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The Indian-American Nobel laureate Subrahmanyan Chandrasekhar
showed there exits an upper limit to the mass that a white dwarf
star may obtain. If a white dwarf exceeds this mass, it cannot
create enough central pressure to keep it from further
collapsing. The more massive a white dwarf becomes the smaller its
diameter becomes until it reaches the Chandrasekhar limit at
which point it collapses suddenly and then rebounds in a massive
explosion throwing off material at speeds up to 10,000 km/sec.
Type I supernovae all tend to have the same light curves and
maximum brightness, potentially making them excellent standard
candles for estimating galaxy distances. They occur in old
stars, and only Type I supernovae are found in elliptical
galaxies and in the central bulge of spiral galaxies where
mainly old stars are found.
Type II supernovae originate in red giant stars with at least 8
to 10 times the Sun’s mass. These stars have short lives living
only several millions of years, because they exhaust their
hydrogen rapidly. If the star is massive enough, after its
hydrogen is exhausted, it will continue element production in
its core converting the core first into helium and then into
carbon. Next, heavier elements are rapidly created until silicon
is made. In a matter of hours to days, silicon fuses into iron,
which is the end of element production, after which the core
rapidly collapses and then rebounds in a massive explosion. As
much as 90% of star’s mass is thrown into space at speeds of
5,000 km/sec. All that remains is a small, very hot neutron star
surrounded by an expanding cloud of gas, an example of which is
the Crab Nebula (M1).
Type II supernovae do not tend to be as bright as Type I, and
they only occur in the spiral arms of galaxies, where,
presumably, there is active star formation, and young massive
stars. Type II supernovae do not show the same consistency in
maximum brightness as do Type I supernovae; however, they still
are thought to be very useful as standard candles for distance
measurement.
The spectra of Type I and Type II supernovae differ as does
their maximum luminosities and their light curves.
However, they are used as standard candles, because they can be
observed in very distant galaxies, since a supernova can obtain
brightness equal to the rest of the galaxy. One or more
supernova explosions in a galaxy cluster provide an excellent
means to judge the relative distance of all the members of the
cluster.
Type Ia supernovae in particular have been found to be markedly
consistent compared to other exploding star types (Sky &
Telescope August 1999, page 40; Sky & Telescope December 1999,
page 18). They reach the same absolute magnitude at maximum
brightness. The adjustment for the zero point of both the nova
and the supernova yardsticks initially came from reviewing
records of historic novae and supernovae in the Milky Way and
estimating their maximum "absolute" brightness by finding stars
nearby them in space whose spectroscopic parallax distance could
be estimated. Even if a supernova’s peak brightness is missed,
it has been found that its “apparent" brightness can be inferred
by its "rate of early decline". This is why immediate attention
is given to supernovae outbursts -- to ideally catch it at its
peak or at least catch the rate of early decline (Sky &
Telescope August 1999, pages 31-37). Allan Sandage of Mt. Wilson
Observatory in conjunction with Gustav Tammann and colleagues at
Basil University in Switzerland using Cepheid variables and the
brightest resolvable red and blue stars in a galaxy calculated
that all Type I supernovae have a peak absolute magnitude of
–19.74 +- 0.19 (Sky & Telescope January 1985, page 18).
Type I supernovae may be further divided into classes: Ia
contains silicon (Si) absorption features in its spectrum, Ib
contains helium (He) features but no Si features, and type Ic
has very weak or almost no He features and lacks Si features.
Type Ia supernova are markedly consistent in the maximum
absolute brightness they achieve and hence can be used as
“standard candles” giving possible + or – 10 percent accuracy to
extreme intergalactic distances up to about twelve billion light
years.
Type II supernovae are less reliable as standard candles,
because their behavior is not as rigidly fixed as that of type
Ia supernovae. However, they have a known range of absolute
magnitudes they may achieve, and by examining their light curves
and spectra, it is possible to derive a reasonable estimate for
the brightness of a given type II supernova, enabling it to be
used as a distance indicator. Although supernovae have a number
of advantages for use as “standard candles” to measure vast
intergalactic distances, they have a number of disadvantages as
well. They are rare events and accurately measuring their
brightness from the background light of the galaxy they inhabit
can be difficult. Only forty to sixty supernovae are now
detected a year with only one out of five or six of them found
to be suitable to be used as a distance indicator.
