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Summer Research Fellowship Programme of India's Science Academies

Influence of Galactic Environment on AGN Jets

Chinmaya Nagar

M.S. University, Baroda, Gujarat

Guided By:

Dr. Bhargav Vaidya

Centre of Astronomy, Indian Institute of Technology, Indore, Madhya Pradesh

ABSTRACT

Astrophysical jets are ubiquitous in the universe and are considered as sign-posts of star formation. The jet feedback, at very large scales (few kpc to Mpc), plays a vital role, both in evolution of galaxies and the cluster in which they are present. Over the last decades, theoretical models of jets have become very complex to analyse, and this has urged the need for computational techniques to understand the interplay of myriad physical processes in them. This project aims at simulating the effects of interstellar environment on jets emanating from AGN using PLUTO code. The emphasis of the work is to study the propagation and behaviour of non-relativistic hydrodynamic gas jets in various environmental conditions and study their profiles in two dimensions.

The PLUTO code is used here to solve hydrodynamic conservation equations, using which we determine the behaviour and structure of under-dense, hot jets and their dependence on various factors like pressure ratio, desnity ratio, Mach number and temperature. These simulations provide an excellent way to understand how matter emitted from AGN interacts with the medium, and subsequently plays a role in the feedback processes. As a test problem, we performed simulations of a spherical blastwave and understood how its structure varies with density and pressure in the ambient medium. To achieve the main goal of the project, we carried out parameter runs, simulating jets with different mechanical power in realistic environments. These simulations were performed for static and density stratified ambient medium. We found empirical relations between user-defined parameters and the jet structure viz., shape of bow shock, jet head position, jet width etc. Such relations help us analyse the physical attributes of jets when compared with observations. We further performed simulations for dynamic and density stratified ambient medium, and added the influence of plasma winds and clouds that are profusely present in inter-galactic and intra-cluster environments. From these simulations we construed how jets interact with their surroundings, and analysed the physics associated with them.

Keywords: Numerical simulations, hydrodynamic jets, interstellar winds, AGN

ABBREVIATIONS & SYMBOLS

pcParsec
csSpeed of sound
kpcKiloparsec
μMean Mass of Atoms
μHMass of Proton
βKing's Index
ρDensity
ηDensity Ratio
KBBoltzmann Constant
HHHerbig-Haro
FRFanaroff-Riley
AGNActive Galactic Nuclei
ICMIntra Cluster Medium
IGNInter Galactic Medium
YSOYoung Stellar Objects
myrMillion Years

INTRODUCTION - Basic Concepts of Astrophysical Jets

An astrophysical jet is a slender channel of high speed gas propagating through a gaseous environment in inter-galactic (IGM) and intra-cluster (ICM) media. These jets are driven from various objects of different size and mass scales. For instance, they can be produced from the vicinity of super-massive black holes in the case of active galactic nuclei (AGN), by star-sized black holes in microquasars, by neutron stars in X-ray binaries, by protostellar cores in young stellar objects (YSO), and by white dwarfs in symbiotic binaries and supersoft X-ray sources. The material of these jets is much more than a simple compressible fluid or gas. The gas may consist of a mixture of ions, electrons, molecules and dust particles, or can be dominated by a magnetic field and relativistic particles.

The processes in jet formation can be summed up as follows:

1. Jets are powered by gravitational energy released through accretion, and by rotational energy of disk and the central star. Magnetic flux is provided by a disk or stellar dynamo, or by the advection of interstellar field.

2. The accreting plasma is diverted and launched as a plasma wind coupled to the magnetic field and accelerated magneto-centrifugally.

