- Email: [email protected]
Kinematics of the parsec-scale jet in BL Lac
New Astronomy Reviews 47 (2003) 641–644 www.elsevier.com / locate / newastrev
Kinematics of the parsec-scale jet in BL Lac C. Reynolds a,b , *, T. Cawthorne b , D. Gabuzda c a
b
Joint Institute for VLBI in Europe, Postbus 2, 7990 AA, Dwingeloo, The Netherlands Department of Physics, Astronomy and Mathematics, University of Central Lancashire, Preston PR1 2 HE, UK c Department of Physics, University College Cork, Cork, Ireland
Abstract An analysis has been made of the three-dimensional trajectories of two components in the parsec-scale jet of BL Lac, constructed using centimetre-wavelength VLBI data at multiple epochs. The 3-D trajectory of each of these components has first been reconstructed assuming that they move with constant speeds. The only plausible trajectories consistent with the observed paths make small angles to the line of sight (less than 158) everywhere along their paths. The flux density variations predicted by variations in Doppler beaming do not agree with the component light curves. We suggest models involving expansion or deceleration in addition to changes in direction to account for the observed flux density changes. 2003 Published by Elsevier B.V.
1. Introduction BL Lacertae (22001420) is the prototype of a sub-class of extragalactic radio sources exhibiting ˚ weak optical emission lines (equivalent width , 5 A, Stickel et al., 1993). BL Lac objects have jets in which discrete components are observed to separate from the core with apparent superluminal speeds. Here, we attempt to reconstruct the 3-D trajectory in BL Lac following the method of Wardle et al. (1994), which they applied to the quasar 3C 345. This method solves for the trajectory of individual components in the jet by assuming that the 3-D speed of each component is a constant and by ascribing any changes in the apparent velocity to changes in the jet direction.
*Corresponding author. Tel.: 144-1-772-201201; fax: 144-1772-892903. E-mail addresses: [email protected] (C. Reynolds), [email protected] (C. Reynolds). 1387-6473 / 03 / $ – see front matter 2003 Published by Elsevier B.V. doi:10.1016 / S1387-6473(03)00112-X
2. The component trajectories, velocities and Doppler beaming The data are taken from Mutel et al. (1990) and Gabuzda and Cawthorne (2003). Assuming of a smoothly curving trajectory, the paths of two components, S1 and S2, in the plane of the sky have been determined by fitting the observed coordinates as a function of time with Legendre polynomials in a least squares sense (Fig. 1). Once this trajectory has been fitted it is straightforward to determine the component velocity in the plane of the sky. It is then possible to calculate the trajectory of the jet in 3 dimensions under the assumption of a constant 3-D speed. We do not know the true 3-D speed, but a lower limit can be derived from the observed speed on the plane of the sky. For any assumed 3-D speed there are two possible solutions which fit the observations corresponding to trajectories where the maximum / minimum angle to the line of sight is never greater / less than the critical angle which maximises the apparent motion which we label Z1
642
C. Reynolds et al. / New Astronomy Reviews 47 (2003) 641–644
Fig. 1. The least squares fits to the observed component positions for (a) component S2, (b) component S1. 5-GHz observations of Gabuzda and Cawthorne (2003) are indicated by filled squares, the 5-GHz observations of Mutel et al. (1990) by open squares, and the 10-GHz observations of Mutel et al. (1990) by open triangles. The core location is indicated by an open circle.
and Z2 respectively. For a given intrinsic speed the Doppler factor is determined by the angle of the component’s trajectory to the line of sight (e.g. Cawthorne, 1991). If we assume that changes in the Doppler factor alone are responsible for the observed changes in flux density then we can test the validity of the large and small angle trajectories by comparing their predictions for the flux variations with the observed flux history. Consider first of all the case of S2. Fig. 2 shows how the flux density would be expected to change for a jet with a true speed of bp 5 0.971 (the minimum 3-D speed allowed by the observations, where beta is expressed as a fraction of c). In this case it would appear that both the Z2 and
the Z1 trajectories can be ruled out by Doppler boosting arguments. The Z2 trajectory predicts a rapid increase in the observed flux density at later epochs. This is not observed. It also involves angles to the line of sight of greater than 908, which are entirely inconsistent with Doppler beaming models and must therefore be deemed unphysical (this trajectory will not be discussed further). The Z1 trajectory predicts a gentle increase in flux density followed by a gentle decrease which is also in disagreement with the observations. Fitting the trajectory with a higher assumed 3-D speed does not improve the quality of the fit. Very similar results are found for S1 as is illustrated in Fig. 2.
