Lecture 6

Question 1

The PSF can be composed of the

Answer 1

instrument and the atmospheric PSF

Question 2

Overall PSF can be measured by observing

Answer 2

a bright point source near the target object

Question 3

For most UV-IR instruments, the image PSF caused by the instrument is

Answer 3

broader than the diffraction pattern

Question 4

Even if you can make the different contributions to the PSF as small as possible you can not get better than

Answer 4

the instrument’s diffraction pattern i.e. diffraction-limited.

Question 5

Instrument PSF can arise from

Answer 5

aperture diffraction; scattering from roughness/dirt on mirrors or other surfaces

Question 6

Aperture photometry

Answer 6

-define apertures of different sizes
-sum counts in each aperture
-counts tend to true counts as aperture size increases
-but background noise also increases with larger apertures

Question 7

Instrumental line profile

Answer 7

in spectroscopy, lines recorded have a profile of intensity versus wavelength that is a combination of the true line profile and the instrumental line profile

also called the spectral PSF

Question 8

Ideally the ILP will be

Answer 8

symmetric, and narrower than the true line profile

Question 9

A single line observed intensity is

Answer 9

O(λ2) = I(λ1) ILP(λ2-λ1)

Question 10

a spectrum contributes to the intensity is

Answer 10

O(λ2) = I * ILP

Question 11

The line of sight velocity distribution (LOSVD) is:

Answer 11

F(v LOS) d v(LOS) = fraction of stars contributing to spectrum

Question 12

spectral velocity u (formula/derivation)

Answer 12

u = c ln λ

Δu/Δλ = c 1/λ

Δu = c Δλ/λ = v(LOS)

Question 13

Galaxy spectral velocity

Answer 13

G(u) ∝ (-∞ ∫ ∞) F(v(LOS)) S(u-v(LOS)) dv(LOS)

G(u) is the observed galaxy spectrum

F(v(LOS)) v(LOS) distribution function

S(u-v(LOS)) stellar spectrum

Question 14

the observed galaxy spectrum is

Answer 14

smeared out version stellar spectrum by LOSVD

Question 15

Cross - correlation

Answer 15

find lag/shift between two signals => log/shift with max CCF

Question 16

v(LOS) of whole galaxy

Answer 16

CCF(v(LOS)) = (-∞ ∫ ∞) G(u) S(u-v(LOS))du

Question 17

if v(LOS) does not align the two signals,

Answer 17

CCF is small

Question 18

if v(LOS) does align the two signals

Answer 18

CCF is large

Question 19

we can estimate v(LOS) by

Answer 19

calculating the CCF for many trial values of v(LOS) and S(u-v(LOS)) and finding its maximum value

Question 20

Auto-correlation

Answer 20

finding a period shift in our data

Question 21

the auto-correlation of a time series

Answer 21

measures how well a signal matches a time-shifted version of itself

Question 22

So the auto-correlation function of time series f is (formula)

Answer 22

ACF(τ) = (-∞ ∫ ∞) f(t) f(t-τ)dt

Question 23

when the lag is a multiple of the period τ = nT

Answer 23

get a max ACF

Question 24

when the lag is half a period out τ = (2n+1) T/2

Answer 24

get a min ACF

Question 25

in |ACF|^2 you will get a peak when

Answer 25

τ = (n+1) T/2