Clouds and red giants interacting with the base of AGN jets

2 MB·English

by  Valenti Bosch-Ramon

Astronomy & Astrophysics manuscript no. paper6 (cid:13)c ESO 2012
January 26, 2012
Clouds and red giants interacting with the base of AGN jets
V. Bosch-Ramon1, M. Perucho2, and M. V. Barkov3
1 Dublin Institutefor AdvancedStudies, 31 Fitzwilliam Place, Dublin 2, Ireland; [email protected]
2 Dept. d’Astronomia i Astrof´ısica, Universitat de Val`encia, C/ Dr. Moliner 50, 46100, Burjassot (Val`encia), Spain;
[email protected]
3 Max-Planck-Institutfu¨r Kernphysik,Saupfercheckweg1, 69117 Heidelberg, Germany; [email protected]
Received ¡date¿ / Accepted ¡date¿
2
ABSTRACT
1
0 Context.Extragalacticjetsareformedclosetosupermassiveblack-holesinthecenterofgalaxies.Largeamountsofgas,
2
dust, and stars cluster in the galaxy nucleus, and interactions between this ambient material and the jet base should

n befrequent, havingdynamical as well as radiative consequences.
a Aims. This work studies the dynamical interaction of an obstacle, a clump of matter or the atmosphere of an evolved
J star,withtheinnermostregionofanextragalacticjet.Jetmass-loadingandthehigh-energyoutcomeofthisinteraction
are briefly discussed.
5
Methods. Relativistic hydrodynamical simulations with axial symmetry have been carried out for homogeneous and
2
inhomogeneous obstacles inside a relativistic jet. These obstacles may represent a medium inhomogeneity or the dis-

rupted atmosphere of a red giant star.
]
E Results. Once inside the jet, an homogeneous obstacle expands and gets disrupted after few dynamical timescales,
H whereasintheinhomogeneouscase,asolid corecansmoothentheprocess,withtheobstaclemass-lossdominatedbya
denseandnarrowtailpointinginthedirectionofthejet.Ineithercase,matterisexpectedtoaccelerateandeventually
h. get incorporated tothejet. Particles can beaccelerated in theinteraction region, and producevariable gamma-raysin
p theambient matter, magnetic and photon fields.
- Conclusions. The presence of matter clumps or red giants into the base of an extragalactic jet likely implies significant
o jetmass-loadingandslowingdown.Fastflare-likegamma-rayevents,andsomelevelofpersistentemission,areexpected
r dueto these interactions.
t
s
a Key words.Galaxies: jets–Gamma rays: galaxies–Stars: AGBand post-AGB
[

1
1. Introduction frequently interact with, and in some cases penetrate into,
v
9 the AGN innermost jet regions. Entrainement of medium
Jetsofactivegalacticnuclei(AGN)arecollimatedoutflows
7 matterleadstojetmass-loading,invokedbyseveralauthors
originatedatthe coreofgalaxies,verylikely inthe vicinity
2 (e.g.Bowman et al.,1996;Laing & Bridle,2002)toexplain
of a supermassive black hole (SMBH) that accretes matter
5 the deceleration of FRI jets between pc-scales, where they
from its environment (e.g. Begelman et al., 1984). The in-
. showrelativisticspeeds,andkpc-scales,wheretheirveloci-
1 ner regions of galaxies contain large amounts of gas, dust,
0 ties aresub-relativistic as shownby the jet andcounter-jet
and stars (e.g. Burbidge, 1970), so there is plenty of ma-
2 symmetric emission.
terial that could interact with the AGN jet. About a 1%
1 Studies of the dynamics of the interaction between
of the present stars are evolved objects (e.g. Young et al.,
: clouds or red giants (RG) after entering into an AGN
v 1977) whose external layers, close to the SMBH, can be
jet have been carried out (e.g. Araudo et al., 2010;
i tidally distorted (see, e.g., Barkov et al., 2010, and refer-
X Barkov et al.,2010,2011).However,previousworkswereof
ences therein). Stellar collisions could also release matter
r analytical nature, mainly focused on the subsequent high-
a totheenvironment(e.g.Young,1977).InAGNwithsignif-
energy emission. Other works have studied the global im-
icantstarformationintheircores,massivestarswithstrong
pact of stars or clouds on the jet propagation and con-
winds will be also present. In bright AGN, hot gas embed-
tent(e.g.Komissarov,1994;Steffen et al.,1997;Choi et al.,
ding denser and cooler clouds is expected to surround the
2005;Hubbard & Blackman,2006; Sutherland et al.,2007;
SMBH (the Broad Line Region -BLR-; e.g. Krolik et al.,
Jeyakumar, 2009), but numerical studies of the conse-
1981; Rees, 1987). In these brightAGN, X-rayheating can
quences of obstacles being inside the innermost regions of
also perturb the external layers of stars even if tidal forces
AGN jets are rare.
