Stellar Distances and Magnitudes - Cornell Universityhosting.astro.cornell.edu/.../astro1101/lectures/6StellarDistancesRev… · Stellar Distances •How do we measure distances to

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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