Date: January 12, 2010

Title: Climbing the Distance Ladder

Podcaster: Christian Ready

Description: The song describes astronomy as the study of things that are far. But how do astronomers know how far away things are? It turns out that there are several methods astronomers use to measure the distances to celestial objects. Some methods are suited for measuring the distances to nearby stars, while other methods work at greater distances. Together, these methods form the “Cosmic Distance Ladder,” allowing astronomers to measure the distances to everything from nearby stars, to galaxies, to the most distant objects in the observable universe.

Bio: Christian Ready began working in astronomy at the age of 13 when he worked at Swarthmore College’s Sproul Observatory. There, he measured the distances to nearby stars by measuring their parallax. After college, he went to work at the Space Telescope Science Institute from 1992 to 1997. There, he served as a Program Coordinator helping astronomers develop observations to be carried out onboard Hubble. Later, he worked at NASA’s Goddard Space Flight Center supporting flight operations for the Rossi X-Ray Timing Explorer. Since 1993, Christian has been a public speaker on the Hubble Space Telescope and other astronomy topics.

Today’s sponsor: This episode of “365 Days of Astronomy” is sponsored by — no one. We still need sponsors for many days in 2010, so please consider sponsoring a day or two. Just click on the “Donate” button on the lower left side of this webpage, or contact us at signup@365daysofastronomy.org.

Transcript:

Hello, I’m Christian Ready. We heard a great intro song describing astronomy as the study of things that are far – stars, nebulae, galaxies, clusters of galaxies, quasars – as the song says, “this stuff is far.” But how do astronomers know how far away these objects are?

After all, when we look up at the night sky, there’s no way to tell which objects are nearby and which ones are farther away. For the most part, the night sky looks like points of light plotted on a giant sphere surrounding the earth. But astronomers have a number of methods to measure the distances to celestial objects. These methods allow astronomers to measure the distances to everything from the closest stars to the farthest galaxies at the edge of the observable universe. Collectively, these methods are known as the Cosmic Distance Ladder, because methods that are used to measure the distance to nearby objects serve as a check against methods that work at greater distances. Today we’ll talk about a few of the methods that form the “rungs” of this ladder.

For nearby stars, astronomers measure the subtle change in their positions in the night sky as the earth revolves around the sun. This phenomenon is called Parallax. Here’s how it works:

If you measure a star’s position in the sky, then make a follow-up measurement of that same star six months later, the star will appear to have shifted in its position relative to the background stars.

This is because as the earth revolves around the Sun over the 6 month period, our perspective on the star changes. The star appears to shift a small angular distance in the sky. Half of this angle is known as the parallactic angle, or the parallax. The parallactic angle forms a long, skinny triangle with the earth and Sun at one end, and the star at the the other end. Some simple trigonometry, allows us to solve for the distance to the star.

If the parallactic angle of a star is 1 arc second, the star’s distance is said to be 1 parsec, which is about 3.26 light years.

The closest star to earth, Proxmia Centauri, has a parallactic angle of 0.77 arc second, or 1.3 parsecs, which works out to about 4.3 light years from earth.

The more distant the star, the smaller its parallactic angle. As a result, astronomers can only measure stars with parallactic angles as small as 0.01 arc second, for a maximum distance of 100 parsecs. The earth’s atmosphere doesn’t allow for any greater precession than this. From space however, more precise measurements of a star’s parallax are possible. From 1989 to 1993, Europe’s Hipparchos satellite was able to measure the distances to stars out to about 200 parsecs by measuring their parallax.

Thousands of stars’ distances have been determined by measuring their parallax. And in 1910, astronomers Ejnar Hertzsprung and Henry Russell independently plotted the color temperature of these stars against their luminosity, or absolute magnitude. This plot is known as the Hertzspring-Russel Diagram.

Most of the stars plotted in the Hertzspring-Russel diagram go about their daily business of fusing hydrogen into helium in their cores. In the Hertzspring-Russel diagram, these stars are plotted in a band raging from high luminosity and high temperature to low luminosity and low temperature stars. Stars in this band are known as Main Sequence stars. Because the distances to these stars are known through measurements of their parallax, their actual, or intrinsic brightnesses can be calculated. This intrinsic brightness is often referred to as the star’s Absolute Magnitude – that is, an imaginary magnitude the star would have if it were 10 parsecs away.

