Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.mso.anu.edu.au/~geoff/HEA/bdo.pdf Äàòà èçìåíåíèÿ: Wed May 31 09:07:13 2000 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 00:18:03 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: http astrokuban.info astrokuban

THE ASTROPHYSICAL JOURNAL, 485 : 112 õ 124, 1997 August 10
( 1997. The American Astronomical Society. All rights reserved. Printed in U.S.A.

UNIFICATION OF THE RADIO AND OPTICAL PROPERTIES OF GIGAHERTZ PEAK SPECTRUM AND COMPACT STEEP-SPECTRUM RADIO SOURCES GEOFFREY V. BICKNELL,1 MICHAEL A. DOPITA,2 AND CHRISTOPHER P. O. OîDEA3
Received 1996 October 2 ; accepted 1997 February 7

ABSTRACT We adopt the view that the classes of active galactic nuclei (AGN) known variously as gigahertz peak spectrum (GPS) sources, compact steep-spectrum (CSS) sources, and compact symmetric objects (CSO) generally represent the same sort of object and show that both their radio spectra and optical emission can be explained by a single model which incorporates the eects produced by the interaction of a jetdriven nonthermal lobe with a dense interstellar medium. Following Begelman, we assume that these sources are young AGNs (ages [ 106 yr) in which the jets are propagating through an interstellar medium in which the hydrogen number density, n decreases as a power law with radius, with the index H dB 1õ2 and n D 10 õ100 cm~3 at 1 kpc. The bow shock preceding the radio lobe is radiative at early H dense environment, and the optical line emission produced by the shocked ISM and the times in such a associated photoionized precursor is proportional to the monochromatic radio power, consistent with the observational data of Gelderman & Whittle. The ionized gas surrounding the lobes has a signiïcant emission measure and a correspondingly high free-free opacity which is responsible for the 0.1õ1 GHz peaks in the radio spectra. For jet energy ÿuxes D1045õ1046 ergs s~1, consistent with the observed radio powers of these objects, the crucial observed anticorrelation between peak frequency and size is readily recovered. The form of the radio spectra (power laws at high and low frequencies) indicate that the absorption is due to a cloudy/ïlamentary medium with an approximately uniform distribution of opacities resulting from a combination of a two-phase interstellar medium, shock shredding of clouds impacted by the bow shock and thermal instabilities in the shocked ISM. The ionized medium enveloping the radio source also forms a Faraday screen which produces high rotation measure and substantial depolarization, readily accounting for another key property of this class of AGNs. Subject headings : radio continuum : galaxies
1

. INTRODUCTION

There has been an increasing amount of interest over the last few years in the classes of extragalactic radio sources known as compact symmetric objects (CSOs : Wilkinson et al. 1994 ; Readhead et al. 1996), gigahertz peaked spectrum (GPS) sources (e.g., OîDea, Baum, & Stranghellini 1991), and compact steep-spectrum sources (CSS ; e.g., Fanti et al. 1990), although the research on these objects can be traced back to the work on "" Compact Doubles îî (Phillips & Mutel 1982) which are a subset of the above classes (Fanti et al. 1990). Following the Caltech-Jodrell Bank (Wilkinson et al. 1994) and Bologna-Jodrell-Dwingeloo surveys (Fanti et al. 1995), these classes of radio sources are now understood to represent an appreciable fraction of luminous radio sources. For example, GPS sources constitute approximately 24% of the Molonglo quasar catalog (Baker, Hunstead, & Brinkmann 1995). For the most part, the separate classes probably represent the same sort of object, the dierent nomenclature being more indicative of the means of discovery rather than of a real physical dierence. CSOs have emerged as a distinct morphological class in VLBI surveys ; their morphology and power is typical of classic double-lobed radio sources, albeit on subgalactic (D100 pc to 1 kpc scale). Moreover, without any exception
1 Astrophysical Theory Centre, Australian National University, Canberra, ACT 0200, Australia. The ANUATC is operated jointly by the Mount Stromlo and Siding Spring Observatories and the School of Mathematical Sciences ; gvb=maths.anu.edu.au . 2 Mount Stromlo and Siding Spring Observatories, Weston PO, ACT 2611, Australia ; mad=mso.anu.edu.au . 3 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD ; odea=stsci.edu.

known to us, every CSO is a GPS source. The converse is not exactly true : there are examples of GPS sources with somewhat distorted morphologies (Dallasca et al. 1995 ; Stranghellini et al. 1996a), and these are therefore inconsistent with the "" symmetric îî part of the CSO deïnition. Nevertheless, in the context of the model presented in this paper this is probably the result of interaction with an ISM which is more inhomogeneous than that in the average CSO or GPS source. For the most part, therefore, GPS sources and CSOs are quite dierent from the more numerous, relativistically beamed, core-jet sources. CSS sources have steep spectra (a Z 0.5)4 at gigahertz frequencies (in contrast to many quasars the spectra of which are ÿat in this frequency range). However, studies of the radio spectra of CSS sources (Fanti et al. 1990, 1985, 1989 ; Kameno et al. 1995) have demonstrated the existence of a turnover at lower frequencies (D100 MHz) for many CSS sources demonstrating, in all likelihood, that GPS and CSS sources dier in degree rather than kind. Scenarios for these sources generally suppose that they are either young, or frustrated in their growth by dense ambient nuclear material (or both) and that the spectral peak results from synchrotron self-absorption (SSA) by the lobe plasma. The SSA model to explain the low-frequency slope of radio sources has been a popular one, especially in view of its success in explaining the spectra of core-jet sources (Blandford & Konigl 1979). Nevertheless, early in the history of the subject of GPS and CSS sources, van Breugel (1981) pointed out that the emission measure of ionized gas implied by the ÿux of narrow line emission from
4 The spectral index a is deïned by F P l~a. l

112


GPS AND CSS RADIO SOURCE PROPERTIES CSS sources, implied that free-free absorption is an attractive explanation for the peak in the radio spectrum. Another simple argument against the SSA hypothesis is that if the properties of the jets in these sources are not substantially dierent from jets in core-dominated sources, then it would be suprising to ïnd nonthermal plasma making the transition from optically thick to optically thin and then becoming optically thick again in the much more extensive lobes. Whatever the cause for the morphology and spectrum, the substantial representation of CSOs, GPSs, and CSSs in radio source catalogs implies that they represent an important phase in the evolution of all active galaxies. A comprehensive physical model for these objects must explain the following properties : 1. Compact (0.1õ10 kpc) symmetric radio lobes between which a core may or may not be seen and which, in the case of radio galaxies, show little if any sign of relativistic beaming. These lobes have the classical FR2 morphology, but at much smaller scales (Fanti et al. 1990 ; Wilkinson et al. 1994 ; Spencer et al. 1989 ; Sanghera et al. 1995 ; Dallacasa et al. 1995). Some indication of relativistic beaming, in the form of prominent jets, is found in CSS quasars (Fanti et al. 1990 ; Spencer et al. 1989 ; Sanghera et al. 1995). 2. Steeply rising (SaT B [1) low-frequency spectra, with ÿux density maxima in the region of 0.1õ10 GHz, and with nonthermal high-frequency slopes 0.5 [ a [ 1.3 (e.g., Fanti et al. 1985, 1989 ; Kameno et al. 1995 ; OîDea et al. 1990 ; Stanghellini et al. 1996b). The low-frequency spectral indices are not indicative of either a single-component synchrotron self-absorbed spectrum or a single-component free-free absorbed spectrum. 3. Very powerful radio emission [logarithmic mean power at 5 GHz, log (P /W Hz~1) D 27.5] (Fanti et al. 5 1990 ; Stanghellini et al. 1996b). 4. An inverse relationship between source size and turnover frequency (Fanti et al. 1990 ; Stanghellini et al. 1996b ; OîDea & Baum 1996). As indicated above, this is a crucial relationship which serves to identify GPS, CSO, and CSS sources as one and the same class of object. 5. Low source polarization (typically [1% in GPS sources and [3% in CSS sources) accompanied in some cases by very high rotation measures (up to several thousand rad m~2) (OîDea et al. 1990 ; Taylor, Inoue, & Tabara 1992 ; Stanghellini et al. 1996b ; Akujor & Garrington 1995 ; Mantovani et al. 1994 ; Sanghera et al. 1995 ; Inoue et al. 1995). 6. Disturbed isophotes in the parent galaxies, pointing to recent interaction (Stanghellini et al. 1993 ; Gelderman 1994), with spectroscopy suggesting large quantities of dust indicating a dense galactic medium (Baker & Hunstead 1996). 7. Very luminous "" narrow line îî emission (up to D1044 ergs s~1). The [O III] luminosity of CSS sources is higher than that of other types of radio galaxies and the velocity widths are also systematically higher (up to D2000 km s~1) (Gelderman & Whittle 1994, 1996). 8. There is a tight correlation between line luminosity and total radio power (Gelderman & Whittle 1996). Begelman (1966) has recently presented an evolutionary model for CSO sources showing that the luminosity-size statistics can be explained if they are relatively young (t D 106 yr) and are forcing their way through a dense galac-

