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Connections between jet physics and the properties of radio-loud and radio-quiet galaxies
New Astronomy Reviews 46 (2002) 365–379 www.elsevier.com / locate / newar
Connections between jet physics and the properties of radio-loud and radio-quiet galaxies Geoffrey V. Bicknell ANU Astrophysical Theory Centre, Research School of Astronomy and Astrophysics, Australian National University, Private Bag, Weston PO, ACT 2611, Australia
Abstract Relationships between jet physics and the evolutionary phases of radio galaxies are discussed. This includes the connection between the properties of relativistic jets and the Fanaroff–Riley classes of radio galaxies and the interaction of jets with the interstellar medium in Gigahertz Peak Spectrum and Compact Steep Spectrum Radio Sources. Jets in Seyfert galaxies are compared with those in classical radio galaxies and recent work suggesting that there are major differences between the two types of jets is summarized. The proposed major differences are principally that Seyfert jets are thermally dominated with subrelativistic speeds whereas Radio Galaxy jets are relativistic electron / positron flows. Hence, the production of jets in Seyferts and radio galaxies are fundamentally different. 2002 Published by Elsevier Science B.V. Keywords: Galaxies: Evolution; Galaxies: Jets; Galaxies: Seyfert; Radio continuum: Galaxies
1. Introduction Before Ledlow and Owen published their striking and fundamental results on the radio and optical properties of FR I and FR II radio galaxies, it was widely believed that there was no possible evolutionary link between the two classes (Ledlow and Owen, 1996; Owen and Ledlow, 1994). FR I radio sources seemed to be dominant galaxies near the centers of clusters; FR IIs seemed to be L , L* galaxies which inhabited the outskirts. However, the existence of a fairly clear luminosity-dependent dividing line between the two classes showed that an evolutionary connection at fixed optical luminosity is possible. The origin of this dividing line remained to be explained and a partial theory is summarized in the following section. Gigahertz Peak Spectrum and Compact Steep Spectrum Galaxies represent another E-mail address: [email protected] (G.V. Bicknell).
intriguing subclass of radio galaxies. These clearly represent an important evolutionary phase of Radio Galaxies but as other papers in this meeting have shown, their evolution is not well understood. In Section 3 of this paper some ideas relating to the interaction of the lobes of these sources with a dense interstellar medium is summarized. It was the emission line properties of Seyfert galaxies which led my colleagues and me to suggest that similar processes to those operating in GPS and CSS sources may be relevant in Seyfert galaxies. If this is the case then significant differences in the velocities and composition of Seyfert jets are implied and this has ramifications for the way in which jets are formed in Seyfert and Radio Galaxies.
2. The Fanaroff–Riley division By now it is well accepted that the differences in
1387-6473 / 02 / $ – see front matter 2002 Published by Elsevier Science B.V. PII: S1387-6473( 01 )00210-X
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morphology between the Fanaroff–Riley types of radio source are related to mass loading: FR I jets are turbulent mass-entraining flows which decelerate from a relativistic velocity effectively to rest or at most a few thousand km s 21 . The features of FR I sources, principally a bright rapidly spreading jet plus relaxed lobe and a slow decline of jet surface brightness with distance from the core are related to the physics of transonic entrainment. FR II jets are relativistic from the core to the lobes (with perhaps some minor deceleration) and their features, principally bright hot spots, lobes much larger than the jets which fuel them and the presence of knots distributed along thin, usually faint jets are related to the physics of hypersonic, low density flows. In Unified Schemes FR I sources are the parent population of BL-Lac objects and FR II sources are the parent population of quasars (Barthel, 1989, 1994), these associations being made possible by the aspect dependence of relativistic flow on the parsec scale. It had of course been known from the original paper of Fanaroff and Riley (1974) that FR I and FR II sources are separated in 1.4 GHz power at about 10 24.5 W Hz 21 with some considerable overlap. Nevertheless, the dramatic separation of FR I and FR II sources in the optical-radio plane discovered by Michael Ledlow and Frazer Owen begged for a straightforward explanation. One suggestion again involves the dynamics of initially relativistic flow so that relativity not only plays a significant role in unifying apparently different Active Galactic Nuclei, but it also plays a role in unifying FR I and FR II sources. The proposal for the ‘cross-unification’ of FR I and FR II sources (Bicknell, 1995) is based on the following method of estimating the jet energy flux and the corresponding radio luminosity. For a jet with pressure, pjet , radius r jet , velocity vjet 5 cb, 2 Lorentz factor, G, and ratio x 5 r c / 4p of cold mater energy density to enthalpy, the energy flux is given by:
F
G
G 21 2 FE 5 4p cpjet r jet 1 1 ]] x G 2 b G
(1)
In order to estimate the jet energy flux, we therefore require its pressure, radius and velocity. (The parameter x turns out to be not as important.) Estimates of these parameters are based on the following: 1. Effectively, the ‘last opportunity’ for a jet to
become a turbulent FR I jet is close to a core radius of the parent galaxy, since that is where the gas density is greatest. Moreover, beyond this point the pressure gradient is not favorable to the production of turbulence. Hence we surmise that most FR I jets become turbulent within the optical core region and that borderline FR I / II cases occur when the transition radius is within about an order of magnitude of the core radius. 2. All jets are initially highly relativistic and the transition to turbulence occurs when the Mach number becomes transonic. As we shall see, this implies a more or less unique velocity for the transition to turbulent flow. 3. Given an unique value for the velocity for the transition to turbulent flow, the other main parameter which is required to determine the jet energy flux is the jet pressure at that point. This is determined by the pressure of the galaxy atmosphere; this is constrained by the X-ray luminosity, other optical parameters and empirical relationships between these and the absolute magnitude of the optical galaxy. Let us consider each one of these points. 1. The association of an unique velocity associated with the transition to transonic flow can be deduced from the following argument. Consider a jet which is initially highly relativistic. The energy flux is conserved exactly. The momentum flux of a confined non-relativistic jet with density r, velocity V and cross-sectional area A propagating in the z direction satisfies the following equation: d ] dz
E rV
2
dPext dA 5 2 ]] dz
r E S1 2 ] dA r D
(2)
ext
and there is a similar equation for relativistic flow (see Bicknell, 1994). A consequence of this equation is that Length-scale for momentum increase ¯ Mach number 2 3 Pressure scale height
(3)
For an initially high Mach number, the momentum flux of a confined jet is therefore approxi-
G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
mately conserved. The momentum flux of a free jet is exactly conserved since it is not sensitive to the background pressure. With this approximation then, the ratio of energy flux to momentum flux is conserved and for an initially relativistic jet this ratio is the speed of light, c. When such a jet decelerates to a subrelativistic velocity, 2
Energy flux 4pVA(1 1 M / 6) ]]]]] 5 ]]]]] 5c Momentum flux rV 2 A
(4)
implying that V M2 ] 5 ]]]] ¯ 0.29 for M 5 1 c 3(1 1 M 2 / 6)
(5)
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( pjet 5 pISM), then we can see that the energy flux is insensitive to the precise point at which the jet transits to turbulence. In most galaxies, pISM R t2 is a slowly varying function of R t . (Typically, pISM R 2t ~ R 0.5 t .) 4. The atmospheric pressure in the centre of the galaxy can be estimated using a simple isothermal atmosphere model. X-ray astronomers often use the following empirical law for the gas distribution. Let n e be the electron density, (central value n c ), the total ion density be n t and the cooling function integrated across the relevant band be L(T ). (The band integrated emissivity is expressed as n e n t L(T ). The empirical model is
2. For higher Mach numbers the full relativistic expressions for the energy and momentum fluxes are required. However, it is worth noting here that as a consequence of Eq. (5), if an initially relativistic jet is supersonic on the kpc scale, then its velocity is necessarily greater than about 0.3 c. Some typical calculations for jets of higher Mach numbers are summarized in Fig. 1. It can be seen that jets typically enter the transonic regime M | 1–2 for V | 0.6–0.7 c.
F G
r2 n e (r) 5 n e,c 1 1 ]2 rc
2 b at
(6)
where bat is a fitted constant. This implies a surface brightness distribution, SX (x) (x 5 projected radius) in X-rays given by 1
F G
x2 SX (x) 5 SX,0 1 1 ]2 rc
22 b at 11 / 2
where 3. For a jet expansion rate a the jet radius at the distance R t from the core where the jet makes the transition to turbulence is r jet 5 a R t and pjet r 2jet 5 a 2 pjet R t2 . Given that the jet pressure is in equilibrium with the interstellar medium by this stage,
G (2bat 2 1 / 2) SX,0 5 p 1 / 2 ne,c nt,c L(T )r c ]]]] G (2bat )
(7)
5. The total X-ray luminosity, LX is related to electron density and ion number density, n t , core radius r c and temperature, T, via: nt 2 3 LX 5 4 p ] n e,c r c LE (T )IX ( bat , r 1 /r c ) ne
S D
where IX 5
E
0
(r 1 / r c )
s1 1 x 2d 22b at x 2 dx,
(8)
In Eq. (8), r 1 is a cutoff radius and LE (T ) is the cooling function integrated over the Einstein band. X-ray astronomers often fit the surface brightness implied by the above empirical law 1
Fig. 1. Mach number vs. bjet for a jet with an initial value of x 5 r c 2 / 4p 5 0 for various values of the initial Lorentz factor.
I note for completeness that in many published fits bat is replaced by 3b / 2 based on some of the original papers on X-ray coronae which mistakenly assumed that the above distribution represented that of gas in a gravitating isothermal sphere. See Killeen et al. (1988).
