University Lowbrow Astronomers

How Far Is Far?

by Lorna Simmons
Printed in Reflections:  October, 1999.

Have you ever wondered how distances in the universe are calculated?  Have you ever been fascinated by the methods used by astrophysicists and cosmologists to search the great unknown?

If we are going to take such an exciting journey, it always starts with that first step.  Although today, there are laser measurements and radar calculations in use for distances in the Solar System.  These measurements would hardly work for the farther objects in the universe, which often are the distances cosmologists really want to know more about.

With the very first rungs of the cosmological distance ladder, after radar and lasers, of course, everything heats up.  Tempers flare.  Friendships are lost.  Personal preferences of the various cosmologists roil the waters of controversy.  Skirmishes turn into battles into wars.  So much in cosmology depends upon the measurements of these distances that winning becomes all in the minds of the combatants.  There is ever present the incredibly difficult task to determine absolutely correct uncertainties for each of the observations.  The errors are usually underestimated, seldom overestimated.  Perhaps I exaggerate too much, but sometimes it seems like a battle.  Cosmology is a hot topic.  Reputations are at stake.

At this moment, we are on the verge of a breakthrough where precise observations will be able to reveal the secrets of distances in the universe.  Because the distance scale leads to calculations of the age of the Universe, its rate of expansion, its density, and inevitably its destiny, such measurements are of immense importance in cosmology.  However, that task is extremely arduous.  On the ladder, every rung depends on previous lower rungs.  A tiny error in the calibration of each rung will magnify the computational errors of measurements farther out on the ladder.  Pretty messy.

It is best to split up the distance indicators into groups - primary and secondary.  The indicators of the primary groups are calibrated from measurements in our very own Milky Way, and the secondary indicators rely on at least one of these primary indicators.  Therefore, the secondary indicators become increasingly less reliable as we get farther out on the distance scale.

Primary Group

To begin our journey up the cosmological distance ladder, the parallax method of determining distance is fundamental to all of the others.  It is the most certain of methods for determining distances outside of the Solar System.  The parallax method uses the elliptical orbit of the Earth around the Sun to determine the baseline for its measurements of the slight changes in the placement of the nearest stars.  Distances to stars within approximately 40 parsecs (pc) can easily be calculated using a simple trigonometry.  An angle is measured in arcseconds at one point of Earth’s orbit, and six months later, at the opposite position of Earth’s orbit, another measurement of the angle in arcseconds is taken.  The slight difference of the observed movement of the celestial object with relation to the seemingly fixed stars creates an angle which subsequently provides the distance to that object in parsecs, one parsec equaling 3.2616 light years (ly).  Note that the recent Hipparcos satellite observations seem to be increasing the range of such parallax measurements to at least 100 parsecs.

Using parallax methods, we next move to the standard candles, of which the Cepheid variables are of first importance.  Cepheid variables are large and very luminous yellow giant stars or supergiants with regular periods of pulsation from about 1 to nearly 70 days.  Over 700 Cepheids have been detected in our own Milky Way and a few thousand Cepheids can be seen in our Local Group of galaxies.  Changes in brightness of Cepheid variables are accompanied by changes in their stellar temperatures and in their radii.  A ratio exists between their periods of pulsation and their light variation (period-luminosity).  The distance to the Cepheids is calculated by measuring their brightness and their periods of brightening.  In other galaxies, noting the periods of the brightening would help determine the distances to such galaxies.  Moderately great distances in the universe can be calculated using Cepheids, although the uncertainties are still very large.

RR Lyrae stars, which are also pulsating variable stars similar to the Cepheid variables, are old population II stars and are common in globular clusters.  Their metallicity and absolute magnitudes are compared, making RR Lyrae stars a major rung up in the cosmological distance ladder.  However, because RR Lyrae have low luminosities they cannot be used much farther than M31, limiting their use.

Many other similar stellar methods exist.  Statistical parallaxes measure radial velocities and the proper motions of groups of stars to calculate distances in the universe to approximately 500 pc.  Other similarly luminous stars, such as W Virginis stars and Mira variables also have a period-luminosity relation.  The brightest red giants in globular clusters are helpful in measuring the distance ladder as are the eclipsing binaries where both spectroscopy and photometry are useful in recording the colors.  Farther out on the ladder, cosmologists obtain exceedingly accurate measurements of the nearest open clusters using the Cepheid Variables in these clusters.  And the Cepheids in these clusters will open the possibility for a new and better calibration of the important period-luminosity relation for Cepheids.

