Transcript Luminosity and magnitude

When you wish upon a star...
shows what a dweeb you really are ..!
Luminosity and all that
•Luminosity
•Inverse square law
•Magnitudes
•Distance, temperature, composition ..
•H-R diagram
Getting our bearings
Luminosity
• Observing apparent
brightness.
• Brightness is the amount of
energy striking per unit area
of the human eye or a
detector.
• The amount we receive is
affected by distance
according to the inverse
square law.
Apparent brightness (energy flux)  Luminosity/distance2
Luminosity and magnitudes
• Apparent brightness.
• Absolute brightness.
• Apparent magnitude
• Absolute magnitude
To compare
intrinsic or
absolute properties
of stars, use a
standard distance
of 10 pc.
Lets make this difficult (actually the ancient
Greeks are to blame)
• Around second century B.C.E., Hipparchus scaled naked eye stars into
a ranking of 1 to 6 ( brightest to least bright).
• 1 – 6 range spans a factor of 100 in apparent brightness. ( a 1st
magnitude star is 100 X brighter than a 6th magnitude star).
• The physiology of the human eye dictates that each magnitude change
of 1 corresponds to a change of 2.5 in apparent brightness.
• Combining both concepts: 2.55  100
A 1 st magnitude star is approximately 100 X brighter than a 6 th
magnitude star
But what does it mean?
• Well, lets look at the
10 pc thing:
10 pc
Apparent Mag. > Absolute
Mag.
Earth
Apparent Mag. < Absolute
Mag.
Apparent brightness vs. absolute brightness?
Oh !
Brightness decreases this way !
Graph of apparent
magnitudes of some
common things in the
sky .
Brightness increases this way !
Luminosity and magnitude
• We know from
Apparent brightness  luminosity/distance2
And 2.55  100 -> 1001/5  2.5.
So for every magnitude change we see with our eyes
the brightness changes 10X.
IDEA! We can build a chart to relate luminosity to
magnitudes:
luminosity
magnitude
Recipe: brightness to luminosity
• To determine a star’s luminosity:
• 1. Determine apparent brightness (use
a chart or for a new star, measure amount
of energy detected per unit time).
• 2. Measure the star’s distance (parallax
method for nearby stars).
• 3. Use: apparent brightness ~ luminosity/ d2
Using our recipe for more stuff
• Let m = apparent brightness
• Use our recipe: luminosity = d2 m.
• Star A: {d = 0.707 pc, m = 1}, Star B:{ d = 2.12 pc, m =
1}.
• Find luminositys for Star A and Star B
More luminosity & magnitude stuff
Making things simpler
• Scale luminosities to
solar luminosity –
this way we won’t
have to deal with
units
• Let m – apparent
magnitude, M –
absolute magnitude.
• Throw in the inverse
square relationship
and some math and….
Tah Dah!!!
D = 10 pc x 10(m –M)/5
We have another formula for distance, D!
Do we believe it! Lets look at an example.
(alot like More Precisely ex., page 447)
Luminosity, temperature, size ….
• We know relationship between luminosity and magnitude
(Table previous slide).
• Using Wien’s Law: (peak emission)  1/temperature
• And Stefan’s law: total energy emitted  temperture4
Wien’s law: the hotter the object the bluer is its emission.
Stefan’s law: energy emitted per unit area increases as the 4th
power of the temperature…..
Luminosity  radius2 * temperture4
Stellar size!
More tools from what we know
• Knowledge of
color/temperature
relationship and now,
luminosity/radius/tem
-perature relationship
combined with
emission/absorption
spectrum we get from
certain stars, lets us
classify our spectra
(OBAFGKM) according
to temperature.
H-R Diagram
Sizes,
Temperature,
Luminosities
And: Stellar
Lifetime:
Star life time ~
1/(star mass)3
Features:
1.
2.
3.
4.
H-R Diagram
http://instruct1.cit.cornell.edu/courses/astro101/java/evolve/evolve.htm
• stellar mass determines lifetime behavior of star
With regards to mass, you may want to note
size/masses of stars that spend:
• all their lives on the main sequence
• some of their lives on the main sequence
• leave main sequence early