1. Observational Cosmology Flashcards
What does the CP state?
We are not in a special place in the universe
So we must be average
This averageness means we see what everyone else sees
What does the CP imply?
Isotropic (same in all directions)
and homogeneous (same in all place)
Does homogeneity mean isotropy if there is no preferred direction in the universe?
Yes, but not vice versa
Evidence for CP?
CMB - isotropy via uniformity of temperature
Galaxy distribution - homogeneity
Temperature of CMB?
2.728 K
In the temperature distribution of the CMB, what is the red strip in the middle?
Emission from our own galaxy
Does CMB test for homogeneity?
No
How do we test for homogeneity?
Galaxy distribution - creating a redshift cone (by measuring redshift as a proxy)
(note there is some observational bias involved)
What is the distance scale?
Bootstrapping from things we can measure distance to locally, using secondary methods
Is redshift a direct measure of distance?
No - but a proxy
Equation for redshift in terms of wavelength?
z = λ_obs - λ_emitted / λ_emitted
How can z be written if v «_space;c?
z = v/c
where v is the apparent velocity of the source
If z > 1, is v > c?
No!
Recession velocities are not real motions. Doppler formula only for v «_space;c
How to measure z of nearby galaxies?
Distinctive features (absorption/emission lines) which occur at known wavelength
Measure z
How to measure z of distant galaxies?
Colour
Are more distant galaxies younger or older?
Younger
Why are more distant galaxies younger?
The light from them has taken longer to reach us to we are seeing them as they were a long long time ago
How does the Lyman break work?
Photons with energy > 13.6eV ionise any atomic H
Late universe (older) largely ionised, but enough atomic H along line of sight that most emission below 13.6 eV is absorbed
Break in spectrum - galaxy only detected in some colours
As galaxy distance increases, where is Lyman break observed?
Progressively redder (longer) wavelengths
What is the only direct distance measure?
Trigonometric parallax
What is the parallax of a star 1 parsec away?
1 arcsec
How does trigonometric parallax work?
Look at how stars appear to move on the sky as the earth orbits the sun
(closer stars move more than further ones)
e.g. line of sight in January vs July
Where is current best parallax data taken from?
Gaia satellite
When do photons ionise atomic hydrogen?
With energy > 13.6 eV
What is the parallax of a star at distance D?
D = 1/p
Error in parallax?
|δD / D| = |δp / p|
For single stars, how far away can we get good parallaxes?
~5000 pc for single stars
Methods on the distance ladder?
2º = Main sequence fitting and cepheids
3º = Tully-fisher relation and SN1a
What diagram can be used for main sequence fitting?
HR diagram
How does main sequence fitting work?
HR diagram - Gaia data
Know spectral type -> know absolute magnitude -> distance (not great for singular stars)
How luminosity varies with stellar temperature for different spectral types
Compare to main sequence of distant clusters
Is main sequence fitting a standard candle method?
No
Are hotter stars redder or bluer?
Bluer
Are colder stars redder or bluer?
Redder
Where do stars spend their lives on the HR diagram?
Early part of their lives on a fixed point of the main sequence
Then move onto giant branch
Do errors propagate through distance ladder?
Yes
What is a standard candle?
An objects whose absolute luminosity can be derived in a distance independent fashion
(If we absolutely know something’s luminosity, we can derive its distance)
Standard candle equation for nearby object?
F = L / 4πr^2
where r is distance to star,
f = flux (apparent brightness)
How does main sequence fitting work, practically?
If you have a cluster of unknown distance, can derive distance by sliding fluxes of its main sequence vertically until it fits onto absolute magnitude of the known main sequence
What is the instability strip for cepheids?
On the HR diagram, above the giant branch
Why are cepheids standard candles?
Their period is prop to their L
How does luminosity of cepheids affect period?
Brighter stars have longer periods
Problems with distance ladder beyond parallax?
Metallicity changes periods
Dust causes objects to appear fainter and redder
Why does the instability strip exist?
Some stars are very luminous but also very extended
So that surface material is only loosely held on by gravity
Radiation pressure vs gravity gives cyclic variations
Which cepheids have lower metallicity?
Type II
Basic idea of Tully-Fisher relation?
Spiral galaxies only: Larger galaxies (more m), more luminous
Assumptions for Tully-Fisher relation?
mass to light ratio M/L = constant (bigger galaxies more luminous)
spiral galaxy surface brightness is constant (flux prop to angular area)
What relation can be derived from Tully-Fisher?
L prop to v^4
(v = rotational velocity of galaxy)
How do we get distance from Tully-Fisher relation?
Measure v to get L
Then compared to observed flux can get distance
How to most reliably measure v for Tully-Fisher?
Emission from atomic H for nearby galaxies
Max distance for Tully-Fisher and why?
