A model for extragalactic radio sources and quasi-stellar objects

Volume 83A, number 8

PHYSICS LETTERS

22 June 1981

A MODEL FOR EXTRAGALACTIC RADIO SOURCES AND QUASI-STELLAR OBJECTS P.F. BROWNE Department ofPure and Applied Physics, University ofManchester, Institute of Science and Technology, Manchester M60 I QD, UK

Received 21 November 1980 Revised manuscript received 30 March 1981 3 inductive electric fields around circular In regions outside galactic halos where charge density is less than =10—19 cm paths of very large radius can accelerate charges to energies of order 1021 eV. Charges deflected down into the galactic halo where the density of atoms is appreciable (1 0—1000 cm3) can instigate cascade showers which radiate into a cone about the forward direction of motion. When the Earth lies within the beam a synchrotron source is seen. Variability, spectrum, and double character all can be explained.

An outstanding problem in contemporary astrophysics is the mechanism by which electrons are accelerated to ultrarelativistic energies in the extragalactic radio sources, both extended and compact. Such electrons are distributed over enormous volumes of space, considerably larger than the visible galaxies and in the case of the giant radio sources comparable with galactic clusters (two components separated by 5.4 Mpc in the case of 3C236) (see refs. [1,2]). There is also the question of the origin of cosmic rays, which may be related to the radio source problem. The non-thermal radiation from such sources is recognized to be generated by the synchrotron mechanism. It is then possible to infer the physical conditions which prevail in the sources. An electron with velocity f3c in a magnetic field B follows a circular or-

v(y)

=

Y3vg =

y2eB/2irmc

=

2.8 X 106’y2B Hz.

(1)

AssumingB = iO—5 G, v ~ Hz implies y = 600 and p = 1018 Hz (4 keV X-rays) implies y = 2 X 108. X-rays now have been detected from active galactic nuclei or Seyfert galaxies [3—5], from the environs of D galaxies [6] and from a high percentage of QSO’s [7,8], and certainly in the latter case the radiation is of synchrotron origin, so that the synchrotron continuum extends from radio to X-ray frequencies. An electron of energy ‘y (in units of mc2) radiates synchrotron power P(7), where [9] P(y) = =

~(e2/mc2)2cy2B2

1.6 X l0~5y2B2erg/s.

(2)

Let n 7 d7

bit of radius rg with angular velocity wg, where wg = eB/ymc, Tg = !3C/Wg and ~y= (1 ~32)-i/2, e and m being the charge and mass of the electron, respectively. When motion is ultrarelativistic (‘y~3~ 1) such an electron radiates predominantly into directions close to the forward direction of motion, specifically into a cone ofthe angie 71means aboutthat the the forward direction. Curvature of orbit emission is directed along the line of sight only for the time required for gyration through angle 2n/’y namely 27T/YWg = 1/7Pg. Moreover the radiation is seen with a Doppler shift to the blue which increases its frequency by a factor 72~ —

Hence the electron radiates at frequencies of order 3Pg

be the number density of electrons with energies in y, 7 + d7, and let 9~,dvbe the flux density in the frequency band p, p + dv. One may attribute the flux in the band v ± to electrons in the band y ± where v and ‘y are related by eq. (1). Then, for a source of volume V at distance d one has 2v ~. (3) PVyn7 = 4~d Eliminating P and i.’ by use of eqs. (2) and (1), one finds 21B~~~(4~d2/V). (4) 7 =‘yn 1.75 X l0 Thus 7 is proportional to the continuum spectrum In the case of the extended radio source Cygnus A 7fl

7

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one measures flux densi y 8000 Jy at 125 MHz and 800 Jy at 3 GHz (1 Jy 1 026W m2 FIz~).The former flux comes from t radio-bright regions of angular dimensions 45” X 3 ‘separated by 85” [10,11], whilst the latter comes om regions of dimensions 25” X 15” separated (at rightness maxima) by 115” [12]. The red shift of z 0.057 implies a distance d = 8.8 X 1026cm for Hu ble constant 60km/s Mpc1. Then 1” corresponds to .38 kpc and the volume of the source, assuming tor idal geometry (see below), is 3 W St V/4ird2 = 2.7 X 1015cm. V = 2.6 1070 Then forXthe 125cmMHz one infers 7177 = 5.4 14B1 cnr3 and ifB = l0~G then 7177 = 5.4 X 109 10 cm3. Also, 2,, =4ird29,,v= lO~~ X erg/s. ,