3. Inertial forces wind up the poloidal field, inducing a toroidal component.

4. The jet plasma is accelerated magnetically.

5. The toroidal field tension collimates outflow into a high-speed jet beam.

6. The plasma velocities subsequently exceed the speed of the magnetosonic waves.

7. Where the outflow meets the ISM, a shock develops, thermalizing the jet energy.

Jets play an important role in the formation of stars and analysing their structure and behaviour is a complicated process. Using computer simulations gives us a better idea about their dynamics. While analytical work is enlightening regarding the general structure and the basic physics of those sources, it relies on many assumptions, e.g. about the geometry of the sources. Numerical modelling frees us of the limiting assumptions of analytic models and allows us to model jets whose behaviour is in better agreement with observation.

We use the laws of fluid mechanics to code our jets and simulate their behaviour in different environments, which yields empirical relations between various jet parameters and the ambient conditions (​Smith 2009​).

Using PLUTO Code

The PLUTO code is a program that allows users to simulate (in all dimensions) various astronomical processes related to HD (hydrodynamics), MHD (magnetohydrodynamics), RHD (relativistic hydrodynamics) and RMHD (relativistic magnetohydrodynamics). We chose to use PLUTO because of its good handling of high Mach number flows and the simplicity with which new problems can be defined. Depending on the kind of environment that is required and the type of jets we are dealing with, we assign various behavioral parameters for the jets. Here, we deal with supersonic, under-dense AGN jets and see how their behaviour changes with variation in Mach values and in the presence of interstellar winds.

OBJECTIVE

We aim to simulate AGN jets using PLUTO code and study their dynamics and the effect of galactic environment on them.

LITERATURE REVIEW

YSO Jets

Protostellar (YSO) jets are produced during the major accretion phase in the star forming process, i.e. during Class 0 and 1 phases of the life of a young star/prostellar core. This process of star formation is assumed to last about 105 years. YSO jets have typical lengths between 0.01 - few pcs. Most of them show a linear chain of bright, traveling knots, frequently identified as Herbig-Haro (HH) objects. They often terminate in a bow shock-like structure which is identified to be the leading working surface where the jet impacts with a slower ambient gas.

With the availability of wide-field CCD arrays, it has become evident that some jets extend to far greater distances showing two or more bow shock structures separated by a trail of diffused gas for many jet radii. Examples of these giant HH flows include HH111 with a total extent of ~ 7.7 pc, HH34 of ~ 3 pc, and HH355 with a total extent of ~ 1.55 pc. In some cases (e.g., HH30 jet), there is no detected bow-shock like feature. Some jets, instead of chains of aligned knots, show larger amplitude side-to-side "wiggles". All the luminous structures produce emission line spectra in the optical and infrared bands mainly. Spectral lines give information regarding local temperature and density, on the bulk velocity of the jet emitting matter and on the presence of shocks along the jet. Temperatures of the YSO jets are not much larger than = 1 - 2 x104 K and the corresponding sound speeds are about 10 km/s. This yields typical Mach numbers for the emitting regions Mj = 20 - 40. The knots move away from the sources at speeds of about 100 - 500 km/s, have radii Rj = 3x1015 cm, and inter-knot separation ∆x = 1016 cm = 3.3 Rj. Typical electron densities range from nj =10 cm-3 for the faintest objects to > 105 cm-3 for the brightest. Furthermore, the high proper motion of the heads of the jets indicate that their density is considerably higher than the density of the surrounding medium. However, observations suggest a jet-to-environment density ratio η = ρj /ρa = 1 - 20. (​Smith 2009​; de Gouveia Dal Pino 2004)

AGN Jets

These jets are observed to emerge from the nuclei of active galaxies, like Seyfert galaxies, distant quasars, and radio galaxies, and may extend for distances up to few Mpc into the intergalactic medium. Some of them are considered to be the largest single coherent structures found in the universe. None of the basic parameters, like jet velocity, Mach number, or jet to the ambient density ratio can be directly constrained by observations in the case of AGN jets. In contrast to YSO jets, the main difficulty in trying to comprehend the nature of jets from Active Galactic Nuclei (and also the jets from galactic black holes) is the absence of lines in the radiation spectrum of these objects. Their emission is typically continuous and non-thermal in a wide frequency range that goes from the radio to the X-ray bands.

