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

# Lecture 35: The Cosmic Distance Scale

## 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!)

Cepheid P-L relation is good but limited:
• 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

Ideally, we could just use the Hubble Law:

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

No single distance method is universal.

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

1 AU = Mean Earth-Sun Distance

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

Calibrated by the AU (size of Earth's orbit).

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

Calibrated by Trigonometric 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
This is enough to reach out to the Large Magellanic Cloud (LMC).

## Step 4: Cepheids

Calibrated by cluster H-R diagrams.

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.
Only works for Spirals because you need young (Population I) star clusters for Cepheids, and Ellipticals have only old Population II stars and no young stars.

## Step 5: Galaxy Standard Candles

Look for new, very bright standard candles that will be found in both Spiral and Elliptical galaxies
• 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

Variety of techniques get used:
• 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

Calibrated by the distance to the Virgo Cluster

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

Tully-Fisher Relation for Spirals:
• 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

Calibrated against all previous steps.

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

Current critical areas:
• 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?

Measuring accurate cosmic distances is essential for answering these questions:

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.

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Updated: 2006 February 18