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General relativistic viscous accretion disc and generation of bipolar jets. Indra nil Chattopadhyay. A ryabhatta R esearch I nstitute of observational scienc ES indra@aries.res.in. Content of Presentation.

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## Indra nil Chattopadhyay

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**AAPCOS'15, Kolkata, 17 October, 2015**General relativistic viscous accretion disc and generation of bipolar jets Indranil Chattopadhyay Aryabhatta Research Institute of observational sciencES indra@aries.res.in**AAPCOS'15, Kolkata, 17 October, 2015**Content of Presentation • Phenomenology of accretion-ejection system in black holes (BH) candidates. • General relativistic flow around BHs. • Importance of relativistic EoS of fluid around BH • Results Collaborators Rajiv Kumar (ARIES )**AAPCOS'15, Kolkata, 17 October, 2015**1. Phenomena of accretion & ejection from BH-candidates • AGNs (centres of Active galaxy) and micro(µ)-quasars (X-ray binaries) are believed to be powered by accretion onto BH! • AGNs & µ-quasars also show relativistic jets coming out of these objects. BH NS Jet from VELA pulsar (Chandra) NGC426 (Hubble) GRS1915+105 (NRAO)**AAPCOS'15, Kolkata, 17 October, 2015**1… contd • Accretion being convergent flow is hotter emits from optical to way up in gamma rays. Jets being cooler generally emits in radio. • Accretion discs are observed in `hard’ and `soft’ spectral state connected by many intermediate states. Low-hard state or LS; High soft state or HS; Intermediate state IM**AAPCOS'15, Kolkata, 17 October, 2015**1… contd… • Jets are observed only in `hard’ and hard intermediate states and not in the soft state. Mirabel & Rodriguez, 1999, Nature Fender,Beloni, 2004, ARA&A**AAPCOS'15, Kolkata, 17 October, 2015**1…contd… • The jet originates very close to the horizon (<100rg), so the entire disc do not participate in jet generation. Junor, Biretta & Livio, 1999, Nature**AAPCOS'15, Kolkata, 17 October, 2015**1… contd… • The hard radiations also exhibit quasi-periodic oscillations (QPOs), which grows from hard state to the hard intermediate but seems to disappear in the soft state. • There is some observation which claims that relativistic ejections follows the disappearance of QPO, others refute it. Maxm QPO freq. QPO freq.. increases No QPO Low QPO**AAPCOS'15, Kolkata, 17 October, 2015**To summarize: The states of µquasars goes from LS IM HS Jets are intrinsic to accretion and evolves with jet states. Jets originate close to the horizon (few tens of rg) QPOs in BHCs are seen only in hard power law photons and not the thermal soft photons, and QPO too evolves with the spectral states pretty much like the jets… AGNs do not show state changes, but the over all morphology of µquasar is a scaled down version of AGNs so the basic tenets of jets in AGN should also be similar… ALL ACCRETION-EJECTION MODELS SHOULD AUTOMATICALLY INCORPORATE THE BASIC PROPERTIES OF JETS. UNFORTUNATELY, AS MOST AREAS OF RESEARCH IN ASTROPHYSICS THERE ARE MANY COMPETING MODELS**AAPCOS'15, Kolkata, 17 October, 2015**2. Accretion disc models • The most seductive idea would be that BH being super attractor, will just gobble up all matter and so matter should be radialy falling into it. But it was shown by Shapiro that, then the EM luminosity is too low. • As a result people jumped into rotation dominated disc like Keplerian disc (Shakura-Sunyaev 1973; Novikov-Thorne 1973) Vr~0, vφ~Kep; optically thick; geometry thin; explains thermal part of EM spectra, but fails to produce power law Various models to explain the non-thermal part**AAPCOS'15, Kolkata, 17 October, 2015**I do not have the time to go through all the models like thick accretion disc (Abramowicz, Paczynskii, Wiita etc), slim disc (Abramowicz, Beloborodov, Sadowskii etc), ADAF (Ichimaru, Narayan, Yi etc), but I would like to point out that we consider all the terms in the equations of motion and therefore we can generate all possible solutions including the models mentioned above. But I would like to point out something else. Accretion ejection is mostly studied in the realm of pseudo-Newtonian potential (pNp). pNps are modifications of Newtonian gravitational potential which regenerates some of the typical length scales as predicted by general relativity (GR). This saves a lot of calculations and gives us some qualitative solutions. One can go deep into the rigours of plasma/radiation physics while avoiding the tedious/complicated calculations of GR. But there are some down side too.