Backflows by AGN jets: Global properties and influence on SMBH accretion

2.2 MB·

by  S. Cielo

Mon.Not.R.Astron.Soc.000,1–16(2016) Printed22February2017 (MNLATEXstylefilev2.2)
Backflows by AGN jets: Global properties and influence on
SMBH accretion
S. Cielo1(cid:63), V. Antonuccio-Delogu2†, J. Silk1,3,4,5, and A.D. Romeo6
7
1 1 Institut d’Astrophysique de Paris (UMR 7095: CNRS UPMC ??? Sorbonne Universit´es), 98 bis bd Arago, F-75014 Paris, France
0 2 INAF/Istituto Nazionale di Astrofisica-Catania Astrophysical Observatory, Via S. Sofia 78, I-95126 Catania, Italy
2 3 Laboratoire AIM-Paris-Saclay, CEA/DSM/IRFU, CNRS, Univ. Paris VII, F-91191 Gif-sur-Yvette, France
4 Department of Physics and Astronomy, The Johns Hopkins University Homewood Campus, Baltimore, MD 21218, USA
b 5 BIPAC, Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, United Kingdom
e 6 Purple Mountain Observatory, 2 Bejing Xilu, 210008 Nanjing, China
F

1
2 Accepted??.Received??;inoriginalform20xx??

]
A
ABSTRACT
G
. Jets from Active Galactic Nuclei (AGN) inflate large cavities in the hot gas envi-
h
ronmentaroundgalaxiesandgalaxyclusters.Thelarge-scalegascirculationpromoted
p
withinsuchcavitiesbythejetitselfgivesrisetobackflowsthatpropagatebacktothe
-
o centreofthejet-cocoonsystem,spanningallthephysicalscalesrelevantfortheAGN.
r Using an Adaptive Mesh Refinement code, we study these backflows through a
t
s series of numerical experiments, aiming at understanding how their global properties
a
depend on jet parameters. We are able to characterize their mass flux down to a scale
[
ofafewkiloparsecstoabout0.5M yr−1foraslongas15or20Myr,dependingonjet
(cid:12)
3 power.Wefindthatbackflowsarebothspatiallycoherentandtemporallyintermittent,
v independently of jet power in the range 1043−45 erg/s.
5 Using the mass flux thus measured, we model analytically the effect of backflows
2 on the central accretion region, where a Magnetically Arrested Disc lies at the centre
8
of a thin circumnuclear disc. Backflow accretion onto the disc modifies its density
7
profile, producing a flat core and tail.
0
WeusethisanalyticmodeltopredicthowaccretionbeyondtheBHmagnetopause
.
1 is modified, and thus how the jet power is temporally modulated. Under the assump-
0 tion that the magnetic flux stays frozen in the accreting matter, and that the jets
7
are always launched via the Blandford-Znajek (1977) mechanism, we find that back-
1
flows are capable of boosting the jet power up to tenfold during relatively short time
:
v episodes (a few Myr).
i
X Key words: galaxies: jets – galaxies:active – methods: numerical
r
a
1 INTRODUCTION: BACKFLOW angular momentum gas, which potentially reaches down to
MORPHOLOGY AND AGN JET very small scales, contributing to the mass and energy sup-
SELF-REGULATION ply in the accretion region around the SMBH. Backflows
carry very hot, high pressure gas; they can thus heavily
The propagation of AGN jets inflates large, hot, turbulent
affect circumnuclear star formation and the properties of
cavities in the interstellar medium of their host galaxies.
theaccretion disc,as aself-regulatingfeedbackmechanism.
Circulation of gas in such cavities gives rise to pronounced
Backflows as a feature of jet-cocoon systems were already
streamsofhotgasflowingbackfromthehotspot(ifpresent,
noticed in the first simulations of the propagation of rela-
asinFRIIradiogalaxies),alongthecavityboundariestothe
tivistic jets into homogeneous atmospheres (Norman et al.
central plane.
1982),andconfirmedinmorerecentsimulations(Rossietal.
