Introduction to Cosmology Flashcards
visible milky way
our galaxy seen ‘edge on’
how to determine distances to stars in the galaxy?
using distance indicators such as types of variable stars or the annual parallax of stars.
or by measuring apparent magnitudes of standard candles.
If we know luminosity and measure its flux from Earth, can estimate distance because…
the flux drops off as the inverse-square of the distance.
the distance modulus formula
expressing idea of distance indicators in terms of magnitudes.
relates apparent and absolute magnitude with a star or galaxy’s distance modulus.
distance modulus
a simple function of its distance in parsecs
parsec
parallax arc second
standard candle
a class of object assumed to have a predictable intrinsic luminosity
commonly used variable star distance indicators
- RR Lyrae stars
- Cepheid variable stars.
RR Lyrae stars
(A and F type giants which are pulsating. Often found in globular clusters)
Cepheid variable stars
F and G type supergiants
pulsate with a period around 1 to 50 days
absolute magnitude can be accurately estimated from their period.
extinction
absorption of starlight by interstellar dust grains which makes stars appear dimmer.
apparent density drop-off was due to extinction and was not a real effect.
how does a galaxy rotate?
not as a rigid body but differentially.
the angular speed of stars around the galactic centre depends on their distances from it.
Inner part rotates like a rigid body. (Think ice skaters holding hands)
Keplerian part
outer part of the disc
called keplerian since orbits approximately obey Kepler’s laws
rotation curve
plot of rotation speed as a function of distance from the centre of the galactic disc
rigid body rotation from x=0 (looks like /)
then kepler rotation after (——-)
estimation of the total mass of the galaxy interior to the Sun’s distance from the galactic centre
using Kepler’s 3rd law
GMgalP^2=4pi^2a^3
Mgal is mass of galaxy interior to a
P is suns orbital period
spiral structure of the galaxy
stars in the disc of the Milky Way are not uniformly distributed.
They lie along spiral arms wound tightly around the galactic bulge.
how can the spiral structure be mapped?
measuring the emission of neutral hydrogen.
Peak at 21cm line, if peak shifted, moving toward/away
the galactic halo
by plotting the rotation curve from radio observations, deduced that galactic disc appears to be embedded in roughly spherical halo of dark matter.
evidence for galactic halo
rotation curve does not drop off as rapidly as expected if only luminous stars in the disc were contributing to gravity.
equating grav force with cent forces, we get v is proportional to r^-1/2 so speed should fall of inversely with the square root of the distance.
dark matter
interacts gravitationally because it has mass but doesn’t electromagnetically.
density wave
spiral shaped wave pattern of high and low density regions.
cause gas to pile up in regions of higher density (like traffic jam)
what does the density wave theory predict?
inside edge of spiral arms are the most active star forming regions
without density wave
structure would be much more chaotic and disordered.
messier catalgue
contains many galaxies eg: andromeda and M31.
In M31, M stands for Messier and then galaxies are numbered.
Hubble identified three main types of normal galaxies. They are:
- Spirals
- Ellipticals
- Irregulars
classification of spiral galaxies
Sa-Sc
Sa has large central bulge and small, tightly spiral arms
Sc has a small central bulge and wide, open spiral arms
properties of spiral galaxies
diameters around 10-100kpc
mass of disc 10^11-10^12
spiral arms contain OB stars, dust and molecular clouds
disc rotates around the centre of the galaxy.
properties of elliptical galaxies
diameters 1-100kpc
masses 10^7-10^13 solar masses
spheroidal in shape
smooth brightness profile
little interstellar gas
properties of irregular galaxies
irregular in shape possibly due to recent collisions or mergers with other galaxies.
why are ellipticals old systems?
have little interstellar gas and dust and very little current star formation. (unlike spirals)
mass-to-light ratio in spirals and ellipticals
higher for ellipticals due to little current star formation.
ellipticals contain smaller proportion of young, massive stars
Hubble tuning fork diagram
NOT an evolutionary sequence
way of representing Hubble’s classification
active galaxies
galaxies whose luminosity is greater than that solely due to the stars they contain
cores of active galaxies
active galactic nuclei
three types of active galaxy
- radio galaxies
- seyfert galaxies
- quasars
properties of radio galaxies
elliptical or giant elliptical
ratio of radio to optical luminosity around 0.1-10
radio source shape double lobed or compact central, often with a jet
radio source spectrum radiation
usually synchrotron radiation.
