Precessing jets and X-ray bubbles from NGC1275 (3C84) in the Perseus galaxy cluster: a view from 3D numerical simulations
D. Falceta-Goncalves, A. Caproni, Z. Abraham, D. M. Teixeira, E. M. de Gouveia Dal Pino
aa r X i v : . [ a s t r o - ph . C O ] M a r Precessing jets and X-ray bubbles from NGC 1275 (3C 84) in thePerseus galaxy cluster: a view from 3D numerical simulations
D. Falceta-Gon¸calves1, A. Caproni1, Z. Abraham2, D. M. Teixeira2 and E. M. de GouveiaDal Pino2 [email protected]
ABSTRACT
The Perseus galaxy cluster is known to present multiple and misaligned pairsof cavities seen in X-rays, as well as twisted kiloparsec-scale jets at radio wave-lengths; both morphologies suggest that the AGN jet is subject to precession.In this work we performed 3D hydrodynamical simulations of the interaction be-tween a precessing AGN jet and the warm intracluster medium plasma, whichdynamics is coupled to a NFW dark matter gravitational potential. The AGNjet inflates cavities that become buoyantly unstable and rise up out of the clustercore. We found that under certain circumstances precession can originate multi-ple pairs of bubbles. For the physical conditions in the Perseus cluster, multiplepairs of bubbles are obtained for a jet precession opening angle > ◦ acting forat least three precession periods, reproducing well both radio and X-ray maps.Based on such conditions, assuming that the Bardeen-Peterson effect is domi-nant, we studied the evolution of the precession opening angle of this system.We were able to constrain the ratio between the accretion disc and black holeangular momenta as 0 . − .
4. We were also able to constrain the present pre-cession angle to 30 ◦ − ◦ , as well as the approximate age of the inflated bubblesto 100 −
150 Myrs.
Subject headings: galaxies: clusters: individual: Perseus — galaxies: jets —methods: numerical N´ucleo de Astrof´ısica Te´orica, Universidade Cruzeiro do Sul - Rua Galv˜ao Bueno 868, CEP 01506-000,S˜ao Paulo, Brazil Instituto de Astronomia, Geof´ısica e Ciˆencias Atmosf´ericas, Universidade de S˜ao Paulo, Rua do Mat˜ao1226, CEP 05508-900, S˜ao Paulo, Brazil
1. Introduction
The powerful radio source 3C 84 is associated to the elliptical galaxy NGC 1275 ( z =0 . . × years andsemi-aperture angle of about 50 ◦ (Dunn, Fabian & Sanders 2006, and references therein).The interaction between AGN jets and the intracluster medium (ICM) has already beenstudied in numerical simulations. Scannapieco & Bruggen (2008) and Bruggen, Sccanapieco& Heinz (2009) studied the evolution of pre-set hot gas bubbles and their role in the dis-tribution of energy in galaxy clusters. Heinz et al. (2006) implemented a self-consistentprocedure by means of AGN jets, though failing in inflating bubbles as observed. Typically,the narrow, relativistic and nonprecessing jets carve the ICM hot gas and release most of itsenergy far from the central region of the system (Vernaleo & Reynolds 2006, O’Neill & Jones2010), an effect known as “dentist drill”. Sternberg et al. (2007) showed that wide jets,with opening angles > ◦ , are able to transfer momentum into a larger area resulting in theinflation of fat bubbles. The same physical properties, however, are expected in precessingAGN jets (Sternberg & Soker 2008a). Large precession angles sustained for long periods canbe able to inflate cavities as observed in the Perseus galaxy cluster.In this work we present a number of hydrodynamical 3D numerical simulations takinginto account the evolution of precessing jets, and study the inflation of cavities that canreproduce the observed emission maps of NGC 1275 at radio and X-rays. We assume in thiswork that the jet precession evolution is due to the Bardeen-Peterson effect. The model isdescribed in Section 2, as well as the numerical setup. In Section 3 we present the main resultsand the comparison between the synthetic and observed features in NGC 1275, followed bythe conclusions.
