1. Announcements
HW #1 will be returned on Wednesday Problem #7 – I wrote the distance incorrectly, should have been x1019 km. But don’t change your HW! Quiz #1 next Friday Study guide handed out today/Wednesday Please turn off all electronic devices Don’t forget to sign the attendance sheet

2. Lecture 11: To the Stars and Beyond
Astronomy 1143 – Spring 2014

3. 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

4. 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…..

5. Method of Trigonometric Parallaxes
June p
December
Foreground
Star
Distant Stars
p = parallax angle

6. Parallax Formula p = parallax angle in arcseconds
d = distance in “Parsecs”
Avoids trig functions, but only works for small angles

7. 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

8. Examples: Proxima Centauri has a parallax p=0.768 arcsec:
Another star has a parallax of p=0.02 arcsec:

9. 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

10. The Current Reach of Parallax

11. Hipparcos & Gaia

12. Reach of Gaia

13. 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

14. Luminosity Assuming 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

15. Standard Candles Objects 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.

16. 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

17. All Stars are not like the Sun

18. Stellar Spectra

19. Spectroscopic Parallax Limits
Distance 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.

21. 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.

22. Period-Luminosity Relationship1 5 10 50
102
103
104
Period (days)
Luminosity (Lsun)
 Cephei Stars
RR Lyrae stars 3
100 30
0.5

23. Cepheid Variables Rhythmically Pulsating Supergiant stars:
Found in young star clusters
Luminosities of ~ Lsun
Brightness Range: few % to 2-3 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

24. Typical Cepheid Light Curves
LCB 171
P ~ 3 days
LCB 272
P ~ 2 days
Period
Period
Brightness
Brightness
time
time
Easier to get a measurement of brightness than a spectrum, especially for a lot of objects at once

25. Example: Cepheid with a 10-day period
P-L Relation
(calibrated)
104
L=5011 Lsun
P=10d (observable)
103
Luminosity (Lsun)
102
Note: before you make this plot, you do need to know the distances to a bunch of Cepheids! Ideally, would be geometric parallax. Right now it is also spectroscopic parallax to star clusters
0.5 1 3 5 10 30 50
100
Period (days)

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

27. Cepheid Variable Limitations
Found only in young star clusters.
Distance Limit:
30-40 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).

28. Cepheids with HST

29. RR Lyrae Variables Pulsating old stars: Period-Luminosity Relation
Luminosity of ~50 Lsun
Brightness Range: factor of ~ 2-3
Period Range: Few hours up to ~ 1 day.
Relatives of Cepheid Variables
Period-Luminosity Relation
Less strong than for Cepheids

30. RR Lyrae Light Curve

31. 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

32. The Cosmic Distance Scale
No 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.

33. Distance Ladder