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(Eq. (6)). This implies a distribution of gravitating matter, which has many of the characteristics of a stellar dominated matter distribution merging into a dark matter distribution with total density given by:
possible to estimate the total radio luminosity from such an approach. However, the relationship between monochromatic power is more directly related to the observations and, in fact, involves fewer parameters. We therefore have
s 2` 3 1 r 2 /r 2c rm 5 ]]2 ]]]] 2p Gr c (1 1 r 2 /r 2c )2
Pn kn 5 ] FE
(9)
The parameter bat is related to the velocity dispersion at infinity by
m m p s `2 ]]] bat 5 kT
(10)
6. This discussion of the relation between X-ray determined and optically determined parameters shows that the X-ray luminosity and the pressure of the atmosphere are related via the optical core radius and the velocity dispersion. Moreover, there is a relationship between the Einstein X-ray and optical luminosities for elliptical galaxies (Donnelly et al., 1990); there are also relationships between core radius and absolute magnitude (Kormendy, 1987) and central velocity dispersion and absolute magnitude (Terlevich et al., 1981). All of these can be combined with the above X-ray gravitating matter model to estimate the central pressure, pc which is interestingly insensitive to absolute magnitude: log pc ¯ 2 8.2 1 0.03MB
(11)
7. Putting all of this together gives an expression for the jet energy flux: log FE ¯ 24.1 2 0.85MB 1 log
HS
D
G 21 1 1 ]] x g 2jet bjet G
J
(12)
which already exhibits the L 2.1 opt dependence of the Owen–Ledlow dividing line. 8. The final connection to the Owen–Ledlow data is made through the relationship between radio source parameters and the ratio, kn , of lobe monochromatic power, Pn to jet energy flux. This is derived simply from the fact that radiating electrons are supplied to the radio lobe at a rate proportional to the energy flux (Bicknell, 1986; Bicknell et al., 1998; Eilek and Shore, 1989). It is
5 C1 (a)sg0 m e c 2d a22 B (a11) / 2 f fe fad t g n 2(a 21) / 2 (13) Here, C1 (a) 5 4p (a 2 2)c 5 (a)c 9 (a)(2c 1 )(a 21) / 2 is expressed in terms of the synchrotron parameters introduced by Pacholczyk (1970), fe is the electron / positron fraction of the lobe internal energy, fad is an adiabatic factor allowing for lobe expansion, B is the lobe magnetic field, and t syn is the synchrotron cooling time. The adiabatic factor fad is 0.75 for a radio lobe expanding at constant pressure into the background. Eq. (13) applies to the power-law region of the spectrum, where cooling has not affected the spectrum. It can only apply up until the point where the lobe is old enough that synchrotron losses start to affect the synchrotron emissivity at the edges of the lobe. The following form of the expression for kn u takes this into account by expressing the time in units of the synchrotron cooling time, t syn . Thus,
kn ¯ C2 (a)sg0 m e c 2d a 22 B (a22) / 2 t 3 fe fad ] n 2a / 2 t syn
F
G
3 p C2 (a) ¯ ] ] 2 4
S D
1/2
1/2 c 21 2 c 1 C 1 (a).
(14)
(15)
This equation also has the advantage that, for typical values of a | 2.4–2.6, the estimate of kn is insensitive to the assumed value for the magnetic field. (We generally adopt a value of B 5 10 mG.) The end result of the above process is a predicted relationship between the radio luminosity of a borderline FR I / II source and the absolute magnitude of the host galaxy. One expects the actual dividing line to be bracketed by 0.1 , t /t syn , 1. The result is shown in Fig. 2 which shows theoretical dividing lines for t /t syn 5 0.1 and 1. These in fact bracket the actual division quite well. In some sense the success
G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
Fig. 2. Radio galaxies in the radio luminosity–optical luminosity plane. The data are from Ledlow and Owen (1996). The open circles represent FR I radio galaxies; the filled circles represent FR II radio galaxies. The lines represent the theoretical relations describing borderline FR I / II radio galaxies. The lower and upper lines represent theoretical relations corresponding to ages of the borderline galaxies being 0.1 and 1.0 synchrotron cooling times respectively.
of this model is quite remarkable, in view of the convoluted way in which the pressure is related to the absolute magnitude It should also be borne in mind that the good fit is also due to the identification of a more or less unique, mildly relativistic velocity at which a jet becomes transonic and hence turbulent. This theory does not say how jets decelerate in the first few hundred parsecs. The notion on which the above theory depends is that given a jet has decelerated to a transonic Mach number in a galaxy of a given absolute magnitude then we can estimate its energy flux, since we can estimate its velocity, pressure and radius. The possibilities for causing deceleration in the first few hundred parsecs include • Mass-injection by stars into jets of less than a critical luminosity (Kommisarov, 1994; Phinney, 1983) • Turbulent deceleration of supersonic (but not hypersonic) jets. Meier (1999) has also discussed reasons for the differences and Mach number for jets in terms of a ‘magnetic switch’ mechanism. In all cases, one
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expects the lower luminosity jets to be affected the most by entrainment processes in the first few hundred parsecs. The viability of the Phinney–Kommisarov mechanism depends upon whether the stellar winds are effectively mixed into the jet (Kommisarov, 1994). What are the ramifications of these ideas for the lifecycle of a radio galaxy?. As I mentioned in the Introduction, one of the singularly important results of the Ledlow–Owen discovery is that it opens up the possibility of evolution of radio sources in a vertical line on their diagram. Let us suppose that following a period of fueling (resulting from a merger?) a radio source goes through a powerful FR II phase in which the jets are hypersonic and relatively unaffected by the interstellar medium. As the source of fuel for the black hole diminishes, the jets become less powerful and make the transition to FR I at a power which depends upon the absolute magnitude, possibly as indicated by the above scenario. There then follows a subsequent, perhaps more long-lived phase wherein the Galaxy continues as an FR I. The relative times spent in the FR I and FR II phases would depend upon the time at which the source crosses the transition line and hence on the absolute magnitude. This scenario could be developed in a more quantitative fashion. It could even be examined observationally now, by imaging radio galaxies in a narrow range of optical luminosity and looking for signs of evolution, as evidenced say by merger characteristics, and examining these as a function of radio luminosity 2 .
3. Gigahertz Peak Spectrum and Compact Steep Spectrum radio sources
3.1. Characteristics of GPS and CSS sources Gigahertz Peak Spectrum (GPS) and Compact Steep Spectrum (CSS) Radio Sources undoubtedly represent an important youthful phase in the lifecycles of Radio Galaxies. Their large fractional representation in radio source catalogues is probably the
2
This idea was the result of discussion with Stefi Baum at this meeting.
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G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
result of significant source evolution (Begelman, 1996), although the precise nature of the evolution is presently not clear (see Conway, these proceedings). Some important radio and optical characteristics of these sources are: • A turnover in the radio spectrum at around a GHz for GPS sources, and lower for CSS sources. • High rotation measures. • Median Power: P5GHz 10 27.5 W Hz 21 • A dominant narrow line spectrum with line widths | few 100–1000 km s 21 . Some ideas that are most likely relevant to understanding these sources are 1. GPS and CSS sources are young ( , 10 6 yr) and impeded in their progress through a dense interstellar medium. 2. Their high luminosities are the result of confinement and the luminosity evolves as the confining pressure decreases (DeYoung, 1993; Begelman, 1996). The emission line spectrum of GPS and CSS sources provides additional information. Bicknell et al. (1997) have argued that both the emission line fluxes and the low frequency turnover result from a dense shell surrounding the radio lobes which is ionized by the bow shock surrounding the expanding radio lobe. In their model, the turnover is produced by free–free absorption. In a variant of the BDO model, Kuncic et al. (1998) suggested that induced Compton scattering (ICS) could also be responsible for the low frequency turnover. In support of this model, the brightness temperatures of GPS and CSS sources are frequently in the range (T b . 10 9 K) where ICS can be important and the low frequency spectral indices cluster around a 5 2 1 (Fn ~ n 2 a ) (Stanghellini et al., 1996b) as predicted by the ICS model. On the other hand, synchrotron self-absorption in several components of each source (see Snellen, these proceedings) represents a popular model for the turnover in both CSS and GPS sources.
3.2. Radiative shocks The characteristic of a radiative shock is that the internal energy of the shocked gas is radiated in less than a dynamical lifetime. Models of low velocity Vsh , 200 km s 21 shocks have been used for some time to explain the optical spectra of supernova remnants, for example Dopita et al. (1980), Dopita et al. (1984) and Russell and Dopita (1990). Fast shocks introduce an additional feature. The postshock temperature T ¯ 5.6 3 10 5 sVshock / 21 2 200 km s d is so high that a UV to soft X-ray flux is produced that ionizes the shock precursor gas. Depending upon the pre-shock density the extent of the precursor can be quite large— | n 21 H kpc where n H is the pre-shock Hydrogen density (Dopita and Sutherland, 1996a,b). The spectrum of high velocity radiative shock is a mixture of collisionally excited and photoionized line emission. One feature of the spectrum is that the [OIII] l4363 line (produced in the hot post-shock zone) is stronger than in pure photoionized models and this helps to explain the higher than expected temperatures inferred for the Narrow Line Regions of many active galaxies. In the model for GPS / CSS sources (see Fig. 3), Bicknell et al. (1997) proposed that a ‘dentist’s drill’ (Scheuer, 1982) jet inflates a high pressure lobe in the ISM, the dynamics of which are described by the CSO 3 model of Begelman (1996) (modified to account for adiabatic losses). Ambient clouds are ionized by the bow shock surrounding the lobe producing the shock excited spectrum described above. The FWHM of the lines indicates that the shocks are indeed fast (up to a thousand km s 21 ) and one consistency check that is required for such fast shocks is that the radiative cooling time is less then the dynamical time, of order the age of the source. This is satisfied for the BDO model but this criterion may be especially pertinent to models in which the head of the lobe is rapidly expanding and most of the emission emanates from the less rapidly expanding sides (see below). In estimating the emission line luminosities, one
3
There is probably a large overlap in physical characteristics of sources which are described as Gigahertz Peak Spectrum, Compact Steep Spectrum and Compact Symmetric Object.
G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
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Fig. 3. Schematic of the GPS / CSS model of Bicknell et al. (1997). A ‘dentist-drill’ jet forces its way though the ISM of the host galaxy. Clouds in the ISM are shock-ionized and photoionized by the UV to soft X-rays from the shocks.
uses the following power-law fits to MAPPINGS output for the total continuum and line luminosities, LT , Hb luminosity, L(Hb ) and [OIII] l5007 luminosity, L([OIII]) from a shock of area A shock cm 2 :
S
Vshock LT 5 1.1n H ]]]] 1000 km s 21
D
S
3
A shock ergs s 21
D
2.4 Vshock 23 21 L(Hb ) 5 1.9 3 10 n H ]]]] ergs s 21 1000 km s 3 Vshock L([OIII]) 5 2.3 3 10 22 n H ]]]] 21 1000 km s
S
A shock ergs s 21
D
(16)
(Sutherland and Dopita, 1993; Dopita and Suther3 land, 1996a,b). The nV A dependence of LT reflects the fact that the kinetic energy flux of the incoming gas is converted into internal energy, thence into ionizing radiation and subsequently into continuum and emission line luminosity.
