ASTRONOMY 3303   Portfolio Exercise #8     Wed, Sep 20, 2017

Please follow along with today's lecture to take note of the answers to the questions. If you don't get all theanswers in class, then answer them at home, and then include this page in your portfolio.

The color-magnitude diagram from SDSS:

What does h73 refer to?

The Luminosity Function (Section 3.10 of Schneider's book)

The luminosity function of galaxies (stars, clusters) describesthe number density of objects of a specific luminosity. Inabsolute magnitude terms, we define Φ(M) dM as thenumber density of galaxies with absolute magnitudes in theinterval (M, M+dM); obviously we can substitute luminosityL so that the number density of galaxies with L in the range(L, L+dL) is Φ(L) dL. The total density of galaxies then is (forthe M case):

The galaxy luminosity function (LF) is often expressed interms of a function first proposed by Schechter (1980), nowdubbed the Schechter Luminosity Function:

Note that α is the faint end slope and L* is theluminosity at which the slope changes fromexponential to power-law. L* is also called the"characteristic luminosity".

The ratio Φ*/L* is a normalization constant which depends on the nature and depth of the dataset for whichthe LF is being computed.

Because of the high quality and sheer number of galaxies in its database, the SDSS has provided a morerobust measurement of the LF. Because of its multi-filter capability, it also provides colors, which in turn allowus to convert the observed optical luminosity into an equivalent stellar mass, taking into account differencesin the star formation histories, averaged over a population Among other things, the SDSS suggests that weshould separate galaxies into two separate populations, so that the LF is better fit by a double Schechter

function of the form:

To the right are results derived from the SDSSfor the luminosity function. Remind yourselfabout the Sersic brightness profile (lastlecture):

What do you notice about the diagram? Doyou have any questions about it?

From the SDSS LF, what do you concludeabout                 -- luminous galaxies?                -- faint galaxies?

Linking luminosity to Mass

Scaling relations: how galaxy properties scale with each other:

In 1976, Faber and Jackson suggested a simple relation for elliptical galaxies between the central velocitydispersion and their luminosity

More recently, this relation has been expanded to include a dependence of size (or surface brightness); this iscalled the "fundamental plane".

The Fundamental Plane (bottom right above), relates the effective radius, Re, the average surfacebrightness within that radius <μ>e and the central velocity dispersion σ0 and is fit bybr>

A similar Tully-Fisher relationfor spirals was proposed in 1977:

where the slope is about α ~ 4.

A more modern version of the Tully-Fisher relation applies to spiral anddwarf galaxies and requires that we take into account the total baryonicmass, gas plus stars. It is thus called the baryonic Tully-Fisherrelation (McGaugh 2012).

Be sure you understand what is plotted on the axes.

What is involved in calculating the baryonic mass of a galaxy?

The black hole knows what galaxy it resides in!