Homework - A galaxy in the local universe

[fab13]

Homework Statement

I have the following questions as homeworks and I would like to get help.

Here's some informations given to help us to answer :

Photometry :
U=11.60

B=11.16

V=10.20

Redshift : z= 0.00780

Central velocity dispersion : $\sigma_{v}$ = 210 km/s

Introduction :

The elliptical galaxy above has been extracted from a survey in the local universe. The table
presents the magnitudes in three different filters, the redshift and the measured central velocity
dispersion.

3. Questions and attempts to solution

Question 1:

Knowing that the Faber-Jackson relation in the B-band filter can be written as: $log \sigma_{v} = -0.1 M_{B} + 0.2$

and the absolute magnitude of the Sun in this band is $M_{B} (Sun)= +5.48$, compute the distance to this galaxy (in Mpc) and its luminosity in the B-band (in solar units).

My element of answer : If $\sigma_{v}$ is given, then we infer $M_{B}$, then I apply the relation of absolute magnitude :

$M = -2.5 log_{10} (\dfrac{L}{4\pi (10pc)^2}) + C$

So I put $M_{B}$ instead of $M$ in above expression and $L$ the luminosity of galaxy.

Can I determine $C$ constant by setting : $M_{B,sun} = 5.48$ and $L=L_{sun}=10^{26}$ Watt ?

Once I have $C$ constant, How can I get the distance of the galaxy ?

Question 2: Estimate the total mass of this galaxy inside a radius R=20 kpc, and the M/L_{B} ratio (in solar
units). You can use the following values for

G = 1.327 1011 km3 s-2 M_Sun -1 and 1 kpc = 3.086 1016 km

Answer 2: Can I use here the formula sor SIS model, i.e :

$M = \dfrac{2\sigma_{v}^2\,R}{G}$

in order to get the total mass of Galaxy ?

and what about the value of $L_{B}$ luminosity ?

Question 3: Suppose that all stars in this galaxy were born in a single major-merger burst event about 10 Gyr ago. From this original burst, what is the fraction of stellar mass still surviving as stars in the main sequence ? Use a Salpeter IMF, and a star formation range between 0.1 and 120 solar
masses.

I saw that Salpeter IMF is equal to : $\xi(M) = \xi_{0}M^{-2.35}$

but how to deal with the fraction of stellar mass still surviving as stars in the main sequence ?

Question 4: If the luminosity in the B band is dominated by stars of in the RG branch, with masses $m ~ 1M_{sun}$
(within ~10%) and average luminosities $~1000 L_{sun}$, estimate the total stellar mass of this galaxy using the same assumptions as in question 3 regarding the IMF. Comment the result

Elements of answer : it seems that I have to take into account, for the total stellar mass, the stars mass of main sequence and the red-giant mass, doesn't it ?

How to perform this calculus ?

Homework Equations

: none equations are provided for this homework
[/B]
Sorry if the answers are simple but I am a beginner in galactic and extra-galactic matters.

Even short answers or suggestions could help me to solve these different questions. Regards

 

[NateD]

!Homework EquationsQuestion 1: Faber-Jackson relation: $\log \sigma_{v} = -0.1 M_{B} + 0.2$Absolute magnitude of the Sun in B-band: $M_{B,Sun} = +5.48$Absolute magnitude: $M = -2.5 \log_{10} (\dfrac{L}{4\pi (10pc)^2}) + C$Question 2: Gravitational constant: $G = 1.327 \times 10^{11} km^3 s^{-2} M_{\odot}^{-1}$1 kpc = $3.086 \times 10^{16} km$Question 3: Salpeter IMF: $\xi(M) = \xi_{0}M^{-2.35}$Question 4:Average luminosities of red-giant stars: $~1000 L_{sun}$