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Astronomy 114
Lecture 15: Properties of Stars
Martin D. Weinberg
[email protected]
UMass/Astronomy Department
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—1/18
Announcements
PS #4 posted; due next Friday (before Spring break)
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—2/18
Announcements
PS #4 posted; due next Friday (before Spring break)
Quiz #1 redux due next Wednesday
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—2/18
Announcements
PS #4 posted; due next Friday (before Spring break)
Quiz #1 redux due next Wednesday
Today:
Properties of Stars
The Nature of Stars, Chap. 19
The Birth of Stars, Chap. 20
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—2/18
Quiz #1
Redo exam questions that you missed
Separate sheets of paper
Turn in on Wednesday before Spring Break
Average of original and new scores
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—3/18
Distances to stars
D = dα
d=
D
α
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—4/18
Distances to stars
D = dα
d=
D
α
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—4/18
Distances to stars
D = dα
d=
D
α
If α = 1 arc sec and D = 1AU then d = 206, 265AU .
This is a PARSEC
Therefore: d(pc) = 1/p(arc sec)
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—4/18
Parallax
Parallax is the first step in the cosmic distance ladder
Fundamental distances, by direct measurement
Hipparcos satellite: measured distances 120,000
stars to high accuracy
Parallax angles of 0.001 arc sec
1
1
d = pc =
pc = 1000 pc = 1 kpc
p
0.001
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—5/18
Parallax
Parallax is the first step in the cosmic distance ladder
Fundamental distances, by direct measurement
Hipparcos satellite: measured distances 120,000
stars to high accuracy
Parallax angles of 0.001 arc sec
1
1
d = pc =
pc = 1000 pc = 1 kpc
p
0.001
Example: Proxima Centauri
p = 0.772 arc sec
1
3.26 ly
1
pc = 1.3 pc = 1.3 pc ×
=
d = pc =
p
0.772
1 pc
4.2 ly
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—5/18
Distance to stars using brightness (1/4)
Stars have different luminosities
Use parallax to determine distance
Brightness of star depends on distance
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—6/18
Distance to stars using brightness (1/4)
Stars have different luminosities
Use parallax to determine distance
Brightness of star depends on distance
Brightness or flux is the
luminosity per area
Luminosity divided by the
area of a sphere: 4πd2
L
b=
4πd2
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—6/18
Distance to stars using brightness (2/4)
Example: flux from Sun on Earth
3.827 × 1026 W
2
=
1353
W/m
b⊙ =
4π(1.50 × 1011 m)2
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—7/18
Distance to stars using brightness (2/4)
Example: flux from Sun on Earth
3.827 × 1026 W
2
=
1353
W/m
b⊙ =
4π(1.50 × 1011 m)2
Can get star’s luminosity from apparent brightness!
L = 4πd2 b
L
=
L⊙
d
d⊙
A114: Lecture 15—09 Mar 2007
!2
b
b⊙
Read: Ch. 19,20
Astronomy 114—7/18
Distance to stars using brightness (3/4)
Star #1 has twice the brightness of Star #2; Star #1 is
at half the distance of Star #2
L1
=
L2
d1
d2
!2
b1
= (0.5)2 ×2 = 0.25×2 = 0.5
b2
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—8/18
Distance to stars using brightness (3/4)
Star #1 has twice the brightness of Star #2; Star #1 is
at half the distance of Star #2
L1
=
L2
d1
d2
!2
b1
= (0.5)2 ×2 = 0.25×2 = 0.5
b2
Star Q has the same luminosity as Proxima Centauri
but has only 1/9 the brightness. How far is Star Q?
