It is p e rtin e n t to ask w hat is th e difference betw een th e flat sp ectru m cores an d th e steep sp ectru m cores in our sam ple of galaxies? In this section we discuss cu rren t m odels for flat sp ectru m radio sources and how they m ay fit into an overall p ictu re of th e radio sources in this sam ple. In p articu lar, we exam ine w hether the tw o different core sp ec tra reflect an in trin sic difference in th e tw o types of cores. To some ex ten t this discussion overlaps w ith th e contents of c h ap te r 7. B ut it is necessary to exam ine cu rren t concepts of radio cores and relativistic beam ing in order to in te rp re t th e in terrelatio n s p resen ted in th e following sections.
F lat sp ectru m sources m ay be u n d ersto o d as a su p erp o sitio n of a num ber of uniform , p artially opaque ra d ia tin g plasm oids (blobs of plasm a) or localised enhancem ents in a je t such as shocks (e.g. K ellerm an and P au lin y -T o th 1981). Figure 4.32a shows th e sp ectru m of sy n ch ro tro n em ission from an homogeneous ensem ble of relativistic electrons (Pacholczyck 1970). T h e salient feature of this sp ectru m is th e peak at frequency um corresponding to th e frequency at which the ra d ia tio n becom es optically th in . For frequencies v <C v m th e em ission is opaque w ith a sp ectru m of —2.5. At higher frequencies v v m the em ission is optically th in w ith th e usual sp ectru m a = (1 — a ) /2 , where a is th e power-law index for th e electron energy d istrib u tio n . T h e frequency v m depends on th e plasm oid size, th e electron num ber density a n d th e m agnetic field stren g th . For a num ber of plasm oids w ith differing physical p a ra m ete rs (for exam ple a tra in of plasm oids expanding from a cen tral source) th e resulting sp ectru m is a sup erp o sitio n of the individual plasm oid sp ectra. A n exam ple of such a su p erposition is shown in
figure 4.32b. This is a four com ponent m odel fit for 0735 + 178 from C o tto n et al.
An elab o ratio n of core m odels involving discrete, uniform plasm oids are the m odels of opaque, non-uniform plasm as (e.g. C ondon and Dressel 1973; de B ruyn 1976; M arsher 1977; and Spangler 1980) These have subsequently found appli catio n in th e relativistic regim e to opaque je t and w ind m odels. C alculation of flux-densities an d sp ectra for je ts involves solution of th e full rad iativ e transfer eq u atio n s given a m odel for the variation of plasm a p aram eters w ithin the jet. M arscher (1980) and B landford and Königl (1979) have p resen ted m odels of com p a ct radio je ts in th e context of relativistic beam ing. R eynolds (1982) gives a m ore general tre a tm e n t of th e problem . These m odels show th a t flat spectrum rad io em ission arises from opaque regions of th e radio jets. These regions are close to th e cen tral engine an d on scales of a few parsecs or less.
In th e case of an opaque plasm a, and because of th e relatively low dynam ic range available in radio interferom etry, it is a useful assum ption to say th a t all em ission at a p a rtic u la r frequency comes from a region for w hich th e optical d ep th is unity. T his is approxim ately where th e syn ch ro tro n sp ectru m peaks ( r ( i/m) ~ 1 in figure 4.32a). For this reason th e sp atial scale to w hich a radio interferom eter is m ost sensitive is in d ep en d en t of th e baseline. For a typical te m p e ratu re of 5 x 10n K, K ellerm ann an d P au lin y -T o th (1981) give th e ch aracteristic size of the rad ia tin g region as:
0 ~ ‘1S ) ly VG H z m aS '
O ur flat sp ectru m sources have typical flux-densities of ~ 10 m Jy to 100 m Jy at 2.29 GHz, corresponding to a ch aracteristic size of ~ 0.2 m as. At redshifts of 0.05 to 0.3, th is corresponds to linear sizes of 0.1 pc to 1 pc.
F lat sp ectru m radio sources are generally associated w ith blazars and the cores of quasars. T hey are ch aracterised by variability, high brightness te m p e r a tu re and a flux-density w hich is a significant fraction of th e to ta l emission. A com m on in te rp re ta tio n of these o b jects is th a t they are com pact, relativistic ra dio je ts viewed end on. R elativistic beam ing boosts th e observed flux-density of th e opaque je ts so th a t th ey dom inate any extended radio em ission from the source. T his view is often referred to as th e “unified schem e” for q uasars (O rr an d Brow ne, 1982)
It is reasonable to ask w h eth er th e flat sp ectru m radio cores in ou r galaxies represent a sim ilar physical phenom enon to quasar cores? T h a t is, do they contain com pact, opaque je ts on parsec scales? In th e rem ainder of this ch ap ter we exam ine w h eth er th e flat sp ec tru m cores in our sam ple are relativistically beam ed an d the steep sp ectru m cores are not. T h e a ltern ativ e is th a t n eith er core is