are negligible (e.g. Shull, 1983; Penston, 1988). Wandering
In this work, we aim at studying numerically the evo-
dark clouds could also be present in the region close to
lution of a dense cloud and the disrupted layers of an RG
the SMBH, as it has been recently discovered in our own
inside an AGN jet. Homogeneous and power-law (plus a
galaxy (Gillessen et al., 2012). It seems therefore unavoid-
solid core) density profiles have been adopted, the former
able that stellar matter and medium inhomogeneities will
to simulate the simplest cloudor RG scenario,andthe lat-
Send offprint requests to: V. Bosch-Ramon, e-mail: terwhatmightbeamorerealisticsituationforadisrupted
[email protected] RG atmosphere. This can allow a characterization of the
1
Bosch-Ramon et al.: Clouds and red giants interacting with AGN jets
dynamical evolution of obstacles inside jets more accurate pation (e.g. emission). Note that here only sudden mass-
than in previous works, as well as a better understand- loss by shocked obstacles is treated; continuous mass-loss
ing of the impact on the jet itself, and the resulting high- via, e.g., stellar winds is not considered (see Araudo et al.
energy radiation. At this stage, we neglect the role of the 2012; Perucho et al., in preparation).A significant dynam-
magnetic field in the jet, accounting only for its ram pres- ical impact will likely have its observable counterpart in
sure, and assume an axisymmetric (2D) interaction, with the form of non-thermal radiation. However, we remark
the star/obstacleatrestin the laboratoryframe.Magnetic also that, even when providing little mass-loading, the oc-
fields and3-dimensional(3D) effects willbe includedinfu- casional penetration of dense and large obstacles within
ture work. the jet could have observable consequences (Araudo et al.,
2010; Barkov et al., 2010, 2011).
Figure1showsasketchofthescenariossimulatedhere.
2. Physical scenario The simulationsaccountfor the phasewhenthe obstacleis
well inside the innermost regionof an AGN jet. Two types
Unlike smoothmedia,which interacts with the jet through
ofobstacleshavebeenconsidered.Thefirsttypeconsistson
a shear layer preventing direct mixing, medium inhomo-
an homogeneous gas sphere, which may represent a dense
geneities like matter clumps, stars, etc., could penetrate
cloudinthe centralAGN regions(e.g.fromthe BLR),ora
effectively into the jet. The requirement for the obstacle
homogeneousbulk of materialfrom the externalRG layers
to enter into the jet is to have a jet perpendicular speed
detached by tidal SMBH forces. The second case considers
vo >∼ vsc, where vsc is roughly the shocked obstacle sound apower-lawprofilewitharadialdependence∝R−2 forthe
speed, i.e. vsc ∼cpρjΓj/ρo, Γj =1/(1−(vj/c)2)1/2 the jet density (plus a solid core), which may represent the RG
Lorentzfactor,andρj andρo the jet andobstacledensities external layers more realistically, or just slightly affected
in the reference frame of the latter. This assumes that the by tidal forces1.
relevant jet pressure comes from bulk motion, which im-
pliesthatthejetpowerL =πR2(Γ −1)ρvc2,whereR is
j j j j j j a) b)
the jet radius. Once the obstacle is inside the jet, neglect-
ing magnetic field effects, a bow-shapedshockforms in the
jet. Another shock with speed v crosses the obstacle, or
sc
inthecaseofanRG,itsexternallayers(e.g.Araudo et al.,
2010; Barkov et al., 2010, and references therein). Being
ofmscotrbaurosmcsctlshaeaicntlftigeaoosn(rteoaenrtdrti,imdruatysehin,,neaw∼mtjhielieltcRabliolase)/tctttm.eoimruA.bcefThettehdlmreor∼nufeegcfwoRherroelt/t,idgvh,thsahctnt,eehrwetohibttoehshbtabasnRtcoalowtech-lasseeshhoohothccabkkes- S(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)h(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)o(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)c(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)k(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)e(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)d(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)o(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)b(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)staDcislerupted RG (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) Cloud
been accelerated by the jet up to a velocity ∼ v (e.g. Bow shock
j
Blandford & Koenigl, 1979; Barkov et al., 2010, 2011). It
Jet
followsthatifthetimeofjetcrossing,t ∼R/v ,issmaller
j j o
thant ,theobstaclewillbeabletoleavethejet;otherwise,
d
BH
itwillbedraggedbythejetandpresumablydisruptedand
mixed with its matter. Accretion disc
For obstacles remaining long enough in the jet, and Fig.1. Sketch of the two scenarios contemplated here. a)
to have a dynamically strong impact on the jet, the ob- PenetrationofanRG,withtheexternallayersdetached(to
stacles have to affect significantly the total jet mass, mo- different degrees) due to gravitational disruption, into the
mentum and energy fluxes. In the present context, it can jet. b) Penetration of a massive clump of matter into the
mean also that enough mass will be entrained to enforce jet.