At parsec scales, close to the source, several AGN jets exhibit a series of bright components (or knots) which travel from the core with apparent superluminal motion (i.e., a velocity apparently greater than the light speed). This apparent effect is interpreted as a consequence of relativistic motions in a jet propagating at a small angle to the line of sight with flow velocity as large as ~ 99% of the speed of light. These inferred jet velocities close to the speed of light suggest that jets are formed within a few gravitational radii of the event horizon of the black hole. Based on their morphology at kpc scales, the extragalactic jets observed in radio galaxies have been historically classified into two categories - Fanaroff and Riley: a first class of objects, usually found in rich clusters of galaxies and hosted by weak-lined galaxies, shows jet-dominated emission and two-sided jets and was named FR I, while a second one, found isolated or in poor groups and hosted by strong emissionline galaxies, presents lobe-dominated emission and one-sided jets and was called FR II. The morphology and dynamics of the jets at kpc scales are dominated by the interaction of the jet with the surrounding extragalactic medium that tends to decelerate the flows to non-relativistic velocities. A clear indication of supersonic speeds in these jets at kpc scales, is the presence of shocks that are resolved in the transverse direction, and the evidence of shocks is given by the behavior of the polarization vector of the synchrotron radiation. Well-resolved jets are often highly linearly polarized and their magnetic fields are thus partially ordered. Detailed polarization maps obtained in the optical and radio bands of the jets of M 87, for example, show that the magnetic field is mainly parallel to the jet axis but becomes predominantly perpendicular in the regions of emission knots, indicating a shock compression of the field lines along the shock front. Polarization can be also detected in the prominent radio lobes and hot spots that form in some jets at the region where they impact with the intergalactic medium. Again, the field direction is oriented along the lobe’s border, i.e., perpendicular to the jet axis indicating compression by shock.

Another parameter to constrain is the jet-to-ambient density ratio. For this parameter we need analytical and numerical modeling and compare qualitatively the spatial density distribution resulting from the calculations, with the observed brightness distributions. Simulations of supersonic, underdense jets are able to reproduce the overall picture of the observed FRII jets. They are, therefore, underdense with respect to the ambient medium, with η ~ 10-5 in the case of pair plasma (proton+electron) jets. YSO jets propagate in a high density ambient medium of molecular clouds and their shocks can, therefore, heat the high density matter that will in turn suffer efficient radiative losses through line emission. On the other hand, extragalactic jets propagate in a tenuous IGM or ICM and the shocks can be considered, with good approximation, adiabatic. They have the main effect of accelerating the particles to relativistic velocities, which in turn, will yield synchrotron radiation in the shocked ambient magnetic field, and the only possible signature that we observe of these shocks is the reorientation of the polarization vector of the radiation (​Smith 2009​; ​Blandford and Payne 1982​).

Testing Simulations on Blastwaves

A blastwave is a spherically expanding shockwave that results from the explosion of stars. There is an increased pressure and flow resulting from the deposition of a large amount of energy in a small, localised volume. This happens in the interstellar medium whenever a supernova goes off. Suppose an explosion instantaneously injects an amount of energy E into an ambient medium of uniform density ρ1. The initial energy release is considered to take place within an infinitesimally small volume. Afterward, a spherical shock will expand into the ambient medium. Early in the course of expansion, the pressure within the shock, P2 ρ1u2sh, is much larger than the ambient pressure P1 and any radiated energy is much smaller than the explosion energy E. This regime, during which the energy E remains constant, is known as the blastwave regime. In a blastwave, the expansion velocity ush(r, t), density ρ(r, t), pressure P(r, t), and other properties, are determined solely by the two initial parameters of the system, E and ρ1. The energy E has the dimensionality ML2T−2 ; the density ρ1 has the dimensionality ML−3 . These two parameters cannot be combined to form a characteristic length scale or time scale for the problem. The solution for the expanding shock front must then be a scale-free or self-similar solution. As mentioned in the article ​Spherical Blastwaves and Supernova Remnants​, the self-similar solution is a function of the dimensionless variable ξ, where

