Astronomy 162:
Introduction to Stars, Galaxies, & the Universe Prof. Richard Pogge, MTWThF 9:30 |

- Measuring the Hubble Parameter, H
_{0} - Distance Methods:
- Trigonometric Parallaxes
- Spectroscopic Parallaxes
- Cepheid Period-Luminosity Relation
- Galaxy Standard Candles
- Galaxy Luminosities
- Redshift Distances

- Limited to ~30-40 Mpc (Hubble Space Telescope)
- Very laborious to use (100's of HST orbits)
- Only works in Spiral or Irregular galaxies
- Only practical out to the Virgo Cluster

This is only next-door in cosmic terms, so we need to seek other methods to estimate very large cosmic distances.

At least nearby, all you need to measure is the cosmological redshift, z, in order to get the distance.

The problem is, **what is H _{0}**?

Must work towards large distances from nearby.

Bootstrap Process:

- Build up from near to far.
- Each step
**calibrates**the next step. - Errors made in early steps affects the accuracy
of
**all**following steps.

Method: Geometric Triangulation

- Radar bounced off inner planets.
- Orbits of planets give the geometry.
- Works throughout the Solar System

Permits measurement of:

- Trigonometric Parallaxes.

Method: Measure stellar parallax angles

- Use Earth as the baseline.
- Ground-based: works out to ~100 pc
- Space-based: works out to 500 - 1000 pc (Hipparcos)

Permits measurements of:

- Luminosities of nearby stars
- Distances to nearby star clusters

Method:

- Relate spectral type to luminosity in calibrated H-R Diagrams.
- Works OK for individual stars.
- Works best for
**clusters**of stars

Permits measurements of:

- Distances to star clusters out to ~50-100 kpc

Method:

- Cepheids: supergiants in young clusters
- Calibrate the Period-Luminosity Relation in the LMC.

Cepheids give distances to:

- Nearby spiral galaxies out to about 30-40 Mpc.

- Type Ia Supernova explosions
- Planetary Nebula luminosity distribution
- Globular Cluster luminosity distribution

Calibrated by:

- Cepheid Period-Luminosity distances to spirals
- Nearby similar objects (from other steps)

- Mix and match to seek consistent results.
- All rely on previous steps, especially Step 4.
- Argue endlessly about the details.

Bottom Line:

- Work out 50-200 Mpc, depending on the method.
- Gives distances to Virgo Cluster galaxies (Spirals and Ellipticals)
- Gives a local estimate of H
_{0}

Method:

- Assume distant galaxies are like nearby ones.
- Find correlations between the luminosity & distance-independent properties of the galaxies.
- Compute a luminosity distance using entire galaxy.

Seek a refined estimate of H_{0} out to greater distances that
gets you beyond the regime where the random (aka "peculiar") velocities
of galaxies due to their orbits around each other or within groups are
important.

- Galaxy Luminosity - Rotation Speed relation
- Rotation speed from 21-cm radio emission (distance independent)

Fundamental Plane Relation for Ellipticals:

- Galaxy Luminosity - Line Width - Size relation
- Measure absorption-line widths from spectra (distance independent)

Method:

- Measure the redshift of a galaxy with spectra.
- Use the estimate of the Hubble Parameter.
- Assume pure "Hubble Expansion" or attempt to correct
for random galaxy motions
**statistically**.

Allows us to probe the Universe on the largest scales observable.

- The most critical is the distance to the LMC, which calibrates the extragalactic Cepheids P-L relation.
- Refinement of other standard candles, especially Type Ia supernovae which could work out to 1000 Mpc.
- Statistical assessment of the random motions of galaxies.

Best Estimate: **H _{0} = 70 +/- 7 km/sec/Mpc**

- Many methods give consistent answers

What is the Hubble Parameter (H_{0})?

- Current expansion rate of the Universe.
- Leads to an estimate of the Age of the Universe.

What is the expansion *history* of the Universe?

- Would tell us the ultimate fate of the Universe.

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Updated: 2006 February 18

Copyright © Richard W. Pogge, All Rights Reserved.