113

tic medium in which the density decreases roughly as r~d with dB 1.5 õ2. In this model, CSOs are both young and, although frustrated in their growth by the ambient ISM, are not conïned by it. In this paper, we build upon this model to show that the properties of GPS and CSS sources follow as a natural consequence of the radio lobeõISM interaction. In our model, the strong radiative shocks which precede the advantage of the lobe into the ISM create an ionized shell of shocked ISM capable of free-free absorbing low-frequency radio emission, thereby causing the peak in the radio spectrum. The observed optical velocity dispersion in the model is determined by a combination of factors : the velocity dispersion in the "" undisturbed îî ISM, which emits the precursor emission ; the geometry of the bubble, which determines the projection factors ; and velocities in the photoabsorption-recombination region of the shock, which are eectively equal to the velocity of the shock preceding the bubble. As a consequence, the observed velocity width is not simply related to the shock velocity but is at least indicative of it. We therefore conclude, from the data of Gelderman & Whittle (1994), that we are dealing with radiative shocks in the approximate range 300 õ1000 km s~1.
2.

DYNAMICS OF A JET-FED LOBE

2.1. T he Dynamical Model for the L obe Clearly, the most important parameter for shock models, determining the shock luminosity and the emission-line ratios, is the velocity of the shock and this, in principle, is determined by the model for the jet-fed lobe. However, the standard model for a single ïxed-direction jet feeding a lobe is insufficient : we know from the observational and theoretical studies of jets on the kiloparsec scale, that jets jitter about in the "" dentistîs drill îî fashion envisaged by Scheuer (1982). This insight led to a number of papers involving numerical simulations of this process (e.g., Williams & Gull 1984 ; Gull, Cox, & Scheuer 1991 ; Clarke 1996 ; Norman 1996). Moreover, it is quite clear that the lobes in the most powerful radio sources are overpressured with respect to the ambient medium as a consequence of the thermalization of jet plasma by the terminating shock (see Begelman & Cioffi 1989). This feature and the dentistîs drill evolution have been incorporated into an analytical model by Begelman (1996). In this model, allowance is made, in a phenomenological fashion, for the jittering of the jet as it feeds nonthermal plasma to the expanding lobe. The main assumption of the model is that the mean pressure, averaged over the hotspot region of the lobe is f times the average lobe pressure where fB 2. De Young (1993) has also carried out numerical simulations of powerful jets propagating in dense environments aimed speciïcally at understanding the physics of CSS and GPS sources. Those simulations were axisymmetric and did not speciïcally involve a dentist drill eect. Nevertheless, De Youngîs conclusion that an evolving radio source interacts with a clumpy two-phase medium in a similar fashion to the way in which it would interact with a smooth medium with the same average density is relevant to our utilization of the Begelman model. The reason for this result is that impact of the radio source on individual clouds shreds them and creates a more uniform medium. Nevertheless, De Young assumed that the clouds are small compared to the jet radius, and it would be useful to carry out simulations involving clouds of larger relative sizes.


114

BICKNELL, DOPITA, & OîDEA

Vol. 485

We have modiïed Begelmanîs treatment slightly to allow for the adiabatic expansion of the lobe plasma since this allows for a more internally consistent evaluation of the energy imparted to the ISM by the expanding lobe. In the evolution equations given below, the following symbols are used (see also Fig. 1) : x , distance of hot spot from the h center of the galaxy ; r , maximum radius of the cocoon ; c pressure ; V , cocoon volume ; E \ 3P V , total cocoon c cc energy ; b , ( jet velocity)/c ; F , jetcenergy ÿux ; o , ambient j E a density ; A , averaged hot spot area. In terms of these h parameters, the lobe evolution equations are b F 1@2 P 1@2 dx jE hB Bf1@2 c , o cA o dt ah a P 1@2 dr cB c , o dt a dV dE cBF . c]P c dt E dt

function of distance from the center. Neglecting the modest variation of background density over the (nonspherical) surface of the lobe, we take (following Begelman 1996) o \ a o (x /x )~d, where x \ 1 kpc is a ïducial distance and o is 0h0 0 0 the ISM density at 1 kpc. The one dierence between the above equations and those of Begelman (1996) is that allowance has been made for adiabatic losses in the cocoon energy equation. This enables a more internally consistent approach to the calculation of the energy imparted to the interstellar medium by PdV work in ° 4. 2.2. T he Solution for L obe Size and Pressure The above equations admit the following solutions for x h and p as functions of time : c x \ x m1@(5~d) , (2.4) h 0 P \ P m(2~d)@(5~d) , (2.5) c 0 where (5 [ d)3f2 F t3 E , 18n(8 [ d) o x5 00 x2 9 0. o P (t) \ 0 f(5 [ d)2 0 t m\

AB AB

AB

(2.1) (2.2) (2.3)

These equations assume that the jet velocity is relativistic and that the cocoon pressure is dominated by relativistic particles. We further assume that the cocoon is semiellipsoidal with semimajor and semiminor axes x and r , h c respectively ; hence, V \ 2n/3x r2 . The galactic ISM c a powerh law, with index [d as a c density is assumed to be

AB AB

(2.6) (2.7)

Expressing the solution in this way immediately provides a way of estimating the relevant jet energy ÿux, F and the E

FIG. 1.õIllustration of the interaction of a jet-fed radio lobe with the dense interstellar medium. The radiative bow shock (dashed line) surrounding the radio lobe collisionally excites the ISM which is shown here as a two-phase medium permeated by dense clouds shown in light gray. The radiation from the shock also photoionizes clouds (medium gray) in the ISM in advance of the bow shock. The shocked clouds are shown as dark gray. When the ionized gas enveloping the radio lobe is sufficiently dense it can free-free absorb the radio emission at GHz frequencies. The ionized medium also forms a Faraday screen which depolarizes the radio emission.