Consider a jet with energy flux, FrmE feeding a radio lobe which is expanding into a medium with mass density r 5 r0 (x /x 0 )2d, where x is the distance from the centre of the galaxy and r0 is the density at an arbitrary scaling distance x 0 which we take to be a kpc. The distance, x h , of propagation the head of the lobe into this medium is described in terms of the similarity parameter 3 (5 2 d ) j 5 ]]]] 18p (8 2 d )
F
2
3
z FE t ]] r0 x 05
G
(17)
(cf. Falle, 1991; Eilek and Shore, 1989). We have for the distance of propagation: x h 5 x 0 j 1 / 52d
(18)
and the lobe pressure is given by:
S Dj
x0 9 Plobe 5 ]]]2 r0 ] t z (5 2 d )
2
22d / 52d
(19)
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The parameter z | 2 was introduced By Begelman to describe the ratio of averaged hot spot pressure to lobe pressure; z 1 / 2 then is the ratio of forward speed to lateral speed of the lobe. An important deduction from this model is the velocity–size relation:
S
6 Vh ¯ 1500 ]] 82d
D
1/3
S DS D 1/3
FE,45 z 1 / 6 ]] n H,0
xh ] kpc
d 22 / 3
(20) 21
45
where the jet energy flux is 10 FE,45 ergs s . In the BDO model, the FWHM of emission lines is indicative of the velocity of propagation of the head of the lobe implying that FE,45 ]] | 0.1–1 n H,0
(21)
This is used below to estimate the ambient number density. The total emission line and continuum luminosity is determined by the work done on the local interstellar medium, so that 3 1 LT 5 ]] FE ¯ ] FE 82d 2
(22)
for d ¯ 2. Since the total luminosity and [OIII] luminosity scale in exactly the same way with density, velocity and temperature, it is straightforward to estimate the [OIII] luminosity as L([OIII]) 5 8.2 3 10
S
P1.4 ]]]] 27 10 W Hz 21
D
42
k1.4 6 ]] ]]]] 8 2 d 10 211 Hz 21
S
D
21
(23)
where the energy flux has been replaced by the monochromatic power, via FE 5 k n21 Pnu with n 5 1.4 GHz. Eq. (23) predicts a linear relationship between [OIII] luminosity and radio power (for a constant kn ). These parameters are plotted in Fig. 4 and one can see that the CSS sources fit this relation for k1.4 ¯ 10 210.5 . This value is higher than what is normally assumed or derived for radio galaxies on the tens of kpc scale (k1.4 | 10 212 –10 211 ), but the difference may be attributed to the larger magnetic field in the smaller CSS sources. Recent HST imaging of CSS sources (de Vries et
al., 1999) confirms this general picture with some important differences. De Vries et al. found evidence for optical line emission aligned with the radio source in a sample of CSS radio galaxies. However, most of the emission appears to be in the wake of the radio plasma rather than from a luminous bow shock. This would be the case if the leading part of the bowshock is so fast it is non-radiative. The dominant optical line emission would then originate from the slower shocks at the sides of the lobes. Indeed, de Vries et al. have argued for bow-shock velocities | a few thousand km s 21 using a similar argument.
3.3. The relationship between turnover frequency and size The anticorrelation between turnover frequency and size (Fanti et al., 1990; Stanghellini et al., 1996a; O’Dea and Baum, 1997) has been the subject of several investigations based upon quite different models. Snellen (these proceedings) has presented a model based upon synchrotron self-absorption of the various components. In the BDO free–free absorption model, the decrease of ambient density with distance from the core of the ionized gas is offered as an explanation for the anticorrelation. In the model investigated by Kuncic et al. (1998), the absorption is due to induced Compton scattering. This process scatters high brightness temperature photons to low energies where they are absorbed and is relevant when the brightness temperature, T b of the source and the Thomson optical depth, tT of the scattering screen satisfy kT b ]] t |1 me c 2 T
(24)
that is, when
S D
Tb tT | 0.59 ]] 10 10
21
(25)
The brightness temperature of a typical nonthermal source increases rapidly towards low frequency so that there is always some frequency at which the process can become important (provided that free– free absorption or self-absorption has not already been established). In this model the anticorrelation
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Fig. 4. [OIII] luminosity as a function of 1.4 GHz radio power for values of log k1.4 5 2 10, 2 11, 2 12, 2 13 and 214 overlaid on data for radio-loud objects and Seyfert galaxies. Data are from Gelderman and Whittle (1996) (GW), Tadhunter et al. (1993) and Morganti et al. (1993) (collectively referred to as TM) and Whittle (1985) (W85). Legend: Filled circles—CSS sources from GW; filled squares—CSS sources from TM; open circles—GW FR II radio galaxies; open squares—TM FR II radio galaxies; diagonal crosses—GW QSOs; plus signs: TM compact flat spectrum sources; open triangles: TM FR I radio galaxies; filled hexagons: Seyfert galaxies from W85. Upper limits are indicated in the usual way.
with source size is the result of the Thomson depth of the ionized layer surrounding the source decreasing with source size due to the decreasing ambient density. A point in favor of the Kuncic et al. model is that the low frequency spectrum of GPS and CSS sources is strongly concentrated at a 5 2 1 (Fn ~ n 2 a ) as predicted by Coppi et al. (1993) for ICS. For the free–free absorption model, one requires a power-law distribution of optical depths (due to a spectrum of cloud sizes?); for the synchrotron self absorption model one requires a distribution of optical depths in the various self-absorbed components. Both free–free absorption and induced Compton scattering are possible if the bow shock is
non-radiative since there still remains a zone of shock-ionized gas surrounding the source. In this case, a substantial photoionized precursor would not be present and most of the absorption would take place in the shocked gas. This is not a significant problem since one expects that this will approximately only halve the optical depth, compared to the radiative models. An interesting feature of the Kuncic et al. model is that the fits to the turnover frequency-size relation tends to push the shock velocities and ambient densities into the non-radiative regime. Clearly, in view of the de Vries images and the implied densities and velocities, this model needs to be revisited.
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4. Radio quiet galaxies
4.1. Radio emission from Seyfert galaxies In many cases, Seyfert galaxies exhibit similar structures to radio galaxies, i.e. jets and lobes, albeit at powers over a thousand times lower. It is only recently, however, that workers have begun to explore the connections and distinctions between the two types of galaxies. Such work is potentially informative, since it can help to delineate the physics of both radio loud and radio quiet galaxies. The work which I am about to describe began as an attempt to see how much of the emission from the narrow-line region of Seyfert galaxies could plausibly be explained in terms of radiative shocks. As we shall see, the investigation has potentially wider ramifications. The starting point of this investigation was the correlation between [OIII] luminosity and radio power for Seyfert galaxies in Fig. 4. The correlation for these galaxies is similar to that for radio galaxies but the correlation is displaced three orders of magnitude to the left in radio power. This correlation has been known in one form or another for some time (see deBruyn and Wilson, 1978; Whittle, 1985), although some workers are looking at samples of radio sources which are more complete with a view to determining whether the ‘gap’ between the separate correlations can be filled in. For now we shall assume that the apparently bimodal distribution in radio power is real and that the Seyfert correlation represents a real physical link between their radio and optical properties. There are other good reasons for suspecting such a link, for example: • Where observations are made at high enough resolution, detailed correspondences between radio and optical features are often found, along with evidence of dynamical structure and sources of local ionization indicative of shocks (Whittle et al., 1988; Goodrich, 1992; Capetti et al., 1996). • In the specific case of NGC 1068 Capetti et al. (1997) have shown, using HST / WFPC2 [OIII] and Ha 1[NII] images overlaid on a VLA radio image of the radio source, that there is a close correspondence between the radio and optical structure.
• The radio axes of Seyferts correspond remarkably to the axes of their ionization cones, again suggesting that the radio and optical emission are causally related (Wilson and Tsvetanov, 1994). An argument against a strong physical link between radio activity and optical emission lines in Seyferts has been the inferred energy flux in the jets. Using the GPS model as a guide a median [OIII] luminosity | 10 42 ergs s 21 requires a jet energy flux | 10 44 ergs s 21 . Given the standard ‘conversion factor’, k1.4 5 P1.4 /FE | 10 212 –10 211 Hz 21 between radio power and jet energy flux, the required energy flux is difficult to understand given the radio powers of Seyferts. Typically P1.4 | 10 23 W Hz 21 so that the inferred jet energy flux would be a puny 10 41 ergs s 21 —about a factor of 10 3 too low. A proposed resolution to this problem comes from a re-examination of Eq. (13) for kn , viz. Pn kn 5 ] FE 5 C1 (a)sg0 m e c 2d a 22 B (a11) / 2 f fe fad t g n 2(a21 ) / 2 (26) What are the factors that could reduce kn in the case of a Seyfert galaxy. For a start, the dynamical ages 6 | 10 yr are generally much less than that of a radio galaxy. However, this is counterbalanced to some extent by the generally higher minimum energy 24 magnetic fields ( | 10 G) in Seyfert lobes. The obvious remaining parameter is the electron / positron fraction fe . In radio galaxies and quasars, we usually (either implicitly or explicitly) take this to be of order unity. If Seyfert jets really are much more powerful than has been assumed, and kn is correspondingly much less, then we generally have no choice other than to assume that fe | 0.01. That is, Seyfert jets contain a much larger fraction of thermal plasma and the radio emission is merely a tracer of the underlying flow. There are several important consequences of this.
4.2. Jet velocities In NGC 1068 high resolution VLA and HST
G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
studies make a good case for a jet-cloud impact between the northern jet and a cloud in the NLR (Gallimore et al., 1996a,b). The emission-line flux from the cloud provides a useful diagnostic for the jet velocity. This is based on the required jet momentum flux (force) required to drive a radiative shock of the required velocity into the cloud. Here is it is useful to distinguish between momentum-driven and energy driven shocks. The radiative shock resulting from the impact of a jet on a cloud is momentum driven, when the jet is much lighter than the cloud. Only a small fraction | ( rjet /rcl )1 / 2 of the jet energy flux is transmitted to the cloud, the rest being advected with the jet. On the other hand, in the GPS / CSO model considered earlier, the jet driven lobe expansion is energy driven, similar to the way in which the expansion of an interstellar bubble is energy driven; the effect of the lobe on the interstellar medium is therefore dominated by the jet energy flux. Another important point is that for a given energy flux, relativistic jets are poor transporters of momentum. The momentum fluxes of relativistic and nonrelativistic jets are given by 1 Momentum flux 5 ] 3 Energy flux c 2 Momentum flux 5 ] 3 Energy flux vjet
(27)
respectively. Hence if a large jet force is required to drive a radiative shock into a dense cloud, and if the jet energy flux is constrained by other considerations (in this case, the total luminosity of the NLR), then the lower the jet velocity the easier it is to satisfy the momentum constraint. When a jet hits a cloud, an oblique shock (or series of oblique shocks) is produced which deflect the jet and create a region of high pressure adjacent to the cloud (see Fig. 5). It is this high pressure region which is responsible for driving a shock into the cloud and if the latter is dense enough, this shock will be radiative. The jet velocity as a function of the pressure Psh in the shocked region is given by 2FE vjet ¯ ]] 3 f psh A sh
375
fraction of jet momentum absorbed by the cloud 4 . A simple analysis of the interaction based upon analysis of the Rankine Hugoniot equations gives f | 0.4– 0.8 depending upon the angle of incidence. It would be interesting to estimate f from numerical simulations which reveal a more complicated situation than that depicted in Fig. 5. The driving pressure is related to the shock velocity by: 2 2 psh ¯ rcl v sh ¯ 1.4n H,cl m p v sh
(29)
and the Ha luminosity provides a further constraint on the parameters of interest via the MAPPINGS derived relation between density and velocity, viz.: L(Ha ) ¯ 5.3 3 10
23
vsh n H,cl A sh ]]]] 1000 km s 21
S
2.4
(30) Combining all of these relations gives the following estimate of the jet velocity: vjet FE,44 0.4 ] ¯ 0.15 f ]]] v sh,8 c L40 (Ha )
(31)
The FWHM | 350–600 km s 21 of those NLR velocities in NGC 1068 which can be attributed to shocks (Dietrich and Wagner, 1998) gives us a good idea of the shock velocity, say 500 km s 21 ; moreover the estimate of jet velocity is insensitive to the actual shock velocity. The estimate of the velocity of the jet is therefore given by: vjet ] | 0.03–0.06 c
(32)
for f | 0.4–0.8 and L(Ha ) ¯ 1.4 3 10 40 ergs s 21 . The inverse dependence of jet velocity on Ha luminosity reflects the inverse dependence of momentum flux on velocity for a given energy flux. This analysis shows that at the site of cloud C 5 approximately 27 pc from the core, the jet velocity is decidedly non-relativistic, underlining a significant difference between jets in Seyferts and radio galaxies.
