The Brightness of The Brightness of StarsStars

The Simple Answer to: How The Simple Answer to: How Bright?Bright?

Quantifying the brightness of stars started Quantifying the brightness of stars started with Hipparchus (2with Hipparchus (2ndnd C. BC) and his C. BC) and his magnitude scalemagnitude scale

He designated the brightest star he could He designated the brightest star he could see as a “1” magnitude and the dimmest a see as a “1” magnitude and the dimmest a “6” magnitude“6” magnitude

Astronomers still labor under a more Astronomers still labor under a more quantified version of this systemquantified version of this system

One tragic consequence is that objects One tragic consequence is that objects brighter than the brightest star have brighter than the brightest star have negative magnitudes!negative magnitudes!

However…However…

We will have to account for:We will have to account for:– Filtering Filtering – DistanceDistance– ReddeningReddening– ExtinctionExtinction

But first things first…But first things first…

Apparent vs AbsoluteApparent vs Absolute

The The Apparent MagnitudeApparent Magnitude of a star is how of a star is how bright it appears to the naked eye, bright it appears to the naked eye, disregarding any interfering factorsdisregarding any interfering factors

On our Hipparchian scale, the Sun would On our Hipparchian scale, the Sun would have an have an apparentapparent magnitude of -26, the magnitude of -26, the Moon -11, and Venus -3Moon -11, and Venus -3

The The Absolute MagnitudeAbsolute Magnitude is how bright a is how bright a star (or other object) would appear at a star (or other object) would appear at a distance of 10 parsecs ~ 32.6LYdistance of 10 parsecs ~ 32.6LY

The Sun’s The Sun’s absoluteabsolute magnitude is 4.83 magnitude is 4.83

The DifferenceThe Difference

Consider a 100W light bulb; 100W is its Consider a 100W light bulb; 100W is its intrinsic brightnessintrinsic brightness– It emits 100W of light no matter how far away It emits 100W of light no matter how far away

it is; at the specified distance of 10 parsecs it it is; at the specified distance of 10 parsecs it would have some (would have some (very tinyvery tiny) absolute magnitude) absolute magnitude

However, since a 100W bulb in your face However, since a 100W bulb in your face seemsseems much brighter than a 100W bulb 10 much brighter than a 100W bulb 10 parsecs away, its apparent magnitude parsecs away, its apparent magnitude would depend on how close or far away it would depend on how close or far away it isis

Rule of ThumbRule of Thumb You can’t add magnitudes, absolute or You can’t add magnitudes, absolute or

apparent, directly because they are apparent, directly because they are calculated with base ten logarithmscalculated with base ten logarithms– A difference of 1 magnitude means a factor of A difference of 1 magnitude means a factor of

2.512 in brightness2.512 in brightness So, if you ask how bright two 3-magnitude So, if you ask how bright two 3-magnitude

stars are together, it’s not 6, it’s not 5.048, stars are together, it’s not 6, it’s not 5.048, it’s 2.25*it’s 2.25*– Don’t worry, you won’t have to calculate the Don’t worry, you won’t have to calculate the

summed brightness of multiple stars, but you do summed brightness of multiple stars, but you do have to know that you can’t just add magnitudeshave to know that you can’t just add magnitudes

– And you must realize that smaller numbers, And you must realize that smaller numbers, even negative numbers, mean brighter objectseven negative numbers, mean brighter objects

*2m = m-2.512log(2) = 2.247 ~ 2.25

Intrinsic Brightness: Blackbody Intrinsic Brightness: Blackbody RadiationRadiation

Stars emit light Stars emit light because they are because they are hot!hot!

Their color is Their color is determined by their determined by their temperaturetemperature

Consequently, their Consequently, their brightness is brightness is dependent on their dependent on their temperature temperature (among other (among other things)things)

Adjustable Wein Curves (if connected)Adjustable Wein Curves (if connected)

Stars that are cool, ~3500K, will be reddish; Stars that are cool, ~3500K, will be reddish; stars that are hot, ~10,000K, will be whitestars that are hot, ~10,000K, will be white

White light is a combination of all colors, so a White light is a combination of all colors, so a hot star will appear brighter than a red star, all hot star will appear brighter than a red star, all other things being equal, because not all light other things being equal, because not all light from a star is visible to the human eyefrom a star is visible to the human eye– This fact obscures a star’s intrinsic brightnessThis fact obscures a star’s intrinsic brightness

FiltersFilters Astronomers use Astronomers use

filters to see how filters to see how bright a star is in a bright a star is in a certain color rangecertain color range

The filters are simply The filters are simply colored glass that colored glass that goes over the mirror goes over the mirror or lens of a telescopeor lens of a telescope

Astronomers say Vega Astronomers say Vega has an Mhas an MVV of 0, which of 0, which means Vega has an means Vega has an absolute magnitude of absolute magnitude of 0 in the V (for visible--0 in the V (for visible--no filters) color bandno filters) color band

See how the red filter lets very littlegreen and practically no blue through?

Intrinsic Brightness: SizeIntrinsic Brightness: Size The surface area of a star is another factor in The surface area of a star is another factor in

the brightness of a starthe brightness of a star Two stars of the same temperature will have Two stars of the same temperature will have

different magnitudes, depending on their sizedifferent magnitudes, depending on their size A red supergiant can emit vastly more light A red supergiant can emit vastly more light

than a red dwarfthan a red dwarf

Apparent Brightness: Apparent Brightness: DistanceDistance

The light received The light received from a star is from a star is dependent on the dependent on the inverse square of its inverse square of its distance from us.distance from us.

Knowing this helps Knowing this helps astronomers find its astronomers find its distance using a distance using a method known as method known as standard candlesstandard candles

Standard candles works this way: say you Standard candles works this way: say you know the intrinsic brightness of a star and know the intrinsic brightness of a star and its magnitude;its magnitude;

If you see an identical star but with a If you see an identical star but with a different magnitude, you can use the different magnitude, you can use the inverse square law to find the distanceinverse square law to find the distance

ReddeningReddening One of several “seeing” problemsOne of several “seeing” problems The dust in the disk of the galaxy absorbs the The dust in the disk of the galaxy absorbs the

blue component of a stars light, making it seem blue component of a stars light, making it seem redder than it is.redder than it is.

ExtinctionExtinction

Another “seeing” problemAnother “seeing” problem Anything in the light path from a Anything in the light path from a

star, nebula, or galaxy absorbs or star, nebula, or galaxy absorbs or scatters lightscatters light

This attenuation is called This attenuation is called extinctionextinction

SummarySummary The brightness of a star or other celestial The brightness of a star or other celestial

object is quantified by its magnitudeobject is quantified by its magnitude Factors that determine the light output of Factors that determine the light output of

a star:a star:– Temperature Temperature color color– SizeSize

Factors that determine its perceived Factors that determine its perceived brightness:brightness:– ColorColor– DistanceDistance– ReddeningReddening– ExtinctionExtinction