significant jet deceleration and energy dissipation, i.e. the
obstacle mass-injection flux M˙ ∼ M˙ = L/(Γ − 1)c2
cr j j
(Hubbard & Blackman, 2006). In addition, t should be
j
significantly longer than td, to allow the jet to drag the 3. Simulations
whole obstacle matter. The value of M˙ can be estimated
as ∼ N χ2M /4t(z ), where N is the number of ob- We have performed three numerical simulations. In simu-
o o j o o
lation 1 (S1), we have calculated the interaction between
stacles (clouds, stars, etc.) within a sphere of radius z ,
o
a homogeneous spherical obstacle and the jet; in simula-
the jet characteristic height, χ = R(z )/z ∼ 0.1, and
j o o
tion2(S2)wehaveintroducedaconstantdensitycoreplus
M = 4πR3ρ /3 the detachable obstacle mass. The value
o o o a power-law profile for the radial variation of the density
of z depends strongly on the scenario under study. It
o out of this core (R−2, see Section 2); in simulation 3 (S3)
might be the size of the BLR (Araudo et al., 2010), a re-
we have reproduced S2 with double resolution. The three
gionin whichSMBH tidalforcesaffectthe RGatmosphere
simulationshave2Daxialsymmetryandhavebeencarried
(Barkov et al., 2010), or the distance at which accretion
out in cylindrical coordinates.This is justified by the sym-
disk X-rays can affect the star external layers. Note that
metricnatureoftheproblemsolved(initialinteractionand
for t ≪t , the obstacles will initially affect just the outer-
d j
most jet shell, but eventually a strong shear layer will de- 1 It is worth noting that the power-law case may also cor-
velop reaching the jet core. For td <∼ tj, the obstacle mass respond to an RG with its wind confined by external pressure
will be more distributed over the jet cross section, likely outside thejet, forming a bubblethat would bebroughtby the
speeding up the process of mass-loading and energy dissi- RGinto thejet.
2
Bosch-Ramon et al.: Clouds and red giants interacting with AGN jets
obstacle ablation), which may only be broken by inhomo- The material of the shocked obstacle can have rather
geneities in the jet that lead, at larger scales than studied complex properties. Once in pressure equilibrium with the
here,to instabilities inthe cometarytailformedby the ob- jet ram pressure, the obstacle is radiation dominated, and
stacle material and subsequent mixing with jet matter. It radiative cooling through thermal Bremsstrahlung may be
shouldbenotedthatthesesimulationsrepresentasimplifi- important. For simplicity, we have modelled the obstacle
cation,andanecessaryinitialstep,ofthemorerealisticsit- asanon-relativisticproton-electronplasma.Thishassome
uation, which would require the obstacle to penetrate into implications for the compression and stability of the ob-
thejetwithtransversalmotion.Thiscanonlybesolvedvia stacle, since the adiabatic coefficient may not be accurate
3D-simulationsandisbeyondthescopeofthisinitialwork. withrespecttorealisticcases,andshockedmatterdensities
We have used the finite-volume code Ratpenat, which (and instabilities) could be enhanced by radiative cooling.
solves the equations of relativistic hydrodynamics in con- However, at this stage of the study the calculations can
servationformusinghigh-resolution-shock-capturingmeth- capturetherelevantaspectsofthesimulatedprocess.More
ods. Ratpenat is a hybrid parallel code – MPI + OpenMP accurate simulations will be performed in the future.
– extensively and intensively tested (e.g., Perucho et al.,
2010). The code includes the Synge equation of state
4. Results
(Synge, 1957) with two populations of particles, namely,
leptons (electrons and positrons) and baryons (protons). 4.1. Homogeneous case
The simulations were performed in Tirant, at the Servei
In S1, the interaction regionrapidly develops the expected
d’Informa`tica of the Universitat de Val`encia, using 16 pro-
structure,withabowshockinthejet,andacontactdiscon-
cessors in S1 and S2, and 32 processors in S3.
InS1,the numericalgridboxexpandsto1015cminthe tinuityseparatingboththeshockedmediaandtheobstacle
radialdirection,withahomogeneousgridupto2×1014cm shocked by a slow shock. The eroded material from the
obstacle is dragged downstream, forming a cylindrical tail
including 400 cells, plus an extended grid with 200 cells
covering the remaining 8×1014cm. In the direction of the surrounded by rarefied jet flow that has crossed the bow
jet flow (axial direction), the grid covers 6×1014cm. The shock.
