Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.mrao.cam.ac.uk/yerac/garcia/garcia.ps Äàòà èçìåíåíèÿ: Wed Feb 22 20:48:05 1995 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 01:44:36 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: annular solar eclipse

An expanding plasmon model for the radio
outbursts of Cir X­1
By J o a n G a r c i a
Departament d'Astronomia i Meteorologia, Universitat de Barcelona, Av. Diagonal 647,
E­08028 Barcelona, Spain
The group of radio emitting X­ray binaries (XRB's), such as SS433, Cyg X­3, LSI+61 ffi 303, Cir
X­1, etc., exhibit highly variable bursting radio emission interpreted as synchrotron radiation
from relativistic electrons. It is possible that these electrons have been shock­accelerated after
supercritical accretion episodes onto the system compact companion. Supercritical accretion
rates occur when the Eddington accretion limit is exceeded, normally during periastron passage.
In this paper, a numerical model for radio outbursts in XRB's is developed. The model is based
on a process of continuous injection of relativistic particles into a spherical expanding plasmon,
ejected following a transitory supercritical accretion event onto the compact star. The relativistic
electrons lose their energy by adiabatic expansion, synchrotron radiation and inverse Compton
effect. Calculations have been carried out for Cir X­1, a XRB exhibiting 16.6 d periodic X­ray
and radio outbursts. The model is applied considering the evolution of two consecutive spherical
plasmons to account for the double­peaked radio flares from Cir X­1, observed at multi­frequency
during the outburst of 1977 May 12­15. A satisfactory fit of the radio light curves with two
plasmon ejection events is obtained.
1. Introduction
Cir X­1 is the only periodic radio emitting X­ray source detected in the Southern
Hemisphere. This object has a wide range of emission in all spectral windows, and
multi­wavelength observations have been reported at X­ray Kaluzienski, et al. (1976),
optical Haynes et al. (1978), infrared Glass, (1978) and radio Haynes et al. (1978).
Such studies suggest that we are dealing with an eccentric binary system with a 16.6
d orbital period, the same period of both X­ray and radio outbursts. Radio outbursts
usually occur after X­ray outbursts, and may exhibit multi­peaked structure. Based on
HI absorption measurements Goss & Mebold (1977) a distance of 8--10 kpc is adopted.
The compact object is probably a neutron star of 1.1 to 1.4 M fi Tennant et al. (1986).
The optical counterpart is not well known because the location in a highly obscured
region, where three faint stars are within 1 00 of the radio position Argue, et al. (1984).
The soft X­ray properties seem to indicate some few solar masses for the primary star
Stewart et al. (1991). However, its X­ray and radio properties do not fit easily into the
high mass or low mass classification.
Another remarkable peculiarity is the existence of a radio nebula surrounding this
source Haynes et al. (1986) with jet­like structure observed inside Stewart et al. (1993).
It has been suggested that Cir X­1 may be a runaway binary Clark, et al. (1975) ejected
from the SNR G321.9­0.3.
2. The model
In the present model, it is considered that a Cir X­1 radio outburst takes place due to
the bipolar ejection of a cloud of synchrotron­emitting relativistic electrons (plasmon),
mixed with ionized thermal gas, following a transitory supercritical accretion event onto
the compact star.
1