(28)
where A sh is the area of cloud affected and f is the
D
4 5
See Bicknell et al. (1998) for details. In the notation of Gallimore et al.
G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
376
Fig. 5. Schematic of a jet-cloud interaction leading to an oblique shock in the jet and a radiative shock driven into the cloud. The former is responsible for the radio emission from a jet ‘knot’; the latter is responsible for the line emission from the cloud.
4.3. The mass flux
ment has occurred into the jet. The initial velocity ~ init , then is given by for an initial mass flux, M
The mass flux in the jet is interesting 2F 2 ~ jet 5 ]]E M vjet
F
3 1 1 ]] M 2jet
vjet 5 1.4 ]] 0.05c
S
D
S D
vinit 2FE ]] ¯ ]] ~ init c M
G
22
FE,44
F
1/2
S
~ init M 1/2 ¯ 0.27F E,44 ]]]] 0.05 M ( yr 21
G
3 1 1 ]] M ( yr 21 M 2jet (33)
This is much higher than what is required to fuel the black hole (|0.05 M ( yr 21 ) and indicates that either the jet represents an outflow from the black hole environs which has a mass flux greater than the accretion flow or more likely, that significant entrain-
D
21 / 2
(34)
This velocity is only mildly relativistic unless the jet mass flux is about 15 times less than the accretion mass flux.
4.4. Relationship to accretion disk coronae There is an interesting relationship between the above jet physics and the properties of accretion disk
G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
coronae. It is highly likely that the X-ray emission from a Seyfert nucleus comes from an accretion disk corona rather than the cold accretion disk itself (Haardt et al., 1994, 1997; Johnson et al., 1997). The Johnson et al. observations indicate that these coronae have Thomson optical depths tc | 1, and temperatures, T c | 100 keV). The optical depth of the corona, combined with its scale height,
S DS D
2kT c h c 5 r g ]]2 mmpc
r ] rg
where r g 5 2GM /c is the gravitational radius of the black hole, allow us to estimate the electron density of the corona through n e,c ¯ tc (sT h c )21 . Suppose then that the corona is at the base of the jet. Then we can estimate a mass flux,
S D S D S D
plasmas moving with Lorentz factors of up to 10 or more. If this comparison is valid, then it argues for a quite different origin for radio galaxy jets—possibly as indicated by Blandford and Znajek (1977) and Meier (1999) and discussed by David Meier in these proceedings.
4.5. Observational support for thermally loaded jets in Seyferts
(35)
2
bjet 21 / 2 ~ init ¯ 0.04CM7 T c,9 ] M 0.1 r outer 1 / 2 n ` ]] ] M ( yr 21 10r g n e,c
377
(36)
where C is the covering factor of the corona, 10 7 M7 M ( is the mass of the black hole, bjet is the jet v /c in the asymptotic regime, r outer is the outer radius of the jet base and n ` is the electron density in the asymptotic regime. It is not difficult to see that, for an initially mildly relativistic jet and with other typical parameters, the initial mass flux would be order or slightly less than the mass accretion rate in NGC 1068 and other similar Seyferts. The upshot of this is that jet flows from Seyferts could begin as winds originating from the inner 10 gravitational radii or so of the accretion disc. Since the coronal sound speed, ¯ 0.012T 1c,9/ 2 c is much less than the escape speed ¯ 0.45(10r g /r)1 / 2 , it is likely that such a wind is magnetically driven. These winds may be collimated further out by the action of pressure gradients, to form a jet. Such a scenario would also explain why Seyfert jets are thermally dominated; radio emission could simply result from the action of internal jet shocks, which accelerate electrons to radio emitting energies, either from the mildly relativistic coronal plasma or from thermal plasma entrained into the jet from the interstellar medium. This invites comparison with jets in radio galaxies and quasars which are widely (but perhaps not universally) believed to be electron / positron
The above combination of theory and interpretation has some significant support in recent observations: • Wilson and Raymond (1999) have detected X-ray emission (presumably from the NLRs) in a sample of Seyfert 2 galaxies. The level of X-ray emission is consistent with emission from shocks with velocities | 200–500 km s 21 at a level which is consistent with the [OIII] emission. • VLBI observations of proper motion in Seyferts (e.g. Ulvestad et al., 1999) show low velocity ( , 0.1c) proper motions of the knots. Whilst knot velocities represent pattern speeds, presumably of internal jet shocks, it would be surprising if at least some of the measured speeds (or limits thereof) are not representative of jet speeds. The absence of any superluminal speeds, or even speeds in excess of 0.5c is therefore strong evidence that the speeds in these jets are in fact, low.
5. Concluding remarks The gains that have been made in understanding the many facets of Radio Galaxies over the last fifteen years or so, place us in a position where accelerating success in understanding the real physical nature of these objects is apparent. Once, we regarded the Fanaroff–Riley division as a convenient descriptive classification for Radio Galaxies. Now, we are aware that the physics of this division is fundamentally important to the way in which relativistic jets are produced in the environment of black holes and how this relates to the evolution of radio galaxies. We certainly do not have comprehensive answers to questions concerning the FR classifi-
378
G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
cation at the present time. However, this aspect of Radio Galaxies will clearly receive even more observational and theoretical attention in the ensuing years. Just as fundamental is the nature of GPS and CSS sources and the as yet not-well-understood way in which they fit in to the evolution of the overall radio-loud population. Seyfert galaxies, until recently a fairly neglected population as far as radio astronomers are concerned, also give us important clues to many of the fundamental questions relating to radio galaxies—principally jet formation and the interaction between jet and accretion disc Physics. If the ideas presented here relating to Seyfert galaxies are correct, then we have the interesting problem of why 10 7 M ( black holes produce slow, predominantly thermal jets and why 10 8 –10 9 M ( black holes produce relativistic electron / positron jets. Perhaps the answer lies with the magnetic switch mechanism which David Meier proposed to distinguish between FR I and FR II radio galaxies. One thing that was apparent in this meeting was the way in which many people are confronting the complex physics of radio galaxies from many different points of view and how rapid progress has become. I would therefore like to thank the organizers for organizing such a stimulating and productive workshop and for organizing financial support from the Space Telescope Science Institute. I would also like to acknowledge the contributions of my colleagues, specifically Mike Dopita, Chris O’Dea, Ralph Sutherland and Zlatko Tsvetanov, to the research on emission line production in AGN, summarised in this paper and their contributions, as well as those of Anton Koekemoer, to many useful discussions on this topic.
References Barthel, P.D., 1989. ApJ 336, 606. Barthel, P.D., 1994. In: Bicknell, G.V., Dopita, M.A., Quinn, P.J. (Eds.), The First Stromlo Symposium: The Physics of Active Galaxies, Astronomical Society of the Pacific Conference Series, Astronomical Society of the Pacific, 175. Begelman, M.C., 1996. In: Carilli, C.L., Harris, D.A. (Eds.), Cygnus A: Study of a Radio Galaxy. University Press, Cambridge, p. 209. Bicknell, G.V., 1986. ApJ 305, 109. Bicknell, G.V., 1994. ApJ 422, 542. Bicknell, G.V., 1995. ApJS 101, 29.
