Finding the Expansion Rate and the Age of the Universe
Learning Goals
1. Determine a value for the Hubble constant through analysis of
measurements of the angular sizes and redshifts of galaxies. 2. Estimate the corresponding age of the universe and compare it
with the age of the Sun and the Milky Way. 3. Explain why Hubble’s law implies that the universe is
expanding. 4. Summarize how our view of the universe has changed as the
value of the Hubble constant has improved.
Galaxy Types: Sizes – Dwarf and Giant
•
An elliptical or irregular galaxy can be a dwarf galaxy or a
giant galaxy.
All spirals are giant; that is, all are approximately the
same actual size.
Standard Ruler
•
•
•
•
Standard Candle: An object where we are quite
confident we know its actual luminosity.
Standard Ruler: An object where we are quite confident
we know its actual size.
Assume all spiral galaxies that look similar are very
close in actual physical size, no matter where located.
Must first KNOW actual size by using the KNOWN
distance to a nearby spiral galaxy - Andromeda galaxy.
Variable Stars: Cepheid Variables Vs. RR Lyrae Variables
These pulsating variable stars are extremely important for
determining distances.
Specifically, they have a relationship between their
pulsation period and luminosity.
Cepheid variables:
•
High-mass stars becoming supergiants.
Periods from 1 to 100 days.
More luminous stars have longer periods.
RR Lyrae variables:
Low-mass stars on the horizontal branch.
Less luminous than Cepheid variables.
Standard Candles
7
Andromeda Galaxy: Measure 𝚯, know D from periodluminosity measurements of Cepheid variable stars,
solve for s.
Distant Galaxy: Measure 𝚯, know s from standard
ruler assumption, get D from small angle formula.
Standard Ruler - Why is assumption important?
👀
How would we know if
the difference in
angular sizes was due
to distances or to the
galaxies actually being
different actual size?
👀
TABLE 26.1
Continued.
Confirmation for galaxies being spiral
GALAXY IMAGE
GALAXY SPECTRUM
GALAXY ID REDSHIFT
VELOCITY
(km/s)
DISTANCE
(Mpc)
NGC 1832 0.00646
1,937
32
NGC 2276 0.00806
2,417
26
NGC 2775 0.00451
1,353
20
TABLE 26.1
Continued.
Confirmation
for galaxies being spiral
GALAXY IMAGE
GALAXY SPECTRUM
GALAXY ID REDSHIFT
VELOCITY
(km/s)
DISTANCE
(Mpc)
NGC 3227 0.00365
1,093
17
NGC 3368 0.00301
903
15
NGC 3623 0.00254
762
8
Standard ruler gives estimate of distances ➔ x-axis
Examination of the redshifts of the spectra gives us the
recessional velocities ➔ y-axis
Expanding Universe: Doppler Shift Measurements
•
Recall: Redshifted spectral lines = movement away; blue shifted
spectral lines = movement toward.
Doppler shift measurements demonstrate that all galaxies, except the
nearest the Milky Way, show redshifts in their spectra.
The closest galaxies show blueshifts due to local gravitational effects.
All galaxies show redshifts on large scales in the universe.
Expanding Universe: Hubble’s Law
•
If we measure distances and velocities, we find Hubble’s law.
=> The recession velocity of a galaxy is proportional to the
distance of that galaxy.
Hubble constant (H0): constant of proportionality.
Hubble’s Law: v = Hod
y = mx + b
v = Ho d + 0
1. find distances to “nearby”
galaxies using standard
candles
2. use spectra to find
recessional velocities
3. fit slope to data
4. find recessional velocities
of far galaxies
5. d = v/Ho
400 Mpc =1.3x109 light years
16