Table Of ContentParameters for Very Light Jets of cD Galaxies
M. Krause and M. Camenzind
Landessternwarte Ko¨nigstuhl, D-69117 Heidelberg, Germany
3
Abstract
0
0
2
RecentChandraX-rayobservationsofjetsincentralclustergalaxiesshowinteresting
n features around the symmetry plane. We have carried out simulations involving
a
bipolar jets, removing the artificial boundary condition at the symmetry plane. We
J
5 use a very low jet density (IGM/jet ≈ 104) and take into account a decreasing
1 density profile. We find that the jet bow shock undergoes two phases: First a nearly
spherical one and second the well-known cigar-shaped one. We propose Cygnus A
1
v to be in a transition phase, clear signs from both phases. Due to inward growing
9 of Kelvin Helmholtz instabilities (KHI) between cocoon and shocked IGM, mass
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entrainment is observed predominantly in the symmetry plane. We propose this
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1 mechanism to produce some of the so far enigmatic X-ray features in the symmetry
0 plane in Cygnus A.
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0
/
h Key words: Hydrodynamics, Simulation, Jet propagation
p PACS: 95.30.L, 47.27.W, 95.30.Lz, 98.38.F, 98.54, 98.58.F, 98.62.Nx, 98.62.Ra,
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o 98.65.Cw, 98.70.Dk
r
t
s
a
: 1 Introduction The displaced hot gas (107 K) has
v
i been detected in several cases (e.g.
X
Soker et al., 2002, and references
r
a Radio galaxies are traditionally therein). An exceptional case is the
knownbytheirradioemission,which Cygnuscluster withitsfamousFRII
arises from magnetised jet plasma, radio galaxy Cygnus A. This is the
accelerated to large velocities in the only nearby (redshift z=0.06) pow-
active nucleus, and expelled up to erful jet source. In Cygnus A, the
Mpc distances. During their growth, leading bow shock can be found on
theydisplaceandcompresstheambi- the X-ray image (Smith et al., 2002,
ent gas. In the central and dominant also compare Chandra homepage).
cluster galaxies (cDGs), this gas is The identification is easy: It closely
usually dense enough to be seen in engulfs and follows the radio lobes in
theX-rayregime bybremsstrahlung. vicinity of the hotspots, and forms
The Chandra observatory can now an almost spherical bubble around
resolve these centers of galaxy clus- theradioemission.Italsoreproduces
ters with unprecedented resolution. the armlength asymmetry. Fromthis
Preprint submitted to Elsevier Science 2 February 2008
data, the axis ratio of the bow shock
can be determined to 1.2. Compar-
ison with the radio data gives a
bow-shock-to-cocoon width of 3.8.
In the symmetry plane, X-ray bright
filaments are present, next to and Fig. 1. Density slice for the 3D simula-
within the radio lobe. Such excellent tion. The jet is injected in the center in
data demands detailed modelling. opposite directions.
We have simulated a jet with the
extensions. The aspect ratio of the
conditions assumed to be present in
bow shock is monotonically increas-
Cygnus A (sec. 2). The simulation is
ing for the whole simulation. At the
bipolar in order to take into account
time shown, one jet arm is longer
interactions of the backflows of the
than the other one by ≈ 10%. The
jets. Because it fails to reproduce
background is slightly asymmetri-
the data, quantitatively, we present
callyperturbed,withthehigherden-
a parameter study in sec. 3. Finally,
sity on the side of the longer jet.
we present a modified jet model for
This shows that the asymmetry is
CygnusAinsec.4anddiscusstheap-
caused by the action of KHIs on the
plication to comparable jet sources.
jet beam. The central part of the
bow shock is pressure driven and its
width turns out to scale as t0.6, for
2 Bipolar 3D Simulation
the whole simulation time.
TheobservedjetinCygnusAhasba-
UsingthecodeNirvana(Ziegler and Yorke,
sically the same features as the sim-
1997), we simulated (Krause, 2002)
ulated one. The bow shock is a big
a bipolar jet in 3D and cylindri-
bubblewithacigarshapedextension
cal coordinates with the param-
ononeside. The armlength asymme-
eters of the Cygnus A jet, esti- try is ≈ 10%. But the bow-shock-to-
mated by Carilli and Barthel (1996): cocoonwidth≈ 1.3andtheaxisratio
beam radius r = 550 pc, velocity
j of the bow shock (> 3) is far-off the
v = 0.4c, power L = 1046 erg/s,
j j observed values. Hence, the assumed
and external density profile ρ(r) =
parameters wer not a good choice.
10−25[1 + (r/35kpc)2]−9/8 g/cm3.
