Download Absolute magnitude

Properties of Stars
http://youtu.be/zaOPsmlJyw8
1
Lecture Learning goals:
! Explain what is meant by the inverse-square law and apply it to
the measurements of light at different distances.
! Define apparent and absolute magnitudes.
! Explain what a “parsec” is and why it is convenient for
astronomers in estimating distances and luminosities of stars.
!Describe the methods used to determine the temperature,
luminosity, and radius of a star.
!State the “goldilocks” analogy for strengths of hydrogen lines in
the spectra of stars OBAFGKM.
2
Inverse square law for light
of light
! Explain what is meant by the inverse-square law and apply it to the measurements
3
at different distances.
Brightness
How the star looks to US HERE ON EARTH.
L
apparent brightness =
4 πD2
Each of these light bulbs will appear to be the same brightness.
1000 times farther away
"
100 Watt
1 Watts
1000 Watt
€
10 times farther away
"
2 x farther away, 1/4 as bright
3 x farther away, 1/9 as bright
4 of light
! Explain what is meant by the inverse-square law and apply it to the measurements
at different distances.
Apparent Magnitude
# Every 5 magnitudes
difference means 100 x
difference in brightness
# One magnitude difference
is 2.512 times in brightness.
(2.5125 = 100)
!Define apparent and absolute magnitudes.
5
When you see only “magnitude,” that means APPARENT magnitude.
1. The magnitude (m) of star A is 1, the magnitude (m) of star B is 6.
How many times brighter is A than B?
a) 5
b) 10
c) 100
d) 1000
2. m of star C is 12, m of star D is 2: How many times brighter is
star D than star C? (Or, equally stated, how many times dimmer
is star C than star D?)
a) 10
•
b) 24
c) 100
d) 10,000
The Sun is the brightest star in the sky, with an apparent
magnitude of about -26.5 Sirius is next in line, with an apparent
magnitude of -1.5; how many times brighter is the Sun than
Sirius?
a) 25
b) 28
c) 100,000
!Define apparent and absolute magnitudes.
d) 10,000,000,000
6
Brightness: Magnitude
•
Some useful definitions:
▪ Brightness of a star is measured by logarithmic
magnitude.
=> Brighter objects have a smaller magnitude.
▪ Apparent magnitude: how bright the star appears
to us in the sky. m
▪ Absolute magnitude: how bright the star would
be at a distance of 10 parsecs from us. M
d is in parsecs
!Define apparent and absolute magnitudes.
PARSEC: Parallax ARc SECond
A star having a parallax of 1 arc second is 1 parsec away
1 parsec (pc) = 3.26 light years
1 kiloparsec (1 kpc) = 1000 pc; 1 megaparsec (1 Mpc) = 1,000,000 pc
Baseline is 1 Astronomical Unit
! Explain what a “parsec” is and why it is convenient for astronomers in estimating
8 distances and
luminosities of stars.
Continuous Spectrum - created by thermal radiator
(blackbody radiation)
Hotter stars look more blue-white than cooler
stars because hot stars emit most of their light at
shorter wavelengths.
Star field in Sagittarius
Wien’s Law
6
2.9 × 10
λ peak =
nm
T
6
2.9 × 10
T =
K
λ peak
€
9
! Describe the methods used to determine the temperature, luminosity, and radius of a star.
http://stardate.org/radio/program/delta-lyrae
10
the words in the equation with the approical expressions for the Stefan-Boltzmann
of a sphere, our equation for the luminoss like this:
J
J
4 ____
__
nosity ( ) = σT
s
(m s)
2
× 4πR2(m 2)
:
L = 4πR2 σT 4 J/s (W)
Suppose w
star in the con
geuse (see the
we know that
3500 K. Its di
and its brightn
times that of th
telgeuse? Usin
the following:
onstants (4, π, and σ) do not change, the lur is proportional only to R2T 4. Make a star 3
nd its surface area becomes 32 = 9 times as
times as much area to radiate, so there is 9
adiation.
Make
a
star
twice
as
hot,
and
each
Describe
the
methods
used
to
determine
the
temperature,
luminosity,
and radius of a star.
!
RB
__
=
Understanding Our Universe, 1st Edition
4
Copyright © 2012 W. W. Norton & Company
√
we know here on Earth applies to the rest of the solar system, the Galaxy, and the Universe. In this tutorial
you will be led through the steps to understanding the Stefan-Boltzmann Law:
The amount of energy put out per second (the number of watts) is proportional to the surface area of the
sphere (4 pi times the radius squared) and the temperature raised to the 4th power. (The σ represents the
−8
-2
-4
Stefan-Boltzmann constant, 5.67 ×10 W·m ·K .)
L = 4" r 2! T 4
You are comparing the ability of a grouping of electric hot plates (shown below as burners on a “stove top”)
of different sizes and temperatures to bring identical pots of water to a boil. The pots are all as large as the
largest hot plate. The temperatures of the hot plates are coded: the lighter the shade of gray, the higher the
temperature.
