In my last posts, I have been talked about stellar magnitudes (apparent and absolute ). But now when we measure those magnitudes we measure them in a particular wavelength range. This range define the sensitivity of a filter. But now for idealism, we also have magnitude which doesn't depend on a particular range of light wavelength, rather measured under all wavelength is called bolometric magnitudes. For apparent magnitudes we use m <sub>bol</sub> and for absolute M <sub>bol</sub>. Why this is important I will explain it in a while.
<h1>Wavelength filters</h1>
<p>Is it possible to determine the color of a star? The answer to that question is yes, it is possible. Now, the next question arrives is, how? The answer is by using filters which are sensitive in a specific range of wavelengths. Practically there is a system known as UBV, where we measure a star's apparent magnitude through three filters.</p>
<IMG SRC="https://upload.wikimedia.org/wikipedia/commons/9/94/1416_Color_Sensitivity.jpg">
<center><a href="https://th.wikipedia.org/wiki/%E0%B9%84%E0%B8%9F%E0%B8%A5%E0%B9%8C:1416_Color_Sensitivity.jpg"> CC BY 3.0</a> By  OpenStax College | Different filters and their peaks </center>
<p>By U filter we measure the star's apparen t magnitude in ultraviolet range. The filter is centered at 365 nm and has a wide range of 68 nm</p>
<p>B filter is used to measure star's blue magnitude. The filter is centered at 400 nm and has a wide range of 98 nm</p>
<p>V filter is used for measuring the star's visual magnitude. It has it's center at 550 nm and bandwidth of 89 nm. </p>
<h1>What is color index and bolometric correction</h1>
Until now we talked about the bolometric and filter apparent magnitude of stars. But we can measure the absolute magnitude of them but for that we need to know the distance and known as  M <sub>U</sub>,  M <sub>B</sub>,  M <sub>V</sub> for UBV filter system. U-B color index is known as the difference between the absolute magnitude through U and B filter and for other's are likewise.
<center><p>U-B = M <sub>U</sub> -  M <sub>B</sub></p></center>
<center><p>B-V = M <sub>B</sub> -  M <sub>V</sub></p></center>
<p>You may ask me now why i am bothering with all this equations? Well, we say mathematics is the language of nature. Every symbol we use have some meaning. As we know when the brightness of a star increases, the magnitude decreases. So, what is the application of B-V? Well, for example, if we measure two star's B-V magnitude, the star which has less B-V value indicates that it is more blue than the other. Fro, the equations we can also see that this color indexes are independent of the distance. We can also measure the difference between bolometric magnitude and visual magnitud and it is known as the bolometric correction.  </p>
<center><p>BC= M <sub>bol</sub> -  M <sub>V</sub></p></center>
<h1>Color-color diagram </h1>
<center><IMG SRC="https://upload.wikimedia.org/wikipedia/commons/e/e9/Effective_temperature_and_color_index.png"></center>
<center><a href="https://en.wikipedia.org/wiki/Color%E2%80%93color_diagram#/media/File:Effective_temperature_and_color_index.png"> CC BY 3.0</a> By  <a href="https://commons.wikimedia.org/wiki/User:Brews_ohare">Brews ohare</a> | Color-color diagram</center>
Color-color diagram is a diagram where we make a graph putting to different color indexes in two axis, U-B in the y axis and B-V in the x axis. It is really hard to place a star in the color-color diagram considering its physical properties as well. If stars were black bodies it would follow the dark strait line in the graph. However, stars are not blackbody. Some light can be absorbed by the stars outer layers and how much it will absorb depends on the wavelength of the star and the temperature of the star and other factors can play a role as well. That is the reason why the color index of supergiant stars and main sequence differs a little bit even though they can be of same temperature. That is all for today.  Have a nice time until my next post.
<h1> Reference</h1>
<p>1. Carroll and Ostlie, An Introduction to Modern Astrophysics</p>
<p>2. Olga Atanackovic, General Atrophysics</p>
<p>3. Mirjana Vukicevic, Theoretical Astrophysics</p>