The density contrast η is 6 × 10−3
at the inlet and the Mach number is
M = 10. 3 Parameter Study
A slice through the computational
volume at a time of 1.6 Myr is shown In order to find out, what parame-
in Fig. 1.Some basic features of such ters differ and in which direction, we
a jet are: Initially, the bow shock performed an axisymmetric study
forms a spherical bubble. Then it with constant background, density
first elongates the bubble, and after contrasts η ∈ [10−5;10−2], and Mach
some time it produces cigar shaped numbers of 3, 8, and 26 (Krause,
2
stant density profile, one obtains
the solution of Castor et al. (1975):
r = (5L/4πρ )0.2t0.6. The criti-
0
cal radius for the first deviation
from spherical symmetry is given
by: r /r = 0.5η−1/4which can be
1 j
checked in the simulations. All the
simulated jets show a high cocoon
pressure, which decreases in time, as
expected for a blastwave with con-
stant energy input. The jet beam
does not react by compression or
expansion, but by adjusting its own
pressure via oblique shock waves.
The result is approximate pressure
Fig. 2. Logarithmic density plots of the equilibrium, besides the hot spot.
parameter study. Top row: η = 10−2,
bottom row: η = 10−4. Left column:
M=3, right column: M=26. Darker
colourcorrespondstolessdenseregions.
4 Discussion
2003). Fig. 2 shows that the trend
found in classical parameter stud-
ies (Norman, 1993, cocoon radius The 3D simulation has falsified the
r ∝ Mη−1/4) is also confirmed here: assumed parameters for Cygnus A.
c
the lighter jets show fatter cocoons. The observed cocoon and bow shock
However,thecocoonsoftheη = 10−4 is wider than in the simulation. This
jets are still under-expanded, which pointstoamoreextremedensitycon-
may be the reason for the indepen- trast. It turns out from the param-
denceofr onM.Thebowshocksare eter study that η ≈ 10−4 is needed
c
spherical at the beginning, because in order to get the observed values.
the pressure inside the jet bubble This agrees well with the extrapola-
drives them faster than the thrust at tions of Rosen et al. (1999) concern-
the jet head. The relevant equation ing the cocoon width. Equation 1
istheforcebalanceatthebowshock, can be used to infer the average jet
which can be transformed into the power (L = 8×1046 erg/s), and the
following integral equation age (t = 27 Myr), which agrees with
estimatesintheliterature.Thesimu-
r t t1
lations have shown that the pressure
M(r)rdr = 2 dt E(t )dt (1)
Z Z 1Z 2 2 has the same order of magnitude in
0 0 0 the whole system. The external pres-
sureintheclustergasis(Smith et al.,
that relates the mass M inside 2002): p ≈ 3×10−10 erg/cm3. The
ext
the radius r to the energy E, in- magnetic energy density in the hot
jected during the time t. For con- spots is u = 9×10−10 erg/cm3
mag,HS
stant energy injection rate and con- or higher (Wilson et al., 2000), as-
3
suming self-synchrotron-Compton in the shocked cluster gas.
origin of the X-ray emission. This
is roughly the equipartition value. SomecDGsshowsimilarfeatureslike
Since the magnetic field in the hot Cygnus A. For example, the X-ray
spots is probably shock-amplified, structure of 3C 317 (Blanton et al.,
this implies a similar value of the 2001) (two elliptical rings, elongated
internal energy in the jet and the in the same direction) can be ex-
cluster gas, as predicted by the plained as a bubble with a cigar
above model. Given the density con- shaped extension, seen at an inclina-
trast of η = 10−4 and taking into tion of 37◦.
account a possibly relativistic jet
(compare Scheck et al., 2002), we es- This work was supported by the
timate: Γ2hρ c2 ≈ 10−8 erg/cm3 (Γ: Deutsche Forschungsgemeinschaft
j
bulk Lorentz factor, h: specific rela- (Sonderforschungsbereich 437).
tivistic enthalpy, ρ : mass density).
j
Consequently, the kinetic power of
the jet is: L = 2πr2ρ Γ(Γh −
kin j j
1)βc3 = 5 × 1045(1 − 1/Γh) erg/s. References
(β = v /c) Since this falls short
j
of the value derived above, the en- Appl, S., Camenzind, M., 1988,
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power: L = r2Γ2βcB2/4 = 5 × Blanton, E. L., Sarazin et al., 2001,
B j
1044(u /u )2Γ2. It follows, ApJ, 558, L15
mag,j mag,HS
that Γ has to be roughly 20. The Carilli, C. L., Barthel, P. D., 1996,
mass flux in the jet is then given by: A&A, Review 7, 1
M˙ = πr2ρ Γβc = 3×10−3h−1M /yr. Castor, J., Weaver, R., McCray, R.,
j j ⊙
Appl and Camenzind (1988) esti- 1975, ApJ, 200, L107
mate the mass flux needed in or- Krause, M., 2002, PhD Thesis, Hei-
der to produce the observed lumi- delberg, Germany, http://www.
nosity in the Cygnus A hotspots ub.uni-heidelberg.de/archiv/2114
downstream of a MHD shock: M˙ = Krause, M., 2003, A&A, accepted,
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rel ⊙ rel
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Comp. Phys. Com. 101, 54.
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