Question

I have the following data: Mass of HI of the galaxy and radius. I thought using the following equation: Nₕᵢ = ∫nₕᵢ ds where the number density would be nₕᵢ = Mₕᵢ /mₕV, where V is the volume. The problem is the volume is defined as the volume of a disk V=πr2h and I do not know the height of the disk, and I don't think it would be correct to asume the galaxy is a sphere. Is there any way to obtain the height or any other way to obtain the column density?

Answer 1

The total mass of hydrogen gas in the Galaxy is estimated using the volume of a cylindrical galaxy and the density and mass of hydrogen atoms. The volume of the Galaxy is calculated from its given dimensions and used alongside the hydrogen atom density and mass to find the total interstellar mass available for star formation.

Step-by-step explanation:

To estimate the mass of the hydrogen gas in our Galaxy, we can use the formula total mass = volume × density of atoms × mass per atom. Given that the Galaxy is cylindrical, we use the formula V = πR²h for volume, where R is the radius of the cylinder, and h is its height. Converting the given diameter of the Galaxy from light-years to centimeters, we calculate that the radius R is 50,000 light-years, or R = 50,000 × 9.5 × 10±17 cm. The height h is 300 light-years, or h = 300 × 9.5 × 10±17 cm. Therefore, the volume V of the Galaxy is:

V = π(50,000 × 9.5 × 10±17 cm)² × (300 × 9.5 × 10±17 cm) = 2.0 × 10±66 cm³.

With the average density of one hydrogen atom per cm³ and the mass of one hydrogen atom at 1.7 × 10²²27 kg, we calculate the total mass of hydrogen gas. To find how many solar-mass stars could be formed from this gas, we divide the total mass of hydrogen by the mass of a solar-mass star (2.0 × 10³30 kg).