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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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) ...
View Full Document

Ask a homework question - tutors are online