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Galaxy NGC4414 from HST Astronomy 162:
Introduction to Stars, Galaxies, & the Universe
Prof. Richard Pogge, MTWThF 9:30

Lecture 22: The Cosmic Distance Problem

Readings: Ch 26, section 26-4

Key Ideas

Geometric Distances
Trigonometric Parallaxes

Luminosity Distances
"Standard Candles"
Spectroscopic Parallaxes
Cepheid Variables
RR Lyrae Variables

The Distance Problem

Measuring accurate distances remains the biggest technical problem in Astronomy.

Distances are necessary for estimating:


Geometric Distances

Direct measurements of distances using geometry.

Solar System Distances:

Stellar Distances:


(Click on the image to view at full scale [Size: 7Kb])


Parallax Limits

Ground-based parallaxes are measured to ~0.01-arcsec

Hipparcos satellite measures parallaxes to ~0.001-arcsec


Luminosity Distances

Indirect distance estimate:
Luminosity Distance Formula

We call this the Luminosity Distance (dL) to distinguish it from distances estimated by other means (e.g. geometric distances from parallaxes).

The only observable is the object's Apparent Brightness, B. The missing piece is the luminosity, (L), which must be inferred in some way.


Standard Candles

Any object whose Luminosity you know ahead of time ("a priori") is known as a Standard Candle.

The way you establish that a class of objects is a standard candle is via a multi-step calibration procedure known as the "Bootstrap Method".

Bootstrap Method:

Once you have a calibration of a set of standard candles, you can then apply them to measuring distances to objects that are too far away for geometric methods like parallaxes.

Spectroscopic "Parallaxes"

Distance-Independent Property:

Physics:

Method:

Spectroscopic Parallaxes
NOTE: Despite the name, the method has nothing to do with measuring geometric "parallaxes".

Distance Limit:

Problems:

While somewhat difficult to use accurately for individual stars, the method of spectroscopic parallaxes works best for clusters of stars where you can average over many measurements.

Periodic Variable Stars

Stars whose brightness varies regularly with a characteristic, periodic (repeating) pattern.

Distance-Independent Property:

Physics:

Schematic Period-Luminosity Relationship

Cepheid Variables

Class of rhythmically pulsating Supergiant stars:

Period-Luminosity Relation:

Method:

Cepheid P-L Relation Distance Determination

Distance Limit:

Problems:

Despite the limitations and problems, Cepheid Variable Stars (specifically delta Cephei stars) are one of the most important Standard Candles we use to measure cosmic distances.

RR Lyrae Variables

Rhythmically pulsating Horizontal-Branch stars:

Period-Luminosity Relation:

Method:

Distance Limit:

Problems:


The Cosmic Distance Scale

No single method will provide distances on all cosmic scales. Instead, we have to rely on a multi-step approach that is carefully calibrated at each step.

This makes the Cosmic Distance Scale look like a ladder with a series of steps going from near to far:

Inaccuracy and imprecision at each step carries forward into the next, making each subsequent step less accurate.

Part of the challenge is to understand the sources of these inaccuracies and taking them into account.


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Updated: 2006 February 5
Copyright Richard W. Pogge, All Rights Reserved.