3. The effect of expansion losses and deceleration In Fig. 3 we show the light curves given in Fig. 2, modified to take into account expansion losses. For the small angle trajectory expansion losses can account in large part for the observed decrease in the components’ flux density. For S1, the initial very rapid decrease in flux density cannot easily be accounted for by expansion losses alone, although the later evolution of the light curve is reasonably well fit with the simple adiabatic expansion model which may indicate that the expansion is not linear. Alternatively, there may be other factors contributing
Fig. 2. The observed flux densities (symbols are as in Fig. 1) and the model flux densities (the solid line is the large angle trajectory (Z2 ), the dashed line is the small angle trajectory (Z1 )) for a constant speed jet. (a) S2, bp 5 0.9711, (b) S1, bp 5 0.987. a 5 0.5 is the assumed source spectral index. The models are normalised such that their mean flux density equals the mean observed flux density.
C. Reynolds et al. / New Astronomy Reviews 47 (2003) 641–644
643
Fig. 3. The observed flux densities (symbols are as in Fig. 1) and the model flux densities (as in Fig. 2) for an adiabatically expanding, constant speed jet. (a) Component S2, bp 5 0.9711, (b) component S1, bp 5 0.987. Each component is assumed to expand at a constant rate by a factor of 10 with an adiabatic expansion index of 2 2.5.
to the change in observed flux density such as deceleration of the jet. To test this possibility the trajectories have been recalculated for a jet with a linear deceleration with time, but no expansion. Choosing an arbitrary initial speed, the 3-D speed has been allowed to decrease linearly to the minimum value allowed by the observations. The Doppler factors have been recalculated and the predicted flux densities for each of the new trajectories are presented in Fig. 4. There is now good agreement between the Z1 trajectory and the observations. The Z1 trajectory makes a maximum angle to the line of sight of 158. The apparent large
changes in angle on the plane of the sky are then the result of projection effects.
4. Conclusions 1. The observed flux history of two components in the jet of BL Lac cannot be modelled using only the variations in the Doppler factor of a constant speed jet to explain the changes in flux density. Expansion losses, deceleration of the jet or a combination of both may explain the observations.
Fig. 4. The observed flux densities and the model flux densities for a decelerating jet with no expansion. (a) Component S2, with initial speed bp 5 0.995 (g | 10), decelerating to bp 5 0.9601 (g | 4). (b) Component S1, with initial speed bp 5 0.999 (g | 22) decelerating to bp 5 0.9835 (g | 5). The symbols are as in Fig. 1.
644
C. Reynolds et al. / New Astronomy Reviews 47 (2003) 641–644
2. Wardle et al. (1994) performed a similar analysis for the quasar 3C 345 and found no evidence for deceleration or expansion. We suggest that, in BL Lac, the deceleration and / or expansion of the components are caused by the same effect which results in the jet failing to maintain its collimation and coherence to scales of hundreds of kpc, as commonly achieved by quasar jets. This idea is consistent with the result from Bowman et al. (1996) that entrainment can occur efficiently in low luminosity jets such as BL Lac, but not in high luminosity jets as in quasars such as 3C 345.
References Bowman, M., Leahy, J.P., Komissarov, S., 1996. MNRAS 279, 899. Cawthorne, T.V., 1991. In: Hughes, P.A. (Ed.), Beams and Jets in Astrophysics. Cambridge University Press, Cambridge, p. 187. Gabuzda, D.C., Cawthorne, T.V., 2003. MNRAS 338, 312. Mutel, R., Su, B., Bucciferro, R., Phillips, R., 1990. ApJ 352, 81. ¨ Stickel, M., Fried, J., Kuhr, H., 1993. A&AS 98, 393. Wardle, J., Cawthorne, T.V., Roberts, D., Brown, L., 1994. ApJ 437, 122.