indicates the presence of strong energy source and intense magnetic field
(synchrotron radiation is x-rays from electrons spiralling around magnetic field)
properties of seyfert galaxies
spiral with unusually luminous, blue nuclei
optical spectra show strong emission lines (narrow and broad)
broadening due to doppler motion of gases
properties of quasars
spectra contains strong emission lines. Balmer lines redshifted to longer wavelenghts (due to Hubble expansion - large distance=large recession velocity)
highly ionised emission lines on H, He, C, N, O, indicating very intense hot radiation field
vary in luminosity indicating compact emitting region
quasar absorption lines
light travelling through dust/gas
allows us to understand the rest of the universe
what powers quasars?
a supermassive black hole at its core
only explanation for such high luminosity produced in small volume
accretion disc
infalling matter forms accretion disc around a black hole
energy released by infalling matter produces two jets, producing beams of synchrotron radiation.
what do the large range of features exhibited by different AGN host galacies depend on?
several factors including:
evolutionary stage
orientation of galaxy
how obstructed the view of the galactic nucleus is
observations to support unified model of AGN
ALMA imaged accretion disc around supermassive black hole at centre of M77
Event horizon telescope imaged black hole in M87
spatial distribution of galaxies
not uniform - appear to be clustered
doppler shift of spectral lines from galaxies
z=λo-λe/λe
where o=observed and e=emitted
what did hubble find from plotting radial velocities of nearby galaxies against distance (from cepheid variables)
galaxies moving away from us and that their recession velocities were approximately proportional to their distance vrec=Hod
units of the hubble constant
kms^-1Mpc^-1
large uncertainties in Ho. Relative distances
Ho cancels V1/V2=d1/d2
red shift survey
accurate maps of the galaxy distribution on large scales using measured redshift to indicate separation
patterns in galaxy distributions that redshift surveys reveal
galaxy clusters
filaments (string/web-like structures)
voids (empty bits)
scales larger than around 30,000 kms^-1
universe begins to look uniform and homogeneous
unlike constellations, galaxy clusters are not ‘line of sight effects’, they are believed to have been…
formed together at the same epoch and are gravitationally bound together
epoch
common moment in time
peculiar velocities
specific velocities for local galaxies
vobs=H0d+vper
what causes peculiar velocities
gravitational interactions with other cluster members
more pronounced for galaxies that are close
vpec usually approx.
300kms^-1
superclusters
galaxy clusters are themselves clustered and the large scale structures they form are superclusters
local group
milky way is part of a small cluster of about 30 galaxies
roughly disc-shaped and about 2 Mpc in diameter
dynamics dominated by milky way and andromeda
nearest galaxies to milky way
large and small magellanic clouds
properties of galaxy group/small cluster
scale around 1Mpc
between 10-100 galaxies
examples: local group,fornax cluster
properties of rich clusters
scale up to 10Mpc
around 1000 galaxies
examples: virgo and coma clusters
properties of superclusters
scale approx 50-100Mpc
many thousand galaxies
examples: local supercluster
where are elliptical galaxies preferentially found?
in the cores of rich clusters
morphological segregation
elliptical and spiral galaxies are found in different locations in clusters
elliptical near centre; spirals on outside
thought to be the consequence of the galaxy formation process
galaxy formation process
believed that spirals existed briefly in galaxy clusters shortly after clusters formed but their discs could not survive the strong gravitational tidal forces in the cores of clusters
if vpec=300kms^-1, H0=71kms^-1, for a galaxy d>100Mpc, vpec is less than 5% of the cosmic expansion velocity. Therefore
Hubble’s law will hold to within a few % as long as not in immediate neighbourhood where vpec affect measurements
cannot rely on Hubble;s law to measure distance to nearby galaxies
what to use if cannot use Hubble’s law
distance indicators that are independent of redshift
estimating value of H0
distance indicators combined with measured recession velocities of more distant galaxies (where Hubble’s law holds)
apparent magnitude of standard candle equation
mobs=Mabs+5logr+25 (Mpc) or -5 in pc
standard candle
small spread in absolute magnitude
luminous at large distances
examples of standard candles in common use
- Sc spiral galaxies
- brightest cluster elliptical galaxies
- type 1a supernovae
primary distance indicators
can be calibrated from theory or from distances measured within immediate neighbourhood. eg: cepheid variables, annual stellar parallax
secondary distance indicators
must be calibrated using a sample of galaxies beyond the local group whose distances have been determined by other methods
eg: type 1a supernovae, tully-fisher relation
cosmological distance ladder
shows how different overlapping measuring techniques allow us to measure distances out to Gpc scales
distance indicators - can get an excellent indication of luminosity by
using other directly measurable quantity that is correlated with absolute magnitude eg: cepheid variables
cepheid variables - period-luminosity relation
a linear relationship exists between mean absolute magnitude and the log of the pulsation period.
