Download Stellar Distances and Magnitudes

10/17/2012
Stellar Distances and Magnitudes
Lecture 6
Obese Bears Acquire Fish Greedily,
Killing Many Luscious Trout
1
10/17/2012
***
A HUGE UNIVERSE
*** ENORMOUS DISTANCES
*** VERY LOW MEAN DENSITIES
*** ALMOST AN EMPTY UNIVERSE
*** 10 TO THE MINUS 31 GM/CUBIC CM
CARL SAGAN PLANET WALK
ALPHA CENTAURI
SEPTEMBER 28, 2012
2
10/17/2012
Speed of Light
• Light travels at fixed speed – c
– 186,000 miles/second, or 3x108 meters/second
• We see the Sun as it was 8.3 minutes ago!
– Nearest star: 4.3 years ago!
– Andromeda galaxy: 2.2 million years ago!
– LEARN THE HISTORY OF THE UNIVERSE
REAL JUMINOSITY
• The spectral type (class) of a star gives us
temperature information, but we don’t know
its luminosity.
• To get the luminosity, we must know the
distance!
• Remember the inverse square law!
3
10/17/2012
Stellar Distances
• How do we measure distances to stars?
• Astronomers use the parallax method to
measure distances to nearby stars.
• The method is similar to that used by
surveyors.
Surveyor’s method
A
baseline

distance
Object

B
Observing the object from points A and B, we can compute
the distance to it from angles  and , and the baseline.
4
10/17/2012
Stellar Parallax
Earth
Now
p
1 AU
d
Sun
6 Months
Later
p = parallax (angle)
d = distance
A nearby star will change position on the sky
relative to distant (background) stars.
Photo taken now
Photo taken 6
months later
5
10/17/2012
How do we get distances?
• We have a very NARROW triangle on the
sky.
p
1 AU
s
d
s p d  d 
s
p
Finding distances
• Parallax is measured in arcseconds.
206265
AU
p
1
d
parsecs (pc)
p
d
For example:
p = 0.2” => d = 5 pc.
6
10/17/2012
Notes on parallax:
• As stars get further away, their parallax becomes
smaller.
• Parallax can not be measured to better than ~0.02”
from the ground (d < 50 pc).
– Interferometry is improving on this for selected
applications
•  Cen has the largest parallax (~0.8”)
• 1 pc = 3.26 ly (light-years)
• 1 pc = 206265 au
Current status
• The Hipparcos Satellite (1989 – 1993)
– Astrometry mission, produced two catalogs
• Hipparcos catalog: ~120,000 stars
– Measured parallaxes to better than 0.002” => d < 500 pc
• Tycho catalog: ~ 1,100,000 stars
– Measured parallaxes and proper motions to ~ 0.025” (40 pc)
• Tycho 2 catalog: 2,500,000 stars
– Update version of Tycho catalog
– Reprocessed raw Tycho data & used 144 other catalogs to obtain
proper motions
– Proper motions to 0.0025”/yr
7
10/17/2012
Statistical Parallax
• The Sun and Solar System are moving at
20 km/sec towards the Hercules constellation.
– 4.1 AU/year!
Importance of Parallax Distances
• Parallaxes are the key to knowing distances in
the universe.
• Nearby stars are the stepping stone to
measuring distance to everything else in the
universe.
• We can now compute the luminosity of stars!
8
10/17/2012
L, f and d
• The luminosity, brightness (flux) and
distance are related by the inverse square
law:
f 

L
4 d 2
Knowing the the brightness and the
distance, we can compute L.
 Cen
The closest stars
Prox
Sun

