << mec ) electron cloud moving
with bulk relativistic motion along the jet axis, and calculate results for an unpolarized,
highly-beamed incident power-law photon source. The spectra of the scattered radiation
exhibit a cut o(cid:11) at gamma-ray energies due to electron recoil. The cut o(cid:11) energy depends
on the observer’s viewing angle and the bulk Lorentz factor of the scattering medium. We
(cid:12)t the OSSE data from Centaurus A with this model and (cid:12)nd that if the scatterers are
not moving relativistically, then the angle the jet makes with respect to our line-of-sight
(cid:14) (cid:14)
is 61 (cid:6) 5 . We predict a high degree of polarization of the scattered radiation below
(cid:24) 300 keV. Future measurements with X-ray and gamma-ray polarimeters could be used
to constrain or rule out such a scenario.
Subject headings: galaxies: individual | galaxies: active | galaxies: jets |
gamma rays: theory | radiation mechanisms: nonthermal |
polarization
1
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1994 2. REPORT TYPE 00-00-1994 to 00-00-1994
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Is the High-Energy Emission from Centaurus A Compton-Scattered Jet
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Radiation?
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Naval Research Laboratory,Code 7650,4555 Overlook Avenue, REPORT NUMBER
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1. INTRODUCTION
Centaurus A (NGC 5128), at a distance of 3-5 Mpc (z=0.0008), is the brightest
extragalactic source at photon energies (cid:15) (cid:24) 100 keV and one of the nearest active galaxies
(see Ebneter & Balick 1983 for a review). The radio emission from Cen A displays a
40 (cid:0)1
twin-jet structure with radio luminosity (cid:24) 10 ergs s , suggesting that Cen A is a
Fanaro(cid:11)-Riley Class 1 (FR1) radio galaxy (Fanaro(cid:11) & Riley 1974). If FR1 galaxies are the
parent population of BL Lac objects, as proposed in one version (Browne 1989; Padovani
& Urry 1990) of the AGN uni(cid:12)cation scenario (see Antonucci 1993), Cen A would be
classi(cid:12)ed as a BL Lac object if its jet were coincident with our line-of-sight. Evidence for
jet emission in Cen A comes from observations of a one-sided X-ray jet near the nucleus
(Feigelson et al. 1981) and, more recently, from observations (Morganti et al. 1991, 1992)
of emission line (cid:12)laments aligned along the direction of the X-ray jet and coincident with
the radio jet out to distances (cid:25) 10-20 kpc from the nucleus. From measurements of [OIII]
line emission, Morganti et al. conclude that the (cid:13)ux of the ionizing radiation in the 2-6
keV band is (cid:25) 200 times greater in the jet direction than along our line-of-sight, consistent
with the hypothesis that the emission is intrinsically beamed rather than collimated by
obscuring material.
Cen A has recently been observed at hard X-ray and gamma-ray energies with the
Oriented Scintillation Spectrometer Experiment (OSSE) on the Compton Gamma Ray
Observatory (CGRO;seeJohnsonet al. 1993,Kinzer et al. 1994). This instrumentoperates
< <
in the energy range 50 keV (cid:24) (cid:15) (cid:24) 10 MeV. The spectra observed from Cen A are much
harder than typical Seyfert spectra (Maisack et al. 1993; Johnson et al. 1994), but Cen
A has not been detected at > 100 MeV energies (R. C. Hartman, private communication,
1993), a range wheremanyblazars showstronggamma-rayemission (Hartmanet al. 1992;
Fichtel et al. 1993). In fact, Cen A is only weakly detected with the Compton Telescope
on CGRO in the 0.75 - 1.0 MeV energy band by combining data from 3 observing periods
(Collmar et al. 1993). A broken power-law gives an acceptable (cid:12)t to the OSSE Cen A data
1
(Kinzer et al. 1994), but provides no physical basis for the spectral softening in the hard
X-ray/soft gamma-ray regime.
In this Letter, we examine whether the high-energy emission from Cen A is scattered
jet radiation, since Comptonscattering of beamedradiation can produce cut o(cid:11)s in photon
spectra (Dermer 1993) due to the kinematic recoil of electrons. The precise value of the
observedcuto(cid:11)energyisafunctionofthescatteringangleandbulkmotionoftheelectrons.