BRIGHTEST GALAXIES IN CLUSTERS; SURFACE BRIGHTNESS FLUCTUATION
AND OTHER GALAXY DISTANCE TECHNIQUE
A number of other distance indicators have been developed based
on galaxy characteristics for galaxies with well established
distances in order to leap-frog farther and farther to distant
galaxies for which more standard distances measurement
techniques are very difficult. Some of these methods have been
demonstrated to be reliable enough to be used as independent
secondary yardsticks in determining the extent of our Universe.
Globular Cluster Luminosity Function (GCLF).
Globular clusters have been used as distance indicators since
they were detected by Edwin Hubble in initial studies of the M31
Andromeda Galaxy. William Baum first used this technique in 1955
to estimate galactic distances to the Virgo cluster by assuming
that the globular clusters of M87 are similar in brightness to
those of M31.
Since then, astronomers have demonstrated that the luminosity
curves of globular clusters of varying sizes is reasonably
independent of the properties of the galaxies they inhabit.
Distance is estimated by determining the apparent magnitudes of
a large sample of a galaxy's globular cluster population and
comparing them with the expected absolute magnitudes for a
similar grouping of globular clusters from one or more galaxies
with known distances.
This method works best for giant elliptical galaxies where
there are as many as 1,000 globular clusters and reddening by
dust and confusion by other kinds of clusters is less. The
method has the capability of measuring galactic distances
reliably as far as 160 million light-years. This method, like
all methods of determining cosmic distances, is being further
refined.
Brightest Galaxies.
After Edwin Hubble was able to resolve the brightest stars in
nearby galaxies, rough yardsticks could now be made for the blue
supergiant stars in some 200 further remote galaxies extending
our yardstick out to roughly 30 million light years from the
earth. However, in the 1940’s Cepheid variables, blue supergiant
stars, and supernovae still could not be resolved for more
remote galaxies. Nor was it possible to derive a reliable
yardstick for a very faint galaxy by measuring its integrated
"apparent" brightness and using it to derive a mean "absolute"
brightness. However, in a cluster of galaxies all galaxy types
are represented -- particularly large elliptical galaxies -- and
it was initially assumed the average "absolute" brightness of
the five brightest members of the cluster would be the same for
all clusters.
Hubble discovered an approximate brightness-distance
relationship, which could use this average total brightness as
an approximate yardstick within a 30 million light year sphere
using the other previous yardsticks to calibrate it. This
brightest galaxy measurement pushed our then visible limits of
the Universe further out to over a billion light years.
Similarly, other techniques were attempted to push the limits of
measuring remote galaxy distances. One of these involved
observations of angular diameters of different star clusters
(open clusters or globular clusters). Still, all of these
alternative methods required calibration from prior methods like
the Cepheid and supernova yardsticks.
Planetary Nebulae Luminosity Function (PNLF).
The brightness of planetary nebulae has emerged as another
reliable distance yardstick particularly for estimating
distances to nearby galaxies. Brightness studies of Milky Way
planetary nebulae indicate that they have very nearly the same
intrinsic brightness. After obtaining absolute brightness of
diverse planetary nebulae, such as the Ring Nebula (M57), the
Dumbbell Nebula (M27) and others whose distances were estimated
by alternative reliable techniques, it was found that there were
only small differences in their brightness resulting from
variations in their physical sizes and chemical compositions.
Planetary nebulae have been detected in the Local Group
galaxies, other nearby galaxy clusters, and even as far away as
the Virgo cluster. The Virgo cluster was determined to be 49
million light years distant using planetary nebulae compared to
about 55 million light years using the supernova technique. This
planetary nebula yardstick is more accurate for determining the
distances to earlytype elliptical and S0 armless spiral
galaxies where the planetary nebulae are more easy to
distinguish from other objects and reddening due to dust is
rare.
Tip of the Red Giant Branch (TRGB).
In 1930, Harlow Shapely outlined various methods for estimating
distances of the Milky Way’s globular clusters, among which was
a distance estimate that assumed the brightest stars in the
globular clusters were red giants of the same absolute
magnitude. Shapely tried using this method in conjunction with
RR Lyrae stars. Unfortunately, this method was flawed, because
it did not recognize star age and metallicity variations, but
the method was sufficiently accurate that it independently
showed that our Milky Way is a galaxy similar to many other
galaxies.
