5 - Parallax and the Cosmic Distance Ladder - Introduction PDF

Preview

Summary

Dr. Alissa Bans; Section 1; Spring Semester 2020...

Description

Astronomy)116)Lab)

Parallax and the Cosmic Distance Ladder

5" Updated'June'1,'2020!

Discussion The Universe is a big place, extending to distances of more than tens of billions of light years, which is over 1023 kilometers. When astronomers talk about “large-scale” distances in the universe, they really mean on the order of many millions to billions of light years away (for reference, 1 lightyear is nearly 6 trillion miles). So, although you might be used to thinking of “small-scale” distances as the distance you walk between classrooms, “small-scale” distances in the universe really go anywhere from here to about a million light years out. For comparison, the Andromeda galaxy is 2.5 million light years away. The Cosmic Distance Ladder Measuring distances is one of the most difficult parts of astronomy, and it becomes more difficult the more distant an object is. For very nearby objects it is possible to measure distance directly, using the method of trigonometric parallax (described below). Beyond the local region of the galaxy (~2000 lightyears), however, it is not possible to measure distance directly, meaning you cannot make a measurement and get a distance from that measurement without doing some calibration first. Calibration must be done with direct measurements, which is why the methods of distance measurement are thought of as rungs on a ladder. Trigonometric Parallax Parallax is the apparent shift in an object’s position when it is viewed from two different locations. For an easy example, hold out your thumb at arm’s length and look at it through only one eye. Then close that eye and open the other, and notice the change in your thumb’s position relative to the background. Stellar parallax works the same way. When one views a star from Earth, then waits half a year and views it again from the opposite side of the Earth’s, the star will appear to shift position a tiny bit relative to the very distant background stars. This shift is due entirely to a change in viewing angle, as the Earth changes position along its orbit. This phenomenon is illustrated in Figure 1. When the Earth is on the right side of its orbit (January), the nearby star will appear to the left of the background star shown. When the Earth is on the left side of its orbit, 6 months later in July, the nearby star will appear to have moved to the right of the background star shown. How far the star appears to have moved during this time is measured as an angle, and is thus directly related to the distance of the star through trigonometry. For comparison, in the second lab you saw the retrograde motion of Mercury in the course. It turns out that this motion is caused by two phenomena: the nearby orbit of Mercury, and the change in the angle from which you view Mercury due to Earth’s motion. (Retrograde motion is the apparent backward motion of a planet among the stars due to the planet’s motion. Parallax is the apparent change in the location of a celestial object, relative to its background, ultimately due to Earth’s motion. Mercury exhibits both.) Since Mercury is so much closer to us than the background stars, you can see a substantially stronger apparent shift in the location of Mercury than with the other planets or the stars themselves. !

1

Figure 1 Cepheid Variable Stars Cepheids are a type of variable star, for which the luminosity of the star changes with time, and does so in a consistent and periodic way. The period of the variation (that is, the duration of the cycle over which the brightness varies) is related to the average luminosity of the star, such that brighter stars have a longer period. Measuring the period of variation is quite easy to do, but measuring the luminosity is much more difficult. In order to measure the luminosity, we need to know the distance, so this method must calibrated. This is done by observing nearby cepheids: the distance to the cepheid is measured using parallax, and that distance can then be combined with the apparent brightness of the cepheid to calculate the luminosity. The periods and luminosities of many nearby cepheids are then graphed, and the shape of the graph shows the relationship between them, as seen in Figure 2. Once the relationship between the period and luminosity is well understood, the relationship is considered well calibrated, and can be used to measure the luminosity of more distant cepheids. Because this method must be calibrated using parallax, it is considered to be the second rung on the cosmic distance ladder. The relationship between period and luminosity for cepheids is very tight, so it is possible to accurately determine the average luminosity of a cepheid simply by measuring the period of the variation. This type of object is known as a standard candle, which is an object that is very bright (and thus is visible from a great distance) and has a known luminosity. Once you have a measurement of the intrinsic luminosity, it can be combined with a measurement of the apparent brightness and used to find the distance of the cepheid. Cepheids are visible at great distances, including in galaxies other than our own. This method can therefore be used to measure the distance to the far reaches of our own galaxy, as well as the distance of many galaxies beyond.

!

2...