Thus an incident power-law beam of photons will, after scattering, retain its power-law
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form in the Thompson regime ((cid:15) (cid:28) mec in the rest frame of the electron), but will be
2
cut o(cid:11) above a certain energy in the Klein-Nishina regime ((cid:15) (cid:29) mec ). In addition, the
scattered radiation can be highly polarized, depending on the scattering angle and initial
photon polarization.
2. ANALYSIS
Consider the Compton scattering of an unpolarized beam of gamma ray photons by
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a cold (kT (cid:28) mec ) cloud moving relativistically along the axis of the beam, which we
dN(cid:13)
take to be the positive z-axis. Let dtd(cid:10)d(cid:15)((cid:15);(cid:10)) represent the rate that photons are emitted
(cid:0)1 (cid:0)1 (cid:0)1
from the central source (photons s sr MeV ). In the single scattering approximation
(cid:0)1 (cid:0)2 (cid:0)1
((cid:28) (cid:28) 1) the photon (cid:13)ux (photons s cm MeV ) scattered into the direction (cid:10)0 with
respect to the z-axis and received by an observer located at distance r from the scattering
cloud is given by the expression
(cid:3) (cid:3) (cid:3)
1 (cid:3) Ne((cid:10) )d(cid:27)C (cid:3) (cid:3) dN(cid:13) (cid:3) (cid:3)
(cid:8)s((cid:15)s;(cid:10)0) = r2[(cid:13)(1(cid:0)(cid:12)cos(cid:18)0)]2 I d(cid:10) jdd(cid:15)(cid:15)(cid:3)(cid:3)sj d(cid:10)(cid:3)0((cid:15) ;(cid:18)s)dt(cid:3)d(cid:10)(cid:3)d(cid:15)(cid:3)((cid:15) ;(cid:10) ): (1)
(cid:3) (cid:3) (cid:3) d(cid:27)C (cid:3) (cid:3)
Here Ne((cid:10) ) is the electron column density in the direction (cid:10) ((cid:10)) and d(cid:10)(cid:3)0((cid:15) ;(cid:18)s) is the
2 (cid:0)1
di(cid:11)erential Compton cross section (cm ster ) for the scattering of a photon with initial
(cid:3) (cid:3) (cid:3) (cid:3) (cid:3)
direction (cid:10) and energy (cid:15) through an angle (cid:18)s into the direction (cid:10)0 with energy (cid:15)s.
The starred symbols represent quantities in the rest frame of the scattering cloud which
2
is moving with velocity (cid:12)c ((cid:13) = 1= 1(cid:0)(cid:12) ) along the z-axis in the stationary frame.
p
2
(cid:3)
For a photon of energy (cid:15) and direction ((cid:18);(cid:30)), the relevant transformations are (cid:30) = (cid:30),
(cid:3) (cid:3)
cos(cid:18) = (cos(cid:18) (cid:0) (cid:12))=(1 (cid:0) (cid:12)cos(cid:18)), and (cid:15) = (cid:13)(1 (cid:0) (cid:12)cos(cid:18))(cid:15). In equation (1) the factor
(cid:0)2 (cid:0)2
(cid:13) (1 (cid:0) (cid:12)cos(cid:18)0) relates the scattered emission in the rest frame of the cloud to the
emission received by the observer (cf. eq. [4.97b] of Rybicki & Lightman 1979).
The scattered photon energy is given by the well-known formula
(cid:3)
(cid:3) (cid:15)
(cid:15)s = (cid:15)(cid:3) (cid:3) ; (2)
1+ mec2(1(cid:0)cos(cid:18)s)
(cid:3) (cid:3) (cid:3) (cid:3) (cid:3) (cid:3)
where cos(cid:18)s = cos(cid:18) cos(cid:18)0+cos(cid:30) sin(cid:18) sin(cid:18)0. It can be seen upon inspection of equation
(2) that the recoil of the electrons imposes a kinematical cut o(cid:11) in the emergent photon
spectrum at an energy in the rest frame of the scatterer given by
2
(cid:3) mec
(cid:15)c = (cid:3): (3)
1(cid:0)cos(cid:18)s
(cid:3)
In this frame the cut o(cid:11) is only a function of the scattering angle (cid:18)s. However, in the
stationary frame, this cut o(cid:11) occurs at an energy given by
2
mec
(cid:15)c = : (4)
(cid:13)(1+(cid:12))(1(cid:0)cos(cid:18)s)
Hence, the cut o(cid:11) in the spectrum is both a function of the scattering angle (cid:18)s and the
bulk Lorentz factor (cid:13) of the scattering cloud.
