skip navigation
Galaxy NGC4414 from HST Astronomy 162:
Introduction to Stars, Galaxies, & the Universe
Prof. Richard Pogge, MTWThF 9:30

Lecture 7: "Starlight, Starbright"
Stellar Brightness

Readings: Chapter 9, Section 19-2 & 19-3

Key Ideas

Luminosity of a star:
total energy output
independent of distance

Apparent Brightness of a star depends upon
distance
luminosity

Photometry & Stellar Magnitudes

How "Bright" is a Star?

There are two ways to answer the question of how bright a star is quantitatively:
Intrinsic Luminosity:
Measures the Total Energy Output by the star in Watts
Distance Independent (it is a physical property of the star itself)

Apparent Brightness:

Measures how bright the star appears to be as seen from a distance.
Depends on the distance to the star

Inverse Square Law of Brightness

The Apparent Brightness of a source is a consequence of geometry. As light rays emerge from a source, they spread out in area:

inverse square-law

Expressed mathematically:
Inverse-Square-Law of Brightness

In words:
The Apparent Brightness (B) of a source is inversely proportional to the square of its distance (d):

Implications:

For a light source of a given Luminosity...

Closer = Brighter
Move 2x closer to a light source
It will appear 22=4 times brighter.

Farther = Fainter
Move 2x further away from a light source
It will appear 22=4 times fainter

Apparent Brightness of Stars

How bright a star appears to be will depend upon:

These are related through the inverse square law of brightness described above.

Brightness-Luminosity Relationship:

This relates the Apparent Brightness of a star (or other light source) to its Luminosity (Intrinsic Brightness) through the Inverse Square Law of Brightness:
Brightness-Luminosity-Distance relationship
At a particular Luminosity, the more distant an object is, the fainter its apparent brightness becomes as the square of the distance.

Appearances can be deceiving...

Does a star look "bright" because

To know for sure, you must know either

Measuring Apparent Brightness

The process of measuring the apparent brightnesses of objects is called Photometry.

Two ways to express apparent brightness:

  1. Stellar Magnitudes
  2. Absolute Fluxes (energy per second per area)
Both are used interchangeably by astronomers.

Magnitude System

Traditional system dating from classical times, invented by Hipparchus of Nicaea, c. 300BC.

Rank stars into "magitudes": 1st, 2nd, 3rd, etc., as follows:

As originally applied by Hipparcus and others, this was a qualitative ranking, as they had no reasonable means of independently measuring brightnesses other than comparing them by-eye to other stars in the sky.

Magnitudes defined this way are measures of the relative brightnesses of stars.


Modern Magnitude System

The modern system of magnitudes defines them as follows:

Examples:

Magnitudes are computationally very convenient to use, but the are somewhat obtusely defined (it is backwards: larger magnitudes = fainter stars).

Unlike the qualitative system of Hipparchus, the modern magnitude system defines the standard of brightness as the bright star Vega (brightest star in the summer constellation of Lyra), and precisely defines the interval of magnitude. This quantification was done in the 19th century and refined throughout the 20th century.


Flux Photometry

Count the photons received from a star using a light-sensitive detector: We now use solid-state detectors like CCDs and similar technologies (with very rare exceptions), as these detectors are far more sensitive and stable than any previous technology.

Calibrate the detector by observing a set of "Standard Stars" of known brightness.


Measuring Luminosity

To measure the Luminosity of a star you need 2 measurements: Together with the inverse square law of brightness, you can compute the Luminosity as
L=4pid^2*B

The biggest source of difficulty, as usual in Astronomy, is measuring the distance accurately...


Practical Issues

In practice, we can use sensitive electronic instruments and photometry to measure the apparent brightnesses of many hundreds of millions of stars.

But, we have good distances (parallaxes) for only about 100,000 stars.

Luminosity is an important quantity for understanding how stars work, and measuring it with accuracy is still a practical issue even in 21st-century astronomy.
Return to [ Unit 1 Index | Astronomy 162 Main Page ]
Updated: 2006 January 7
Copyright Richard W. Pogge, All Rights Reserved.