(homogeneous) obstacle is located at z = 1014cm, with Figure 2 shows a snapshot of the simulation at t≃9×
radius R = 1013cm, and the rest of the grid is filled by 104s,whichcorrespondstotheinitialphase.Aftert=2.3×
o 105s, the shock has completely crossed the obstacle. The
the jet flow. The resolution used in S1 is 20 cells/R , with
o pressureattheapexofthebowshockoscillatesbetween103
a total of 600×1200 cells. In S2, the grid expands to 3×
1014cm,withahomogeneousregionupto1014cmusing320 and 1.5×103dyn/cm2, and the temperature of the post-
cells, and 200 cells extending the grid 2×1014cm further. shock gas is at this point ≃ 1012K2. After the obstacle
Along the symmetry axis,the gridis 3×1014cm long.The matter is heated by the shock, it expands, increasing the
obstacleislocatedatz =2.5×1013cm,ithasaradiusR = cross-sectionoftheinteractionwiththejetflow.Uptothis
o
1013cm, with aninner coreof constantdensity with radius point, the mass-load by obstacle material is modest (see
of 2.5×1012cm, and a surrounding region with decreasing Sect. 4.3) and mainly due to continuous ablation from its
outer layers. This gas accumulates in a cylindrical region
density (see Sect. 2) up to R . As in S1, the rest of the
o
withradius ofthe orderofR ,forminga cometary-liketail
grid is filled by jet flow. The resolution used in S2 is 32 o
ofobstaclegasseparatedfromtherarefied,shockedjetflow
cells/R , with a total of 520×960 cells. In the case of S3,
o
byasmoothshearlayerinwhichlittlemixingoccurs,asno
the simulationis focused on a smaller regionof S2, using a
instabilities are triggered in the layer during this phase.
resolution 64 cells/R with a total of 320×960 cells that
o
cover a grid size of 5×1013cm in the radial direction and Figure3 showsthe trends inenergy flux,mass flux,ob-
1.5×1014cm in the axial direction. stacle mean density (averaged over the grid area Aj) and
velocity along the axial direction for a snapshot at a rela-
The jet is modelled in all three simulations as a mat-
tively early stage. In this plot, the energy flux is separated
ter dominated flow with proton-electron composition. The
into kinetic plus rest-mass energy flux (L −L =
properties of the jet in S1 have been chosen to result in j,g1 j,int,g1
(ρ(hW −1)W −ρWε)vA, with h being the enthalpy, W
a total jet kinetic power L = 2 × 1044erg/s for a jet j j
j,s1 the Lorentz factor, and ε the specific internal energy), and
radius R = 1015cm, with jet velocity v = 0.866c =
j j internalenergyflux(L =ρWε)vA).Thesevariables
2.6×1010cm/s, density ρ = 1.35×10−18g/cm3, tem- j,int,g1 j j
j,s1 givean idea ofthe amountofenergyflux inthe formof in-
perature T = 1010K, adiabatic exponent γ = 1.45, and
j j ternalenergyorkinetic andrest-massenergy.Afractionof
Mach number Mj = 16.8. With these parameters, the ki- Lj,g1inthisphaseismainlyinvestedinheatingtheshocked
netic power of the jet within the homogeneous simulated jet material, with only a small amount transferred to the
grid is Lj,g1 = 8×1042erg/s and the mass flux is M˙j,g1 = obstacle gas (upper panels in Fig. 3). Some fraction of this
2.8×1021g/s. In S2 and S3, the jet density usedis slightly energymaygotonon-thermalparticles.The gasinthetail
larger ρj,s23 = 2.4×10−18g/cm3, giving a total jet power expands and accelerates along the z coordinate,reaching a
withinaradiusR ofL =3.5×1044erg/s.Inthecaseof meanaxialspeed v ≃1.2×108cm/s (bottom left panelin
j j,s23 z
S2,Lj,g2 =3.5×1042erg/sandM˙j,g2 =1.25×1021g/s,and, Fig. 3), with vz ≃109cm/s right on the symmetry axis.
forS3,L =8.75×1041erg/sandM˙ =3.12×1020g/s. Aftertheobstacleisshocked,instabilitiesdevelopinside
j,g3 j,g3
anddisruptit,detachingclumpsofmaterialandenhancing
The obstaclein S1 hasdensity ρ =1.35×10−12g/cm3
o turbulentmixingwiththejetflowinthecometary-liketail.
and temperature T = 104K, with a total mass M ≃ 6×
o o Theinstabilitiesmanagetoteartheexternalportionsofob-
1027g. In the case of S2, the obstacle has a core density
staclegasatt≃7×105s,asthejetflowpenetratesthrough
ρ = 1.25×10−10g/cm3 within the inner 2.5×1012cm,
o
and a decreasing density ∝ R−2 (R is the spherical radius 2 Thee± temperaturecouldbesignificantlylowerduetopair
here),startingwithρ=1.7×10−11g/cm3 at2.5×1012cm. production (e.g. Bisnovatyi-Kogan et al., 1971).
3
Bosch-Ramon et al.: Clouds and red giants interacting with AGN jets
Fig.2. Combined maps of logarithm of pressure (left panel, upper half), density (left panel, lower half), axial velocity
(right panel, upper half), and jet mass fraction (right panel, lower half) at t ≃ 9×104s for S1. The plots make use of
the axisymmetric nature of the simulation.Jet mass fraction equals 1 for pure jet material,0 for pure obstacle material,
and values in between indicate mixing. Units are cgs.