Kinematics of the parsec-scale jet in BL Lac C. Reynolds a,b , *, T. Cawthorne b , D. Gabuzda c a
b
Joint Institute for VLBI in Europe, Postbus 2, 7990 AA, Dwingeloo, The Netherlands Department of Physics, Astronomy and Mathematics, University of Central Lancashire, Preston PR1 2 HE, UK c Department of Physics, University College Cork, Cork, Ireland
Abstract An analysis has been made of the three-dimensional trajectories of two components in the parsec-scale jet of BL Lac, constructed using centimetre-wavelength VLBI data at multiple epochs. The 3-D trajectory of each of these components has first been reconstructed assuming that they move with constant speeds. The only plausible trajectories consistent with the observed paths make small angles to the line of sight (less than 158) everywhere along their paths. The flux density variations predicted by variations in Doppler beaming do not agree with the component light curves. We suggest models involving expansion or deceleration in addition to changes in direction to account for the observed flux density changes. 2003 Published by Elsevier B.V.
1. Introduction BL Lacertae (22001420) is the prototype of a sub-class of extragalactic radio sources exhibiting ˚ weak optical emission lines (equivalent width , 5 A, Stickel et al., 1993). BL Lac objects have jets in which discrete components are observed to separate from the core with apparent superluminal speeds. Here, we attempt to reconstruct the 3-D trajectory in BL Lac following the method of Wardle et al. (1994), which they applied to the quasar 3C 345. This method solves for the trajectory of individual components in the jet by assuming that the 3-D speed of each component is a constant and by ascribing any changes in the apparent velocity to changes in the jet direction.
*Corresponding author. Tel.: 144-1-772-201201; fax: 144-1772-892903. E-mail addresses: [email protected] (C. Reynolds), [email protected] (C. Reynolds). 1387-6473 / 03 / $ – see front matter 2003 Published by Elsevier B.V. doi:10.1016 / S1387-6473(03)00112-X
2. The component trajectories, velocities and Doppler beaming The data are taken from Mutel et al. (1990) and Gabuzda and Cawthorne (2003). Assuming of a smoothly curving trajectory, the paths of two components, S1 and S2, in the plane of the sky have been determined by fitting the observed coordinates as a function of time with Legendre polynomials in a least squares sense (Fig. 1). Once this trajectory has been fitted it is straightforward to determine the component velocity in the plane of the sky. It is then possible to calculate the trajectory of the jet in 3 dimensions under the assumption of a constant 3-D speed. We do not know the true 3-D speed, but a lower limit can be derived from the observed speed on the plane of the sky. For any assumed 3-D speed there are two possible solutions which fit the observations corresponding to trajectories where the maximum / minimum angle to the line of sight is never greater / less than the critical angle which maximises the apparent motion which we label Z1
642
C. Reynolds et al. / New Astronomy Reviews 47 (2003) 641–644
Fig. 1. The least squares fits to the observed component positions for (a) component S2, (b) component S1. 5-GHz observations of Gabuzda and Cawthorne (2003) are indicated by filled squares, the 5-GHz observations of Mutel et al. (1990) by open squares, and the 10-GHz observations of Mutel et al. (1990) by open triangles. The core location is indicated by an open circle.
and Z2 respectively. For a given intrinsic speed the Doppler factor is determined by the angle of the component’s trajectory to the line of sight (e.g. Cawthorne, 1991). If we assume that changes in the Doppler factor alone are responsible for the observed changes in flux density then we can test the validity of the large and small angle trajectories by comparing their predictions for the flux variations with the observed flux history. Consider first of all the case of S2. Fig. 2 shows how the flux density would be expected to change for a jet with a true speed of bp 5 0.971 (the minimum 3-D speed allowed by the observations, where beta is expressed as a fraction of c). In this case it would appear that both the Z2 and
the Z1 trajectories can be ruled out by Doppler boosting arguments. The Z2 trajectory predicts a rapid increase in the observed flux density at later epochs. This is not observed. It also involves angles to the line of sight of greater than 908, which are entirely inconsistent with Doppler beaming models and must therefore be deemed unphysical (this trajectory will not be discussed further). The Z1 trajectory predicts a gentle increase in flux density followed by a gentle decrease which is also in disagreement with the observations. Fitting the trajectory with a higher assumed 3-D speed does not improve the quality of the fit. Very similar results are found for S1 as is illustrated in Fig. 2.
