1. 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

2. 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?

3. 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 (2012)

4. 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

5. 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

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

7. 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 𝜈 ′ −𝛼− 5 2
𝑃 𝑒− = 𝑢′ 𝑔 3 ≈𝛽 𝑢 ′ 𝐵 =𝛽 𝑏′ 𝜇 0
𝐷= 1 𝛾(1− 𝑣 𝑐 𝑐𝑜𝑠𝜃

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

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

15. 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)
(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)

16. 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)

17. Alpha Model
Based on accretion disk model of Shakura and Sunyaev Astronomy & Astrophysics (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

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

19. 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