spectra-part2 - #2 assigned dit opportunity 3 colloquium is...

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Unformatted text preview: #2 assigned dit; opportunity 3 colloquium is “Simulating Galaxies, One Star e” by Tom Abel (Stanford). an 137, 3:45pm (coffee/cookies), 4:15 pm (talk) If you attend and write up a brief summary on the talk, you can get 1 point of extra credit ; . Undergraduate Astronomy Club meets on Thursdays at 8:00pm in E88 437 NASA, NOAO, ESAand The Hubble Heritage Team (STSCI/AURA) Last Time: Bohr Model H energy levels: eV is the electron volt,: 1.602 x 10'12 erg = 1 eV Energy (eV) Note: other elements have different allowed energies. _1D *12 Lyman Bqlmer Paschen AST 203 (Spring 2011) Example: Sineg Ionized He (Kutner: 3.6) Consider the 201 transition (what does this mean?) 2 Force balance: me” (2e)e r T2 E = _e_2 7. Total energy: E = $771502 _ (2e)e T This is 4x the . . H Quantization: energy L = mew = 7172 n2h2 2771.364 1 54.4 eV 7” : E = _ — = _ 2m662 E2 n2 n2 Note: neutral He would be different and more complicated. AST 203 (Spring 2011) Example: Singly Ionized He 20: 3 —> 2 transition AE: 54.4 eV 54.4 eV 32 22 > = 7.56 eV Positive value indicated that energy is released in the form of a photon. he he X 10i27 erg . S) . X 1010 cm/S) _r A Z = 1.64 10 o 6V - X 10—12 erg/6V X Cm = 164 nm AST 203 (Spring 2011) Emission and Absorption n=3 Electron orbits not arbitrary— angular momentum quantized “=2 / n=1 0 ’\/\/\/\/‘-> Electron transition from high to a low energy level —> photon (of specific frequency) emitted. (Wikipedia) Absorption of a photon of the right energy: electron moves to higher level. AST 203 (Spring 2011) Formation of Spectral Lines What determines the strength of lines in stellar spectra? To see Ha , we need to lots of H sitting around in the n = 2 state. If there is a lot of H, but all of it is in the ground state (n=1), then nothing will produce the Ha photons. Higher gas T, greater likelihood of finding the atoms in higher energy states. AST 203 (Spring 2011) Excitation # of atoms / unit volume in a given state: population. Excitation processes change level populations. Electrons can jump levels by: Emitting or absorbing a photon. Collisions between atoms An atom with an electron in state m that collides with a second atom can jump to level n. Energy difference (En — Em) taken from the second atom's KE. Similarly, collisions can de-excite an atom. AsT 203 (spring 2011) Excitation Higher T —> atoms move faster —> higher the collision rate. Thermodynamics: average kinetic energy per atom is 3 E _ éka. so higher T = more energy available for collisional excitation. Here, Tk is called the kinetic temperature. Temperature is just a measure of the average kinetic energy of a particle. AsT 203 (spring 2011) Excitation The true distribution of velocities is much more spread out—note the high velocity tail. ZkT 6 Z W 5 _ 4 , 3kT [L Urms : — m 3 We won't worry about the functional form of this 1 ’ distribution in this class. 0 1000000 2000000 3000000 4000000 U (cm/s) AST 203 (Spring 2011) Excitation In thermodynamic equilibrium, Boltzmann distribution gives ratio of two level populations: E a &€*l(ErEi)/ka] 7% 92‘ 92'an (statistical weights) measure degeneracy of states of an energy level. Clearly as T —> 0 ,nj/nz- —> 0 , and the atom is in its ground state. Simply put: higher energy levels less likely to be occupied by electrons. AST 203 (Spring 2011) Excnaflon (Carroll and Osllie, Ch. 8) 0.035 Fraction of electrons in n=2 state increases with T. mo, At T ~ 85000, ~ 1/2 of the “025' electrons are in n=2. ,. “I 0.020 7 Mill +21 3 0.015 7 0.010 — 0.005 7 0.000 0 5000 10000 15000 20000 25000 T(K) Expectation: hotter stars should have stronger H lines AST 203 (Spring 2011) Ionkafion At high T, some atoms will have KE greater than the ionization potential of an atom—ionization. No electron —> no line emission or absorption. Now: gas of atoms, ions, and electrons. Collisions between ions and electrons —> recombination. Ionization equilibrium: rate of ionization = rate of recombination. * We will not go into the detail that you text does for computing the fraction of a gas ionized. AST 203 (Spring 2011) lonkafion Electrons can be from any ionized atom, notjust H Some ionization energies (in eV): Atom Singlylonized Doublylonized H 13.6 He 24.6 54.5 C 11.3 24.4 N 14.5 29.6 0 13.6 35.1 Na 5.1 47.3 K 4.3 31.8 Ca 6.1 11.9 Fe 7.9 16.2 Notation: neutral species of an atom, roman numeral I; singly ionized species with ll; doubly ionized with lll, AST 203 (Spring 2011) lonkafion 1.0 0.8 7 0.6 e nm’[n,+n”) 0.2 - 0.0 0 5000 10000 15000 20000 25000 1'(K) ln stars, T at which half of the H is ionized is ~ 9600 K The steep fall off for T > 10000 K due to ionization. AST 203 (Spring 2011) Excitation + Ionization x10— "2.5.711." 