Astronomical Spectroscopy Spectroscopy is the study of the way matter absorbs/emits light. a SPECTRUM is like a fingerprint of an object collection of photons of different wavelengths, frequencies, or energies a BLACKBODY spectrum is the first step to fingerprinting a blackbody re-emits all energy (i.e. photons) it absorbs emits a characteristic distribution of photons a blackbody curve is the shape of the emitted light from an object even YOU emit a blackbody spectrum

brightness Bν(T) has units of erg s -1 cm-2 Hz -1 ster -1 Blackbody Equation Planck radiation law (Planck Function) 2hν3 1 Bν(T) = ---------- --------------- c2 e(hν/kT) - 1 brightness Bν(T) has units of erg s -1 cm-2 Hz -1 ster -1 Rayleigh-Jeans tail hν << kT Bν(T) ~ (2ν2/c2) kT decreasing freq … shallow second power drop Wien cliff hν >> kT Bν(T) ~ (2hν3/c2)e-(hν/kT) increasing freq … steep exponential drop

Blackbody Spectrum (2ν2/c2) kT (2hν3/c2)e-(hν/kT)

Temperature Scales °F °C °K

Blackbody Spectrum and Temp position of blackbody depends on temperature … …so, objects of different temperatures look different colors!

λ max (in microns) = 2900 / T (in Kelvin) 1. Wein’s Law location of blackbody curve peak determined by temperature … take derivative of blackbody equation … use blackbody curve as a THERMOMETER … Wobble Law … peak moves left/right λ max (in microns) = 2900 / T (in Kelvin) Sun has T = 5800 K … λ max = 2900 / 5800 K = 0.5 microns (or 5000 Å) YOU have T = 310 K … λ max = 2900 / 310 K = 9.4 microns

2. Stefan-Boltzmann Law L ~ R2 T4 height of blackbody curve determined by temperature AND SIZE … integrate blackbody equation over all angles and frequencies … hotter object … more photons … bigger object … more photons … Size Law … peak moves up/down to more/less energy luminous energy = surface area X energy/area E total = L = 4πR2 σT4 ( in erg s -1) L ~ R2 T4 Sun has T = 5800 K now, but when it turns into a red giant … T drops to ~ 2900 K … L drops by factor of 16 R increases to 100 X radius today … L rises by factor of 10000 together … L increases by factor of 600 … we’re COOKED!

Spectral Features: Light and Matter atoms are made up of particles protons, neutrons, electrons H is simplest … 1 proton, 1 electron (if neutral) He is next … 2 protons, 2 neutrons, 2 electrons (if neutral) C is # 6 … 6 protons, 6 neutrons, 6 electrons (if neutral) # protons DEFINES the element Bohr Atom is a model that explains interaction of light and atoms invokes particle nature of photons  discrete amounts of energy are needed for absorption/emission  e¯ orbitals at specific energy levels

Bohr Atom energy levels

electron options once excited by photon, electron has options … 1. re-emits 2. cascades 3. ionized

Atoms are easy, Molecules … molecules are made up of more than one atom each atom provides options absorption + rotation + vibration He (easy) ………….. C (not bad) CO (ugh!) 

H atom vs. H2 molecule

Link to Spectroscopy each atom/isotope/molecule has a fingerprint a combination of atomic fingerprints is emitted by each object a galaxy, a star, a planet, or YOU emit a complicated spectrum

Spectrum of the Sun

Emission and Absorption

Creation of Spectra

Four Types of Spectra 1. CONTINUOUS spectrum = BLACKBODY spectrum atoms are wiggling … photons emitted … light bulb, Sun (sort of) 2. ABSORPTION spectrum atoms catching photons … see dark lines … He in Sun, Earth CO2 3. EMISSION spectrum atoms pitching photons … see bright lines … aurorae, meteors 4. REFLECTION spectrum combination of catching/pitching … bright + dark features … Jupiter’s atmosphere absorbs some sunlight, reflects some

Earth Radiation J H K L M trace gas

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