<p>Photometry and Spectrometry have changed astrophysics forever. It was Fraunhofer who first determined that different stars have different kinds of spectra. Although in the beginning it was only three types but with modern technology and many improved instruments now we can make a very subtle distinction. </p>
<h1>Classification of stars according to their spectra and a little bit of history</h1>
<p>During the end of 19<sup>th</sup> century, an astronomer named <b>Edward Pickering</b> and his female colleagues started a revolution in the field of <b>spectral taxonomy</b>. They dived the stars according to how strong they look in their hydrogen absorption line. It starts with the capital letter A. In the same time, another colleague of him named <b>Antonia Maury </b> was trying to use another system which she was using to measure how wide the spectral lines are and according to this method she put B group in front of A. Then <b>Annie Cannon</b> was the one who combined these both and put O before B and A and subdivided them for example,from A0 to A9. So, the classification goes like O B A F G K M and it later became the temperature sequence. O is the hottest blue star and M is the coolest red star. We remember the sequence by the sentence " Oh Be A Fine Girl Kiss Me".  The hot stars indicate that they are early-type stars and those close to the end are called late-type stars. The subdivisions also play the same rule. For example, M0 is an "early M star" and M9 will be "late M type star". Cannon has classified around 200,000 stars which are included in <b>Hendry Draper Catalogue</b> and many stars are referred to their HD number. For example, Betelgeuse is known commonly HD 39801. </p>
<img src="https://upload.wikimedia.org/wikipedia/commons/5/5a/Astronomer_Edward_Charles_Pickering%27s_Harvard_computers.jpg"><center><a href="https://commons.wikimedia.org/wiki/File:Astronomer_Edward_Charles_Pickering%27s_Harvard_computers.jpg">CCO</a> | Pickering's Harvard Astronomy Group</center>
<p>But for Vega (A0 star ) has a strong hydrogen absorption line than the sun (G2 star) but the sun has a strong calcium absorption line than Vega. So, the question was is these different spectral lines in different stars is because of their formation inside or the surface structure. Lucky for us then Quantum revolution has already started and it gave us the explanation of why and absorption and an emission line is created. When in an atom an electron jumps from on lower orbital to a higher orbital it has to absorb a photon which has the same amount of energy as the energy difference in between the two orbitals. That is how an absorption line is created. Vice versa when an electron goes from a higher to lower energy, one photon has to be emitted to carry away the energy between the two orbitals. That is how emission lines are created. For example, Balmer lines are created when election moves from the second orbital to the higher. For example, Balmar absorption lines are created when electron make an upward transition from n=2 orbital and emission lines happen when from high energy orbital electron moves in orbital n=2. So, all these spectral lines of different stars are because of the electrons in different atomic orbitals in the outer layers of the stars.</p>
<center><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/9/9a/Spectral_lines_of_the_hydrogen_atom.svg/528px-Spectral_lines_of_the_hydrogen_atom.svg.png"></center><center><a href="https://commons.wikimedia.org/wiki/File:Spectral_lines_of_the_hydrogen_atom.svg">CCO</a> |Spectral lines of hydrogen atom</center>
<p>It's really hard to explain the formation of spectral lines because the electron can be found in any of the orbitals of the atoms. The atoms can be also in different ionization state and can have a completely different stage of orbitals. In astronomy ionization stages are indicated by roman numbers. For example, HI is neutral hydrogen and HII is one time ionized hydrogen and any atom after helium is count as metals in astrophysics. The reason for it is in the outer space most of the elements are hydrogen and helium. Later in because of the discovery of <b>Brown dwarf stars</b> we added L and T in the Harvard classification of stars. Brown dwarfs are stars having so less mass to trigger the nuclear reaction and have the temperature between 1300 K (L) to 2500 K(T).</p>
<h1>Hertzsprung and Russell diagram</h1>
<p>At the beginning of 20<sup>th</sup> century, data about an increasing amount of celestial objects were collected about astronomical objects. It was then the astronomers came to know how wide-ranging the absolute magnitude and stellar luminosity is. O star tends to be the most luminous and brightest and M be the opposite. The work on the binary star showed there is a direct correlation between the mass and luminosity of a star. So, that made the O type o stars the most massive stars. From here the theory of stellar evolution originated from although it was mostly incorrect. It was thought all stars are born as O type stars massive and bright and then with time it loses its mass and fade away and become cool M type stars which we know in today that not correct. But it was a very first great step toward explaining the problem of stellar evolution.</p>
<center><img src="https://upload.wikimedia.org/wikipedia/commons/4/46/Star_types_T_through_O.png"></center><center><a href="https://commons.wikimedia.org/wiki/File:Star_types_T_through_O.png">CC BY 3.0</a> by<a href="https://commons.wikimedia.org/w/index.php?title=User:Isna_%27Kasamee&action=edit&redlink=1">Isna 'Kasamee</a>  |Types of star</center>
<p>So, the idea that stars gradually lose their brightness and fade away was correct. That means there should be a direct correlation between the absolute magnitude of the star and the class were it is. An amateur astronomer and engineer Hertzsprung analyzed the data of stars which are most accurate and found a correlation and Russel as well at the same time. In this diagram in the horizontal axis is the spectral group or the temperature of the star and in the vertical axis is the luminosity or the absolute magnitude of the star. With time H-R diagram became one of the most important diagrams in astrophysics.  Although in the beginning, there were only a small amount of stars in the diagram as there were not a lot of stars whose absolute magnitude was correctly known. The key thing in this diagram is as the luminosity decreases the absolute magnitude increase( negative absolute magnitude star is more luminous than the positive)</p>
<center><img src="https://upload.wikimedia.org/wikipedia/commons/7/78/H-R_diagram_-edited-3.gif"></center><center><a href="https://commons.wikimedia.org/wiki/File:H-R_diagram_-edited-3.gif">CC BY-SA 2.5</a> by<a href="http://www.atlasoftheuniverse.com/me.html">Richard Powell</a>  |H-R diagram</center>.