ξ=rtlρ1mEn \xi = r t^l \rho_1^m E^n

The exponents l, m, and n can be determined if ξ if dimensionless. As ξ has the dimensionality L1−3m+2nT l−2nM m+n. Thus, the required solution has exponents l = −2/5, m = 1/5, and n = −1/5. So, we can write

ξ=r(ρ1Et2)1/5 \xi = r(\frac{\rho_1 }{Et^2})^{1/5}

When expressed in dimensionless units, the properties of the expanding shockwave will depend only on ξ. For example, the radius of the spherical shock is

rsh=ξ0(Et2ρ1)1/5 r_{sh\;}=\xi_0 (\frac{Et^2}{\rho_1})^{1/5}

ξ0 is a factor of the order of unity (for γ = 5/3, it is seen that ξ0 = 1.17). Thus, the rate of expansion of the shock is given as, ush=25ξ0 (Eρ1t3)1/5 u_{sh}=\frac{2}{5} \xi_0  (\frac{E}{\rho_1 t^3})^{1/5}

Hence,

ush=25ξ05/2(Eρ1)1/2rsh3/2 u_{sh}\;=\;\frac25\xi_0^{5/2}(\frac E{\rho_1})^{1/2}r_{sh}^{-3/2}

The shock wave slows as it expands. Using typical values for supernova explosions,

rsh=2.3pc(E1051erg)1/5(ρ11024gcm3)1/5(t100yr)2/5 r_{sh}\;=\;2.3\;pc\;(\frac E{10^{51}\;erg})^{1/5}\;(\frac{\rho_1}{10^{-24}\;g\;cm^{-3}})^{-1/5}\;(\frac t{100\;yr})^{2/5}
ush=9000kms1(E1051erg)1/5(ρ11024gcm3)1/5(t100yr)3/5 u_{sh}=\;9000\;km\;s^{-1}\;(\frac E{10^{51}\;erg})^{1/5}\;(\frac{\rho_1}{10^{-24}\;g\;cm^{-3}})^{-1/5}\;(\frac t{100\;yr})^{-3/5}
visit0002.png
    Expanding blastwave without boundaries.

    The above simulation depicts a density ('rho') stratified expansion of a blastwave, where the pressure at the core of the shock is much greater than the ambient pressure.

    visit0004.png
      Blastwave with all refelctive boundaries.

      The above simulations depict a density ('rho') stratified expansion of a blastwave, where the pressure at the core of the shock is much greater than the ambient pressure.

      Jet Simulations and Analysis

      Setting up a basic simulation

      The first step to knowing how to create a simulation for a jet is to quantify parameters like density ratio, Mach number, pressure, etc. Because we are dealing with AGN jets, the radius of the jet core will be larger than the radius of the jet. As mentioned in the PLUTO manual ​http://plutocode.ph.unito.it/files/userguide.pdf​, the PLUTO code simulates jets based on the following hydrodynamic equations:

      ρt+(ρυ)=0  \frac{\partial\rho} {\partial t}\;+ \nabla\cdot(\rho\overrightarrow\upsilon)=0 
      ρ[vt+(υ)υ]=p+ρg \rho\lbrack\frac{\partial \overrightarrow v}{\partial t}+(\overrightarrow\upsilon\cdot\nabla)\overrightarrow\upsilon\rbrack=-\nabla p+\rho \overrightarrow g
      Et+(E+p)υ=ρυg \frac{\partial E}{\partial t} + \nabla\cdot(E+p) \overrightarrow\upsilon = \rho \overrightarrow\upsilon \cdot \overrightarrow g

      where E=32nKBT+12ρυ2 E = \frac{3}{2}nK_BT + \frac{1}{2} \rho \upsilon ^ {2}

      Here, n is the number density of gas particles in the jet.