Weconsidertwocasesfortheincidentphotonnumberintensity: (1)amono-directional
power-law beam along the positive z-axis, given by
dN(cid:13)1 1 (cid:0)(cid:11)
((cid:15);(cid:18)) = k1(cid:15) (cid:14)(cos(cid:18) (cid:0)1); (5)
dtd(cid:10)d(cid:15) 2(cid:25)
and (2) a power-law photon source which is isotropic in a frame moving relativistically
along the positive z-axis with velocity (cid:12)0c. The emission in the stationary frame in case 2
is beamed by virtue of relativistic motion and we have
(cid:0)(cid:11)
dN(cid:13)2 k2(cid:15)
((cid:15);(cid:18)) = 2+(cid:11): (6)
dtd(cid:10)d(cid:15) [(cid:13)0(1(cid:0)(cid:12)0cos(cid:18))]
3
Synchrotron-selfComptonmodels(e.g., Bloom&Marscher1993)andmodelsinvolving the
Comptonscattering of external photons(Dermer& Schlickeiser 1993; Sikora, Begelman, &
Rees 1994) both produce beaming patterns characterized by equation (6). The constants
k1 and k2 in equations (5) and (6) are easily normalized to the total jet luminosity or
photon number.
In the rest frameof the scattering cloud, the expressions for the received radiation are
(cid:3) (cid:3)(cid:0)(cid:11) (cid:3)
dN(cid:13)1 (cid:3) (cid:3) k1(cid:15) (cid:14)(cos(cid:18) (cid:0)1)
(cid:3) (cid:3) (cid:3)((cid:15) ;(cid:18) ) = (cid:3) (cid:11) (7)
dt d(cid:10) d(cid:15) 2(cid:25)[(cid:13)(1+(cid:12)cos(cid:18) )] ;
(cid:3)
dN(cid:13)2 (cid:3) (cid:3) (cid:3) (cid:0)(2+(cid:11)) (cid:3)(cid:0)(cid:11)
(cid:3) (cid:3) (cid:3)((cid:15) ;(cid:18) ) = f(cid:13)(cid:13)0[1+((cid:12) (cid:0)(cid:12)0)cos(cid:18) (cid:0)(cid:12)(cid:12)0]g k2(cid:15) : (8)
dt d(cid:10) d(cid:15)
The scattered photon (cid:13)ux is obtained by substituting equation (7) or (8) into equation (1)
and using the expression
2 (cid:3) 2 (cid:3) (cid:3)
d(cid:27)C (cid:3) (cid:3) r0 (cid:15)s (cid:15)s (cid:15) 2 (cid:3)
(cid:3)((cid:15) ;(cid:18)s) = (cid:3) (cid:3) + (cid:3) (cid:0)sin (cid:18)s (9)
d(cid:10)0 2 (cid:18)(cid:15) (cid:19) (cid:18)(cid:15) (cid:15)s (cid:19)
2 2 (cid:0)13 2
where r0 = e =mec = 2:82 (cid:2)10 cm is the classical electron radius (e.g. Rybicki &
Lightman 1979). For the mono-directional power law beam (case 1) we have
2 (cid:11) (cid:11) (cid:3)(cid:0)(cid:11) (cid:3) (cid:3)
Ner0k1(cid:13) (1(cid:0)(cid:12)) (cid:15) (cid:15)s (cid:15) 2 (cid:3)
(cid:8)s1((cid:15)s;(cid:18)0) = 2 2 2 (cid:3) + (cid:3) (cid:0)sin (cid:18)0 ; (10)
2r (cid:13) (1(cid:0)(cid:12)cos(cid:18)0) (cid:18)(cid:15) (cid:15)s (cid:19)
(cid:3) (cid:3) (cid:3)
where (cid:15) is obtained by inverting equation (2) with (cid:18)s = (cid:18)0. For case 2 the scattered (cid:13)ux
is
2 (cid:3) (cid:3)
Ner0k2 (cid:3) (cid:3)(cid:0)(cid:11) (cid:15)s (cid:15) 2 (cid:3)
(cid:8)s2((cid:15)s;(cid:18)0) = 2 2 2 d(cid:10) (cid:15) (cid:3) + (cid:3) (cid:0)sin (cid:18)s
2r (cid:13) (1(cid:0)(cid:12)cos(cid:18)0) I (cid:18)(cid:15) (cid:15)s (cid:19) (11):
(cid:3) (cid:0)(2+(cid:11))
(cid:2)f(cid:13)(cid:13)0[1+((cid:12) (cid:0)(cid:12)0)cos(cid:18) (cid:0)(cid:12)(cid:12)0]g ;
Inderiving equation (11), we haveassumedthat thescattering regionhasconstantelectron
column density Ne and is much larger than the angular extent of the beam. This result is
correct in a regime where the light-travel time through the cloud is small in comparison
with the time scale of variation of the central source. A relativistically correct formalism
of the time-dependent system is in preparation by the authors.
