Brightness and Distance Measurement

1. Brightness and Distance Measurement

2. Flux and Intensity/Brightness • Flux (density) (Wm-2Hz-1) • Energy • Time • Area • Frequency/Wavelength interval • Intensity/surface brightness (Wm-2Hz-1sr-1) • Flux density / unit solid angle • Magnitude - -2.5log10(Flux density/ reference flux density) – absolute magnitude

3. Magnitude • Nova seen by Hipparchos in 134BC prompted earliest known comprehensive star catalogue - 850 stars • Hipparchos characterised brightness by “Magnitude” in the range 1 to 6. Brightest 1, the just visible 6. • We still use magnitudes • Physiology of the eye means his magnitude difference of +1 implies, in modern units, a brightness ratio of 2.512 (10(2/5))

4. Luminosity • Inverse square law • Luminosity Watts • Effects of Dust

5. Cosmic Distances • Geometry • Standard candles are objects for which we are likely to know the true luminosity. Some astronomical objects make good standard candles, but never perfect. • Standard rulers are objects for which we are likely to know the true size. Some astronomical objects make good standard rulers, but never perfect.

6. Creating a Cosmic Distance Ladder • Radar (the replacement method for Kepler’s Law, P2 ~ a3) • Parallax • Moving clusters • Cepheid Period/Luminosity Relationship • Supernovae • Redshift and Hubble’s Law

7. The Distance Chain • Radar ranging: Solar-system. • Parallax: Solar-neighborhood. • MS fitting: Milky Way. • Cepheids: Galaxies up to 30 Mpc. • WD supernovae and TF relation: Distant galaxies. • Hubble’s law: Universe.

8. The Distance Chain

9. Radar Measurements • Beam travels at speed of light, c • Measure the time it takes beam to leave Earth, • bounce off planet (or whatever), and return to Earth. • This represents the time for the beam, traveling at c, • to cover twice the distance between Earth and the • target object. 2d = c t d = ct/2 d

10. Distances to Nearby Stars Parallax : determined by the change of position of a nearby star with respect to the distant stars, as seen from the Earth at two different times separated by 6 months.

11. parallax angle Parallax • Gold standard for astronomical distances. It is based on measuring two angles and the included side of a triangle • The parallax of a star is one-half the angle • Astronomers usually say the Earth-Sun distance is 1 astronomical unit, where 1 au = 1.5x1013 cm, and measure small angles in arc-seconds. Parallax to Proxima Centauri is only 0.76” • Gold standard for astronomical distances. It is based on measuring two angles and the included side of a triangle • The parallax of a star is one-half the angle • Astronomers usually say the Earth-Sun distance is 1 astronomical unit, where 1 au = 1.5x1013 cm, and measure small angles in arc-seconds. Parallax to Proxima Centauri is only 0.76” Approximation! D = Earth-Sun distance parallax D = Earth-Sun distance parallax

12. The Nearest Stars Distance to Alpha or Proxima Centauri is ~4 x 1013 km (~4.2 light-years) Distance between Alpha and Proxima Centauri is ~23 AU Centauri is ~4 x 1013 km (~4.2 light-year

13. The Solar Neighborhood Some stars are within about 2 x 1014 km (~ 20 light-years)

14. The Solar Neighbourhood • Nearest neighbours • 66 stars within a radius of 5.18 pc • Hence So, average separation ~ 1.29 pc

15. Stellar Clusters • Stars are are often found to be moving through space in groups or clusters • two major groups are recognized • Globular clusters • Galactic clusters • loose (open) structures typically containing 100 to 1000 stars • irregular in shape and always found in the galactic plane • sizes typically range from 5 to 20 pc • typically 0.1 to 5 stars per cubic parsec

16. VS VS Moving (Galactic) Cluster Method (1) • a collection of stars that have a common space motion • Composed of stars that formed out of the same gas cloud and are moving through space along nearly parallel paths

17. Moving cluster method (2) Convergent point When seen from the Earth the stars in a moving cluster all appear to be traveling towards the same point in the sky (the convergence point) The convergence point is due to a perspective effect e.g., the convergence of parallel lines effect

18. VR VS VT Moving cluster method (3) • the projected tracks of the stars appear to converge to a point at an angle A away from the location of the cluster Sun To convergence point A

19. Moving cluster method (4) • The position of the convergence point is found by measuring the proper motions of the stars • the tracks are projected forward on a star map • Once the convergence point has been found the distance to the cluster can be determined.

