Todd Thompson
Department of Astronomy
The Ohio State University

Key Ideas

Measuring the Hubble Parameter, H₀

Distance Methods:

Trigonometric Parallaxes

Spectroscopic Parallaxes

Cepheid Period-Luminosity Relation

Galaxy Standard Candles

Galaxy Luminosities

Redshift Distances

The Distance Problem (again!)

• 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.

Hubble's Law & its Discontents

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

The problem is, what is H₀?

Steps to the Hubble Parameter

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.

Step 1: The Astronomical Unit

Method: Geometric Triangulation

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

Permits measurement of:

• Trigonometric Parallaxes.

Step 2: 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

Step 3: Spectroscopic Parallaxes

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

Step 4: Cepheids

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.

Step 5: Galaxy Standard Candles

• 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)

Step 5 (cont'd): The Bottom Line

• 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 H₀

Step 6: Galaxy Luminosities

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 H₀ 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.

Step 6 (cont'd): Specific Techniques

• 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)

Step 7: Redshift Distances

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.

Current Status

• 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: H₀ = 70 +/- 7 km/sec/Mpc

• Many methods give consistent answers

Why do we care?

What is the Hubble Parameter (H₀)?

• 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.