Another way of measuring the universe is the converging-point method, using the proper motion of open clusters.  The average velocities of open clusters is compared to that of the Sun and is large with respect to the proper motions of stars.  Hence, those stars can be thought of as moving toward the same point in the universe.  For example, the distance to the Hyades can be determined using this method.  Next, another method called “main-sequence fitting” compares the apparent magnitude with the absolute magnitude of a star, permitting the distance to that cluster to be calculated.

Secondary Group

There are a number of secondary distance indicators for measuring even farther out into the universe.  First, there is the Tully-Fisher relation which uses spiral galaxies to calculate distances easily; well, almost easily for professional cosmologists.  There are several versions of the Tully-Fisher relation.  The first type measures the absolute magnitude of the galaxy, while the second type uses the infrared spectrum.  The third type determines the rotational velocity of the galaxy.  Another method, called the Fundamental Plane, finds similar relations for elliptical galaxies.

Supernovae, particularly Type Ia, are frequently used and are exceedingly promising standard candles.  Supernovae are some of the brightest objects in the Universe and are visible to exceedingly high redshifts.  The distances can be estimated because Type Ia supernovae have extraordinarily precise variations in light and color variations.  The distribution of absolute magnitudes at maximum light seems to be very narrow.  A few cases where Type Ia supernovae have been unusually red or spectroscopically peculiar lack this relation.  Most recently, Type Ia supernovae have shown that the universe is accelerating in its expansion.  So far, the Type Ia supernovae have given promising results in this study.  Time will tell.

Next, the Sunyaev-Zel’dovic effect appears when the Cosmic Microwave Background Radiation (CMBR) passes through galactic clusters which contain extremely hot intracluster gas.  The accompanying dimming of the CMBR is measured as resulting from the scattering of the CMBR photons in the intracluster gas and results in a measure of the physical depth of the cluster.  This, combined with the angular extension of the cluster, gives its distance.  This method reaches far into the universe.

Finally, there are Quasi-stellar Objects (QSOs) or Quasars which have undergone gravitational lensing.  The time delay is measured between the fluctuations in the multiple images of these distant objects.  This probes into the very distant universe and perhaps will become useful in future cosmological tests.  Using QSOs is a problem because this method is dependent on the measuring of the lensing mass in front of the QSO which leads to quite large uncertainties in the resulting calculations.

In addition to all of the above, there are many other secondary methods for determining cosmic distances.  However, there is much greater scatter in their measurements making the accuracy much less certain.

In closing, it is important to mention the doppler effect shown by blueshift and redshift calculations which are part of the cosmologists’ tools to determine velocities of objects, both toward and away from the observer, within the Milky Way.  Outside of the Milky Way, redshifts and blueshifts are calculated within our Local Group of galaxies to determine relative radial velocities toward and away from our galaxy.  Extragalactic sources, including quasars, also show a doppler effect which results from the expansion of the universe.  Recessional velocities of distant galaxies can be exceedingly large and the expression for redshift of “z” is used in these cases.  Redshifts, themselves, exhibit a photon energy loss in radiation for overcoming the effects of recession or expansion.  Using Hubble’s law for distance determination, the measurements of galactic redshifts are also used to calculate the distances of galaxies.  Redshifts can also be produced by the presence of strong gravitational fields, as predicted by Einstein’s General Theory of Relativity.  It should be understood that, although galactic redshifts can be interpreted as caused by the relativistic doppler effect alone, both the expansion and the gravitation fields of the universe are involved.  Therefore, we should be aware that redshifts may, alternatively or in combination, be considered as doppler redshifts, gravitational redshifts, and/or cosmological redshifts.

So next time you wonder about the accuracy of the methods for determining cosmic distances, rest assured that the cosmologists are handling it just fine - if we can ever get them away from the battlefield.

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Copyright © 2013, the University Lowbrow Astronomers. (The University Lowbrow Astronomers are an amateur astronomy club based in Ann Arbor, Michigan).
This page originally appeared in Reflections of the University Lowbrow Astronomers (the club newsletter).
This page revised Sunday, March 9, 2014 4:30 PM.
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