Age of Universe and Mass Tracers

Question 1

What is the Hubble law?

Answer 1

Redshifts of nearby galaxies are linearly related to distance

Question 2

What about the Hubble law shows that it doesn’t violate the CP?

Answer 2

The recession is true everywhere (symmetric) - another galaxy would see the universe receding around it too

Question 3

What does the gradient of a velocity vs distance graph give?

Answer 3

H_o as the equation of the line is
v = H_o 𝑥

Question 4

What are the units of the Hubble constant (H_o)?

Answer 4

km/s/Mpc = s^-1

Question 5

What is Hubble time?

Answer 5

How old the universe would be after the Big Bang (all galaxies would be on top of each other in a singularity)

1/H_o = 13.4 Gyrs (the age of coasting universe - same rate at all time, expanding constantly)

Question 6

What is the value of Hubble constant?

Answer 6

73.2 km/s/Mpc

Question 7

What is the value of little h ?

Answer 7

0.73

Question 8

What is a coasting universe?

Answer 8

An empty universe which is expanding faster than it actually is (no gravity)
so the universe must be younger as it does contain objects

Question 9

Are there any stars which are older than Hubble time?

Answer 9

No as if we were to see stars older than 50 billion years, this model would not be correct

Question 10

What would happen if the universe wasn’t expanding?

Answer 10

It wouldn’t be stable and it would contract and collapse again

Question 11

What happens in the expanding universe on a small and large scale?

Answer 11

small scale ( ~ 10 Mpc): things can interact and move around

large scale: everything moves smoothly with the expansion

Question 12

How can radioactive decay be used to derive the age of the universe?

Answer 12

By looking at the abundance of radioactive elements in the solar system and stars:
Earth ~ 4 Gyr
Sun ~ 5 Gyr

Question 13

What makes radioactive decay a crude way of deriving the age of the universe?

Answer 13

A wide range between 10 - 15 Gyr for age of universe so not very useful

Question 14

How do clusters of old stars indicate the age of the universe?

Answer 14

When stars leave the MS they are running out of hydrogen

The more massive (hotter & bluer) a star the earlier this happens and they disappear so it is stars similar in mass to the Sun that provide best evidence for older ages (11-13 Gyr)

Question 15

What does the main sequence turnoff the colour-magnitude diagram show?

Answer 15

The age of the universe by using the temperature of clusters at this point

Question 16

What does no blue stars visible in a cluster indicate?

Answer 16

The whole population of stars is old (red stars)

Question 17

Are the results from the old clusters and radioactive elements in agreement with expansion age?

Answer 17

Yes

Question 18

How is the mass of stuff in the universe measured?

Answer 18

Using mass - to - light ratios

Nearby stars: M/L ~ 2
Evolved stellar population: M/L ~ 10

Question 19

Where is there evidence of dark matter?

Answer 19

From clusters of galaxies showing evidence of collisionless dark matter (doesn’t react easily with anything else) and non-baryonic dark matter (not protons, neutrons etc)

Question 20

How is the rotation of gas in stars measured to find the mass?

Answer 20

Using map which shifts in the spectrum with position
(same technique can be used for bright emission line objects)

Using atomic hydrogen (HI) 21cm emission which traces neutral gas that fills galaxies so good tracer (only applies to spiral galaxies not elliptical)

Question 21

How is the HI 21cm emission used?

Answer 21

If an electron is at a higher energy state, it will spin flip and go down to a lower energy state (spin flip transition)

Question 22

When can a circular Keplerian orbit be seen?

Answer 22

If galaxy is seen edge on and rotating

Question 23

What is the Virial theorem for gravitationally bound systems?

Answer 23

2 KE + PE = 0

Question 24

What is the expected relationship between v and R for rotating gas?

Answer 24

v is inverse proportional to the square root of R (applies to large R from bulge in spiral galaxies) as M/L is assumed as constant

Question 25

What is visible further than R?

Answer 25

Atomic hydrogen

Question 26

What is assumed to not be correct at mass at large R and how is this corrected?

Answer 26

That most of mass should be within R but rotation curves show that this isnt the case as the curve doesn’t descend at all and v stays constant at large R
(therefore much more mass at large R than we can see)

By using models which include the halo around the galaxy

Question 27

How does the M/L in the bulge compare to the halo in spiral galaxies?

Answer 27

The halo has an M/L 5 times greater than the bulge

Question 28

What is the large M/L caused by and where is this visible?

Answer 28

Dark matter which is visible in spiral galaxies due to the motion of cluster of galaxies indicating excess mass due to increase in speed
AND
From x-ray observations showing neutral gas tracers which are heated by galaxies motion.
The x-ray emission traces from heated gas allow for mass estimates based on temperature

Question 29

Why can’t dark matter be seen?

Answer 29

It doesn’t emit any electromagnetic radiation so does not scatter light

Question 30

What is gravitational lensing?

Answer 30

Mass bends light due to presence of dark matter
The arcs seen in the images show background galaxies which bend light and a large M/L is found (so mass can be found)

Question 31

What does the bullet cluster show?

Answer 31

Gravitational lensing (blue) and x-rays (red) both present. Both red and blue areas are separate from one another, indicating that dark matter is separate from normal matter.

It indicates that dark matter is not an ordinary gas

Question 32

What does the M/L of rotation curves and clusters of galaxies indicate about the universe?

Answer 32

M/L ~ 50-300
mass of the universe is partly hidden (dark matter)
Dark matter is distributed differently from stars and galaxies
(optical part of galaxies: M/L ~ 10)

Question 33

How does the final v ~ constant relationship get formed on a rotational velocity curve ?

Answer 33

By extending the mass where there is no obvious source, the halo curve becomes visible (halo is collisionless to large extent)

Question 34

Where is most of the light shown to be on a rotation curve?

Answer 34

Near the centre, giving the disk curve and the v ~ v^-1/2 relationship