In the case of the co 2vi’ tends to be about c tween 50 GHz and 2 ke ‘~ 2v~’has decreased by a

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pact extragalactic nstant at 2 X 1046sources erg/s beX-rays, but at 500 MHz ctor of order 1/100 which

is quite different to Cy us A [13]. The double compone t character of very many radio sources has encour ged the view that the sources are by matter pelled at and relativistic velocity frompowered the central nucleuse [14—17] the observation ofjets in some sour es [18—20]is regarded as supporting evidence. But the theory essentially is empirical in the absence of mechanism to explain the relativistic expulsion, an then to convert the energy into ultrarelativistic elec on energies. In this letter I offer an alternative vie point, which is based on the existence of large scale e ctric fields under conditions of very low free charge d nsity n. Charged particles are accelerated to the fields and then givehighes rise t cosmic cosmicray rayenergies showersin onsuch encountering clouds in gala tic halos, Large scale electric fie ds are most likely to be in ductive. Consider, for ex mple, contraction of a large scale magnetic field of p oidal geometry associated with a~effiptical galaxy, hich one envisages to be of Morgan type D (elliptical like inner region with extended envelope) since t se are the strongest radio sources [21]. Let F be a ircuit surrounding such a system in the plane norm ito its dipolar axis. The contraction will draw liii s of magnetic field across r, causing the magnetic flu c1’ linked with r to change with time. Then, in accor ce with Faraday’s law of induction there will arise ound r an electric fieldE of strength

E = —(2irrcY~d’I/dt. (5) In such a field the tangential velocity of an electron changes in accordance with d(7j3mc)/dt = —(e/2iTrc) d~/dt, (6) where we neglect the force of radiative reactionP(’y)/c. A magnetic force e(~X B) also acts on the electron in the direction normal to the acceleration (6). In the betatron accelerator the magnetic field B would have just the correct strength B 0 atofpoints F to maintain the charge in a circular orbit radiuson r. That is, r would be the radius of gyration for field B 0, so that 7(32mc2/r=e(3B 0. (7) B0 must change with time so that Bo/713 is constant. Then, by integration of eq. (6) and definition of k by cI~= irr2~one finds from eqs. (6) and (7) the betatron condition B 0 = .~B. When B0(t) has increased to its present value the will have been accelerated 2 = electron eB to energy 7mc 0 r/13 ~ eB0 r. Thinking of Cygnus A one might put2 r = 1021 3 X 1023 cm and = 1 o—~G, in eV, which is Bo about the maxiwhich case ymc mum observed cosmic ray energy. This is not the first suggestion that the betatron acceleration mechanism may have application for the origin of cosmic rays, but the conditions required for its operation have not received investigation [221. If B ‘~B 0 an accelerated electron will not be sufficiently deflected to maintain a circular orbit of radius r. IfB ~ B0 it will be deflected too much, and in fact will drift in the radial with velocity DE = cE 2 [9]. This is thedirection case in which the plasma X B/B around r remains tied to the lines of magnetic field, co-contracting with the field. To see this introduce a circuit I” which contracts with velocity bE. The rate of change of flux linked with F’ is given by

d~’/dt=

B• dI X UE + a (JJB. .dS)/at r

(8)

—

—

ff[v X (UE X B)

+

aB/at] ‘ds = 0,

the last integrand vanishing because E u E X B/c. Since 4’ is constant F’ will enclose a fixed number of field lines. In this circumstance a current would not flow around F, but any force F which opposes the at407

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tainment of yE will drive a current. F might be a centrifugal force. If E changes with time E will change with time and the opposing inertial force can be shown to drive current density/ = (pc2/B2)aE/caz’ where p is mass density [23]. Induced currents will normally involve only very small drift velocities of free charges. But if the density n of the latter is sufficiently small then whatever charges may be present will be accelerated to relativistic velocity in an attempt to produce sufficient current for total flux linked with F to remain constant. One may identify F with a toroid in of the radius r and cross 2.If electrons toroid have sectionalj3c area velocity theirØ~r) current will be J~x~2r2nej3c.At the centre of the toroid the current wifi produce a magnetic field ~B(0) given by 2 ~B(0)=2irJ/rc=2ir 2 nel3~r.

