Abstract
We present diagrams depicting the expected inter-dependences of two key kinematical parameters of radio knots in the parsec-scale jets of blazars, deduced from VLBI observations. The two parameters are the apparent speed (υ app = cβ app) and the effective Doppler boosting factor (δ eff) of the relativistically moving radio knot. A novel aspect of these analytical computations of β-δ diagrams is that they are made for parsec-scale jets having a conical shape, with modest opening angles (ω up to 10°), in accord with the VLBI observations of the nuclei of the nearest radio galaxies. Another motivating factor is the recent finding that consideration of a conical geometry can have important implications for the interpretation of a variety of radio observations of blazar jets. In addition to uniform jet flows (i.e., those having a uniform bulk Lorentz factor, Γ), computational results are also presented for stratified jets where an ultra-relativistic central spine along the jet axis is surrounded by a slower moving sheath, possibly arising from a velocity shear.
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Attridge, J. M., Roberts, D. H., Wardle, J. F. C. 1999, ApJ, 518, L87.
Baan, W. A. 1980, ApJ, 239, 433B.
Barthel, P.D. 1994, PASP, 54, 175.
Begelman, M. C., Blandford, R. D., Rees, M. J. 1984, Reviews of Modern Physics, 56, 255.
Begelman, M. C., Rees, M. J., Sikora, M. 1994, ApJ, 429, L57.
Bicknell, G. V. 1985, PASAu, 6, 130.
Biretta, J., Junor, W., Livio, M. 2002, New Astr. Rev., 46, 239.
Blandford, R. D. 2001, PASA, 224, 499.
Celotti, A. 2001, ASPC, 250, 93.
Chiaberge, M., Celotti, A., Capetti, A., Ghisellini, G. 2000, A&A, 358, 104.
Collin-Souffrin, S. 2006, AIPC, 861, 587.
Dermer, C. D., Chiang, J. 1998, New Astr., 3, 157.
Dodson, C. D. 2006, PASJ, 58, 243.
Dodson, R., Edwards, P. G., Hirabayashi, H. 2006, PASJ, 58, 243.
Falcke, H., Biermann, P. L. 1996, A&A, 308, 371.
Fujisawa, K., Kobayashi, H., Wajima, K., Hirabayashi, H., Kameno, S., Inoue, M. 1999, PASJ, 51, 537.
Ghisellini, G. 2004, New Astr. Rev., 48, 375.
Ghisellini, G., Tavecchio, F., Chiaberge, M. 2005, A&A, 432, 401.
Giovannini, G. 2004, Ap&SS, 293, 1.
Giovannini, G., Cotton, W. D., Feretti, L., Lara, L., Venturi, T. 2001, ApJ, 552, 508.
Giroletti, M. et al. 2004, ApJ, 600, 127.
Gopal-Krishna 1995, Proc. Natl. Acad. Sci., 92, 11399.
Gopal-Krishna, Dhurde, S., Wiita, P. J. 2004, ApJ, 615, L81 (Paper I).
Gopal-Krishna, Wiita, P. J., Dhurde, S. 2006, MNRAS, 369, 1287 (Paper II).
Gopal-Krishna, Dhurde, S., Sircar, P., Wiita, P. J. 2007, MNRAS, in press.
Hardcastle, M. J., Alexander, P., Pooley, G. G., Riley, J. M. 1999, MNRAS, 304, 135.
Henri, G., Saugé 2006, ApJ, 640, 185.
Horiuchi, S., Meier, D. L., Preston, R. A., Tingay, S. J. 2006, PASJ, 58, 211.
Hughes, P. A., Aller, H. D., Aller, M. F. 1985, ApJ, 298, 296.
Jester, S., Harris, D. E., Marshall, H. L., Meisenheimer, K. 2006 ApJ, 648, 900.
Jorstad, S. G., Marscher, A. P., Lister, M. L., Stirling, A. M., Cawthorne, T. V., Gómez, J.-L., Gear, W. K. 2004, AJ, 127, 3115.
Jorstad, S. G. et al. 2005, AJ, 130, 1418.
Kaiser, C. R. 2006, MNRAS, 367, 1083.
Kellermann, K. I. et al. 2004, ApJ, 609, 539.
