4.5.1: Discussion of radio source lengths.

In document Optical emission lines in radio sources of intermediate power (Page 183-186)

T heoretical tre a tm e n t of th e grow th of radio sources has te n d ed to con­ c e n tra te on class II radio sources. This is presum ably because they dom inated early flux lim ited surveys (such as th e 3C survey) and hence have received m ore a tte n tio n from theoreticians an d observers alike.

T he general form of class II radio source m odels is of high velocity beam s of p lasm a im pacting on th e in terg alactic m edium . T he p oint of im pact is m arked by a working surface w ith a high radio surface brightness com m only referred to as “h o tsp o ts.” T he m otion of th e h o tsp o ts in to th e in terg alactic m edium is com m only assum ed to be governed by ram pressure balance (B landford an d Rees 1974). T h e velocity of th e h o tsp o ts, an d therefore th e grow th ra te of th e radio source depends very m uch on th e density of th e ex tern al m edium an d assum ptions as to th e evolution of th e h o tsp o t size. For exam ple in Scheuer’s (1974) m odel A th e beam is assum ed to possess a c o n stan t opening angle. As th e w orking surface progresses outw ards th e velocity of th e head falls off as Vh oc D~ l . B aldw in (1982) modified this m odel to include a m edium which falls off in d en sity causing th e head to decelerate less rapidly w ith distance. This m odification a tte m p ts to reconcile th e Scheuer m odel w ith th e d istrib u tio n of 3C R radio sources in th e pow er vs. linear size plane. A m ore recent m odel due to G opal-K rishna an d W iita (1987) exam ines th e evolution of a beam th ro u g h a galactic halo in to a h o t, low density intergalactic m edium . T h e salient featu re of all of these m odels is th a t th e evolution of a class II radio source depends not only on th e pow er in th e beam , b u t also on th e environm ent th ro u g h w hich the beam propogates. T his is th o u g h t to produce a cosmological effect (d istin ct from cosmological geom etry) in th a t radio sources of a given power are sm aller w ith increasing redshift {e.g. K ap ah i 1985). T his effect has been a ttrib u te d to a h o tte r an d denser in terg alactic m edium a t earlier epochs (W iita and G opal-K rishna 1987; B arth el and Miley 1988).

A recent stu d y by O ort et al.( 1987) finds th a t radio source size, for a given radio pow er decreases, as (1 + z ) ~ 3. In add itio n to an an ti-co rrelatio n betw een radio source size and redshift, O ort et al. (1987) present evidence for a correlation betw een radio source size an d radio power in th e sense: D oc P0 3 . This correla­ tio n m ay not be saying an y th in g profound ab o u t radio source size. It m ay m erely be tru e th a t for optically th in radio sources th e radio power is p ro p o rtio n al to th e em ittin g volume. W ith o u t m aking any physical claim s, we only in ten d to com pare our linear size d a ta w ith those of O ort et al. (1987) in order to establish th e credibility of our m easurem ents.

Figure 4.34 presents a plot of to ta l pow er a t 1.4 GHz as a function of linear size for th e sources in our sam ple. T h e linear sizes are tak en from ta b le 3.9b and we have norm alised our length d eterm in atio n s to a redshift of 2 = 0.08 (following

O ort et al. (1987)) using a (1 + z)~ 3 law. Different sym bols rep resen t different m orphological classes. T here ap p ears to be no difference in th e d istrib u tio n of p ro jected linear size w ith m orphological class. We have te sted for a correlation betw een linear size and to ta l pow er w ithin our sam ple. T h e results d epend on th e statistic a l test em ployed. A Cox p ro p o rtio n al h azard test* (Isobe et al. 1987) yields a significance for th e correlation of 75%, while K en d all’s generalised ta u test* yields a significance of 98% for th e correlation. Clearly th ere is room for arg u m en t b u t we prefer to take th e conservative line an d do not claim a significant correlation w ithin our d a ta set. A line of best fit perform ed using B uckley-Jam es regression* yields D (z = 0.08) oc p ° -24±0-12 which is consistent w ith th e relatio n

D {z = 0.08) oc P 0-31 found by O ort et al. (1987).

