One of the important relations in Astronomy. It lets us Measure the distance to distance objects. Each rung on the ladder is calibrated using lower-rung calibrations. Distance Objects Technique 1-100 AU = 5-500 x 10-6 pc Sun, Solar System Radar, timing orbits, geometry 1-100 pc Nearby stars Earth-based Parallax 1000 pc Galactic stars 10,000 pc Cepheid and other Variable stars 10-100 kpc Globular clusters 0.1-1 Mpc 10-50 Mpc Cepheids (Earth Measurements) Cepheids (HST Measurements) >50 Mpc Spiral Galaxies Space-based Parallax (Hipparcos Satellite) Luminosity-Period relation Stellar Main sequence and post-main sequence fitting Luminosity-Period relation Luminosity-Period relation Tully-Fisher relation, Faber Jackson relation 1-1000 Mpc Supernovae Type Ia Light Curve Measurements
In 1925 Edwin Hubble discovered Cepheid Variables in M31 (Andromeda Nebula ). Hubble continued his search for Cepheids, and determined the distances to 18 galaxies. At the same time, V. M. Slipher at Lowell Observatory looked at velocity shifts of extragalactic nebulae using the Calcium HK lines (Ca II, like in the Sun). Distance (Mpc) 24.3 57.1 214 v=1210 km s -1 v=15,000 km s -1 v=21,600 km s -1 557 v=39,300 km s -1 Vesto Slipher (1875-1969) 871 v=61,200 km s -1
Radial velocities of nebulae measured by Slipher: NGC velocity (km/sec) 221-300 224-300 598 ~zero 1023 +200 roughly 1068 +1100 3031 + small 3115 +400 roughly 3627 +500 4565 +1000 4594 +1100 4736 +200 roughly 4826 + small 5194 + small 5866 +600 7331 +300 roughly Vesto Slipher (1875-1969)
We can compare these velocities with a three other velocities: orbital speed of the Earth around the Sun ~ 30 km/sec orbital speed of Sun around center of Galaxy ~ 220 km/sec Escape speed from our Galaxy is (Vesc) 2 = 2 G MGal / rgal With a mass of the Galaxy of 2.5 x 10 12 solar masses and a radius of 25 kpc, the escape speed is about 930 km/sec. Vesto Slipher (1875-1969)
In 1929, Hubble showed that the velocities and distances are linearly correlated, and satisfy v = H0 d where v is the recessional velocity (km/s) and d is the distance (Mpc). H0 is a constant, Hubble s Constant and has units of km s -1 Mpc -1.
The Extragalactic Distance Scale
Size of Grid x 1.01
Size of Grid x 1.02
Size of Grid x 1.03
Points the farthest away, also have moved the furthest. Size of Grid x 1.04
The Extragalactic Distance Scale
Size of Grid x 1.01
Size of Grid x 1.02
Size of Grid x 1.03
Size of Grid x 1.05
Size of Grid x 1.07
Size of Grid x 1.10
The effect of doubling the size of the Earth, as viewed from Salt lake City
Hubble initially derived a value of H0 = 500 km/s/mpc. He could only see Cepheids out to a few Mpc. For more distant galaxies, we assumed that the brightest star he could see was the same luminosity for each galaxy. In most cases the brightest star he could see was instead a Globular Cluster (containing lots and lots of stars). He perceived stars being ~100x more luminous intrinsically, thus he thought their distances must be (100) 0.5 ~ 10x nearer than they are. Hubble relation (also called Hubble Flow ) gives us a way to measure the distance of an object knowing only its redshift: v = H0 d or d = cz / H0 for z << 1. For z < 2, the approximate relation holds:
Note that H0 has units of inverse time! (km/s/mpc). Rewriting H0 = 500 km/s/mpc = 1.6 x 10-17 s -1. To estimate how long all galaxies were in the same place in space and time, calculate the time it would take for a galaxy with a velocity v to have traveled a distance d: t = d / v = d / (H0 d) = H0-1 = (1.6 x 10-17 ) -1 s = 1.96 Gyr. This gave an age to the Universe. How does this compare to other ages in this class? At the same time, physicists were solving Einstein s theory of General Relativity and coming up with an expanding Universe theory. In 1917, Willem de Sitter (1872-1935) concluded the Universe is expanded (or contracting). Einstein himself solved his equations and introduced a Cosmological Constant to keep the Universe static. In 1930, when presented with Hubble s data we recanted. He called this the biggest blunder of his career.
One of the important relations in Astronomy. It lets us Measure the distance to distance objects. Each rung on the ladder is calibrated using lower-rung calibrations. Distance Objects Technique 1-100 AU = 5-500 x 10-6 pc Sun, Solar System Radar, timing orbits, geometry 1-100 pc Nearby stars Earth-based Parallax 1000 pc Galactic stars 10,000 pc Cepheid and other Variable stars 10-100 kpc Globular clusters 0.1-1 Mpc 10-50 Mpc Cepheids (Earth Measurements) Cepheids (HST Measurements) >50 Mpc Spiral Galaxies Space-based Parallax (Hipparcos Satellite) Luminosity-Period relation Stellar Main sequence and post-main sequence fitting Luminosity-Period relation Luminosity-Period relation Tully-Fisher relation, Faber Jackson relation 1-1000 Mpc Supernovae Type Ia Light Curve Measurements
Supernovae as Distance Indicators Supernovae Type Ia (SN Ia) are special. They are probably white dwarf stars with a giant companion that is providing material to the white dwarf. Once the WD accretes a mass of 1.4 M, it explodes and destroys itself. Because SN Ia all have a common progenitor, they likely have similar properties. They are standard candles. Empirically they all have a peak maximum light of MB=MV=-19.3 +/- 0.03. All you do is measure the apparent magnitude and then you get the Distance Modulus and thus the distance! m - M = DM = 5 log (d / 10 pc) In practice, there is a correlation between the maximum brightness (MB) and the rate of decline of its light curve. This is an empirical relation, and has been calibrated. Astronomers watch the rate of decline at several wavelengths. This is the multicolor light curve shape (MLCS) method.
Supernovae as Distance Indicators Supernovae are seen in very distant galaxies, > 1000 Mpc distant
Determining the fate of the Universe depends on our ability to measure the distance to very distant galaxies (billions of light years distant) In mid-1990s methods were developed to do this with Supernovae
Determining the fate of the Universe depends on our ability to measure the distance to very distant galaxies (billions of light years distant) In mid-1990s methods were developed to do this with Supernovae
Determining the fate of the Universe depends on our ability to measure the distance to very distant galaxies (billions of light years distant) In mid-1990s methods were developed to do this with Supernovae
Supernovae as Distance Indicators The correlation between luminosity and decay time can be calibrated. One quantifies this as the time it for the flux to drop by a factor of 2. Riess et al. 1995, ApJL, 438, L17 Time since peak
Many different distance indicators can be tested against each other. Gives averages. For example, as of 1992 (Jacoby et al. 1992, PASP, 104, 599) had as the distance to the Virgo Cluster of galaxies: Method Distance (Mpc) Range (Mpc) Cepheids 15-25 29 Tully Fisher 15.8 +/- 1.5 > 100 Faber-Jackson 16.8 +/- 2.4 > 100 Type Ia Supernovae 19.4 +/- 5.0 >1000
Distance Modulus = 5 log( d / 10pc) The fact that ΩΛ is so much greater than ΩM implies expansion of the Universe is accelerating Difference between data and the best-fit model Riess et al. 1998
the fate of the Universe depends on the how much mass the Universe contains and how fast it is expanding