Curtis-Shapley Debate:
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A galaxy is any of the billions of systems of stars and interstellar
matter that make up the Cosmos. Composed primarily of star, gas, dust and
dark matter, galaxies are the `atom' of cosmology. Galaxies vary considerably in size, composition, and structure, but nearly all of them are arranged in groups, or clusters, of from a few to as many as 10,000 members each. The diameters of galaxies are generally measured in tens of thousands of light-years. The distance between galaxies within a cluster averages approximately 1,000,000-2,000,000 light-years, and the spaces between clusters of galaxies may be a hundred times as great. Each galaxy is composed of innumerable stars--most likely from hundreds of million to more than a trillion stars. In many galaxies, as in the Milky Way Galaxy, clouds of interstellar gas and dust particles known as nebulas can be detected.
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At the end of the 19th century it was unclear the size of the Universe, mostly
due to the lack of any kind of method to determine distance beyond a few
hundred parsecs. At the turn of the century, the Dutch astronomer Jacobus
Kapteyn used the latest data of the day to postulate a model for the Galaxy
- and the universe in his eyes - that consisted of a flattened stellar
system 10 kiloparsecs (30,000 light years) in diameter and 2 kiloparsecs
(6,000 light years) in thickness. He placed the sun near the center of this
universe. Kapteyn used the parallax method to calibrate the distance to the
nearest stars, and proper motions and apparent brightnesses to estimate
the distances to successively further stars. Kapteyn's extensive application
of the method of star counts used by Herschel also confirmed his results
for the dimensions of the Galaxy, or `Kapteyn's Universe' as it was called. In 1918 and 1919 Shapley published articles in the Astrophysical Journal elucidating a new model for the Galaxy based on Cepheid distances from the period-luminosity relation. Basing his model on the asymmetric distribution of globular clusters, Shapley estimated that the diameter of our Galaxy was 100 kiloparsecs, 10 times larger that Kapteyn's value. Shapley also placed the center of the Galaxy some 20 kiloparsecs distant from the Sun, a drastic, dramatic shift in location. In his view, this large meta-Galaxy was the universe and the spiral nebulae were simply one relatively minor population of mostly gaseous objects contained within it.
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If Shapley's values are correct, then the next question that arises is are
there any objects outside of our Galaxy. The obvious canidiates are the
numerous spiral nebula discovered in photographic surveys of the skies.
Objects in the sky divided into two categories: stars and diffuse nebula.
Many of these nebula appeared irregular, such as the Orion Nebula. But many
also had a symmetry to them that indicated rotation (i.e. spiral nebula).
Shapley's measurments then focused astronomers into asking whether spiral
nebula were internal to the Galaxy (possibly star systems in formation) or
external to the Galaxy, i.e. island universes in themselves. The issue became confused with the detection of proper motion in the spiral nebula by van Maanen. Van Maanen measured motion in seconds of arc per year, an angular rate of motion, by comparing photographs of the same region of the sky taken years apart. Knowing the distance to the spiral nebulae would allow the conversion of his measured angular rate of rotation to a rotational velocity in kilometers per second. The distances to the spiral nebulae were not known but Shapley argued that if the nebulae were placed well outside the boundaries of the Galaxy, as Curtis and others had suggested, the rotational velocities implied would be a substantial fraction of the speed of light! This was an unreasonable result and thus he argued that the real distances to the spiral nebulae must be closer to bring their implied rotational velocities in to a physically acceptable range.
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Both Shapley and Curtis were correct on a major point, and each was
incorrect on a major point. Shapley was correct that our sun was well
off from the center of our Galaxy. Let's not take this point lightly.
He, like Copernicus before him, had moved humanity's place in the cosmos
far away from where it was previously. As Copernicus had moved it from
the Earth to the Sun, Shapley moved it, almost single-handedly, from the
Sun to the center of the Galaxy. This in itself is truly historic.
Shapley was also correct that our Galaxy was much bigger than Kapteyn
had hypothesized previously. Another major point where Shapley was
correct was about the usefulness of Cepheid variables as distance
indicators. The distance scale of the Galaxy he obtained from them was
too large but not far off by astronomical standards - and Cepheids
continue to be cornerstones of our knowledge of distances to further
objects even today. Curtis, however, was correct that spiral nebulae are external galaxies. This was the first time this was shown with valid scientific evidence, and this point in itself is also truly historic. In fact, there is no precedent for this - it is an accomplishment that is unique in history. Curtis was also correct that van Maanen's measurements of the rotation of these nebulae were inaccurate. In view of his arguments against using Cepheids as distance scale indicators, it is ironic that this point was ultimately settled in his favor by Hubble's discovery of Cepheids in the Andromeda Nebula several years after the debate.