0 1 1 . 0 5000 10000 15000 20000 25000 T(K) Combining ionization and excitation —> T at which most H in n = 2 state: The steep fall off for T > 10000 K due to ionization. AST 203 (Spring 2011) Intensities of Spectral Lines Low T, most of the H is in the ground state: little chance of absorption in the Balmer series— Ha line is weak. Moderate T, H is still neutral, but more is in excited states: population with n = 2—some Ha absorption. As T increases, there will be more and more n = 2 population— Ha line becomes stronger. Very high T, most H ionized— Ha line will becomes weak again. AST 203 (Spring 2011) Intensities of Spectral Lines We can perform this same analysis for the other elements. Note that in stars, H is by far the most abundant element, followed by He, and then everything else. Temperature (K) 50.000 25,000 10,000 8000 6000 5000 4000 3000 I I I I I I (eIIIso DUI? IIoueo) Line strength —> 05 B0 A0 F0 GO K0 M0 M7 Spectral type Note: astronomers call all elements other than H and He metals AST 203 (Spring 2011) M stars Coolest end of the spectrum. T < 3500 K—appear red. No Ha absorption, but some lines from neutral metals are seen. T low enough for molecule formation (e.g. CN and TiO). T from 3500 to 5000 K. Neutral lines dominate. K stars Most H is still in the ground state. Note: astronomers call all elements other than H and He metals AST 203 (Spring 2011) G stars T between 5000 and 6000 K. H lines are stronger than in K stars. (“sumo pue mus) Ionized metal lines appear (e.g. Ca ll; low ionization energy) The Sun is a G2 type star. Relative Flux F stars T between 6000 and 7500 K. T > a G star—ionized metal lines stronger. V Notice how the location of the peak changes with T 4000 5000 6000 7000 8000 9000 AST 203 (Spring 2011) Wavelength (A) uluuvTu—w I .l A stars T ~ 7500 to 10000 K—white—blue. H lines strongest in A stars. Notice where Balmer H7 lines peak (iiewoo pue BAiis) Some ionized metal lines still present. Vega = A0. A0: absolute bolometric magnitude = 0, B — V = 0 05V ‘ ovnuv Relative Flux 354V l Ha M M B stars T ~ 10000 to 30000 K—blue. H lines are weaker because of ionization. A1 3V W W ASW E W W M—‘vww AQFOV W Lines of neutral and singly ionized I I I __ I I I I I I I I He 4000 5000 6000 7000 3000 9000 AST 203 (Spring 2011) Wavelength (A) 0 stars T > 30000 K—hottest stars Earliest spectral types observed are 03 stars Very few of these observed. H lines are very weak—lots of ionization. Sineg ionized He lines still present. Very few lines in the visible spectrum; some UV lines. AST 203 (Spring 2011) The Hertzprung-Russell diagram Absolute magnitude of a lot of stars —> look for trends. Stars in cluster at ~ same distance: differences in m are the same as differences in M Parallax studies can yield the distances to lots of stars. Both spectral type and B — V are related to temperature, so we can make that the independent variable. AST 203 (Spring 2011) AST 203 (Spring 2011) Hertzprung-Russell Diagram Horizontal axis: spectral class, B — V, or T (increasing to left). Vertical axis: Luminosity or absolute magnitude. main sequence: diagonal line running through all the spectral classes. Some T-L combinations not realized in nature. Wide range in L for stars of the same T. Low L population: white dwa rfs. AST 203 (Spring 2011) iiIIIII EiiIiiIi 1|] i:ii:ii:i 1 [Hill] [I Lilli i] i:ii:ii:i‘i 1] [Hill] [ii The Globular Cluster Messier 55 by +1 i:i Colour {B V} Luminosity Class Vertical position in H-R diagram—the luminosity class. Main sequence stars are luminosity class V (Sun = G2 V) Subgiants denoted lV Giants lll Supergiants I (sometimes la and lb) Stars between giants and supergiants are marked with ll. Spectral type G star with luminosity 10 000x higher main sequence must be larger (why?)—giants and supergiants. AST 203 (Spring 2011) Example Star of spectral type G2 has M = 14.72—what is its radius? From recitation #2: M = 4.72 — 2.5log Lo I log = (4.72 — M)/2.5 = —4 Same spectral type of the Sun but puts out 1/10000th of the energy! Same spectral type —> same T—we can find the radius: L 47TR20'T4 R L —=— —= —:\/1—4:.1 LG 47ng>aT4 : RG ll LG 0 0 0 This star has a radius ’l/100th of the Sun—it is a white dwarf. AST 203 (Spring 2011) Spectroscopic Parallax Determine the spectral type of a star based on observations Spectral type —> absolute magnitude distance Measure the apparent magnitude AST 203 (Spring 2011) ...
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