No. 1, 1997

GPS AND CSS RADIO SOURCE PROPERTIES

115

FIG. 2.õRatio i of monochromatic radio power to jet energy ÿux as a function of the magnetic ïeld for a spectral index of 0.7, a lower cuto Lorentz l factor, c \ 1, and the age parameter f f t \ 105 yr (solid lines), 105.5 yr (short-dashed lines), and 106 yr (long dashed lines). 0 e ad

ambient density parameter, o . Expressing o and F in 0 0 E terms of m and P gives 0 2n(8 [ d) P x3 0 0m, (2.8) F\ E (5 [ d) t o\ 0 x ~2 f(5 [ d)2 0 P . 0t 9

Another implication of the above model is that the work done by the expanding cocoon on the ambient medium is 3 dV \ F. P c dt 8[d E (2.13)

AB

(2.9)

For d \ 2 this amounts to 0.5 F . This relation is used in ° 4 E to evaluate the emission-line luminosities. 2.4. Jet Energy Flux and Radio Power The above expressions for hot-spot distance, pressure, velocity, etc., all involve the jet energy ÿux which we have estimated above to be of order 1045 ergs s~1. Since the median power at 5 GHz of GPS sources in the Stanghellini et al. (1996b) sample is 1027.5 W Hz~1, the implied ratio of monochromatic power to jet energy ÿux D10~10.5. It is important to determine whether this is consistent with the energy budget of GPS sources, and this, in turn, is useful when we come to examine the relationship between emission-line luminosity and monochromatic radio power in ° 4. In considering the energy budget, we take E to be the L total lobe energy, f to be the fraction of the internal energy e in electrons and positrons, B the lobe magnetic ïeld, t the age of the source, and c the lower cuto in the electron 0 Lorentz factor distribution. For the above dynamical model, E \ f F t, where the adiabatic factor is f \ ad (5 [ d)/(8 L d). Expressing the synchrotron emissivity [ ad E (integrated over 4n solid angle) in terms of the electron pressure, one obtains for the ratio of monochromatic synchrotron power P to energy ÿux : l P i \ l B 4n(a [ 2)c (a)c (a) f f 59 e ad lF E l ~a t, (2.14) ] (c m c2)a~2B(a`1)@2 0e 2c 1 where the c are the synchrotron parameters deïned by Pacholczycki (1970) and the electron distribution N(E) P E~a. In this expression, i depends mainly upon the l magnetic ïeld, B, and the age, t. For the generic parameters for GPS sources quoted earlier (p D 10~6 dyne cm~2 and t [ 106 yr) the equipartition magnetic ïeld, B D 4 ] 10~3 G. Hence, values of i for l \ 1.4 and 5 GHzeq plotted in are Figure 2 for c \ 1, l10~4 \ B \ 10~2, and f f t \ 105, 0 ad 105.5, and 106 yr. It is evident from these plots ethat a magnetic ïeld of the above order of magnitude, or perhaps

A dynamical age D106 yr seems relevant for these sources : if their ages were much shorter, we would probably see very few. An age [ 106 yr is also implied by the model of Begelman (1996) which takes luminosity-size evolution into account. Typical sizes of GPS sources are D350 pc and typical pressures are D10~6 dyne cm~2. To attain these sizes in a timescale of t Myr implies that m D 1 for x \ 350 pc5 ; this 6 0 gives (for d \ 2) F D 5 ] 1044t~1 ergs s~1, and the hydroE at 350 pc is 730t2 cm~3, translating to a 6 gen number density 6 number density at 1 kpc of 90 cm~3. We show in subsequent sections that these estimates are reasonably indicative. However, better agreement with parameters in the following sections is obtained if the typical age is slightly less than 1 Myr. 2.3. V elocity of Advance as a Function of Distance The above solution implies that the velocity of advance of the sides of the cocoon, f~1@2dx /dt as a function of the h distance of the head of the cocoon from the nucleus, x , is h given by x *(d~2)@3+ h , V \V c 0x 0 where

AB

(2.10)

F 1@3 3 E f1@6 (2.11) V\ 0 [18(8 [ d)n]1@3 o x2 00 6 1@3 F 1@3 f1@6 E,45 , (2.12) \ 1500 km s~1 8[d n H, 0 F is the energy ÿux in units of 1045 ergs s~1, and n is E,45 0 the hydrogen number density at 1 kpc. Note that for d \ 2 (the upper end of the range favored by Begelman) the shock velocity is independent of the size of the lobe.
5 Note that we have chosen x \ 350 pc here for convenience. In the 0 ensuing treatment we refer number densities and scales to x \ 1 kpc. 0

AB ABCD

AB


116

BICKNELL, DOPITA, & OîDEA

Vol. 485

slightly less, is consistent with i B 10~10.5 provided that f 5 e is not too much less than unity and the age is not too much less than 106 yr. The magnetic ïeld may be less than its equipartition value for the following reasons : in the evolving lobe, a tangled magnetic ïeld behaves like a relativistic gas. Therefore, the magnetic pressure should approximately track the particle pressure. Assuming that most of the kinetic energy dissipated at the jet shock goes into relativistic particles, the ÿux of particle energy into the lobe is of order the kinetic energy ÿux of the jet. On the other hand, the ÿux of magnetic energy into the lobe is approximately equal to the magnetic energy ÿux in the jet and is correspondingly less than the particle energy ÿux by a factor of order the Alfven number of the jet. Dynamo action may amplify the ïeld to near equipartition ; however, it remains to be demonstrated that a dynamo would work in this situation. Moreover, in the case of kiloparsec scale FR2s which are morphologically similar to the sources studied here, simulations (Clarke 1996) show that the observed ïlamentation depends upon the magnetic energy density being less than the particle pressure. Blandford (1996) has also argued that the magnetic ïeld in Cygnus A is subequipartition on account of the small-scale ordering of the polarization. On the other hand, the necessity for a subequipartition magnetic ïeld decreases if f f > 1. e ad A value of i D 10~10.5 is about 1 order of magnitude l one normally takes for large-scale radio higher than what sources. For example, such a value implies that a lobe fed by a 1043 ergs s~1 jet (normally considered to be borderline FR1/2) would have a power D1025.5 W Hz~1, about 1 order of magnitude higher than the FR1/2 break. This apparent discrepancy is consistent with the luminosity-size evolution discussed by Begelman (1996), which, as he showed, is implied by the evolutionary dependence of the quantity B(a`1)@2 t in equation (2.14) above. (For example, for a spectral index a \ 0.7, i P t~0.7.) l We conclude, therefore, that values of i D 10~10.5 can be consistent with the energy budget of the lclasses of radio source we are considering here. However, given the uncertainties in the above calculation and the simplicity of an homogeneous model, variations from this value by up to 1 order of magnitude are to be expected.
3

Since n \ n (x/x )~d, using equation (2.4) for the distance of 0 0 the hot spot from the center of the galaxy together with the following equation for the hot spot velocity, 3x 0 m(1@5~d) , v\ h 5[d t gives for the ratio of cooling time to elapsed time t 3 2.9 rad \ 1.7 n~1s*(d`2.9)+@(5~d)+t*(6.9d~10.8)@(5~d)+ , 0 6 5[d t (3.3) where t is the source age in Myr and 6 f2F (5 [ d)3 E (106 yr)3 s\ 18n(8 [ d) o x5 00 (5 [ d)3 f2F E,45 . \ 0.85 8[d n 0 For d \ 2, (3.2)

AB

AB AB

(3.4)

AB

t c B 15(f2F )1.63n~2.63t . E,45 0 6 t

(3.5)

. CONDITIONS FOR RADIATIVE SHOCKS

As the radio lobe pushes its way out through the dense interstellar medium close to the nucleus, a strong shock is driven into this medium. Provided that the shock can become radiative within an evolutionary timescale, then cooling losses supply a powerful source of EUV photons that is available both to pre-ionize an extensive precursor H II region and support a high emission measure recombination region in the shock. Both of these ionized regions can then contribute to the free-free absorption of the nonthermal emission from within the lobes. From detailed models of fast radiative shocks with solar abundance and velocities in the range 500 õ1000 km s~1, we ïnd that they become radiative and cool to the recombination temperature of hydrogen in a timescale t Myr, where rad, 6 t B 1.9 n~1V 2.9 ; (3.1) rad, 6 3 V is the shock velocity velocity in units of 1000 km s~1, and n 3 ~3 is the hydrogen particle density. cm In order that the shock be radiative we require the cooling time to be less than a dynamical time, i.e., t /t [ 1. rad