Bicknell, G.V., Dopita, M.A., O’Dea, C.P., 1997. ApJ 485, 112. Bicknell, G.V., Dopita, M.A., Tsvetanov, Z.I., Sutherland, R.S., 1998. ApJ 495, 680. Blandford, R.D., Znajek, R.L., 1977. MNRAS 179, 433. Capetti, A., Axon, D.J., Machetto, F.D., 1997. ApJ 487, 560. Capetti, A., Axon, D.J., Machetto, F.D., Sparks, W.B., Boksenberg, A., 1996. ApJ 469, 554. Coppi, P., Blandford, R.D., Rees, M.J., 1993. MNRAS 262, 603. deBruyn, A.G., Wilson, A.S., 1978. A&A 64, 433. de Vries, W., O’Dea, C.P., Baum, S.A., Barthel, P.D., 1999. ApJ 526, 27. DeYoung, D.S., 1993. ApJ 402, 95. Dietrich, M., Wagner, S.J., 1998. A&A 338, 405. Donnelly, R.H., Faber, S.M., O’Connell, R.M., 1990. ApJ 354, 52. Dopita, M.A., Binette, L., Dodorico, S., Benvenuti, P., 1984. ApJ 276, 653. Dopita, M.A., Dodorico, S., Benvenuti, P., 1980. ApJ 236, 628. Dopita, M.A., Sutherland, R.S., 1996a. ApJS 102, 161. Dopita, M.A., Sutherland, R.S., 1996b. ApJ 455, 468. Eilek, J.A., Shore, S.S., 1989. ApJ 342, 187. Falle, S.A.E.G., 1991. MNRAS 250, 581. Fanaroff, B.L., Riley, J.M., 1974. MNRAS 167, 31P. 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. Gallimore, J.F., Baum, S.A., O’Dea, C.P., 1996a. ApJ 464, 198. Gallimore, J.F., Baum, S.A., O’Dea, C.P., Pedlar, A., 1996b. ApJ 458, 136. Gelderman, R., Whittle, M., 1996. Private communication. Goodrich, R.W., 1992. ApJ 399, 50. Haardt, F., Maraschi, L., Ghisellini, G., 1994. ApJ 432, L95. Haardt, F., Maraschi, L., Ghisellini, G., 1997. ApJ 476, 620. Johnson, W.N., Zdziarski, A.A., Madejski, G.M., Paciesas, W.S., Steinle, H., Lin, Y., 1997. In: Proceedings of the Fourth Compton Symposium, AIP Conf. Proc. 410, 283. Killeen, N.E.B., Bicknell, G.V., Ekers, R.D., 1988. ApJ 325, 165. Kommisarov, S.S., 1994. MNRAS 269, 394. Kormendy, J., 1987. In: de Zeeuw, T. (Ed.), Structure and Dynamics of Elliptical Galaxies. IAU. Dordrecht, Netherlands, p. 17. Kuncic, Z., Bicknell, G.V., Dopita, M.A., 1998. ApJ 495, L35. Ledlow, M.J., Owen, F.N., 1996. AJ 112, 9. Meier, D.L., 1999. ApJ 522, 753. Morganti, R., Killeen, N.E.B., Tadhunter, C.N., 1993. MNRAS 263, 1023. O’Dea, C.P., Baum, S.A., 1997. AJ 113, 148. Owen, F. N. and Ledlow, M.J., 1994. In: Bicknell, G.V., Quinn, P.J., Dopita, M.A. (Eds.), The First Stromlo Symposium: The Physics of Active Galaxies, PASP Conference Series, Astronomical Society of the Pacific, 319. Pacholczyk, A.G., 1970. Radio Astrophysics. Freeman, San Francisco. Phinney, E.S., 1983. Ph.D. Thesis, University of Cambridge. Russell, S.C., Dopita, M.A., 1990. ApJS 74, 93. Scheuer, P.A.G., 1982. In: Heeschen, D.S., Wade, C.M. (Eds.), Extragalactic Radio Sources. IAU Symposium 97. Reidel, Dordrecht, p. 163. Sutherland, R.S., Dopita, M.A., 1993. ApJS 88, 253.
G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379 Tadhunter, C.N., Morganti, R., di Serego-Aligheri, S., Fosbury, R.A.E., Danziger, I.J., 1993. MNRAS 263, 999. Terlevich, R., Davies, R.L., Faber, S.M., Burstein, D., 1981. MNRAS 196, 381. Ulvestad, J.S., Wrobel, J.M., Roy, A.L., Wilson, A.S., Falcke, H., Krichbaum, T.P., 1999. ApJL 517, L81.
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Connections between jet physics and the properties of radio-loud and radio-quiet galaxies Geoffrey V. Bicknell ANU Astrophysical Theory Centre, Research School of Astronomy and Astrophysics, Australian National University, Private Bag, Weston PO, ACT 2611, Australia
Abstract Relationships between jet physics and the evolutionary phases of radio galaxies are discussed. This includes the connection between the properties of relativistic jets and the Fanaroff–Riley classes of radio galaxies and the interaction of jets with the interstellar medium in Gigahertz Peak Spectrum and Compact Steep Spectrum Radio Sources. Jets in Seyfert galaxies are compared with those in classical radio galaxies and recent work suggesting that there are major differences between the two types of jets is summarized. The proposed major differences are principally that Seyfert jets are thermally dominated with subrelativistic speeds whereas Radio Galaxy jets are relativistic electron / positron flows. Hence, the production of jets in Seyferts and radio galaxies are fundamentally different. 2002 Published by Elsevier Science B.V. Keywords: Galaxies: Evolution; Galaxies: Jets; Galaxies: Seyfert; Radio continuum: Galaxies
1. Introduction Before Ledlow and Owen published their striking and fundamental results on the radio and optical properties of FR I and FR II radio galaxies, it was widely believed that there was no possible evolutionary link between the two classes (Ledlow and Owen, 1996; Owen and Ledlow, 1994). FR I radio sources seemed to be dominant galaxies near the centers of clusters; FR IIs seemed to be L , L* galaxies which inhabited the outskirts. However, the existence of a fairly clear luminosity-dependent dividing line between the two classes showed that an evolutionary connection at fixed optical luminosity is possible. The origin of this dividing line remained to be explained and a partial theory is summarized in the following section. Gigahertz Peak Spectrum and Compact Steep Spectrum Galaxies represent another E-mail address: [email protected] (G.V. Bicknell).
intriguing subclass of radio galaxies. These clearly represent an important evolutionary phase of Radio Galaxies but as other papers in this meeting have shown, their evolution is not well understood. In Section 3 of this paper some ideas relating to the interaction of the lobes of these sources with a dense interstellar medium is summarized. It was the emission line properties of Seyfert galaxies which led my colleagues and me to suggest that similar processes to those operating in GPS and CSS sources may be relevant in Seyfert galaxies. If this is the case then significant differences in the velocities and composition of Seyfert jets are implied and this has ramifications for the way in which jets are formed in Seyfert and Radio Galaxies.
2. The Fanaroff–Riley division By now it is well accepted that the differences in
1387-6473 / 02 / $ – see front matter 2002 Published by Elsevier Science B.V. PII: S1387-6473( 01 )00210-X
G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
366
morphology between the Fanaroff–Riley types of radio source are related to mass loading: FR I jets are turbulent mass-entraining flows which decelerate from a relativistic velocity effectively to rest or at most a few thousand km s 21 . The features of FR I sources, principally a bright rapidly spreading jet plus relaxed lobe and a slow decline of jet surface brightness with distance from the core are related to the physics of transonic entrainment. FR II jets are relativistic from the core to the lobes (with perhaps some minor deceleration) and their features, principally bright hot spots, lobes much larger than the jets which fuel them and the presence of knots distributed along thin, usually faint jets are related to the physics of hypersonic, low density flows. In Unified Schemes FR I sources are the parent population of BL-Lac objects and FR II sources are the parent population of quasars (Barthel, 1989, 1994), these associations being made possible by the aspect dependence of relativistic flow on the parsec scale. It had of course been known from the original paper of Fanaroff and Riley (1974) that FR I and FR II sources are separated in 1.4 GHz power at about 10 24.5 W Hz 21 with some considerable overlap. Nevertheless, the dramatic separation of FR I and FR II sources in the optical-radio plane discovered by Michael Ledlow and Frazer Owen begged for a straightforward explanation. One suggestion again involves the dynamics of initially relativistic flow so that relativity not only plays a significant role in unifying apparently different Active Galactic Nuclei, but it also plays a role in unifying FR I and FR II sources. The proposal for the ‘cross-unification’ of FR I and FR II sources (Bicknell, 1995) is based on the following method of estimating the jet energy flux and the corresponding radio luminosity. For a jet with pressure, pjet , radius r jet , velocity vjet 5 cb, 2 Lorentz factor, G, and ratio x 5 r c / 4p of cold mater energy density to enthalpy, the energy flux is given by:
F
G
G 21 2 FE 5 4p cpjet r jet 1 1 ]] x G 2 b G
(1)
In order to estimate the jet energy flux, we therefore require its pressure, radius and velocity. (The parameter x turns out to be not as important.) Estimates of these parameters are based on the following: 1. Effectively, the ‘last opportunity’ for a jet to
become a turbulent FR I jet is close to a core radius of the parent galaxy, since that is where the gas density is greatest. Moreover, beyond this point the pressure gradient is not favorable to the production of turbulence. Hence we surmise that most FR I jets become turbulent within the optical core region and that borderline FR I / II cases occur when the transition radius is within about an order of magnitude of the core radius. 2. All jets are initially highly relativistic and the transition to turbulence occurs when the Mach number becomes transonic. As we shall see, this implies a more or less unique velocity for the transition to turbulent flow. 3. Given an unique value for the velocity for the transition to turbulent flow, the other main parameter which is required to determine the jet energy flux is the jet pressure at that point. This is determined by the pressure of the galaxy atmosphere; this is constrained by the X-ray luminosity, other optical parameters and empirical relationships between these and the absolute magnitude of the optical galaxy. Let us consider each one of these points. 1. The association of an unique velocity associated with the transition to transonic flow can be deduced from the following argument. Consider a jet which is initially highly relativistic. The energy flux is conserved exactly. The momentum flux of a confined non-relativistic jet with density r, velocity V and cross-sectional area A propagating in the z direction satisfies the following equation: d ] dz
E rV
2
dPext dA 5 2 ]] dz
r E S1 2 ] dA r D
(2)
ext
and there is a similar equation for relativistic flow (see Bicknell, 1994). A consequence of this equation is that Length-scale for momentum increase ¯ Mach number 2 3 Pressure scale height
(3)
For an initially high Mach number, the momentum flux of a confined jet is therefore approxi-
G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
mately conserved. The momentum flux of a free jet is exactly conserved since it is not sensitive to the background pressure. With this approximation then, the ratio of energy flux to momentum flux is conserved and for an initially relativistic jet this ratio is the speed of light, c. When such a jet decelerates to a subrelativistic velocity, 2
Energy flux 4pVA(1 1 M / 6) ]]]]] 5 ]]]]] 5c Momentum flux rV 2 A
(4)
implying that V M2 ] 5 ]]]] ¯ 0.29 for M 5 1 c 3(1 1 M 2 / 6)
(5)
367
( pjet 5 pISM), then we can see that the energy flux is insensitive to the precise point at which the jet transits to turbulence. In most galaxies, pISM R t2 is a slowly varying function of R t . (Typically, pISM R 2t ~ R 0.5 t .) 4. The atmospheric pressure in the centre of the galaxy can be estimated using a simple isothermal atmosphere model. X-ray astronomers often use the following empirical law for the gas distribution. Let n e be the electron density, (central value n c ), the total ion density be n t and the cooling function integrated across the relevant band be L(T ). (The band integrated emissivity is expressed as n e n t L(T ). The empirical model is
2. For higher Mach numbers the full relativistic expressions for the energy and momentum fluxes are required. However, it is worth noting here that as a consequence of Eq. (5), if an initially relativistic jet is supersonic on the kpc scale, then its velocity is necessarily greater than about 0.3 c. Some typical calculations for jets of higher Mach numbers are summarized in Fig. 1. It can be seen that jets typically enter the transonic regime M | 1–2 for V | 0.6–0.7 c.
