The Extragalactic Distance Scalepeople.physics.tamu.edu/.../lecture_distance_ladder.pdfThe Extragalactic Distance Scale Note that H 0 has units of inverse time ! (km/s/Mpc). Rewriting

The Extragalactic Distance ScaleOne 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 Space-based Parallax (Hipparcos Satellite)

10,000 pc Cepheid and other Variable stars

Luminosity-Period relation

10 -100 kpc Globular clusters Stellar Main sequence and post-main sequence fitting

0.1 - 1 Mpc Cepheids (Earth Measurements)


10-50 Mpc Cepheids (HST Measurements)


>50 Mpc Spiral Galaxies Tully-Fisher relation, Faber Jackson relation

1 - 1000 Mpc Supernovae Type Ia Light Curve Measurements

Saturday, January 5, 2013

The Extragalactic Distance Scale

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).

Vesto Slipher (1875-1969)

Distance (Mpc)

24.3

57.1

214

557

871

v=1210 km s-1

v=15,000 km s-1

v=21,600 km s-1

v=39,300 km s-1

v=61,200 km s-1




Radial velocities of nebulae measured by Slipher:

NGC velocity (km/sec) 221 -300 224 -300 598 ~zero1023 +200 roughly1068 +11003031 + small3115 +400 roughly3627 +5004565 +10004594 +11004736 +200 roughly4826 + small5194 + small5866 +6007331 +300 roughly




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 1012 solar masses and a radius of 25 kpc, the escape speed is about 930 km/sec.


The Extragalactic Distance ScaleIn 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.





Size of Grid x 1.01



Size of Grid x 1.02



Size of Grid x 1.03



Size of Grid x 1.04

Points the farthest away, also have moved the

furthest.





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”.


The Extragalactic Distance ScaleOne 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 Space-based Parallax (Hipparcos Satellite)

10,000 pc Cepheid and other Variable stars


10 -100 kpc Globular clusters Stellar Main sequence and post-main sequence fitting

0.1 - 1 Mpc Cepheids (Earth Measurements)


10-50 Mpc Cepheids (HST Measurements)


>50 Mpc Spiral Galaxies 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 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











Riess et al. 1995, ApJL, 438, L17

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.

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



Riess et al. 1998

Distance Modulus= 5 log( d / 10pc)

Difference between data and the best-fit

model

The fact that ΩΛ is so much greater than ΩM implies expansion of the

Universe is accelerating


the fate of the Universe depends on the how much mass the Universe contains and how fast it is expanding



Documents

The Extragalactic Distance Scalepeople.physics.tamu.edu/.../lecture_distance_ladder.pdfThe Extragalactic Distance Scale Note that H 0 has units of inverse time ! (km/s/Mpc). Rewriting