In 1974, Harris proposed in his doctoral thesis that the
apparent B-band luminosities of the brightest red giants could
be used as distance measuring rods to globular clusters even if
the giant branch was sensitive to star age and metallicity.
Unfortunately, atmospheric line-blanketing effects in the
optical spectrum causes substantial measurement problems in the
optical portion of the spectrum. The TRGB method as a Population
II distance indicator currently uses the I-band (an infrared
band) luminosity of the brightest RGB stars. The magnitude of
TRGB stars are very insensitive to metallicity and age in this
wavelength. Therefore, unlike the Cepheid period-luminosity
relation that requires adjustment for system metallicity, this
method can be applied to any type of elliptical, irregular, or
spiral galaxy. More importantly, the TRGB galaxy distance
indicator can be used for ground-based as well as HST
observations.
Tully-Fisher Relation (TF).
In 1974, radio telescope observations were employed to measure
the width of the 21 cm neutral hydrogen lines in galaxies. The
width of this radio spectrum line gives an indication of the
rotation rate of a galaxy, which can be reasonably correlated
with the galaxy’s absolute magnitude. Luminous galaxies spin
faster than dim ones. In 1977, this concept that the internal
dynamics of a galaxy were related to its size and luminosity was
fully developed by Brest Tully and Richard Fisher. The
Tully-Fisher relation extends the realm of measurable galaxy distances far beyond the
Virgo Cluster.
Currently, the Tully-Fisher relation is being used as a primary
distance indicator for literally: thousands of galaxies singly,
in groups, and in clusters with an estimated accuracy of ±15%
for the distance of a single spiral galaxy out to perhaps 750
million light years. This is particularly important, since it
provides a way to estimate distances to galaxies both within and
outside of clusters. This is important, because the dynamics of
galaxies associated with large clusters, such as the Virgo
Cluster, are significantly influenced by the cluster’s mass.
This influence may alter the properties of a galaxy. Some
methods used to estimate its distance, such as its red shift
(see below), are inaccurate without proper corrections being
made. Before the Tully-Fisher relationship was discovered,
astronomers had to infer remote galaxy distances primarily from
their spectral radial velocities.
Although the Universe had initially been assumed to be expanding
uniformly from the time of the Big Bang based on the red-shift
of distant galaxies (to be discussed in the next section), the
Tully-Fisher relation made it possible to look for
irregularities in that expansion independent of galaxy
velocities – and it did reveal large-scale departures from
uniformity. Thus far, the most notable departure is the
so-called Great Attractor, which seems to be influencing galaxy
motions in this part of the Universe. The Attractor was
hypothesized in 1988, and since then additional large-scale
flows have been mapped in other parts of the sky mostly based on
Tully-Fisher distances.
Surface Brightness Fluctuation Technique (SBF).
Another promising technique to measure galaxy cluster distances
is the surface brightness fluctuation technique (SBF) (Sky &
Telescope, September 1997, page 20; January 2001, pages 22-23)
pioneered by John L. Tonry of the University of Hawaii. The
statistical smoothness of an elliptical galaxy’s glow is
measured pixel by pixel on high-resolution CCD images of the
largest and brightest elliptical galaxies in a cluster. The
average pixel-by-pixel fluctuation tells how close the glow is
to being resolved into the galaxy’s brightest stars, thereby
providing an indirect means of establishing the galaxy’s
distance. Using this technique for the Virgo galaxy cluster,
yields a distance of 55 million light years for the cluster’s
center.
Fundamental Plane for Elliptical Galaxies (FP or FPEG).
In 1976, Faber and Jackson found a correlation exists in
elliptical galaxies between the stellar velocity dispersion and
the intrinsic luminosity similar to the relation between
rotation velocity and luminosity for spiral galaxies. Elliptical
galaxies are found to occupy a “fundamental plane” where an
elliptical galaxy’s effective radius is tightly correlated with
the surface brightness within it and the central velocity
dispersion of the galaxy. Studies have shown that this technique
results in approximately 10-20% scatter in the distance estimate
for a cluster with elliptical galaxies.
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