Post on 18-Jan-2021
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Stellar Distances and Magnitudes
Lecture 6
Obese Bears Acquire Fish Greedily, Killing Many Luscious Trout
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*** 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
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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!
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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
distance
bas
elin
e
Observing the object from points A and B, we can compute the distance to it from angles and , and the baseline.
Object
A
B
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Stellar Parallax
1 AU
d
Earth Now
6 Months Later
p = parallax (angle) d = distance
p
Sun
Photo taken now Photo taken 6 months later
A nearby star will change position on the sky relative to distant (background) stars.
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How do we get distances?
• We have a very NARROW triangle on the sky.
1 AU
d
p
s
s p d ds
p
Finding distances
• Parallax is measured in arcseconds.
dp
dp
206265
1
AU
parsecs (pc)
For example: p = 0.2” => d = 5 pc.
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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
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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!
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L, f and d
• The luminosity, brightness (flux) and distance are related by the inverse square law:
f L
d
4 2
Knowing the the brightness and the distance, we can compute L.
The closest stars
Star Parallax Dist. Luminosity Visual (“) (pc) (Lsun=1) mag
Proxima Centauri 0.763 1.31 5x10-5 11.1
Centauri A 0.741 1.35 1.45 -0.1
Centauri B 0.741 1.35 0.4 0.6
Barnard’s Star 0.522 1.81 4x10-4 9.5
Wolf 359 0.426 2.35 2x10-5 13.5
Lalande 21185 0.397 2.52 5x10-3 7.5
Sirius A 0.377 2.65 23 -1.5
Sirius B 0.377 2.65 2x10-3 8.3
Sun
Cen
Prox
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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.
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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
mV MV
Sun: -26.8 4.77
Full Moon: -12.6 (32)
Sirius: -1.47 1.4
Canopus: -0.72 -3.1
Arcturus: -0.06 -0.3
Deneb: 1.26 -6.9
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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.
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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.
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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.
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Lum
ino
sity
(Lsu
n)
10-4
10-2
102
104
106
1
O B A F G K M
Spectral Class
Schematic Hertzsprung-Russell Diagram
Ab
solu
te M
agn
itu
de
-10
-5
0
5
10
15
Supergiants
Giants
White Dwarfs
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.
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Ia
Ib
II
III
IV
V
Lum
ino
sity
(Lsu
n)
10-2
102
104
106
1
B A F G K M Spectral Class
Main-sequence
brightest supergiants
supergiants
bright giants
giants
sub-giants
Luminosity Classes
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