Suchbackflowsaredrivenbythethermodynamicsofthe
2008; Perucho & Mart´ı 2007). Mizuta et al. (2010) distin-
gas, and — once in the central plane — consist of very low
guish between two types of backflows, according to the dif-
ferentgeometriesoftheflowitself:astraight backflow,with
flowlinesextendingfromthetipofthehotspotbacktothe
(cid:63) e-mail:[email protected] origin, and a bent backflow, where the flow lines acquire
† e-mail:[email protected]
(cid:13)c 2016RAS
2 Cielo et al.
curvature. In early 2D simulations, precursors of what we acircumnuclear-nucleardiscextendeduptoabout100pc),
present in this work, Antonuccio-Delogu & Silk (2010) also where they may generate further inflows.
noticedtheformationofthisfeature,andthatthebackflow After this stage, this secondary inflow may enter the
evolved from a bent to a straight geometry. In that work, magnetosphere of the BH, where the dominating energy
backflow was described as large-scale vorticity created by sourceisthemagneticfield,ultimatelyresponsibleoflaunch-
sharp gradients in the thermodynamic state of the gas at ing the jets.
thehotspotandcavityboundaries,preciselyasstatedbya Throughoutthiswork,weaimtofollowbackflowsfrom
fundamental theorem of fluid dynamics, known as Crocco’s starttoend.Thisisimportantwhenweconsidertheireffect
theorem (Crocco 1937). This can be understood from the asasourceofhotgasaccretionontothecentralBH,capable
Euler momentum equation: of triggering further jet activity or increasing the power of
an already running jet in a self-regulating context.
∂v Westartfromthelargestscales(kpcorlarger)bymak-
−v×∇×v=−∇h+T∇S (1)
∂t ing use of the hydrodynamic simulations, described in Sec-
tion2andinterprettheresultsonthebasisofCrocco’s the-
HereSistheentropyandh=U+p/ρ+v2/2 isthestagna- orem. For this purpose, we will provide visual snapshots of
tion enthalpy (Cap 2001; Shu 1992). Even for a stationary the density field, as well as histograms of the gas spatial
flow,Crocco’stheoremstatesthatvorticitycanonlybecre- distribution along the z-axis (Section 3).
ated by finite gradients of enthalpy h and/or entropy S. Next, we proceed by investigating, with similar meth-
Antonuccio-Delogu & Silk (2010) pointed to the con- ods, the flow of gas which has already reached the z = 0
nection between backflows with large-scale vorticity in the plane.Inordertoquantifytheimpactparameterofthegas
cavity. The flow begins near the hot spot (HS), where a at this stage, we plot the evolution of its circularization ra-
curved shock front induces a jump in entropy and a gradi- dius and calculate the mass flux within 2 kpc (Section 4).
ent in the Bernoulli constant transverse to the shock. The We then explore the effects of this infall onto the cir-
downstream gas thus gains a vorticity (Shu 1992), and its cumnuclearregion,notresolvedinoursimulations,assuming
flow is then confined between the dense and hot bow shock that the innermost magnetized structure is a Magnetically
from the outer side, and the hot turbulent cavity gas from Arrested Disc (Section 5).
the inner side. Finally,inSection6wedevelopsomequantitativecon-
Thisgoesonuntilthegasfallsbacktothecentralplane siderations of how the processes described above influence
andfollowsthecavityedge(orcollideswithmirrorbackflows the rate of mass accretion onto the central SMBH and the
in a bipolar jet) falling down towards the jet origin with productionofthejetitself(viatheBlandford-Znajekmech-
very low impact parameter (and thus angular momentum), anism from Blandford & Znajek 1977).
although its inflow velocities reach up to several hundreds
km s−1.
In three dimensions, however, this mechanism loses
2 SETUP AND SIMULATION DESCRIPTION
some effectiveness, as with the additional degree of free-
domthevelocitycouldbedirected(inabsenceofothercon- We run our simulation using the hydrodynamic, Adap-
straints)anywhereinthez=0plane.Also,theflowissub- tive Mesh Refinement (AMR) code FLASH v. 4.2 (Fryxell
ject to more effective hydrodynamic instability, which can et al. 2000). In our computational setup, we solve the non-
slow and disrupt it. relativisticEulerequationsforanidealgaswithspecificheat
In previous 3D simulations, Cielo et al. (2014) showed ratio γ = 5/3 (see Appendix A for more details). In order
that despite the unarguably reduced efficiency, substantial to properly model the energetic of the system, we include
backflows(alwaysaround1M(cid:12)yr−1)reachthecentralfew a static, spherical gravitational potential of the host dark
hundredparsecs.Thedurationofsuchbackflowsvarieswith matter halo (following a NFW profile), as well as the self-
jet power (higher powers move cavities away from the cen- gravity of the gas. This set-up is an evolution of that used
tre at earlier times, killing backflows), but always encom- in Cielo et al. (2014) — henceforth C14.