2 Joan Garcia: A plasmon model for Cir X­1
During this process, fresh relativistic electrons can be injected into the plasmon, which
is assumed to be in adiabatic expansion.
In the course of the expansion, assumed to occur at a constant velocity v, the electrons
will be subjected to adiabatic, synchrotron and inverse Compton energy losses, that are
given by:
(a) Adiabatic expansion losses:
`
dE
dt
'
adi
= \Gammaff a
E
r ; (2.1)
where ff a is a constant depending on the geometry and the expansion velocity.
(b) Synchrotron losses:
`
dE
dt
'
syn
= \Gammaff s B 2 E 2 ; (2.2)
where ff s = 2:37 \Theta 10 \Gamma3 (cgs).
(c) Inverse Compton losses:
`
dE
dt
'
com
= \Gammaff c URE 2 ; (2.3)
where ff c = 3:97 \Theta 10 \Gamma2 (cgs) and UR represents the radiation energy density.
Let N (E; t)dE be the energy distribution function of relativistic particles. Its time
evolution is controlled by the following continuity equation:
@N (E; t)
@t +
@
@E
`
N (E; t)
dE
dt
'
= Q(E; t); (2.4)
where
\Gamma dE
dt
\Delta
includes all the energy loss mechanisms and Q(E; t) is the source term
(number of particles injected per unit time and per unit energy interval).
It is assumed that injected particles have an energy power law spectrum of index p,
with energy limits E d Ÿ E Ÿ E u , and that the injection process takes place, at a constant
rate, during a finite interval t f . Thus, the source term is:
Q(E; t) =
ae
Q o E \Gammap for t Ÿ t f
0 for t ? t f
(2.5)
By integrating over the energy limits, the relationship between the mass of relativistic
particles injected per unit of time, —
M rel , and the parameter Q o , is:
—
M rel '
m e Q o E 1\Gammap
d
(p \Gamma 1)
; (2.6)
being m e the mass of the electron and E d !! E u has been assumed.
Assuming magnetic flux conservation, the evolution of the magnetic field can be written
as:
B = B o
`
r
r o
' \Gamma2
; (2.7)
where the subscript zero indicates initial values at t=0.
On the other hand, for the radiation energy density UR is used the approximation of
Paredes et al. (1991):
UR /
`
r
r o
' \Gamma2
; (2.8)
At this point, the calculation of synchrotron emission and absorption coefficients, as well
as that of radio flux density, follows a treatment parallel to that of Paredes et al. (1991).

Joan Garcia: A plasmon model for Cir X­1 3
Magnetic field at ro Bo = 2:3 G
Initial expansion velocity vo = 8:8 \Theta 10 8 cm s \Gamma1
First Injection time interval tf = 1:3 d
Plasmon Injection rate of relativistic electrons —
Mrel = 6:8 \Theta 10 \Gamma14 M fi d \Gamma1
Power law index p = 1:5
Ejection date 12.15 May 1977
Magnetic field at r0 Bo = 2:0 G
Initial expansion velocity vo = 7:2 \Theta 10 8 cm s \Gamma1
Second Injection time interval tf = 2:2 d
Plasmon Injection rate of relativistic electrons —
Mrel = 6:4 \Theta 10 \Gamma14 M fi d \Gamma1
Power law index p = 1:6
Ejection date 13.15 May 1977
Table 1. Physical parameters of the plasmons.
3. Application of the model to Cir X­1 and results
The model described above has been applied to the radio light curves of Cir X­1 as
observed by Haynes et al. (1978) at 1.4, 2.3, 5.0 and 8.4 GHz. The main features of this
outburst were:
(a) A double­peaked structure at 5.0 and 8.4 GHz, with peaks separated about 1 day.
(b) At 1.4 and 2.3 GHz the flare is broad and does not seem to have double­peaked
structure.
Before modelling the data points, the quiescent spectrum of Cir X­1 (Haynes et al.
(1978))
S š = 0:3
`
š
5 \Theta 10 9 Hz
' \Gamma0:5\Sigma0:1
Jy; (3.9)
has been subtracted from all of them.
I have carried out numerical calculations for the flux density at these four frequencies
during the outburst. Two plasmon ejection events have been considered to account for
the double­peaked flare observed. The computed radio light curves take into account
the overlapping of both plasmons. The best fit parameters of each plasmon are given in
Table 1. In Figure 1, we can see that the present model reproduces acceptably well the
observed data at several frequencies simultaneously.
4. Future work
A possible improvement of the present model could be achieved by using a time de­
pendent injection term in the following way:
Q(E; t) = q(t)E \Gammap : (4.10)
The time dependence of the injection function could be specially important for X­ray
binary systems where the accretion rate changes significantly along the orbital phase. In
particular, when the accretion is due to a stellar wind, it can be shown that the function
—
M(t) exhibits two well defined peaks for orbits of high eccentricity Taylor et al. (1992).
Those peaks could be related to the double peaked radio outbursts in objects such as Cir
X­1.
I am grateful to J.M. Paredes and J. Mart'i for their helpful discussions and comments.

4 Joan Garcia: A plasmon model for Cir X­1
Figure 1. Observed data of Cir X­1 for the 1977 May double­peaked radio outbursts at the
frequencies of 8.4, 5.0, 2.3 and 1.4 GHz. The continuous line is the model fit carried out using
the parameters of Table 1.
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Joan Garcia: A plasmon model for Cir X­1 5
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