Because of the relationship between a star’s Absolute Magnitude and its color temperature, the Hertzprung-Russel diagram is a powerful tool for determining the distances to stars. Simply measure the color temperature of a main sequence star, infer its absolute magnitude from the Hertzspring-Russel diagram, and compare that to the star’s apparent magnitude to determine its distance. After all, the farther away something is, the dimmer it appears!

This technique is known as Main-Sequence Fitting and it is a particularly useful way of measuring the distances to clusters of stars. Because the stars in a cluster are the same distance from earth, they can be plotted according to their Apparent Magnitude and their color temperature. The resulting plot resembles a Hertzsprung-Russel diagram, except the “Main Sequence” of the stars in the cluster appear to be dimmer because they are much farther away than the imaginary 10 parsecs of the stars in the Hertzsprung-Russel diagram. The difference between apparent magnitude from the stars in the cluster and the absolute magnitude of their counterparts in the Hertzsprung-Russel diagram is the result of their distance. This difference in magnitude is often referred to as the Distance Modulus.

Main-Sequence Fitting is capable method of measuring the distances to stars out to about 300,000 light years, and is a good method for measuring the distances to stars and clusters within our Milky Way Galaxy. But in order to measure the distances to galaxies beyond the Milky Way, we need to search for objects with brighter Absolute Magnitudes.

One such class of object is known as a Cepheid Variable star. A Cepheid Variable is an unstable star that is undergoing a series of expansions and contractions. As the star physically grows in size, it grows dimmer, as it contracts, it gets brighter.

Cepheid Variables pulsate with a period between 1 to 100 days. Cepheids also have a well-defined Period-Luminosity relationship: the shorter the period, the lower the luminosity. The longer the period, the higher the luminosity.

Because of its Period-Luminosity relation, a Cepheid Variable acts as a “Standard Candle.” Simply measure its pulsation period to determine its Absolute Magnitude. Then compare its absolute magnitude to its apparent magnitude to determine the distance.

Cepheids are much brighter than most Main-Sequence stars, making them detectable even in distant galaxies. If a Cepheid Variable is detected in a distant galaxy, the distance to the host galaxy can be determined. In 1924, Edwin Hubble discovered Cepheid Variables in the Andromeda Nebula. Prior to Hubble’s discovery astronomers debated whether the universe was confined to the Milky Way Galaxy or if so-called “spiral nebulae” were in fact “island universes.”

When Hubble discovered Cepheids in the Andromeda Nebula, he used their Period-Luminosity relationship to calculate their distance. Hubble found Andromeda to be at least 1 million light years from Earth, well beyond the diameter of the Milky Way (whose size, I should mention, was determined by measuring the distances to Cepheid Variables.) Even though we now know its distance to be at least 2.2 million light years, Hubble showed that the great spiral in Andromeda was not a nebula, but a galaxy in its own right, with its own population of stars, nebulae, and star clusters. This historic observation ushered in a new field of study in astronomy called Cosmology – the study of the universe on a grand scale.

Cepheids are the primary Standard Candle in cosmology. The Hubble Space Telescope measured the distances to galaxies by identifying their Cepheids as far away as 65 million light years.

But even with the Hubble Space Telescope, Cepheid Variables are too faint to be detected at even greater distances. In order to measure further, even brighter standard candles must be identified.

Supernovae are the brightest stellar explosions in the Universe. A sub-type of Supernova, a Type Ia, occurs when a white dwarf star in a binary star system begins to accrete material from its red giant companion. As the red giant expands, more of its material falls onto the white dwarf. As more material falls onto the white dwarf, the white dwarf grows in mass. When the white dwarf’s mass reaches 1.4 times the mass of the sun, it collapses under its own weight and explodes in a Supernova explosion some 10 billion times the luminosity of the sun.

Because Type 1a supernovae always occur when the white dwarf reaches 1.4 solar masses, the luminosity of these events are the same no matter where they occur within the universe. Therefore, if we can detect a Type Ia supernova, we can use it as a Standard Candle and measure the distance to its host galaxy.

But how do astronomers know that a supernova is Type Ia? After all, it could be a Type II Supernova, which is an explosion of a single star. Since the mass of a single star going supernova can vary from one star to the next, their energy output can also vary. So how do astronomers know that a supernova is in fact of Type Ia?

