Download The star Epsilon UMa, or more commonly known as Alioth

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Introduction:
The star Epsilon UMa, or more commonly known as Alioth (meaning “the black
horse”), is the third star from the tail-end of the Big Dipper located approximately 80.9 ±
1.2 light years away.9 Alioth and the Big Dipper are also a part of the constellation Ursa
Major, also known as The Great Bear. In Greek mythology, it is said that there once was
a daughter of King Lycaon named Callisto that was chosen to be the servant of the hunter
Artemis. Zeus, who is well known for seducing many young women, impregnated
Callisto. Artemis did not take kindly to this because the one thing that she valued most
above all else was her chastity, so she banished Callisto. Callisto gave birth to a son
named Arcas, which made Zeus’s wife Hera very jealous. Out of revenge, Hera turned
Callisto into a bear. Arcas grew up and became a great hunter and one day he found his
mother who was in the form of a bear. Arcas was just about to kill his mother when Zeus
intruded on the matter and saved her by grabbing them both by their tails, swinging them
over his head and throwing them into the sky as the Greater and Lesser Bears. This also
explains why the two bears have such long tails.7,8 One inconsistency in the story is that it
does not explain how or when Arcas was changed into a bear. As with all myths there are
many versions by many people.
Alioth’s Motion:
The position of Alioth in our night sky is not a fixed position, but is actually
moving in what is called a “proper motion”. This motion has to do with the fact that all
the stars that we see, including our own sun, are orbiting the center of the Milky Way
Galaxy. Alioth is one of the 13 stars in the Ursa Major moving group where all of these
stars have a common proper motion which is approximately 111.71 mas/yr right
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ascension and -8.99 mas/yr declination.12,11 Figure 1 is an illustration of how the stars in
the big dipper have changed since approximately 100,000 BC to the present day, and
what they will look like in another 98,000 years. It is believed that the stars in the Ursa
Major moving group have a common age of approximately 500 million years from the
idea that they all formed from the same protostellar nebula, which would explain the
common proper motion.12 The coordinates of Alioth at present day are approximately 12h
54m 01.6s right ascension and +550 57` 35.4`` declination and the parallax is
approximately 40.3 ± 0.62 mas.11
Figure 1.2 Movement of the big dipper over 200,000 years
Henry Draper:
From the year 1911 to 1914 Annie Jump Cannon classified approximately
200,000 spectra and the results were collected together in what is known as the Henry
Draper Catalogue.3 One of the main ways that stars are referred to is by the number that
each star is designated in this catalogue. For Alioth, the Henry Draper number is
HD112185.11
Categorizing Alioth:
The spectral class of Alioth is given as A0pCr.2 The different spectral types in
order are O B A F G K M where each spectral type is classified by the temperature of the
star going from the hottest blue O type star to the coolest red M type star. A very easy
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way to remember these classes in order is by remembering that “Only Bored
Astronomers Find Gratification Knowing Mnemonics”. Alioth’s spectral type is A in
which for these stars the color of the light emitted ranges from a very light blue to white
and the approximate surface temperature ranges from 7,500 to 11,000 degrees Kelvin.
The average luminosity of these stars is around 80 solar luminosity (1 solar luminosity
equaling 3.83 x 1033 ergs/s), the average mass is approximately 3.2 solar masses (1 solar
mass equaling 1.989 x 1030 kg) and the average radius is 2.5 solar radii (1 solar radii
equaling 6.96 x 109 m).6 The main characteristic of this spectral type is that the hydrogen
absorption line is strongest for earlier A type stars and decreases toward the later A type
stars. Also, the calcium II absorption lines are weakest for the earlier A type stars and
stronger for the later A type stars.3 The words “later” and “earlier” when talking about the
stars in a spectral type refer to the fact that the spectral types are each broken up into a
decimal type system ranging from 0 to 9. Stars that are classified as A0 are earlier stars
and are higher in temperature then the later A9 stars. Alioth is labeled as an A0 star
which means that it is one of the hottest stars in the A spectral type. The letter p in the
spectral class of Alioth stands for “peculiar” because the spectrum of its light is quite odd
which was described earlier. The letters Cr in Alioth’s spectral class designation
represents the most dominant spectral line for this star, as mentioned before this line is
the chromium spectral line. The specifications of Alioth are that it has a mass of 3 solar
masses, a radius of 4 solar radii, and a luminosity of 108 times that of the Sun.11 The
mass of Alioth agrees with the average mass for an A type spectra star but the luminosity
and radius of Alioth are higher. Because Alioth is so large and luminous for its class, one
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might say that Alioth is a borderline main sequence – giant star according to page A-15
for A0 stars in Carroll & Ostlie’s An Introduction to Modern Astrophysics the textbook.