2. The model
The basic idea of this work relies on the fact that a precessing jet, originated in thecentral region of NGC 1275, interacts with the intracluster gas resulting in the inflationof bubbles. These may rise outward of the cluster core, while new bubbles are constantlyformed and grow at different position angles due to jet precession.Several processes may lead to jet precession, such as magnetic torques, warped discs 3 –and gravitational torques in a binary system (Pizzolato & Soker 2005). In this work, weattributed jet precession to the Bardeen-Petterson torques acting on the viscous accretiondisc that originates the jet, which must be tilted with relation to the equatorial plane of thecentral Kerr black hole (Bardeen & Petterson 1975). In fact, since the origin of the accretiondisc is probably related to merging processes, it is very unlikely that the BH and the infallingmaterial momentum are perfectly aligned, making the Bardeen-Peterson effect a probableprecessing mechanism in such an environment. This effect also induces the alignment of thedisc and the black hole angular momenta, explaining the presence of twisted jets in severalobserved AGNs (Liu & Melia 2002, Caproni et al. 2004, 2006, 2007, Fragile & Anninos 2005,Martin, Pringle & Tout 2007, Chen, Wu & Yuan 2009).Under the approximation of a constant surface density accretion disc, Scheuer & Feiler(1996) showed that, for small misalignment angles, its time evolution results in an exponen-tial decay of the precession angle ϕ ( t ) in timescales of the order of the precession period.However, King et al. (2005) pointed out that this behavior is not universal, and more com-plex time evolutions could be obtained for different disc structures. Assuming the totalangular momentum vector, defined as J T = J BH + J D , being respectively J D and J BH thedisc and black hole angular momenta, is fully conserved, King et al. (2005) derived theequation that rules the time dependency of ϕ ( t ): ddτ (cos ϕ ) = ± sin ϕ s(cid:18) J T J BH (cid:19) − sin ϕ, (1)where τ = t/T prec , T prec is the precession period and the ’+’ and ’-’ signs correspond, re-spectively, to the alignment and counter-alignment of the involved angular momenta vectors.Notice that ϕ = arccos[( J BH · J D ) / ( J BH J D )] is the angle between the disk and the black holeangular momenta, while ϕ D = arccos[( J T · J D ) / ( J T J D )] represents the angle between the diskand the total angular momenta. Since J T is constant, from Eq.(1) it is possible to obtainthe time evolution of both ϕ and ϕ D . In order to simulate the inflation of the observed cavities detected in X-rays, as well asthe jet geometry observed at radio wavelengths, we performed a number of hydrodynamicalsimulations that provide the evolution of the jet interaction with the ICM, as well as theformation of the bubbles.The model was implemented in a well-tested Godunov scheme, in which we integrate 4 –the full set of hydrodynamical equations in conservative form (Falceta-Gon¸calves, Kowal &Lazarian 2008, Burkhart et al. 2009 and Le˜ao et al. 2009). The radiative cooling modulewas computed independently, as we calculate ∂P∂t = (1 − γ ) n Λ( T ) after each timestep, where n is the number density, P is the gas pressure, γ the adiabatic constant and Λ( T ) is theinterpolation function from an electron cooling efficiency table for an optically thin gas (Gnat& Sternberg 2007).The external gravity was introduced through a fixed distribution of dark matter follow-ing the NFW profile (Navarro, Frenk & White 1996), ρ DM ( r ) = ρ s ( r/r s )(1 + r/r s ) , (2)where r s represents the characteristic radius of the cluster, ρ s = M s / (4 πr s ) the mass density,and M s the absolute mass within the radius r s . From isothermal pressure equilibrium the gasdensity may be described by n ( r ) = n [cosh( r/r s )] − . This equation represents the initialdensity distribution for all runs. The temperature was initially set as uniform, being T = 10 K. As initial setup for the simulations we used an initial core density n = 5 × − cm − and r s = 30 kpc, which resulted in a profile similar to the empirical density distribution (Sanderset al. 2004). The computational domain corresponded to three dimensional (3D) cubeswith physical size L = 100 kpc in each direction. The cubes were homogeneously dividedinto fixed 256 and 512 cells, the later corresponding to ∼ . v jet = 20 c s (which corresponds to ∼ km s − ) in both opposite directions of the jet that forms anangle ϕ D ( t ) with respect to the x-axis of the cube, which coincided with the total angularmomentum of system. The geometry of the simulated jet is cylindrical, i.e. the velocityfield of the launched jet is uniform. The temperature is set as T jet = 10 T , and the density n jet = 0 . n , resulting in a total mass loss rate of ∼ . ⊙ yr − and a total kinetic power of L kin = 10 erg s − . The assumed geometry is shown in Fig. 1. The total angular momentumof the system J T , i.e. the precession symmetry axis, is set in the x direction. The jet precessesaround the x-axis with an opening angle ϕ D and an angular velocity ˙ θ = 2 πT − . Initially,we set θ = 0.In the simulations, the precession period is assumed to be constant as T prec = 5 × yr,close to the value of 3 . × yr obtained by Dunn, Fabian & Sanders (2006). We run severalmodels for different initial precession angles ϕ D (0) to study its role on the formation ofbubbles. 5 –As discussed above, the behavior of ϕ D ( t ) depends mostly on the ratio of the angularmomenta of the disc and BH. Since this value is unknown, we have initially assumed in thesimulations an alignment law ϕ D ( t ) ∝ exp( − t/τ ∗ ), following Scheuer & Feiler (1996), andvaried τ ∗ , according to the values in Table 1, except for Model
3. Results
From the simulated data, obtained under the assumption of exponential decay for ϕ D ,assuming the gas to be optically thin we constructed X-ray emission maps for different linesof sight. In this case, the X-ray emission can be represented by the emission measure,defined as the integral of the squared density along the line of sight ( EM = R n ds ), anddirectly compared to the observations. Once the synthetic emission maps for all models werecalculated, it was possible to visually recognize the morphological structures formed up to t = 4 T prec .As main result we found that only models with ϕ D (0) ∼ ◦ and τ ∗ > . ϕ D (0) result in single pairs of bubbles, being their widthsproportional to ϕ D (0). Also, models with ϕ D (0) = 60 ◦ but τ ∗ < . cooling flow ) isobserved (see Falceta-Gon¸calves et al. [2010], for details). At later stages, as more energyis released by the AGN, this flow is reversed and an outward flux of ∼ − is seen at t = 3 T prec = 150Myr. The temperature gradient of the ICM, however, is still present, asdiscussed below.In Fig. 2 we show Y-Z central slices of model t = 3 T prec .The density cut (left pannel) clearly shows the existence of two disconnected bubbles. Thedensity profile across the bubble shell reveal a density contrast ρ peak /ρ ICM ∼ .
7, similar tothe values obtained by (Sternberg & Soker 2009). This ratio corresponds to 2 . t = 2 T prec ,and 3 .
