Atoms and spectral linesAtoms: small dense nucleus consisting of protons and neutrons, usually with:

p ≈ n.

Light electrons orbit the nucleus like planets around a star, but more complicatedorbits!

In Bohr’s model electron orbits are quantized. That is, electrons stay in discrete,well-defined ‘shells.’ More precisely,….

1. Orbits (shells) balance Coulomb attraction and centripetal force,

€

mv2

r=(Ze)er2

.

The discreteness comes from the assumption that orbitalangular momentum is quantized -

mvr = nh/(2π)

2. Note especially the existence of a lowest or ground stateorbit with n=1.

This doesn’t exist classically, it is an intrinsically quantumphenom.

3. The spacing between the orbits gets smaller for large n.

Proof:

€

mr

nh2πmr

2

=(nh /(2π ))2

mr3 =Ze2

r2

where we've substituted for v.

∴ rn =(nh /(2π ))2

mZe2 .

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Then, Δr = rn+1 − rn =(h /2π)2

mZe2

(n +1)2 − n2[ ],

Δrr

=2n +1n2 ≈

2n

, for large n.

In terms of orbital energy:

€

En = 12mv

2 −Ze2

r= −

me4Z 2

2n2(h /2π)2

so, ΔE = En+1 − En = −me4Z 2

2(h /2π)21

(n +1)2 −1n2

.

0

-E1

Energy levels

4. There exists a continuum, E ≥ 0, where electrons are no longer bound.

5. The structure of orbits is different for each element. The orbits are drawncloser in for elements with more protons, larger A, Z.

6. Within shells there can be subshells (quantum numbers l, m, …). The numberof electrons in the outer shell largely determines the chemistry.

7. The Pauli exclusion principle states that no more than 2 electrons can occupya given orbital.

Line Radiation

Absorption:e- lifted from the ground state Eg to excited state Ee by absorbing a photon ofenergy: ε = hν = Ee - Eg

More generally, hνnm = En - Em,

for n > m.

Emission:e- spontaneously drops to lower orbits, until it reaches the ground state.

Photon emitted in each transition. How?

“After the fifty years of concious brooding have brought me no closer to the answer tothe question, ‘What are light quanta?’ Of course today every rascal thinks he knows theanswer, but he is deluding himself.” (A. Einstein, 1951)

Ee

Eg

The most important example of emission & absorption lines in astronomy is thespectrum of the hydrogen atom.

Ly α121.6nm

Lyman series

Hα656.3

Hβ486.1

Balmer series

Paschen series

Excitation and IonizationAt low temperatures and with no external disturbances atoms like to live in theground state. Two ways to excite electrons to higher energy levels.

1. Collisional excitation

e-

Atom

Some of the relative kinetic energy of the collision is used to boost theelectron.

Given a Maxwellian velocity distribution…

Low T <--> exponentially few fast collisions <--> little excitation.

High T <--> many fast collisions <--> lots of excitation.

2. Collisional ionization

If enough energy is imparted to the electron in the collision it may be knocked free.

e-

3. Photoabsorption

Electron absorbs photon with energy equal to the difference between levels.

For photoionization need Ephoton > |Ebind|.

Atom

Kirchhoff’s laws redux: we can now understand them from a microscopicpoint of view.

2. Low density, non-opaque gas that is hotenough to excite n = 2,3,… levels effciently

---> emission lines.

1. Very hot, opaque gas, with much ionization,excitation and recombination

---> continuum emission.

3. Cold gas: photoabsorption

---> reemission into random directions

+ absorption lines in forward direction.

Kirchhoff’s laws and stellar spectra1. Approximate thermal continua come from radiation originating in deep

layers, with many scatterings on the way up.

2. Massive stars have very hot outer layers ---> emission lines superimposedon the continuum.

I

λ −−>

3. Less massive stars have cooler outer layers ---> absorption lines.

I

λ −−>

Spectral classification: arranging the starsStars can be classified by the relative strengths of important lines in their spectra(as well as by color). The development of the Henry Draper system(OBAFGKM) was an important accomplishment during the early 20th century.

Originally, it was a sequence A-P based on the strength of the Balmer lines, butas it evolved some letters were dropped, others rearranged.

Recall: the optical Balmer line series goes from level n to level 2 in hydrogen.

In reality, need to use lines from other elements too.

Spectral Classification Criteria (from text)

Type Characteristics

O (1,2…, 9) Strong HeII (He+) lines, in absorption or emission. Strong UV continuum. Weak HeI. Prominent H lines. SiIV, OIII, NIII, CIII.

B Strong HeI in absorp. H lines stronger. MgII, SiII.

A H lines at max in A0. FeII, SiII, MgII at max. Some CaII. Weakneutral metals.

F H lines weaker. CaII H&K stronger. Neutral metals stronger.

G CaII lines dominate. H very weak. FeI, MnI, CaI become stronger.CH G-band strong.

K Neutral metals strong. Begion TiO bands.

M Neutral metals and molecules (CH, TiO, etc.).

Luminosity Class: the 2nd dimension.Spectral classification has a 2nd dimension. It was discovered empirically thatintrinsically brighter stars have narrower lines. This led to the Morgan-Keenanluminosity classification.

MV (near G0)

I (a, ab, b) Supergiant -5, -8

II “ Bright giant -2, -4

III “ Giant 0, -2

IV Subgiant 1, 2

V Dwarf (main sequence) 3, 4

VI Subdwarf

The complete spectral type (e.g., G2V) nearly uniquely places a star in the HRdiagram (later).

Physics of luminosity class= pressure broadening due to surface gravity

E.g., compare a giant and dwarf at the same surface temp.

P ~ ρT is lower in the giant, so the thermal Doppler line width is lower.

Dependence of L.C. on abundancesClassification schemes assume solar abundances. Slight changes are needed formetal-poor stars.

OBAFGKM and more. Each spectral type is divided into 10 subclasses, A0, A1, A2, ...A9 etc. The spectraltypes and sub-classes represent a temperature sequence, from hotter (O stars) to cooler (M stars), and fromhotter (subclass 0) to cooler (subclass 9). The temperature defines the star's "color" and surface brightness.

Spectral Type Surface Temperature Distinguishing FeaturesO > 25,000K H; HeI; HeIIB 10,000-25,000K H; HeI; HeII absentA 7,500-10,000K H; CaII; HeI and HeII absentF 6,000-7,500K H; metals (CaII, Fe, etc)G 5,000-6,000K H; metals; some molecular speciesK 3,500-5,000K metals; some molecular speciesM < 3,500K metals; molecular species (TiO!)C < 3,500K metals; molecular species (C2!)

Stars are also classified by luminosity class. Luminosity classes are determined from spectral features andphotometric measurements, coupled with information regarding the distance to the star and theamount ofextinction of the starlight from interstellar material. The luminosity class designation describes the size(gravitational acceleration in photosphere) of a star from the atmospheric pressure. For larger stars of a givenspectral type, the surface gravity decreases relative to what it was on the main sequence, and this decreasesthe equivalent widths of the absorption lines.

Luminosity Class Description Comments0 Hypergiants extremeIa Supergiants! large and luminousIb Supergiants! less luminous than IaII Bright Giants III Giants IV Sub-Giants V Dwarfs Main Sequencesd Sub-Dwarfs D White Dwarfs

From cfa-www.harvard.edu/~pberlind/atlas/htmls/note.html

Sample stellar spectra

A0V B1V

O6V

F6V

G0V

K3V

M2VN-type

AGB