Jet-envelopes in rotating Seyfert galaxies

W. Steffen^1,2, A. Lim³

¹Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK
²Instituto de Astronomía y Meteorología, Universidad de Guadalajara, Av. Vallarta 2602, 44130 Guadalajara, Jal., Mexico
³University College, Gower Street, London WC1E 6BT, GB

Abstract:

We present hydrodynamic simulations in three dimensions of the non-adiabatic interaction of a nuclear jet with a rotating narrow-line region (NLR) in a Seyfert galaxy. We find that this scenario reproduces the main features of some lobe-like NLRs which otherwise are difficult to explain. It does also reproduces the important structural radio and optical features of NLRs which show point-symmetry, which may be attributed to the rotation of the galaxy. We present a direct comparison of simulated optical and radio images obtained with HST and radio-interferometry, respectively.

Presentamos simulaciones hidrodinámicas no-adiabáticas de la interacción de un jet nuclear con la zona de li'ineas angostas (narrow-line region, NLR) en galaxias tipo Seyfert. Encontramos que este modelo reproduce las principales características de algunos NLR del tipo lóbulos que de otra manera son difíciles de explicar. Los cálculos también reproducen características radio-ópticas importantes de NLRs que muestran simetría puntual que puede atribuirse a la rotación de la galaxia. Presentamos comparaciones directas entre imágenes simuladas y observadas en longitudes de onda ópticas y de radio.

Introduction

The narrow-line regions (NLR) in Seyfert galaxies with jets emanating from their active nucleus in most cases show evidence for strong interaction between the NLR-gas and the radio-emitting jet plasma. The radio-optical structure of most NLRs can be separated into two different classes: jet-like and lobe-like morphologies. In the jet-like NLRs, the optical emission is concentrated along a strongly elongated centre-brightened structure. In this type of NLR the radio emission is usually directly superimposed on the optical emission. Observations of lobe-like NLRs, in contrast, show a few filaments of optical emission surrounding a ``hot-spot'' radio component on either side of the centre of the galaxy.

Steffen et al.(1997a,b) have presented hydrodynamical models of the lobe-like and the jet-like NLRs. In the first case an adiabatic jet produces a bow-shock in a uniform ambient medium, which cools and forms a roughly cylindrical optically observable shell around the jet. However, there are lobe-like cases which appear to emit only in the curved bow-shock region and not significantly in the cylindrical shell around the jet (e.g. Mrk 573, Falcke et al. 1998; NGC 3393, Malkan et al.1998, see Figure 1 ).

This requires additional effects. As we show in this paper, a rotating ISM interacting with the jet can reproduce this structure.

Both, the lobe-like and the jet-like NLRs, in some cases show evidence for point-symmetry (e.g. Mkn3, Capetti et al.1996, Kukula et al.1999; IRAS0421+0400, Holloway et al.1996, Steffen et al.1996). The point-symmetry affects both the radio and the optical structure. There are two simple mechanisms which can produce this kind of symmetric distortions. They are 1) propagation of the plasma outflow at an inclined angle to the density gradient in a stratified ISM and 2) a side-wind due to the rotation of the galaxy could bend the jet and/or distort the zone of interaction. However, in a spiral Seyfert galaxy the oblique propagation of a jet through the stratified ISM will always be combined with a side-wind due to the rotation of the galaxy. In this paper we concentrate on the model which considers only the distortion caused by a side-wind produced by the rotating ISM.

The problem of a collimated jet propagating through an interstellar medium which is rotating around the source of the jet can not be dealt with in a two-dimensional description. In this paper we apply a new three-dimensional adaptive grid code (Reefa) to this problem. The new hydrodynamical code prior to inclusion of the adaptive grid has been described in Lim & Raga (1998). In terms of the astrophysical situation the simulations presented in this paper differ from previous calculations in three ways. First, the ambient medium is assumed to rotate according to a solid body, i.e. the wind-velocity is not uniform. Second, the cooling time of the shocked ambient medium is small compared to the cooling time-scale of the propagating jet. Third, the cooling time of jet itself is large compared to the dynamical timescale. The assumption of solid body rotation is appropriate for most NLRs, since their size is usually smaller than 1 kpc.

   
The path of the jet

Due to the side wind the path of the jet is going to be altered. The resulting shape of the jet for the case of a uniform side wind has been calculated in the past by Begelman, Rees and Blandford (1979) and Cantó and Raga (1995) for adiabatic and isothermal jets, respectively. Wilson and Ulvestad (1982) and Steffen, Holloway and Pedlar (1996) have numerically investigated the bending of adiabatic jets in Seyfert galaxies under the influence of the side wind produced by the ISM with more complex velocity structures corresponding to the rotation curves of spiral galaxies. In this section we derive an approximate analytical expression for the path of the jet in a side wind with a velocity increasing linearly with distance. The density of the ISM is assumed to be uniform.

Cantó and Raga find that in the region near the stagnation point the path of an adiabatic and an isothermal jet are identical. In our case the stagnation point is at the base of the jet, since here the wind is perpendicular to the flow direction of the jet. Hence, we may directly consider the slightly simpler isothermal case, even though the jet itself is likely to behave adiabatically.

