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:

Expressed mathematically:

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:

• How bright it is physically (Luminosity)
• How far away it is (Distance).
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:
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

• it is intrinsically very luminous?
• it is intrinsically faint but located nearby?
To know for sure, you must know either
• 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 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:

• 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.
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:
• 5 steps of magnitude = factor of 100 in brightness
• Bigger magnitude = fainter star.
• The standard of brightness is the star Vega (0th magnitude)

Examples:

• 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 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:
• Photographic Plates (old-school: 1880s to 1960s)
• Photoelectric Photometer (photomultiplier tube: 1930s to 1990s)
• Solid State Detector (e.g., photodiodes or CCDs)
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:
• the Apparent Brightness (flux) measured via photometry, and
• the Distance to the star measured in some way
Together with the inverse square law of brightness, you can compute the Luminosity as

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.

• 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% luminosity).
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.
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Updated: 2006 January 7