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This week at Astro 3303 • I’m teaching for the next 3 weeks • HW#6 is due Wednesday • If you need help, please email/visit me! • HW#7 will be posted Wed; HW #8-10 deal with your final project! • 2nd 30min test is Nov 11. Covers material through Wed Nov 6. • Today: • Relativistic Doppler formula and why we need cosmology • Determining distances: the extragalactic distance scale • Reading: • Chapter 4; start looking at Chapter 5 Evidence for the Big Bang Model • Olber’s paradox: (Heinrich Olbers: 1823) • The sky is dark at night. • Hubble’s Law & the expansion of the Universe (Edwin Hubble: 1927) • If the universe is finite in space and time and is expanding, it must have been smaller in the past. • The Cosmic Microwave Background (CMB) Radiation (Arno Penzias and Robert Wilson: 1965) • Thermal spectrum with equivalent temperature of 3 degrees => 3 degree blackbody radiation = CMB • Abundance of the elements via primorial nucleosynthesis • The large scale structure of the universe: the way galaxies are seen today to cluster into groups, clusters and superclusters. Large Scale Structure Our cosmological model must explain how the structure developed to look this way (and not something else) and it has to do it in 13.7 billion years (not earlier, not later) Smoother earlier on Time => Galaxies, clusters, superclusters and voids today Early History • Slipher (~1912) noticed that spiral nebulae showed almost predominantly redshifts. • By 1925 he had radial velocities for 40 galaxies • Hubble used the 100-inch telescope on Mt. Wilson to measure distance to 18 galaxies • Found linear relation between increasing redshift and increasing distance, now known as Hubble’s law Ho d = v ~ cz • Of course. A major goal of HST has been to measure Ho ~ 72 km/s/Mpc Sometimes use Ho ~ 100 h km/s/Mpc = (1010 yrs)-1 Hubble’s Law The dominant motion in the Universe is the smooth expansion known as the “Hubble flow”. Hubble’s Law: Vobs= HoD where Ho is Hubble’s “constant” and D is distance in Mpc Spread in velocity for objects in a cluster due to their orbital motion within the cluster. “redshift” z = An object at z is receding at velocity: λ(obs) - λ(rest) λ(rest) = (z+1)2 -1 V = (z+1)2 +1 c 1+v/c 1-v/c –1 Note that as vc, z > 1 Relativistic Doppler Formula • We observed galaxies/quasars with redshifts of ~7-10 • That does not mean that they are traveling faster than the speed of light This reduces to the simple Doppler formula for v << c. For z= 10, this becomes v=c 1 -( ) 1 11 2 = 0.995 c In fact, the Cosmic Microwave Background photons have a redshift z = 1000! Distant galaxies • The galaxy ON-108036 • It has a redshift of 7.2. • That redshift corresponds to a “look back time” of 12.9 Gyr, or an epoch of only 749 Myr after the Big Bang occurred. • PE #11: What is its recessional velocity? (The galaxy with z~10.3 is still unconfirmed; this one is for sure.) Distant galaxies • The galaxy ON-108036 • It has a redshift of 7.2. • That redshift corresponds to a “look back time” of 12.9 Gyr, or an epoch of only 749 Myr after the Big Bang occurred. V = 0.992 c What stars have MS lifetimes of 750 Myr? (see PE#3) Measuring extragalactic distances Primary distance methods: • Measure distance to some “standard candle” (object whose luminosity you can infer) within the galaxy • Works for nearest systems (where e.g. we can resolve the individual stars) or, in very special cases, also for distance systems. Hubble’s Law: • Observationally “low-cost” (but not exactly “cheap”) • Measure the redshift => measure the distance • Need to worry however about orbital motions in groups/clusters (and other similar effects) Determining distances • Parallax • Good for nearby stars; not for extragalactic objects… until now/soon! • Method of spectroscopic parallax • Need to know position of object(s) on H-R diagram • Can be used for nearby galaxies where we can detect the stars individual (“resolved stellar populations”) • “Tip of the Red Giant Branch” • Cepheid Period-luminosity relation distances • Can be used for relatively nearby objects (distances closer than about 50 million light years) • Similar method used for Supernovae Type 1a • Hubble’s Law • Works as long as we understand the “tricks” Cosmic distances • Because of the Earth's revolution around the Sun, nearby stars appear to move with respect to very distant stars. • The parallax of a star is the apparent angular size of the ellipse that a nearby star appears to trace against the background stars. • A parsec is the distance at which a star would be if its parallax where exactly 1 second of arc. 1 A.U. = Astronomical unit = Mean Earth-Sun distance 1 parsec = 3.26 