150 Mpc
Difficult measuring atomic H at greater distances
And cannot measure rotation in face-on spiral galaxy since no Doppler shifts
Is a SN1a a standard candle?
Yes (once corrected for event duration)
Why are SN1a used if they are very rare?
Visible to large distances (z~2) as very bright at peak
When do SN1a occur?
White dwarf accretes material from a companion then explodes
(not a collapse of a massive star)
Do all SN1a show the same intrinsic peak brightness?
No
What do we need to know for SN1a to measure distance?
Know brightness, and spectrum to give z (i.e., and show they are type 1a)
How can different peak brightnesses of SN1a be fixed?
Since peak L prop to duration of event
(less luminous SN fade mroe quickly)
Limitations of SN1a?
Some rare events are much brighter - fainter so need to be excluded. But enough nearby SN to compare.
Environment (metallicity, but small effect) and dust (but proven to not be in dusty regions)
So all in all disproven
Hubble law?
v = H0 x
Equation for parameter h?
h = H0/100
Units for H0?
Inverse time
km/s / Mpc
Best value of H0?
73.2 km/s/Mpc
What is a Hubble time?
1/H0 (= 13.4Gyr)
Age of an empty ‘coasting’ universe
Methods to derive age of the universe?
- Radioactive dating
- Age of oldest stellar clusters (best)
How are stellar clusters used to derive the age of the universe?
Stars (dwarfs) leave the main sequence when core H is all used up (becoming giants)
Giants move up giant branch as they age
More massive (hotter, bluer, younger) then the earlier they evolve off the MS - use up H faster
Temperature at the MS turnoff dep. on age (models)
Oldest stars seen?
11-13 Gyr - agreement with expansion age
Do you need to know the distance to a cluster to estimate its age?
No
But contamination from other background/ foreground stars small and see individual stars
Why are stars similar in mass to the sun good for age of universe?
More massive stars disappear quickly
Mass tracers?
Directly - counting stars, galaxies etc.
Motion of stars/gas in galaxies
Motion of galaxies in clusters of galaxies
Gravitational lensing
How does mass-to-light ratio help in measuring total mass?
Determine M compared to L and count the stars
What is the mass to light ratio of a the sun?
1 solar mass / 1 solar luminosity = 1
Relationship between M and L for MS stars?
L prop to M^B with B~3.5
M/L for nearby stars?
~2
M/L for old evolved stars?
~10
How can rotation be measured?
Stars - shifts in spectrum with position
Bright emission line objects in the same way
HI 21cm emission (atomic)
Why does HI emit at 21cm?
Spin flip transition
Why does rotation show visible and non-visible mass?
Stars and gas move in orbits under the influence of their own collect mass
So motion traces gravitational potential whether visible or not
Equation for Keplerian orbit?
v^2 = GM(<R) / R
i.e., v prop to 1/sqrt(R)
balance of kinetic and potential energies
How do velocity curves work?
Look for Doppler shifts in gas or stars relative to general motion it has
Limitation of using stars regions for rotation curves?
Visible light doesn’t stretch as far as the gas
Emission lines
Where can we use 21cm emission for rotation curves?
Spiral galaxies (abundant)
Weak in elliptical
Where can bright emission lines be from for rotation curves?
HII regions (ionised gas)
Molecular clouds (CO)
What occurs in a spin flip transition?
Coupling of electron spin with proton spin in nucleus
Generates µ, so there is an alignment for which energy of system is minimised
What relationship should a rotation curve obey?
v prop to 1/sqrt(R)
Why might a rotation curve be proportional to what we expect?
If we assume M/L ratio constant, assume most mass (and light) in centre of spiral galaxy
Expect v to drop off since prop to 1/sqrt(R)
HII traces stay constant as r increases - DARK MATTER
Why is M/L>1 in the halo of a spiral galaxy?
Lots of mass - but can’t see it
M/L ~ 50+
Why is dark matter in halos of spiral galaxies not explained by atomic hydrogen?
There is not enough hydrogen to explain results
Why is it hard to measure properties around elliptical galaxies?
Usually have little atomic hydrogen (HI)
Does motions of galaxies show excess mass, as well as stars/gas?
Yes
How does motions of galaxies allow for x-ray observations?
Galaxy motions heat up tenuous (low density) gas in IGM to millions of K
Emits x-rays
Amount of x-ray emission depends on total mass
How does gravitational lensing work?
Mass bends background light
Measure mass directly from modelling distortion
What techniques are combined in the bullet cluster?
Gravitational lensing, x-ray emission
Galaxies don’t collide - gas does so lags
How do we know dark matter is distributed differently?
Optical part of galaxies has M/L~10
Rotation curves / clusters of galaxies M/L~ 50-300
How do we know dark matter is not baryonic?
Halos are mostly collision-less
As if particles collide, one loses energy and would fall to the centre (whereas M/L very large)
So it is not baryonic
