1: GALAXIES IN THE UNIVERSE

Question 1

Define Galaxies.

Answer 1

They are large systems of stars

Question 2

Define parsec.

Answer 2

Distance at which star has p = 1”

Question 3

What is characteristic of cepheids?

Answer 3

Variation in brightness with time

Question 4

What can cepheid periods be related to?

Answer 4

Luminosities

Question 5

How was the existence of external galaxies confirmed?

Answer 5

By observations made in Cepheids in other spiral and irregular nebulae.

Question 6

What two equations define redshift?

Answer 6

1 + z = observed wavelength/emitted wavelength

z = v/c

Question 7

What is the typical radial velocities of stars?

Answer 7

10-100 km/s

Question 8

Why are spiral nebulae unable to be Galactic objects?

Answer 8

They move away from us at velocities reaching 2000 km/s. They exceed the escape velocity for the Galaxy.

Question 9

Redshifts are used for the dynamics of objects. How is this observed in a rotating disk galaxy seen edge-on?

Answer 9

One side will be approaching the observer (blue-shifted) and the other receding (red-shifted).

Question 10

What can the observed rotation velocity for a galaxy tell us?

Answer 10

Can be used to estimate its distance.

Question 11

If stars at the edge of the visible disk move in circular orbits at velocity v around a mass M, then the gravitational force must match the centripetal acceleration. What is the equation for this?

Answer 11

GM/(thetaD)^2 = V^2/thetaD

Question 12

What is the linear relationship equation between recession velocity cz and distance, D?

Answer 12

cz = H_o * D

Question 13

What is the moving cluster method and what does it tell us?

Answer 13

It is used to determine the distance to nearby star clusters. If all the cluster stars are moving together with parallel velocity vectors, their motion will appear to converge at some point in the sky.

Question 14

In the moving cluster method, if the angular distance of a star from the convergent point is theta, what equation relates its radial and tangential velocities?

Answer 14

v_t = v_r tan theta

Question 15

What equation relates distance, radial velocity, and proper motion?

Answer 15

D = (v_r)tan θ/4.74µ

Question 16

What is spectroscopic parallax?

Answer 16

Once we have calibrated the relationship between the colour and luminosity of stars, from a cluster at a known distance, we can use it as a distance indicator; we deduce L for a star from its colour and
use the flux F and the inverse square law.

Question 17

What is the equation for apparent magnitude?

Answer 17

m = −2.5 log10 F + constant,

Question 18

What is the equation for absolute magnitude?

Answer 18

M = −2.5 log10 L + constant.

Question 19

What equation relates apparent and absolute magnitude?

Answer 19

m − M = 5 log10(D/10).

Question 20

What does the method of distance determination known as ‘MS fitting’ involve?

Answer 20

If we look at other star clusters, the standard MS will just be shifted in magnitude by the distance modulus to the cluster.

Question 21

Where is the majority of stars in the H-R diagram populated?

Answer 21

The main sequence - from bright and blue (hot) to faint and red (cool).

Question 22

As well as the main sequence, what does the H-R diagram of a typical cluster also contain?

Answer 22

A ‘giant branch’ of red
giant stars which have evolved off the MS, increasing in size and luminosity. The stars at the tip of the red giant branch have quite characteristic luminosities, so this ‘TRGB’ provides another distance
indicator for any star cluster (or galaxy) in which individual stars can be resolved.

Question 23

What is the interstellar medium (ISM)?

Answer 23

It’s gas and dust that acts like the fog between the stars.

Question 24

The foreground absorption by dust in our Galaxy depends on the direction in the sky. Where is absorption greater?

Answer 24

Nearer to the Galactic plane, as we are looking through a greater depth of ISM.

Question 25

Approximating our
Galaxy by a uniform slab with the Sun in the central plane, how does the line of sight length vary?

Answer 25

The line of sight length varies as cosec b, where b is called the Galactic latitude (with b = 0 in the Galactic Plane).

Question 26

Each element of length removes a certain fraction of the light, so if I(x) is the intensity of the light
after it has passed through a length x of the ISM from its source, then after a further distance ∆x. What equation represents this?

Answer 26

I(x + ∆x) = I(x) − ∆I = I(x)[1 − κ∆x], where κ represents the rate at which the light is absorbed (absorption coefficient).

Question 27

What is the rate of change of intensity with respect to x and what is the solution?

Answer 27

dI/dx = −κI. The solution is I = (I_c)*e^(−κx)

Question 28

What equation relations original intensity and the optical depth?

Answer 28

I = (I_c)e^(−τ)

Question 29

How is the equation original intensity and optical depth translated into magnitudes? What does m_c and A represent in the equation?

Answer 29

m = mc − 2.5 log(e^−τ) = mc + 1.086τ = mc + A

m_c is the magnitude in the absence of absorption. A is the absorption.

Question 30

What is selective extinction/reddening?

Answer 30

It changes the apparent colour of obscured objects…it is the difference in extinction at two different wavelengths, e.g.
in the B and V bands, written E(B − V ).

Question 31

What is a rough estimate of the absorption in the blue band when looking all the way out of the Galaxy?

Answer 31

A_B ~ 0.2 cosec b magnitudes

Question 32

How can we deduce A-B (absorption in blue band) by looking at FIR emission?

Answer 32

As the absorption is due to dust, which then re-emits at longer wavelengths

Question 33

Working in the near infra-red to reduce the absorption by intervening interstellar dust, the P − L relation for Cepheids in terms of I-band magnitudes is what?

Answer 33

M_I = −1.3 − 3.5 log P, where P is in days

Question 34

What is the accepted value for Hubble’s constant?

Answer 34

H_0 = 70 ± 2 km s−1Mpc−1