This equation shows the consistency of our inference of a fairly high density environment for these sources. For jet ÿuxes D1045.5 ergs s~1 and normal ISM densities with n D 1 cm~3 would mean that the shock would be nonradiative on timescales [105 yr. When n D 10 õ100, the 0 shock at the head of the lobe is radiative up to ages D106 yr, and this seems appropriate for these sources. Note also that the above value of t /t has been calculated c for the shock in advance of the hot spot. This is a factor of f1@2 faster than the wall shock at the sides of the cocoon so that the cooling timescale is a factor of f1.44 B 2.7 longer. Therefore, when the head shock becomes nonradiative, the wall shock remains radiative for approximately 1.7 times longer and most of the optical line emission emanates from the sides of the source. That is, an "" ionization cone îî has been produced. The fact that the wall shocks are radiative early in the expansion of the bubble while the ambient density is high ensures that the emission measure of the shocked gas and its precursor are also high. Since the radio-free-free opacity depends essentially upon the emission measure, it is feasible that the shocked interstellar medium provides the required free-free opacity in these sources. This is addressed further in ° 5.
4

. RELATIONSHIP BETWEEN EMISSION-LINE LUMINOSITY AND RADIO POWER

4.1. Estimates of Hb and [O III] Emission-L ine L uminosities The expansion work done on the interstellar medium is mediated by the shock that precedes the advance of the nonthermal lobe into the surrounding dense gas. In the case that this shock is fully radiative, the total shock luminosity, L , and the Hb and [O III] j5007 line luminosities (L and Hb L T III]) resulting from a shock of velocity V and area A ([O sh sh into a medium with unshocked hydrogen density n are H (following Dopita & Sutherland 1996) : n H L \ 1.14 V 3 T 3 cm~3

A BA B

A sh ergs s~1 , cm2

(4.1)


No. 1, 1997 L

GPS AND CSS RADIO SOURCE PROPERTIES

117

n H \ 1.91 ] 10~3 V 2.41 Hb 3 cm~3

A BA B

A sh ergs s~1 , cm2 (4.2) A sh ergs s~1 , cm2 (4.3)

nosity. MAPPINGS models of 500 õ1000 km s~1 shocks show that the ratio of Ha ] [N II] to Hb luminosities is approximately constant at 5.2 ^ 0.2. Hence equation (4.2), L (Ha ] [N II]) \ 4.0 ] 1042 f~0.098

n H L ([O III]) \ 2.3 ] 10~2 V 3 3 cm~3

A BA B

where V is the shock velocity in units of 1000 km s~1. Since 3 the shock luminosity is equal to the rate of work done by the expansion of the lobe, i.e., 3 F, L\ T 8[d E it follows that L (Hb) \ 8.5 ] 10~4 (4.4)

i ~0.80 P 0.80 1.4 1.4 ] n0.20 H, 0 10~11 1027 W Hz~1 ] x ~0.20(d~2) h ergs s~1 x 0
4.2.1. [O III] L uminosity

ABA AB

AB B

6 0.80 8[d

(4.9)

4.2. Comparison with Observational Data GW in their study of the optical properties of CSS sources have determined the luminosities of a number of spectral lines, including [O III] j5007 and Ha ] [N II]. Combining data relating to radio galaxies, radio loud quasars, CSS radio galaxies, and CSS quasars, they have demonstrated the existence of correlations (albeit with some scatter) between emission-line ÿuxes and monochromatic radio power over about 5 decades in either parameter. The CSS sources ït neatly into the high-power end of this correlation. Tadhunter et al. (1993) and Morganti, Killeen, & Tadhunter (1993) (referred to hereafter as TM) have also obtained [O III] luminosities and radio powers for the Wall & Peacock (1985) sample. These relate principally to extended radio sources. However, there are a number of unresolved sources in this sample which have subsequently been shown to be CSS sources (Morganti 1996, private communication). Therefore, we have combined the two samples in order to increase the statistics. Moreover, it is of interest to compare the relation between radio and optical emission for the compact and extended sources. Thus, in Figure 3 we present the [O III]j5007/1.4 GHz radio data from these two samples with theoretical predictions, derived from equation (4), overlaid on the data. In view of the unavoidable uncertainty in the parameter i 1.4 (see ° 2) theoretical lines are drawn for i \ 10~10.5, 1.4 10~11, and 10~11.5, respectively. It is evident from Figure 3 that the theoretical lines bracket most of the data for the high-power (P Z 1025.5 1.4 W Hz~1) sources. However, there are some intriguing features to the diagram. The ïrst is that the CSS sources ( ïlled symbols) lie to the right of the mean correlation. A mean value of i B 10~10.5 seems most appropriate. On the 1.4 other hand, the quasars (crosses) lie to the left with an appropriate mean i B 10~11. This may be a result of an 1.4 extra source of ionization in the quasars or it may imply more efficient production of radio emission in the CSS sources. The second feature is that for P [ 1025.5 W Hz~1, the [O III] luminosities of the radio1.4 galaxies (open symbols) are, on average, about 1 order of magnitude less than implied by the theoretical lines and any sensible value of i . Our interpretation of this feature is that these 1.4 (presumably borderline FR1/2) galaxies represent those in which the bow shock has ceased to be radiative and has broken out of the dense environment surrounding the nucleus (see ° 3). In this case, the conversion of jet energy ÿux into [O III] emission appears to be considerably less efficient (about 5%) and may occur, for example, through the interaction of the jets with dense clouds in the galaxy

L ([O III]) \ 1.0 ] 10~2

AB AB

6 V ~0.59F ergs s~1 , (4.5) E 8[d 3 6 F ergs s~1 . 8[d E (4.6)

Since the [O III] and total line luminosities depend upon the same power of the shock velocity, the velocity dependence cancels out in the ïnal expression relating L ([O III]) to energy ÿux. However, there is a weak dependence of Hb luminosity upon shock velocity. Since the lobe (and shock) areas are dominated by the sides of the cocoon, we therefore use the cocoon velocity given by equation (2.10) to estimate L (Hb), with the result that L (Hb) \ 6.7 ] 1041 f~0.098 ]

AB

x ~0.20(d~2) h ergs s~1 x 0 6 0.80 i ~0.80 1.4 n0.20 \ 6.7 ] 1041 f~0.098 H, 0 10~11 8[d ]

AB A

6 0.80 F0.80 n0.20 E,45 H, 0 8[d

P 0.80 x ~0.20(d~2) 1.4 h ergs s~1 , 1027 W Hz~1 x 0 (4.7)

AB B AB

AB

where P is the monochromatic radio power at 1.4 GHz and i is1.4 conversion factor from jet energy ÿux to monothe l chromatic radio power as discussed in ° 2. This relationship shows a very weak dependence on the scaling density n 0 and the size of the source, x . The Hb luminosity is indepenh dent of size for d \ 2. The [O III] luminosity in terms of jet energy ÿux and radio power is L ([O III]) \ 1.0 ] 1043 \ 1.0 ] 1043 ]

A

P l ergs s~1 . 1027 W Hz~1

AB A BA B B
6 8[d

6 F ergs s~1 8 [ d E,45 i ~1 1.4 10~11 (4.8)

For the purpose of comparison with the observational data presented by (Gelderman & Whittle 1996, hereafter GW) we also give here the theoretical Ha ] [N II] lumi-


118

BICKNELL, DOPITA, & OîDEA

Vol. 485

FIG. 3.õContribution to the optical depth parameter / n2 T ~1.35 dl 4 from dierent temporal regions of the postshock gas for a shock evelocity of 600 km s~1. They are parameterized by the magnetic parameter, Bn~1@2 (in units of kG cm3@2). Solid line, Bn~1@2 \ 2 ; dotted line, Bn~1@2 \ 4; dashed line, Bn~1@2 \ 8. Note that the dominant contribution to the integral is from the recombination/cooling zone, the beginning of which is marked by the point where the curves abruptly steepen.