errors with cepheid variables
- statistical scatter (Mabs at given period not always straight line)
- systematic errors - due to extinction (light absorbed slightly by gas/dust so stars appear dimmer)
cepeids often in spiral arms - lots of star formation/dust
Reasons why Hubbles original data gave Ho value of around 500kms^-1
- Only measured velocities out to around 1000kms^-1 within which peculiar velocities dominate
- Grossly underestimated distances to calibrating galaxies due to wrong absolute magnitude for cepheid variables, making wrong correction for extinction and misclassifying objects as cepheids when they were not
Reason for disagreement over H0=50 or 100 kms^-1Mpc^-1 in 1980s
Disputes over distance to the Virgo galaxy cluster
To determine H0, need to combine primary band secondary distance indicators. Why?
- H0 estimates require both accurate distances and recession velocities
- Primary distance indicators only extend to around 20Mpc
- At 20Mpc observed radial velocities of galaxies still seriously affected by peculiar motions
Cosmological distance ladder
Combination of two or more primary and secondary distance steps
Secondary distance indicator: type Ia supernovae
All have ~same mass so very similar peak luminosities
When do type Ia supernovae occur
When white dwarf accreted sufficient matter from binary companion to push itself over mass limit, causing a thermonuclear explosion
By plotting SNIa light curve we can determine
Apparent magnitude at maximum light
Why are SNIa good standard candles
Hubble diagram is linear
(Plot of maximum apparent magnitude against log of recession velocity)
If Max constant then Max-5log10H0+25 constant
Tully fisher relation for spiral galaxies
Linear relationship between absolute magnitude and log of recession velocity
(Rotation velocity usually velocity in flat part of rotation curve)
Why is Tully fisher relation a secondary distance indicator
Requires to be calibrated using set of nearby galaxies whose distance has been determined through primary distance indicators
Tully fisher equivalent for elliptical galaxies
Relation between intrinsic diameter of galaxy and range in velocity of central stars
Problematic because no suitable large elliptical galaxies within local group
Reasons for being unable to calibrate all secondary distance indicators before HST
- Lack of elliptical galaxies in local group
- Lack of local group spirals suitable to calibrate Tully fisher relation
- Lack of local SNIa to calibrate Hubble diagram
After launch of HST, cepheids became directly observable within nearby clusters. This allowed
Direct calibapration of secondary distance indicators and provided link to more distant clusters where hubbles law assumed to hold within few percent
Taking one big jump
Fewer steps = fewer errors
HST allowed us to miss out
Local group rung on distance ladder and get to H0 in only two steps
Olber’s paradox
Why is sky dark at night
Star in every line of sight if universe is infinite
Solution to Olber’s paradox
- Stars have finite lifetimes
- Speed of light finite so only stars within a finite distance can be observed
- Universe has a finite age
Hot Big Bang model
Standard model for origin and evolution of Universe
Universe began between 10 and 20 billion years ago and has been expanding ever since
Cosmological principle
Assumption that universe is homogeneous and isotropic
Universe homogenous
Looks the same no matter where you are in it
Universe isotropic
Universe looks same no matter what direction you look in
What scale does cosmological principle hold
Scales larger than ~30000kms^-1
Obviously not going to hold on small scales
Universe can be described by size of
Dimensionless number that we call the cosmic scale factor R(t)
Measures characteristic size of universe at time t
What does expansion look like (analogy)
Axis gets bigger and system gets bigger but individual coordinates the same
Proper distance r(t)
The actual separation measured in Mpc
Co-moving separation
Separation expressed in coordinate system that expands along with the background space
not changed by expansion of universe
(Think ggow and NY on globe regardless of size)
R0
Present day value for scale factor
