Question: Optically thick Bremsstrahlung.


Oppositely directed jets of plasma that are bright radio sources originate in the nuclei of many radio galaxies. They emerge along the

axis of an ‘accretion disc’, as shown in Fig. 1. The radio jet emits synchrotron radiation and the accretion disc emits Bremsstrahlung,

but at radio wavelengths, the jet is normally much brighter than the disc, the latter being essentially invisible. In one such radio

galaxy, 3C84, the jet directed away from the observer (the ‘counterjet’) is obscured as a result of free-free absorption by the accretion

disc at frequencies below 22 GHz, i.e. the accretion disc has opacity greater than 1 for frequencies below 22 GHz. Assume that the

temperature of accretion disc T = 104 K, that its thickness is 1.4 pc and that it is viewed at θ = 45° to the axis.

Find the number density of electrons in the accretion disc.

Hints: Use the Gaunt factor g appropriate to radio wavelengths (given as below) and find an expression for the emissivity. Then consider

the criterion for opacity >1.

g(ν,T) = √3/2π [ln⁡((128ϵ_0^2 k^3 T^3)/(m_e e^4 ν^2 Z^2 ))-0.76]

Where ν is frequency, ϵ is permittivity of free space 8.854 x 10-12 Fm-1, k is Boltzmann’s constant 1.381 x 10-23 J K-1, m_e is mass of

electron 9.109 x 10-31 kg, e is charge on the electron 1.602 x 10-19 C and Z can be assumed as 1 for fully ionised gas.

Remember throughout this question that the calculations involve the Bremsstrahlung of the accretion disc and not the synchrotron radiation

from the jet. See note below diagram.
Figure 1: The jet and counterjet emerge along the axis of the accretion disc. Radiation from the counterjet is absorbed by the disc at

READ ALSO :   Resource: Appendix A. Write a 1,400- to 1,750-word autobiographical research paper that analyzes the influences of race as it relates to your community. In your paper, write your first-person account of how human interactions in your community have been racialized. For the community, you may consider relations within your neighborhood, local government, service groups, clubs, schools, workplace, or any environment of which you are a part. Answer the following questions and provide examples: Do members of your community look like you? In what ways do they look the same or different? How do leaders within your community treat people who are like you? How do they treat people who are different? How do other members of your community treat people who are like you? How do they treat people who are different? Do your texts or work manuals contain information by or about people like you? Do the local media represent people like you? If so, in what ways? What are some similarities and differences between you and the people who are in leadership positions in your community? Do you think minority group interests are represented within your community? If you could resolve any inequities within your community, what would you change? How and why? Which main concepts from the text relate to race? Apply some of these concepts to your project. Include the following elements in your paper: The thesis addresses racial issues in your local community. The content is comprehensive and accurate. The paper itself draws on your personal experiences with and opinions about cultural diversity in your community. Three sources are used, and one source is a community member, leader, or representative from a local community organization. The paper is written in first-person point of view, with an autobiographical approach. Text concepts are applied to your observations. Assignment questions are answered. The paper includes perspectives from supporting sources. The conclusion is logical, flows from the body of the paper, and reviews the major points. Paragraph transitions are present. The tone is appropriate. Sentences are well-constructed. The paper, title page, and references follow APA guidelines. Rules of grammar, usage, and punctuation are followed. Spelling is correct. Post your completed research as an attachment.

frequencies below 22GHz.




Note: In most radio galaxies, the counterjet is hidden as a result of relativistic aberration, which greatly diminishes the intensity of a

source moving away from the observer. 3C84 is an unusual case: its jets are thought to move too slowly for relativistic aberration to be

significant – it seems the counterjet is hidden at low frequencies only by free-free absorption.