26 at t = 1 T prec . Adiabatic strong shocks result in density enhancements of ∼
4. Thisfactor can be even larger if cooling is fast. At early stages, the jet shock with the ICM gas 6 – x y z j D q Jet Total angular momentum
Fig. 1.— Scheme used in the simulations for the jet launching. The total angular momentumof the system, i.e. the precession axis, is chosen to lay in the x direction. The jet precessesaround the x-axis with an opening angle ϕ D and an angular velocity ˙ θ = 2 πT prec . We set θ = 0 as initial setup.Table 1: Description of the simulationsModel resolution ϕ D (0) a τ ∗ Output1 - 4 256 ◦ ◦ ◦ ◦ . ◦ ∼ . b multiple pairs of bubbles a the value of τ = t/T prec at which ϕ D ( τ ∗ ) = ϕ D (0) /e , assuming ϕ D ∝ exp ( − t/τ ∗ ) - except for Model b for this model, a self-consistent solution of Eq.1 was obtained for ϕ D ( t ), giving an approximate alignmenttimescale. Fig. 2.— Central Y-Z slices for density (left), in cm − , temperature (center), in K, andkinetic energy (right), in erg.cm − , at t = 3 T prec . The plots are shown in logarithmic scales.The total length of the box in each direction corresponds to L = 100 kpc.is supersonic. As the bubble expands the shocks become weaker and the density contrast isreduced.The temperature map (center) is directly correlated to the density map. Here, theradiative cooling is responsible for the low temperature at the core ( T core ∼ K). Thecooling timescale τ cool ≃ n k B T / n , T ) ∼
75 Myr gives a central temperature T ∼ K after 150 Myr, in agreement with the simulations. Within the bubbles, the temperature ofthe low density gas decreases mostly due to adiabatic expansion as T ∼ × ( tR bub ) γ − .The bubbles shown in Fig. 2 present a radius R bub ∼ −
15 kpc, which gives T ∼ (2 − × K. For r >
15 kpc, the cooling has not have enough time to decrease the gas temperature.This positive temperature gradient, together with a decreasing expansion velocity of thebubble, results in a sharp decrease of the Mach number of the shock fronts. A consequence isthe appearance of sound waves instead of sharp shock fronts. These waves can be recognizedas archs in the kinetic energy map in Fig. 2 (right), and were detected by Graham et al.(2008).In Fig. 3 we present the emission maps obtained for three different lines of sight -along x (first row), y (center row) and z directions (third row). Columns 1-3 represent theevolutionary stage at t = 1, t = 2 and t = 3 T prec . The emission measure was normalizedby its maximum value calculated for each frame. It is noticeable the difference in observedmorphology depending on the orientation of the line of sight. It occurs because of the twistedshape of the cavities due to the precessing jets. The inflated bubbles typically detach fromthe rest of the forming structure at t ∼ (1 − T prec .The simulated jets inflated the bubbles in timescales of ∼
70 Myrs when they detach, 8 –
Fig. 3.— Emission measure ( EM = R n ds ) maps for the density distribution obtained fromModel t = 1 (1 st column), t = 2 (2 nd column) and t = 3 T prec (3 rd column). The integration occurs along x (first row), y (center row) and z directions (thirdrow). The total length of the box in each direction corresponds to L = 100 kpc.at a distance r max ∼ D bubble ∼ −
30 kpc. This value is in a good agreement with theanalytical approximation for jet inflated bubbles (see Eq. 3 in Soker [2004]).Compared to previous numerical simulations of the evolution of rising bubbles, whereartificial bubbles are introduced in the ICM, (e.g. Bruggen, Sccanapieco & Heinz 2009), thecavities created self-consistently in our simulations are stable for longer periods. Basically,the jet is able to continuously input energy into the bubbles, at least until detachment. Also,the rising speed of a continuously inflatted bubble is smaller, reducing the Rayleigh-Taylorinstability effect (Sternberg & Soker 2008b). 9 –
As discussed above, using a simple model of exponential decay for ϕ D ( t ), it was possibleto constrain the empirical thresholds of ϕ D (0) ∼ ◦ and τ ∗ > .
0, in order to obtaintwo misaligned pairs of bubbles. However, to compare with the observed maps, a moredetailed evolution of the precession is needed. Using Eq. 1, we determined the basic physicalparameters of the system that lead to the given thresholds for the initial precession angleof the jet, as well as the decaying timescale. It was possible to reproduce the needed ϕ D (0)and τ ∗ for ϕ (0) = 110 ◦ − ◦ and J D /J BH = 0 . − .