Can give another interpretation of redshift of light from distance object in terms of
Amount by which the Universe has expanded since light from object was emitted
What are cosmological redshifts due to
Result of stretching of wavelength of object’s light as it propagates through expanding space
not due to motions of distant objects
Proper velocity
Rate of change of proper distance
Hubbles law expressed using proper velocity
v=dr/dt=d/dt(Rs) = Rdot . s = R dot / R x (Rs) = R dot/ R r
Hubbles constant is not constant in
Time but constant in space at any given time
Condition defining Big Bang
R(t) —>0 at t=0
Estimating time elapsed since Big Bang
Assuming constant expansion rate H(t)=H0 for all t
V=Hor=distance/time=r/t
Ie t=H0^-1
t in years for H0 in km/s/Mpc
Including gravity in Hubble time
Give age smaller than Hubble time as gravity will slow down expansion
Friedmann’s equation
Semi derive equation for the evolution of R(t) using only Newtonian concepts
Derivation of friedmann’s equation basis
Galaxy mass m, proper distance r from centre of sphere containing many galaxies
Gravitationally attracted by other galaxies within sphere, force equivalent to that of point mass of sphere
Uniform density
Kinetic energy of galaxy
KE=1/2m r dot ^2 = 1/2 Rdot ^2 s^2
Potential energy of galaxy
PE= -GMm/r = -4/3piR^2s^2Gpm
Total energy of galaxy
Constant
1/2ms^2[R dot^2 - 8piG p R^2/3 = constant
Simplifies to R dot ^2 / R^2 -8piGp/3= -k/R^2 (k constant)
What does Freidmann’s equation describe
How gravity slows the rate of expansion of the Universe
Second equation for evolution of scale factor
Using general relativity
For normal matter ( density and mean pressure > or =0)
Cannot have a static universe as that would require R double dot=0
(Common belief at time was static universe)
How did Einstein fix his steady universe problem
Introducing an extra constant lambda - cosmological constant (think of as integration constant)
Positive value of lambda
Behaves like ‘anti gravity’
Repulsion force that overcomes attraction of gravity on very large scales
Evidence for cosmological constant >0
Type Ia SN, CMBR, pattern of galaxy clustering
Cosmological constant currently - dark energy
k=1
Universe is closed with positive curvature
PE>KE
Celestial sphere, globes
BOUNDED: expands then recollapses
k=-1
Universe open with negative curvature (Pringle, KE>PE, expanding forever
UNBOUNDED: expands indefinitely
k=0
Universe flat with zero curvature
KE=PE
JUST UNBOUNDED: slows to R dot =0 as R approaches infinity
Analytic solution of Friedmann’s equation is straightforward when
Cosmological constant =0 and case of flat universe k=0
I’d assume universe is matter dominated and mass is conserved
(dR/dt)^2=A/R
A is constants which do not depend on time
Solution to Freidmann’s equation
R(t)=at^2/3
Critical density
When k=0, rearrange Friedmann for p
Density required to just close the universe
p>pcrit
Universe recollapses
p<pcrit
Universe expands indefinitely
omega (t)
Dimensionless parameter = p(t)/pcrit(t)
Omega >1
Universe closed
Omega<1
Universe open
Omega =1
Universe flat
Methods of estimating matter density of universe
Visible stars in Milky Way
Galaxy rotation curves
Galaxy clusters
Gravitational lending
Hubble diagram and standard candles
Large scale structure
Matter density - visible stars in Milky Way
Assume all stars in galaxy are one solar mass
Count up all the stars and divide by volume
Not very practical, what about elliptical galaxies
Matter density - galaxy rotation curves
Measuring rotation velocity of clouds of neural hydrogen gas within disc of spiral galaxies as a function of their radial distance from centre, can deduce amount of mass inside that radius
Observed velocity >expected - dark matter
Matter density - galaxy clusters
Assuming galaxy cluster is virialised (steady state)
Virial theorem (balance o PE and KE)
2KE+PE=0
Can rearrange for virial mass estimate using <v^2> (3D mean square peculiar velocity)
Matter density- gravitational lending
General relativity predicts light deflected in strong gravitational field
Weak lensing
Light from distant galaxies is distorted by passage through an intervening cluster
Amount of distortion allows cluster mass density to be estimated
