Download Monday, April 15

Homework: Parallax
• Given p in arcseconds (”), use
d=1/p to calculate the distance
which will be in units “parsecs”
• By definition, d=1pc if p=1”, so
convert d to A.U. by using
trigonometry
• To calculate p for star with d given
in lightyears, use d=1/p but
convert ly to pc.
• Remember: 1 degree = 3600”
• Note: p is half the angle the star
moves in half a year
Our Stellar Neighborhood
Scale Model
• If the Sun = a golf ball, then
–
–
–
–
–
Earth = a grain of sand
The Earth orbits the Sun at a distance of one meter
Proxima Centauri lies 270 kilometers (170 miles) away
Barnard’s Star lies 370 kilometers (230 miles) away
Less than 100 stars lie within 1000 kilometers (600 miles)
• The Universe is almost empty!
• Hipparcos satellite measured distances to nearly 1
million stars in the range of 330 ly
• almost all of the stars in our Galaxy are more distant
Reminder: Three Things Light Tells Us
• Temperature
– from black body spectrum
• Chemical composition
– from spectral lines
• Radial velocity
– from Doppler shift
Luminosity and Brightness
• Luminosity L is the total power
(energy per unit time) radiated
by the star, actual brightness of
star, cf. 100 W lightbulb
• Apparent brightness B is how
bright it appears from Earth
– Determined by the amount of
light per unit area reaching Earth
– B  L / d2
• Just by looking, we cannot tell
if a star is close and dim or far
away and bright
Brightness: simplified
• 100 W light bulb will look
9 times dimmer from 3m
away than from 1m away.
• A 25W light bulb will look
four times dimmer than a
100W light bulb if at the
same distance!
• If they appear equally
bright, we can conclude that
the 100W lightbulb is twice
as far away!
Same with stars…
• Sirius (white) will look 9
times dimmer from 3
lightyears away than from 1
lightyear away.
• Vega (also white) is as
bright as Sirius, but appears
to be 9 times dimmer.
• Vega must be three times
farther away
• (Sirius 9 ly, Vega 27 ly)
Distance Determination Method
• Understand how bright an object is
(L)
• Observe how bright an object appears (B)
• Calculate how far the object is away:
B  L / d2
So
L/B  d2 or
d  √L/B
Homework: Luminosity and Distance
• Distance and brightness can be used to find
the luminosity:
L  d2 B
• So luminosity and brightness can be used to
find Distance of two stars 1 and 2:
d21 / d22 = L1 / L2 (since B1 = B2 )
i.e. d1 = (L1 / L2)1/2 d2
The Magnitude Scale
• A measure of the apparent
brightness
• Logarithmic scale
• Notation: 1m.4 (smaller brighter)
• Originally six groupings
– 1st magnitude the brightest
– 6th magnitude is 100x dimmer
• So a difference of 5mag is a
difference of brightness of 100
• Factor 2.512=1001/5 for each mag.
Absolute Magnitude
• The absolute magnitude is the apparent magnitude
a star would have at a distance of 10 pc.
• Notation example: 2M.8
• It is a measure of a star’s actual or intrinsic
brightness called luminosity
• Example: Sirius: 1M.4, Sun 4M.8
– Sirius is intrinsically brighter than the Sun
Finding the absolute Magnitude
• To figure out absolute magnitude, we need to
know the distance to the star
• Then do the following Gedankenexperiment:
– In your mind, put the star from its actual position to a
position 10 pc away
– If a star is actually closer than 10pc, its absolute
magnitude will be a bigger number, i.e. it is
intrinsically dimmer than it appears
– If a star is farther than 10pc, its absolute magnitude
will be a smaller number, i.e. it is intrinsically brighter
than it appears
Measuring the Sizes of Stars
• Direct measurement is possible for a few
dozen relatively close, large stars
– Angular size of the disk and known distance
can be used to deduce diameter
Indirect Measurement of Sizes
• Distance and brightness can be used to find
the luminosity:
L  d2 B
(1)
• The laws of black body radiation also tell us
that amount of energy given off depends on
star size and temperature:
L  R2  T4 (2)
• We can compare two values of absolute
luminosity L to get the size
Sizes of Stars
• Dwarfs
– Comparable in
size, or smaller
than, the Sun
• Giants
– Up to 100 times
the size of the Sun
• Supergiants
– Up to 1000 times
the size of the Sun
• Note: Temperature
changes!
Classification of the Stars:
Temperature
Class
O
B
A
F
G
K
M
Temperature
30,000 K
20,000 K
10,000 K
8,000 K
6,000 K
4,000 K
3,000 K
Color
blue
bluish
white
white
yellow
orange
red
Examples
Rigel
Vega, Sirius
Canopus
Sun,  Centauri
Arcturus
Betelgeuse
Mnemotechnique: Oh, Be A Fine Girl/Guy, Kiss Me
The Key Tool to understanding Stars: the
Hertzsprung-Russell diagram
• Hertzsprung-Russell diagram is luminosity vs.
spectral type (or temperature)
• To obtain a HR diagram:
– get the luminosity. This is your y-coordinate.
– Then take the spectral type as your x-coordinate, e.g.
K5 for Aldebaran. First letter is the spectral type: K
(one of OBAFGKM), the arab number (5) is like a
second digit to the spectral type, so K0 is very close to
G, K9 is very close to M.
Constructing a HR-Diagram
• Example: Aldebaran, spectral type K5III,
luminosity = 160 times that of the Sun
L
1000
160
100
Aldebaran
10
1
Sun (G2V)
O B A
F
G
K
M
Type
… 0123456789 0123456789 012345…
The
HertzprungRussell Diagram
• A plot of absolute
luminosity (vertical
scale) against
spectral type or
temperature
(horizontal scale)
• Most stars (90%) lie
in a band known as
the Main Sequence
Hertzsprung-Russell diagrams
… of the closest stars
…of the brightest stars