What is Astronomy? (xiv)

(BEING CONTINUED FROM  23/02/23)

PART I
The Signal Observed
The radiation from an astronomical source can be thought of as a signal that provides us
with information about it. In order to relate the signal received at the Earth to the
physical conditions within an astronomical source, however, we first need ways to
describe and measure light. This requires setting out the basic definitions for quantities
involving light and the relationships between them. The definitions range from those
associated with values measured at the Earth to those that are intrinsic to the source
itself. We do this without regard (yet) for the processes that actually generate the light,
an approach similar to what is often followed in Mechanics. For example, first one
studies Kinematics which relates distances, velocities, and accelerations and the
relations between them. Later, one considers Dynamics which deals with the forces
that produce these motions. Measuring light involves a deep understanding of how the
measurement process itself affects the signal and also how the Earth’s atmosphere
interferes. Our instrumentation imposes its own signature on an astronomical signal
and it is important to account for this imposition. These steps are fundamental and lay
the groundwork for turning the measurement of a weak glimmer of light into an
understanding of what drives the most powerful objects in the Universe.

1
Defining the Signal
… the distance of the invisible background [is] so immense that no ray from it has yet been able to
reach us at all.
–Edgar Allan Poe in Eureka, 1848
1.1 The power of light – luminosity and spectral power
The luminosity, L, of an object is the rate at which the object radiates away its energy
(cgs units of erg s1 or SI units of watts),
dE ¼ L dt ð1:1Þ
This quantity has the same units as power and is simply the radiative power output from
the object. It is an intrinsic quantity for a given object and does not depend on the
observer’s distance or viewing angle. If a star’s luminosity is L at its surface, then at a
distance r away, its luminosity is still L.
Any object that radiates, be it spherical or irregularly shaped, can be described by
its luminosity. The Sun, for example, has a luminosity of L ¼ 3:85 1033 erg s1
(Table G.3), most of which is lost to space and not intercepted by the Earth
(Example 1.1).
Example 1.1
Determine the fraction of the Sun’s luminosity that is intercepted by the Earth. What
luminosity does this correspond to?
At the distance of the Earth, the Sun’s luminosity, L, is passing through the imaginary
surface of a sphere of radius, r ¼ 1 AU. The Earth will be intercepting photons over only

the cross-sectional area that is facing the Sun. This is because the Sun is so far away that
incoming light rays are parallel. Thus, the fraction will be

When one refers to the luminosity of an object, it is the bolometric luminosity that is
understood, i.e. the luminosity over all wavebands. However, it is not possible to
determine this quantity easily since observations at different wavelengths require
different techniques, different kinds of telescopes and, in some wavebands, the

(TO BE CONTINUED)

Judith A. Irwin
Queen’s University, Kingston, Canada

NOTES

1.When ‘Galaxy’ is written with a capital G, it refers to our own Milky Way galaxy.

2.Speed and velocity are taken to be equivalent in this text unless otherwise indicated.

SOURCE  http://www.math.uct.ac.za/