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This last section is a short essay that summarizes the ways astronomers find
distances to various objects in the universe.
Why care so much about finding distances in astronomy? If you know the
distance to a star, you can determine its luminosity and mass. You can then
discover a correlation between luminosity, mass, and temperature for
main sequence stars that our physical theories must account for. Finding
distances to stellar explosions like planetary
nebulae and supernovae enables you to find the power needed to make the gaseous
shells visible and how much was needed to eject them at the measured speeds.
Stellar distances and distances to other gaseous nebulae are necessary for
determining the mass distribution of our galaxy. Astronomers have then been able to
discover that most of the mass in our Galaxy is not producing light of any kind
and is in a dark halo around the visible parts of the Galaxy.
Finding distances to other galaxies enables you to find their mass, luminosity,
and star formation history among other things. You are better able to hone in on
what is going on in some very active galactic cores and also how much dark
matter is distributed among and between galaxy cluster members. From galaxy
distances, you are also able to answer some cosmological questions like the
large-scale geometry of space, the density of the universe needed to stop
the expansion (called W [``Omega'']), age of the
universe, and whether or not the universe will be expanding.
The cosmological questions will be discussed fully in the
next
chapter on cosmology. This is only a
quick overview of the reasons for distance measurements and is by
no means an exhaustive list of reasons why distance measurements
are so important.
Now let's take a look at the distance scale ladder. The bottom
foundational rung of the ladder is the most accurate and the most certain of all the
distance determination methods. Each rung depends on the rung below and it is less
certain than the previous one.
The Earth and Distance to the Sun. Radar reflections
from Venus and its angular separation from the Sun are used to calculate the
numerical value of the Astronomical Unit (AU). You can use radar to measure distances
out to 50 AU.
On the next rung of the distance scale ladder, you can convert trigonometric
parallax measurements into distances to the nearby stars using their
angular shift throughout the year and the numerical value of the Astronomical
Unit. Distances to nearby clusters like the Hyades or the Pleiades are found
via trigonometric parallax or the moving clusters method (another geometric
method). The cluster's main sequence is calibrated in terms of absolute
magnitude (luminosity). Geometric methods are used to find distances out
to about 100 parsecs (or several hundred parsecs with Hipparcos' data).
On the next rung outward the spectral type of star is determined from its
spectral lines and the apparent brightness of the star is measured. The
calibrated color-magnitude diagram is used to get its luminosity and then its distance
from the inverse square law of light brightness.
The entire main sequence of a cluster is used in the same way to find the
distance to the cluster. You first plot the cluster's
main-sequence on a color-magnitude diagram with apparent magnitudes, not
absolute magnitude. You find how far the unknown main sequence needs to be
shifted vertically along the magnitude axis to match the calibrated main sequence.
The amount of the shift depends on the distance.
The age of the cluster affects the main sequence. An older cluster has only fainter
stars left on the main sequence. Also, stars on the main sequence brighten slightly at a
constant temperature as they age so they move slightly vertically on the
main sequence. You must model the main sequence evolution to get back to the
Zero-Age Main Sequence. This method assumes that all Zero-Age main sequence stars
of a given temperature (and, hence, mass) start at the same luminosity. These
methods can be used to find distances out to 50 kiloparsecs.
Continuing outward you find Cepheids and/or
RR-Lyrae in stars clusters with a distance known through main sequence
fitting. Or you can employ the more direct ``Baade-Wesselink method'' that uses the
observed expansion speed of the variable star along the
line of sight from the doppler shifts in conjunction with the observed angular expansion rate
perpendicular to the line of sight. Since the linear expansion rate depends
on the angular expansion rate and the distance of the star, the measurement
of the linear expansion rate and angular expansion rate will give you the
distance of the variable star.
RR-Lyrae have the same time-averaged luminosity (about 49 solar luminosities or an
absolute magnitude MV = +0.6). They pulsate with
periods < 1 day. Cepheids pulsate with periods > 1 day. The longer
the pulsation, the more luminous they are. There are two types of Cepheids: classical
(brighter, type I) and W Virginis (fainter, type II). They have different
light curve shapes. The period-luminosity relation enables us to find
distances out to 4 megaparsecs (40 megaparsecs with the Hubble Space Telescope).
