Module 22: Stellar Magnitudes and Distance
If a star is at a distance of 100 parsecs from us, compare by
apparent brightness at 100pc = absolute brightness (at 10pc)/ 100
Absolute brightness
apparent brightness seen at standard distance of 10 parsecs from the star ∴ only use inverse, no formula
The apparent brightness of our sun is ~1000 watts per square meter. At a distance of 30x the earh-sun distance, the apparent brightness of our sun is
apparent brightness/ distance^2 = 1000/ 30 x 30 = 1.1 watts per square meter
Standard Candle
apparent light source which we know the absolute magnitude ∴ can measure apparent magnitude and calculate distance about 90% of all stars
At a distance r from star
area of the sphere is 4πr^2
Low Magnitude
bright star, can be negative
High Magnitude
dim star
Spectral type
the sort of light a star produces can be recognized from 10 million parsecs out
Luminosity
total light output of a star energy emitted/time
A star is observed to have an apparent brightness which is 10^-6 times its absolute brightness, how far away is it?
10,000 parsecs
Cruising far from the Sun, we notice that the Sun's apparent brightness has dimmed to 0.1 watts per square meter. We know that the apparent brightness at a distance of 1au is 1000 watts per square meter. How far from the Sun are we?
1000 watts x .1 apparent brightness = 100 au
A star at a distance of 1000pc should have an apparent brightness equal to its absolute brightness multiplied by
10^-4 standard distance 10pc is multiplied by 100, so brightness is divided by 100^2 or multiplied by 1/10,000
Distance Formula
DM = 10^(DM/5) x 10 parsecs
Adding 5 to magnitude
divide brightness by 100
Apparent brightness
energy/time that enters our telescope = luminosity / 4πr^2
Evolutionary Correction
errors from when measuring very very distant stars whose light was emitted billions of years ago to detect errors, use multiple standard candle objects
Spectroscopic Parallax
finding distances by using stars of known spectral type able to find distances farther away than heliocentric parallax method we must assume stars with same spectral type as our sun is exactly like it
Apparent magnitude
how bright a star looks to us (describing apparent brightness)
Absolute magnitude
how bright the star really is (describing absolute brightness at 10 parsecs)
Naked eye limits
ideal, up to magnitude 6 city, up to 4 stars on horizon more difficult
If one star is 10 times as far away as the other
it will have only 1/100 the apparent brightness as closer star
Subtract 5 from magnitude
multiply brightness by 100
Distance Modulus
the difference between apparent magnitude - absolute magnitude