Question

3 The galaxy luminosity function is a useful way to characterise the distribution of the number of galaxies as a function of the luminosity of galaxies. It is often given by the form called the Schechter Function: $\Phi_\star(L)dL = n_\star \left(\frac{L}{L_\star}\right)^\alpha \cdot e^{-L/L_\star} \frac{dL}{L_\star}$ a) Explain what the value $\alpha$ represents and give typical values found in galaxy populations. Explain how a galaxy population with a lower (more negative) value of $\alpha$ would differ from a larger value of $\alpha$. b) Show that at low values of $L$ this function can be approximated by $\Phi(L)dL = n_\star \left(\frac{L}{L_\star}\right)^\alpha \frac{dL}{L_\star}$, using small number approximations. c) For two different galaxy populations the fitted values of $\alpha$ are $\alpha = 1$ and $\alpha = -1$, respectively. Plot the distribution of these luminosities for these systems using the approximation in b). At what value of $L$ do these two luminosity distributions intersect?

          3
The galaxy luminosity function is a useful way to characterise the distribution of the number
of galaxies as a function of the luminosity of galaxies. It is often given by the form called the
Schechter Function:
$\Phi_\star(L)dL = n_\star \left(\frac{L}{L_\star}\right)^\alpha \cdot e^{-L/L_\star} \frac{dL}{L_\star}$
a) Explain what the value $\alpha$ represents and give typical values found in galaxy populations.
Explain how a galaxy population with a lower (more negative) value of $\alpha$ would differ from a
larger value of $\alpha$.
b) Show that at low values of $L$ this function can be approximated by
$\Phi(L)dL = n_\star \left(\frac{L}{L_\star}\right)^\alpha \frac{dL}{L_\star}$,
using small number approximations.
c) For two different galaxy populations the fitted values of $\alpha$ are $\alpha = 1$ and $\alpha = -1$, respectively.
Plot the distribution of these luminosities for these systems using the approximation in b). At
what value of $L$ do these two luminosity distributions intersect?

3
The galaxy luminosity function is a useful way to characterise the distribution of the number
of galaxies as a function of the luminosity of galaxies. It is often given by the form called the
Schechter Function:
Φ⋆(L)dL = n⋆((L)/(L⋆))^α· e^-L/L⋆(dL)/(L⋆)
a) Explain what the value α represents and give typical values found in galaxy populations.
Explain how a galaxy population with a lower (more negative) value of α would differ from a
larger value of α.
b) Show that at low values of L this function can be approximated by
Φ(L)dL = n⋆((L)/(L⋆))^α(dL)/(L⋆),
using small number approximations.
c) For two different galaxy populations the fitted values of α are α = 1 and α = -1, respectively.
Plot the distribution of these luminosities for these systems using the approximation in b). At
what value of L do these two luminosity distributions intersect?

Added by Carol S.

Question

Please give Ace some feedback