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3. The equation for the luminosity function defined by Schechter is: $\Phi(L)dL = N_0 \left(\frac{L}{L_}\right)^\alpha \exp\left(-\frac{L}{L_}\right)\frac{dL}{L_}$ (a) For the faintest galaxies, $L << L_$. Show that in that case the Schechter function is a power law. (b) Considering only this regime of the faint galaxies, compute the total luminosity emitted by galaxies between luminosities $L_{min}$ and $L_{max}$. Compute this for values of $\alpha$ of -1, -2 and -3. Discuss which galaxies dominate the luminosity in this regime for the different values of $\alpha$.

          3. The equation for the luminosity function defined by Schechter is:
$\Phi(L)dL = N_0 \left(\frac{L}{L_*}\right)^\alpha \exp\left(-\frac{L}{L_*}\right)\frac{dL}{L_*}$ 
(a) For the faintest galaxies, $L << L_*$. Show that in that case the Schechter function is a
power law.
(b) Considering only this regime of the faint galaxies, compute the total luminosity emitted
by galaxies between luminosities $L_{min}$ and $L_{max}$. Compute this for values of $\alpha$ of -1, -2
and -3. Discuss which galaxies dominate the luminosity in this regime for the different
values of $\alpha$.

3. The equation for the luminosity function defined by Schechter is:
Φ(L)dL = N0 ((L)/(L*))^α(-(L)/(L*))(dL)/(L*)
(a) For the faintest galaxies, L << L*. Show that in that case the Schechter function is a
power law.
(b) Considering only this regime of the faint galaxies, compute the total luminosity emitted
by galaxies between luminosities Lmin and Lmax. Compute this for values of α of -1, -2
and -3. Discuss which galaxies dominate the luminosity in this regime for the different
values of α.

Added by James R.

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