Astron. Astrophys. 337, 69-79 (1998)

5. Discussion

5.1. Hotspot advance speeds and source age

The fact that the A2 and C2 gaussian components are compact and lie at the leading edges of the minilobe emission regions strongly argues that they should be interpreted as hotspots where two oppositely directed jets terminate (see Fig. 1a,b). In Sect. 4.2 we considered the relative separation rates of the different components of 0710+439, and found the highest significance detection to be that of the apparent separation rate of A2-C2 at . Since CSOs are dominated by unbeamed emission we expect for a sample selected on total flux density that the angle between the jet axis and the sky plane is about . Such an orientation for 0710+439 is compatible with the hotspots appearing at the extreme ends of the radio emission and not superimposed on the diffuse minilobe, and is also consistent with a hotspot-core arm-length ratio which is close to one (Readhead et al 1996c). Given such an orientation we expect that the average of the two hotspot advance speeds through the external medium should be only slightly larger than that estimated from the observed separation rate (i.e. approximately ).

Of prime astrophysical importance is the estimated age of 0710+439. A simple estimate based on dividing the overall projected size of 0710+439 by the measured projected hotspot separation rate gives yrs, implying that 0710+439 is a very young radio source. In assessing the reliability of this estimate we must be aware that what have actually measured (see Sect. 4.2) is the instantaneous rate of separation of the two hotspots at the present epoch; not directly the mean rate of increase of size of the whole source. Since hotspots are nearly always observed, as in 0710+439, to lie close to the ends of the lobes in which they are embedded the mean expansion speed of the whole source must equal the mean separation rate of the hotspots. However there are several mechanisms which would cause the instantaneous hotspot advance speeds to vary about their mean values. Variations in the external density due to encounters with clouds is one obvious mechanism. Another possibility is the so-called 'dentist's drill' phenomena (Scheuer 1982) in which the position of hotspot's working surface moves around either due to jet precession initiated at the central engine or hydrodynamic instabilities acting on the incoming jet. In this model the hotspot executes a corkscrew like-path in space and the mean rate of advance is significantly smaller than the total instantaneous speed of the hotspot. Related effects show up in recent three-dimensional numerical jet simulations (Norman 1996). These simulations also show variations in hotspot pressures and hence advance speed due to the effects of vortex shedding and cocoon turbulence acting on the incoming jet which in turn effect the jet collimation and the area over which the thrust of the jet is deposited. Due to such effects the simulations predict that instantaneous forward hotspot advance speeds (i.e. in the direction of the jet axis) can vary by factors of order two (Norman 1996).

Whatever the physical mechanism that is acting there is empirical evidence that in 0710+439 instantaneous and mean hotspot speeds are different. In 0710+439 as in other CSOs the distances from the two hotspots to the core are very similar, i.e. the ratio of these distances (the `arm length ratio') is only 0.95 (Readhead et al. 1996c) which implies the mean advance speeds of the two hotspots have been the same averaged over the history of the source. In contrast as discussed in Sect 4.4. it is probable that the present instantaneous advance speeds for A2 and C2 are different from each other. Below we discuss which of the possible mechanisms is operating in 0710+439 and its impact on our age estimate.

The simplest explanation for the instantaneous speed variations is that C2 is presently interacting with a dense cloud while A2 advances rapidly through an intercloud medium. If around 100 such clouds have been encountered by each hotspot there would be enough cloud encounters to explain why the arm length ratio is close to unity, yet few enough to explain the constant velocity of A2 over 13 years. If cloud collisions were the reason for hotspot speed variations then our best estimate for the source age would depend inversely on the fraction of time, f , the hotspots spent transversing the intercloud medium. We can argue that since we apparently detect such an advance in the first CSO for which we have more than a decade of monitoring f is unlikely to be less than 0.1, and so we obtain an upper age limit of 11 000 yrs. Arguing against such a cloud mechanism operating is the expectation that if C2 were embedded within a dense cloud one might reasonably expect its pressure to increase in response to the higher density, in fact we observe that the pressure in C2 is less than in A2. In addition we believe it is unlikely (although still possible) that the 'dentist's drill' effect is a significant cause of the apparent speed variations since as we discuss in Sect 4.1. the change in the apparent A2-C2 vector is mainly in its length and not its orientation. Except for certain unlikely orientations of the source and its hotspots in space one would expect hotspots effected by the dentist drill phenomena to show significant side-to-side motions.