FIG. 4.õPredicted [O III] luminosity as a function of radio power for three values of the parameter log i \[10.5, [11.0, and [11.5 over1.4 laid on data for extragalactic radio sources. Filled circles, CSS sources from GW ; ïlled squares, CSS sources from TM ; open circles, GW FR2 radio galaxies ; open squares, TM FR2 radio galaxies ; crosses, GW QSOs ; plus signs, TM compact ÿat spectrum sources ; open triangles, TM FR1 radio galaxies. Upper limits are indicated in the usual way.

5

. FREE-FREE ABSORPTION OF THE RADIO EMISSION

(e.g., Sutherland, Bicknell, & Dopita 1993) but not with a single large conïning dense cloud as we have invoked for the GPS/CSS sources. These speculations could be settled by a morphological comparison of the emission-line luminosity from sources in the various parts of the diagram.
4.2.2. [Ha] ] [N II]

5.1. Free-Free Absorption by Shocked and Precursor Gas In our model, the radio lobe is surrounded by fast radiative shocks. Such shocks have very high emission measure both in their photoionized precursors and in their recombination/cooling zones, as established in the previous section. This gives rise to free-free absorption of the radio emission. The free-free optical depth at radio wavelengths is given by q \ 1.1 ] 10~25 l~2.1 l 9

P

Figure 4 shows the theoretical lines for the Ha ] [N II] luminosity overlaid on the observational data for CSS radio galaxies, radio galaxies and "" other îî radio galaxies from (Gelderman & Whittle 1996). The predicted line ÿux depends upon the density in a minor fashion, and the theoretical lines correspond to a scaling density of n \ 10 cm~3. Again, the theoretical lines bracket a large part0of the data, and the small number (4) of CSS sources lie to one side of the correlation and appear to be best ït by i B 10~10.5. Without a corresponding data set to that of1.4 TM, the dropo of radio galaxies from the general correlation at P B 1025.5 W Hz~1 is not evident. Nevertheless, there is 1.4 still a group of radio galaxies to the right of the line deïned by i \ 10~10.5 which could represent a less efficient con1.4 version of jet energy to Ha ] [N II] luminosity. Note that there is greater scatter in the [O III] diagram compared to that in the Ha ] [N II] diagram. This is probably the result of reddening. Indeed Baker & Hunstead (1996) have argued that the CSS sources in the Molonglo quasar sample are substantially reddened (A B 4) because V of the large Balmer decrement. Given that the [O III] ÿuxes are aected by absorption, it is not necessary to assume as large a radiative efficency, i , as has been assumed above. 1.4

n2 T ~1.35 dl , e4

(5.1)

where l is the frequency in GHz and T is the electron 9 4 temperature in units of 104 K (Lang 1980). We have used steady-ÿow, plane-parallel shock models to establish values of the integral in the above equation. In principal, the integrals of n2 T ~1.35 through the shock e4 and precursor regions depend on the adopted value of the magnetic parameter Bn~1@2. However, the dependence upon this parameter is weak, as shown in Figure 5. Note also that Figure 5 shows that, in the shock region, by far the largest contribution to the integral comes not from the postshock cooling ÿow, but from the photoionized layer in the recombination zone of the shock (as a result of the dependence on the temperature). These shock models show that, for steady state, one-dimensional shocks viewed at normal incidence :

P

n2 T ~1.35 dl \ 1.78 ] 1022V 2.3n(H) (shock) , e4 3

\ 9.06 ] 1021V 1.5n(H) (precursor) , (5.2) 3 where V is the shock velocity in units of a thousand km 3 s~1. (These expressions are for values of B/n1@2 \ 4 kG


No. 1, 1997

GPS AND CSS RADIO SOURCE PROPERTIES

119

FIG. 5.õPredicted Ha ] [N II] luminosity as a function of radio power at 1.4 GHz for three values of the parameter log i \[10.5, [11.0, and 1.4 [11.5 overlaid on data for extragalactic radio sources. The ïlled and open circles, represent respectively, GW CSS radio galaxies and normal radio galaxies.

cm3@2.) The integral through the shock is somewhat greater than the integral through the precursor mainly because of the lower temperature that is encountered in the photoabsorption/recombination zone of the shock. These equations imply that free-free absorption by a 1000 km s~1 shock could produce a GHz peak source provided that the preshock hydrogen density, n(H), is of order 100 cm~3. In this case the radiative shock thickness is D3 pc, and the total thickness of the photoionized precursor is D100 pc. These parameters are quite consistent with those derived in previous sections and imply that the ionized gas is typically conïned to a relatively thin shell around the nonthermally emitting lobes of typical GPS sources the sizes of which range from about 100 pc to 3 kpc (Fanti et al. 1990 ; Stranghellini et al. 1996a). One-dimensional models are an approximation because, as we show below, the interpretation of the spectra of GPS and CSS sources probably require that some regions of the source be broken up into a number of clouds and/or ïlaments. Nevertheless, we use the integrated emission measure from the MAPPINGS output to approximate the mean optical depths in the dierent shock regions and also to establish the scaling relations with shock velocity. We return to this point after discussing the shape of the GPS spectra. 5.2. Absorption from an Ensemble of Clouds The catalog of spectra by Stanghellini et al. (1996b) provide a strong constraint on the nature of the absorbing region. In particular, the low-frequency spectrum, in both radio galaxies and quasars, is usually well ïtted by a power law with a mean spectral index D[1 (F P l~a). This is l especially evident in the (usually small) sources whose turnover is in the tens of GHz range, so that the low-frequency end of the spectrum is well sampled.

If the radio spectrum were absorbed by a uniform screen of ionized plasma, the spectrum would behave as exp ([al~2.1) at low frequencies, inconsistent with the observed spectra. We therefore model the spectrum as the result of the absorption of a nonthermal power law by clouds with a range of optical depths. There are two possible origins for such a structure. (1) The medium surrounding the source exists in two phases. This would give spatially variable absorption in both the precursor and shocked gas. Such clouds would also be shredded by the passage of the fast shocks adding extra structure to the absorbing screen. (2) The postshock gas is thermally unstable. Thus, even in the case of a uniform external medium it will develop a porous screen of clouds and ïlaments in the photoionization/recombination region of the postshock ÿow. Since the optical depths through the postshock region and the precursor region are comparable, both of these regions are required to exhibit a range of optical depths in order to account for the low-frequency power law. The investigation of both of the above scenarios constitute an interesting exercise in the computational astrophysics of radiative shocks beyond the scope of this paper. Nevertheless, some insight into the second case can be obtained by the following argument. Let us consider the fate of an inhomogeneity in the postshock ÿow and compare its resultant surface area in the recombination region to the surface area that would result in the strictly onedimensional, unperturbed case. Treating the perturbed ÿow as a quasi-one-dimensional steady ÿow, then mass conservation implies that the density, o , velocity, v , and rec surface area, A of the cloud in therec recombination region rec B F , where F is the mass ÿux through satisfy o v A rec rec rec M the initial area of the shock. NowM density in the recomthe bination zone is determined by the approximately isobaric shock pressure and the recombination temperature ; the velocity is determined by the energy equation and is approximately independent of the perturbation. Hence the surface area of the perturbed cloud is approximately equal to that which would hold in the unperturbed cloud. Moreover, if we trace the mass of gas which eventually makes up the recombination region of the ÿow, then since this is conserved, inhomogeneities which result in a smaller surface area (than the one-dimensional case) will have a larger transverse size and a larger optical depth and conversely for inhomogeneities which result in a larger surface area. Thus the eect of postshock thermal instabilities is likely to be a range of optical depths through the postshock gas. We also expect that gas which has been shredded in shocks should also show a distribution of optical depths. Nevertheless, the details of optical depth variations in these circumstances clearly requires further investigation. The spectral model developed below serves to outline the type of optical depth variation that is necessary in order to explain GPS and CSS spectra.