**AAPCOS'15, Kolkata, 17 October, 2015**Achievements while using pseudo-potential: Qualitatively, the LS & HS were obtained as a self-consistent solutions (Chakrabarti & Titarchuk 1995, Mandal& Chakrabarti 2008, 10) Origin of jets and QPOs can easily be explained as a consequence of oscillating shocks. The jet states tallied with spectral states & post-shock disc (PSD) being the base of jet, satisfies observational criterion that jet base is smaller than the entire disc. (Das, IC, Nandi, Molteni 2014, MNRAS)**AAPCOS'15, Kolkata, 17 October, 2015**Inherent problems of pNps: Matter speed can exceed light speed `c’ outside the horizon. This causes problem while computing spectra (may give rise to bulk motion Comptonization where it is none existent). The effective potential on the horizon goes to -∞ while in GR it is 0. The definition of specific angular momentum in pNp regime is same for particles and fluids… but it is different in GR Assuming the disc viscosity arises due to shearing flow then the shear is in pNp… under the same assumptions in GR this is , where, is 4-velocity, , v. Away from the equatorial plane, the surfaces of constant angular momentum is simple cylinders, in GR it is von-Zeipel surfaces, which also coincides with entropy constant surface in GR. So for correct physics around BH, GR should be used.**AAPCOS'15, Kolkata, 17 October, 2015**Relativistic Fluid equation of state (EoS) • A fluid is relativistic, on account of its (a) bulk speed (v~c), and/or (b) if random speed of constituent particles ~c i.e., kT ~ rest energy.. • As matter flows onto a BH: (a) at r large, v~0, T~small; (b) as r≤ few×10rg, v≥0.1c, T~1012K; Adiabatic index Γ, 5/3 4/3 EoS of rel. Fluid can be computed by considering the relativistic formula for particle energy and integrating it MB distribution and was obtained by Chandrasekhar, Synge, Cox & Giulli, which is ratio of modified Bessel’s function. We used an approximate EoS to the exact one, which is algebraic but very correct.**AAPCOS'15, Kolkata, 17 October, 2015**Relativistic equations of motion: where, Projecting it onto a spatial coordinate gives relativistic Navier Stokes equation, and projecting it along the 4-vel gives us first law of thermodynamics. We also assume the r-φ component of viscous stress tensor is dominant, the metric is Schwarzschild and eqs are in steady state, the accretion equations are Radial Azimuthal Accretion rate 1st Law of thermodynamics**AAPCOS'15, Kolkata, 17 October, 2015**Simplifying these eqs we get, (A) (B) (C ) A, B, C are integrated to find the solution. However, at some point rc eq. (A) takes 0/0 or critical form, so the derivative at this critical point or sonic point is found by L’Hospital’s rule. However, the sonic point itself is found by a unique method.**AAPCOS'15, Kolkata, 17 October, 2015**Integrating the equations of motions gives us the generalizedrelativistic Bernoulli constant (constant even in presence of viscosity) Integrating the first law of thermodynamics assuming no dissipation gives the adiabatic law which combined with accretion rate gives us constant of entropy, entropy-accretion rate…. (non-rel version P=kρГ The horizon is a coordinate singularity so cannot start integration there. We choose a point very close to rg, where gravity dominates all processes, matter falls close to free fall and is constant there, We supply with guess values of vin to find the solution.**AAPCOS'15, Kolkata, 17 October, 2015**Jet equations of motion: It can be shown the surface of constant angular momentum coincides with von-Zeipel surface (VZS) characterized by von-Zeipel parameter (Abramowicz 1971, 78, Chakrabarti 1985), given by A relation like completely specifies the VZS, and the streamline of the jet is specified. The shocked accretion disc naturally spews bipolar jets, Since jets move away from equatorial plane the Bernoulli constant Is modiefied too ….**AAPCOS'15, Kolkata, 17 October, 2015**The jet equations along the stream line are For a accretion solution with shock we consider the jet launch site to be half way between shock location and inner critical point, and then play around with & n to see where the jet blows….**AAPCOS'15, Kolkata, 17 October, 2015**Accretion solutions for parameters**AAPCOS'15, Kolkata, 17 October, 2015**All possible solution**AAPCOS'15, Kolkata, 17 October, 2015**The jet geometry changes with Kerr parameter as well as VZ parameter. Not all channels are good for powerful jets. This itself tells us that by just having a shock there will not be powerful jets.**AAPCOS'15, Kolkata, 17 October, 2015**Conclusion: (1) GR jets are faster. Without any extra acceleration one can achieve jets with speeds >0.2c, in pNp jets are much weaker. (2) This promises even higher speeds for Kerr BH, moreover the jet geometry is dimpled towards the axis, which might prefer intrinsic non-steady shocks. Which is good news since much of the phenomenology of Blazars etc are explained by travelling shocks. (3) The mass outflow rate is maximum around 4.5% of inflow rate in pNp it may go as high as 10%. (4) Accretion solution generates all possible solutions, starting from ADAF to shocked accretion disc, the latter can automatically fire mildly-relativistic jets.**AAPCOS'15, Kolkata, 17 October, 2015**Thank You

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