4
2
InFigure1, weplot thescatteredphotonspectramultiplied by(cid:15)s forvariousscattering
angles and bulk Lorentz factors (cid:13). The spectral index (cid:11) of the incident photon spectrum
is set equal to 1.6, close to values measured for Cen A at hard X-ray energies (e.g., Baity
et al. 1981). The dotted curves represent the (cid:13)ux obtained using equation (10) (case 1)
and the solid curves were obtained using equation (11) (case 2). In case 2, we plot the
2 2 2
quantity 2mec r (cid:8)s2=Ner0k2 and take (cid:13)0 = 10. The normalization of the (cid:13)ux in case 1
was adjusted to make the low-energy (cid:13)uxes for case 1 and case 2 coincide.
2
Figure1. Scatteredphoton (cid:13)uxmultipliedby (cid:15)s as a functionof energyfor various
scattering angles. The di(cid:11)erent panels correspond to bulk Lorentz factors of the
scattering cloud of (cid:13) = 1;3. The dotted (solid) curvesrepresentcase 1 (case 2) as
describedin the text.
5
For case 1, the mono-directional beam, the high-energy cut o(cid:11)s (cid:15)c are very sharp due
to the kinematic constraint expressed by equation (4). At (cid:15) (cid:28) (cid:15)c, the spectra are power
<
laws with spectral indices equal to (cid:11). Slight spectral softenings are apparent at (cid:15) (cid:24) (cid:15)c. For
case 2, the cut o(cid:11)s are less sharp than in case 1 due to the angular extent of the incident
beam. This e(cid:11)ect is enhanced for larger bulk Lorentz factors of the scattering cloud. For
(cid:13) = (cid:13)0, the incident beam becomes isotropic (see eq. [8]).
In general, the scattered radiation will be partially polarized with the direction of the
electric (cid:12)eld vector perpendicular to the jet axis. The degree of polarization as a function
of scattering angle is given by the expression (e.g. McMaster 1961):
2 2 2 2
Q +U +V sin (cid:18)s
(cid:5)((cid:15)s;(cid:18)s) = p I = (cid:15)(cid:15)s + (cid:15)(cid:15)s (cid:0)sin2(cid:18)s; (12)
where I, Q, U and V are the Stoke’s parameters (e.g. Rybicki & Lightman 1979) of the
scattered radiation. Equation (12) is valid for a mono-directional beam. To obtain the
degree of polarization of a Comptonscattered beamin case 2 it is necessary to averagethis
expression in the starred system over the angular extent of the incident beam weighted
(cid:3)
dN(cid:13)s
by the di(cid:11)erential scattering rate dt(cid:3)d(cid:10)(cid:3)sd(cid:15)(cid:3)s, which is proportional to the integrand in
equation (11). This follows from the additivity of the Stoke’s parameters and the fact
that U = V = 0 for Compton scattering of an unpolarized beam by unpolarized electrons.