3. The effect of expansion losses and deceleration In Fig. 3 we show the light curves given in Fig. 2, modified to take into account expansion losses. For the small angle trajectory expansion losses can account in large part for the observed decrease in the components’ flux density. For S1, the initial very rapid decrease in flux density cannot easily be accounted for by expansion losses alone, although the later evolution of the light curve is reasonably well fit with the simple adiabatic expansion model which may indicate that the expansion is not linear. Alternatively, there may be other factors contributing
Fig. 2. The observed flux densities (symbols are as in Fig. 1) and the model flux densities (the solid line is the large angle trajectory (Z2 ), the dashed line is the small angle trajectory (Z1 )) for a constant speed jet. (a) S2, bp 5 0.9711, (b) S1, bp 5 0.987. a 5 0.5 is the assumed source spectral index. The models are normalised such that their mean flux density equals the mean observed flux density.
C. Reynolds et al. / New Astronomy Reviews 47 (2003) 641–644
643
Fig. 3. The observed flux densities (symbols are as in Fig. 1) and the model flux densities (as in Fig. 2) for an adiabatically expanding, constant speed jet. (a) Component S2, bp 5 0.9711, (b) component S1, bp 5 0.987. Each component is assumed to expand at a constant rate by a factor of 10 with an adiabatic expansion index of 2 2.5.
to the change in observed flux density such as deceleration of the jet. To test this possibility the trajectories have been recalculated for a jet with a linear deceleration with time, but no expansion. Choosing an arbitrary initial speed, the 3-D speed has been allowed to decrease linearly to the minimum value allowed by the observations. The Doppler factors have been recalculated and the predicted flux densities for each of the new trajectories are presented in Fig. 4. There is now good agreement between the Z1 trajectory and the observations. The Z1 trajectory makes a maximum angle to the line of sight of 158. The apparent large
changes in angle on the plane of the sky are then the result of projection effects.
4. Conclusions 1. The observed flux history of two components in the jet of BL Lac cannot be modelled using only the variations in the Doppler factor of a constant speed jet to explain the changes in flux density. Expansion losses, deceleration of the jet or a combination of both may explain the observations.
Fig. 4. The observed flux densities and the model flux densities for a decelerating jet with no expansion. (a) Component S2, with initial speed bp 5 0.995 (g | 10), decelerating to bp 5 0.9601 (g | 4). (b) Component S1, with initial speed bp 5 0.999 (g | 22) decelerating to bp 5 0.9835 (g | 5). The symbols are as in Fig. 1.
644
C. Reynolds et al. / New Astronomy Reviews 47 (2003) 641–644
2. Wardle et al. (1994) performed a similar analysis for the quasar 3C 345 and found no evidence for deceleration or expansion. We suggest that, in BL Lac, the deceleration and / or expansion of the components are caused by the same effect which results in the jet failing to maintain its collimation and coherence to scales of hundreds of kpc, as commonly achieved by quasar jets. This idea is consistent with the result from Bowman et al. (1996) that entrainment can occur efficiently in low luminosity jets such as BL Lac, but not in high luminosity jets as in quasars such as 3C 345.
References Bowman, M., Leahy, J.P., Komissarov, S., 1996. MNRAS 279, 899. Cawthorne, T.V., 1991. In: Hughes, P.A. (Ed.), Beams and Jets in Astrophysics. Cambridge University Press, Cambridge, p. 187. Gabuzda, D.C., Cawthorne, T.V., 2003. MNRAS 338, 312. Mutel, R., Su, B., Bucciferro, R., Phillips, R., 1990. ApJ 352, 81. ¨ Stickel, M., Fried, J., Kuhr, H., 1993. A&AS 98, 393. Wardle, J., Cawthorne, T.V., Roberts, D., Brown, L., 1994. ApJ 437, 122.