The Brightness of Stars

The Simple Answer to: How Bright? Quantifying the brightness of stars started with Hipparchus (2 nd C. BC) and his magnitude scale Quantifying the brightness of stars started with Hipparchus (2 nd C. BC) and his magnitude scale He designated the brightest star he could see as a “1” magnitude and the dimmest a “6” magnitude He designated the brightest star he could see as a “1” magnitude and the dimmest a “6” magnitude Astronomers still labor under a more quantified version of this system Astronomers still labor under a more quantified version of this system One tragic consequence is that objects brighter than the brightest star have negative magnitudes! One tragic consequence is that objects brighter than the brightest star have negative magnitudes!

However… We will have to account for: We will have to account for: –Filtering –Distance –Reddening –Extinction But first things first… But first things first…

Apparent vs Absolute The Apparent Magnitude of a star is how bright it appears to the naked eye, disregarding any interfering factors The Apparent Magnitude of a star is how bright it appears to the naked eye, disregarding any interfering factors On our Hipparchian scale, the Sun would have an apparent magnitude of -26, the Moon -11, and Venus -3 On our Hipparchian scale, the Sun would have an apparent magnitude of -26, the Moon -11, and Venus -3 The Absolute Magnitude is how bright a star (or other object) would appear at a distance of 10 parsecs ~ 32.6LY The Absolute Magnitude is how bright a star (or other object) would appear at a distance of 10 parsecs ~ 32.6LY The Sun’s absolute magnitude is 4.83 The Sun’s absolute magnitude is 4.83

The Difference Consider a 100W light bulb; 100W is its intrinsic brightness Consider a 100W light bulb; 100W is its intrinsic brightness –It emits 100W of light no matter how far away it is; at the specified distance of 10 parsecs it would have some ( very tiny ) absolute magnitude However, since a 100W bulb in your face seems much brighter than a 100W bulb 10 parsecs away, its apparent magnitude would depend on how close or far away it is However, since a 100W bulb in your face seems much brighter than a 100W bulb 10 parsecs away, its apparent magnitude would depend on how close or far away it is

Rule of Thumb You can’t add magnitudes, absolute or apparent, directly because they are calculated with base ten logarithms You can’t add magnitudes, absolute or apparent, directly because they are calculated with base ten logarithms –A difference of 1 magnitude means a factor of in brightness So, if you ask how bright two 3-magnitude stars are together, it’s not 6, it’s not 5.048, it’s 2.25* So, if you ask how bright two 3-magnitude stars are together, it’s not 6, it’s not 5.048, it’s 2.25* –Don’t worry, you won’t have to calculate the summed brightness of multiple stars, but you do have to know that you can’t just add magnitudes –And you must realize that smaller numbers, even negative numbers, mean brighter objects *2m = m-2.512log(2) = ~ 2.25

Intrinsic Brightness: Blackbody Radiation Stars emit light because they are hot! Stars emit light because they are hot! Their color is determined by their temperature Their color is determined by their temperature Consequently, their brightness is dependent on their temperature (among other things) Consequently, their brightness is dependent on their temperature (among other things)

Adjustable Wein Curves (if connected)

Stars that are cool, ~3500K, will be reddish; stars that are hot, ~10,000K, will be white Stars that are cool, ~3500K, will be reddish; stars that are hot, ~10,000K, will be white White light is a combination of all colors, so a hot star will appear brighter than a red star, all other things being equal, because not all light from a star is visible to the human eye White light is a combination of all colors, so a hot star will appear brighter than a red star, all other things being equal, because not all light from a star is visible to the human eye –This fact obscures a star’s intrinsic brightness

Filters Astronomers use filters to see how bright a star is in a certain color range Astronomers use filters to see how bright a star is in a certain color range The filters are simply colored glass that goes over the mirror or lens of a telescope The filters are simply colored glass that goes over the mirror or lens of a telescope Astronomers say Vega has an M V of 0, which means Vega has an absolute magnitude of 0 in the V (for visible--no filters) color band Astronomers say Vega has an M V of 0, which means Vega has an absolute magnitude of 0 in the V (for visible--no filters) color band See how the red filter lets very little green and practically no blue through?

Intrinsic Brightness: Size The surface area of a star is another factor in the brightness of a star The surface area of a star is another factor in the brightness of a star Two stars of the same temperature will have different magnitudes, depending on their size Two stars of the same temperature will have different magnitudes, depending on their size A red supergiant can emit vastly more light than a red dwarf A red supergiant can emit vastly more light than a red dwarf

Apparent Brightness: Distance The light received from a star is dependent on the inverse square of its distance from us. The light received from a star is dependent on the inverse square of its distance from us. Knowing this helps astronomers find its distance using a method known as standard candles Knowing this helps astronomers find its distance using a method known as standard candles

Standard candles works this way: say you know the intrinsic brightness of a star and its magnitude; Standard candles works this way: say you know the intrinsic brightness of a star and its magnitude; If you see an identical star but with a different magnitude, you can use the inverse square law to find the distance If you see an identical star but with a different magnitude, you can use the inverse square law to find the distance

Reddening One of several “seeing” problems One of several “seeing” problems The dust in the disk of the galaxy absorbs the blue component of a stars light, making it seem redder than it is. The dust in the disk of the galaxy absorbs the blue component of a stars light, making it seem redder than it is.

Extinction Another “seeing” problem Another “seeing” problem Anything in the light path from a star, nebula, or galaxy absorbs or scatters light Anything in the light path from a star, nebula, or galaxy absorbs or scatters light This attenuation is called extinction This attenuation is called extinction

Summary The brightness of a star or other celestial object is quantified by its magnitude The brightness of a star or other celestial object is quantified by its magnitude Factors that determine the light output of a star: Factors that determine the light output of a star: –Temperature  color –Size Factors that determine its perceived brightness: Factors that determine its perceived brightness: –Color –Distance –Reddening –Extinction