5.3. A Spectral Model
5.3.1. T he Spectrum Resulting from a Distribution of Optical Depths

The speciïc intensity of a ray passing from the radio lobe through the absorbing screen is I \ A~a exp ([al~2.1) , l l (5.3)


120

BICKNELL, DOPITA, & OîDEA

Vol. 485

where A characterizes the amplitude of the incident synchrotron spectrum, a is the spectral index, and, as described above, a P / n2 T ~1.35 dl. Since we do not have a come4 prehensive theory for the distribution of optical depths in the absorbing clouds, we allow for a range of values of the parameter a via a power-law distribution Pap, where p [ [1 and a varies between 0 and a maximum value a . In 0 the light of the above discussion we do not expect the power law to be too steep, i.e., the index p should be reasonably close to zero. We further assume that the amplitude, A, of the incident synchrotron spectrum varies more slowly over the face of the lobe than the variation of the absorption parameter, a (i.e., the length scale of the shock and/or ISM inhomogeneities is much less than the size of the lobe) then the average value of I is given by l p ] 1 a0 exp ([al~2.1)ap da (5.4) SI T \ A l ap 00 l 2.1(p`1)~a (l@l0)~2.1 upe~u du (5.5) \ A(p ] 1) l 0 0 l 2.1(p`1)~a l ~2.1 c p ] 1, , (5.6) \ A(p ] 1) l l 0 0 where we have deïned the characteristic frequency l by 0 a \ l2.1 and 0 0 x c(p ] 1, x) \ up exp ([u)du 0 is the incomplete gamma function of order p ] 1. A factor of la has been absorbed into A. It is straightforward to 0 show that the low- and high-frequency limits of equation (5.6) are given by

P AB AB

P C

AB D

P

FIG. 6.õFits of the model spectrum to three sources in the sample of Stanghellini et al. (1996). The spectrum for 1143-245 has been shifted down by a factor of 10 to avoid confusion. The parameters of the ïts are given in Table 1.

l 2.1(p`1)~a , l>l ; SI T \ A!(p ] 2) 0 l l 0 l ~a , l?l . (5.7) \A 0 l 0 Hence, the low-frequency spectral index, a , is given by l a \ a [ 2.1(p ] 1) , (5.8) l and the inferred value of p, characterizing the distribution of absorbing clouds is

AB

AB

p\

a[a l[1 . 2.1

(5.9)

If the parameter a (equivalently, the frequency l ), describ0 ing the maximum0value of the absorption by the ensemble of clouds does not vary signiïcantly over the area of the lobe, then equation (5.6) with I replaced by the monochrol matic power P should provide an adequate representation l of the source spectrum. The variation of the line of sight over the lobe is a geometrical factor that could give rise to signiïcant variation of l . Variation in the local shock 0 velocity, to which the optical depth is quite sensitive, is another factor which could lead to signiïcant variation of l . The major eect on the spectrum of a variation of l , 0 0 with p remaining constant, would be a broadening of the spectral peak but with the same asymptotic low- and highfrequency slopes. Examples of the ït of the above spectrum to three sources in the Stanghellini et al. (1996b) sample are shown in Figure 6, and the parameters of the ïts are given in Table 1. Since,

in each case, the ït involves four parameters and approximately 10 data points, these ïts cannot be taken as compelling evidence that this form of spectrum is correct. However, it is reassuring that a comparatively simple and analytical expression should provide such an excellent ït to the data. If the low-frequency power law is the result of absorption in either the shock or precursor component, and if the other component is uniform, then one would expect to see the signature of an exponential cuto in the spectra. For some of the sources in the Stanghellini et al. (1966b) sample, with turnovers near 1 GHz, the low-frequency coverage is inadequate to say whether this is the case or not. However, in the sources with peaks at higher frequencies, there is no indication of such a signature. This suggests a range of optical depths in both precursor and shocked regions and that the ISM surrounding the source is clumpy and presumably is in a two-phase form. If this deduction is correct there will likely be a contribution to the optical depth from shock shredding of clouds together with associated thermal instabilities.
5.3.2. T he Distribution of the Parameter p

We have assumed that the spectrum is of the form given by (5.7) and used the Stanghellini et al. (1996b) compilation of low- and high-frequency spectral indices to calculate the
TABLE 1 PARAMETERS OF SPECTRAL FITS Source 0457]024 ...... 0738]313 ...... 1143[245 ...... A 3.0 4.1 2.7 0 1.85 5.4 2.0 l a 0.6 0.85 0.65 p 0.0 [0.26 0.0


No. 1, 1997

GPS AND CSS RADIO SOURCE PROPERTIES
TABLE 2 VELOCITIES CORRESPONDING TO ENERGY FLUX AND NUMBER DENSITY d 2........ 2........ 2........ 2........ 2........ 2........ 2........ 2........ 2........ 0.8 ...... 0.8 ...... 0.8 ...... log F E (ergs s~1) 45.0 45.5 46.0 45.0 45.5 46.0 45.0 45.5 46.0 45.0 45.5 46.0 n 0 (cm~3) 1 1 1 10 10 10 100 100 100 10 10 10 V 0 (km s~1) 1680 2470 3630 782 1150 1680 363 532 782 735 1080 1580

121

distribution of p implied by our model. The mean value of p is [0.17 and its standard deviation is 0.25, consistent with the above inference of a nearly uniform distribution. It should be noted, however, that the describing the spectrum in this way is possibly an oversimpliïcation. The optical depth distribution in the precursor and postshock regions could well be dierent since the former is mainly determined by the preexisting distribution of dense clouds and the latter by instabilities. Nevertheless, for the following deductions of turnover frequency versus source size the assumption of a single value of p is not overrestrictive, as is evident below, and the introduction of two values of this parameter is an unwarranted complication at this stage. One could criticize the assumption of a power-law distribution of optical depths, as being ad hoc. On the other hand, the interpretation of the observed spectra in terms of free-free absorption demands a distribution of optical depths with the general features that we have inferred, i.e., a reasonably broad distribution of the absorption parameter with no particular value of this parameter dominating. 5.4. Relationship between T urnover Frequency and Size We now combine the previous results to show that a theoretical relationship between turnover frequency and source size is readily produced to explain the important observed inverse correlation between these parameters. In terms of our theoretical spectrum, the frequency of the peak in the spectrum depends upon the parameters l \ a1@2.1 0 and p. The ratio of the peak frequency, l , to l varies 0n a i pvalue0 p6 B [0.17 minor way with p and for the mean implied by the data, l B 1.08nu . We further assume that 0 the mean value of thepabsorption parameter, SaT, is given by the sum of equations (5.2). Since SaT \ (p ] 1)/(p ] 2)a , 0 then, combining equation (5.1) for the free-free optical depth, equations (5.2) for the optical depths in the shock and precursor regions and inserting the density dependence of the background, p ] 2 0.48 l B 1.1 p p]1 (1.96 ] 10~3V 2.3 ] 9.97 ] 10~4V 1.5)0.48 3 3 x ~0.48d , (5.10) ] n0.48 0 kpc with p B [0.17 and the shock velocity V in units of 1000 3 km s~1 given by the expression in equation (2.10) for the cocoon expansion velocity as a function of distance from the source. Plots of this relationship for selected parameters compared to the data (Fanti et al. 1990 ; Stanghellini et al. 1996b ; OîDea & Baum 1996) are shown in Figure 7. Three panels show the predicted relationship between turnover frequency and size for the density power-law index, d \ 2 and three energy ÿuxes (1045, 1045.5, and 1046 ergs s~1) and n , the density at 1 kpc equal to 1, 10, and 100 cm~3. For 0 this value of d the best ït is provided by n B 10 cm~3, and 0 the range of jet energy ÿuxes, which are consistent with the range of radio luminosities, accounts for the spread in the data. The velocities corresponding to the various energy ÿux and number density parameters are shown in Table 2. It is evident from that table that for energy ÿuxes Z 1045 ergs s~1 and for n \ 1 cm~3, the shock velocities are too 0

