# Homework - A galaxy in the local universe

• fab13
In summary, the given homework questions involve determining the distance and luminosity of an elliptical galaxy based on photometry data and the Faber-Jackson relation, estimating the total mass and M/L ratio of the galaxy using the SIS model, and determining the fraction of stellar mass still surviving as stars in the main sequence after a major-merger burst event. Equations provided include the Faber-Jackson relation, absolute magnitude of the Sun in B-band, absolute magnitude, gravitational constant, and the Salpeter IMF.
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

!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}##

## 1. What exactly is "Homework - A galaxy in the local universe"?

"Homework - A galaxy in the local universe" is a scientific research project that focuses on studying galaxies within our local universe. It aims to understand the formation, evolution, and properties of these galaxies through various observational and theoretical methods.

## 2. Why is this research important?

This research is important because galaxies are the building blocks of our universe and understanding them can provide insights into the larger structure and formation of the universe. Additionally, studying galaxies can also help us understand the processes that govern the formation and evolution of stars and planets.

## 3. How is this research being conducted?

This research is being conducted through a combination of observations using telescopes and data analysis, as well as theoretical models and simulations. Scientists use a variety of instruments and techniques to collect data on galaxies and then use mathematical models to analyze and interpret the data.

## 4. What have been the major findings of this research so far?

Some of the major findings of this research include the discovery of new types of galaxies, such as dwarf galaxies and ultra-diffuse galaxies, as well as a better understanding of the role of dark matter in galaxy formation and evolution. This research has also provided insights into the properties and behavior of supermassive black holes at the center of galaxies.

## 5. How does this research impact our daily lives?

While this research may not have a direct impact on our daily lives, it contributes to our understanding of the universe and the world around us. It also has practical applications in fields such as astronomy, physics, and technology. Additionally, the knowledge gained from this research can lead to new advancements and innovations in various industries.

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