Following Cantó and Raga, from the pressure balance of the side wind and the jet it is found that

$$\rho_{\rm a}v_{\rm a}(y)^2 \cos^2\phi = \frac{\dot{M}_{\rm j}v_{\rm j}^3}{\pi {\rm c}^2} \kappa^2,$$ (1)

where $\dot{M}_{\rm j}$ and $v_{\rm j}$ are the mass-loss rate and the velocity of the jet, respectively. The density and velocity of the ISM are given by $\rho_{\rm a}$ and $v_{\rm a}(y)$, respectively, while $\phi$ designates the angle between the direction of the jet at distance z from the centre of the galaxy.

For the conditions of our problem we find

$$\frac{{\rm d}z}{{\rm d}y} = {\rm tan}\left[\frac{y^2}{2\lambda_0 y_0}\right].$$ (2)

where $\lambda_0^2$ and y₀ are constants. An approximate analytical expression for the shape of the jet near the origin can be found by integration of the series expansion of the tan-function in that region. The result is

$$z(y) = \frac{y^3}{6\lambda_0 y_0}$$ (3)

This is a parabola of one degree higher than that obtained from a uniform side wind. Hence, as was to be expected, initially the bending is rather weak, but at larger distances it is stronger than in the case of a wind with constant velocity.

   
The hydrodynamic simulation

The inviscid Euler equations are solved on a binary adaptive 3D-grid using the Flux-Vector Splitting method due to van Leer (1982), with the mass density conservation equation written separately for each of the ionic and neutral components. The radiative energy loss is computed with the prescription described by Biro et al. (1995). The collisional ionisation of Hydrogen by electron impact is included with the rate coefficients of Cox (1970) and recombination with the interpolation formulae of Seaton (1969). We solve the equations on a grid with maximum resolution of $65\times257\times257$ points (physical size: $0.65\times10^{20}$cm, $2.57\times10^{20}$cm, $2.57\times10^{20}$cm) in the x, y and z directions, respectively.

The jet has an initial radius $r_j={5.3\times 10^{18}}$ cm, density n_j=0.8 cm^-3, temperature T_j=10⁴ K and velocity v_j=3000 km s^-1 (parallel to the z-axis). The undisturbed environment has a density n_e=1.8 cm^-3, temperature T_e=10⁴ K. In order to simulate the jet moving out into the solid-body rotation field of a galaxy, The environment has a linear velocity increase in the z-direction given by the equation:

$${v_{y}(z)}=v_{y}(z_{max}).{z\over{z_{max}}}.$$

The quantity v_y(z_max)=200 km s^-1 is the sidewind velocity at the top (z=z_max) face of the grid, the sidewind velocity vector runs perpendicular to the jet ejection velocity in the direction of increasing y.

   
Results

The effect of the rotation of the interstellar medium on the jet is significant and to some degree not as immediately expected.

Firstly, some expected results are that the cocoon of the jets bends in the downstream direction of the sidewind. The density of the cooling envelope is higher on the upstream side, since the relative speed of the expanding shock within the ISM is increased on the upstream side and decreased on the downstream side. The highest optical emission from the cold envelope is therefore found on the upstream side of the jet.

The shape of the bent jet is however not as expected and does not follow the path calculated in Section 2. The reason is that the jet itself is protected from the effect of ram pressure exerted by the moving ISM, since it is embedded in the hot cocoon. It is the cooling envelope which 'feels' the ram pressure. Since the pressure within the hot cocoon is comparably uniform, the jet is not significantly bent until it hits the dense envelope and is reflected from it. This does not produce the continuous curvature expected from the ram pressure, rather than a localised kink. The difference in curvature between the jet and the envelope will be significant as long as the width of the envelope is comparable to its length. As soon as the radius of the envelope is very small compared to its length the angle of reflection of the jet as it makes contact with the envelope will become smaller and smaller, such that the jet basically follows the envelope.

This result leads to the following possible conclusions concerning the jets in Seyfert galaxies which are bent by the rotating ISM. Firstly, those galaxies which show smoothly bending jets with a directly superimposed optical envelope might have radii much smaller than the 1.8 pc used in our simulations. Secondly, others with jets bending suddenly at nearby optical clouds, have been interpreted as jets reflected at preexisting clouds. However, as shown with our simulations, such a ``cloud'' could actually be the result of the interaction of the jet with the interstellar medium. A prominent possible example is the bending of the jet in NGC 1068 at an optical knot.

The consequences of this reflection are quite dramatic. Firstly, the reflection is associated with a strong shock in the jet, which produces significant radio emission. Secondly, as the jet-cocoon structure propagates further with significantly modified direction, a bulge in the cold envelope is produced at the position of the reflection. Here the density of the envelope is higher than anywhere else and hence the emission, too. Consequently, a radio knot is directly associated with enhanced optical emission in such a region. However, the detailed appearance, whether the optical emission appears as a thin filament or an extended blob naturally depends on the viewing angle (as shown in the volumetric rendering of the radio and optical emission in Figure 2 ).

For a comparison with observations it has to be borne in mind that the approximation of a uniform ISM is not very accurate. The effects of enhancements of densities and emission may be interpreted to some degree as multiplication factors applied to the varying local conditions prior to interaction. However, this point of view has to be taken with caution, since the emission and densities resulting from shock compression are ``critical'' phenomena, as shown in this context by Steffen et al.(1997b). Here regions of higher than critical densities will cool catastrophically after being shock-heated, while those of lower density will not cool significantly. Since the effective shock velocity is very different on the upstream side and the downstream side, the critical densities will also be very different, resulting in strongly varying densities of the optically visible clouds upstream and downstream of the ISM-wind.

Acknowledgements

WS acknowledges the receipt of a PPARC research associateship and travel support from the University College London.

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