F G
r2 n e (r) 5 n e,c 1 1 ]2 rc
2 b at
(6)
where bat is a fitted constant. This implies a surface brightness distribution, SX (x) (x 5 projected radius) in X-rays given by 1
F G
x2 SX (x) 5 SX,0 1 1 ]2 rc
22 b at 11 / 2
where 3. For a jet expansion rate a the jet radius at the distance R t from the core where the jet makes the transition to turbulence is r jet 5 a R t and pjet r 2jet 5 a 2 pjet R t2 . Given that the jet pressure is in equilibrium with the interstellar medium by this stage,
G (2bat 2 1 / 2) SX,0 5 p 1 / 2 ne,c nt,c L(T )r c ]]]] G (2bat )
(7)
5. The total X-ray luminosity, LX is related to electron density and ion number density, n t , core radius r c and temperature, T, via: nt 2 3 LX 5 4 p ] n e,c r c LE (T )IX ( bat , r 1 /r c ) ne
S D
where IX 5
E
0
(r 1 / r c )
s1 1 x 2d 22b at x 2 dx,
(8)
In Eq. (8), r 1 is a cutoff radius and LE (T ) is the cooling function integrated over the Einstein band. X-ray astronomers often fit the surface brightness implied by the above empirical law 1
Fig. 1. Mach number vs. bjet for a jet with an initial value of x 5 r c 2 / 4p 5 0 for various values of the initial Lorentz factor.
I note for completeness that in many published fits bat is replaced by 3b / 2 based on some of the original papers on X-ray coronae which mistakenly assumed that the above distribution represented that of gas in a gravitating isothermal sphere. See Killeen et al. (1988).
G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
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(Eq. (6)). This implies a distribution of gravitating matter, which has many of the characteristics of a stellar dominated matter distribution merging into a dark matter distribution with total density given by:
possible to estimate the total radio luminosity from such an approach. However, the relationship between monochromatic power is more directly related to the observations and, in fact, involves fewer parameters. We therefore have
s 2` 3 1 r 2 /r 2c rm 5 ]]2 ]]]] 2p Gr c (1 1 r 2 /r 2c )2
Pn kn 5 ] FE
(9)
The parameter bat is related to the velocity dispersion at infinity by
m m p s `2 ]]] bat 5 kT
(10)
6. This discussion of the relation between X-ray determined and optically determined parameters shows that the X-ray luminosity and the pressure of the atmosphere are related via the optical core radius and the velocity dispersion. Moreover, there is a relationship between the Einstein X-ray and optical luminosities for elliptical galaxies (Donnelly et al., 1990); there are also relationships between core radius and absolute magnitude (Kormendy, 1987) and central velocity dispersion and absolute magnitude (Terlevich et al., 1981). All of these can be combined with the above X-ray gravitating matter model to estimate the central pressure, pc which is interestingly insensitive to absolute magnitude: log pc ¯ 2 8.2 1 0.03MB
(11)
7. Putting all of this together gives an expression for the jet energy flux: log FE ¯ 24.1 2 0.85MB 1 log
HS
D
G 21 1 1 ]] x g 2jet bjet G
J
(12)
which already exhibits the L 2.1 opt dependence of the Owen–Ledlow dividing line. 8. The final connection to the Owen–Ledlow data is made through the relationship between radio source parameters and the ratio, kn , of lobe monochromatic power, Pn to jet energy flux. This is derived simply from the fact that radiating electrons are supplied to the radio lobe at a rate proportional to the energy flux (Bicknell, 1986; Bicknell et al., 1998; Eilek and Shore, 1989). It is
5 C1 (a)sg0 m e c 2d a22 B (a11) / 2 f fe fad t g n 2(a 21) / 2 (13) Here, C1 (a) 5 4p (a 2 2)c 5 (a)c 9 (a)(2c 1 )(a 21) / 2 is expressed in terms of the synchrotron parameters introduced by Pacholczyk (1970), fe is the electron / positron fraction of the lobe internal energy, fad is an adiabatic factor allowing for lobe expansion, B is the lobe magnetic field, and t syn is the synchrotron cooling time. The adiabatic factor fad is 0.75 for a radio lobe expanding at constant pressure into the background. Eq. (13) applies to the power-law region of the spectrum, where cooling has not affected the spectrum. It can only apply up until the point where the lobe is old enough that synchrotron losses start to affect the synchrotron emissivity at the edges of the lobe. The following form of the expression for kn u takes this into account by expressing the time in units of the synchrotron cooling time, t syn . Thus,
kn ¯ C2 (a)sg0 m e c 2d a 22 B (a22) / 2 t 3 fe fad ] n 2a / 2 t syn
F
G
3 p C2 (a) ¯ ] ] 2 4
S D
1/2
1/2 c 21 2 c 1 C 1 (a).
(14)
(15)
This equation also has the advantage that, for typical values of a | 2.4–2.6, the estimate of kn is insensitive to the assumed value for the magnetic field. (We generally adopt a value of B 5 10 mG.) The end result of the above process is a predicted relationship between the radio luminosity of a borderline FR I / II source and the absolute magnitude of the host galaxy. One expects the actual dividing line to be bracketed by 0.1 , t /t syn , 1. The result is shown in Fig. 2 which shows theoretical dividing lines for t /t syn 5 0.1 and 1. These in fact bracket the actual division quite well. In some sense the success
G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
Fig. 2. Radio galaxies in the radio luminosity–optical luminosity plane. The data are from Ledlow and Owen (1996). The open circles represent FR I radio galaxies; the filled circles represent FR II radio galaxies. The lines represent the theoretical relations describing borderline FR I / II radio galaxies. The lower and upper lines represent theoretical relations corresponding to ages of the borderline galaxies being 0.1 and 1.0 synchrotron cooling times respectively.
of this model is quite remarkable, in view of the convoluted way in which the pressure is related to the absolute magnitude It should also be borne in mind that the good fit is also due to the identification of a more or less unique, mildly relativistic velocity at which a jet becomes transonic and hence turbulent. This theory does not say how jets decelerate in the first few hundred parsecs. The notion on which the above theory depends is that given a jet has decelerated to a transonic Mach number in a galaxy of a given absolute magnitude then we can estimate its energy flux, since we can estimate its velocity, pressure and radius. The possibilities for causing deceleration in the first few hundred parsecs include • Mass-injection by stars into jets of less than a critical luminosity (Kommisarov, 1994; Phinney, 1983) • Turbulent deceleration of supersonic (but not hypersonic) jets. Meier (1999) has also discussed reasons for the differences and Mach number for jets in terms of a ‘magnetic switch’ mechanism. In all cases, one
369
expects the lower luminosity jets to be affected the most by entrainment processes in the first few hundred parsecs. The viability of the Phinney–Kommisarov mechanism depends upon whether the stellar winds are effectively mixed into the jet (Kommisarov, 1994). What are the ramifications of these ideas for the lifecycle of a radio galaxy?. As I mentioned in the Introduction, one of the singularly important results of the Ledlow–Owen discovery is that it opens up the possibility of evolution of radio sources in a vertical line on their diagram. Let us suppose that following a period of fueling (resulting from a merger?) a radio source goes through a powerful FR II phase in which the jets are hypersonic and relatively unaffected by the interstellar medium. As the source of fuel for the black hole diminishes, the jets become less powerful and make the transition to FR I at a power which depends upon the absolute magnitude, possibly as indicated by the above scenario. There then follows a subsequent, perhaps more long-lived phase wherein the Galaxy continues as an FR I. The relative times spent in the FR I and FR II phases would depend upon the time at which the source crosses the transition line and hence on the absolute magnitude. This scenario could be developed in a more quantitative fashion. It could even be examined observationally now, by imaging radio galaxies in a narrow range of optical luminosity and looking for signs of evolution, as evidenced say by merger characteristics, and examining these as a function of radio luminosity 2 .
3. Gigahertz Peak Spectrum and Compact Steep Spectrum radio sources
3.1. Characteristics of GPS and CSS sources Gigahertz Peak Spectrum (GPS) and Compact Steep Spectrum (CSS) Radio Sources undoubtedly represent an important youthful phase in the lifecycles of Radio Galaxies. Their large fractional representation in radio source catalogues is probably the
2
This idea was the result of discussion with Stefi Baum at this meeting.
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result of significant source evolution (Begelman, 1996), although the precise nature of the evolution is presently not clear (see Conway, these proceedings). Some important radio and optical characteristics of these sources are: • A turnover in the radio spectrum at around a GHz for GPS sources, and lower for CSS sources. • High rotation measures. • Median Power: P5GHz 10 27.5 W Hz 21 • A dominant narrow line spectrum with line widths | few 100–1000 km s 21 . Some ideas that are most likely relevant to understanding these sources are 1. GPS and CSS sources are young ( , 10 6 yr) and impeded in their progress through a dense interstellar medium. 2. Their high luminosities are the result of confinement and the luminosity evolves as the confining pressure decreases (DeYoung, 1993; Begelman, 1996). The emission line spectrum of GPS and CSS sources provides additional information. Bicknell et al. (1997) have argued that both the emission line fluxes and the low frequency turnover result from a dense shell surrounding the radio lobes which is ionized by the bow shock surrounding the expanding radio lobe. In their model, the turnover is produced by free–free absorption. In a variant of the BDO model, Kuncic et al. (1998) suggested that induced Compton scattering (ICS) could also be responsible for the low frequency turnover. In support of this model, the brightness temperatures of GPS and CSS sources are frequently in the range (T b . 10 9 K) where ICS can be important and the low frequency spectral indices cluster around a 5 2 1 (Fn ~ n 2 a ) (Stanghellini et al., 1996b) as predicted by the ICS model. On the other hand, synchrotron self-absorption in several components of each source (see Snellen, these proceedings) represents a popular model for the turnover in both CSS and GPS sources.
3.2. Radiative shocks The characteristic of a radiative shock is that the internal energy of the shocked gas is radiated in less than a dynamical lifetime. Models of low velocity Vsh , 200 km s 21 shocks have been used for some time to explain the optical spectra of supernova remnants, for example Dopita et al. (1980), Dopita et al. (1984) and Russell and Dopita (1990). Fast shocks introduce an additional feature. The postshock temperature T ¯ 5.6 3 10 5 sVshock / 21 2 200 km s d is so high that a UV to soft X-ray flux is produced that ionizes the shock precursor gas. Depending upon the pre-shock density the extent of the precursor can be quite large— | n 21 H kpc where n H is the pre-shock Hydrogen density (Dopita and Sutherland, 1996a,b). The spectrum of high velocity radiative shock is a mixture of collisionally excited and photoionized line emission. One feature of the spectrum is that the [OIII] l4363 line (produced in the hot post-shock zone) is stronger than in pure photoionized models and this helps to explain the higher than expected temperatures inferred for the Narrow Line Regions of many active galaxies. In the model for GPS / CSS sources (see Fig. 3), Bicknell et al. (1997) proposed that a ‘dentist’s drill’ (Scheuer, 1982) jet inflates a high pressure lobe in the ISM, the dynamics of which are described by the CSO 3 model of Begelman (1996) (modified to account for adiabatic losses). Ambient clouds are ionized by the bow shock surrounding the lobe producing the shock excited spectrum described above. The FWHM of the lines indicates that the shocks are indeed fast (up to a thousand km s 21 ) and one consistency check that is required for such fast shocks is that the radiative cooling time is less then the dynamical time, of order the age of the source. This is satisfied for the BDO model but this criterion may be especially pertinent to models in which the head of the lobe is rapidly expanding and most of the emission emanates from the less rapidly expanding sides (see below). In estimating the emission line luminosities, one
3
There is probably a large overlap in physical characteristics of sources which are described as Gigahertz Peak Spectrum, Compact Steep Spectrum and Compact Symmetric Object.