<p>Most of the star densely group in a track and are some stars above the track and some bellow. This track is known as the main sequence. Our sun belongs to this sequence. This track starts from the upper left and ends in the bottom right. In the upper right is the hottest and brightest O and B stars and in the bottom right is the faint and cold red dwarfs. The stars in the main sequence are mostly stable and spend most of their life in this phase. A small number of bright supergiant and giant (absolute magnitude >0) stars stays above the main sequence track and they mostly fall in all the groups. Those star below the main sequence with high temperature are called the white dwarfs (absolute magnitude >10) which is a very interesting type of star but I will leave that topic for another day. </p>
<p>Now, let us look into a very simple but very important equation in astrophysics--</p>
<center>http://quicklatex.com/cache3/94/ql_9c685562da6f688fef8ddeac89c36394_l3.png</center>
<p> L is luminosity, R is for radius and T is for temperature. So, we can see that here luminosity mostly depends on temperature and radius. So, the most luminous stars will fall in group O and B and the faint will fall in the group M. Most of the stars follow this rule. That is why they are basically in the main sequence. But there are so stars which don't follow this rule. These stars are although in the same spectral group but they have a huge difference in their luminosity because of their huge difference in their size. So, that is why the cold red giant is luminous and hot white dwarfs are fainter stars. Supergiants fall to almost all the spectral group. The name giant and dwarf are chosen because for the same spectral group in the case of luminosity there is a huge difference based on radius.</p>
<h1>Morgan Keenan luminosity classes</h1>
Hertysprung wanted to know is there a difference in spectra between a main sequence star and a giant star which are in the same spectral group. The answer was given by Antonia Maury. The difference is in the strength of the spectral line. Later it was Morgan and Keenan worked on this problem and it is known as MK classification. In this system, they used two parameters which are the spectral class and the luminosity. They divided the stars in seven classes according to luminosity.Which are-
<p>1. Supergiants with more subclasses(Ia, Iab, Ib)</p>
<p>2. Bright giants</p>
<p>3. Giants</p>
<p>4. Subgiants</p>
<p>5. Mainsequence</p>
<p>6. Subdwarfs</p>
<p>7. White Dwarfs</p>
<p>The difference in the spectra of stars which belongs to the same class but with different luminosity is so small rather than stars from different spectral class. For example, the difference in spectral line of a giant star and a dwarf is only in the wideness of the spectral lines.  Giant stars are apparently huge in radius and that's why it has less gravitational pull. So, the atmosphere is thin and vast and spectral lines are narrow. The condition in white dwarf stars are quite opposite to the giant star and that's why the spectral lines are wide.</p>
<h1>Application of H-R diagram</h1>
<h2>Determining stellar distance</h2>
<p> If we really know the spectral class and luminosity class of a star we can easily determine the absolute magnitude from the H-R diagram. For, giant and the main sequence star the absolute magnitude can be measured very easily without much error. As we know it is easy to measure the apparent magnitude and we use the formula underneath to find the parallax. Parallax found in this way is called spectral parallax.</p>
<center>http://quicklatex.com/cache3/38/ql_8a9867fdd23cb3623916fce077b4a638_l3.png</center>
Here p is parallax, M is absolute magnitude and m is apparent magnitude. By measuring the parallax we can easily measure the distance. Distance measured in this way is less correct than measured through trigonometric parallax but distance measure in this way is very important for which it is not possible to measure the trigonometric parallax.
<h2>Determining the mass of the star</h2>
<p>Mass can be only determined in one way as I said up and that is through binary stars but through H-R diagram we can also calculate the mass of the star with some errors. If we look at the H-R diagram we know for the main sequence star mass decrease from upper left to the bottom right and that is true for temperature as well as the radius. So, for that reason the surface gravitational acceleration is constant. </p>

<center><img src="https://upload.wikimedia.org/wikipedia/commons/1/17/Hertzsprung-Russel_StarData.png"></center><center><a href="https://en.wikipedia.org/wiki/Hertzsprung%E2%80%93Russell_diagram#/media/File:Hertzsprung-Russel_StarData.png">CC BY 4.0</a> by<a href="https://www.eso.org/public/images/eso0728c/">ESO</a>  |H-R diagram to to determine mass through radius</center>
<p>From the diagram above we can easily find the radius of a main sequence star and using the formula below we can find the mass</p>
<center>http://quicklatex.com/cache3/d6/ql_bfb628534d67354a9d47304d75cc22d6_l3.png</center>
Here, M is mass, R is the radius, G is gravitational constant and g is gravitational acceleration.
<h1>Final thought</h1>
Stellar spectra which is formed in the outer later of a star gives us almost all information about the star's radius, temperature, mass, and other parameters as well. We can also determine one from the another as well. So, the classification of stars done by the Harvard astronomers created the basic foundation of astrophysics and again every information we know from the outer space depends mostly on spectral absorption lines and emission lines. That's all for today, don't forget to ask me in comments if you are interested in this topic or any topics about astrophysics. 
<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>
<p>4. <a href="http://astronomy.swin.edu.au/cosmos/H/Hertzsprung-Russell+Diagram">Cosmos</a>
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