d1
d2
!2
(L1 /L2 )
=
(b1 /b2 )
d1
d2
v
s
u
u (L1 /L2 )
1
t
=
=
A114: Lecture 15—09 Mar 2007
(b1 /b2 )
1/9
=3
Read: Ch. 19,20
Astronomy 114—8/18
Distance to stars using brightness (4/4)
Stellar Luminosity Function
Take p larger than p∗
Observe apparent
brightness of stars
Compute
number
within volume of the
sphere with radius
d = 1/p∗
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—9/18
Magnitude scale
Greek astronomer Hipparchus divided stars into six
classes or magnitudes (2nd century BC)
1st magnitude is brightest, 6th magnitude is faintest
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—10/18
Magnitude scale
Greek astronomer Hipparchus divided stars into six
classes or magnitudes (2nd century BC)
1st magnitude is brightest, 6th magnitude is faintest
Sensitivity of human eye is logarithmic
Magnitude difference of 1 corresponds log(1000) 3
to −2.5 log(F1 /F2 )
log(100)
2
log(10)
1
log(1)
0
log(0.1)
-1
log(0.01) -2
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—10/18
Magnitude scale
Greek astronomer Hipparchus divided stars into six
classes or magnitudes (2nd century BC)
1st magnitude is brightest, 6th magnitude is faintest
Sensitivity of human eye is logarithmic
Magnitude difference of 1 corresponds log(1000) 3
to −2.5 log(F1 /F2 )
log(100)
2
1 magnitude is factor 1001/5 = 2.512 in log(10)
1
brightness
log(1)
0
2 magnitudes is 2.512 × 2.512
log(0.1)
-1
log(0.01) -2
5 magnitudes is 100
10 magnitudes is 100 × 100 = 10000
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—10/18
Measuring colors of stars (1/3)
Our perception of the color of star is telling us about
the ratio of energy at different wavelengths
Can get surface temperature of a star from its color
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—11/18
Measuring colors of stars (1/3)
Our perception of the color of star is telling us about
the ratio of energy at different wavelengths
Can get surface temperature of a star from its color
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—11/18
Measuring colors of stars (1/3)
Our perception of the color of star is telling us about
the ratio of energy at different wavelengths
Can get surface temperature of a star from its color
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—11/18
Measuring colors of stars (2/3)
Astronomers use filters to measure brightness in
specific ranges of wavelengths
A typical scheme is three filters (UBV):
1. Ultraviolet
2. Blue
3. Visible
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—12/18
Measuring colors of stars (3/3)
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—13/18
Spectra of stars reveal temperature (1/2)
Overall, stars have blackbody (thermal) spectra
Relative strength of absorption lines is a sensitive
probe of temperature
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—14/18
Spectra of stars reveal temperature (2/2)
Overall, stars have blackbody (thermal) spectra
Relative strength of absorption lines is a sensitive
probe of temperature
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—15/18
Spectral classes
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—16/18
Inferring the size of stars (1/2)
Use UBV photometry or spectral class to estimate
temperature
Recall: L = 4πR2 σT 4
2 σT 4
For Sun:L⊙ = 4πR⊙
⊙
Ratio:
L
L⊙
!
=
R
R⊙
!2
T
T⊙
!4
Solve for radius:
R
=
R⊙
A114: Lecture 15—09 Mar 2007
T
T⊙
!−2 s
Read: Ch. 19,20
L
L⊙
Astronomy 114—17/18
Inferring the size of stars (2/2)
Example: Betelgeuse
L = 60, 000 (L⊙ = 6 × 104 L⊙ )
T = 3500K (T⊙ = 5800K )
Ratio of radii:
R
3500
=
R⊙
5800
A114: Lecture 15—09 Mar 2007
−2 q
6 × 104 = 6.7 × 102 = 670
Read: Ch. 19,20
Astronomy 114—18/18
Inferring the size of stars (2/2)
Example: Betelgeuse
L = 60, 000 (L⊙ = 6 × 104 L⊙ )
T = 3500K (T⊙ = 5800K )
Ratio of radii:
R
3500
=
R⊙
5800
−2 q
6 × 104 = 6.7 × 102 = 670
R⊙ = 6.96 × 105 km
1AU = 1.5 × 108 km
R = 670 × 6.96 × 105 km = 4.7 × 108 km = 3.1AU
A114: Lecture 15—09 Mar 2007
Read: Ch. 19,20
Astronomy 114—18/18