passesafewMyr.Furthermore,thebackflowgaswasfound Wechooseacubic3DcomputationaldomainandCarte-
to be stable against hydrodynamics instabilities, although sian coordinates. The side of the box is in all runs fixed to
the simulations covered just the first few million years. L=640 kpc, much larger than the maximum extent of the
Observations of backflows have been quite challenging jets, in order to encompass most of the halo, whose typi-
for a long time, as the gas is hot but very sparse, and only cal size R is ∼ 250 kpc. The resolution, defined as the
200
mildlyrelativistic,soeasilyoutshinedbythejets.However, size of the smallest computational element, is in all cases
observationalcharacterizationofbackflowshasrecentlybeen fixed to ∆r = 78.125pc (see Appendix A). All the bound-
emerging;inparticularLaing&Bridle(2012)observedback- ary conditions are set to the FLASH outflow (i.e. zero-
flows in two low-luminosity jetted radio-galaxies. In partic- gradient) default value. We present two families of runs,
ular, a mildly backflowing component around the lobes is mainly differing in jet power P . In both series, the dark
jet
needed in order to fit the emission and polarization radio matter halo density follows a spherical NFW profile with
maps. R = 0.25 Mpc, M = 1.71×1012M and a concen-
200 200 (cid:12)
AGN are multi-scale systems, and as the backflows get tration parameter c = 7.8 (Dutton & Maccio` 2014). We
200
to closer to the central BH, they experience all the rele- then fill this potential well with hot coronal gas, having a
vant physics at different scales (Antonuccio-Delogu & Silk uniform temperature T and metallicity ([Fe/H] = -1.0) in
0
2007): after the thermodynamics-dominated circulation in hydrostatic equilibrium within the dark matter potential.
thecavities,theywillcollidewithacentralstructure(likely, We achieve the latter condition by adopting the following
(cid:13)c 2016RAS,MNRAS000,1–16
Backflows in cocoons 3
Simulation Halo Jet Backflowingmass
(atgiventime)
Name Resolution tmax M200 tcool,0 Pjet Mjet ∆tjet m˙ p˙ Total central
[pc] [Myr] [M(cid:12)] [yr] [erg/s] [Myr] [M(cid:12)/yr] [M(cid:12)/yrkm/s] [M(cid:12)] [M(cid:12)]
Elongated Cavity series
EC42 78.125 473 1.7×1012 6×108 1042 5 79 0.0088 167.22 4.84×105 1.28×104
20Myr 20Myr
EC43 78.125 140 1.7×1012 6×108 1043 5 42 0.0190 776.15 4.69×105 7.11×103
10Myr 10Myr
EC44 78.125 115 1.7×1012 6×108 1044 5 21 0.0409 3603 9.92×105 1.9×104
7Myr 7Myr
Round Cavity series
RC44 78.125 23.1 2.6×1012 4×108 1.12×1044 5 5.37 0.0237 2900 6.90×104 1.04×105
10Myr 10Myr
RC45 78.125 22.2 2.6×1012 4×108 1.12×1045 5 5.37 0.0510 13461 4.84×104 6.80×104
8Myr 8Myr
RC46 78.125 22.2 2.6×1012 4×108 1.12×1046 5 5.37 0.1098 62548 2.71×105 4.34×104
7Myr 7Myr
Table1.Parameters,timingsandbubblecharacteristics.Allsimulationparameters:runspecifications(name,smallestcellside,simula-
tiontime),haloparameters(mass,centralcoolingtime),jetparameters(powerofeachofthetwojets,Machnumber,lifetime,massand
momentuminjectionfluxes)andtotalbackflowgasmassatthegiventime(i.e.thetotalmassinthebackflowregionisolatedinFigures
2to??).
constant temperature profile, introduced by Capelo et al. rounder cavities than their EC counterparts for three rea-
(2010): sons:
(cid:18) (cid:19)
[Φ(r)−Φ(0)] • theyareintrinsicallyhotter,astheyaremorepowerful(i.e.
