Compact Energy Sources
Quasars are extremely luminous at all wavelengths. They also
exhibit variability in this luminosity
on timescales as little as months, weeks, or even
hours. As we now discuss, this variability implies
that their enormous energy output
originates in a very compact source.
Light Speed and Source Size
By physical arguments, if an energy source of a certain size
is to exhibit a well-defined period in its luminosity, some signal must travel through the object to "tell" it to
vary. Since such a signal can travel no faster than light velocity, the maximum size
of an object varying with
some characteristic time is the distance that light could have traveled during that time. If
the period for variation is P and the speed of light is
c, the maximum size of the source exhibiting the
variation is D ~ cP, as illustrated in the top right figure.
For example, if a source is observed to vary its light output substantially over a period of a week,
the spatial extent of the energy-producing region can be no larger than the distance light can travel in a
week (a "light week").
The following table gives the distances traveled by light in some fixed periods of time.
|
Distances Covered by Light in a Fixed Time
|
| Time |
Kilometers |
Astronomical
Units |
Parsecs
|
| Year |
9.46 x 1012 |
63,240 |
3.07 x 10-1
|
| Month |
7.88 x 1011 |
5270 |
2.58 x 10-2
|
| Week |
1.82 x 1011 |
1216 |
5.90 x 10-3
|
| Day |
2.59 x 1010 |
173 |
8.41 x 10-4
|
| Hour |
1.08 x 109 |
7.21 |
3.50 x 10-5
|
| Minute |
1.80 x 107 |
0.120 |
5.84 x 10-7
|
| Second |
3.00 x 105 |
0.002 |
9.73 x 10-9
|
|
|
|
|
|
From this
table we see, for example,
that a light week corresponds to a distance of 1216 AU and a
light month to 5270 AU.
Light Hours Implies Solar System Size
By the preceding arguments, if a source varies its intensity on a scale of a day or less, the size
of the energy source must be less than the distance light can travel in a few hours. From the
preceding table, this is comparable to the
size of the Solar System. For example, the table indicates that light travels 7.2 AU in an
hour, so in 10 hours it
covers about 72 AU. This is almost the diameter of Pluto's orbit.
Thus, the observation that some quasars vary their light output substantially on a timescale of a day or less
implies that
their prodigious energy source is contained within a volume the size of the Solar System or smaller.
This is incredibly small for an object outputting energies far
greater than that of large galaxies.
To set this in perspective, we have concluded that a quasar outputs thousands of times
more energy than a galaxy like the Milky Way from
a volume smaller than the Solar System.
But the volume of the Milky Way is about 1023
times the volume
of the Solar System, if we consider both to be spherical and include only the visible part of each.
This implies immediately that we are dealing with a very unusual energy source for quasars.
It must at the same time be remarkably powerful yet remarkably compact.