Announcements HW #1 will be returned on Wednesday Problem #7 – I wrote the distance incorrectly, should have been 2.2706x1019 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

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…..

Method of Trigonometric Parallaxes June p December Foreground Star Distant Stars 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: 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

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

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.

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 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.

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) Luminosity (Lsun)  Cephei Stars RR Lyrae stars 3 100 30 0.5

Cepheid Variables Rhythmically Pulsating Supergiant stars: Found in young star clusters Luminosities of ~ 103-4 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

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

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)

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

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).

Cepheids with HST

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

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 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.

Distance Ladder