AB

AB

high compared to the observations. Indeed, these shock velocities are beyond the domain of validity of the emissionline models. However, for d \ 2 and n \ 10 õ100 cm~3, 0 most of the shock velocities, especially those corresponding to the lower energy ÿuxes, are consistent with the observations. The same is true for the d \ 0.8, n \ 10 models 0 when it is taken into account that here the velocity decreases with size as x~0.4. The presence of the cocoon velocity in equation (5.10) for the turnover frequency means that the dependence on the density parameters d and n is not as marked as one might 0 initially expect. The ïrst three panels of Figure 7 show the dependence upon density. The dependence upon d is shown by the lower right-hand panel which corresponds to d \ 0.8 and n \ 10 cm~3. This provides a better ït to the slope of 0 the data. However, because of the insensitivity of this slope to d, the best we can say from the ït to the turnover frequencyõsize relationship alone, is that dB 0.8õ2.2, encompassing the range dB 1.5 õ2 inferred by Begelman (1996) from luminosity-size statistics. These ïts to the turnover-size relation do not depend sensitively on our model for the spectrum. Dierent assumptions on the spatial distribution of absorbing clouds give a dierent weighting to the contributions to the optical depth from shock and precursor region. However, as long as the distribution of optical depths around the mean is not wildly skewed, approximately the same expression for the turnover frequency is obtained in all circumstances.
6.

POLARIZATION

One of the key features of GPS sources is that they are weakly polarized with typical fractional polarizations D1% while at the same time exhibiting large rotation measures, typically between 0 and D1000 rad m~2 but sometimes as high as several thousand rad m~2 (OîDea et al. 1990 ; Taylor et al. 1992 ; Wilkinson et al. 1994 ; Stanghellini et al. 1996b). This has a natural explanation in terms of our model. The rotation measure through the ionized gas surrounding the lobes is substantial and variations in rotation measure can produce such a large Faraday dispersion that the sources are almost completely depolarized. There is a contribution to the rotation measure from the magnetic ïeld (approximately interstellar) existing in the


122

BICKNELL, DOPITA, & OîDEA

Vol. 485

FIG. 7.õTheoretical ïts to the turnover frequency vs. size data for GPS and CSS sources. Jet energy ÿuxes of 1045, 1045.5, and 1046 ergs s~1 are represented by solid, dotted, and dashed lines, respectively. Filled dots represent data from Fanti et al. (1990), Stanghellini et al. (1996a), and OîDea & Baum (1996). Other parameters for the theoretical ïts are indicated in each panel.

precursor region and the varying magnetic ïeld existing in the ionized postshock region. In the MAPPINGS shock models, the ïeld is taken to be perpendicular so that B P n . Therefore, the quantity / n Bdl which is required to H e evaluate the rotation measure along a ray is proportional to / n n dl which is readily estimated from the mappings eH models. We have for a shock of velocity V thousand 3 km s~1 :

P P

n n dl \ 9.7 ] 1022V 3.4n cm~5 (shock) , eH 3H n n dl \ 2.4 ] 1022V 2.5n cm~5 (precursor) . (6.1) eH 3H

with variation of the rotation measure across the lobe due to ïeld reversals, it is not suprising that GPS and CSS sources are substantially depolarized. Indeed, in order to keep the predicted rotation measure between the observed limits of 0 and 1000 rad m~2 (Stanghellini et al. 1996b), it is necessary to invoke a large number (D10 õ100) of magnetic ïeld reversals across the source, especially for higher shock velocities. Some ïeld tangling could also be induced by shocks in individual clouds. Hence, a prediction of this theory is that high-resolution VLBI observations should reveal a rich rotation measure structure perhaps similar to that observed in Cygnus A (Dreher, Carilli, & Perley 1987).
7

Taking the angle between the magnetic ïeld and the line of sight to t, the rotation measure, / \ 2.5 ] 1024 / n B cos e t dl and / \ 2.5 ] 1010V 3.4B rad m~2 (shock) , 3 ISM \ 5.7 ] 109V 2.5B rad m~2 (precursor) . (6.2) 3 ISM For a characteristic interstellar magnetic ïeld D1 ] n1@2 H kG and n D 10 cm~3 and a shock velocity, say D500 km H equations give rotation measures D7000 cos t s~1, these and 1500 cos t rad m~2 for shock and precursor, respectively. These estimates should be indicative of more general magnetic ïeld conïgurations. With rotation measures of this order of magnitude and

. DISCUSSION AND CONCLUSIONS

In this paper we have proposed a consistent picture of the optical and radio properties of the classes of AGNs variously known as compact symmetric objects, compact steep spectrum sources, and gigahertz peak spectrum sources. This picture uniïes the optical and radio properties of these sources in that it shows that the crucial relationship between turnover frequency and size discovered by Stanghellini et al. (1996b), can be explained by free-free absorption by ionized gas produced in radiative shocks surrounding the expanding radio source. Moreover, the predicted relationship between optical line emission and radio power which is a natural consequence of our model agrees well with the data.


No. 1, 1997

GPS AND CSS RADIO SOURCE PROPERTIES

123

The main parameters determining the physics of the radio sourceõISM interaction are the energy ÿux in the jet and the ambient density of the interstellar medium. We have shown that the required energy ÿuxes are consistent with the level of radio emission provided that the ratio, i , l of monochromatic power to jet energy ÿux is a factor of a few higher for these compact sources than it is for kiloparsec-scale Fanaro-Riley class 1 (FR1) and class 2 (FR2) galaxies. This is, in turn, consistent with the luminosity-size evolution proposed by Begelman (1996) and may necessitate a magnetic ïeld strength less than the equipartion value. A value of i B 10~10.5 gives a good ït to 1.4 the correlation between radio and emission-line power discovered by Gelderman & Whittle (1996). We have no independent estimate of the density of the interstellar medium surrounding this class of AGNs. However, we have shown that our favored value for the mean hydrogen density at 1 kpc, n B 10 õ100 cm~3 is consistent with source dynamics (sizes0and estimated ages), the condition for radiative shocks to form, and the relationship between the peak radio frequency and source size. In addition, lower and higher values of this parameter give wall shocks which are, respectively, too fast or too slow to be consistent with the observed line widths. The immediate implication of this is that these sources should contain a large amount of cold material. If the matter is spherically distributed, the mass within radius r, M(r) B 4.5 ] 108n (3 0 [ d)~1(r/kpc)3~dM (for d ¹ 2). For a nonspherical dis_ is indicative. Hence, if dB 1.5 õ2, tribution, this estimate n B 10, and if the distribution extends to, of order, the size 0 of the largest sources (D10 kpc), some 3 ] 109õ1011 M of gas are implicated. This is consistent with the amount of_ gas which can be fed into the central regions of a galaxy in a merger. It is also qualitatively consistent with the substantial visual absorption, SA TB 4, estimated in CSS sources V by Baker & Hunstead (1996). We note that the imaging data of Stanghellini et al. (1993) and Gelderman (1994) support the notion that GPS and CSS sources are formed in merging/interacting systems. The column depth of neutral material is also of interest for the low-frequency cuto in X-ray observations. This is dominated by the distribution of gas close to the source, and, in estimating it, we exclude the region evacuated of

