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Measuring distances is key to know any property of astronomical objects

• Physical size is angular size x (distance) • The Luminosity is the flux x (distance squared) • Masses are measured with velocities and

physical lengths, again need distance to convert an angle to a physical size and determine mass

Surveying outside the solar system

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Solar system • orbit geometry • radar ranging

Geometric Distances: the gold standard

Stars • parallax

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Ground-based parallaxes accurate to ~0.01-arcsec • good distances out to 100 pc • < 1000 stars this close

Hipparcos satellite measures parallaxes to ~0.001-arcsec

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

New GAIA spacecraft 0.00002 arc seconds!!! • Good parallaxes for a Billion stars • Accurate (1% or better) for 20 Million stars • At the distance to the Galactic Center, individual

Parallax Limits

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Indirect distance estimate: • Measure the object's Apparent Brightness, B • Assume the object's Luminosity, L • Solve for the object's Luminosity Distance, dL, by

applying the Inverse Square Law of Bright

We to know the true luminosity of the source!

Luminosity Distances

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When we have the Luminosity "a priori”, it’s a Standard Candle. • We “build” standard candles by “Bootstraping": • Calibrate nearby objects with Parallax distances • Identify distant similar objects • Assume that the distant objects have the same

intrinsic Luminosity as the nearby objects With “calibrated candles”, you can measuring distances that are too far away for geometric methods like parallaxes. “Standardized” or “Calibrated” candles would be a better term, but “Standard” is ubiquitous

Standard Candles

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Moving cluster distances

Fundamental distance method applicable to Hyades (the nearest cluster) and slowly moving outward Stars in cluster have common space motion. But because of the perspective effect, the proper motions appear to converge on a given point in sky – the convergent point.

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Data

Proper motions of stars in the Hyades cluster, showing the convergent point located in the sky but several degrees away from the cluster itself.

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For the Hyades the moving cluster method gives mV – MV (distance modulus) = 3.25 Hence d = 44.3 pc.

This is a fundamental distance determination in astronomy, relative to which distances to other more distant objects are measured.

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Nearby clusters

Distances of some well-known clusters

Cluster distance Hyades 44 pc Pleiades 127 pc Praesepe 159 pc Sco-Cen 170 pc M67 830 pc h Persei 2250 pc χ Persei 2400 pc

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Distance-Independent Property: the star’s spectrum • Build up a calibrated H-R Diagram for nearby

stars with good parallax distances • Get Spectral Type & Luminosity Class of the

distant star from its spectrum. • Locate the star in the calibrated H-R Diagram • Read off the Luminosity • Compute the Luminosity Distance (dL) from is

measured Apparent Brightness

Spectroscopic "Parallaxes"

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The name is nonsense,picked to make it sound reliable

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Luminosity Classes are only roughly defined. • H-R diagram location depends on composition • Faint spectra give poor classifications. • Highly inaccurate for single stars, better when

fitting an entire cluster of stars

Problems:

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• A period is Distance-Independent

• Period-Luminosity Relations exist for certain classes of periodic variable stars.

• Hence, measuring the Period gives the Luminosity IF you calibrate the relationship with parallax

Some stars are very regular variables “pulsing”

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• “Eddington valve” (1917) with HeII<>HeIII (1953) • The more He is heated, the more ionized it is • Doubly ionized He is more opaque than singly • So, the more ionized, the less transparent • It tries to settle in and be “small and hot”, but

that makes it opaque and increases radiation pressure on outer layer

• It expands and cools which makes it transparent and now the radiation pressure is too low to keep it there, so it collapses….

Cepheid mechanism

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• Delta Cephei, the namesake • Polaris—the closest (Hipparcos parallax) • it’s distance estimate has changed from 133pc to

105 pc in the last 10 years!, • Eta Aquilae • Zeta Geminorum • Beta Doradus • RT Aurigae

“Famous” Cepheids

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• Four day period • Increasing 4.5s/yr • evolving through instability strip? • primary or overtone pulsation? • Ptolemy observed it, if his observations are

correct, it would be “a magnitude”, e.g. 2.5x brighter now then then. That’s 100x greater change than expected from stellar evolution

Polaris

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Rhythmically pulsating Supergiant stars, found in young star clusters • Luminosity of ~ 103-4 Lsun • Brightness changes: few percent to a factor of 2-3 • Period Range: 1 to ~50 days. • Period-Luminosity Relation: • Longer Period = Higher Luminosity • P = 3 days, L ~ 103 Lsun • P = 30 days, L ~ 104 Lsun Can see these stars out to 100Mlyr, hundreds of galaxies, a few clusters of galaxies, opportunity to calibrate something else to go further!

Cepheids: Brighter is Better!

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Problems: • No Cepheids have precise parallaxes

• some low quality with Hipparcos • the Pleiades is the right age, there just isn’t one

• Two types of Cepheids with different P-L relations (delta Cephei and W Virginis stars).

Despite problems, Cepheids (specifically delta Cephei stars) are one of the most important Standard Candles for (extragalactic) cosmic distances.

Cepheids

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Rhythmically pulsating Horizontal-Branch stars: • Found in old clusters, Galactic bulge & halo • Luminosity of ~50 Lsun • Brightness Range: factor of ~ 2-3 • Period Range: few hours to ~ 1 day. • Relatives of Cepheid Variables (mechanism) • PL Relation not as strong as that of Cepheids

Fainter, but we get the distances to old stars, tie them together with Globular Clusters (GCs) Use them in the closest galaxies None close enough for parallaxes, but GC calibrators

RR Lyrae Variables

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Uniform expansion

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The expansion of the Universe..

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Just how far are galaxies?

Distances to Galaxies

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Rung 1: Find the AU, without it, we can’t do “parallax” to nearby stars

Rung 2: Geometric methods: Find the distance to nearby clusters using parallax. The key ones are the Hyades cluster which is close and the Pleiades which is the right age for Cepheids (although it doesn’t have any…)

The Rungs of the classical distance Scale

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Rung 3: “Main sequence fitting” aka “Spectroscopic parallax”, match the main sequences in clusters with other clusters. Here, is where the Pleiades is important as it is a better “template” to match to clusters with Cepheids

Rung 4: In the old days, we got distances to a few nearby galaxies using the Cepheids P-L relation. With space telescope, this increased to dozens

Distance Scale

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Rung 5: Calibrate some property of galaxies with it’s luminosity using Cepheids for the calibrators

The typical one is to compare the internal velocity scale of galaxies (dispersions for ellipticals where the motions are mostly random called “The Faber-Jackson Relationship”, circular velocities for disks where things are moving in circular orbits, “The Tully-Fisher relationship”)

Distance Scale

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Dispersion velocities in ellipticals

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Rotation velocities in spirals

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Rung 6: With a calibrated Hubble expansion law from Rung 5, the “Hubble constant” can be used to get distances from the velocities of recession

Calibrate the Hubble expansion law

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Hubble law

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When we see a “redshift” for a galaxy, this bundles the expansion of the universe together with the peculiar motion of the galaxy (e.g. it’s motion within a cluster or another structure)

Some complications are great new areas of research

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What the Universe really looks like in redshift space…