Because of the extreme variance of variable stars (pun!), discussing all of them adequately would be unfeasible. Instead this discussion will be limited to Cepheid Variable stars.

Variable Stars are simply stars that change brightness in the night sky. Though to the casual observer, this might seem like a rather simple notion (that stars change brightness), it is in fact an incredibly complex and highly mathematical process. The period, or amount or amount of time between a given star's brightest points, varies significantly between each variable star. Each star's brightness on a given day has been recorded for decades, which has yielded significant data on the periods of countless Variable Stars. Though this is done in many places, the largest collective group to do this in America is AAVSO, or the American Association of Variable Star Observers. This information has been used to classify Variable Stars into separate groups.

WHY ARE THESE IMPORTANT TO US OR TO ASTRONOMERS?

A Variable Star's period is what Astronomers use to classify them. Within groups, the period of different variable stars can vary, though they will generally have similar shaped light curves. A light curve is simply a graph which plots a given star's brightness against time. Depending on the type of Variable Star the period can range from only a few days to decades long. In addition, the change in brightness can vary significantly; it can have a change of less than one or a change of 7 or 8. Clearly the differences between Variable Stars can be as large as the actual changes in brightness the star experiences. These simple changes are what allow the Cepheid to be one of the most important findings to the field of Astronomy.

The Cepheid variable's change in luminosity is due to the expansion and contraction in an alternating pattern. Sir Arthur Eddington was a supporter of the Cepheid pulsations theory which proposed that the star's pulsation is the result of two opposing actions. While the force of gravity would cause the star to contract, the outward pressure of the gas would tend to expand the star. It is postulated that as the star contracts under the force of gravity, the pressure increases. Since temperature is directly related to pressure, the temperature increases, which again increases the pressure, and so on. The inertia of the system causes the star to continue its tendency to contract, but the increasing pressure begins to build as an opposing force and eventually wins over so that an expansion begins. The cycle then reverses itself, whereby pressure and temperature are dropping as the star expands, but the force of gravity is fighting to pull the star inward. The forces battle against each other until gravity takes the upper hand and causes the star to again contract. The cycle then continues with the opposing forces as the star expands and contracts. Why this specific cycle only occurs in specific stars is uncertain, though it is believed that the helium atmosphere of the star plays a large role. The helium is what expands and contracts, allowing for the cycle to take place.

cepheid.gif
This is a sample light curve of a Cepheid. Also, this shows the relationship between the length of a star's period to it's Absolute Magnitude


It is important to note that for all stars, a smaller apparent magnitude is equivalent to a brighter star. i.e. a star of magnitude 3 is significantly brighter than one of magnitude 6.

Cepheids are Variable Stars with an extremely regular period, especially for an astronomical body. Henrietta Swan Leavitt discovered a relationship between the period and Absolute Magnitude of Cepheids (shown in the above graph). Using this relationship and an equation known as the distance modulus, it became possible to determine the distances of Cepheids, and thus nearby objects, with exterme precision.

In all equations the following variables are used:
M = Albsolute Magnitudei
m = Apparent Magnitude
D = Distance
P = Period

The Absolute Magnitude of a Cepheid Variable Star with a given period is given be the equation:

M = -2.81Log(P) - (1.43 ± 0.1)

Using the Absolute Magnitude found here and the value for Apparent Magnitude at the star's maximum, find distance with the following equation:

m - M = -5 + 5Log(D) which can be rewritten to D = 10 ^ ((m - M + 5) / 5)

A history of the Cepheid Variable



An explanation of parallax, what it is and why it can be used in astronomy.



SOMEWHERE ON THIS PAGE YOU MUST PRESENT YOUR “ESSAY” IN WHICH YOU ADDRESS THE QUESTIONS LISTED ON THE PROJECT OUTLINE AND THOSE BELOW. BE SURE TO HAVE THIS PART SEPARATE FROM THE CUT AND PASTE AND EMBEDDED ITEMS THAT YOU HAVE INCLUDED. YOU MUST REFERENCE (URL) ANY OUTSIDE SOURCES OF INFORMATION. THIS 500 TO 1000 WORD ESSAY MUST BE IN YOUR OWN WORDS – NOT CUT AND PASTED FROM A WEB SITE.
SPECIFICALLY:
WHAT EQUATIONS OR THEORY DID WE LEARN THAT RELATES TO YOUR TOPIC?
WHAT IS THE HISTORY OF THIS TOPIC?
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WHERE IS IT HEADED IN THE FUTURE?

