How Do Scientists Determine The Temperature of A Star?

How do you measure your body temperature? The simplest answer is "using a thermometer". But, is it so in case of stars as well? The answer is a big NO. As we know, the Temperature of A Star can range upto several thousand Kelvins. But, till date, no such thermometer is available that can withstand such high temperatures. Moreover, even if such a thermometer with super powers is there, who is going to use it on stars billions of light years away? So, how do we really measure the temperature of stars? Here is where the indirect methods come to our rescue. In order to overcome the above mentioned problems, Astrophysicists use a number of indirect techniques of temperature measurement. Let's have a look at some of these one by one!

Wien's Displacement Law :

Wien's displacement law is concerned with the radiation spectrum of a black body. According to this, the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature. Using this inverse relation between wavelength and temperature, the temperatures of stars can be estimated. However, this is only applicable to stars that have spectra which closely approximates to that of a blackbody. Moreover, the flux-calibrated spectra of the star under consideration should also be available. However, this method does not give very accurate results as stars are in general not black bodies.

Stefan's law :

Another law that can be put in use to measure temperature of stars is the Stefan's law. The Stefan–Boltzmann law describes the power radiated from a black body in terms of its temperature. According to this law, the total radiant heat power emitted from a surface is proportional to the fourth power of its absolute temperature. {L=4 \pi R^{2} \sigma T^{4}} . Here, σ is the Stefan-Boltzmann constant, L is the luminosity, R and T are the radius and temperature of the star under consideration.

At first, we measure the total flux of light coming from the star. Combining these factors, scientists estimate the luminosity. And using interferometers, radius of star can be found . Eventually, the temperature is measured by plugging all these terms in the Stefan's formula. The limiting factor here is the difficulty in measuring the radii of the largest or nearest stars. So measurements exist only for a few giants and a few dozen nearby main sequence stars. However, these act as the fundamental calibrators against which astrophysicists compare and calibrate other techniques.

By spectrum analysis of a Star:

We know that atoms/ions have different energy levels. And, the population of these levels depend on temperature. Higher levels are occupied at higher temperatures and vice versa for lower levels. The tansitions between levels can result in the emission or absorption of light at a particular wavelength depending on the energy difference between the levels concerned. Generally, a star is hotter on the inside and cooler on the outside. The cooler, overlying layers absorb the radiations coming out from the centre of the star . This results in absorption lines in the spectrum we obtain.

The spectrum analysis consists of measuring the strengths of these absorption lines for different chemical elements and different wavelengths. The strength of an absorption line depends primarily on the temperature of the star and the amount of a particular chemical element. However, several other parameters like gravity, turbulence, atmospheric structure etc. can also influence it. This method gives temperature measurements with a precision as good as +/-50 Kelvins.

Colour - Temperature Relationship:

Another method to measure temperature of stars is by analysing their colour. Although all stars appear white, they have different colours when carefully viewed. The variations are a result of their temperature. The cold stars appear red, and hot ones are blue. We measure the colour of a star by an instrument called photoelectric photometer. This involves passing the light through different filters and finding the amount that passes through each filter. The measurements from the photometer are converted to temperature, using standard scales. This method is highly useful when a good spectrum of a star is not available. The results obtained in this method are accurate upto +/- 100-200 K . However, this method gives poor results for cooler stars.

Each of the above mentioned methods have their own perks and limitations. Still, Astrophysicists all over the globe widely use these methods and they end up giving satisfactory results.

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