4, in Eq. 1. For smaller values of ϕ (0) it was not possible to obtain ϕ D (0) > ◦ , while for ϕ (0) > ◦ counter alignmentoccurred instead. For each value of ϕ (0) the ratio J D /J BH determines the alignment timescale( τ ∗ ), which is well constrained. From Eq. 1 we obtained the variation of ϕ as a functionof time calculated from Eq. 1, assuming ϕ (0) = 120 ◦ and J D /J BH = 1 . ϕ D and ϕ BH are also obtained, which are respectively the angles between J D and J BH in relation to thex-direction defined by J T .A new simulation (Model cells) and the timeevolution of ϕ D given by Eq. 1. In order to best reproduce the observed X-ray and radiomaps we varied the orientation of the line of sight and calculated the emission measure, toaccount for the X-ray synthetic map, and integrated the temperature distribution to trackthe jet and its energetic particles, which could be comparable to the observed synchrotronradio maps, if the structure of the magnetic fields is not complex. The best match betweenthe observed and synthetic maps occurred for a specific line of sight inclined 40 ◦ with respectto the total angular momentum of the system.In Fig. 4 we included the observed 328 MHz VLA radio map of 3C 84 (a) and the deep CHANDRA observations of the extensive X-ray emission map surrounding NGC1275 (b)(Fabian et al. 2003), which can be compared to the temperature integrated map (c) and theemission measure (d), respectively, for this specific line of sight.Visually, the X-ray map is well reproduced by the simulations, except for the fact thatthe farthest pair of bubbles is well aligned in the simulations. In the observed maps thereis a slight misalignment of the “ghost cavities”. This may be related to complex motions ofthe ICM. The internal cavities are in very good agreement with the observations. Comparedto the radio maps, the projected energy of particles is also similar. In this synthetic mapthe jets seem to be misaligned. Actually, this is an effect of projection. At the core, the jetpoints almost towards the observer. The result is the formation of two hot spots in the SW- NE direction. 10 –
Fig. 4.— a) 328 MHz VLA radio map credit NRAO/VLA/G.Taylor , b) credit:NASA/CXC/IoA/A.Fabian , c) temperature integrated along the line of sight normalizedby its maximum and d) emission measure normalized by its maximum value. Panels c and d correspond to the projection of the mentioned quantities along a line of sight inclined 40 ◦ with respect to the total angular momentum of the system. The synthetic maps shown werezoomed to better fit the observations. In both cases the total length of the image is 70kpcin each direction.This comparison is not straightforward. A self-consistent distribution of the magneticfield is required in order to accurately calculate the synchrotron radio emission of the jets.Full MHD simulations can be used in the near future for this purpose. Qualitatively, weexpect the magnetic energy to decrease with radius, and the magnetically weighted maps ofprojected particle energy would provide stronger emission closer to the AGN. In this case,the map presented in Fig. 4c would be more similar to Fig. 4a. If the simulations trulycorresponds to the actual scenario of NGC 1275, the timescale used for the synthetic maps, t = 3 T prec , reveals that we may expect a current precession angle ϕ D ∼ ◦ − ◦ , and anevolutionary age of about 100-150 Myrs for the two pairs of bubbles. 11 –
4. Conclusions