High
Medium
Low
1. For each pair of hot plates (read horizontally), circle the one that will boil the water more quickly. Is
there a set of burners for which there is no way to tell? If so, which ones?
! Describe the methods used to determine the temperature, luminosity, and radius of a star.
The H-R Diagram
13
! Describe the methods used to determine the temperature, luminosity, and radius of a star.
H-R Diagram: O and M Stars
▪ On far left end of the
main sequence are
the O stars: hotter,
larger, and more
luminous than the
Sun.
•
▪ On far right end of the
main sequence are
the M stars: cooler,
smaller, and fainter
than the Sun.
! Describe the methods used to determine the temperature, luminosity, and radius of a star.
Cool stars
are red.
Hot stars
are blue.
The H-R Diagram
Hotter
107
0R
Supergiants
105
100
–10
£
R£
–5
10 R
103
102
All stars with a
radius of 1 R£ lie
along this line.
1R
101
0.1
1
0.01
10–1
10–2
10
0.00
–3
10–4
10–5
1R
MA
IN
£
£
Giants
SE
0
QU
EN
CE
R£
Sun
+5
R£
White
dwarfs
+10
£
H-R diagrams are sometimes
plotted with either spectral type
or temperature.
40,000 30,000
20,000
+15
10,000
3000 2500
6000
Surface temperature (K)
O5
B0
B5
A0
Spectral type
F0
G0
K5
15
M5
! Describe the methods used to determine the temperature, luminosity, and radius of a star.
More luminous
Visual luminosity relative to Sun
104
Absolute visual magnitude
Simulation of the
actual relative
sizes of a giant
star versus the
Sun.
1,00
106
http://media.wwnorton.com/college/astronomy/animations/interactive/hrexplorer.html
! Describe the methods used to determine the temperature, luminosity, and radius of a star.
! Classify stars and organize this information.
1 Ångstrom = 10-10 meters
Composition: Spectral Types Subclasses
•
▪ Absorption lines depend primarily on temperature of photosphere.
▪ Full sequence for stars radiating mostly in the visible: OBAFGKM
▪ Each spectral type is broken down into 10: 0-9.
=> The Sun is type G2.
! Classify stars and organize this information.
Composition: Emission
•
▪ Emission: an electron emits a photon and drops to a
lower energy state, losing energy.
▪ The photon’s energy is equal to the energy difference
between the two levels.
Composition: Absorption
•
▪ Absorption: an electron absorbs the energy of a photon
to jump to a higher energy level.
▪ The photon’s energy must be equal to the energy
difference between the two levels.
Composition: Absorption Lines
•
▪ For stars, astronomers look at the dark absorption lines in
stars’ spectra.
▪ These absorption lines help determine a star’s
temperature, composition, density, pressure, and more.
Sun (G2 V) as a Blackbody Radiator
22
!State the “goldilocks” analogy for strengths of hydrogen
lines in the spectra of stars OBAFGKM.
•
Spectral type O stars are so hot, the photons so
energetic that almost all of the hydrogen atoms are
ionized.
•
Spectral type M stars are so cool, the photons do not
have enough energy to excite the hydrogen electrons
to the second energy level.
•
Spectral type A stars are just the right temperature that
photons can excite electrons to second energy level
where they can absorb photons of a range of energies
Colors represent filter regions.
U
B
V
! Classify stars and organize this information.
R
I
U
B
V
! Classify stars and organize this information.
R
I
U
B
V
! Classify stars and organize this information.
R
I
U
B
V
! Classify stars and organize this information.
R
I
U
B
V
! Classify stars and organize this information.
R
I
U
B
V
! Classify stars and organize this information.
R
I
U
B
V
! Classify stars and organize this information.
R
I
!State the “goldilocks” analogy for strengths of hydrogen
lines in the spectra of stars OBAFGKM.
•
Spectral type O stars are so hot, the photons so energetic that almost
all of the hydrogen atoms are ionized.
•
Spectral type M stars are so cool, the photons do not have enough
energy to excite the hydrogen electrons to the second energy level.
•
Spectral type A stars are just the right temperature that photons can
excite electrons to second energy level where they can absorb
photons of a range of energies
Lecture Learning goals:
! Explain what is meant by the inverse-square law and apply it to
the measurements of light at different distances.
34
! Define apparent and absolute magnitudes.
! Explain what a “parsec” is and why it is convenient for
astronomers in estimating distances and luminosities of stars.
!Describe the methods used to determine the temperature, luminosity,
and radius of a star.
!State the “goldilocks” analogy for strengths of hydrogen lines in the
spectra of stars OBAFGKM.
•
Spectral type O stars are so hot, the photons so energetic that
almost all of the hydrogen atoms are ionized.
•
Spectral type M stars are so cool, the photons do not have
enough energy to excite the hydrogen electrons to the second
energy level.
•
Spectral type A stars are just the right temperature that photons
can excite electrons to second energy level where they can
absorb photons of a range of energies