G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
371
Fig. 3. Schematic of the GPS / CSS model of Bicknell et al. (1997). A ‘dentist-drill’ jet forces its way though the ISM of the host galaxy. Clouds in the ISM are shock-ionized and photoionized by the UV to soft X-rays from the shocks.
uses the following power-law fits to MAPPINGS output for the total continuum and line luminosities, LT , Hb luminosity, L(Hb ) and [OIII] l5007 luminosity, L([OIII]) from a shock of area A shock cm 2 :
S
Vshock LT 5 1.1n H ]]]] 1000 km s 21
D
S
3
A shock ergs s 21
D
2.4 Vshock 23 21 L(Hb ) 5 1.9 3 10 n H ]]]] ergs s 21 1000 km s 3 Vshock L([OIII]) 5 2.3 3 10 22 n H ]]]] 21 1000 km s
S
A shock ergs s 21
D
(16)
(Sutherland and Dopita, 1993; Dopita and Suther3 land, 1996a,b). The nV A dependence of LT reflects the fact that the kinetic energy flux of the incoming gas is converted into internal energy, thence into ionizing radiation and subsequently into continuum and emission line luminosity.
Consider a jet with energy flux, FrmE feeding a radio lobe which is expanding into a medium with mass density r 5 r0 (x /x 0 )2d, where x is the distance from the centre of the galaxy and r0 is the density at an arbitrary scaling distance x 0 which we take to be a kpc. The distance, x h , of propagation the head of the lobe into this medium is described in terms of the similarity parameter 3 (5 2 d ) j 5 ]]]] 18p (8 2 d )
F
2
3
z FE t ]] r0 x 05
G
(17)
(cf. Falle, 1991; Eilek and Shore, 1989). We have for the distance of propagation: x h 5 x 0 j 1 / 52d
(18)
and the lobe pressure is given by:
S Dj
x0 9 Plobe 5 ]]]2 r0 ] t z (5 2 d )
2
22d / 52d
(19)
G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
372
The parameter z | 2 was introduced By Begelman to describe the ratio of averaged hot spot pressure to lobe pressure; z 1 / 2 then is the ratio of forward speed to lateral speed of the lobe. An important deduction from this model is the velocity–size relation:
S
6 Vh ¯ 1500 ]] 82d
D
1/3
S DS D 1/3
FE,45 z 1 / 6 ]] n H,0
xh ] kpc
d 22 / 3
(20) 21
45
where the jet energy flux is 10 FE,45 ergs s . In the BDO model, the FWHM of emission lines is indicative of the velocity of propagation of the head of the lobe implying that FE,45 ]] | 0.1–1 n H,0
(21)
This is used below to estimate the ambient number density. The total emission line and continuum luminosity is determined by the work done on the local interstellar medium, so that 3 1 LT 5 ]] FE ¯ ] FE 82d 2
(22)
for d ¯ 2. Since the total luminosity and [OIII] luminosity scale in exactly the same way with density, velocity and temperature, it is straightforward to estimate the [OIII] luminosity as L([OIII]) 5 8.2 3 10
S
P1.4 ]]]] 27 10 W Hz 21
D
42
k1.4 6 ]] ]]]] 8 2 d 10 211 Hz 21
S
D
21
(23)
where the energy flux has been replaced by the monochromatic power, via FE 5 k n21 Pnu with n 5 1.4 GHz. Eq. (23) predicts a linear relationship between [OIII] luminosity and radio power (for a constant kn ). These parameters are plotted in Fig. 4 and one can see that the CSS sources fit this relation for k1.4 ¯ 10 210.5 . This value is higher than what is normally assumed or derived for radio galaxies on the tens of kpc scale (k1.4 | 10 212 –10 211 ), but the difference may be attributed to the larger magnetic field in the smaller CSS sources. Recent HST imaging of CSS sources (de Vries et
al., 1999) confirms this general picture with some important differences. De Vries et al. found evidence for optical line emission aligned with the radio source in a sample of CSS radio galaxies. However, most of the emission appears to be in the wake of the radio plasma rather than from a luminous bow shock. This would be the case if the leading part of the bowshock is so fast it is non-radiative. The dominant optical line emission would then originate from the slower shocks at the sides of the lobes. Indeed, de Vries et al. have argued for bow-shock velocities | a few thousand km s 21 using a similar argument.
3.3. The relationship between turnover frequency and size The anticorrelation between turnover frequency and size (Fanti et al., 1990; Stanghellini et al., 1996a; O’Dea and Baum, 1997) has been the subject of several investigations based upon quite different models. Snellen (these proceedings) has presented a model based upon synchrotron self-absorption of the various components. In the BDO free–free absorption model, the decrease of ambient density with distance from the core of the ionized gas is offered as an explanation for the anticorrelation. In the model investigated by Kuncic et al. (1998), the absorption is due to induced Compton scattering. This process scatters high brightness temperature photons to low energies where they are absorbed and is relevant when the brightness temperature, T b of the source and the Thomson optical depth, tT of the scattering screen satisfy kT b ]] t |1 me c 2 T
(24)
that is, when
S D
Tb tT | 0.59 ]] 10 10
21
(25)
The brightness temperature of a typical nonthermal source increases rapidly towards low frequency so that there is always some frequency at which the process can become important (provided that free– free absorption or self-absorption has not already been established). In this model the anticorrelation
G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
373
Fig. 4. [OIII] luminosity as a function of 1.4 GHz radio power for values of log k1.4 5 2 10, 2 11, 2 12, 2 13 and 214 overlaid on data for radio-loud objects and Seyfert galaxies. Data are from Gelderman and Whittle (1996) (GW), Tadhunter et al. (1993) and Morganti et al. (1993) (collectively referred to as TM) and Whittle (1985) (W85). Legend: Filled circles—CSS sources from GW; filled squares—CSS sources from TM; open circles—GW FR II radio galaxies; open squares—TM FR II radio galaxies; diagonal crosses—GW QSOs; plus signs: TM compact flat spectrum sources; open triangles: TM FR I radio galaxies; filled hexagons: Seyfert galaxies from W85. Upper limits are indicated in the usual way.
with source size is the result of the Thomson depth of the ionized layer surrounding the source decreasing with source size due to the decreasing ambient density. A point in favor of the Kuncic et al. model is that the low frequency spectrum of GPS and CSS sources is strongly concentrated at a 5 2 1 (Fn ~ n 2 a ) as predicted by Coppi et al. (1993) for ICS. For the free–free absorption model, one requires a power-law distribution of optical depths (due to a spectrum of cloud sizes?); for the synchrotron self absorption model one requires a distribution of optical depths in the various self-absorbed components. Both free–free absorption and induced Compton scattering are possible if the bow shock is
non-radiative since there still remains a zone of shock-ionized gas surrounding the source. In this case, a substantial photoionized precursor would not be present and most of the absorption would take place in the shocked gas. This is not a significant problem since one expects that this will approximately only halve the optical depth, compared to the radiative models. An interesting feature of the Kuncic et al. model is that the fits to the turnover frequency-size relation tends to push the shock velocities and ambient densities into the non-radiative regime. Clearly, in view of the de Vries images and the implied densities and velocities, this model needs to be revisited.
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4. Radio quiet galaxies
4.1. Radio emission from Seyfert galaxies In many cases, Seyfert galaxies exhibit similar structures to radio galaxies, i.e. jets and lobes, albeit at powers over a thousand times lower. It is only recently, however, that workers have begun to explore the connections and distinctions between the two types of galaxies. Such work is potentially informative, since it can help to delineate the physics of both radio loud and radio quiet galaxies. The work which I am about to describe began as an attempt to see how much of the emission from the narrow-line region of Seyfert galaxies could plausibly be explained in terms of radiative shocks. As we shall see, the investigation has potentially wider ramifications. The starting point of this investigation was the correlation between [OIII] luminosity and radio power for Seyfert galaxies in Fig. 4. The correlation for these galaxies is similar to that for radio galaxies but the correlation is displaced three orders of magnitude to the left in radio power. This correlation has been known in one form or another for some time (see deBruyn and Wilson, 1978; Whittle, 1985), although some workers are looking at samples of radio sources which are more complete with a view to determining whether the ‘gap’ between the separate correlations can be filled in. For now we shall assume that the apparently bimodal distribution in radio power is real and that the Seyfert correlation represents a real physical link between their radio and optical properties. There are other good reasons for suspecting such a link, for example: • Where observations are made at high enough resolution, detailed correspondences between radio and optical features are often found, along with evidence of dynamical structure and sources of local ionization indicative of shocks (Whittle et al., 1988; Goodrich, 1992; Capetti et al., 1996). • In the specific case of NGC 1068 Capetti et al. (1997) have shown, using HST / WFPC2 [OIII] and Ha 1[NII] images overlaid on a VLA radio image of the radio source, that there is a close correspondence between the radio and optical structure.
• The radio axes of Seyferts correspond remarkably to the axes of their ionization cones, again suggesting that the radio and optical emission are causally related (Wilson and Tsvetanov, 1994). An argument against a strong physical link between radio activity and optical emission lines in Seyferts has been the inferred energy flux in the jets. Using the GPS model as a guide a median [OIII] luminosity | 10 42 ergs s 21 requires a jet energy flux | 10 44 ergs s 21 . Given the standard ‘conversion factor’, k1.4 5 P1.4 /FE | 10 212 –10 211 Hz 21 between radio power and jet energy flux, the required energy flux is difficult to understand given the radio powers of Seyferts. Typically P1.4 | 10 23 W Hz 21 so that the inferred jet energy flux would be a puny 10 41 ergs s 21 —about a factor of 10 3 too low. A proposed resolution to this problem comes from a re-examination of Eq. (13) for kn , viz. Pn kn 5 ] FE 5 C1 (a)sg0 m e c 2d a 22 B (a11) / 2 f fe fad t g n 2(a21 ) / 2 (26) What are the factors that could reduce kn in the case of a Seyfert galaxy. For a start, the dynamical ages 6 | 10 yr are generally much less than that of a radio galaxy. However, this is counterbalanced to some extent by the generally higher minimum energy 24 magnetic fields ( | 10 G) in Seyfert lobes. The obvious remaining parameter is the electron / positron fraction fe . In radio galaxies and quasars, we usually (either implicitly or explicitly) take this to be of order unity. If Seyfert jets really are much more powerful than has been assumed, and kn is correspondingly much less, then we generally have no choice other than to assume that fe | 0.01. That is, Seyfert jets contain a much larger fraction of thermal plasma and the radio emission is merely a tracer of the underlying flow. There are several important consequences of this.