1.2 1.0
1.0
0.8
nergy Flux 00..68 Mass Flux 0.6
m. E m.
Nor 0.4 Nor 0.4
0.2
0.2
0.0
0 1•1014 2•1014 3•1014 4•1014 5•1014 6•1014 0 1•1014 2•1014 3•1014 4•1014 5•1014 6•1014
z (cm) z (cm)
-15
1.2•108
1.0•108
-20
m/s) 8.0•107 3g/cm))
v(cz 6.0•107 ρ g(( -25
o
l
4.0•107
-30
2.0•107
0
0 1•1014 2•1014 3•1014 4•1014 5•1014 6•1014 0 1•1014 2•1014 3•1014 4•1014 5•1014 6•1014
z (cm) z (cm)
Fig.3. Axial cuts of different quantities for S1 at t ≃6×105s, before the instabilities completely destroy the obstacle.
The top left panel shows L −L for the jet material (solid line) normalized to its injection value 8×1042erg/s,
j,g1 j,int,g1
and the internal energy luminosity L normalized to its maximum value, 8×1040erg/s (dashed line); the red solid
j,int,g1
line stands for the internal energy luminosity in the jet material, and the blue dotted line (very close to the bottom)
for the internal energy luminosity in the obstacle material. The top right panel shows the mass flux, normalized to its
maximumvalue(4.7×1022g/s).Thebottomleftandrightpanelsshowthemeanvelocity(averagedoverthegridsection)
and density in the obstacle gas.
the obstacle. This process repeats itself in smaller clumps rialremainingatthesymmetryaxis,allofthemalsotornby
thathavebeendetachedfromtheobstacleandinthemate- thejet(seeFigs.4and5).Theseclumps moveradiallyand
4
Bosch-Ramon et al.: Clouds and red giants interacting with AGN jets
Fig.4. Same as Fig 2 at t≃1.1×106s
are accelerated when entering the region of rarefied (post-
shock)jetmaterial,reachingmeanvelocities≃3×109cm/s.
At the same time, the jet ram-pressurestarts to effectively
push the obstacle remains from its original location along
the z-direction, dragging them downstream to the end of
the grid. The left and central panels of Fig. 6 show the in-
crease in mass flux and mean density when the rest of the
obstaclecrossesthroughtheaxiallocationswheretheseval-
uesarecomputed(halfandendofthegrid,alongtheaxis).
Atthesametime,therightpanelshowsastrongdecreasein
the meanvelocityatthe plottedlocations,whichis accom-
panied by a drop of the mean Mach number from M =16
j
to values <5.
Figure 7 shows the same plots as Figure 3 but at
t≃1.15×106.Atthistimethecross-sectionoftheobstacle
ismaximum,asshownbytheupper panelinFigure5.The
plotsshowthatthetransferofenergyfromthejetmaterial
to the obstacle is maximal in this situation, with the jet
losingalmostallofthe initialkineticandmassenergyflux,
which is put into internal energy flux of the jet and the
obstacle (and potentially into non-thermal particles), plus
kinetic and mass energy flux of the obstacle material (not
shown). The latter is revealed by the large mean velocities
reached by the obstacle material (bottom left panel). The
mass flux shows an increase by nearly two orders of mag-
nitude with respectto the originaljetflux inthe simulated
region,andtheobstaclemeandensityalongthe gridisalso
larger by several orders of magnitude, depending on the
position along the axis, than that shown in Figure 3.
4.2. Inhomogeneous case
In this case, the interaction of the jet with the obstacle
is steadier than in the homogeneous case. The pressure
at the apex of the bow shock oscillates between 2× 103
and 2.5×103dyn/cm2, and the temperature of the post-
shock gas there is again ≃ 1012K. The ablation of mass
from the outer, more dilute layers of the obstacle occurs
at a smoothly increasing rate, until t ≃ 8 × 105s, when
a significant portion of those layers is detached from the
denser core. After that, almost the whole obstacle beyond
2.5×1012 cmhas beenshocked,andthe tailis loadedwith
this gas. At obstacle radii < 2.5×1012 cm the density is Fig.5. Same as left panel in Fig. 2 at t ≃ 1.15×106s,
so high that the material is not affected by the jet during t≃1.3×106s and t≃1.45×106s.
the simulation (as expected for the stellar layers below the
photosphere). Unlike in S1, shocking the obstacle external
5
Bosch-Ramon et al.: Clouds and red giants interacting with AGN jets
-16.0 2.5•1010
22.4
-1log(Mass Flux (g s))2222..02 ρ3log( (g/cm))--1176..05 v(cm/s)z12..50••11001100
21.8 -17.5
1.0•1010
2.0•1054.0•1056.0•1058.0•1051.0•1061.2•1061.4•106 2.0•1054.0•1056.0•1058.0•1051.0•1061.2•1061.4•106 2.0•1054.0•1056.0•1058.0•1051.0•1061.2•1061.4•106
Time (s) Time (s) Time (s)
Fig.6. Mass flux (left panel), mean density (central panel), and mean velocity (right panel) versus time for S1 at
z =3×1014 (half grid, black lines) and 6×1014cm (end of the grid, red lines).
