Transcript Determination of a magnetization parameter of the parsec

Determination of a magnetization parameter of the parsec-scale AGN jets
V.S.
1P.N.Lebedev
1
Beskin ,
Y.Y.
Physical Institute, Moscow, Russia;
1
Kovalev ,
2Moscow
E.E.
2
Nokhrina
Institute of Physics and Technology, Dolgoprudny, Russia
The frequency-dependent shift of the apparent parsec-scale AGN jet’ base allows us to determine a magnetization of jets. Results
of the first estimate of the magnetization parameter are presented and discussed.
Introduction
Abstract
The observed shift of the core of the relativistic
AGN jets as a function of frequency allows us to
evaluate the number density of outflowing plasma
and, hence, the multiplicity parameter l = n/nGJ.
The value l ~ 1013 obtained from the analysis of
more than 20 sources shows that for most of jets
the magnetization parameter s ~10–100. Since the
magnetization parameter is the maximum possible
value of the Lorentz factor of the relativistic bulk
flow, this estimate is consistent with the observed
superluminal motion.
Method
To determine the multiplicity parameter l and the
magnetization parameter s one can use the dependence
on the visible position of the core of the jet from the
observation frequency [5-9]. This effect is associated
with the absorption of the synchrotron photon gas by
relativistic electrons in a jet. The apparent position of the
nucleus is determined by the distance at which for a
given frequency the optical depth reaches unity. Such
measurements were performed in [13] for 20 objects (see
Table 1). Observations at nine frequencies allowed to
approximate the apparent position of the nucleus as a
function of frequency
where r0 is the position of the bright area of the emission,
r is the apparent position of the nucleus in mas, and n is
the frequency. Here, the quantities , measured in mas,
and , measured in mas·GHz, are the measured
parameters of this approximation. Knowing this
dependence and assuming the equipartition of energy
between the particles and the magnetic field, one can
write down
Here DL (Gpc) is the object distance,  (rad) is the
opening angle of ejection,  (rad) is the angle of view, 
is the Doppler factor, z is the red-shift, and K is the
dimensionless function of the minimum and maximum
Lorentz factor of electrons in their power-law
distribution in energy [9]. Thus, for the 20 objects for
which parameter  was measured, we can estimate the
magnetization parameter s.
One of the most important parameters in magneto-hydrodynamic (MHD) models of relativistic jets is the dimensionless
multiplicity parameter l = n/nGJ, which is defined as the ratio of the particle concentration n to the so-called Goldrech-Julian (GJ)
concentration nGJ = B/2ce (i.e., the minimum concentration required for the screening of the longitudinal electric field in the
magnetosphere). It is important that the multiplicity parameter associates with the magnetization parameter s, which determines the
maximum possible bulk Lorentz factor of the flow, which can be achieved [1]
, where
Here Wtot (erg/s) is the total energy losses of the compact object. If the inner parts of the accretion disc are hot enough, these
electron-positron pairs can be produced by two-photon collisions, the photons with sufficient energy delivering from the inner parts
of the accretion disk [2]. In this case, l ~ 1010 –1013, and the magnetization parameter s ~ 102 – 103. The second model takes into
account the appearance of the region where the GJ plasma density is equal to zero because of the GR effects that corresponds to the
outer gap in the pulsar magnetosphere [3, 4]. This model gives l ~ 102 –103, and s ~ 1010 –1012.
Table 1. The apparent frequency-dependent shift of the nuclei, the
multiplicity parameter l, and the magnetization parameter s.
Object
, mas·GHz
z
l, 1013
s
0148+274
0342+147
0425+048
0507+179
0610+260
0839+187
0952+179
1004+141
1011+250
1049+215
1219+285
1406-076
1458+718
1642+690
1655+077
1803+784
1830+285
1845+797
2201+315
2320+506
3.4
1.0
2.2
1.7
3.6
2.3
1.4
2.4
2.1
1.8
2.5
1.2
2.4
1.9
1.5
1.1
2.8
2.3
3.3
1.3
1.3
1.6
0.6
0.4
0.6
1.2
1.5
2.7
1
1.3
0.1
1
1
0.8
1
0.7
0.6
0.1
0.3
1
21.0
3.7
6.5
3.6
14.5
11.2
5.9
14.3
9.0
7.8
6.2
3.9
11.3
6.5
5.4
6.6
9.8
0.5
6.5
3.8
4.8
27
15
28
6.9
9.0
16
7
11
12
16
26
8.9
15
19
15
10
199
15
27
Here  is taken from observations of 20 objects [13], the red-shift z is
taken from [10], and the distance to the object was determined from
the redshift. For the five objects for which the red-shift is unknown, we
took z = 1. As the half-opening angle, the angle between the jets and
the line of sight (viewing angle) and Doppler factors were taken typical
values:  = 6,  = 9o ,  = 2o, except for objects 1803+784 and
2201+315. Doppler factor and the angle of view for the source
1803+784 was taken from [6], and the half opening angle of jet of this
object was taken from [12]. Doppler factor and viewing angle for
2201+315 is taken from [12]. In addition, we have put for the full
power losses Wtot = 1047 erg/s, which corresponds to the Eddington
luminosity for the central object mass 109 Msun.
Conclusions
The obtained values of the multiplicity parameter l of
the order 1013–1014 are consistent with the model [2].
At the same time, this value corresponds to the
concentration of particles which were found in [5]. The
magnetization parameter s of the order of 10 or several
dozen is in agreement with the Lorentz factor values
estimated [14] from VLBI jet kinematics
measurements. Additionally, for 1803+784 Lorentz
factor is suggested to be equal to 9.5 [3] , whereas we
found s= 10.2. For 2201 +315 we have  = 8.1 and s
= 15.4. In both cases  < s. For different types of
objects (quasars, blazars, and radio galaxies) found in
[6] the average Lorentz factors range from 2 to 17, that
is about ten, which support our point of view as well.
Thus:
1. By measuring the apparent shift of the core jet
emission as a function of frequency for 20 objects we
obtained the estimates of the multiplicity l ~ 1013,
which corresponds to the effective production of
secondary particles.
2. For most objects the magnetized parameter s ~ 10,
which is in good agreement with the observed
superluminal motion.
References
[1] Beskin V.S. Phys. Uspekhi, 53, 1199 (2010)
[2] Blandford R., Znajek R.L., MNRAS, 179, 433 (1977).
[3] Beskin V.S., Istomin Ya.N., Pariev V.I. Sov. Astron., 36, 642
(1992).
[4] Hirotani K., Okamoto I., ApJ, 497, 563 (1998).
[5] Lobanov A.P., A&A, 330, 79 (1998).
[6] Howatta T., Valtaoja E., Tornikoski M., Lähteenmäki A., A&A,
498, 723 (2009).
[7] Gould R.J., A&A, 76, 306 (1979).
[8] Hirotani K., ApJ, 619, 73 (2005).
[9] Marscher A.P., ApJ, 264, 296 (1983).
[10] Kovalev Y.Y., Lobanov A.P., Pushkarev A.B., Zensus J.A., A&A,
483, 759 (2008).
[11] Savolainen T.,Homan D.C., Hovatta T., Kadler M., Kovalev Y.Y.,
Lister M.L., Ros E., Zensus J.A., A&A, 512, A24 (2010).
[12] Jorstad S.G. et al. Astron.J., 130, 1418 (2005).
[13] Sokolovsky, K.V., et al., A&A, in press; arXiv:1103.6032 (2011).
[14] Cohen, M.H., et al., ApJ, 658, 232 (2007).