ρ (r)=ρ exp −µm (2)
g 0 p k T faster)butatinjectiontheyhaveallthesameinternalMach
B 0
number M =5(inotherwords,theMachnumberrelative
where µ is the mean molecular weight of the gas, Φ(r) the jet
to the environment changes).
gravitationalpotentialandk theBoltzmannconstant.For
B • the core of the halo in which they propagate is slightly
the normalization, we follow McCarthy et al. (2008) in set-
colder;
ting the ratio of gas to dark matter mass within the halo
• theythermalizealargerpartoftheirtotalenergy,asmore
R to0.85timesthecosmicbaryonfraction(takeninturn
500 powerful jets have shorter lifetimes, and thermalization is
from Komatsu et al. 2011). Once the normalization of the
more efficient at early stages.
gas profile is fixed, the gas properties are thus completely
specifiedbythechosenT0,oralternativelybythegascentral The jets are modelled by injecting gas in the central
cooling time, which we report in Table 1 (column 5). region for a prescribed lifetime. The injection power, mass
The first family is the EC series (for Elongated Cav- and momentum flux are also reported in Table 1 for each
ities), where the DM halo has a mass fixed to 1.7 × run (columns 6, 9 and 10, respectively); a given kinetic
1012M and a central cooling time of 6×108 yrs. For this power also corresponds to a specific lifetime ∆t (column
(cid:12) jet
series, we launch three runs, differing only in the jet me- 8 of Table 1). In the EC series, backflows on the central
chanicalpowerP ,whichassumesvaluesof1042,1043 and plane significantly fade before the end of the jet’s active
jet
1044 erg/s (run EC42, EC43 and EC44, respectively). The phase; in the RC series, however, there are residual back-
second series (denoted the RC series, for Round Cavities), flows even after the jets are switched off. In some cases the
differsfromtheECseriesmostlyinthatitfeaturesahigher injection velocities resulting from these parameters choices
halo mass, a slightly shorter cooling time (a consequence are slightly superluminal. The ram pressure of the local en-
of a denser hot gas phase) and higher values of P (runs vironmentwherethejetemerges,however,bringsthejetto
jet
RC44,RC45andRC46;seeTable1foracompletelistofall non-relativistic velocities in the first few cells1. The overall
parameters). jet/Hot Spot advancement velocity is however much slower
The dependence of the cavity’s shape on the jet/halo thanthat(maximumabout1.5×104km/s,Figure1),sothis
physical parameters was previously investigated in C14. high nominal injection speed does not affect the evolution
Briefly, the cavity shape is linked to these parameters via of the cavities.
thejet’sthermalpressure:ajethavinghigherthermalpres- The jets advance through the Interstellar Medium
sure(orpropagatinginacolderenvironment)willoriginate
rounder cavities as the over-pressure determines isothermal
expansion; on the contrary a cold jet with a small ratio be- 1 Wehadalsotriedincreasingthejet’scrosssectionandlowered
tween internal and kinetic pressure will inflate elongated the velocity to keep the injected power constant, but the results
cavities. This being said, in our case the RC jets create areindistinguishableaftersufficientlylongtimes.
(cid:13)c 2016RAS,MNRAS000,1–16
4 Cielo et al.
100 20
EC42 RC44
EC43 RC45
80
EC44 15 RC46
] ]
c 60 c
p p
k k
[ [ 10
x x
a 40 a
m m
z z
5
20
0 0
0 50 100 150 0 10 20 30
t [Myr] t [Myr]
Figure 1. Location of the bow-shock (i.e., jet advancement) with time. LEFT: EC (for Elongated Cavities) series. RIGHT: RC (for
Round Cavities) series. Velocities are of order 1000 km/s in most cases, although the highest power jets of each series can reach up to
tenfoldhighervelocities,e.g.EC44beforethejetswitchesoff).
(ISM), initially producing a hot, localized shock in the Hot a cleaner flow, as backflows are otherwise contaminated by
Spot (HS)andabow-shockregion,accordinglytotheprevi- gaspatchesthat‘bounce”onthecavitywalls.Whilethisis
ous findings of C14. In Figure 1 we show the location z contemplatedinourCroccotheoremdescription,theresult-
max
of the bow-shock region, simply defined as the geometrical ing velocity field shows many spurious features. The con-
extent along the jet axis of the hot spot; this gives an idea straintswecanputonthemassflowswiththisanalysisare
oftheactualadvancespeedofthejetsandoftheireffecton for this reason only lower limits.