1.2 1.0
1.0
0.8
nergy Flux 00..68 Mass Flux 0.6
Norm. E 0.4 Norm. 0.4
0.2 0.2
0.0
0 1•1014 2•1014 3•1014 4•1014 5•1014 6•1014 0 1•1014 2•1014 3•1014 4•1014 5•1014 6•1014
z (cm) z (cm)
6•109
-16
5•109
-18
v(cm/s)z 34••110099 ρ 3g((g/cm)) -20
o
2•109 l -22
1•109
-24
0
0 1•1014 2•1014 3•1014 4•1014 5•1014 6•1014 0 1•1014 2•1014 3•1014 4•1014 5•1014 6•1014
z (cm) z (cm)
Fig.7. Axial cuts of different quantities for S1 at t≃1.15×106s, the time of maximum cross-sectionof the interaction
between the obstacle and the jet (see Fig. 5). The top left panel shows L −L for the jet material (solid line)
j,g1 j,int,g1
normalized to its injection value 8×1042erg/s, and the internal energy luminosity L normalized to its maximum
j,int,g1
value, 3.6×1042erg/s (dashed line); the red solid line stands for the internal energy luminosity in the jet material, and
the blue dotted line for the internalenergyluminosity in the obstaclematerial.The toprightpanel showsthe mass flux,
normalizedto itsmaximumvalue(1023g/s).Thebottomleftandrightpanelsshowthe meanvelocityanddensityinthe
obstacle gas.
layers does not lead to an enlargement of the bow shock travelling around the core and through the outer layers of
cross-section, since the radial drop in density smoothens the obstacle. In the central right panel, these layers have
the process to some extent. As shown later, this effect is alreadybeencompletelyshockedandalargeamountofgas
enhanced by a low resolution (see Sect. 4.2.1). thathasbeendetachedfromthecoreisvisibleasabumpin
the tail between z =5×1013cm and z =7×1013cm. The
Figure 8 shows a series of maps of the whole process.
bottom panels show this bulk of mass propagating down-
The upper left panel corresponds to the initial phase. The
stream.
nexttwopanels(toprightandcentralleft),showtheshock
6
Bosch-Ramon et al.: Clouds and red giants interacting with AGN jets
Fig.8.SameasleftpanelinFig.2 forsimulationS2 attimes t≃5×104s, t≃1.6×105s,t≃4.3×105s, t≃7.9×105s,
t≃1.25×106s and t≃1.8×106s from top to bottom and left to right.
The upper panels in Fig.9 show the normalizedL − density of the external layers. On the symmetry axis, the
j,g2
L and mass flux versus distance along the axis at maximum axial velocity is v ≃109cm/s at the end of the
j,int,g2 z
t ≃ 3.1×105s, i.e. still during the initial phase. As seen grid, as in the case of S1, but at z =3×1014cm, i.e., half
in the figure,the jet loses a small amountof kinetic energy the distance needed in S1 to reach the same velocity.
flux,whichisusedto heatthe jet materialandto heatand
accelerate obstacle material. The mass flux falls a factor
of ten from the obstacle itself to its tail, where it has a
constant value. The lower panels in Fig. 9 show the values
Figure 10 shows the mass flux within the grid and the
of mean velocity and density of the obstacle gas versus z
meandensityfortwodifferentz-values,namelyathalf(z =
at the same time. The values obtained for the density in
1.5×1014cm) andatthe endofthe grid(z =3×1014cm),
this initial quasi-steady regime of S2 are similar to those
versus time. These plots show that the mass load grows
obtained for S1. Regarding velocity, the obstacle material
smoothly with time at z = 1.5×1014cm until t ≃ 1.4×
is accelerated to v ≃1.9×108cm/s at the end of the grid,
106s,whichcorrespondstothetimeofpassageoftheclump
which is a factor of 3 larger than the velocity reached by
of mass ablated around t ≃ 8×105s. By the end of the
theobstaclematerialinS1atthesameaxialdistance.This
simulation, this clump has not still reached the end of the
difference is in part due to the smaller total mass flux in
grid. The mean velocity of the simulated portion of the jet
S2 (see left panels in Figs. 6 and 10), caused by the lower
is not significantly reduced during the whole simulation.
7
Bosch-Ramon et al.: Clouds and red giants interacting with AGN jets
1.2 1.0
1.0
0.8
nergy Flux 00..68 Mass Flux 0.6
m. E m.
