Astronomy

In Astronomy, teams answer questions on math and physics relating to the year's topic. For 2012, the topic of Astronomy will be stellar evolution and type Ia supernovae. Some questions pertain to specific DSOs on the year's DSO list.

''This page is for the general Astronomy information. For specific topics, see the following pages:

Determining Distances
A large part of the Astronomy event is being able to determine distances to objects in space from Earth. Often a question will give certain information and the participant will have to interpret and use the information to find the distance, luminosity, or some other characteristics of the object in question.

Cepheids and RR Lyrae


Cepheids and RR Lyrae are two types of variable stars that are especially good for finding distances to galaxies or other groups of stars because they have direct correlations between luminosity and period. In both Cepheids and RR Lyrae, the longer the period, the higher the luminosity. Cepheids typically have periods of about 1 to 50 days. Type I Cepheids, or Classical Cepheids, are brighter, newer Population I stars (see section about stellar populations below for an explanation). Type II Cepheids are similar to Type I in terms of the relationship, but they are smaller, dimmer Population II stars. These are also called W Virginis stars. RR Lyrae are different from Cepheids in that they are older and fainter than Cepheids. RR Lyrae stars typically have shorter periods than Cepheids - usually less than one day. They have masses about half that of our Sun, and are Population II stars. Also, the luminosity does not increase as much to a change in period, as most RR Lyrae have absolute magnitudes close to 0.75. Therefore, they are only useful in our galaxy and the one closest to us, Andromeda. RR Lyrae have been linked to globular clusters, since most variable stars in globular clusters are RR Lyrae. They are named after the original RR Lyrae in the constellation Lyra.

These variable stars are useful in calculations because once the period is found, the luminosity can be calculated or determined through the use of a period-luminosity graph. Then, through other formulas, the distance can also be determined. This gives them the use as "standard candles" in galaxies relatively close to ours in our universe. NGC 4603, one of the listed DSO's, is the furthest galaxy that a Cepheid has been used to calculate distance at 108 million light years away.

Distance Equations
There are many equations that are used to find distances to objects in space. Several of these equations can be found in the [[Media:Formula Sheet.pdf|Astronomy formula sheet]].

Triangulation is often used to determine distances. This method is based on parallax shifts, apparent changes in a star's location when viewed from different locations. The parallax of a star is one-half the angular shift produced over 2 AU, or six months. In short, it is the angle subtended by 1 AU. The parallax decreases as distance increases. A star's distance in parsecs (one arcsecond) is equal to 1\parallax. Parallax can only be used to measure stars up to 1000 parsecs away.

Hubble's Law
Hubble's Law uses the fact that objects in space are receding from us to determine distance. Edwin Hubble found that the recessional velocity is proportional to the distance away an object is and created an equation, $$v=H_oD$$, where v is the recessional velocity, $$H_o $$ is Hubble's constant, and D is the distance. The exact value of Hubble's constant is disputed, but most values are about 70.

The value of v is found by looking at an object's spectrum. The recessional velocity is the redshift multiplied by the speed of light, and in order to find redshift, a spectrum must be used. Redshift is how much a spectrum shifts toward the red side of the spectrum due to recession. Redshift, or Z, is found by dividing the change in wavelength of the spectrum by the wavelength the object was expected to have.

Distance Modulus
The distance modulus equation is also very important. It relates an object's distance with the difference between the apparent magnitude (m) with the absolute magnitude (M). This difference is known as the distance modulus.
 * $$5(log(d)-1)=m-M$$ where d is in parsecs

This equation can be written in many different ways so that different values can be found, but the essential purpose of the formula remains the same. A good way to practice using this equation before the competition is to take the apparent magnitude and approximate distance to a DSO and use them to find the absolute magnitude. This experience will be a time-saver if you have to use it during the test.

Stellar Populations
Populations of stars are classified by their metallicity, or by how much heavy metals a star has. Population I has the greatest concentration of metals, and most of them are relatively new stars that have taken metals expelled from other stars. The Sun is included within this group, as are many stars in the outer reaches of our galaxy. Population II has some heavy metals, but not as much as Population I, as they are older and did not benefit from as much metal dust as newer stars did. Stars in globular clusters and near the core of our galaxy belong to this population. Smaller galaxies also have more stars in this population. There is also a hypothetical Population III consisting of the very first stars with little to no metal content, as they did not exist near the beginning of the universe. They did not last very long, but helped the metals to form for the later populations.

Stellar Life Cycle
For information regarding stellar evolution, please see the Stellar Evolution main page.

The Competition
The competition usually consists of a test, which may be PowerPoint or station-based. Each team member may bring a laptop or a binder. It is advisable to bring as much information as you can, as a wide breadth of material may be covered. Organize your information so that it is easily referenced during the exam. Most Astronomy tests include mathematical computations, so it is important to have a calculator and a formula sheet ready.

Useful Resources

 * [[Media:Formula Sheet.pdf|Formula Sheet for Math Portion of Astronomy]] for the mathematical section
 * Good overall site for the basics of Astronomy
 * American Association of Variable Star Observers
 * Images from the Chandra X-Ray Observatory
 * NASA Astronomy Picture of the Day
 * Reach for the Stars for some sample pictures
 * Basic note sheet for the 2010-2011 DSOs
 * SIMBAD Astronomy Database for DSOs
 * NASA Space Math provides work sheets for a wide variety of Astronomy math problems