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Cepheid Distances to Galaxies:
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A Cepheid variable are pulsating variables that swell and shrink due to
internal forces. The size (and/or the shape) changes as they swell or
shrink. Cepheid variables have a period from one to seventy days and have
a strict period-luminosity relationship. Their brightness depends upon
their period. Cepheid variables are luminous yellow giant or supergiant stars. In a little more detail, as radiation streams out, some He+ in the atmosphere of the star is ionized to He+II, making the atmosphere more opaque. The decreased transparency of the stellar material blocks the energy flux and heats the gas. The increased pressure pushes the envelope out, thus increasing the star's size. As the star expands, it cools and He+II gains an electron, converting back to He+. Cepheid variables are brightest when they are the hottest, which is close to the minimum size. Even though the temperatures of Cepheid variables do differ as they change size, the range is relatively small. Therefore, the size and period of a Cepheid variable are more influential in determining its luminosity. If two Cepheid variables have periods that differ by a factor of two, the longer period Cepheid variable is approximately 2.5 times more luminous than the shorter period one. There are two types of Cepheid variables, type I and type II. Type II Cepheid variables have a shorter period and lower luminosity than type I. Type II has a lower luminosity by about 1.5 magnitudes.
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Cepheid variables were fist found in Cepheus, near Cassiopeia, in the
Northern sky. Henrietta Leavitt produced a catalogue of 1777 variable
stars in the Magellanic Clouds. In 1912, she managed to obtain the
magnitudes and periods for 25 variables in the Small Magellanic Cloud
(SMC). She was the first person to realize a period-luminosity relation in
the stars. She studied the delta Cephei star and noted that it slowly
diminishes in brightness and remains near minimum for most of the time. It
then rapidly increases to a brief maximum. Leavitt decided that
since all of these variable stars are probably close to the same distance
from Earth, their periods are associated with their luminosity. In
conclusion, she stated that the parallaxes of some variables of this type
might be measured, even though she never did the calculations herself.
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Danish astronomer Ejnar Hertzprung realized that if the PL relation could
be calibrated, then the absolute magnitudes of members of this group of
variable stars could be determined directly from their periods. After
this, it would be straightforward to obtain their distances. In 1913, he
used the term Cepheid and it has remained the name of these stars. He used
statistical parallax to obtain his zero point, and estimated the distance
to the SMC. He came up with 3000 light years, which is very far off from
our current estimate of 210,000 light years. Harlow Shapley formed his
own calibration of the zero point in 1918. His zero point was
approximately 1.5 magnitudes too dim, but they did not realize this for
many years. His mistake was using type II Cepheid variables. He was
unaware that there are two types and tried to make calculations using
both. Even though his zero point was wrong, he did manage to come up with
a decent model of our galaxy.
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In the mid-1920s, Edwin Hubble finally settled the Curtis-Shapley debate. He used Cepheid distance
measurements and the 100 inch Hooker Telescope at Mount Wilson (the largest in the world at
that time). He identified Cepheid variable stars in the Andromeda Galaxy (M31). He
used the distance to M31 to show that it was greater than what Shapley and Curtis proposed was
the extent of our Milky Way galaxy. M31 is approximately 2,500,000 light years away, much
greater than what either Shapley or Curtis estimated as the diameter. He also determined that
the spiral nebulae were in fact other galaxies and not just clouds of dust. He is most famous
for discovering that the universe is expanding.
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During WWII, Walter Baade undertook a detailed study of M31. He was able to take advantage of
almost unlimited telescope time and excellent seeing conditions due to wartime blackouts. He
and Hubble discussed an apparent discrepancy in the then current distance calibration. They
could not understand why the globular clusters associated with Andromeda appeared to be 1.5
magnitudes fainter than those in the galaxy. Baade decided that there were really two
different types of Cepheid variable stars in 1956. It took scientists a long time to realize
that they had been using two different populations because distance calibrations had been in
good agreement with Shapley (because his calculations were wrong)
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Contents of Galaxies:
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Clearly, the most obvious componet to a galaxy is its stars. But unlike a globular cluster,
the stars in a galaxy may have a range of masses, ages and chemical composition. Thus, the
color of a galaxy, as given by starlight, will be a mixture of colors from different stellar
populations within the galaxy. For example, the following diagram is an HR diagram of the stars within a few thousand parsecs of the Sun. This will contain field stars, halo stars, new stars formed in the arms of the disk of our Galaxy and old stars. The resulting HR diagram is much more complicated than that of a globular cluster.
