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## The Cosmic Distance Scale

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**The Cosmic Distance Scale**Laura A. Whitlock / Sonoma State U Rohnert Park, CA**Outline**• A quick review of notation and units • An examination of Distance • Measuring inside our solar system • Measuring to “nearby” stars • Measuring distant objects • Measuring the Universe Remember: Big or small, numbers are given meaning in our Universe!**Powers of Ten**• Scientific Notation • 10n means 10 x 10 x 10 x 10 … [n times] • 10-n means 1/(10 x 10 x 10 ….) [n times] • There are 1010 –1011 stars in our Galaxy, and a similar number of galaxies in the Universe**And remember...**To Multiply & Divide 10a •10b = 10 a + b 10a ÷10b = 10 a - b**How Many Grains of Sand?**If Earth were made of sand, would it contain more or less than a googol (10100) grains of sand? • Draw a 1 cm segment. Mark pencil points along the segment to get an estimate of the number of tightly packed grains of sand in 1 linear cm. • Calculate the number of grains of sand in 1 cubic km. (Remember: 100 cm = 1 m , 1000 m = 1 km) • Earth’s radius is about 6400 km. Use the equation for the volume of a sphere {V = (4/3)pr3} to calculate the number of grains in a sandy Earth.**A Quick Tour from the Unimaginably Tiny to the**Incomprehensibly Big**Powers of Ten**…an oldie, but a goodie!**Units for Time and Distance**• Kilometer (km) = .621 miles • Light-year (lt-yr) = The distance light travels in one year in a vacuum. 1 lt-yr = 9.5 x 1012 km • Parsec = 3.3 light-years (Mpc = 1,000 pc) • arc-second = (1 degree/3600)**Creating a Cosmic Distance Ladder**• Radar (the replacement method for Kepler’s Law, P2 ~ a3) • Parallax • Cepheid Period/Luminosity Relationship • Supernovae • Redshift and Hubble’s Law**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**But...**Radar techniques are only feasible for objects inside our solar system. We need a longer ladder!**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**The Solar Neighborhood**Some stars are within about 2 x 1014 km (~ 20 light-years)**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.**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. Arc-seconds are often denoted by ¢¢, just like inches. But don’t be confused! Approximation! D = Earth-Sun distance parallax**Historical Note**The first stellar parallax (of the star 61 Cygni) was measured by Friedrich Wilhelm Bessel (1784-1846) in 1838. Bessel is also known for the Bessel functions in mathematical physics.**Parallax**Parallax to Proxima Centauri is only 0.76 ¢¢**So...**Only the nearest stars to us have a measurable parallax. We need a longer ladder!**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!**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!**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**If no Cepheids can be seen...**We need another ladder!**Crab Nebula**• Observed by Chinese astronomers in 1054 AD • Age determined by tracing back exploding filaments • Crab pulsar emits 30 pulses per second at all wavelengths from radio to TeV**Infrared/Keck**Radio/VLA Crab Nebula**Optical/Palomar**Optical/HST WFPC2 Crab Nebula**X-ray/Chandra**Crab Nebula and Pulsar**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**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 • Good to 20% as a distance measure**But to really“measure the Universe”...**We need a ladder and a theory to stand it on!**Historical Note**• Edwin Hubble discovered that the Universe is expanding!**What Hubble Found**The Hubble constant Ho = 558 km s -1Mpc -1 is the slope of these graphs Compared to modern measurements, Hubble’s results were off by a factor of ten!**Hubble’s Law**• v = Ho * d Ho is called the Hubble constant. It is generally believed to be around 65 km/sec/Mpc… plus or minus about 10 km/sec/Mpc. • Note: The further away you are, the faster you are moving!**Implications of Hubble’s Law**Distance = velocity/(Hubble constant) • To get a rough idea of how far away a very distant object is from Earth, all we need to know is the object's velocity. • The velocity is relatively easy for us to measure using the Doppler effect, or Doppler shift.**Doppler Shift**Wavelength is shorter when approaching Stationary waves Wavelength is longer when receding**What It Looks Like**Comparison of laboratory to blue-shifted object Comparison of laboratory to red-shifted object**v**l - lo Dl = = = z l c lo Doppler Shift / Redshift Redshift, z, is a non-relativistic approximation to the Doppler shift**Hubble’s Law Revisited**• v = Ho d = cz • where • v = velocity from spectral line measurements • d = distance to object • Ho = Hubble constant in km s-1 Mpc -1 • z is the redshift Space between the galaxies expands while galaxies stay the same size**Example**A certain absorption line that is found at 5000Å in the lab is found at 5050Å when analyzing the spectrum of a particular galaxy. We then conclude that this galaxy is moving with a velocity v = (50/5000) * c = 3000 km/sec away from us. Putting it altogether now, if the object is moving away from us at 3000 km/ sec, its distance from us (according to the Hubble’s Law) is d = v/Ho = 3000/65 = 46 Mpc or 1.4 x 108 light-years**And so the Universe is...**v = H0d and d =vt Solving for t, we find the age of the Universe is: t ~ 1/H0 If H0 = 65 km/s/Mpc, then the age of the Universe is ~ 16 x 109 yr or 16 billion years**Books and Slides**• Mitton, Jacqueline and Mitton, Simon, Scholastic Encyclopedia of Space, Scholastic Inc., 1998. • Fraknoi, Andrew, A Grand Tour of the Universe Slide Set, Astronomical Society of the Pacific.**Videos**• Powers of Ten: $39.95 through the Astronomical Society of the Pacific Catalog. http://www.aspsky.org/catalog/vt110.html or write to: ATTN: Catalog, ASP, 390 Ashton Ave, San Francisco, CA 94112 • Cosmic Voyage: $29.95 through the Astronomical Society of the Pacific Catalog. http://www.aspsky.org/catalog or write to: ATTN: Catalog, ASP, 390 Ashton Ave, San Francisco, CA 94112**Web**• Cosmic Distance Ladder – 3 labs - http://www.astro.washington.edu/labs/Distance_Ladder.html • Extragalactic Cosmic Distance Scale - ttp://www.uq.edu.au/~phjross/ph227/galaxy/candles.htm • Cosmic Distance Ladder I: Parallax - http://209.52.189.2/article.cfm/astronomy/11999 • Cosmic Distance Ladder II – Stars as Standard Candles - http://209.52.189.2/article.cfm/astronomy/13217**More Web**• Seeing is Believing! – Determining the Distance to Venus http://www.amtsgym-sdbg.dk/as/venus/ven-dist.htm • Stellar Parallax Lab http://einstein.uhh.hawaii.edu/spacegrant/lab2/lab2.html**More Web**• Cosmic Distance Scale http://csep10.phys.utk.edu/astr162/lect/cosmology/cosmicd.html • Cepheid Variables and the Cosmic Distance Scale Lab http://einstein.uhh.hawaii.edu/spacegrant/lab4/lab4.html**Wrap Up…at long last!**• Presentation will appear at http://perry.sonoma.edu/nbsp/materials/distances.html Thanks for coming!