*HR diagram simulation:* http://astronomy.nmsu.edu/geas/labs/hrde/hrd_explorer.html ## 2.1 Introducing spectral lines #### Hydrogen lines lowest energy level of H is the ground state which is *E$_1$=-13.6 eV* The excited states are *E$_n$ = $\dfrac{-13.6 eV}{n^2}$ {where n is the energy level, 2,3,4...}* A photon with the right amount of energy allows the hydrogen atom to go to a higher energy state. As the electron falls back to a lower energystate it will transmit a photon with the frequency: *f = $\dfrac{E_f-E_i}{h}$ {h = 6.626 x 10$^{-34}$ J Hz$^{-1}$ * with *c = f$\lambda$* we get: *$\lambda$ = $\dfrac {ch} {E_f-E_i}$* when we fill in all the constants (c, h, eV): $\lambda$ = $\dfrac{1.24082 x 10^{-6}}{E_f-E_i}$ ## 2.2 Spectral lines in stars #### Spectral lines strength The spectral line can have different forms( shallow, wide, etc). The strength of a spectral line is quantified by its [[../Glossary/equivalent width]]. The factors that contribute to the strength of a line are: - temperature - the abundance of the relevant element - the efficiency of the corresponding transition #### Stellar classes The type of star depends on photospheric temperature and is distinguished by the absorption lines: ![[Pasted image 20231109215711.png|300]] The [[../Glossary/Harvard Spectral Classification]] distinguishes O,B,A,F,G,K and M stars. Each class has 10 subdivisions from 0 (hotter, "earlier") to 9 (cooler, "later") . mnemonic: **Only Brilliant Astronomers Find Glowing, Kosmic Matter** ![[../Assets/Pasted image 20231109215611.png|300]] #### Using spectra to classify stars ![[../Assets/Pasted image 20231111195214.png|300]] #### [[../Glossary/luminosity]] and spectra A more luminous star will have narrower absorption lines then a less luminous star with the same temperature. The difference in Lum is because of the radius (L = 4$\pi$ R$^2$ $\sigma$ T$^4$) as the temp is equal. A small star has a denser atmosphere which leads to [[../Glossary/pressure broadening]]. This makes it possible to measure the luminosity of a star from the width of the absorption lines. The [[../Glossary/Morgan-Keenan]] (MK) spectral classification system supplements the temperature-based classes of the Harvard system with [[../Glossary/luminosity class]] ranging from I (most luminous) to V (least luminous). Our Sun is a G2 V star. #### Composition and spectra A final property of stars which can be determined from high-quality spectra is their composition: the relative [[../Glossary/abundance]] of different elements in their atmospheres. ## 2.3 The [[../Glossary/Hertzsprung-Russel diagram]] - The H–R diagram reveals that most stars occupy four regions with characteristic combinations of temperature and luminosity: - the [[../Glossary/main sequence]] in a band from high to low luminosities and temperatures - [[../Glossary/red giants]] with moderate luminosities and relatively low temperatures - [[../Glossary/super giants]] with high luminosities and a range of temperatures - and [[../Glossary/white dwarf star]] with low luminosities and relatively high temperatures. ![[../Assets/Pasted image 20231111203856.png|300]] ## 2.4 Other sources of spectral lines #### 2.4.1 Molecular spectra In a comparable way to single atoms, the electrons in molecules can occupy a range of permitted quantum states associated with different energy levels. Molecules can absorb and emit photons and undergo electronic transitions between energy levels; they can also be excited to higher energy levels by collision with other atoms or molecules, imparting kinetic energy. The energy required to completely separate an atom from the molecule is [[../Glossary/dissociation energy]]. There are also non-electronic transitions: - [[../Glossary/vibrational transitions]] - [[../Glossary/rotational transitions]] molecular electronic transitions require more energy than the vibrational transitions, rotational transitions require the least energy. Therefore ($\lambda$ = $\dfrac{hc}{E_f-E_i}$ ) we find the molecular elec trans lines in the *UV*, vibrational in the *IR* and rotational in the *microwave/radio* region. ![[../Assets/Pasted image 20231114091755.png|300]] #### 2.4.2 Molecules in space CO is a marker for molecular hydrogen (h$_2$). #### 2.4.3 The 21 cm line The 21 cm (0.211m) line shows the presence of neutral atomic hydrogen (H I). This radiation is due to the [[../Glossary/spin-flip transition]] of the electron. ## reference [[../Assets/TMA 2]] [[Astronomy]]