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And there is no expectataion that all galaxies have similar stellar populations. For example,
the HR diagram below is from a dwarf galaxy which displays evidence of several distinct
eposides of star formation in its past as traced by different main sequences and red giant
branches.
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The second major component to galaxies is gas and dust, i.e. the ISM.
Approximately 99% of the mass of the interstellar medium is in the form of
gas with the remainder primarily in dust. The total mass of the gas and
dust in the interstellar medium is about 15% of the total mass of visible
matter in the Milky Way. Of the gas in the Milky Way, 90% by mass is
hydrogen, with the remainder mostly helium. The gas appears primarily in
two forms 1) Cold clouds of atomic or molecular hydrogen and 2) Hot
ionized hydrogen near hot young stars. The clouds of cold molecular and
atomic hydrogen represent the raw material from which stars can be formed
in the disk of the galaxy if they become gravitationally unstable and
collapse. Although such clouds do not emit visible radiation, they can be
detected by their radio frequency emission.
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Interstellar dust grains are typically a fraction of a micron across
(approximately the wavelength of blue light), irregularly shaped, and
composed of carbon and/or silicates. Absorption of light by dust causes
large dark regions in our galaxy and in other galaxies, as this picture of
the Milky Way looking toward the center indicates. These dust clouds are
visible if they absorb the light coming through them. We then refer to
these clouds as dark nebulae such as the adjacent Horsehead Nebula. On the
other hand, light can reflect from clouds of dust and gas, giving rise to
sometimes beautiful reflection nebulae. Dust has two major effects on
light passing through it: 1) The light is dimmed by the dust; this is
called interstellar extinction 2) The light that does pass through the
dust is depleted in blue wavelengths because the size of the dust grains
favors scattering blue light. This is called interstellar reddening,
because the resultant transmitted light is more red than it would have
been otherwise. This implies that transmitted light will be more red, but
reflected light will be more blue. (On Earth, the blueness of the sky is
due to similar effects in scattering of light from molecules in the
atmosphere.)
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| Lastly, a majority of a galaxy's mass is in the form of dark matter. The most robust evidence for dark matter comes from the rotation curves of spiral galaxies. Using 21 cm emission, the velocities of clouds of neutral hydrogen can be measured as a function of r, the distance from the center of the galaxy. In almost all cases, after a rise near r=0, the velocities remain constant out as far as can be measured. The dark matter problem has been around for decades, and there is now consensus that we don't know what the most common material in the Universe is. It is ``seen" only gravitationally, and does not seem to emit or absorb substantial electromagnetic radiation at any known wavelength. It dominates the gravitational potential on scales from tiny dwarf galaxies, to large spiral galaxies like the Milky Way, to large clusters of galaxies, to the largest scales yet explored. The universal average density of dark matter determines the ultimate fate of the Universe, and it is clear that the amount and nature of dark matter stands as one of the major unsolved puzzles in science. |
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It is widely accepted that there are vast amounts of unseen material in the universe, perhaps
10 times as much as in detectable galaxies and intergalactic gas. What is the evidence? The
basic conclusion comes from galaxy rotation curves, mass distributions inferred from hot gas
around ellipticals, the velocity dispersions in clusters of galaxies, and mass tracing via
gravitational lensing. Not only do we need to know how much of this exists, but where it is -
its distribution can distinguish among stellar remnants, hot and cold elementary particles
like massive neutrinos or axions,... Recall that most of these techniques are sensitive only
to dark matter that is concentrated around galaxies (or more accurately, that galaxies are the
marbles rolling up and down hills in dark matter, and that they have had time to fall to the
bottom). The amount of dark matter is often given in relation to luminous material through the mass-to-light ratio M/L, most often taking light at the B band; units are solar masses per solar luminosity. Young stellar populations may have values well below unity; older populations may go as high as of order 10, while the dynamical values for elliptical galaxies and clusters reach hundreds. Since some of the dynamical estimates have the same D2 dependence on assumed distances as does luminosity, the M/L ratio is often distance-independent.
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