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Lecture 11:To the Stars and Beyond

Astronomy 1143 – Spring 2014

Key Ideas:Distances=key measurement in astronomy

Geometric Distances• Trigonometric Parallax• Most reliable distances

Luminosity Distances• Uses Standard Candles – objects whose luminosity

you know ahead of time• Spectroscopic Distances• Period-Luminosity Distances

Each method only works out so far in distance --must use closer methods to calibrate other methods

Our Place in the Universe

We can see about 6000 stars with the naked eye and millions-billions more with a telescope

How far away are they?

How are they distributed?

Is the Milky Way the only galaxy?

How far away are other galaxies?

Building the distance ladder…..

p

December

Method of Trigonometric Parallaxes

June

Distant Stars

ForegroundStar

p = parallax angle

Parallax Formula

p = parallax angle in arcseconds

d = distance in “Parsecs”Avoids trig functions, but only works for small angles

Parallax Second = Parsec (pc)

Fundamental distance unit in Astronomy

“A star with a parallax of 1 arcsecond has a distance of 1 Parsec.”

1 parsec (pc) is equivalent to:–206,265 AU–3.26 Light Years–3.085x1016 km

Examples:Proxima Centauri has a parallax p=0.768 arcsec:

d1

p

1

0 0250 pc= = =

.

Another star has a parallax of p=0.02 arcsec:

Parallax Limits

Ground-based parallaxes are measured to a precision of ~0.01-arcsec

• good distances out to 100 pc • < 1000 stars this close

Hipparcos parallaxes have a precision of ~0.001-arcsec (at best)

• good distances out to 1000 pc• Measured for ~100,000 stars

The Current Reach of Parallax

Hipparcos & Gaia

Reach of Gaia

Luminosity Distances

Indirect distance estimate:• Measure the object’s Apparent Brightness, B• Assume the object’s Luminosity, L• Solve for the object’s distance, d, by applying

the Inverse Square Law of Brightness

LuminosityAssuming a luminosity is a critical step.

We need to find something that we can observe about an object that tells us its luminosity

For example: • We can look at the color of an object• We can look at the spectrum of an object• We can look at the lightcurve of an object

Then we need to calibrate it by knowing the luminosity of an identical object

Standard CandlesObjects whose Luminosity you know ahead of time.

• Calibrate the Luminosities of nearby objects for which you have distances from Trigonometric Parallaxes.

• Identify distant but similar objects, using a distance-independent property that they share.

• Assume that the distant objects have the same Luminosity as the nearby objects.

Examples of Standard Candles

Normal Stars • Spectral type is the same as a star with a

known luminosity – say a star with a known parallax

Pulsating Stars• Evolved Stars can be unstable• Small Changes in Luminosity• Period-(Average) Luminosity Relationship

All Stars are not like the Sun

Stellar Spectra

Spectroscopic Parallax LimitsDistance Limit:

• Practical limit is few 100,000 pc – need to get spectra of individual stars

Problems:• Stars within each class do not have exactly the

same luminosity

• Depends on composition.

• Faint spectra give poor classifications.

Method works best for clusters of stars, rather than for individual stars.

Periodic Variable Stars

Stars whose brightness varies regularly with a characteristic, periodic pattern.

Distance-Independent Property:Period (repetition time) of their cycle of

brightness variations.

Physics:Period-Luminosity Relations exist for certain

classes of periodic variable stars.

Measuring the Period gives the Luminosity.

Period-Luminosity Relationship

1 5 10 50

102

103

104

Period (days)

Lum

inos

ity

(Lsu

n)

CepheiStars

RR Lyraestars

3 100300.5

Cepheid Variables

Rhythmically Pulsating Supergiant stars:• Found in young star clusters

• Luminosities of ~ 1034 Lsun

• Brightness Range: few % to 23 times• Period Range: 1 day to ~50 days.

Period-Luminosity Relation:• Longer Period = Higher Luminosity

• P = 3 days, L ~ 103 Lsun

• P = 30 days, L ~ 104 Lsun

Typical Cepheid Light Curves

LCB 171P ~ 3 days

LCB 272P ~ 2 days

time time

Bri

ghtn

ess

Bri

ghtn

ess

PeriodPeriod

Easier to get a measurement of brightness than a spectrum, especially for a lot of objects at once

Example: Cepheid with a 10-day period

1 5 10 50

102

103

104

Period (days)

Lum

inos

ity

(Lsu

n)

3 100300.5

L=5011 Lsun

P=10d (observable)

CepheidP-L Relation(calibrated)

Example

You measure the period of a Cepheid to be 5.4 days. What is its luminosity?

Cepheid Variable LimitationsFound only in young star clusters.Distance Limit:

• 3040 Megaparsecs (Hubble Space Telescope)• Crucial for measuring distances to galaxies.

Problems:• Few Cepheids with good Trigonometric

Parallaxes• P-L relation may depend on Composition• Two types of Cepheids with different

P-L relations ( Cephei and W Virginis).

Cepheids with HST

RR Lyrae Variables

Pulsating old stars:• Luminosity of ~50 Lsun

• Brightness Range: factor of ~ 23• Period Range: Few hours up to ~ 1 day.• Relatives of Cepheid Variables

Period-Luminosity Relation• Less strong than for Cepheids

RR Lyrae Light Curve

RR Lyrae Star Limitations

Found in old clusters, Galactic bulge & halo

Distance Limit:• ~1 Megaparsec (Hubble)• Limited to our Galaxy & Andromeda

Problems:• No RR Lyrae stars with good Trigonometric

Parallaxes• Less bright than Cepheid stars, so useful only

relatively nearby

The Cosmic Distance ScaleNo single method will provide distances on all cosmic scales:

• Calibrate parallaxes using the AU• Calibrate spectroscopic parallaxes using geometric

parallaxes• Calibrate Cepheid and RR Lyrae star distances

using clusters with spectroscopic or geometric parallaxes

Imprecision at each step carries forward, making subsequent steps less precise.

This is the challenge of measuring distances.

Distance Ladder