4.2. Jet velocities In NGC 1068 high resolution VLA and HST
G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
studies make a good case for a jet-cloud impact between the northern jet and a cloud in the NLR (Gallimore et al., 1996a,b). The emission-line flux from the cloud provides a useful diagnostic for the jet velocity. This is based on the required jet momentum flux (force) required to drive a radiative shock of the required velocity into the cloud. Here is it is useful to distinguish between momentum-driven and energy driven shocks. The radiative shock resulting from the impact of a jet on a cloud is momentum driven, when the jet is much lighter than the cloud. Only a small fraction | ( rjet /rcl )1 / 2 of the jet energy flux is transmitted to the cloud, the rest being advected with the jet. On the other hand, in the GPS / CSO model considered earlier, the jet driven lobe expansion is energy driven, similar to the way in which the expansion of an interstellar bubble is energy driven; the effect of the lobe on the interstellar medium is therefore dominated by the jet energy flux. Another important point is that for a given energy flux, relativistic jets are poor transporters of momentum. The momentum fluxes of relativistic and nonrelativistic jets are given by 1 Momentum flux 5 ] 3 Energy flux c 2 Momentum flux 5 ] 3 Energy flux vjet
(27)
respectively. Hence if a large jet force is required to drive a radiative shock into a dense cloud, and if the jet energy flux is constrained by other considerations (in this case, the total luminosity of the NLR), then the lower the jet velocity the easier it is to satisfy the momentum constraint. When a jet hits a cloud, an oblique shock (or series of oblique shocks) is produced which deflect the jet and create a region of high pressure adjacent to the cloud (see Fig. 5). It is this high pressure region which is responsible for driving a shock into the cloud and if the latter is dense enough, this shock will be radiative. The jet velocity as a function of the pressure Psh in the shocked region is given by 2FE vjet ¯ ]] 3 f psh A sh
375
fraction of jet momentum absorbed by the cloud 4 . A simple analysis of the interaction based upon analysis of the Rankine Hugoniot equations gives f | 0.4– 0.8 depending upon the angle of incidence. It would be interesting to estimate f from numerical simulations which reveal a more complicated situation than that depicted in Fig. 5. The driving pressure is related to the shock velocity by: 2 2 psh ¯ rcl v sh ¯ 1.4n H,cl m p v sh
(29)
and the Ha luminosity provides a further constraint on the parameters of interest via the MAPPINGS derived relation between density and velocity, viz.: L(Ha ) ¯ 5.3 3 10
23
vsh n H,cl A sh ]]]] 1000 km s 21
S
2.4
(30) Combining all of these relations gives the following estimate of the jet velocity: vjet FE,44 0.4 ] ¯ 0.15 f ]]] v sh,8 c L40 (Ha )
(31)
The FWHM | 350–600 km s 21 of those NLR velocities in NGC 1068 which can be attributed to shocks (Dietrich and Wagner, 1998) gives us a good idea of the shock velocity, say 500 km s 21 ; moreover the estimate of jet velocity is insensitive to the actual shock velocity. The estimate of the velocity of the jet is therefore given by: vjet ] | 0.03–0.06 c
(32)
for f | 0.4–0.8 and L(Ha ) ¯ 1.4 3 10 40 ergs s 21 . The inverse dependence of jet velocity on Ha luminosity reflects the inverse dependence of momentum flux on velocity for a given energy flux. This analysis shows that at the site of cloud C 5 approximately 27 pc from the core, the jet velocity is decidedly non-relativistic, underlining a significant difference between jets in Seyferts and radio galaxies.
(28)
where A sh is the area of cloud affected and f is the
D
4 5
See Bicknell et al. (1998) for details. In the notation of Gallimore et al.
G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
376
Fig. 5. Schematic of a jet-cloud interaction leading to an oblique shock in the jet and a radiative shock driven into the cloud. The former is responsible for the radio emission from a jet ‘knot’; the latter is responsible for the line emission from the cloud.
4.3. The mass flux
ment has occurred into the jet. The initial velocity ~ init , then is given by for an initial mass flux, M
The mass flux in the jet is interesting 2F 2 ~ jet 5 ]]E M vjet
F
3 1 1 ]] M 2jet
vjet 5 1.4 ]] 0.05c
S
D
S D
vinit 2FE ]] ¯ ]] ~ init c M
G
22
FE,44
F
1/2
S
~ init M 1/2 ¯ 0.27F E,44 ]]]] 0.05 M ( yr 21
G
3 1 1 ]] M ( yr 21 M 2jet (33)
This is much higher than what is required to fuel the black hole (|0.05 M ( yr 21 ) and indicates that either the jet represents an outflow from the black hole environs which has a mass flux greater than the accretion flow or more likely, that significant entrain-
D
21 / 2
(34)
This velocity is only mildly relativistic unless the jet mass flux is about 15 times less than the accretion mass flux.
4.4. Relationship to accretion disk coronae There is an interesting relationship between the above jet physics and the properties of accretion disk
G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
coronae. It is highly likely that the X-ray emission from a Seyfert nucleus comes from an accretion disk corona rather than the cold accretion disk itself (Haardt et al., 1994, 1997; Johnson et al., 1997). The Johnson et al. observations indicate that these coronae have Thomson optical depths tc | 1, and temperatures, T c | 100 keV). The optical depth of the corona, combined with its scale height,
S DS D
2kT c h c 5 r g ]]2 mmpc
r ] rg
where r g 5 2GM /c is the gravitational radius of the black hole, allow us to estimate the electron density of the corona through n e,c ¯ tc (sT h c )21 . Suppose then that the corona is at the base of the jet. Then we can estimate a mass flux,
S D S D S D
plasmas moving with Lorentz factors of up to 10 or more. If this comparison is valid, then it argues for a quite different origin for radio galaxy jets—possibly as indicated by Blandford and Znajek (1977) and Meier (1999) and discussed by David Meier in these proceedings.
4.5. Observational support for thermally loaded jets in Seyferts
(35)
2
bjet 21 / 2 ~ init ¯ 0.04CM7 T c,9 ] M 0.1 r outer 1 / 2 n ` ]] ] M ( yr 21 10r g n e,c
377
(36)
where C is the covering factor of the corona, 10 7 M7 M ( is the mass of the black hole, bjet is the jet v /c in the asymptotic regime, r outer is the outer radius of the jet base and n ` is the electron density in the asymptotic regime. It is not difficult to see that, for an initially mildly relativistic jet and with other typical parameters, the initial mass flux would be order or slightly less than the mass accretion rate in NGC 1068 and other similar Seyferts. The upshot of this is that jet flows from Seyferts could begin as winds originating from the inner 10 gravitational radii or so of the accretion disc. Since the coronal sound speed, ¯ 0.012T 1c,9/ 2 c is much less than the escape speed ¯ 0.45(10r g /r)1 / 2 , it is likely that such a wind is magnetically driven. These winds may be collimated further out by the action of pressure gradients, to form a jet. Such a scenario would also explain why Seyfert jets are thermally dominated; radio emission could simply result from the action of internal jet shocks, which accelerate electrons to radio emitting energies, either from the mildly relativistic coronal plasma or from thermal plasma entrained into the jet from the interstellar medium. This invites comparison with jets in radio galaxies and quasars which are widely (but perhaps not universally) believed to be electron / positron
The above combination of theory and interpretation has some significant support in recent observations: • Wilson and Raymond (1999) have detected X-ray emission (presumably from the NLRs) in a sample of Seyfert 2 galaxies. The level of X-ray emission is consistent with emission from shocks with velocities | 200–500 km s 21 at a level which is consistent with the [OIII] emission. • VLBI observations of proper motion in Seyferts (e.g. Ulvestad et al., 1999) show low velocity ( , 0.1c) proper motions of the knots. Whilst knot velocities represent pattern speeds, presumably of internal jet shocks, it would be surprising if at least some of the measured speeds (or limits thereof) are not representative of jet speeds. The absence of any superluminal speeds, or even speeds in excess of 0.5c is therefore strong evidence that the speeds in these jets are in fact, low.
5. Concluding remarks The gains that have been made in understanding the many facets of Radio Galaxies over the last fifteen years or so, place us in a position where accelerating success in understanding the real physical nature of these objects is apparent. Once, we regarded the Fanaroff–Riley division as a convenient descriptive classification for Radio Galaxies. Now, we are aware that the physics of this division is fundamentally important to the way in which relativistic jets are produced in the environment of black holes and how this relates to the evolution of radio galaxies. We certainly do not have comprehensive answers to questions concerning the FR classifi-
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G.V. Bicknell / New Astronomy Reviews 46 (2002) 365 – 379
cation at the present time. However, this aspect of Radio Galaxies will clearly receive even more observational and theoretical attention in the ensuing years. Just as fundamental is the nature of GPS and CSS sources and the as yet not-well-understood way in which they fit in to the evolution of the overall radio-loud population. Seyfert galaxies, until recently a fairly neglected population as far as radio astronomers are concerned, also give us important clues to many of the fundamental questions relating to radio galaxies—principally jet formation and the interaction between jet and accretion disc Physics. If the ideas presented here relating to Seyfert galaxies are correct, then we have the interesting problem of why 10 7 M ( black holes produce slow, predominantly thermal jets and why 10 8 –10 9 M ( black holes produce relativistic electron / positron jets. Perhaps the answer lies with the magnetic switch mechanism which David Meier proposed to distinguish between FR I and FR II radio galaxies. One thing that was apparent in this meeting was the way in which many people are confronting the complex physics of radio galaxies from many different points of view and how rapid progress has become. I would therefore like to thank the organizers for organizing such a stimulating and productive workshop and for organizing financial support from the Space Telescope Science Institute. I would also like to acknowledge the contributions of my colleagues, specifically Mike Dopita, Chris O’Dea, Ralph Sutherland and Zlatko Tsvetanov, to the research on emission line production in AGN, summarised in this paper and their contributions, as well as those of Anton Koekemoer, to many useful discussions on this topic.
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