Lecture 4

HOW BRIGHT IS A STAR?

Key Concepts

• Apparent Brightness (alias INTENSITY) = how much light reaches Earth
• Intrinsic Brightness (alias LUMINOSITY) = total amount of light a star emits
• Apparent Brightness depends upon Intrinsic Brightness & Distance

(1) The apparent brightness of a star (its intensity) is a measure of how much light from the star reaches Earth.

Apparent brightness of a star is given by its INTENSITY (also known as its FLUX).

Intensity = Energy / time / area

To find intensity of a star:

• Measure energy of photons reaching your telescope
• Divide by area of telescope mirror
• Divide by time spent looking at star

Intensity is an ``observable quantity'' (something we can measure).

In metric system, intensity has units of

Joules / second / square meter = watts / square meter

Examples:

• The Sun : I = 1360 watts / square meter
• Sirius : I = 1/10,000,000 watts / square meter

Sirius has an apparent brightness very much smaller than the Sun's (no surprise there).

Another way of describing apparent brightness: Apparent Magnitude

Relic of ancient Greek astronomy:

• brightest stars seen by naked eye: apparent magnitude = m = 0
• faintest stars seen by naked eye: m = 6

Now extended to stars with smaller or larger intensity. For instance:

• Sun: m = -26.5
• Sirius: m = -1.4
• Proxima Centauri: m = 11.0

A difference of 5 magnitudes = a factor of 100 in intensity.

(2) The intrinsic brightness of a star (its luminosity) is a measure of the total amount of light a star emits.

Intrinsic brightness of a star is given by its LUMINOSITY.

Luminosity = L = Energy / time

In metric system, luminosity has units of

Joules / second = watts

Luminosity is not a directly observable quantity (though it is something we would dearly like to know).

(3) The apparent brightness of a star depends both on its intrinsic brightness (or luminosity) and its distance from the Earth.

Measure the intensity; measure the distance; THEN you can compute the luminosity.

Important Equation: Relation Between Apparent Brightness (Intensity) and Intrinsic Brightness (Luminosity)

I = L / ( 4 pi d² )

• I = intensity of the star
• L = luminosity of the star
• d = distance to the star
• pi = 3.14159265 (but you knew that already)

Examples:

Sun: I = 1360 watts / square meter

d = 1 AU = 1.5 x 10¹¹ meters (150 billion meters)

L = 4 pi d² I = 3.8 x 10²⁶ watts (380 trillion trillion watts)

Sirius has a luminosity equal to 24 times that of the Sun.

Proxima Centauri has a luminosity equal to 0.00006 times that of the Sun.

Another way of describing absolute brightness: Absolute magnitude

Absolute magnitude = M = apparent magnitude a star would have IF it were at a distance of 10 parsecs (32.6 light years).

For instance:

• Sun: M = 4.8
• Sirius: M = 1.4
• Proxima Centauri: M = 15.5

Most stars in our neighborhood are less luminous than the Sun.

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