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