      The equations (7a), (7b) and (7c) represent conservation of mass (continuity equation), conservation of momentum and conservation of energy, respectively. Here, ρ represents the density, υ represents the velocity, p is the pressure, g is the gravity vector, and E is the internal energy of the jet. In our simulations, g is set to zero because we are focussing on the jet region that is very far from any gravitational influence of black hole. Also, we assume the jets expand adiabatically and hence, follow ideal equation of state. We first consider the fully developed jets in HH 1–2 and set the parameters as shown in the table below. The evolution time of the jet is 2.2 x 1010 s (roughly 12,000 yrs) and it spans 5 x1011 km on each side of its nozzle.

      Table of units 
      γ = 5/3
      Rj = 3x1015 km
      Cs = 2 km s -1
      Ta = 50 K
      Tj = 500 K
      ρj = 1.6x10-22 g cm-3
      ρa = 1.6x10-21 g cm-3
      Mj = 280
      Screenshot from 2018-07-06 16-39-22.png
        3a: Velocity stratification in log scale; 3b: Density stratification; 3c:Pressure stratification in log scale
        jet_fig.jpg
          Cross-sectional view of a jet.

          All our jets are underdense, with a proper density ratio between the jet and surrounding medium. In such a situation, the jet-head advances into the ambient medium with a speed υhd << υjt , where υhd and υjt are the jet-head advance speed and the bulk speed of the jet material, respectively in units of cs in the frame where the undisturbed ambient medium (UAM) is at rest. The jets develop significant structure (long-lived vortices) that move with the jet-head, and therefore present an obstacle for the incoming UAM, as seen by an observer moving with the jet-head.

          DYNAMICS OF AGN JETS

          Observations of powerful outflows from AGN show that they have a considerable effect on the energy and morphology of their host galaxy cluster. These jets show peculiar behaviour under the influence of torrential galactic winds and different external conditions. We study two crucial types of environmental effects and compare the simulated results with theoretical results.

          Simulations using King's Profile

          Since AGN jets remain collimated over huge distances, they are expected to be in approximate pressure equilibrium with their surroundings. In fact, if a jet does not start out in pressure equilibrium, unbalanced pressure forces at its jet-ambient medium interface cause the jet to either expand, or contract until approximate pressure equilibrium is reached. In the ‘standard model’ for double radio galaxies, underdense jets at larger distances from the central engine create a strong bow-shock. This bow-shock encloses a hot and overpressured cocoon (compared to the undisturbed ambient medium). Since we do not know the exact conditions for such cocoons when we start our simulations, we set the jets up in direct pressure equilibrium with the undisturbed ambient IGM. In the case of the radially uniform, or homogeneous jet, we set the pressure equilibrium up by equating the jet pressure to the pressure of the ambient medium. For jets with a spine–sheath jet structure on the other hand, the pressure profile is not trivial (​Walg et al 2013​).

          We now define a non-uniform ambient density profile known as King's profile, which is given as ​​

          ρ=ρ0[1+(rjrc)]3β/2 \rho = \rho_0 [1 + (\frac{r_j}{r_c})]^{-3\beta/2}

          Here, ρ0 is called central density, and is given the value 1.0 (non-dimentional) in our simulations, which makes it equal to

          1.67 x 10-25 g cm-3, which is the unit density we have predefined, and β is an integer, known as King's Index. We study how this ambient density profile influences the jet, by studying the variation in the position of jet head with different values of β. Then we keep β constant and vary Mj to obtain the relationship between jet power (ℙ) and jet head position. The duration of jet evolution is 1.5 x 1015 s (roughly 50 myr).

