Question

5. (a) Draw a schematic diagram for the spectral energy distribution of a typical star-forming galaxy between 1 GHz and 1000 GHz, showing clearly the main emission mechanisms and their dependance on frequency [6 points]. (b) Describe how each of these mechanisms results in the emission of electro-magnetic radiation at radio wavelengths [3 points]. (c) The radio galaxy Cygnus A has a flux density of $S_{325 MHz} = 6000$ Jy and $S_{1400 MHz} = 1600$ Jy at 325 MHz and 1.4 GHz, respectively. Calculate the spectral index of Cygnus A between these two frequen- cies and determine whether this is consistent with a thermal or non-thermal emission process [2 points]. (d) The power emitted by an accelerated charge is given by Larmor's formula, $\frac{2}{3}\frac{q^2a^2}{c^3}$, where the symbols have their usual meaning. Show that for a weak electron-ion interaction, as illus- strated in the figure below, the total energy emitted is given by, $\frac{\pi Z^2e^6}{4 m^2c^3b^3v}$, where the symbols have their usual meaning [9 points].

          5. (a) Draw a schematic diagram for the spectral energy distribution of a typical star-forming galaxy
between 1 GHz and 1000 GHz, showing clearly the main emission mechanisms and their dependance
on frequency [6 points].
(b) Describe how each of these mechanisms results in the emission of electro-magnetic radiation at
radio wavelengths [3 points].
(c) The radio galaxy Cygnus A has a flux density of $S_{325 MHz} = 6000$ Jy and $S_{1400 MHz} = 1600$ Jy at 325
MHz and 1.4 GHz, respectively. Calculate the spectral index of Cygnus A between these two frequen-
cies and determine whether this is consistent with a thermal or non-thermal emission process [2 points].
(d) The power emitted by an accelerated charge is given by Larmor's formula,
$\frac{2}{3}\frac{q^2a^2}{c^3}$,
where the symbols have their usual meaning. Show that for a weak electron-ion interaction, as illus-
strated in the figure below,
the total energy emitted is given by,
$\frac{\pi Z^2e^6}{4 m^2c^3b^3v}$,
where the symbols have their usual meaning [9 points].

5. (a) Draw a schematic diagram for the spectral energy distribution of a typical star-forming galaxy
between 1 GHz and 1000 GHz, showing clearly the main emission mechanisms and their dependance
on frequency [6 points].
(b) Describe how each of these mechanisms results in the emission of electro-magnetic radiation at
radio wavelengths [3 points].
(c) The radio galaxy Cygnus A has a flux density of S325 MHz = 6000 Jy and S1400 MHz = 1600 Jy at 325
MHz and 1.4 GHz, respectively. Calculate the spectral index of Cygnus A between these two frequen-
cies and determine whether this is consistent with a thermal or non-thermal emission process [2 points].
(d) The power emitted by an accelerated charge is given by Larmor's formula,
(2)/(3)(q^2a^2)/(c^3),
where the symbols have their usual meaning. Show that for a weak electron-ion interaction, as illus-
strated in the figure below,
the total energy emitted is given by,
(π Z^2e^6)/(4 m^2c^3b^3v),
where the symbols have their usual meaning [9 points].

Added by Lourdes A.

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