Our favoured explanation for hotspot speed differences in 0710+439 is that these are simply related to differences in pressures of the hotspots and hence in the corresponding ram pressure velocities through a smooth external medium. Such pressure variations and resulting speed variations are as we have noted predicted by recent three-dimensional numerical simulations (Norman 1996). Assuming that A2 is close to its equipartition pressure (supported by the analysis of the frequency of its Synchrotron Self Absorbed turnover, Conway et al. 1992) and that the source is orientated not too far from the sky plane then ram pressure arguments imply an external density of 1.83 cm^-3. This value is similar to that estimated in the CSO 2352+495 (3 - 10 cm^-3, Readhead et al. 1996a) and is consistent with what is expected for the NLR intercloud medium. The data are consistent with C2 having the same external density as A2 and a lower advance speed simply as a consequence of its lower pressure. Since the equipartition pressure of C2 is 0.3 of A2, the expected advance speed for the same external density is 0.55 of A2, given the A2-C2 separation rate this implies a C2 advance speed of , which is within of the observed B2-C2 separation rate of . If hotspot pressure variations are the cause of the hotspot speed variations then the observed differences in pressure between the two hotspots within individual CSOs of between 4 and 6 (see Readhead et al 1996b) imply, assuming the same external densities around each hotspot, that hotspot speed variations vary over a factor of about two within each source. We therefore expect ratios between instantaneous and mean separation rates to be of the same order and hence estimate an upper limit to the age of 0710+439 of approximately 3000yrs.

Given our age estimates and estimates of the jet thrust (Readhead et al. 1996a) we can compare the mechanical luminosity required to drive the hot spots forward with the radio luminosity and jet power. For an age of 1100yrs the combined mechanical luminosity of the two hotspots is erg s^-1, while the radio luminosity of the two hotspots is about erg s^-1. Following the arguments used in Readhead et al. (1996a) from the measured hotspot sizes and pressures the upper limit on the total power supplied by the jets is erg s^-1. A lower limit on the total jet power can be obtained by adding together the radio power and mechanical work. The total jet luminosity is (for h=0.6) therefore in the range erg s^-1 to erg s^-1 and the efficiency of conversion of jet energy to radio emission is between 8% and 31%. In contrast for classical FRII (Fanaroff & Riley 1974) radio galaxies we estimate upper limits on hotspot radiative efficiencies of a few percent by comparing total radio luminosities to estimates of the jet luminosities given by Rawlings & Sanders (1991).

5.2. Implications for CSO models

Our best estimate for the mean hotspot advance speed in 0710+439, given our observations, i.e , is somewhat larger than that estimated by other authors for the CSO population in general (e.g. Readhead et al. 1996b estimates ). If hotspot pressures and hence advance speeds vary with time it might be that the true mean advance speeds in 0710+439 are up to a factor of two less than our best estimate (see Sect. 5.1) but a difference between predictions and observations still remains. One possibility, given that one would expect a range in properties from CSO to CSO, is that 0710+439 lies at the extreme end of the population and is growing faster than the typical CSO. However, Conway et al. (1994) tentatively detected, based on two global 5 GHz epochs, mean hotspot advance velocities of in another CSO, 0108+388. A similar rate of advance was also detected by Taylor et al (1996) in the same source. Recently a mean hotspot advance speed of has been confirmed in 0108+388 by three epoch global 5 GHz observations (Owsianik et al. 1998). Conway et al. (1994) also detected a hotspot advance speed of 0.065 in the object 2021+614 which may also be a CSO. Finally for the CSO 2352+495 Readhead et al. (1996a) gives age estimates of 1200 - 1800 yrs based on synchrotron ageing and 1500 - 7500 yrs from energy supply arguments. For this source of size 120pc an age near the lower end of the allowed range, i.e. 1500 yrs gives a mean hotspot advance speed of .

The lower estimate of hotspot advance speeds for the CSO population in general () made by Readhead et al. (1996a) was based on a two part argument, namely: i) it was argued that hotspot pressures adjusted to the external density so that hotspot advance speeds are constant. Therefore advance speeds of high pressure hotspots in young sources transversing the dense ISM are the same as in the classical double sources; ii) Classical double sources, based primarily on observations of Cygnus A, have advance speeds of .

The first part of the above argument was based on detailed observations of three CSOs, in which the arm-length ratios are close to one and therefore the mean advance speeds for the two hotspots must be the same, despite in each case the pressures of the two hotspots being quite different. Readhead et al. (1996b) explicitly assumed that the characteristics of the hotspots are constant in time and that the pressure ratios measured now are typical of the whole history of these sources. It follows that hotspot advance speeds must be independent of hotspot pressure. It was postulated that this could be achieved if a mechanism existed where the hotspot pressure always adjusted to the external density so that ram pressure balance gave a constant advance speed.