          Screenshot from 2018-07-07 20-41-44.png
            Density (left) and velocity (right) simulations for β = 1.5
            Screenshot from 2018-07-13 08-14-37.png
              Velocity in log(left) and density (right) for β = -2.0

              We try to fit power laws to get better empirical estimations of the parameter relationships. As it is evident, the plot is non-linear and follows the relation 60.9x0.2 60.9x^{0.2}. Also, as the value of β decreases, the jet becomes slower and less collimated. This decreases the size and pressure of the bow-shock and ultimately retards the evolution of the jet. The jet power is given as P=πrj2Mj[12Mj2ρj+γγ1Tjρj] \mathbb{P} = \pi r_j ^ {2} M_j [\frac{1}{2}M_j ^ {2} \rho_j + \frac{\gamma}{\gamma-1} T_j \rho_j] For β = 1 and Tj = 105 K, we see almost a linear trend between jet power and jet head position, given by the equation y=46.8x1.07 y=46.8x^{1.07}    

              head_beta.png
                Variation in head position with King's Index
                Screenshot from 2018-07-20 10-00-07.png
                  Head postion versus jet power.

                  Influence of Crosswind on Jets - Deflection by a Crosswind

                  In the presence of a cross wind, υw ≠ 0, the jet is subjected to an unbalanced transverse ram pressure force, ρwυw2. Particularly, if the cross wind results from a crossing shock, the jet cocoon (cavity) will be crushed and stripped away from the propagating jet. From that point, the jet interacts directly with the wind, and we can estimate the induced transverse pressure gradient within the jet as Pjxρwυw22rj \frac {\partial P_j }{\partial x_\perp} \approx \frac {\rho_w \upsilon_w ^ {2}} {2r_j} Then, the transverse acceleration of a steady jet is determined by the relation (​​Jones et al 2017​​).

                  wΓj2 υjc2·υjρwυw22rj(1Γj2υj2/c2)

                  where Γj is the Lorentz factor of the jet velocity, υj. We can use υj~υjb as a way to estimate the length b \ell_bℓb​ over which the transverse ram pressure from the wind will deflect by 90°, that is, the jet bending length. If we neglect the second term within the parantheses in eqution (8), we get

                  b=2rjwΓj2υj2ρwυw22rjTmjρwυw2

                  In terms of jet Mach number Mj and wind Mach number Mw, we can write

                  b2rj γjγw·Mj2Mw2·PjPw

                  If the jet and wind pressures are comparable, the ratio of jet bending length, b \ell_b to jet diameter, 2rj is roughly (Mj/Mw)2. Now, we know that the beam and the crosswind are supersonic, hence, their interaction must be mediated by shock waves. There is a well-defined bow shock in the ambient medium, followed by a rapid propagation of an oblique shock across the cross-section of the jet. While the angle this oblique shock makes with respect to the beam is determined by the jet Mach number, it seems essential that such a shock should mediate the transition of the beam from a transverse velocity that is intially zero and, thus, supersonic with respect to the ambient medium to a transeverse velocity that is subsonic with respect to the material inside the ambient medium's bow shock. This inital oblique shock deflects the beam and is one of the essential shock structures for a supersonic beam in a crosswind. We call this the primary oblique shock. Once the jet material has passed through the primary oblique shock, the jet has developed a transverse velocity that is subsonic with respect to the shocked ambient medium. One of the jet models, called BRB model, assumes that the jet interacts with a supersonic crosswind with Mach number Mm. This forms a bow shock, and the termination pressure P behind the shock is given by the following equation (​​Balsara and Norman 1992​​).

                  P=Pm(γ+12)(γ+1)/(γ1)Mm2[γ(γ1)/2Mm2]1γ1 P = P_m(\frac{\gamma+1}{2})^{(\gamma+1)/(\gamma-1)} {M_m^2}{[\gamma-(\gamma-1)/2M_m^2]} ^ {\frac{-1}{\gamma-1}}

                  The pressure in the jet after the jet fluid has crossed the primary oblique shock is given by

                  P=Pj[1+2γγ+1(Mj2sin2ϕ1)] P = P_j[1+\frac{2\gamma}{\gamma+1}(M_j^2sin^2\phi-1)]

