29:50 Modern Astronomy
Fall 2002
Lecture 7 ...September 11, 2002
The Nearest Stars and How We Know Their Distances

e quindi uscimmo a riveder le stelle ...Final line of Inferno, Dante

Today we move beyond the solar system and begin discussing the stars, which are perhaps the most obvious and striking phenomenon of astronomy.

I will begin by stating what I am sure all of you already know; the stars are suns, only much further away. Equivalently, the sun is just a nearby star that we happen to be orbiting. Given this, detailed studies of the sun give us some insight into the properties of stars. This realization dates from at least the beginning of the modern scientific era, and probably extends back much further.

However, we can go beyond this and ask a number of other, more inquisitive questions about the nature of stars. This is a list which I think an inquistive person looking up at the night sky would ask.

• What are they? (we've already answered that)
• How far away are they?
• How hot are they? (You can guess that from what we have learned).
• How massive are they? Are they all the same mass as the Sun?
• What are they made of?
• How do they evolve? What are their life cycles?
• Do they have planets around them?

It turns out that we can answer all of these basic questions. For some of the questions, we have known the answer for a long time. For the last question, the answer has started to be answered in the affirmative in only the last year or so.

The Distances of Stars

The standard direct method of measuring the distances to stars utilizes the method of trigonometric parallaxes. This is a common surveying technique, and there is nothing magical about it. Those of you in the lab portion of the course are doing this project this week, and it is illustrated in Figure 16-1 of your textbook.
Figure 16-1.
In surveying, you put a stick in the ground, move back and forth, and see the stick shift its position against a fixed background of distance objects. In astronomy we utilize the motion of the Earth, and watch a relatively nearby star shift against a backdrop of more distant stars. The more distant the star, the smaller the size of this shift. A distance of parsec corresponds to a parallax of one arcsecond.

With this technique, astronomers using ground-based telescopes were able to measure accurate distances to about 1000 stars which are in the relative vicinity of the Earth. The closest of these is Alpha Centauri, a triple star system at a distance of 1.33 parsecs.
Show transparency with nearest ones.

This number probably doesn't do much for you, so let's relate it to other systems of units. This is important to belabor at this point because the parsec will be our new yardstick of distance in discussing stellar and galactic astronomy. In terms of our fundamental system of units, a parsec is meters. A more tactile description is to note that a parsec is 206,265 astronomical units, the yardstick we have been using to measure distances in the solar system. If the distance from the Earth to the Sun were 1 centimeter, the distance to the nearest star Alpha Centauri would be 2.74 kilometers or 1.6 miles away!.

Another way of describing interstellar distances is via the unit of the light year. Early in my astronomy education I learned that real astronomers sneered at the light year, and preferred the ``real'' unit of the parsec. Actually, you can argue that the light year is at least as physically fundamental as the parsec, and a lot more physically transparent. A light year is simply the distance a light ray, traveling at 186,000 miles per second would travel in one year. The size of this distance can be appreciated by the fact that the planet Saturn, now visible in the constellation Taurus in the morning sky, is 1.27 light hours away! The distance to Alpha Centauri is 4.3 light years away. Think about the implications of this fact for interstellar travel.

In 1990 a European satellite named Hipparchus was launched, which measured parallaxes from space. Precise parallaxes were measured for 118,000 stars. A list of the 150 nearest stars, now with precision distances, is given in the Hipparchus URL .

OK, now having said that we can measure the distances to the nearby stars, we can establish a list of the closest stars. Appendix 11 of your textbook has the ``Top 25''. Before looking at that table, I could ask which stars you would expect to find. The natural response would be the brightest ones. If all stars have the same luminosity, then the brightest ones should be the closest.

A map of nearby space, with the names of our stellar neighbors, is given at the following stellar neighbor URL.

This expectation runs into some surprises. Although some of the brightest stars are among the nearest, such as Sirius, Procyon, Alpha Centauri, and Altair, it is not a general statement. Furthermore, most of the nearest stars are real surprises.

Appendix 11 from book.
Here we can see a lot of familiar stars such as Alpha Centauri, Sirius (note A & B..there are two of them), Procyon, and others you could find on your SC1 star chart, such as Eridani and Ceti. However, there are large numbers of objects with strange names. This indicates very faint objects, in almost every case too faint to see without a telescope. The names of these stars are just their catalog entry names.

Question for audience: what's up?

Another way of representing this is with the SC1 chart, and indicating the nearby stars and apparently bright stars.
SC1 chart with distances to bright stars indicated.
Stellar magnitudes. Let's introduce the system of stellar magnitudes. This is an old fashioned and in some ways awkward system introduced in the 2nd century BC by Hipparchus. He classified stars the same way you would hotels, first class, second class, third class, roach-specials etc. Hipparchus originally had 1st magnitude stars being the brightest, 2nd magnitude the next brightest, etc., down to fifth magnitude being about the best a person with good eyesight in a very dark, very clear sky could pick out.

Transparency of SC1 chart

Nowadays the system has been made good and quantitative, and we have negative numbers as well as positive numbers. Table 16-1 of your textbook gives specific examples of certain celestial objects on the magnitude system.

At this point a complication needs to be introduced. The magnitude system is not a linear system. This means that a second magnitude star is not twice as bright as a first magnitude star. It is 2.512 times as bright. Before you start thinking this is a conspiracy on the part of astronomers to make life miserable for advertising majors, I would hasten to point out that it is because the human eye, like all the other sense organs, is a nonlinear detector.

The mathematical definition of the magnitude system is as follows. If stars 1 and 2 have magnitudes (strictly speaking apparent magnitudes) and , then the ratio R of the power received in radiation is

with R > 1 if star 1 is brighter. A table giving the brightness ratio in terms of magnitude difference is given in Table 16-2 of your textbook.
Table 16-2 of textbook.

1 magnitude difference = 2.5, 2 mag diff.= 6.3, 3mag=16, 4mag=40, and 5 magnitude difference = a factor of 100 in light energy received.

A smaller magnitude corresponds to a larger flux in the form of light energy. If we think back to the beginning of this lecture, we can see that there are two reasons why a star might appear bright. The first is distance. The closer a star is, the brighter it will appear to us. The second is luminosity. If a star is intrinsically luminous, it could appear very bright even at a great distance. One would like a parameter which was representative of the luminosity of a star.

This parameter is provided by the Absolute Magnitude of a star. The absolute magnitude is defined as the apparent magnitude a star would have if it were at a distance of 10 parsecs. The absolute magnitudes of stars are listed in the last column of Appendix 11. It has some interesting surprises. The Sun has an absolute magnitude of 4.85. This means if it were at a distance of 10 parsecs (not very far away on the stellar scheme of things) it would be invisible from inside Iowa City, and it would be difficult even in a dark sky setting. Sirius has an absolute magnitude of 1.41, and would be a bright star at 10 parsecs, even though not as bright as it presently is.

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