In this work we have studied the role of precessing AGN jets, and the evolution ofthe precession angle with time, on the morphology of the inflated cavities of NGC 1275,in the Perseus Cluster. For that, we used a number of hydrodynamical simulations of theICM plasma interacting with precessing jets. We varied the precession angle as well as thejet alignment timescales. We found that, in order to reproduce the morphology of cavitiesobserved in this system, a precession angle as large as ϕ = 60 ◦ is required during a timescaleof at least 3 precession periods. In such conditions, the jets are responsible for the inflation oftwo pairs of bubbles, as seen in NGC 1275. It is worth to mention the interesting agreementbetween this value and the jet half opening angle predicted by Soker (2004), and Sternberg& Soker (2009) in terms of precessing jets in 2.5D simulations. We also found that thecondition v jet ≪ c is required for the inflation of fat bubbles (Sternberg & Soker [2008a]).The synthetic emission measure obtained from the simulations matches the morphologiesof the cavities observed in X-rays if the line of sight is inclined by 40 ◦ with respect to the totalangular momentum of the system. Also, the projected temperature matches the synchrotronemission map, though a magnetic field distribution would be required for a direct, and moreprecise, comparison. From the simulations, and assuming the Bardeen-Peterson effect to bedominant in this system, we were also able to estimate the current precession angle of theAGN jet, ϕ D ∼ ◦ − ◦ , and its age, t ∼ − α , though this may be related tointernal turbulence excited by SNe or recent mergers, as shown in Falceta-Gon¸calves et al.(2010).The authors thank Prof. Noam Soker for helpful comments that helped improve this pa-per. D.F.G. thanks the financial support of the Brazilian agencies FAPESP (No. 2009/10102-0) and CNPq (470159/2008-1). REFERENCES
Bardeen, J. M., Petterson, J. A. 1975, ApJ, 195, L65Bruggen, M., Sccanapieco, E. & Heinz, S. 2009, ApJ, 395, 2210Burkhart, B., Falceta-Gon¸calves, D., Kowal, G., Lazarian, A. 2009, ApJ, 693, 250 12 –Caproni, A., Mosquera Cuesta, H. J., Abraham, Z. 2004, ApJ, 616, L99Caproni, A., Livio, M., Abraham, Z., Mosquera Cuesta, H. J. 2006, ApJ, 653, 112Caproni, A., Abraham, Z., Livio, M., Mosquera Cuesta, H. J. 2007, MNRAS, 379, 135Chen, L., Wu, S., Yuan, F. 2009, MNRAS, 398, 1900Dunn, R. J. H., Fabian, A. C., Sanders, J. S. 2006, MNRAS, 366, 758Fabian A.C., Sanders J.S., Allen S.W., Crawford C.S. Iwasawa K., Johnstone R.M., SchmidtR.W. & Taylor G.B. 2003, MNRAS, 344, 43Falceta-Gon¸calves D., Lazarian A. & Kowal G. 2008, ApJ, 679, 537Falceta-Gon¸calves D., de Gouveia Dal Pino E. M., Gallagher J. S. & Lazarian A. 2010, ApJL,708, 57.Fragile, P. C. & Anninos, P., 2005, ApJ, 623, 347Gnat O. & Sternberg A. 2007, ApJ, 168, 213Graham J., Fabian A. C. & Sanders J. S. 2008, MNRAS, 386, 278Heinz, S., Bruggen, M., Young, A. & Levesque, E. 2006, MNRAS, 373, 65King, A. R., Lubow, S. H., Ogilvie, G. I., Pringle, J. E. 2005, MNRAS, 363, 49Le˜ao, M. R. M., de Gouveia Dal Pino, E. M., Falceta-Gon¸calves, D.,Melioli, C., Geraissate,F. 2009, MNRAS, 394, 157Liu, S., Melia, F. 2002, ApJ, 573, L23.Martin, R. G., Pringle, J. E., Tout, C. A. 2007, MNRAS, 381, 1617Navarro J. F., Frenk C. S. & White S. D.M. 1996, ApJ, 462, 563O’Neill, S. M. & Jones, T. W. 2010, ApJ, 710, 180Pizzolato, F. & Soker, N. 2006, AdSpR, 36, 762Sanders J. S., Fabian A. C., Allen S. W. &Schmidt R. W. 2004, MNRAS, 349, 952Scannapieco, Evan; Brggen, Marcus 2008, ApJ, 686, 927Scheuer P. A. G., Feiler R. 1996, MNRAS, 282, 291 13 –Soker, N. 2004, A&A, 414, 943Sternberg, A., Pizzolato, F. & Soker, N. 2007, ApJ, 656, L5Sternberg, A. & Soker, N. 2008a, MNRAS, 384, 1327Sternberg, A. & Soker, N. 2008b, MNRAS, 389, L13Sternberg, A. & Soker, N. 2009, MNRAS, 398, 422Vernaleo, J. C. & Reynolds, C. S. 2006, MNRAS, 645, 83Walker, R. C., Dhawan, V., Romney, J. D., Kellermann, K. I., Vermeulen, R. C. 2000, ApJ,530, 233