Review of basic concepts about AGNs

Review of basic concepts about AGNs

This lecture is part of the course "physics of active galactic nuclei" offered to graduate students in astrophysics by Rodrigo Nemmen and Joao Steiner at IAG USP.

https://rodrigonemmen.com/teaching/active-galactic-nuclei/

C5ca9433e528fd5739fa9555f7193dac?s=128

Rodrigo Nemmen

May 20, 2016
Tweet

Transcript

  1. 1.
  2. 3.

    cosmic rays Fermi High-energy Astrophysics Gemini Swift Chandra HST VLA

    ALMA* SOAR GMT E-ELT LLAMA CTA neutrinos gravitational waves?
  3. 4.
  4. 6.

    Ghisellini Difference between intensity and flux Difference between intensity and

    flux Intensity: measure of irradiated energy along a light ray (directional)
  5. 7.

    Ghisellini Difference between intensity and flux Difference between intensity and

    flux you see each element of the surface under a different angle θ
  6. 8.

    t: Basics 5 ch e is gle al ⃗ n

    sees disk Ghisellini Difference between intensity and flux inside the shell. to F nsity I and the total flux F must account for the fact t of the surface is seen under a different angle θ. See sider the projected area, and introduce a cos θ term in F = I cosθdΩ (1.15)
  7. 11.

    8 1 Some Fundamental Definitions Fig. 1.4 A layer of

    total optical depth τν ≫ 1 is observed face-on (left) and from an angle θ from its normal (right). The two observers receive always the emission produced in the shell of unit optical depth. But an optical depth of unity corresponds to the length AB (left) or CD (right). The two lengths are equal (AB = CD), but one is inclined, therefore the two volumes are different (by the factor DH/AB = cosθ) Ghisellini At an inclined angle of observation, the emitting volume is less by a cosθ factor
  8. 12.

    Mean free path (for a photon) Average distance traveled by

    a photon without interacting Distance for which ⌧⌫ = 1 Path (for a photon) is the average distance ℓ traveled by a photon t corresponds to a distance for which τν = 1: τν = 1 → σνnℓν = 1 → ℓν = 1 nσν (1.44)
  9. 13.
  10. 18.

    1.13 The Electric Field of a Moving Charge 19 Fig.

    1.10 The electric field produced by a charge initially in uniform rectilinear motion that is suddenly stopped. At large distances, the electric field points to where the charge would be if it had not been stopped. At closer distances, the electric field had time to “adjust” and points to where the charge is. There is then a region of space where the electric field has to change direction. This Electric field produced by an accelerated charge Ghisellini
  11. 19.

    1.13 The Electric Field of a Moving Charge 19 Fig.

    1.10 The electric field produced by a charge initially in uniform rectilinear motion that is suddenly stopped. At large distances, the electric field points to where the charge would be if it had not been stopped. At closer distances, the electric field had time to “adjust” and points to where the charge is. There is then a region of space where the electric field has to change direction. This Electric field produced by an accelerated charge Ghisellini electromagnetic wave (radiation) c t Run Mathematica demonstration
  12. 22.

    Pattern of emitted radiation of accelerated charges Ghisellini he ge

    el to hat the pattern of the emitted radiation has a maximum per-
  13. 28.
  14. 29.

    ! 1

  15. 30.

    Penrose, R. The apparent shape of a relativistically moving sphere.

    Proc. Camb. Philos. Soc. 55, 137 (1959) 
 Terrel, J. Invisibility of the Lorentz contraction. Phys. Rev. 116, 1041 (1959) 
 We figured out apparent shapes of relativistic objects >50 years after special relativity was published
  16. 34.

    Observed timescales and frequencies from relativistic sources A Lamp remains

    on for B ✓ t0 e Non-relativistic case: te = t0 e
  17. 35.

    Observed timescales and frequencies from relativistic sources A Lamp remains

    on for B ✓ t0 e Δt between arrival of first and last photon?
  18. 37.

    The relativistically moving square 3 Beaming orresponding to Γ =

    √ 2 and to CB = ℓ′ √ 2, Note that we have considered the square (and Ghisellini cos ↵ =
  19. 48.

    Relativistic source radiating isotropically in its rest-frame: beaming based on

    http://math.ucr.edu/home/baez/physics/Relativity/SR/Spaceship/spaceship.html
  20. 49.
  21. 50.

    Doppler factor δ4 as a function of viewing angle, for

    different values of Γ Ghisellini n I = 4I0 L = 4L0 for a single, relativistic blob
  22. 51.

    Moving in a homogeneous radiation field (i.e. relativistic blob moving

    in the BLR of a radio loud AGN) Ghisellini 3 Beaming hi, nice to meet you. I am relativistic blob escaping from a black hole
  23. 52.

    Moving in a homogeneous radiation field (i.e. relativistic blob moving

    in the BLR of a radio loud AGN) Ghisellini actor Γ . In the rest of the blob the oming from 90° in are seen to come at 1/Γ . The energy seen by the blob is by a factor ∼Γ 2 ll of broad line clouds. For simplicity, assume that the broad line photons uced by the surface of a sphere of radius R and that the jet is within it. As- so that the radiation is monochromatic at some frequency ν0 (in frame K). moving (in frame K′) observer will see photons coming from a cone of semi- 1/Γ (the other half may be hidden by the accretion disk): photons coming 3 Beaming S frame S’ frame U F U' F'
  24. 54.
  25. 57.
  26. 58.
  27. 60.

    Apparent velocity as a function of viewing angle, for different

    values of Γ Ghisellini 3 Beaming rent on of ction r the nel
  28. 61.

    Useful relativistic tranformations Ghisellini 3.4 A Question 45 Table 3.1

    Useful relativistic transformations ν = ν′δ frequency t = t′/δ time V = V ′δ volume sinθ = sinθ′/δ sine cosθ = (cosθ′ + β)/(1 + β cosθ′) cosine I(ν) = δ3I′(ν′) specific intensity I = δ4I′ total intensity j(ν) = j′(ν′)δ2 specific emissivity κ(ν) = κ′(ν′)/δ absorption coefficient TB = T ′ B δ brightn. temp. (size directly measured) TB = T ′ B δ3 brightn. temp. (size from variability) U′ = (1 + β + β2/3)Γ 2U radiation energy density within an emisphere Dividing by ta = te(1 − β cosθ) we have the measured apparent velocity as βc t sinθ β sinθ