the hot gas. We set an additional threshold on theradial (w.r.t. the ori-
The jets expand up to a maximum z-distance ranging gin) velocity: v (cid:54) −225 km/s. This is to exclude coherent
r
from a few tens up to about 100 kpc in the EC runs (with cooling flows (or occasional highly-turbulent spots) at late
a clear turnover when the jets are switched off), while they times; this selection does not significantly change the back-
reachabout20kpcintheRCones,mainlyduetotheshorter flow mass at the epochs considered in this study.
simulation time. In any case, in this work ,we focus on the Coolingflowshowevercandevelopafterabout50or100
first few tens of Myr, as backflows arise at these times. Myr, i.e.later than thetime intervals during which thejets
areon.Adiscussionofthecoolingflowsisoutsidethescope
of this paper; as we see from the slices shown, backflows
reachhighvelocities(often(cid:54)−2500km/s)sothisselection
3 GALACTIC-SCALE BACKFLOWS AROUND
does not exclude any significant part of the backflows even
CAVITIES
at late times.
ThepredictionofCrocco’stheoremthatbackflowsoriginate
Finally,wecutouttheinnermost±2kpcofgasfromthe
fromtheHSandthenflowalongthelobe/bubbleboundary
cavity selection (Figure 2 and 3), which will be the object
isverifiedinthesimulationsrun,ascanbeseenbylookingat
of Section 4 (as one can see from Figure 4 and 5).
Figures2and32,whereweshowvisualslicesofthedensity
The backflows initially appear as thin layers contained
field along the y = 0 plane (left columns). The backflows
within the cavity/dense-shell interface (left panels in fig-
followadifferentcolourscheme(colourlegendontheright),
ures 2 and 3); thus in 3D these flow layers wrap the en-
inordertohighlightthemwithintheircontextinthecocoon;
tire inner cavity. Since the cavities at this stage reproduce
thebackflowregionisalsorecognizableasitistheonlyone
thelobesobservedinradio-galaxies(seeC14),backflowscan
where the velocity field is superimposed3.
appear around most 10−20 kpc galactic radio-lobes. After
We define the backflow regions to include all grid cells
10−20Myr,thecocoondevelopsaninternalstructure:the
whose velocities point towards the jet origin within a ±45
lobes detach from the central plane, and leave a gap filled
degrees cone.
by denser gas. Following C14, we call this the lobe phase.
This(ratherconservative)selectionisnecessarytoview
During this phase, turbulence develops as a consequence of
shocks and shearing between the different gas layers, which
createsturbulenteddiesthroughKelvin-Helmholtz(KH)in-
2 Some animations of the simulations are available from
stabilities.
https://blackerc.wordpress.com/people/salvatore-cielo/
3 SeethecolourlegendatthebottomofeachpanelintheFigure Thelarge-scalebackflowsareaffectedbythisstructure,
forthemagnitudesofthearrows. and can converge back to the jet axis following the bubble
(cid:13)c 2016RAS,MNRAS000,1–16
Backflows in cocoons 5
800
EC42 20 Myr
EC42 40 Myr
600
]
3
-
c
p
k
400
M
[
fb
200
800
EC43 10 Myr
EC43 30 Myr
600
]
3
-
c
p
k
400
M
[
fb
200
800
z [kpc]
EC44 7 Myr
EC44 14 Myr
600
]
3
-
c
p
k
400
M
[
fb
200
0
0 10 20 30
z [kpc]
Figure 2. LEFT: 40x80 kpc number density slices (in cm−3)
along the y = 0 plane for the EC runs (increasing power from
top to bottom, increasing time from left to right). The backflow
regions(v·rˆ(cid:54)0)arehighlightedingreen(colourpaletteonthe
top-rightofeachplot),andhavethevelocityfieldsuperimposed
(velocityisgiveninkm/sandfollowsthebottomcolourlegendof
eachpanel).RIGHT:densityhistograms(withafixedbinampli-
tudeof500pc)ofthez-distributionofthesamebackflowinggas;
i.e.thetotalmassoverthetotalvolumeofthepartofthegreen
regionthatfallsineachbin(inM(cid:12)kpc−3).Runnameandtime
areindicatedineachpanel.Notehowbackflowsmovefartherout
thecentralregionwithincreasingtime.
