Weighing Machine for Stars

You have probably seen all the ridiculously large numbers in astronomy and you must have thought that how do you calculate all of this? How is it possible to calculate so many details of stars and galaxies which are hundreds of light years away from us? We do all of these calculations based on the light we receive from these stars.

In my last two articles I explained how we figure out velocity, temperature, chemical composition and distance of a star. If you haven’t read them I would highly recommend you to do so.

In this article, I am going to discuss about how we calculate the mass of these stars and galaxy using their light.

First let’s discuss this for our beloved Sun. We calculate the mass/ light ratio for our sun which tells us about how much mass is required to produce 1 unit light.

Ƴ(sun) (mass/light ratio) = 2*10^30 kg/ 3.8*10^36 watt

= 5300 kg/ watt

To make calculations easier we equate this to 1 solar mass/ solar luminosity.

Luminosity is Energy received per second.

Let’s take a example of galaxy called M33. We will figure out its mass.

We can do so by,

Mass(m33) = L(m33). Ƴ(m33)

Now a question arises, how do we figure out the light to mass ratio if we don’t know the mass?

We also know the relation between luminosity and distance. (I explained it in my last article called A forgotten hero-Leavitt).

Flux (energy/ unit area) = Luminosity/ 4πD^2

Thus, L= F. 4πD^2

Calculation of Luminosity of M33

Here, we have practically calculated the flux of m33 and distance of m33 using Cepheid variable star relation.

Now the most interesting part is how do we calculate the mass/light ratio?

We use the “Hertzsprung- Russell Diagram” for that.

Hertzsprung Russel Diagram

Here you can see stars aligned according to their temperature and luminosity. From comparison between Sun and the other stars we calculated that on average a star in our galaxy or some other galaxy has as

(Mass/Velocity Ratio) Ƴ= 4 solar mass/ solar luminosity

Substituting values of L and Ƴ in given equation,

Mass(m33) = L(m33). Ƴ(m33)

We can figure out the mass of the galaxy on basis of the assumption that the other galaxy consists of stars similar to that of Milky Way.