Determining+Characteristics

Once an object’s redshift has been measured you can use it to determine an object’s velocity, distance and luminosity. If an object is relatively nearby, its velocity can be approximated by the equation: v = cz, where “c” is the speed of light (c 3.0 x 105 km s-1). But this equation fails for more distant objects. For example, if an object has a redshift greater than one, this equation incorrectly calculates that the object is moving faster than the speed of light! The correct equation for determining velocities is:

v = c((1 + z)^2 - 1/(1 + z)^2 +1)

Note that this equation is accurate for all objects, nearby and distant, and you should use this equation to determine the velocity of the objects you study in this project. As discussed earlier, Hubble’s Law can be used to determine distance for relatively nearby galaxies only. For the distant objects we are studying, the relationship between velocity and redshift is more complex. Which equation we use depends upon our assumptions about the nature of the Universe, which are not known for certain. However, in a simple model of the Universe (known as the “empty Universe” model), an object’s distance is related to its redshift by the equation:

d = (cz/Ho)(1 + 0.5z/1+ z)

As mentioned before the value of Hubble’s constant (H0) is known to be approximately 75 km s-1 Mpc-1. Since it takes light so long to travel to us from these objects we are in effect looking back in time. Because they are so luminous, AGN are some of the most distant objects in the Universe that we can study; and by observing them we are in effect investigating the Universe as it was long ago, when it was young and a very different place than it is now. When we observe an object with a telescope we measure its “flux,” which is the amount of energy per second that we see from the object. However, what we really want to know is an object’s “luminosity,” which is the total amount of light it emits per second. Astronomers are interested in determining an object’s luminosity because it tells us how much energy it is producing. This in turn is used to understand the true nature of the object. In the case of AGN, we know that they are extremely energetic because they are so luminous. This was one of the first clues that active galaxies must have another source of energy. Starsalone could not produce all the energy seen. According to the inverse-square law, flux and luminosity are related by the square of the distance to the object. For example, if two objects have the same luminosity but the first object is twice as far away as the second, the flux of the first object will be one-quarter that of the second. The relationship between flux and luminosity for very distant objects is given by:

L = 4π f d^2 (1+z)^2

In this equation “L” is the object’s luminosity, “f” is the measured flux and “d” is the distance to the object calculated above. Note that this equation is slightly different than the normal inverse-square law. There is an additional (1+z)^2 term which takes into account that the object is moving. Since it is moving away from us, the rate at which the photons (particles of light) arrive slows down, making it seem fainter. Further, when the photons do arrive they are redshifted, and so appear to have less energy. The additional (1+z)2 term corrects for these two effects. Before we can determine an object’s luminosity we must first determine its flux. This is a little complicated, so first let us discuss a few important concepts. Flux is measured in units of energy per unit of area per unit of time per unit of wavelength. Astronomers like to use units of erg cm-2 s-1Å-1(1 erg = 10-7 Joule). The luminosity is the total energy emitted from an object and is measured in units of erg s-1. In general this refers to the total amount of energy produced, called the “bolometric luminosity,” which includes the entire electromagnetic spectrum (radio waves through ga