CAN YOU FIND ANY PHOTOS OR VIDEOS RELATED TO VARIABLE STARS?
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Sonia Bansal - How can Variable Stars help astronomers understand the universe?
Answer: Variable Stars, specifically Cepheids, have allowed astronomers to know exact distances to distant heavenly bodies. This insight was what lead to discoveries such as Hubble's "Expanding Universe" theory. With this thought, astronomers realized that if the universe is expanding, then it must have initially started from one point; thus the Bing Bang Theory was born.

Nauma Haider - What groups are Variable Stars sorted into based on their respective periods?
Answer: Because there are quite so many different types of variable stars, I won't list all of them, but here are a few, grouped together appropriately:
Pulsating Variables
Long Period Variables
Mira Type
Semiregular
Cepheids
RR Lyrae
Cataclysmic (Eruptive) Variables
Flare Stars
Dwarf Novae
X-Ray Binaries
Supernovae
Type Ia
Type II

Robert Lopez - If variable stars are constantly changing, is there an average brightness or does the star gradually lose/gain brightness after a long period of time?
Answer: This greatly depends on the Variable Star you are talking about. This can easily be determined by the light curve of the star. Cepheids for example, if you look at the light curve above, have an average brightness somewhere right in between they're minimum and maximum. However, there are many variable stars that are completely irregular. For example, Epsilon Aurigae is a binary star that remains at maximum brightness for the majority of its period. Every 27.12 years, a second body eclipses in front of it, lowering the brightness. So this star's average brightness would be very close to its maximum brightness. Essentially, there is no real rule for an 'average brightness' nor are astronomers really concerned with it. The more interesting thing to look at is minimums, maximums, and why these things actually occur.

Brandon Siegenfeld- Do Variable stars ever stabilize, if so how?
Answer: For the most part, the answer is no. But there are variable stars known as "semiregular variables" which do very obscure things with their periods. They can have large fluctuations in their period length or in their minimum and maximum values. Also, they can occasionally stop varying entirely. The reason the answer to your question is still no, is that almost all semiregular variables that stop varying restart shortly afterward.

Sam Edwards - How can Cephied Variable stars be used to measure distances?
Answer: Cepheids are Variable Stars with an extremely regular period, especially for an astronomical body. Henrietta Swan Leavitt discovered a relationship between the period and Absolute Magnitude of Cepheids (shown in the above graph). Using this relationship and an equation known as the distance modulus, it became possible to determine the distances of Cepheids, and thus nearby objects, with exterme precision.

Greg Sturm - Does the contraction and expansion only affect brightness or is the amount of energy/heat radiating from the star variable as well? Also, have any planets been discovered on a variable star?
Answer: The contraction and expansion does in fact effect heat and energy radiation, though to what extent I am not sure. If there are any planets orbiting a variable star, it is not highly publicized. I would not rule out the possibility, for a planet is merely a chunk of rock that happens to be orbiting these big balls of fire.

Will Chan - How have these stars help astronomers with their current research?

Kevin Norris - How are apparent and absolute magnitude defined?
Answer: Apparent magnitude is defined as the measure of brightness as seen by an observer on Earth with the absence of the Earth's atmosphere. The scale is a relative scale using the star Vega (apparent magnitude .03) as a referance point. Due to historical reasons (which i won't get into here, but can be easily found), the scale is logarithmic. the ratio of brightness between two stars is equal to (100^(.2)) ^ (the difference in magnitudes).
Absolute magnitude is defined simply as the apparent magnitude of a star assuming the observer was 10 parsecs from the object.

James Song- Are interference patterns related to variable stars?
Answer: If you are referring to interference patterns such as the ones we discussed in optics (Young's double slit experiment), then no, interference patterns are not related to variable stars.

Sohini Sheth- What is the closest Cepheid Variable star to the earth that scientists have discovered thus far? (yes i just said thus)

Douglas Chin - If a star with varying luminous intensity were located directly behind a star with a constant luminous intensity, then would the star in front appear to be varying the same as the one behind it?