Distances

Parallax

• Near objects appear to move more than far objects against a distant horizon.

• Trigonometric parallax is used to measure distance to near stars.

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Parsec

• Stellar distances are inversely proportional to the parallax angle.

– Earth’s radius fixed

– Define distance by angle

• The parsec (pc) is the distance that would result in one arc second of parallax.

– 1 pc = 3.086 1016 m

– 1 pc = 2.06 105 AU

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Near Stars

• The Hipparcos satellite measured parallax of 118,000 stars.

– Resolution: 0.001 arc-second and 0.2% luminosity.

• Gaia launches in 2011 to measure 109 stars in the galaxy

Arcturus 11.3 pc (ESA)

Spectroscopic Parallax

• The Hipparcos data provides very precise distances.

– Use for absolute magnitudes

– Precise HR diagram

• Distant stars can be fit on the main sequence.

– Measure luminosity and apparent magnitude

Star Clusters

• Spectroscopic parallax assumes stars on the main sequence.

– Better to average stars at the same distance

• Globular clusters are dense with 100,000 stars in a 20-100 pc region with less than 0.3 pc separating the stars.

• Open clusters tend to be smaller and younger.

Cluster Types

Type I Clusters

– Hot young stars

– Lots of gas and dust

– Abundant in heavy elements

• Active star formation

Type II Clusters

– Old red stars

– No gas and dust

– Few heavy elements

• No star formation, just old stars

Standard Candle

• Up to 30 pc distance is measured with parallax.

– Less certainty to 300 pc

– Longer distances by spectroscopic parallax

• The best measure of large distances are variable stars.

– Luminosity directly related to the period.

Vibrational Modes

• Thermal motion in a star relates the speed to potential energy.

• Radial pressure waves move at the speed of sound.

• The period of vibration is inversely proportional to the square root of the density.

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Cepheid Variables

• Cepheid variables are massive relatively cool stars.

– ~ 4 to 15 M

– Color classification F to K

• The period and apparent luminosity determine the distance.

• Density ~ 10-3 kg/m3

• Vibrational period ~ 106 s

RR Lyrae Variables

• RR Lyrae variables are short period white variables.

– ~ 1 M

– Color classification A

• These are type I stars.

– Found in globular clusters

– Useful for galactic distances

• Density ~ 10 kg/m3

• Vibrational period ~ 4 104 s

Variables in M3

RR Lyrae stars in one night time lapse

Instability Strip

• Cepheid and RR Lyrae stars fall in a narrow band on the HR diagram.

– Instability strip

– Not on main sequence

• As stars pass through band they oscillate.

Band of Stars

• The sun is in a galaxy called the Milky Way.

– Observed as a diffuse band

– Millions of stars in a telescope

• The Milky Way is thicker in some directions.

– Appears as a band across the sky

Disk

• The band of the Milky Way is the same view a viewer would have sitting inside a disk of stars.

• This disk has type I stars with gas and dust.

top view side view

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Halo

• Astronomers measure the distance to globular clusters.

• Type II globular clusters are in a sphere around one point.

• This sphere is the galactic halo.

• The center of the sphere is the center of the galaxy.

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Size and Shape

• To view the galaxy from inside, we

– measure the distance to globular clusters

– measure distributions of hydrogen gas in the disk.

• The Milky Way is 50,000 pc across with a central bulge.

• The stars group in arms.

Galactic Structure

• The galactic nucleus is bright and massive.

• It is obscured by the dust of the galactic disk.

• The Milky Way is probably similar to M83.