The periods and apparent brightnesses of Cepheids in other nearby
galaxies are measured to get their distances. Then the galactic flux and the
inverse square law of brightness are used to get the galactic luminosity.
You can find the
geometric sizes of H-II regions in spiral and irregular galaxies. From this
you can calibrate the possible H-II region size--galactic luminosity relation.
Or you can calibrate the correlation between the width of
the 21-cm line (neutral hydrogen emission line) and the spiral galaxy luminosity.
The width of the 21-cm line is due to rotation of the galaxy. This
correlation is called the Tully-Fisher relation: infrared luminosity = 220 ×
Vrot4 solar luminosities if Vrot is
given in units of km/sec. Elliptical galaxies have a correlation between their luminosity and
their velocity dispersion, vdisp, within the inner few
kpc called the Faber-Jackson law:
vdisp approximately equals 220 ×
(L/L*)(1/4) km/sec, where
L* = 1.0 × 1010 ×
(Ho/100)-2
solar luminosities in the visual band and the Hubble constant Ho =
60 to 70 km/sec/Mpc.
Cepheids are found in other nearby galaxies to get their distance. Then the
luminosity of several things are calibrated: (a) the supernova type 1a maximum
luminosity in any type of galaxy; (b) the globular cluster luminosity
function in elliptical galaxies; (c) the blue or red supergiant stars relation in
spirals and irregulars; (d) the maximum luminosity--rate of decline relation of
novae in ellipticals and bulges of spirals; and (e) the planetary nebula
luminosity function in any type of galaxy.
The Rung 5 methods can be used to
measure distances out to 50 to 150 megaparsecs depending on the particular
method.
The Hubble Law is calibrated using rung 4 methods for nearby galaxy distances
and rung 5 methods for
larger galaxy distances. If those rung 5 galaxies are like the nearby ones (or
have changed luminosity in a known way), then by measuring their apparent brightness
and estimating their luminosity OR by measuring their angular size and
estimating their linear size, you can find their distance. You need to
take care of the effect on the measured velocities caused by the Milky Way
falling into the Virgo Cluster. You can also calibrate the galaxy cluster
luminosity function.
The Hubble law relates a galaxy's recession (expansion) speed with its
distance: speed = Ho × distance. Measuring the
speed from the redshift is easy, but measuring the distance is not. You can
calibrate the Hubble Law using galaxies out to 500 megaparsecs.
This is the final rung in the distance scale ladder. You use the Hubble Law
for all far away galaxies. You can make maps of the large-scale structure of the
universe. The Hubble Law is also used to determine the overall geometry of
the universe (how the gravity of the universe as a whole has warped it).
You will see in the next chapter that the geometry of the universe determines
the fate of the universe.
Rung 4 is the critical one now for the distance scale ladder. With the
fixed Hubble Space Telescope, astronomers are able to use the Cepheid
period-luminosity relation out to
distances ten times further than what can be done now on the ground. The
ground measurements of the Hubble constant are 50 to 100 km/sec/Mpc (a
factor of two in range!). With Cepheid observations at farther away
distances, astronomers have constrained its value to between 64 and 80 km/sec/Mpc
with a best value of 72 km/sec/Mpc. The
value of 1/Ho is a rough upper limit
on the age of the universe (assuming constant recession speeds!). The new
Hubble constant measurement then implies an universe age of about 14 billion years.
The favorite model for how the recession
speeds have changed over the history the universe gives an age a little
less than that of about 13 billion years with this value for the Hubble constant.
This agrees with the ages derived for the oldest
stars (found in globular clusters) of about 12 to 13 billion years.
- Why is finding accurate extragalactic distances so important?
- What are the more accurate or more certain ways to measure distances?
What are the less accurate (less certain) ways to measure distances? What
assumptions do we make when using the less certain techniques?
- What is the Hubble Law? What two things does it relate? Why is it
important?
Go back to previous section
last updated: 26 May 2001
Is this page a copy of Strobel's
Astronomy Notes?
Author of original content:
Nick Strobel