Star
Proxima Centauri
 Centauri A
 Centauri B
Barnard’s Star
Wolf 359
Lalande 21185
Sirius A
Sirius B
Parallax Dist. Luminosity Visual
(“)
(pc)
(Lsun=1)
mag
0.763
1.31
5x10-5
11.1
0.741
1.35
1.45
-0.1
0.741
1.35
0.4
0.6
-4
0.522
1.81
4x10
9.5
-5
0.426
2.35
2x10
13.5
-3
0.397
2.52
5x10
7.5
0.377
2.65
23
-1.5
-3
0.377
2.65
2x10
8.3
9
10/17/2012
Comparing stars
• If all stars were at the same distance, it would
be easy to compare their properties.
• But we can - Find stellar distance
- Use inverse square law to find
what it’s brightness would be at a
standard distance.
Absolute Magnitude
• mv - apparent magnitude
– How bright a star appears in the sky.
• Mv - absolute magnitude
– Brightness if the star were at 10 pc
– This is an intrinsic property of the star!
• To get Mv we must know the distance to the
star.
10
10/17/2012
Relating Apparent (mv) and Absolute (Mv)
Magnitude
• Suppose a star has mv = 7.0 and is located 100
pc away.
• It is 10 times the standard distance.
• Thus, it would be 100 times brighter to us at
the standard distance.
• Or 5 magnitudes brighter
• => Mv = 2.0
Example magnitudes
Sun:
Full Moon:
Sirius:
Canopus:
Arcturus:
Deneb:
mV
-26.8
-12.6
-1.47
-0.72
-0.06
1.26
MV
4.77
(32)
1.4
-3.1
-0.3
-6.9
11
10/17/2012
The Distance Modulus Equation
• The relation between mv and Mv is written in
equation form as:
mv - Mv = - 5 + 5 log10( d )
where d is in parsecs.
• mv - Mv is called the distance modulus.
12
10/17/2012
Examples
• Deneb: mv = 1.26 and is 490 pc away.
mv - Mv = - 5 + 5 log10( d )
1.26 - Mv = - 5 + 5 log10( 490 ) = -8.5
=> Mv = -7.2
• Sun: mv = -26.8, d = 1 AU
-26.8 - Mv = - 5 + 5 log10( 1/206265 )
=> Mv = 4.8
Bolometric Magnitude
• The absolute bolometric magnitude is the
brightness at ALL wavelengths.
• Usually represented by M.
• Mv is the absolute visual magnitude.
13
10/17/2012
Magnitude Summary
• mv = Apparent Magnitude
– apparent visual brightness of a star on the sky.
• Mv = Absolute Magnitude
– visual brightness the star would have if it were at 10 pc.
• M = Bolometric Magnitude
– total brightness (all wavelengths) of a star if it were at 10
pc.
Luminosity vs. Color of Stars
• In 1911, Ejnar Hertzsprung investigated the
relationship between luminosity and colors of stars
in within clusters.
• In 1913, Henry Norris Russell did a similar study of
nearby stars.
• Both found that the color (temperature, spectral
type) was related to the luminosity.
14
10/17/2012
106
Schematic Hertzsprung-Russell Diagram
-10
104
-5
102
0
Giants
1
5
10-2
Absolute Magnitude
Luminosity (Lsun)
Supergiants
10
White Dwarfs
10-4
15
O
B
A
F
G
K
M
Spectral Class
Notes on H-R Diagram
• There are different regions
– main sequence, giant, supergiant, etc.
• Most stars lie along the main-sequence.
• For a given spectral class (e.g. K), there can be
more than one luminosity.
– i.e. main-sequence, giant or supergiant
• On the main sequence, there are many more
K and M stars than O and B stars.
15
10/17/2012
106
Luminosity Classes
brightest supergiants
Ia
supergiants
104
Luminosity (Lsun)
bright giants
102
Ib
II
III
giants
IV
sub-giants
1
Main-sequence
V
10-2
B
A
F
G
K
Spectral Class
M
Hipparcos H-R Diagram
Hertzsprung-Russell (M_V, B-V) diagram for the
16631 single stars from the Hipparcos Catalogue
with relative distance precision better than 10%
and sigma_(B-V) less than or equal to 0.025
mag. Colours indicate number of stars in a cell
of 0.01 mag in (B-V) and 0.05 mag in V
magnitude (M_V).
Note that this sample is biased towards more
luminous stars.
From:
http://astro.estec.esa.nl/Hipparcos/vis_stat.html
16