Calculating+Velocity+Distance+and+Luminosity

How Do I apply the tools to AGN?


 * Velocity, Distance and Luminosity**

After you have found out what the redshift, z, is then you can find out what the velocity, distance and the luminosity of the galaxy that you are looking at.


 * To get Velocity:**

If an object is pretty close (close enough that the redshift is less than or equal to one) then you can use the equation: v=cz where v is the velocity, c is the speed of light, and z is the redshift.

If the redshift is greater than one then use this equation: For near galaxies use Hubble’s Law: For farther galaxies we have to define a model of the universe first. One of the simplest models of the universe we have is the "empty Universe" model and from that we can use: to find the distance of the galaxy we are looking at.
 * To get distance:**

AGN is one of the farthest and brightest objects in the universe because we can observe the light from its luminosity (explained below) and the time it takes for the light to reach us is so long (because it's so far away) that it is as if we are looking back in time to the origins of the universe.

What we see through the telescope is the flux of the galaxy, the energy per second of the light we see. But, what we want is the luminosity or the total amount of light it emits per second. Luminosity is essential because it tells us the amount of energy the galaxy is producing.
 * To get luminosity:**

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: This equation relates luminosity, L, flux, f, distance, d, and the shift, z.

We have to use the flux over the whole wavelength so we have to integrate or find the total flux over the wavelengths (the area under the "curve". We can see a demonstration in the picture below over a part of the wavelength.

Source: https://sjhsrc.wikispaces.com/distance+of+galaxy [|AGN_Spectroscopy.pdf]