Introduction to Stars, Galaxies, & the Universe
Prof. Richard Pogge, MTWThF 9:30
Lecture 7: "Starlight, Starbright"
Readings: Chapter 9, Section 19-2 & 19-3
- Luminosity of a star:
- total energy output
- independent of distance
- Apparent Brightness of a star depends upon
- Photometry & Stellar Magnitudes
How "Bright" is a Star?
There are two ways to answer the question of how bright a star
- Intrinsic Luminosity:
- Measures the Total Energy Output by the star in Watts
- Distance Independent (it is a physical property of the star itself)
- 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:
- Expressed mathematically:
- In words:
- The Apparent Brightness (B) of a source is inversely proportional to the
square of its distance (d):
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
- How bright it is physically (Luminosity)
- How far away it is (Distance).
This relates the Apparent Brightness of a star (or other light source)
to its Luminosity (Intrinsic Brightness) through the
Inverse Square Law of
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
- it is intrinsically very luminous?
- it is intrinsically faint but located nearby?
- the distance to the star, or
- some other, distance-independent property of the star
that clues you in.
Measuring Apparent Brightness
The process of measuring the apparent brightnesses of objects is called
Two ways to express apparent brightness:
Both are used interchangeably by astronomers.
- Stellar Magnitudes
- Absolute Fluxes (energy per second per area)
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.
- 1st magnitude stars are brightest stars,
- 2nd magnitude stars are the second brightest,
- and so forth...
- The faintest stars visible to the naked eye are 6th magnitude.
Magnitudes defined this way are measures of the relative brightnesses
Modern Magnitude System
The modern system of magnitudes defines them as follows:
- 5 steps of magnitude = factor of 100 in brightness
- Bigger magnitude = fainter star.
- The standard of brightness is the star Vega (0th magnitude)
- 10th mag star is 100x fainter than a 5th mag star.
- 20th mag star is 10,000x fainter than a 10th mag star.
- Faintest stars measured this far are ~30th magnitude.
Magnitudes are computationally very convenient to use, but the are
somewhat obtusely defined (it is backwards: larger magnitudes = fainter
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.
Count the photons received from a star using a light-sensitive
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.
- Photographic Plates (old-school: 1880s to 1960s)
- Photoelectric Photometer (photomultiplier tube: 1930s to 1990s)
- Solid State Detector (e.g., photodiodes or CCDs)
Calibrate the detector by observing a set of "Standard
Stars" of known brightness.
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
- the Apparent Brightness (flux) measured via photometry, and
- the Distance to the star measured in some way
The biggest source of difficulty, as usual in Astronomy, is measuring
the distance accurately...
In practice, we can use sensitive electronic instruments and photometry
to measure the apparent brightnesses of many hundreds of millions of
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
- Only that number of stars have direct estimates of their Luminosities.
- Since Luminosity depends on distance squared, small errors in
distance are effectively doubled (a 10% distance gives a 20%
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Updated: 2006 January 7
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