                  Here, Mj = υj /c is the Mach number of the jet, Pj is the inlet pressure of the jet and Φ is the angle that the primary oblique shock makes with the inlet velocity. As the et pressure is matched with the ambient medium, we get

                  sin2ϕ=1γ[γ+12]2γ/(γ1)(Mm2/Mj2)γ(γ1)/2Mm2(1/γ1)+γ12γ1Mj2 sin^2\phi = \frac{1}{\gamma}[\frac{\gamma+1}{2}]^{2\gamma/(\gamma-1)}({M_m^2/M_j^2}){\gamma-(\gamma-1)/2M_m^2}^{-(1/\gamma-1)}+\frac{\gamma-1}{2\gamma} \frac {1}{M_j^2}

                  For Mj and Mm >> 1, we get

                  sin2ϕ[γ+12γ1/2]2γ/(γ1)+γ12γ1Mj2 sin^2\phi \approx [\frac{\gamma+1}{2\gamma^{1/2}}]^{2\gamma/(\gamma-1)} + \frac{\gamma-1}{2\gamma}\frac{1}{M_j^2}

                  For γ = 5/3, we get

                  sinϕ1.084MmMj sin\phi \approx 1.084\frac{M_m}{M_j}

                  Thus, it is seen that the angle the primary oblique shock makes with the inlet velocity is dependent on the ratio of Mach numbers of the wind and the jet. We use equation (14) to compare the theoretical and observed results.

                  Comparison of Bend Angle 
                  MmMjΦtheoretical = sin-1 [1.084 (Mm/Mj)]Φsimulation
                  404006.22°12.09°
                  604009.35°15.0°
                  8040012.52°17.1°
                  10040015.72°18.43°
                  12040020.64°22.03°
                  Screenshot from 2018-07-15 13-49-03.png
                    Shock diamond structure of jet (on left) and measurement of bend angle (on right)

                    The observed results vary from the theoretical results mainly because the position from which we throw the crosswind has significant effect on bend angle.

                    wind_vs_bend_2.png
                      Variation of bend angle with wind velocity

                      The wind speed also has an effect on the radius of curvature of the jet, and it ise seen that the bending formula which is based on ram pressure scaling relationship is given as Rrj=ρjMj2ρmMm2\frac {R}{r_j} = \frac{\rho_jM_j^2}{\rho_mM_m^2} where R is the radius of curvature of the jet, rj is the jet radius and ρj and ρm are the densities of the jet and crosswind respectively. We say that the jet is fully bent over when the jet is first seen to be propagating at 90° to the direction of inital flow. Thus, for calculating the radius of curvature, we take the vertical distance at which the jet channel was observed to fully bend over from the lower horizontal axis of the simulations. It is evident that the radius of curvature of the bent jet is inversely proportional to square of the wind velocity. We vary the wind velocity keeping Mj = 400, rj = 1.0 and ρj/ρm = η = 0.6. All these values are in code units (non-dimensional units) for ease of calculation. Thus, we have the relation R=96000/Mm2R = 96000/M_m^2

                      Variation in radius of curvature with jet velocity
                      MwRtheoretical = 96000/Mm2Rsimulation
                      406080
                      6026.6730
                      801520
                      1009.610
                      1206.678.5
                      Screenshot from 2018-07-16 20-29-44.png
                        Measurement of radius of curvature.

                        As shown, the radius of curvature (dotted red line) is determined by measuring the distance between the position of right-angled bend from the point of injection of cross-wind (200th grid point).

                        Screenshot from 2018-07-17 00-29-42.png
                          Comparison of plots for inverse square law (theoretical results on top and simulated results on bottom) 

                          CONCLUSION

                          We have performed a systematic study of the basic properties of jet-driven molecular outflows using time-dependent hydrodynamic simulations and simple analytic models. We use these simulations to study the effect of environmental parameters on the behaviour of jets and understand their interaction with the ambient medium and see how these parameters affect the jet structure and profile which gives us an idea about their feedback mechanism.