For j3 1 one requires that ,i2nr < (2ir2e)~~B(0) ~O8~(0).

(9)

(10)

Thinking of Cygnus A, one might substitute z~B(0) = 105 G, r = 3 X 1023cm and i~ = 1/5. Then (10) yields n < l019 cm3. How, then, does one reconcile such a low charge density with the estimate 7fl ~5 3 for the density of charges in the 7energy X 1 0~cm band 1000<7<3000 which radiate at 125 MHz? The only possibility would seem to be a cosmic ray shower. Charged particles in the very low density region, although few in number, will be accelerated to energies of order 1021 eV (see above) which is the maximum observed cosmic ray energy. If such partides spiral inward to regions of smaller r where the density of atoms N may be comparatively high, they will initiate cosmic ray showers in which the number of particles multiply by pair creations in a cascade process. Heitler [24] describes cascade processes in detail. The most probableprocess is emission of a 7ray photon by bremsstrablung (cross section ~d) followed by pair creation in the field of a second atom of medium (cross section If E0 is the energy the of the incident charge the ~,alr). most probable photon energy is hi’ ~E 0, so that energy tends to be shared equally among cascade electrons and positrons. Pair creation a single interaction is less probable a factor ofin order 1/137. It is convenient to writeby ~rad = kmd~andØ~= k . where ~ = a2/l37 = 5.8 X 1 0~ cm2 (a = e2~2)and where krad and kpajr ~,

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are numerical constants of order unity whose values depend on whether or not shielding is important. Assuming a shielded hydrogen atom, krad = 23.0 and k~r= 16.1. Then the thickness of the medium for one stage of the cascade multiplication of particles will be (Ncbmd)’ + (Nc~pajr)1= L8 X 1026 N~ cm. For a medium of thickness 3.6 X 1023 cm one would obtain 2N X I ~ cascade stages. If the photon energy becomes insufficient for pair creation the cascade of course will cease irrespective of the thickness of the medium. We have estimated E 0 1021 eV for the instigating primary particle, and 1 ~ eV typicalwill charges radiating at 100 MHz. Then thefor primary have produced of the order of 1012 particles, for which the number of cascade stages is x where 2’~ = 1012, yieldingx = 40. From 2NX l0~ = 40 one infersN= 2 X -l0~cm3, which seems reasonable. . —19 If the 3 primary particles satisfy (10) then n 3, 0 <10 cm and hence for the radiating charges n < l0~cm which is consistent with the estimate for based on

Th only alternative to the cascade hypothesis would be to satisfy (10) by a very small i~rather than a very small n. It is difficult to justify a sufficiently small i~.One might argue athat therestriction betatron acceleration mechanism imposes severe on possible orbits. Of course the orbits may be around a magnetic flux tube of sub-galactic dimensions (vortex tube with associated helical magnetic field). Synchrotron emission from an electron of energy 717W2 is confined to a cone of angle 7_i about the forward direction, and the angular spread of the electrons and positrons in a shower is of the same order due to relativistic aberration. Hence the radiation from a shower is highly anisotropic, and has a spectrum which depends on the direction of the Earth (0E) relative to the shower axis. The flux from electrons with 7>0 ~ is not intercepted by the Earth. The power radiated by a shower with s stages of pair creation is of order 2~P( Since P(7) ~ 72the and 2 is the 7). primary energy, 2~y ‘ye, where ‘-y0mc shower power is proportional to 7. Since this power is radiated into solid angle 7—2, the flux density received an on-axis is proportional to 73showor 3!2. Atatany instant position one receives radiation from i’ with a range of values of s, but they are not equally ers probable. One must remember that positive and negative charges, having been accelerated around F in op-

