Radiative Transfer/Absorption

Question 1

How does photon intensity change through matter?

Answer 1

Photon Attenuation Law

I = Ioe^-t as decay rate proportional to intensity

Absorption probability

Low energy photons -> photoelectric absorption —> rapid decay
Medium energy photons —> Compton scattering —> moderate decay
High energy photons —> pair production —> depends on threshold

Question 2

Equation that governs photon absorption in matter? Solution?

Answer 2

dN/dl = -nsigmaN

N(l) = Noe^-t where t = nsigmal

Question 3

What is optical depth physically?

Answer 3

t = nsigmal = Nh sigma

Expected number of interactions along the path and lets you judge transparent vs opaque.

t «1 —> transparent
t» 1 —> opaque
t =1 —> significant absorption

Question 4

Mean Free Path of photon

Answer 4

Lambda = 1/n sigma

Tells you how far photons travel before absorption.

Question 5

How does photoelectric absorption depend on energy?

Answer 5

sigma ~ E^-8/3

Explains why soft-X-rays absorbed first.

Question 6

Why do we use column density Nh?

Answer 6

Nh = nh l

Observable and avoids geometry details and almost all X-ray absorption recorded in Nh

Question 7

Where does exponential absorption come from?

Answer 7

dN = -n sigma N dl

Shows absorption is probabilistic.

Question 8

Why do X-Ray spectra harden through gas?

Answer 8

Low energy soft photons absorbed more efficiently so higher optical depth whereas high-energy hard photons are leee absorbed so spectrum has more high energy photons and hardens.
Because sigma (E) decreases rapidly with energy.

Question 9

How many photons did a telescope detect from a source?

Answer 9

S = st A (QE)

Question 10

What sets detection significance?

Answer 10

SNR = S / root(S + B)

Used to estimate exposure time as it’s proportional to root(t)

Question 11

Why does absorption produce an exponential?

Answer 11

Each photon has a constant probability of interaction per unit length.