Download Lecture 12

Properties of Stars
• How do we measure stellar luminosities?
• How do we measure stellar temperatures?
• How do we measure stellar masses?
Brightness of a star depends on both distance and luminosity.
Its color tells us its temperature (recall blackbody radiation).
Luminosity:
Amount of power a
star radiates
(energy per second =
watts)
Apparent brightness:
Amount of starlight
that reaches Earth
(energy per second
per square meter)
Thought Question
These two stars have about the same luminosity—
which one appears brighter (i.e. has a larger apparent
brightness) ?
A. Alpha Centauri
B. The Sun
Luminosity passing
through each sphere
is the same.
Area of sphere:
4π (radius)2
Divide luminosity by
area to get brightness.
The relationship between apparent brightness
and luminosity depends on distance:
Brightness =
Luminosity
4π (distance)2
We can determine a star’s luminosity if we can
measure its distance and apparent brightness:
Luminosity = 4π (distance)2  (Brightness)
Thought Question
How would the apparent brightness of Alpha
Centauri change if it were three times farther away?
A.
B.
C.
D.
It would be only 1/3 as bright.
It would be only 1/6 as bright.
It would be only 1/9 as bright.
It would be three times as bright.
The parallax
angle depends
on distance.
Parallax Angle as a Function of Distance
Parallax Angle and Distance
p = parallax angle
1
d (in parsecs) =
p (in arcseconds)
d (in light-years) = 3.26 
1
p (in arcseconds)
• One degree has 60 ‘arcminutes’ and one arc minute has 60 arcseconds.
• So there are 3600 arcseconds in one degree.
Parallax and Distance
p = parallax angle
1
d (in parsecs) =
p (in arcseconds)
d (in light-years) = 3.26 
1
p (in arcseconds)
The inverse of the parallax angle in arcseconds equals the distance to an
object in parsecs.
• The nearest star is about 4 light years away, so p = 0.75 arcseconds.
• This is the largest parallax angle, all other stars have small p values.
Most luminous
stars:
106LSun
Least luminous
stars:
10-4LSun
(LSun is luminosity
of the Sun)
Hottest stars:
50,000 K
Coolest stars:
3000 K
(Sun’s surface
is 5800 K)
Remembering Spectral Types
(Hottest)
O B A F G K M
(Coolest)
• Oh, Be A Fine Girl/Guy, Kiss Me
• Only Boys Accepting Feminism Get Kissed
Meaningfully
Thought Question
Which of the stars below is hottest?
A.
B.
C.
D.
M star
F star
A star
K star
Lines in a star’s spectrum correspond to a spectral type
that reveals its temperature:
(Hottest)
O B A F G K M
(Coolest)
Spectral Type
• Spectral types form a temperature classification
system.
• It is based on the fact that different spectral lines
occur at different temperatures.
• The problem is that you need very long exposure
times to measure faint spectral lines.
• So can only do a few thousand stars this way.
• To classify millions of stars we use the stars color to
estimate the blackbody temperature (i.e. to estimate
the spectral type).
• The color of a star can be measured with only a very
short exposure time.
To measure Stellar mass we use
Binary Stars
Orbit of a binary star system depends on
the strength of gravity.
So the orbits depend on the mass of the
two stars.
Types of Binary Star Systems
• Visual binary
• Eclipsing binary
• Spectroscopic binary
About half of all stars are in binary systems.
Visual Binary
We can directly observe the orbital motions of these stars.
We can only see visual binaries if they are very near Earth.
Eclipsing Binary
We can measure periodic eclipses.
Spectroscopic Binary
We determine the orbit by measuring Doppler shifts.
Isaac Newton
We measure mass using
gravity.
Direct mass measurements
are possible only for stars in
binary star systems.
p2
=
4π2
a3
G (M1 + M2)
p = period
a = average separation
This should look familiar … it is Newton’s general expression
for Kepler’s 3rd Law.
Need two out of three
observables to measure mass:
1. Orbital period (p)
2. Orbital separation (a or r = radius)
3. Orbital velocity (v)
For circular orbits, v = 2πr / p
v
r
M
Most massive
stars:
100MSun
(some very rare
stars may have
> 100 MSun)
Least massive
stars:
0.08MSun
(MSun is the
mass of the
Sun.)
• Now do the lecture tutorial section on
Binary Stars.
• When you have finished do the tutorial
section on Parallax and Distance.