This correlation m ay be induced by selection effects. A lthough o u r use of u p p e r lim its does include inform ation on unresolved sources th ere m ay be oth er po p u latio n s of sources such as large low -lum inosity sources w hich are excluded from our sam ple because of th e selection criteria, or even because of th e way in w hich radio sources are discovered. O ort et al. (1987) claim th a t th e ir resu lts are not induced because they are derived from ind ep en d en t surveys.

O ort et al. (1987) o b tain ed these results using m edian values from th e ir own d a ta (th e Leiden-Berkeley D eep-Survey) plus published results from o th e r surveys (G avazzi an d P erola 1978, M achalski an d C ondon 1985). It is in terestin g to com pare ou r sam ple w ith th e resu lts from these surveys. Figure 4.35 reproduces figure 9b in O ort et al. (1987) T h e filled circles are tak en from th a t publication (corrected to Ho = 100 k m s ' 1 M p c- 1 ). T h e open circle represents th e m edian radio pow er and m edian linear size of o u r sam ple. Clearly, the linear sizes derived

* These statistic a l tests tak e in to account u p p e r lim its and are discussed in ch ap ter 6.

from our sam ple are in agreem ent w ith values and tren d s found in these oth er statistic a l studies.

Finally we note the form of th e p ro jected linear size d istrib u tio n function shown in figure 4.36 It follows an exponential d istrib u tio n w ith a 125.5 kpc scale size. T he x 2 value for this fit is consistent w ith the theoretically expected value. T he form of this size d istrib u tio n is in agreem ent w ith th a t which Ekers and Miley (1977) derive from 3C radio sources. We briefly note th a t for a uniform ly orien ted p o p u latio n th e effects of p ro jectio n do not significantly a lter the shape of th e linear size d istrib u tio n . Hence th e d ep ro jected linear size d istrib u tio n is expected to follow an exponential d istrib u tio n w ith a scale size of aro u n d 200 kpc.

4.5.2:

Source length and spectral index.

We have already discussed the expected preference for relativistically beam ed radio cores to be associated w ith radio sources of sm all p ro jected linear size. In figure 4.37 we present tw o frequency histogram s of p ro jected linear size for the radio sources in our sam ple. T he histo g ram in figure 4.37a is for radio sources w ith flat sp ectru m cores while figure 4.37b represents radio sources w ith eith er steep sp ectru m cores or u n d etected cores. U nresolved sources are rep resen ted by arrow s in th eir ap p ro p riate histo g ram bins. T h e difference betw een th e two distrib u tio n s is evident. We have applied a num b er of n o n -p aram etric tw o-sam ple te sts which take in to account u p p e r lim its (Feigelson and Nelson 1985) and all show th e two d istrib u tio n s to be significantly different to b e tte r th a n 99.9% confidence. We note here th a t our definition of flat-core ( a < 0.5) and steep core ( a > 0.5) is consistent w ith th e b im o d ality in th e core sp ectral index d istrib u tio n discussed in ch ap ter 3. T h e definition of th e tw o sam ples is therefore not a rb itra ry and the difference betw een th e p ro jected size d istrib u tio n s for th e two sam ples is not a function of an a rb itra ry definition.

In figure 4.37 we have included th ree sources w ith u n d etected cores (at b o th 1.4 GHz and 5 GHz) in th e p o p u latio n of steep sp ectru m cores because, according to th e beam ing hypothesis radio sources w ith weak cores belong to th e sam e class as sources w ith steep sp ectru m cores. T h a t is, sources w ith weak cores a n d /o r steep sp ectru m cores are o rien ted at large angles to th e line of sight. Rem oving th e sources w ith u n d etected cores from th e sam ple does not change our conclusion th a t th e p ro jected size d istrib u tio n for th e steep sp ectru m core sources is significantly different from th e p ro jected linear size d istrib u tio n for the flat sp ectru m core sources.

T he m ost striking result here is th e absence of flat sp ectru m core sources w ith sm all p ro jected linear size. It ap p ears th a t th e presence of a flat sp ectru m core is not an ind icato r of relativ istic beam ing. However, this arg u m en t alone

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Figure 4.34: Radio source length plotted as a function of total power at 1.4 GHz.

Open circles represent class I sources, filled circles represent class II sources while

In document Optical emission lines in radio sources of intermediate power (Page 183-186)