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

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: 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.