Transcript To understand how to find the brightness of stars

Goal: To understand how to find
the brightness of stars and what
they mean.
Objectives:
1) To learn about Absolute brightness
2) To learn about the Magnitude system
3) To learn about Apparent brightness
4) To understand Apparent magnitude
5) To understand Absolute Magnitude
6) To explore what we can learn about stars
by comparing their Apparent and Absolute
brightnesses
Absolute brightness
• Absolute brightness is how bright an object
really is.
• Absolute brightness does not change with
distance as it is the amount of light the thing
actually radiates.
• The sun has an absolute brightness of 2 * 1033
erg/sec (which is enough to power the entire
USA for 3 million years!).
• The earth in the infrared has an absolute
brightness of about 1 * 1024 erg/sec (which is still
enough energy to power the USA for a day).
Luminosity
• A more common turn for an objects actual
brightness is Luminosity
• An object’s luminosity depends only on the
temperature and size of the object (as it
radiates like a blackbody).
• You don’t need to memorize or use this
equation, just understand how it works:
• L = 4πσ R2 T4 (σ is called the StefanBoltzmann constant)
Magnitude
• However, it is usually difficult to measure an
objects actual brightness.
• We have to know how far away it is as well as
how hot and how big it is.
• Also, as we have seen, brightness can greatly
differ from star to star (by factors of trillions).
• So, we need a convention to be able to scale
this down to something that we can fit on a
single scale.
• We do this by using magnitudes.
Ancient “magnitude” scale
• Ancient astronomers had no way to measure
directly how bright an object was.
• So, they devised a way to give comparative
estimates for how bright in the sky objects
looked.
• The brightest star in a constellation was defined
to be first magnitude.
• The next brightest was 2nd magnitude.
• And so on – and we can see down to about 6 or
7th magnitude in a “dark” sky with our naked eye.
Modern “magnitude” scale
• However we have long since calibrated the
scale to make it more exact.
• To do this we have defined the “apparent”
brightness of the star Vega to be magnitude 0 in
all colors and wavelengths (it should be noted
that some # of ergs per second will have a
different magnitude in different
colors/wavelengths).
• After that we use a logarithmic scale.
• Like in ancient times, we made smaller #s be
brighter objects.
logarithmic scale
• A logarithmic scale is a scale that instead of
going up by adding 1 we go up by multiplying a
factor.
• So, instead of 1,2,3, we go by X1, X2,X3.
• X can be anything.
• For stars, X is about 2.5.
• So, 5 orders of magnitude is a factor of 2.55
(which turns out to be about a factor of 100)
• Some scales also have logarithmic scales for
both axis. These are called log-log plots.
Apparent Brightness
• What do you think apparent brightness
means?
• A) The brightness of an object from a
distance of 10 parsecs
• B) How bright the object actually is
• C) How bright the object appears to be
from your perspective
• D) The time it takes light to get from the
object to us.
Apparent Brightness
• What do you think apparent brightness
means?
• C) How bright the object appears to be
from your perspective
• So, apparent brightness depends on how
bright the object actually is AND how far
away it is.
Further away
•
•
•
•
•
•
•
•
Imagine a campfire.
The campfire emits heat – which is just infrared light.
The fire emits this heat in all directions – in a sphere.
If you move twice as far away from the fire, by what
factor doe the amount of heat you get from the fire
decrease?
A) 4
B) 2
C) 1.4
D) you no longer get any heat
Further away
•
•
•
•
•
•
•
•
•
Imagine a campfire.
The campfire emits heat – which is just infrared light.
The fire emits this heat in all directions – in a sphere.
If you move twice as far away from the fire, by what
factor doe the amount of heat you get from the fire
decrease?
A) 4
Light emitted spreads out over an area, and the area of a
sphere depends on the radius squared.
So, the light drops as the radius squared.
So, you get 4 times less light.
If you went 3 times further away it would be a ninth, ect.
Apparent Magnitude
• So, the further away a star is, the dimmer it will
appear to be.
• Our sun is much closer to us than any other star,
so it appears to be very bright.
• If you scale the brightness logarithmically, then
how bright a star appears to be is its Apparent
Magnitude.
• But if a star gets 10 time further away, then it
would be 100X dimmer (or 5 magnitudes).
Some examples
• The sun from viewed from the earth has a apparent
magnitude of -26.
• The brightest star in the night time sky is Sirius at -1 (that
is a factor of 10 billion times dimmer than the sun).
• The Hubble Space Telescope can see to about
magnitude 30 (which is about a trillion times dimmer than
Sirius).
• So, larger #s are dimmer.
• Pluto is 14th magnitude.
• Alpha Centauri A/B (Rigel) are magnitudes 0/1.
• Alpha Centauri Proxima (the red dwarf) has a magnitude
of 10.7
Apparent vs Absolute
• Do apparent and/or absolute magnitudes
depend on how far the star is from us?
(answers are by apparent, absolute)
• A) yes, yes
• B) yes, no
• C) no, yes
• D) no, no
Apparent vs Absolute
• Do apparent and/or absolute magnitudes
depend on how far the star is from us? (answers
are by apparent, absolute)
• B) yes, no
• Apparent magnitudes depend on distance (if the
star is further away it appears dimmer).
• However absolute magnitudes do not depend on
distance.
• Absolute magnitude is how bright the star
actually is.
Absolute Magnitude
• The Absolute Magnitude of a star is how
bright the star would be if it was place at a
distance of 10 parsecs.
• This magnitude is independent of distance
from earth.
• Example, the absolute magnitude of our
sun is about +5.
Why is this all important?
• Well, if you know how bright a star is supposed
to be and how bright it appears to be you can tell
how far away it is.
• If you know how far away a star is, how bright it
appears to be, and what its temperature is, then
you can find what its actual brightness is, and
with it how big it is (in size, not mass).
• Also, as we will see later, from the size and
distance you can get other values such as a
possible age and what type of star it is.
On the horizon
• As we will see in the coming weeks, the
changes in brightness of an object can tell
us a great deal about it also.
Conclusion
• The brightness of a star depend on its
temperature and radius.
• The apparent brightness of a star depends
on its absolute brightness and its distance
from us.
• The absolute brightness is independent of
distance.
• From all this we can find distances and
sizes of stars.