In addition, the degree of polarization is a Lorentz invariant quantity in the sense that
(cid:3) (cid:3) (cid:3)
(cid:5) ((cid:15)s;(cid:18)s) = (cid:5)((cid:15)s;(cid:18)s). Hence, we obtain the expression
(cid:3)
(cid:3) dN(cid:13)s (cid:3) (cid:3) (cid:3)
(cid:3) (cid:3) (cid:3) d(cid:10) dt(cid:3)d(cid:10)(cid:3)sd(cid:15)(cid:3)s (cid:5) ((cid:15)s;(cid:18)s)
h(cid:5)((cid:15)s;(cid:18)0)i = h(cid:5) ((cid:15)s;(cid:18)0)i = H (cid:3) dN(cid:13)(cid:3)s : (13)
d(cid:10) dt(cid:3)d(cid:10)(cid:3)sd(cid:15)(cid:3)s
H
In Figure 2, the degree of polarization is plotted as a function of energy for various
scattering angles and bulk Lorentz factors. Here, as in Figure 1, we set (cid:11) = 1:6 and
(cid:13)0 = 10. For a stationary scattering cloud (panel a), the degree of polarization is greatest
2 (cid:14)
for Thomson scattering ((cid:15) (cid:28) mec ) through 90 . The maximum polarization for a cloud
6
with bulk relativistic motion is found in the direction cos(cid:18)s = (cid:12), which follows from the
invariance of the degree of polarization.
Figure 2. The degree of polarization of the scattered radiation as a function of
energy for the various scattering angles. The di(cid:11)erent panels correspond to bulk
Lorentz factors of the scattering cloud of (cid:13) = 1;3. The dotted (solid) curves
represent case 1 (case 2) as described in the text. The dashed curve in panel a is
the predicteddegree of polarization for Cen A.
The (cid:12)nite angular extent of the beam in case 2 has the e(cid:11)ect of increasing the degree
of polarization relative to the mono-directional case in the Klein-Nishina regime. This is
more pronounced for larger bulk Lorentz factors of the scattering cloud. The bump just
below the high-energy cut o(cid:11) in panel (b) is the result of the increasingly limited domain
7
of the angular integration with increasing photon energy imposed by the Klein-Nishina
cross section in equation (13).
3. RESULTS AND DISCUSSION
We consider the case where the scattering cloud is at rest ((cid:13) (cid:24)= 1, (cid:12) (cid:28) 1), and (cid:12)t
the spectrum given by equation (10) for a mono-directional beam to the data obtained
with OSSE for Cen A during 17-31 October 1991 (Kinzer et al. 1994). This is done
by folding the model photon (cid:13)ux through the full OSSE response matrix and conducting
2
the (cid:31) search in count space. There are three free parameters in this (cid:12)t: the overall
2 2
normalization, Ner0k1=2r ; the spectral index of the incident beam, (cid:11); and the scattering
angle, (cid:18)0. The results are shown in Fig. 3 where the curve correspondsto the best (cid:12)t with
2
a reduced (cid:31) of 0.997 for 158 degrees of freedom, giving a probability of 0.496 to obtain
this much or more scatter in the data. The parameters for this (cid:12)t are (cid:11) = 1:68 (cid:6) 0:03,
(cid:14) (cid:14) 2 2 (cid:0)4 (cid:0)1 (cid:0)2 (cid:11)(cid:0)1
(cid:18)0 = 61 (cid:6) 5 and Ner0k1=2r = (9:8 (cid:6) 1:3) (cid:2) 10 (photons s cm MeV ). The
polarization of the gammaray emission is shownas a function of energy for this inclination
angle by the dashed curve in panel (a) of Figure 2. The emission is approximately 60%
<
polarized for (cid:15) (cid:24) 300 keV, but the polarization falls rapidly to zero above this energy.
Thus we (cid:12)nd that if the scattering cloud is at rest, the jet in Cen A is directed at an
(cid:14) (cid:14)
angle of 61 (cid:6)5 with respect to our viewing direction. Studies of the distribution of HII
(cid:14) (cid:14)
regions in NGC 5128 imply that the direction of our line-of-sight is oriented by 73 (cid:6)3
(cid:14) (cid:14)
(Graham 1979) or 72 (cid:6)2 (Dufour et al. 1979) with respect to the normal to the plane
of the disk of the HII regions and, presumably, Cen A’s galaxy. If one can assume that
the jet axis is perpendicular to this plane, then the results of these studies are within
2(cid:27) of our inferred angle. If the cloud is moving relativistically, as might be suggested by
<
time variability in the OSSE Cen A data on time scales (cid:24) 0.5 days (Kinzer et al. 1994),
then the deduced angle could be much di(cid:11)erent. For example, if (cid:13) = 2, then a similar
(cid:14)
analysis produces a (cid:12)t with an inclination angle (cid:25) 35 . Nonrelativistic scatterers could
be provided, however, by material con(cid:12)ning the jet, high-energy particles decelerated to
8