                          AGNs are common in clusters, and especially in disturbed clusters. These AGNs expel fast plasma jets that plow through the ICM and those interactions will influence the ICM and its evolution. Impacts between ICM shocks and winds will distort and even disrupt the AGN structures that form. We have laid out a simple summary of some of the essential dynamical relationships involved in AGN/ICM interactions and given basic relations to evaluate shock interactions with low density cavities created by AGN jets. One notable aspect of the relationships we derive is the essential roles of the internal Mach number of the jet flow and the Mach number of ICM shock. The ratio of these two Mach numbers is central to evaluating the interactions between the AGN and a dynamical ambient environment. This provides a potentially useful link that can help develop quantitative understanding of ICM dynamical states.

                          Moreover, we also see a rich interplay of subsonic phenomena, viz. oblique shocks, the focusing of characterisitics and compressible Rayleigh-Taylor instabilties mediating the evolution of the flow. The presence of a primary oblique shock is essential in ensuring that the transverse velocity of the beam becomes subsonic with respect to its windward and leeward sides. ​​

                          ACKNOWLEDGEMENTS

                          I would like to thank the Indian Academy of Sciences (IASc –INSA) for providing me a great opportunity to work at an esteemed institute where I got to interact with a highly experienced faculty at the Centre of Astronomy. This internship was a very unique experience that helped me delve into uncharted fields and opened me up to some amazing fields of work.

                          I heartily thank Dr. Bhargav Vaidya who guided me throughout this project for his critical supervision, guidance and encouragement. I appreciate his ability make concepts easy to comprehend and his constructive way of approaching problems.

                          I would also like to thank Dr. Manoneeta Chakraborty for guiding me during the initial days of my internship and helping me adjust to a new computational platform.

                          And last but not the least, I am thankful to Dr. Arun Anand, Dept. of Applied Physics, M.S. University, Baroda, for providing my letter of recommendation to Indian Academy of Sciences, and to Dr. Bishwajit Chakrabarty, Head of the Department, Dept. of Applied Physics, M.S. University, Baroda, for being supportive of this opportunity.

                          References

                          • Smith, Michael D. (2009). Astrophysical Jets and Beams.

                          • Elisabete M. de Gouveia Dal Pino, Astrophysical Jets and Outflows: https://arxiv.org/pdf/astro-ph/0406319.pdf

                          • Blandford, R. D. and Payne, D. G. (1982). Hydromagnetic flows from accretion discs and the production of radio jets.

                          • http://www.astronomy.ohio-state.edu/~ryden/ast825/ch5-6.pdf

                          • http://plutocode.ph.unito.it/files/userguide.pdf

                          • Walg, S. and Achterberg, A. and Markoff, S. and Keppens, R. and Meliani, Z. (2013). Relativistic AGN jets I. The delicate interplay between jet structure, cocoon morphology and jet-head propagation. 433,

                          • Jones, T. W. and Nolting, Chris and O’Neill, B. J. and Mendygral, P. J. (2017). Using collisions of AGN outflows with ICM shocks as dynamical probes, 6-9

                          • Balsara, Dinshaw S. and Norman, Michael L. (1992). Three-dimensional hydrodynamic simulations of narrow-angle-tail radio sources. I - The Begelman, Rees, and Blandford model. 393,

                          Source

                          • Fig 4: http://www.tifr.res.in/~tifrjet/presentations/vdWesthuizen.pdf
                          • Fig 5: ​​Outflows and Jets: Theory and Observations: http://www.mpia.de/homes/fendt/Lehre/Lecture_JETS2/lecture_ss11-jets.htmlhttp://www.mpia.de/homes/fendt/Lehre/Lecture_JETS2/lecture_ss11-jets.html​​.
                          • Fig 10: ​Balsara, Dinshaw S. and Norman, Michael L. (1992). Three-dimensional hydrodynamic simulations of narrow-angle-tail radio sources. I - The Begelman, Rees, and Blandford model, fig.1, 636​​.
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