A luminosity class can also categorize each star. The classes range from I to VI in
roman numerals and a D at the end. The I class is subdivided into three categories: Ia-O,
Ia, and Ib. The type of star that relates to these luminosity classes is given in table 1.
Class
Ia-O
Ia
Ib
II
III
IV
V
VI
D
Type of Star
Extreme, luminous supergiants
Luminous supergiants
Less luminous supergiants
Bright giants
Normal giants
Subgiants
Main-sequence (dwarf) stars
Subdwarfs
White dwarfs
Table 1.3 Luminosity classes of stars
Since Alioth is a main sequence star, its luminosity class is V.
Into the depth of Alioth:
Alioth is an alpha-CV type variable star and one of the brightest in its
constellation. An Alpha-Canum Venaticorum type star (or alpha-CV) is a rotating
variable that usually shows a very small difference in visual magnitude, or brightness, as
it rotates. This irregular surface brightness may be due to certain magnetic effects of the
star. Alioth itself is noted to have one of the weakest magnetic fields for the alpha-CV
type class. It is only 100 times that of earth and approximately 15 times weaker than
those common in alpha-CV type class stars.5 Alioth has a rotation period of
approximately 5.09 days with a rotation speed of 38 km/s in which its apparent visual
magnitude changes from 1.76 to 1.79 and back again.11
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Alpha-CV type stars are divided into three main groups depending on which
spectral lines are most dominant. These three types of spectral lines are silicon,
manganese, or as in Alioth’s case, chromium-strontium lines.8 These stars usually lack
the more common elements that are found in stars and have an unusual abundance of
metals that are not very common in most stars. It was found that the 7 most abundant
metals for Alioth are calcium, chromium, iron, magnesium, manganese, thallium, and
strontium. Using a Doppler imaging code to analyze elements in complex spectral line
blends, it is possible to map the structure of where these elements are located in the star.
It was found that chromium, iron, and manganese tend to be most dominant at the
magnetic polar region of Alioth and very little of these elements are found at the
magnetic equator. Strontium is very much like the three mentioned except that it is only
found at one of the poles. The element thallium tends to be the opposite of chromium,
iron and manganese where it is strongly detected at the magnetic equator and not at the
magnetic poles. It seems that Magnesium and calcium is unlike all the rest because there
is no apparent pattern to its location in the star.4
Alioth has a mass of 3 solar masses. Because of this, the CNO cycle dominates
for the production of hydrogen to helium-4 in the core of this star. The CNO cycle uses
carbon, nitrogen and oxygen as catalysts for the nuclear reaction from hydrogen to
helium-4 and is most dominant in stars that are greater than 1.3 solar masses. Because the
energy generation in the core of this star is due to the strongly temperature dependent
CNO cycle, then convection will dominate the core as a means to emit the energy from
the core to the surface of the sun. The convection process involves hot buoyant mass
elements rising from the core and transporting excess energy outward. The mass element
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cools as it travels outward and looses energy where it then begins to fall toward the core
again to be reheated and begin the process once more. This process is more efficient for
a star that is above 1.3 solar masses because the rate of energy generation changes
quickly with radius. The radiation process (where energy is simply radiated outward from
the core) is not efficient for transporting the large amount of energy being released by
nuclear reactions in the core. Outside of the core, the radiation process is efficient enough
to transport the energy because the energy being transmitted is over a larger area than in
the core.3 This is illustrated in Figure 2.
Figure 2. How energy is transmitted in a 3 solar mass star
Alioth’s Magnitudes:
Different stars have different apparent and absolute bolometric magnitudes. An
apparent bolometric magnitude is a number scale invented by a Greek astronomer
Hipparchus. This scale describes how bright a star appears in the night sky ranging from
1 for the brightest star to 6 for the dimmest star able to be seen with the naked eye. A
difference of 5 magnitudes on this scale corresponds to a factor of 100 in brightness. An
absolute bolometric magnitude is the same as the apparent bolometric magnitude if the
star were located 10 parsecs (or 3.26 light years) away from the observer. Both of these
magnitudes are measured over all wavelengths of the light that is emitted by the star.