(cid:13)c 2016RAS,MNRAS000,1–16
6 Cielo et al.
400
RC44 10 Myr
RC44 20 Myr
] 300
3
-
c
p
k
200
M
[
bf
ρ 100
400
RC45 8 Myr
RC45 15 Myr
] 300
3
-
c
p
k
200
M
[
bf
ρ 100
400
z [kpc]
RC46 7 Myr
RC46 15 Myr
] 300
3
-
c
p
k
200
M
[
bf
ρ 100
0
0 10 20 30
z [kpc]
Figure 3.SameasFigure2fortheRCruns.Thecontoursshow
numberdensitycentral(y=0)slicesofthetotalandbackflowing
gas,andcorrespondingdensityhistogramsalongthezaxis.The
RC series has rounder cavities, but also higher jet power and
shorter lifetimes. Total mass and duration of backflows in the
lobesarereducedcomparedtoECseries(notethereducedscale
on the y axis). The path of the backflows changes too, since it
followsmorecloselythecavity’sshape.
(cid:13)c 2016RAS,MNRAS000,1–16
Backflows in cocoons 7
boundaries (right panels in Figure 2 and 3). In their path, Asforthetotalgasmassaccumulatedatthecentre,itseems
they also take part in the cocoon’s turbulent motion, both tobeapproximatelyconstant(about5×105 M intheEC
(cid:12)
near the HS and along the shearing cavity boundary; they case,5×104 M intheRCcase),exceptforthemostpow-
(cid:12)
alsocontributetogeneratetheshear,astheyinitiallyconsist erful(andshortest-lived)jetevents,inwhichitincreasesby
oflaminarflowsinrelativemotionwithrespecttoboththe a large factor (about 2 and 5, respectively).
inner cavities and the outer bow-shock.
TheseaspectswereanalysedbyC14andtheflowswere
found to be stable against KH instability4. Regardless of
4 KILOPARSEC-SCALE BACKFLOWS ON
how much they contribute to the generation of turbulent
THE CENTRAL DISC
motions,thebackflowsareperturbedandfragmentedbyit:
onecanclearlyseepatchesofcoherentinwardradialvelocity Wenowturnourattentiontothecentralregion.InFigures
in Figure 3, more prominent at later times (panels on the 4 and 5 ,we plot density slices along the z =0 plane, again
right)andwithintheinnermost∼5kpc,wherethecavities with backflowing gas highlighted, and with velocity arrows
start to detach from the centre. superimposed.
Thebackflowscangainvorticityandmomentumattwo Thebackflowinthecentralplaneismoreregularduring
differentsites:firstattheHS,wheretheystarttheirjourney thefirstfewMyr,andmorepatchyafterwards,participating
around the lobes, and later near the z = 0 plane, since in the turbulence of the cocoon gas that affects the entire
after the lobe phase backflows must bend again, this time cavity.Inthiscase,themasstransportissignificantevenfor
following the jet beam chimney that connects the lobe to the low power jets. There is more mass involved in central
the jet origin. disc backflows in the RC runs than in the EC series (see
Nearthecentralregion,thebackflow followsinsteada Table1,lastcolumn)notablydifferentfromwhatisseenfor
ratherstraightpattern.Themassofthegasinvolvedinthe the cavity-wide backflows described in Section 3.
backflows (Table 1, column 12), as well as the time it takes Duetoaxialsymmetry,weexpectthatthebackflowing
togetbacktothecentralplanedependonthecavityshape gas in the central disc should have on average little to zero
andsize,andonthehotspotpressure(enthalpy)whichgives angular momentum, and thus flow directly towards the BH
the initial kick. accretion disc.
After a sufficiently long time, the HS are usually too In order to test this prediction, we need to trace the
far away from the centre, and the backflows stop halfway. angular momentum of the gas. In Figures 4 and 5 (right
A few Myr after the jet has been switched off (t (cid:62) ∆tjet) panels), we plot the evolution of the circularization radius
, the lobes turn into roughly spherical bubbles and detach —aproxyforangularmomentum—withinasmallcentral
completely from the centre. We refer to this stage as the cylindrical selection.
