Name: ________________________ Period: ____ Date: ____________

Activity 3: Student Worksheet

A. Finding the Size of an Active Galaxy Flare Region

1) Use the equation: diameter = cDt = (3 x 108 m/s) x Dt to determine the diameter of the active regions of AGs in meters and in units of the solar system diameter (use 1013 meters for the solar system diameter), for flares of duration Dt = 1 hour, 1 day, 1 week and 1 year.

2) Given the diameter of the sun (1.4 x 109 meters), what is the fastest the entire sun can vary in brightness, as measured in seconds?

B. Measuring the Size of an Active Galaxy Flare Region
The plot to the right is real astronomical data taken by the EGRET gamma-ray instrument that was onboard NASA’s Compton Gamma Ray Observatory. It observed the active galaxy 3C279 for several years, and found many flares and other variations in the AG’s light.

There are two characteristic timescales for the variation shown. One is the “rise time,” or time it takes the brightness to reach its peak. The other is the “decay time,” or the time it takes for the brightness to drop back down to the normal level.

For the following exercise, assume the normal level of brightness for 3C279 is about 1x10^-2 photons/m^-2s^-1 (that is, the “1” on the graph’s y-axis).

Using only the data points where the flare is brightening, draw a “best-fit” line through the points. Do the same for the points where the flare is fading.

Use your hand-drawn line to determine the time duration (?t) for the rise time of the flare. From that, calculate the size of the emitting region using size = c?t in both meters and in solar systems.

Use your hand-drawn line to determine ? t for the decay time duration of the flare. From that, calculate the size of the emitting region using size = c?t in both meters and in solar systems.

Using your hand-drawn line to the rising portion of the flare, determine the slope and intercept of the line (y = mx + b).

Do it again, but for the decaying portion of the flare.

If the flare had continued to rise for two more weeks, how bright would it have been?

C: Measuring the Energy Emitted by an Active Galaxy Flare

From the graph, it’s possible to determine the total energy emitted during the maximum
of the flare and compare it to the energy emitted by the Sun. First, convert the units of the graph from photon flux to energy flux. Assume that each gamma ray hitting the detector has an energy of 100 MeV. Calculate the maximum flux in MeV m^-2 s^-1.

A more standard unit of energy is the Joule, which is equal to 6.3 x 10^18 eV. Remembering that 1 Mev is 10^6 eV, what is the flare flux in Joule m^-2 second^-1?

The flux is the amount of energy hitting a square meter here on Earth. The total energy emitted by the flare every second is spread out over a sphere centered on the flare, with a radius equal to the distance from the Earth to the flare. The distance to 3C279 is about 4 x 10^9 light years, and there are 9.5 x 10^15 m in a light year. The surface area of a sphere is A= 4pr^2 where “r” is the radius of the sphere. What is the total surface area of the sphere?

The total luminosity emitted in the flare each second, is given by E = (Area) x (Flux).
Calculate the energy in Joules/sec.

The Sun’s luminosity is about 4 x 10^26 Joules/second. What is the ratio of the luminosity at the flare maximum to the solar lunimosity?

There are about 3 x 10^7 seconds in a year. How many years would it take for the Sun to emit as much energy as the flare did in a single second?