Nor 0.4 Nor 0.4
0.2 0.2
0.0
0 5.0•1013 1.0•1014 1.5•1014 2.0•1014 2.5•1014 3.0•1014 0 5.0•1013 1.0•1014 1.5•1014 2.0•1014 2.5•1014 3.0•1014
z (cm) z (cm)
-15
1.5•108
m/s) 1.0•108 3g/cm)) -20
v(cz ρ og(( -25
l
5.0•107
-30
0
0 5.0•1013 1.0•1014 1.5•1014 2.0•1014 2.5•1014 3.0•1014 0 5.0•1013 1.0•1014 1.5•1014 2.0•1014 2.5•1014 3.0•1014
z (cm) z (cm)
Fig.9. Axial cuts of different quantities for simulation S2 at t ≃ 3.1×105s, during the initial phase, before the shock
completely crosses the obstacle. The top left panel shows L −L for the jet material (solid line) normalized
j,g1 j,int,g1
to its injection value 3.5×1042erg/s, and the internal energy luminosity L normalized to its maximum value,
j,int,g1
5.6×1040erg/s (dashed line); the red solid line stands for the internal energy luminosity in the jet material, and the
blue dotted line for the internal energy luminosity in the obstacle material. The top right panel shows the mass flux,
normalized to its maximum value (4×1022g/s). The bottom left and right panels show the mean velocity and density
in the obstacle gas.
21.7
-15.5
-1s)) 21.6
Flux (g 3g/cm)) -16.0
ass 21.5 ρ g(( -16.5
M o
g( l
o
l 21.4 -17.0
21.3 -17.5
5.0•105 1.0•106 1.5•106 5.0•105 1.0•106 1.5•106
Time (s) Time (s)
Fig.10. Mass flux (left) and mean density (right) versus time for simulation S2 at z =1.5×1014 (half grid, black lines)
and 3×1014cm (end of the grid, red lines).
4.2.1. Inhomogeneous case: high resolution
SimulationS3reproducesaregionofS2withdoubleresolu-
tion, and half of its grid size along and across, resulting in
8
Bosch-Ramon et al.: Clouds and red giants interacting with AGN jets
aphysicalgridsizeof5×1013cm×1.5×1014cm.Fromthe Fig. 8 and the bottom left one in Fig. 11. When part of
results, we see that the apex pressure and temperature in the expanded material in S3 enters the rarefied regionsur-
S3areverysimilartothoseinS2.Figure11showsdifferent roundingthecylindricaltailbehindtheobstacle,itisaccel-
snapshots of the simulation, at the same instants as for S2 erated, reaching mean velocities v ≃ 109cm/s. In S2, the
c
but stopping at t ≃ 1.25×106s. At first sight, both simu- expansionoftheclumpisnotasimportant,sothepressure-
lationsfollowthe samephases,i.e.,a quasi-steadyphasein driven acceleration has a smaller effect.
which the outer layers of the obstacle are being crossed by
the shock and the mass-loss is smoothly increasing, and a
4.3. Mass-loading
secondphase,startingwhentheouterregionhasbeencom-
pletely crossed by the shock, and a large amount of gas is On the axis, the acceleration of the obstacle material is
detachedfromthecoreanddraggeddownstream.However, basically linear with distance during the initial phase in
themaindifference,whichcanonlyberelatedtothenumer- all three simulations. A simple extrapolation of the linear
ical resolution, is that this detached clump of gas is larger growthresults in 1.25×1016cmas the shortestdistance to
andproduces some widening ofthe jet-obstacle interaction accelerate the obstacle gas to ∼v in S1. Taking the mean
j
cross-section(compareFigs.8and11att≃7.9×105s),af- obstacle gas velocity, this distance becomes a factor of ten
terthewholeouterlayersoftheobstaclehavebeenshocked larger. In the case of S2 and S3, the extrapolation of the
att≃4×105s.Thus,thismaterialreceivesalargertransfer linear accelerationon the axis implies 6.5×1015cm, which
ofenergyfromthejet,andisacceleratedinamoreefficient becomes 3.25× 1016cm for S2 and 1.3×1016cm for S3,
way, reaching z = 1.5×1014cm at t ≃ 106s, compared to takingmeanobstaclegasvelocities.However,we haveseen
t≃1.4×106s in S2, as shown in Fig. 13. thatthisprocessiscriticallydependentonthewayinwhich
Figure12showsthemassfluxacrossthesimulatedgrid, themassablationisproduced.Ifablationmass-loadispro-
and the mean obstacle gas velocity anddensity, versus dis- duced at a smaller rate, the acceleration is more efficient
tance along the axis at a time similar to that in Fig. 9. We fortheablatedgas.Inaddition,iftheextractedgasclumps
haveomittedtheluminosityplotbecauseitshowsthesame widen enough to face the rarefied jet region, the obstacle
behavior in both S2 and S3. However,at the time of maxi- material can be accelerated by pressure gradients up to a
mumobstacleexpansioninS3,i.e.t≈7.9×105s,therepro- 5–10% of the jet velocity already at ∼ 1014cm, as for S1
cessedluminosityissmallerthanS1att≈1.15×106s,but andS3.ForS2,theobstaclegasdoesnotexpandenoughto
significantlylargerthaninS2.Regardingthe massflux,we favor acceleration in the rarefied jet gas region. This ma-
observethat it keeps smaller relative (and absolute) values terial is confined around the symmetry axis, although this
inS3thaninS2.ThetailisnarrowerinS3thaninS2.The seems to be an effect of numerical dissipation. We remark
mean obstacle gas density along the tail has similar values that in either case, the draggedmatter reaches z-velocities
in both simulations, as well as the temperature. However, > v /χ soon after being shocked, which confirms that it
o
the mean obstacle gas velocity presents largervelocities by will remain in the jet as long as t is at least few times
d
a factor of 2 in S3 than in S2. The smaller value of the shorter than t (see Section 2).