bubble phase. At this time, cooling flows can occur near the LetLbethemodulusofthespecificangularmomentum
z=0plane.Anyresidualbackflowswillthencease;however vectorofagasparcelinacomputationalcell.Wedefinethe
analogous circulation patterns will persist in the bubble for circularizationradiusr astheradiustheparcelwouldhave
c
all its lifetime (bubbles from light, supersonic jets such as if it were on a circular orbit within its host Dark Matter
thesecreatevortex-ring-shapedcavities;seee.g.Guo2016). halo:
L2
IntheECruns,large-scalebackflowsaremoreextended r = (3)
c GM(r )
and carry more mass; although the jet power is on average c
lesser, it can drive the gas around the cavities efficiently HereM(r)isthemassofdarkmatter5 withinr.Theevalu-
(also because jet lifetimes are correspondingly longer). ationofequation3isparticularlysimpleasourdarkmatter
In the RC runs instead, the presence of more spheri- halo is spherically symmetric, thus it is straightforward to
cal cavities forces streamlines to gain more curvature since find the implicit solution of equation 3. In using the full
thestart,untiltheyreachthez=0plane.Alsotheflowap- modulus of the 3D angular momentum of the gas in each
pearsmorefragmentedintheRCcase,asmoredisconnected cell L, rather than its z-component only (L (cid:54) L), we are
z
patchesareclearlyvisibleintheslices.Thisisprobablydue making a conservative estimate.
totheincreasedturbulenceinthecocoonenvironmentgen- We evaluate r for all the gas cells of the backflowing
c
eratedbyhotterandmorepowerfuljets.Suchpatcheslinger gas only, selected with the same velocity threshold as in
for up to about 10 Myr near or within the central plane. Section 3. This time though we select a cylinder centred on
In order to estimate the backflow location and mass trans- the jet origin and having 2 kpc radius in the xy plane, and
port, in Figure 2 and 3, we add density histograms of the a thickness of about 300 pc (four simulation cells in total)
backflowing gas distribution along the z-axis, for the same along the z axis. The mass-weighted average value of r is
c
snapshots shown in the slices; the total mass in the region plotted for each snapshot time (thick lines in the plots of
for the first snapshot is also reported in Table 1. In many Figures4and5)togetherwiththeminimumandmaximum
ECruns,oneseesthatinitiallythedistributionextendsback values in the selected region (shaded area around the lines)
to the first central few kpc and then moves farther away at and a 2 kpc line (in black). In general, gas having r < r
c
latertimes.ThisislesstruefortheRCruns,althoughover- willalwaystendtomigratetosmallerdistances,thusfalling
all the mass involved is smaller by a factor 5 or 10. towards the central BH. In this case, we can conclude that
4 In C14 the resolution was slightly better than in the present 5 Weneglectself-gravityofthegas,althoughitisaccountedfor
work,howeverthesimulationslastedonly∼6Myrorless. inthesimulations
(cid:13)c 2016RAS,MNRAS000,1–16
8 Cielo et al.
4
EC42
Range
3.5 Mean
2 kpc
3
2.5
]c
pk 2
[
c
r
1.5
1
0.5
0
0 5 10 15 20 25 30
t [Myr]
15
EC43
Range
Mean
2 kpc
10
]c
p
k
[
c
r
5
0
0 5 10 15 20 25 30
t [Myr]
15
EC44
Range
Mean
2 kpc
10
]c
p
k
[
c
r
5
0
0 5 10 15 20 25 30
t [Myr]
Figure4.LEFT:Gasdensityslicesalongthez=0plane;similar
to Figure 2, but for the gas in the central region. RIGHT: time
evolutionofcircularizationradiusrcofthegaswithinthecontrol
cylinderofradius2kpcandheight0.2kpcasmass-average(thick
lines)andmin-maxrange(shadedarea).Largebackflowvolumes
oftenshowrc<2kpc(blackline).Valuessmoothedforclarity.
(cid:13)c 2016RAS,MNRAS000,1–16
Backflows in cocoons 9
25
RC44
Range
Mean
2 kpc
20
15
]c
p
k
[
c
r
10
5
0
0 5 10 15 20 25 30
t [Myr]
25
RC45
Range
Mean
2 kpc
20
15
]c
p
k
[
c
r
10
5
0
0 5 10 15 20 25 30
t [Myr]
35
RC46
Range
30 Mean
2 kpc
25
20
]c
p
k
[
rc15
10
5
0
0 5 10 15 20 25 30
t [Myr]
Figure 5. Same as figure 4 for the RC run family (notice also
the different vertical scale); qualitatively, the results are similar,
asthereisalwayssomegaswithlowrc,althoughmostoftenthe
mass-averagedrc islargerthan2kpc.