Other types of magnitudes that stars are designated are the U, B, and V magnitudes.
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These letters stand for the ultraviolet, blue, and visual magnitude, respectively. The
ultraviolet magnitude is measured at a wavelength of 3650 Ǻ, the blue magnitude is
measured at a wavelength of 4400 Ǻ and the visual magnitude is measured at a
wavelength of 5500Ǻ.3 The there are two color indices for a star, the U-B color index and
the B-V color index. Alioth’s B-V color index is -0.02 and its U-B color index is 0.02.11
Since the lower the magnitude the higher the intensity, this means that Alioth emits high
intensity light at the wavelength 4400 Ǻ.
Position on HR Diagram:
There are different types of Hertzsprung-Russell, or HR, diagrams. One type is a
scattergram graph of the luminosity vs. temperature for a large number of various stars.
Alioth has a surface temperature of approximately 9650 ± 250 K and a luminosity that is
108 times that of the sun. From this, one can approximate the position of Alioth on the
HR diagram as that shown in Figure 3.
Figure 3.10 HR diagram with approximate location of Alioth
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What Alioth Is Doing Now:
Since Alioth is so large and luminous for its class, it is suggested that Alioth is
near the end of its main sequence lifetime.5 Figure 4 illustrates the path that a star takes
during its main-sequence and post-main-sequence lifetime for different solar masses.
Alioth is a 3 solar mass star and path is shown in red in Figure 4. According to its present
luminosity and surface temperature, the point at where it is located now on this track is
shown by the blue circle. According to this, Alioth has already gone through points 1, 2,
3, and 4 and is now proceeding to point 5. The time that it will take Alioth to go from
point 4 to 5 is approximately 4.51 million years.3 In this time the radius of the star will
increase and the effective surface temperature will decrease and will enter the sub-giant
branch. When the star nearly reaches point 5 the mass of the isothermal core will become
too great and will start to contract where the luminosity will dramatically increase from
around 108 to 315 solar luminosity.
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Figure 4.3 Main-sequence and post-main-sequence evolution of stars
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Bibliography:
1
Ancient Egyptian Astronomers, Retrieved April 02, 2006 from the World Wide Web:
http://www.geocities.com/blobrana/features/ursamajor.htm
2
Alioth, Retrieved April 02, 2006 from the World Wide Web:
http://www.astro.wisc.edu/%7Edolan/constellations/hr/4905.html
3
Carroll & Ostlie, An Introduction To Modern Astrophysics, 1996
Doppler Imaging of the Ap star ε Ursae Majoris: Ca, Cr, Fe, Mg, Mn, Ti, Sr.,
LUEFTINGER T., KUSCHNIG R., PISKUNOV N.E., WEISS W.W.,
Astron. Astrophys., 406, 1033-1042 (2003) - August(II) 2003
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5
Kaler J., Alioth, Retrieved April 02, 2006 from the World Wide Web:
http://www.astro.uiuc.edu/~kaler/sow/alioth.html
6
Star Classification, Retrieved April 02, 2006 from the World Wide Web:
http://www.enchantedlearning.com/subjects/astronomy/stars/startypes.shtml
7
StarrySkies, Retrieved April 02, 2006 from the World Wide Web:
http://starryskies.com/The_sky/constellations/ursa_major.html
8
The Constillations Web Page, Retrieved April 02, 2006 from the World Wide Web:
http://www.dibonsmith.com/uma_con.htm
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The Dome of the Sky, Retrieved April 02, 2006 from the World Wide Web:
http://domeofthesky.com/clicks/alioth.html
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The Hertzsprung-Russell Diagram, Retrieved April 02, 2006 from the World Wide
Web: http://cassfos02.ucsd.edu/public/tutorial/HR.html
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Wikipedia, The Free Encyclopedia, Retrieved April 02, 2006 from the World Wide
Web: http://en.wikipedia.org/wiki/Alioth
12
Wikipedia, The Free Encyclopedia, Retrieved April 02, 2006 from the World Wide
Web: http://en.wikipedia.org/wiki/Ursa_Major_Moving_Group