Surveying outside the solar system 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 1 Geometric Distances: the gold standard Solar system Stars • orbit geometry • parallax • radar ranging 2 Parallax Limits 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 3 Luminosity Distances 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! 4 Standard Candles 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 5 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. 6 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. 7 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. 8 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 9 Spectroscopic "Parallaxes" 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 10 The name is nonsense, picked to make it sound reliable 11 Problems: 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 12 Some stars are very regular variables “pulsing” • 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 13 Cepheid mechanism • “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…. 14 “Famous” Cepheids • 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 15 Polaris • 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 16 Cepheids: Brighter is Better! 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! 17 Cepheids 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. 18 RR Lyrae Variables 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 19 Cosmic Distance Scale We will have to define and revisit this when we talk about the expansion of the Universe 20.