light years = 206265 A.U. Distance from Sun to center of Milky Way ~ 8.0 kpc Distance from Milky Way to Andromeda ~ 800 kpc (2.9 million lt yr) Local Group Proper Motions • 1920s van Maanen claimed to see M33 spin! • mas/yr motions Spiral nebulae nearby (Galactic) • Hubble argued more distant (extra-galactic) • van Maanen’s error not found M33 Extragalactic Masers • Seen in lines of OH, SiO, methanol and H20. • MASER stands for Microwave/Molecular Amplification by Stimulated Emission of Radiation. As proposed by Einstein in 1917, an electron (or an excited molecular state) interacting with an e-m wave of a certain freq may drop to a lower energy level, creating a new photon with the same phase, frequency, polarization and direction of travel as the photons of the incident wave. A “maser” occurs when atoms have been induced into an excited energy state and amplify the radiation at the proper frequency. • Arise in cool molecular regions near sites of massive star formation; the UV radiation acts to “pump” the stimulated emission. • Individual maser components have typical sizes of 1012m (corresponding to 0.01 arcsec at 1 kpc; unresolved in extragalactic objects), and are arranged in clusters typically 3·1014 - 1015 m (~ a few arcsec) in diameter. In some active galaxies, we observe “megamasers”. Micro-arcsec Astrometry with the VLBA Fringe spacing: qf~l/D ~ 1 cm / 8000 km = 250 mas Centroid Precision: 0.5 qf / SNR ~ 10 mas Systematics: path length errors ~ 2 cm (~2 l) shift position by ~ 2qf ~ 500 mas Relative positions (to QSOs): DQ ~ 1 deg (0.02 rad) cancel systematics: DQ*2qf ~ 10 mas Extragalactic Proper Motions • Parallax accuracy: sD ~ 10% at 10 kpc (can’t do galaxies yet) M33 • Proper motion: same techniques, but sm ~ T-3/2 • M33 & IC10 1) see spin (van Maanen) 2) see galaxy’s motion Andreas Brunthaler’s PhD Thesis Extragalactic Proper Motions • M33/IC133 – M33/19 masers VLBA: Dmx = 30 +/- 2, Dmy = 10 +/- 5 mas/yr HI: Dvx = 106 +/-20, Dvy = 35 +/- 20 km/s D = 750 +/- 50 +/- 140 kpc sm sv • Improvements in Rotation Model & 3rd maser source: sD < 10% possible Brunthaler, Reid & Falcke The method of “spectroscopic parallax” 1. Observe the star’s apparent brightness. 2. Observe the star’s spectrum; determine its spectral class and luminosity class. 3. Place the star on the H-R diagram; estimate its luminosity. 4. Use luminosity and apparent brightness to get distance. Good for normal stars, clusters of stars, some very nearly galaxies (tip of the red giant branch) TRGB Tip of the Red Giant Branch 2.Observe their apparent brightness Apparent brightess 1. Assume that the bright stars at the tip of the red giant branch always have the same luminosity faint blue color red Cepheid Variables • Cepheid variables: Analogs of the star Ceph • Giant, post-main sequence stars which pulsate due to instabilities. • As the envelope of the star expands and contracts, the star’s brightness changes. http://zebu.uoregon.edu/~soper/StarLife/cepheid1.gif Cepheid Variables • Cepheid variables: Analogs of the star Ceph • Giant, post-main sequence stars which pulsate due to instabilities. Apparent brightness varies over time in repeated fashion http://www.astro.lsa.umich. edu/Course/MMSS/Intera ctive/Ex1.4/lightcur.jpg Cepheid Period-Luminosity Relation • Henrietta Leavitt discovered a relationship between the period of pulsation and the mean luminosity of the star. 1. Identify the star as a Cepheid variable by studying its spectrum (if possible) and/or by the shape of its lightcurve. 2. Calculate its period. 3. Use the Period-Luminosity relationship to determine the Luminosity. 4. Use the inverse-square law to calculate how far a star of that luminosity would have to be in order to appear as a star of that observed apparent brightness. http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit4/plrelation.gif HST Key Project Main goal: determine Ho to within 10% by observing Cepheids in nearby galaxies. PE #12: NGC 4258 as a case study PE #12: NGC 4258 as a case study Composite image: • Yellow: optical • Purple: radio continuum • Blue: X-ray • Red: Spitzer IR X-ray/radio continuum arms (purple/blue) are offset from the stars/gas/dust arms. X-ray/radio arms not seen in optical; appear associated with shocked material and the SMBH NGC 4258 • BVI survey of 2 fields using HSTACS + 1 previously done with HSTWFPC2 • 281 Cepheids with periods from 4 to 45 days • Observed 12 separate epochs 12/03 to 1/04 Macri+ 2006, ApJ 652, 1133 NGC 4258 Color composite images • Inner field (left) • Outer field (right) Macri+ 2006, ApJ 652, 1133 NGC 4258 • Master V-band image of inner field. • Locations of Cepheids shown (circles) Macri+ 2006, ApJ 652, 1133 NGC 4258 • Individual finding charts for the Cepheids. • Each image is 2.5 arcsec on a side. Macri+ 2006, ApJ 652, 1133 NGC 4258 • CMD of outer field • Cepheids are filled/open • Other stars in small dots • Dashed/solid lines represent spread in LMC Cepheids • Arrow indicates effect of internal selective extinction E(B-V) = 0.2 mag Macri+ 2006, ApJ 652, 1133 NGC 4258 • CMD of inner field • Cepheids are filled/open • Other stars in small dots • Dashed/solid lines represent spread in LMC Cepheids • Arrow indicates effect of internal selective extinction E(B-V) = 0.2 mag Macri+ 2006, ApJ 652, 1133 NGC 4258 • Representative light curves of Cepheids in inner field Blue: B Green: V Red: I Macri+ 2006, ApJ 652, 1133 NGC 4258 • BVI periodluminosity relations for the brighter Cepheids in the inner field • Lower right shows period-luminosity relation adopted using combination of methods and extinction They use the maser distance (next) and the P-L relation for LMC to get Hubble constant Macri+ 2006, ApJ 652, 1133 H2O maser in NGC4258 • Radiospectroscopy and VLBI of H2O molecules reveal a thin disk in Keplerian rotation. • Rotation and distance yield an enclosed mass of Keplerian Disk M 4 x 107 M within 0.3 lightyears. Miyoshi et al. (1995), Herrnstein et al. (1997), Humphreys et al. (2008) NGC 4258 NGC 4258 NGC 4258 H20 masers at 22 GHz VLBA @ 22 GHz • Angular resolution ~ 200 µas (microarcsec) • Spectral resolution ~ 1 km/sec • Radial velocity (l.o.s.) = GM/R sin θ where θ is the azimuthal angle in the disk measured from the BH, R is the radial distance from the BH, M is the mass of the BH. Close to l.o.s., sin θ ~ b/R, where b is the impact parameter, so Vz ~ b GM/R3 NGC 4258 Over time, masers are tracked as they orbit, and eventually disappear from sight. Their velocities increase by about 8 km/s/yr from 430 km/s to 530 km/s; we only see them when their maser emission is beamed along the l.o.s. Geometric distance: • Measure their doppler shifts => km/s • Measure the proper motions of the masers over time => “/year • Comparison of the angular velocities in the latter measurement with the absolute velocities in km s-1 in the former measurements yields the distance. Distances to far off galaxies: SNeIa • 1998 and 1999: Two independent teams studying exploding stars in very distant galaxies found that the galaxies are further away than predicted! The universe is expanding, but…. The expansion is accelerating! Dark energy!? SN in M51 Distant SNeIa SNe Types SNeIa Using SNe to determine distances • What measurements would you make? • Observe the supernova suddenly brighten, then fade over time. • Identify it as a SN of Type Ia from its “light curve” (how it brightens and fades) and probably from taking spectra (which shows heavy elements like chromium, aluminum, etc) • What assumptions would you need to invoke? • That all SN of Type Ia have the same luminosity when they are at their maximum apparent brightness, i.e. that SNeIa are “standard candles”. • So, if we observe a supernova’s light curve and apparent brightness, we can derive its distance. • Then we can compare that distance to the distance we expect from its redshift and Hubble’s law => any differences tell us about the geometry of the universe. Determining distances from SNe • What measurements would you make? • Observe the supernova suddenly brighten, then fade over time. • Identify it as a SN of Type Ia from its “light curve” (how it brightens and fades) and probably from taking spectra (which shows heavy elements like chromium, aluminum, etc) • What assumptions would you need to invoke? • That all SN of Type Ia have the same luminosity when they are at their maximum apparent brightness. • That you can properly account for dust obscuration within the galaxy in which the SN resides. • How do you derive the distance to a galaxy with a SNeIa? • Now we have: luminosity and apparent brightness. • Remember that: Luminosity => distance Apparent brightness (Distance)2 Using SNe Ia as standard candles Velocity = c X z Apparent brightness • Identify a set of objects whose luminosity is taken to be constant: “standard candles” ??? • Then plot their apparent brightness versus their redshift • => Determine “Hubble’s Law” over large distances Redshift z (or velocity) NOTE: for small z, cz ~ recessional velocity c X z = H(t) x Distance “Hubble parameter” units: (km/s)/Mpc • We assume all SnIa reach the same maximum luminosity. • Then we observe the maximum apparent brightness. Faint Apparent brightness • Type Ia supernovae as “standard candles” Evidence for acceleration • => They appear to be too Bright faint/further away! => Acceleration Distant SNeIa appear fainter than we expect Applies on small scales