20. Moving cluster method (5) • How the method works: • find the convergence point from a proper motion study of the cluster (this entails a lot of hard work) • determine the angle A for each star • pick specific stars and measure their radial velocities (VR) • key point of method is that: VT = VR tan(A) • and we also know: VT = 4.74 d(pc )m(arc. sec) • So:

21. The Hyades • The Hyades is an important cluster of stars • The cluster is used as a “standard cluster” for finding the distance to other clusters (more on this later) and for calibrating the properties of stars • It is an old galactic cluster (age ~ 6.6 x 108 yrs) • galactic clusters will typically only survive for a few billion years • Various studies find a distance of 46 pc

22. Moving cluster method (6)

23. Cepheids • Cepheid variable stars are pulsating stars, named after the brightest member of the class, Delta Cephei. • Cepheids are brightest when they are hottest, close to the minimum size. Since all Cepheids are about the same temperature, the size of a Cepheid determines its luminosity. • Thus there is a period-brightness relationship for Cepheids. • Since it is easy to measure the period of a variable star and they can be very bright, Cepheids are wonderful for determining distances to galaxies! • RR Lyrae stars

24. Cepheid Variables • Pulsating variable bright stars that follow a simple period-luminosity relation. • The longer the time period between peaks in brightness, the greater the stellar luminosity. • Cepheids are primary standard candles to determine distances in the Milky Way and other galaxies.

25. L =K P1.3 Cepheid Variables Henrietta Leavitt studied variable stars that were all at the same distance (in the LMC or SMC) and found that their pulsation periods were related to their brightnesses Polaris (the North Star) is not constant, it is a Cepheid variable!

26. Distances to Cepheids • Distance to closest Cepheid (Delta Cephei) in our Galaxy can be found using parallax measurements. This determines K in the period-luminosity relation (L = KP1. 3) • Since the period of a Cepheid is related to its absolute brightness, if you observe its period and the apparent brightness, you can then derive its distance (to within about 10%) Absolute Brightness Apparent Brightness = 4 p distance2

27. Main-Sequence Fitting • Measure parallax to nearby star cluster (Hyades, Pleiades). • Compare MS of distant cluster to that of a nearby one. • Luminosity-distance formula (chapter 13): apparent brightness=L/4d2

28. Supernova 1987A in LMC D = 47 kpc Distances to Supernovae Brightest SN in modern times, occurred at t0 Measure angular diameter of ring, q Measure times when top and bottom of ring light up, t2 and t1 Ring radius is given by R = c(t1-t0 + t2-t0)/2 Distance = R / q

29. Distances to Supernovae • Type Ia supernovae are “standard candles” • Occur in a binary system in which a white dwarf star accretes beyond the 1.4 Mo limit and collapses and explodes • Decay time of light curve is correlated to absolute luminosity

30. White Dwarf Supernovae • Cepheid distances are used to calibrate the distances to WD supernovae. • HST has been used to determine the Cepheid distance to several historical WD supernovae. • As expected WD supernovae are good standard candles.

31. Standard Rulers • Size of HII regions • Size of planetary nebulae • Size of galaxies

32. Galaxy Clusters • Calibrate galaxies in these

33. Hubble’s Law • Edwin Hubble determined the distance to M11 (1924) and other spiral galaxies using Cepheids. • In 1929, he announced that the more distant a galaxy is, the greater its redshift and hence the faster it is moving away from us. • Hubble’s law: v=H0d where v is the recession velocity, d stands for distance and H-naught is Hubble’s constant expressed in units of km/s/Mpc.

34. Using Hubble’s Law to Measure Distances • We can use a galaxy’s recession velocity to determine its distance: d=v/H0 • However, galaxies may have peculiar motions that change their velocity, particularly in the Local Group and nearby galaxy clusters. • The distances we find with Hubble’s law are only as accurate as our best knowledge of Hubble’s constant.

35. Hubble’s data

36. Hubble relation

37. Measuring Hubble’s Constant • One of the main missions of Hubble Space Telescope. • Distant Cepheids can be measured with HST up to 30 Mpc (108 l.y.) reaching the nearest galaxy clusters such as the one in Virgo. • However, this is not enough to calibrate Hubble’s constant.

38. Tully-Fisher Relation • Both the luminosity and the rotation speed of a spiral galaxy depend on the mass, and hence they are connected with a simple relation. • This relation allows to use large spiral galaxies as standard candles. • H0=65 +/-10 km/s/Mpc.

39. The Distance Chain - reminder

40. urls for Distances • http://hyperphysics.phy-astr.gsu.edu/hbase/astro/distance.html • http://curious.astro.cornell.edu • http://imagine.gsfc.nasa.gov • http://imagine.gsfc.nasa.gov/docs/ask_astro/ask_an_astronomer.html • https://sites.google.com/a/uw.edu/introductory-astronomy-clearinghouse/home • https://sites.google.com/a/uw.edu/introductory-astronomy-clearinghouse/labs-exercises/distances-to-stars-using-measured-parallax