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posite senses, will initiate positely directed showers. An electron in the initial st ges of an approaching cascade is passing through the mal stages of a receding cascade where it has a high hance of creating a pair by interaction with a show r particle. This reduces the path over which the el tron radiates at high frequencies. By contrast, the th when low-p radiation is being emitted may be le gthened by the finite thickness of the medium, perha s explaining why excess centimeter radiation is so times seen [26]. Compare radio spectra for extended ources [25] and for QSO’s [27]. Variability is a characte stic of compact radio sources, particularly QSO’s and BL Lac objects. Since some 1012 radiating charg are timed with respect to a single primary particle fo the cascade shower, variability is to be expected. Fl ctuations of beam direction as well as arrival times will contribute to the variability. Since beam angle in eases with wavelength the time scale of the variations should increase with wavelength. This has been note for BL Lac objects [281. Variations will have the lar est amplitudes for narrow beam sources, which also s ould be the brightest; a classic example of this cor lation is 3C446 [13]. Variability has been correlate with strong linear polarization (3%—30%) and wit steep optical spectra [13]. Regarding the latter see re [29,301. A 7-ray transient recor d on March 5, 1979 by instruments on some nine pace probes was remarkable for the shortness ofits ise-time (<0.2 ms) and its high flux density (103 er s1cm2 lasting for 120 ms). From the relative del s of arrival it was possible to locate the source to wit ‘ an error box of 1’ X 2’, and only the supernova re nt ~ in the Large Magellanic Cloud then em rged as a likely source. But at 55 kpc the 7-ray lumin ‘ty becomes an improbable io4445 erg/s, assuming is tropic radiation. If the source radiates anisotropic lly with small beam angle the luminosity could be m ny orders of magnitude less, and the very short i-i time could be due to beam rotation. Positrons will be induc vely accelerated around F in the opposite sense to el trons, and on attaining energies of order 1021 eV hey too will initiate cascade showers on descen - g into denser layers of the halo. Hence one expects t see two radio-bright regions on either side of the centr galaxy, with a concentra.

22 June 1981

tion of emission toward the outermost boundary exactly as observed for Cygnus A [121. Of course the Earth must lie in or near to the plane of F. This explains why a majority of extragalactic radio sources, whether giant, extended or compact, are double sources. The theory applies to all extragalactic synchrotron sources, including QSO’s and BL Lac objects. Thus, one expects pairing of QSO’s, or even multiple groups if several ring currents are linked with the same changing flux. There exists now considerable evidence for groups of associated QSO’s, in some instances with discrepant red-shifts. Often pairing is suggested either by symmetrical positioning on either side of a visible galaxy, or simply by similar red-shifts, or similar brightness and spectra. Striking examples are the eight QSO’s aligned across NGC 3384 [3,5], the two triplets of colinear QSO’s found by Arp and Hazard [36] [suggested pairing of red-shifts, (1.62, 1.72), (0.54, 0.51), (2.12, 2.15)], and the double QSO 0957 + 561 A and B [371. In the latter case the components are separated by only 6’ and their properties are extremely similar although there are differences of radio structure [38— 40]. The current view is that we seen two images of a single source due to bending of light as it passes close to an intervening cluster [411,but there are difficulties with this hypothesis and it cannot be applied to other associations of QSO’s. For further evidence for pairing of QSO’s see refs. [42—44]. Of course ássociations of QSO’s imply an unexplained component of red-shift. In the case of three QSO’s (3C273, 3C345, 3C279) and one galaxy (3d 20) superluminal expansion of radio components has been seen [45—47].This phenomenon can now receive a straightforward explanation. One views a beam of electrons and positrons approaching along the line of sight, and experiencing magnetic force normal to the line of sight. Let some electromagnetic disturbance propagate radially outward from the beam axis, either along the magnetic field or normal to it. In the rest frame of the electrons the disturbance propagates transverse distance i~y’in time In the Earth frame it propagates 2~yin time &, where Ay = /~y’and i~t= y&’. But due to the Doppler effect one measures not & but &~,where &~= (1 (3)& = (1 (3)112(1 ÷(3)_h12&’.Hence ~y/&~ can exceed c considerably. &‘.

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—

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