j
obstaclemass-lossduringtheinitialphasecouldberespon- Efficient mixing of shocked jet and obstacle material
sible for this difference, as indicated by the mean velocity could enhance acceleration (as in S1 and S3), significantly
of the obstacle gas rightat the regionof interaction,which reducing the distance needed by the entrainedgasto reach
is a factor two larger in S3 than in S2. the jet speed. When the obstacle gas expands due to heat-
Figure 13 shows the mass flux, mean density and mean ing, efficient mixing may happen as a consequence of the
velocity at z = 7.5×1013 and 1.5×1014 cm versus time. growth of instabilities that disrupt the obstacle (S1), or
NotethatadirectcomparisonbetweenS2andS3herecan- due to the obstacle material expanding into a region oc-
not be done, as the physical cross section of the numerical cupied by shocked jet flow (S3). However, if the mass-loss
grid is different in both simulations. However, Fig. 13 al- from the obstacle is too slow and/or the obstacle gas does
readygivesinterestinginformationregardingthemass-load not expand enough, all the ablated gas will flow through
process. In S3, the mass flux, which should be similar to the tail. In this case, instabilities in the layer between the
that in S2 when dominated by the outer material of the tail and the shocked jet flow would be necessary to favor
obstacle, presents smaller values during the initial quasi- mixingandsubsequentaccelerationoftheobstaclegas.On
steady phase and larger values when the aforementioned the one hand, the tail is dense and surrounded by the rar-
largeclumpisdetachedfromthecore.Thisimpliesthatthe efied shocked jet gas, which is a very stable configuration
obstacle mass-loss is slower in S3 during the initial phase in terms of Kelvin-Helmholtz or shear-layer instabilities.
and, thus, after the obstacle has been completely crossed This is so because of the large relative inertia that the tail
by the initial shock, there is still a significant amount of has under these conditions. On the other hand, any asym-
materialattachedto the core.UnlikeS3,inS2the obstacle metry in the medium surrounding the tail, which can be
mass-loss is faster initially, and when the obstacle is com- givenby inhomogeneities inthe jet orsimply by the obsta-
pletely shocked,the smaller amountof gasleft inthe outer cletransversemotion,willresultinthetriggeringofhelical
layers,when detached,is notenoughto increase the obsta- perturbationsthatareverydisruptive.Thelattercannotbe
cle cross-section. To which extent a larger increase in the observedin2Daxisymmetricsimulationsasthosepresented
resolutioncouldevenchangetheresultsfurtherinthesame here, but should appear in 3D simulations. In conclusion,
direction should be studied. the distances given in the previous paragraph for obstacle
The more efficient acceleration found in S3 and the material acceleration should be regarded as upper limits.
higher values of the mass flux relies on the expansion of The fact that they are of the order of the interaction z in
o
theobstaclegasaftert≃4×105s,asinS1.Theexpansion thiswork,∼1016 cm,likelyimpliesthatthejetwillnotget
of the obstacle gas in S3 is very different from that of S2, significantly diluted during the process and will be able to
as clearly seen comparing, e.g., the middle right panel in fully incorporate the obstacle matter.
9
Bosch-Ramon et al.: Clouds and red giants interacting with AGN jets
Fig.11. The upper panels show the same parameters as Fig. 2 for simulation S3 at time t≃5×104s. The central and
bottom panels are similar to the left ones in Fig. 2 at t≃1.6×105s, t≃4.3×105s, t≃7.9×105s, and t≃1.25×106s
from top to bottom and left to right.
1.0
0.8 2.0•108 -15
Norm. Mass Flux00..46 v(cm/s)z11..05••110088 ρ 3log((g/cm))--2250
0.2 5.0•107
-30
0
0 2.0•10134.0•10136.0•10138.0•10131.0•10141.2•10141.4•1014 0 2.0•10134.0•10136.0•10138.0•10131.0•10141.2•10141.4•1014 0 2.0•10134.0•10136.0•10138.0•10131.0•10141.2•10141.4•1014
z (cm) z (cm) z (cm)
Fig.12. Axial cuts of different quantities for simulation S3 at t ≃ 3.1 × 105s, during the initial phase, before the
shock completely crossesthe obstacle.The left panelshows the normalizedmass flux, normalizedto its maximum value,
3.7×1022g/s. The central and right panels show the mean velocity and density in the obstacle gas.
10