neutral gas by the radio bubble. The column density n B col n x (d [ 1)~1(x /x )~(d~1). For n B 10 cm~3 and a mean 00 h0 0 size x B 350 pc, n D 1023 cm~3. h col We have pointed out that the spectra of GPS and CSS sources, which generally show both high- and lowfrequency power laws, cannot be ïtted with a model which involves free-free absorption in an evenly distributed absorbing screen since this would imply an exp ([al~2.1) cuto at low frequencies. Clearly, a distribution of optical depths is implied, and we have shown that a simple powerlaw distribution of the parameter a \ / n2 T ~1.35 dl proe4 portional to ap gives a low-frequency power-law spectrum. We have argued that a distribution of opacities would be produced by thermal instabilities in the radiative bow shock. However, the fact that there is no clear signature of exponential absorption by a uniform shock-photoionized medium, external to the radio source, suggests that this medium is also clumpy and presumably has a two-phase structure. Hence, variable opacity in the preionized ISM and variations in opacity resulting from the shredding of these clouds by the bow shock should also contribute to the overall opacity of the source. As we have emphasized in ° 5 the source of the variation in opacity does not aect the general ït to the peak frequencyõsize relation so that the ït to this relationship is secure. The inference of an absorbing screen with these properties is a feature of the model which can be checked with a three-dimensional radiative shock calculations. We also emphasize that the assumption of a power-law distribution of opacities is probably not essential. It is likely that any broad distribution of optical depths would suffice. The depolarization of GPS and CSS sources is an inevitable consequence of this theory. In fact, the estimates of the local rotation measure in ° 6 suggest that a large number of ïeld reversals are necessary in order that the integrated rotation measure be as low as observed. Thus, rotation measures inferred from VLBI observations should show a rich and varied structure. We would like to thank R. S. Sutherland for useful discussions during the course of this work and M. Begelman, the referee of the original manuscript, for numerous constructive comments.

REFERENCES Akujor, C. E., & Garrington, S. T. 1995, A&AS, 112, 235 Baker, J. C., & Hunstead, R. W. 1996, ApJ, 452, L95 Baker, J. C., Hunstead, R. W., & Brinkmann, W. 1995, MNRAS, 277, 553 Begelman, M. C. 1996, in Cygnus A : Study of a Radio Galaxy, ed. C. L. Carilli, & D. A. Harris (Cambridge : Cambridge Univ. Press), 209 Begelman, M. C., & Cioffi, D. F. 1989, ApJ, 345, L21 Blandford, R. D. 1996, in Cygnus A : Study of a Radio Galaxy, ed. C. L. Carilli & D. E. Harris (Cambridge : Cambridge Univ. Press), 264 Blandford, R. D., & Konigl, A. 1989, ApJ, 232, 34 Clarke, D. A. 1996, in ASP Conf. Ser. 100, Energy Transport in Radio Galaxies and Quasars, ed. P. E. Hardee, A. H. Bridle, & J. A. Zensus (San Francisco : ASP), 319 Dallacassa, D., Fanti, C., Fanti, R., Schilizzi, R. T., & Spencer, R. E. 1995, A&A, 295, 27 De Young, D. S. 1993, ApJ, 402, 95 Dopita, M. A., & Sutherland, R. S. 1996, ApJS, 102, 161 Dreher, J. W., Carilli, C. L., & Perley, R. A. 1987, ApJ, 316, 611 Fanti, C., Fanti, R., Dallacassa, D., Schilizzi, R. T., Spencer, R. E., & Stanghellini, C. 1995, A&A, 302, 117 Fanti, C., Fanti, R., Parma, P., Schilizzi, R. T., & van Breugel, W. J. M. 1985, A&A, 143, 292 Fanti, C., et al. 1989, A&A, 217, 44 Fanti, R., Fanti, C., Schilizzi, R. T., Spencer, R. E., Rendong, N., Parma, P., van Breugel, W. J. M., & Venturi, T. 1990, A&A, 231, 333 Gelderman, R. 1994, Ph.D. thesis, Univ. Virginia Gelderman, R., & Whittle, M. 1994, ApJS, 91, 491 õõõ. 1996, ApJ, in press (GW) Gull, C. I., Cox, S. F., & Scheuer, P. A. G. 1991, MNRAS, 252, 558 Inoue, M., Tabara, H., Kato, T., & Aizu, K. 1995, PASJ, 47, 725 Kameno, S., et al. 1995, PASJ, 47, 711 Lang, K. 1980, Astrophysical Formulae (Berlin : Springer) Mantovani, F., Junor, W., Fanti, R., Padrielli, L., & Saikia, D. J. 1994, A&A, 292, 59 Morganti, R., Killeen, N. E. B., & Tadhunter, C. N. 1993, MNRAS, 263, 1023 (TM) Norman, M. L. 1996, in ASP Conf. Ser. 100, Energy Transport in Radio Galaxies and Quasars, ed. P. E. Hardee, A. H. Bridle, & J. A. Zensus (San Francisco : ASP), 319 OîDea, C., Baum, S., & Stanghellini, C. 1991, ApJ, 380, 66 OîDea, C. P., & Baum, S. A. 1996, AJ, submitted OîDea, C. P., Baum, S. A., Stanghellini, C., Morris, G. B., Patnaik, A. R., & Gopal-Krishna, 1990, A&AS, 84, 549 Pacholczyck, A. G. 1970, Radio Astrophysics (San Francisco : Freeman) Phillips, R. B., & Mutel, R. L. 1982, A&A, 106, 21


124

BICKNELL, DOPITA, & OîDEA
Stanghellini, C., OîDea, C. P., Baum, S. A., & Laurikainen, E. 1993, ApJS, 88, 1 Sutherland, R. S., Bicknell, G. V., & Dopita, M. A. 1993, ApJ, 414, 510 Tadhunter, C. N., Morganti, R., Aligheri, diSerego, S., Fosbury, R. A. E., & Danziger, I. J. 1993, MNRAS, 263, 999 (TM) Taylor, G. B., Inoue, M., & Tabara, H. 1992, A&A, 264, 421 van Breugel, W. 1981, in IAU Symposium 110, VLBI and Compact Radio Sources, ed. R. Fanti, K. Kellerman, & G. Setti (Dordrecht : Reidel), 59 Wall, J. V., & Peacock, J. A. 1985, MNRAS, 216, 173 Wilkinson, P. N., Polatidis, A. G., Readhead, A. C. S., Xu, W., & Pearson, T. J. 1994, ApJ, 432, L87 Williams, A., & Gull, S. F. 1984, Nature, 310, 33

Readhead, A. C. S., Taylor, A. C. S., Pearson, T. J., & Wilkinson, P. N. 1996, ApJ, 460, 634 Sanghera, H. S., Saikia, D. J., Ludke, E., Spencer, R. E., Foulsham, P. A., Akujor, C. E., & Tzioumis, A. K. 1995, A&A, 295, 629 Scheuer, P. A. G. 1982, in IAU Symp. 97, Extragalactic Radio Sources, ed. D. S. Heeschen & C. M. Wade (Dordrecht : Reidel), 163 Spencer, R. E., McDowell, J. C., Charlesworth, M., Fanti, C., Parma, P., & Peacock, J. A. 1989, MNRAS, 240, 657 Stanghellini, C., OîDea, C., Baum, S., Dallacassa, D., Fanti, R., & Fanti, C. 1996a, ApJ, in preparation Stanghellini, C., OîDea, C. P., Baum, S. A., & Fanti, C. 1996b, ApJ, in preparation