Stellar Radius: A concept based on purely physics..

Hello... If you have been following my blogs, I discussed about stellar radii in my last blog. Stellar Radius is a key piece of information in the catalogues of many telescopes. It in general helps determining the size of the exoplanets and furthermore it gives a basic idea of the star itself. So...

 . What is Stellar Radius?

 Astronomers use the stellar radius as a unit of measurement to describe the size of stars in relation to the Sun. In simple terms, it is just used to measure the size of the star.

 . How is Stellar Radius measured?

Stellar Radius is measured through the luminosity and temperature through the Stefan-Boltzmann law. Yes, I know, it sounds complex but I will try to explain it in a much easier way. 

 So, what is Stefan Boltzmann law? This law describes and correlates power emitted by a black body with its temperature. It is given by P=kAT⁴   

 

P=Power emitted by the star (Luminosity of the Star)

k=Stefan Boltzmann Constant (5.670734*10^-8 Wm^-2K^-4)

A=Radiating Area (As the stars are spherical, the surface area can be given by 4πr²)

T=Surface Temperature in Kelvin

 

The entire thing further transforms into L=k*4πr²*T⁴

The r otherwise defined as the radius is the main thing we aim to achieve.

 

To make this entire process significantly easier, we calculate the entire thing with respect to the sun. When we form a ratio, the proportionality constant disappears and the equation is only in the form of temperature and luminosity.

 

 R, T and L are Radius, Temperature and Luminosity respectively and the subscript s refers to the data of our star Sun.

So, all in all, we need the temperature and luminosity of the stars along with the basic values of Sun. So, how do we measure that?

 

. Measuring temperature

Astronomers in general classify stars into seven main types, identified by the letters O, B, A, F, G, K, and M based on their temperatures. To achieve that, they have to compare the spectra of the star to that of a black body. Atoms have different energy levels. Higher levels are occupied at higher temperatures and vice versa. The transitions between this level results in emission or absorption of light. The spectrum analysis in comparison with the spectrum to that of black body to determining the temperature of the body.

 

. Measuring Luminosity

Luminosity is defined by this formula L=4πd²*b where d is defined as the distance from the earth to star. ‘b’ is defined as the apparent brightness. A question might arise how do we measure the distance? Well, it is measured by the usage of parallax. Parallax is the observed displacement of an object caused by the change of the observer's point of view. It’s basically a relative change in the position of the stars in respect to brightness.

 Now, that we have calculated the luminosity and temperature it becomes much simpler to calculate stellar radius. The value of the radius helps further expands into determining the size of planets. Sometimes, it surprises me that some law determined by mere human beings explains so much related to stars and planets. This might have been a difficult blog to follow to but if you did... Thank You!

 

Stay tuned for more...