Microlensing
Light from stars in LMC and bulge of Milky Way distorted by dark matter crossing line of sight , temporary rise in brightness of background stars
Shape of microlensed star’s light curve allows one to lace constraints on mass of lensing object e
Monitoring programmes have checked brightness of millions of LMC
Matter density - Hubble diagram of standard candles
Nearby objects: relation between apparent magnitude and log redshift is linear
Distant objects: relation begins to curv, amount of curve tells us about curvature of the Universe
Matter density - large scale structure
Patterns in galaxy redshift surveys can be used to place limits on omega0
Higher matter density = stronger pattern of galaxy clustering
Studying patterns of galaxy peculiar velocities can also be used
Baryonic matter
Think of as everyday matter
Interacts electromagnetically
Conclusive evidence for existence of dark matter
Estimates of matter density from visible stars are a factor of 100 smaller than estimates from galaxy clusters, large scale motions and gravitational lensing
Dark matter
Simply matter that cannot be seen through telescope
Can be baryonic or non baryonic
Baryonic dark matter candidates
Gas clumps in galaxy halos and clusters
MACHOs such as brown dwarfs and undetected white dwarfs (unlikely after HST)
Non baryonic dark matter candidates
WIMPS (weakly interacting massive particles) such as massive neutrinos, exotic particles or primordial black holes
Hot dark matter
If non baryonic dark matter was moving relativistically at the time of decoupling from baryonic matter eg neutrinos
Cold dark matter
If non baryonic dark matter was moving non-relativistically at decoupling
How does CMBR provide support for cosmological principle
CMBR is isotropic to better than on part in 10^4
Early universe: free electrons scattered photons so much that
Universe was effectively opaque (think fog)
Think going through crowded room and getting scattered, cannot walk in a straight line, have to move past people
Matter and radiation in early universe
Coupled since photon interacted so strongly with free eclectics
At what temp could free protons and electrons combine to form neutral hydrogen
3000K
Why did early universe fog clear
Neutral hydrogen formed which was much less effective at scattering photons
Photons can now propagate freely
Epoch of recombination
Matter and radiation decoupled
CMBR consists of
Photons that were emitted at the epoch of recombination and have travelled towards us ever since
Typical energy of a black body photon of temperature T
Given by Etyp=kT
Etypical value for 3000K and why it is a problem
Approx 0.26eV but know ionisation energy of hydrogen is 13.6eV
Going backwards from 13.6eV gives T=15800K
How can you explain the difference in Etypical
Black body photons have a distribution of energies
There’s a long tail of photons with energy E>kT
Energy density of matter in Universe
u=pmatterc^2
Universe is currently matter dominated
umatter»uradiation
Epoch of matter radiation equality
n= urad/umat
Epoch at which mean energy densities of matter and radiation are equal
Big Bang model and standard model valid from when
10^-40 seconds after Big Bang
Quark hadron transition
Quark soup condenses
Universe cooled enough to form stable hadrons
Quarks no longer exist as free particles
Primordial nucleosynthesis
Cooled sufficiently to allow protons and neutrons to combine together and form stable light nuclei
Omega B
=pB/pcrit = baryon density/critical density
Dipole anisotropy
CMBR not perfectly smooth
Not believed to be intrinsic to CMBR but instead due to our peculiar motion which causes a Doppler shift of radiation that varies with direction
Tiny variations in temperature of CMBR indicate
Universe was not completely smooth when CMBR was emitted
Hot dark matter smooths out clustering on small scales so
In models with hot dark matter, we expect to see large structures forming first and then later fragment
Models where dark matter is cold
Structures form on both small and large scales from the outset
Concordance model
5% of matter and energy in Universe today from baryons
Rest consists of dark matter (25%) and dark energy (70%)