Fortunately, nature provides us with a clue. It turns out that Type Ia supernovae fade or decay in a particular manner. By measuring the rate of the supernova’s decay, astronomers can determine if the supernova in question is of Type Ia.

Type Ia Supernovae have allowed astronomers to make some of the most farthest-reaching distance measurements in the universe. In fact, astronomers using the Hubble Space Telescope have used Type Ia Supernovae to pinpoint the distances galaxies as far away as 8 billion light years from earth.

Of course, Supernovae are much less common in the cosmos and are relatively short-lived events. Even if you are lucky enough to find one, it has to be the right type in order to serve as a good distance indicator.

However, galaxies themselves are very common in the universe and they can be used as their own Standard Candles.

In 1977, astronomers Brent Tully and Richard Fisher showed that there is a relationship between a spiral galaxy’s intrinsic luminosity and its rotational velocity. By measuring the Doppler shift of the spiral arms of the galaxy, the velocity of the arms rotating toward us and the arms rotating away from us indicate the velocity of stars orbiting the center of the galaxy. The greater the rotation velocity, the greater galaxy’s mass. The greater the mass, the more stars there must be. The more stars there are in the galaxy, the greater its intrinsic luminosity. Therefore, if you can measure the rotation velocity of the galaxy, you can infer it’s intrinsic luminosity and compare that to its apparent magnitude to calculate its distance.

The Tully-Fisher relation works for spiral galaxies because their rotational velocities can be measured. But when we look at the most distant galaxies and the most distant quasars, they do not have any spiral structure. This is because these galaxies are so far from earth that we see them as the were when the universe was much younger and the galaxies themselves had not yet formed spiral arms and begun rotating. To estimate their distances, we must rely on Hubble’s Law.

In the 1920’s, Edwin Hubble discovered that not only did galaxies exist outside of our Milky Way, but that the farther the galaxies were from us, the faster away they were receding. Hubble discovered that the Universe was expanding. His study of this expansion of the universe led to Hubble’s law, which states that velocity of their recession is equal to its distance multiplied by a constant. This constant is known as the Hubble Constant.

Therefore, in to measure the distance to a very distant galaxy, simply measure its doppler shift to find its recessional velocity, then divide that velocity by Hubble Constant in order to determine its distance. All astronomers needed to know was the value of the Hubble Constant.

In theory, this should be pretty easy – all one had to do was calculate the velocities and distances to several galaxies and average their results together to calculate the Hubble Constant.

But due to uncertainties in measurements made by ground-based telescopes, the Hubble Constant could not be accurately determined. Values of the “constant” ranged anywhere from 50 to 90 km/sec/Mpc. That’s a pretty wide range of possible values for a “constant.”

Astronomers using the Hubble Space Telescope made the most precise distance measurements to galaxies using Cepheid Variable stars, and calculated the Hubble Constant at 74.2 ± 3.6 km s−1 Mpc−1. This an extraordinarily precise measurement, just +/- 5%. But astronomers want to measure the Hubble Constant to an even greater level of precision. The James Webb Space Telescope, scheduled to be launched in 2014 will undoubtedly be used for this task.

The methods we’ve talked about today are only some of the “rungs” of the Cosmic Distance Ladder. In fact, much of the work in astronomy involves refining the accuracy of these different distance indicators. For example, in 2011, the European Space Agency will launch the Gaia satellite. One of Gaia’s missions will be to make the most precise measurements of the parallax of stars out several thousand parsecs away (vs the 100 parsec limit we can measure from the ground.) Gaia will help confirm some of the physical assumptions astronomers make in order to use farther-reaching distance methods.

As the song says, “this stuff is far.” But what’s remarkable is that we can actually measure just how far.

End of podcast:

365 Days of Astronomy
=====================
The 365 Days of Astronomy Podcast is produced by the Astrosphere New Media Association. Audio post-production by Preston Gibson. Bandwidth donated by libsyn.com and wizzard media. Web design by Clockwork Active Media Systems. You may reproduce and distribute this audio for non-commercial purposes. Please consider supporting the podcast with a few dollars (or Euros!). Visit us on the web at 365DaysOfAstronomy.org or email us at info@365DaysOfAstronomy.org. Until tomorrow…goodbye.