(cid:13)c 2016RAS,MNRAS000,1–16
10 Cielo et al.
allgasparcelshavingr <2kpcwillalwaysstaywithinthe 1.5
c
selection. EC42
In almost all runs, the average of r stays above the
c EC43
2kpcline:weinterpretthiscircumstanceasarisingfromthe
EC44
fact that backflows have quite high characteristic velocities
]
that do not necessarily have a negligible impact parameter, y
1
thus resulting in some floor values for L and r . A note- /
c
worthyexceptionisrunEC42,inwhichbackflowsreachthe
centralregionafter10Myr,whilelatertheaverager stays M
c
[
alwayswellbelow2kpc.Onthecontrary,inbothEC43and
t
d
EC44 they grow smoothly up to a relatively early peak at /
5 kpc around 7 Myr then decline back to 2 or 3 kpc. lc0.5
M
From the figures we can draw up two general conclu-
d
sions:
• There is always backflow with r < 2 kpc, as the shaded
c
area always extends down to almost zero.
• Statistically,thereisalwaysasignificantmassfractionable
to migrate to smaller radii at all times. 0 10 20 30
t [Myr]
About the second point, although flow masses are not in-
dicated in the figures, we see from Table 1 that the total 1.5
values are around 104 M or a few times that. Note also RC44
(cid:12)
that angular momentum is not necessarily conserved in the RC45
small-scale flows. It could be dissipated through viscosity, RC46
or again through the thermodynamic action described by Model
Crocco’stheorem,aspatchesorstreamsofgasfromthethe
y] 1
oppositesidesofthebipolarjetcollideinthez=0plane,as /
inthe2D-simulationsbyAntonuccio-Delogu&Silk2010;in
support of this, the average r clearly decreases with time. M
c
Thus the values in Figures 4 and 5 are just upper limits on dt [
RC. /
d
In Figure 6 we show the mass flux6 through the same M 0.5
d
cylindrical region used to estimate r .
c
We consider only the net flux through the side surface
of the cylinder, as in most cases the flux through the bases
is dominated by the jet outflow. This selection may miss
some of the bent backflows at the lobe base, thus also in
this respect we are just putting lower limits to the mass 0
0 10 20 30
flux.
The flows in Figure 6 start with negative values (i.e. t [Myr]
there is net outflow, not plotted) due to the predominance
of the jet outflow, which still pushes the initial dense envi- Figure 6.Massfluxthroughacylindricallayeraroundthecen-
ronment gas outwards for the first 5−10 Myr. tral region, radius 2kpch−1, height 0.2kpch−1. The coloured
All RC runs present several flux peaks between 5 and curves are for the EC runs (top) and the RC runs (bottom), as
15Myr,reachingabout1M /y;thesepeaksoriginatedfrom indicatedbythekey.Themassfluxishigherbyafactorofafew
(cid:12)
in the RC case. The black curve is a model backflow mass flux
the patchy nature of the backflows, but in the RC44 and
inspired by the RC simulations; this is the model we will adopt
RC46cases,wecanseeabackgroundfluxofabout0.5M /y
(cid:12) asmassflowprofileinSection5.
until 15 or 20 Myr. As noted in C14, similar values could
indeedprovidesubstantialcentralgasaccretion,whichcould
contribute to establish a jet self-regulation mechanism; this 5 PARSEC-SCALE BACKFLOWS AND
is the subject of Section 5. ACCRETION DISC KINEMATICS
Incomparison,backflowsintheECcaseinvolvemasses
In order to estimate the impact of the backflow on the ac-
smaller by a factor of a few (around 0.25M /y. They also
(cid:12) cretion region, in this section we present a model of the
tendtopeakatlatertimes(10to30Myr),possiblybecause
backflow-accretiondiscinteraction,whichextendstheanal-
oftheirdifferentmorphologywhichmakesthebackflowgas
ysis to scales too small to be reproduced in our numerical
traversealargerdistancebeforeapproachingthecentralre-
experiments.
gion.
Inthismodel,thecentralaccretionregionisassumedto
host a magnetically arrested disc (hereafter MAD, see Fig-
ure7).TheMADoccupiesasmallregionaroundthecentre
of a circumnuclear-nuclear disc in the z = 0 plane, around
6 Inournotation,apositivefluxmeansinflow which the backflows accumulate.
(cid:13)c 2016RAS,MNRAS000,1–16