Richard Anantua (UC Berkeley) Towards Multi-Wavelength Observations of Relativistic Jets from General Relativistic Magnetohydrodynamic Simulations Richard Anantua (UC Berkeley) Collaborators: Roger Blandford (Stanford), Jonathan McKinney (UMD), Anthony Readhead (Caltech), Alexander Tchekhovskoy (UC Berkeley), Craig Walker (NRAO) Tue 6-13-2017  

M87: A Good Example Giant elliptical galaxy located in the Virgo Cluster 5.4x107ly from us. M87’s jets source from radio to gamma rays. M87’s 6x109M⨀ (Gebhardt et al., 2011) central black hole has angular width (3.9μas)— comparable to that of Sgr A* (5.3μas). 43GHz (7mm) VLBA M87 (Courtesy of Craig Walker (NRAO)) What is the mechanism of nonthermal jet emission at various locations in the jet?

Jet Simulation Assumptions and Fluid Equations - Geometrically thick disk - Magnetically arrested disk - Jet power derived from flux threading black hole of mass M and spin a/M=0.92 Mass conservation Energy-momentum conservation McKinney, Tchekhovskoy and Blandford MNRAS 423 3083 (2012)

Stationary Axisymmetric Self-Similar Semi-Analytic Model Assume stationary (d/dt=0), axisymmetric (d/dφ=0) and at z=50M, fitting forms , where Derive v, B, I (and more), and scale to other altitudes BPoloidal (arrows) & BToroidal (colors) at various jet segments 10M<z<102M 102M<z<103M 103M<z<104M

Hosting and Manipulation of Simulation Data . 1.) Read in simulation datablock solving GRMHD equations for ρ, ug, vμ and bμ in Galaxy Frame 2.) Rotate Observer Frame about Galaxy Frame 3.) Interpolate and project functions of Galaxy Frame quantities onto Observer Frame

State Variables and Equation of State Fluid and Galaxy Frame Magnetic fields are related as Magnetic flux conservation

Beta and Bias Models Form simple synchrotron prescription assuming rough equipartition of particle and magnetic energy for constant β in Beta Model Generalize to Pe/b2n  Const. in Bias Model Transform Iν~D3, jν~D2 and αν~D-1 with Doppler factor 𝑗′ 𝜈 ∝ 𝑢 ′ 𝑔 𝑏 ′ 1+𝛼 𝜈 ′ −𝛼 , 𝛼′ 𝜈 ∝ 𝑢 ′ 𝑔 𝑏 ′ 𝛼+ 3 2 𝜈 ′ −𝛼− 5 2 𝑃 𝑒− = 𝑢′ 𝑔 3 ≈𝛽 𝑢 ′ 𝐵 =𝛽 𝑏′ 2 2 𝜇 0 𝐷= 1 𝛾(1− 𝑣 𝑐 𝑐𝑜𝑠𝜃

Intensity Map Jet Isolation From Energy Density Cut (θ,Φ)=(90°,0°), Emissivity: jν~b’1.5 Contour: ug/ρ=0.1 (θ,Φ)=(20°,0°) Emissivity: jν~b’1.5 Disk subtraction: ug/ρ>0.1

Superluminal Features? Features moving with apparent speed 6c in M87 observed by Hubble (Biretta, J. A., Sparks, W. B., & Macchetto, F., 1999, ApJ 520, 621) Projection/finite c effect: (θObs,ΦObs)=(20°,0°), TObs=2000M,2056M,…,2560M Emissivity: j’ν~b’1.5 Disk subtraction: bμbμ/ρ>10 θ

Jet Collimation Simulated collimation increases with n in models where Pg~ b2n Observed collimation profile: Emissivity: j’ν~b’1.5 (left), j’ν~ b’3.5 (right) (θObs,ΦObs)=(20°,0°) Tobs=2000M Disk subtraction: x2+y2-(z/2)2<-402, |z|<40M x2+y2<402, |z|>40M

Jet Magnetic Substructure Investigate perturbations ei(mΦ+nz+lR+ωt) for (m=0) instability (pinch) or magnetic Kelvin-Helmholtz (m=1) instabilities (wobble) (θObs,ΦObs)=(15°,0°), Tobs=2000M,2056M,...,2560M Emissivity: j’ν~b’1.5 Disk Subtraction: 0.5|z|>x2+y2>20M M87 Observation at 15 GHz (2 cm) Kovalev, Lister, Homan, Kellermann (2007) ApJL, 668, 27

Polarization Maps Simulation maps of Stokes Q and U (θ,Φ)=(20°,0°) Emissivity: j’ν~b’1.5 Disk subtraction: 0.5|z|>x2+y2>20

Instrumentation and Convolution Use 25μas beam width of Event Horizon Telescope to construct point spread function Before Convolution In both panels: (θObs,ΦObs)=(15°,0°) Tobs=2056M Emissivity: j’ν~b1.5 Disk subtraction: 0.5|z|>x2+y2>20

Emission and Absorption Prescriptions These are prescriptions for j=j1+j2 and 𝜒=( 𝜒 1 +𝜒 2 )/2

Observing Stationary Axisymmetric Self-Similar Model The self-similar, stationary axisymmetric model applied to M87 projected on an observer plane at 20 viewing angle compared to VLA observation: Blandford and Anantua, Journal of Physics: Conf. Series 840 (2017) 012023 (θObs,ΦObs)=(20°,0°) Emissivity: j’ν~be’1.5 β=10-7 E-field direction in red 43 GHz VLA observation (Epoch G) w./E field vectors Courtesy of Craig Walker (NRAO)

vs. Current Density Model Connecting Simulations with Observations: M87 43 GHz Radio Map Time Series vs. Current Density Model Current density model based on having particles accelerated at current layers 𝑊′= 𝜇 0 𝐿 𝐽𝑆𝑞 𝑐𝑗′ 𝜇 𝑗′ 𝜇 𝑡′= min { 𝑡′ rad , 𝑡′ exp } (θObs,ΦObs)=(20°,0°), Tobs=2000M,2056M,…,2560M Emissivity: Current Density Model Disk Subtraction:|z|>35M LJSq=1e4M M87 43 GHz VLA maps 21-Day frame rate, Epochs A,B,D-L Courtesy of Craig Walker (NRAO), Chun Ly (UCLA), Bill Junor (Los Alamos) and Phil Hardee (U. Alabama)

Alpha Model Based on accretion disk model of Shakura and Sunyaev Astronomy & Astrophysics 24 337 (1973), where α is efficiency of momentum transport, and S is shear strain 𝑊 ′ = 1 2 𝜏 ′ 𝑆 ′ , 𝑆 ′ = 𝛾 2 𝑑 𝑣 𝑧 ′ 𝑑𝑠 ,   𝛼= 10 −4

Shear Model Based on Newtonian shear with dynamic viscosity  𝜇 ′ = 𝐿𝑆 3𝑐 𝜌 𝑐 2 + 𝑏 𝜇 𝑏 𝜇 2 𝜇 0 𝑢 𝑔 3 + 𝑏 𝜇 𝑏 𝜇 2 𝜇 0 𝐿 𝑆 =10 2 𝑀

Conclusion and Future Directions Self-consistent GRMHD simulations can be used to replicate observational signatures of AGN jets such as M87— including superluminal features, polarization and optical depth from synchrotron radiation process, and of surveys by changing orientation More sources, e.g., quasar 3C 279, can be compared with simulations for variability, etc. in other processes, e.g., inverse Compton The next generation EHT will provide horizon scale observations comparable to inner jet simulations observed with general relativistic ray tracing