In contrast 3-D numerical simulations (Norman 1996) indicate that due to hydrodynamic effects individual hotspots can rapidly vary their pressures around some mean value as they move outward, with corresponding variations in their ram-pressure advance speeds. Differences in pressures between hotspots seen in maps may therefore be just temporary features of sources. Arm length ratios close to one are simply explained if external densities and mean hotspot pressures on each side of the source are the same, so that mean advance speeds are the same. It follows that no special mechanism is required which adjusts hotspot pressure to external density in order to explain the observations. The main motivation which led Readhead et al. (1996b) to propose a universal constant hotspot advance speed for both CSOs and classical sources is therefore removed.

In contrast to Readhead et al.'s (1996b) observational approach Begelman (1996) has calculated the evolution expected for a simple theoretical model of a source with an over-pressurised cocoon and a hotspot whose mean pressure is a fixed ratio to that of the cocoon. In this model the advance speed depends on the density versus distance of the external medium , such that the advance speed where l is the source size and . For n in the plausible range 1.5 to 2.0, then is in the range -0.17 to 0.0. It is therefore possible that hotspot advance speeds in CSOs are somewhat faster than in classical sources. Since CSOs are 1000 times smaller than classical sources if n were 1.5, we expect advance speeds which are about 3 times faster.

Readhead et al. (1996a) estimated advance speeds in classical sources to be , mainly based on Cygnus A results. However it appears that Cygnus A is an unusual source in that it lies in an unusually dense environment (Barthel & Arnaud 1996, Reynolds & Fabian 1996). In other FRII's external densities are estimated to be 30 times smaller (Rawlings & Saunders 1991) yet hotspot pressures are only 3 times smaller (Readhead et al. 1996b), implying that typical ram pressure advance speeds in classical sources might be closer to . Hotspot advance speeds can also be estimated independently from electron spectral ageing arguments and from arm-length asymmetries in classical double sources. Using the first method the data of Rawlings & Saunders (1991) indicate advance speeds of ; other studies indicate velocities which are greater than (e.g. Liu et al. 1992). Such estimates might however be larger then the real advance speeds since strictly speaking they measure the sum of the advance speed of the hotspot and the speed of the backflow from it (see Liu et. al. 1992 and Scheuer 1995). This would be consistent with the fact that for the same sample of sources observations of jet/counter-jet side arm length ratios indicate (Scheuer 1995) smaller advance speeds of . The present data on hotspot advance speeds does not yet yield a define conclusion but certainly allows the possibility that these speeds could be a factor of three larger than estimated by Readhead et al. (1996a).

Combining a typical FRII advance speed of say with the probable weak evolution of hotspot advance speeds with source size we find that mean hotspot advance speeds in CSOs can plausibly be or larger. We conclude that the size of the measured hotspot speed in 0710+439 is compatible with the predictions of theoretical models. Such fast speeds imply that sources have only a short lifetime in the CSO phase. The fact that up to 10% of sources in flux limited samples at 5 GHz are CSOs therefore means either that i) not all CSOs evolve into classical sources; some exhaust their fuel before reaching 100kpc size (Readhead et al. 1994) or ii) there is strong luminosity evolution in their radio emission. We favour the second explanation, strong luminosity evolution of the required amount to explain the source size distribution is in fact predicted by the theoretical models. For instance the Begelman (1996) model predicts a radio luminosity proportional to approximately assuming a constant jet mechanical power. For the weakly evolving hotspot advance velocity predicted for an external density of the form , the predicted number of sources in each decade of size then exactly matches the observations (Begelman 1996). As first noted by Readhead et al. (1996a) for 2352+495, and as we find for 0710+439 (see Sect. 5.1), the limits on the radiative efficiency for CSOs compared to classical sources empirically demonstrate that the expected luminosity evolution does in fact occur and with a magnitude (a factor of 30 from CSO to classical sources) consistent with that expected by theory. Given this efficiency evolution one would expect 0710+439 to evolve into a source of radio luminosity W Hz^-1, i.e. a weak FRII. We conclude that CSOs are probably very young extragalactic radio sources and that furthermore they probably evolve into lower luminosity FRII classical double radio sources.

© European Southern Observatory (ESO) 1998

Online publication: August 6, 1998
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