Komissarov, S. S. 1990, Soviet Astron. Lett., 16, 284.
Konopelko, A. K., Mastichiadis, A., Kirk, J. G., de Jager, O. C., Stecker, F. W. 2003, ApJ, 559, 851.
Krawczynski, H. et al. 2001, ApJ, 559, 187.
Laing, R. A. 1980, MNRAS, 193, 439.
Laing, R. A. 1993, “Radio observations of jets: large scales” In: Space Telescope Sci. Inst. Symp. 6: Astrophysical Jets (eds) Burgarella D., O’Dea C. (Cambridge: CUP), 95.
Lind, K. R., Blandford, R. D. 1985, ApJ, 295, 358.
Livio, M. 1997, ASPC, 121, 845.
Lobanov, A. P., Zensus, J. A. 2001, Science, 294, 128.
Ly, C., Walker, R. C., Wrobel, J. M. 2004, AJ, 127, 119.
Macquart, J.-P., de Bruyn A. G. 2006, A&A, 446, 185.
Marscher, A. P. 1980, ApJ, 235, 386.
Marscher, A. P., Marchenko, S. 1999, ASPC, 159, 417.
Marscher, A. P., Gear, W. K. 1985, ApJ, 298, 114.
Meier, D. L. 2003, New Astr. Rev., 47, 667.
Meier, D. L., Koide, S., Uchida, Y. 2001, Science, 291, 84.
Nesci, R., Massaro, E., Rossi, C., Sclavi, S., Maesano, M., Montagni, F. 2005, AJ, 130, 1466.
Phinney, S. 1985, In: “Astrophysics of Active Galaxies and Quasi-stellar Objects”, Mill Valley: University Science Books (ed.) Miller J. S. (Oxford University Press) 453.
Piner, B. G., Unwin, S. C., Wehrle, A. E., Edwards, P. G., Fey, A., Kingham, K. A. 1999, ApJ, 525, 176.
Piner, B. G., Edwards, P. G. 2004, ApJ, 600, 115.
Piner, B. G., Edwards, P. G. 2005, ApJ, 622, 168.
Pellettier, G., Roland, J. 1989, A&A, 224, 24.
Qian, S. J., Quirrenbach, A., Witzel, A., Krichbaum, T. P., Hummet, C. A., Zensus, J. A. 1991, A&A, 241, 15.
Rickett, B. J., Kedziora-Chudczer, L., Jauncey, D. L. 2002, ApJ, 581, 103.
Ryle, M., Longair, M. S. 1966, MNRAS, 136, 123.
Scheuer P. A. G. 1996, ASPC, 100, 333.
Scheuer P. A. G., Readhead, A. C. S. 1979, Nature, 277, 182.
Schilizzi, R. T., de Bruyn, A. G. 1983, Nature, 303, 26.
Sikora, M., Begelman, M. C., Madejski, G. M., Lasota, J.-P. 2005, ApJ, 625, 72.
Sol, H., Pelletier, G., Asseo, E. 1989, MNRAS, 237, 411.
Spada, M., Ghisellini, G., Lazzati, D., Celotti, A. 2001, MNRAS, 325, 1559.
Swain, M. R., Bridle, A. H., Baum, S. A. 1998, ApJ, 507, L29.
Tavecchio, F., Maraschi, L., Sambruna, R. M., Urry, C. M. 2000, ApJ, 544, 23.
Tavecchio, F., Maraschi, L., Sambruna, R. M., Urry, C. M., Cheung, C. C., Gambill, J. K., Scarpa, R. 2004, ApJ, 614, 64.
Urry, C. M., Padovani, P. 1995, PASP, 107, 803.
Vermeulen, R. C., Cohen, M. H. 1994, ApJ, 430, 467.
Wagner, S., Witzel, A. 1995, ARA&A, 33, 163.
Wiita, P. J. 2006, J. Korean Physical Soc., 49, 1753.
Zensus, J. A. 1997, ARA&A, 35, 607.
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Gopal-Krishna, Sircar, P. & Dhurde, S. Kinematical diagrams for conical relativistic jets. J Astrophys Astron 28, 29–40 (2007). https://doi.org/10.1007/s12036-007-0004-8
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DOI: https://doi.org/10.1007/s12036-007-0004-8