How far? The Distance Ladder.
(see http://www.astro.ucla.edu/~wright/distance.htm for more details.)
Determining distances is one of the more difficult tasks in astronomy. No single
method works in all cases, rather different methods work in different ranges of
distance. Using them consecutively to estimate the distance of far objects is like
climbing the rungs of a ladder.
The most important rungs include:
- trigonometric parallax (ground or space-based) to nearby stars
- main sequence fitting to clusters
- variable stars (RR Lyrae, Cepheids) to clusters and galaxies
- explosive stars (novae and supernovae, maybe gamma-ray bursts) to galaxies
- galaxy systematics (Tully-Fisher, E galaxy color luminosity or fundamental
plane) to galaxies.
- Hubble Law
Trig. Parallax (aka surveying).
The usual baseline in astronomy is
the diameter of the Earth’s orbit
around the Sun.
This does not work too far out,
because the angle gets too small to
measure.
D(pc) = 1/θ arcsec
1 pc. ≈ 3.1 light year ≈ 3.1 x 1016m
Presently hard to do much better
than θ ≈ 0.01”.
Cepheid Period-Luminosity Relation
Cepheids are luminous, pulsating stars (P ≈
1-50 days). See fig. in text.
Henrietta Leavitt discovered that their
period is proportional to their luminosity.
Can use clusters of known distance,
containing Cepheids to calibrate the
relation.
Period --> L + apparent mag. --> distance
HST observed Cepheids of galaxies out to
the Virgo cluster…
Supernova
Can calibrate the true luminosity from the light curve or color variations.
Two types of SN, I and II, and also subtypes. Most accurate colorluminosity calibrations for SN type Ia.
This our second example
of a ‘standard candle.’
I.e., a light source whose
true luminosity can be
determined, then
compared to its apparent
luminosity to get a
distance estimate.
Most distance ladder
rungs involve standard
candles.
M51, July 2005, type II
Tully-Fisher Relation
For spiral galaxies: L ~ vrot4.
Measure rotation velocity from 21 cm line of H.
Use calibrated T-F relation to get luminosity.
Compare to apparent luminosity to get distance.
Elliptical galaxies obey a similar relation.
The Hubble Law
In the 1920s V. Slipher measured galaxy radial velocities via Doppler shifts.
(Most galaxies show redshifts (receding).)
E. Hubble observed Cepheids for
distance measurements. Found larger
redshifts for more distant galaxies.
Specifically,
V = Hod,
Where conventionally v is in km/s and d
in Mpc.
We now understand this as a result of
the overall expansion of the universe.
From http://cfa-www.harvard.edu/~huchra/hubble/
Determining Ho has been one of the ‘holy grails’ of modern astrophysics.
It sets the scale of the universe. Once it’s determined we can use the Hubble to
get galaxy distances. (This is not a standard candle method.)
It reflects the age of the universe.
Change in its slope (curvature) hints at the future of the universe.
If all distant galaxies are moving away from us are we the center of the
universe? No!!!
In an expanding universe:
all galaxies move away from each other. Like points on a balloon as
you blow it up.
more distant galaxies move faster, if the size of the universe
increases steadily.