AST 112 – Activity #4 the Stellar Magnitude System

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Students: ______

AST 112 – Activity #4

The Stellar Magnitude System

Purpose

To learn how astronomers express the brightnesses of stars

Objectives

 To review the origin of the magnitude system  To calculate using base-ten logarithms  To set the scale for apparent magnitudes  To define absolute magnitude in terms of apparent magnitude and distance  To determine the distance to a star given its apparent and absolute magnitudes

Introduction

The stellar magnitude system ranks stars according to their brightnesses. The original idea came from the ancient Greek scientist Hipparchus (c. 130 B.C.), who proclaimed the brightest stars to be of the first “magnitude”, the next brightest of the second magnitude, and so on down to 6th magnitude for the dimmest stars. Modern astronomers have adopted this general idea, adding specific mathematical and astronomical definitions. We explore how astronomers describe star brightnesses below.

Part #1: Stellar magnitude scales

1. Given the information in the introduction, does the number used to represent a star’s magnitude increase or decrease with increasing brightness?

2. Astronomers define a difference of 5 magnitudes to be equivalent to a multiplicative factor of 100 in brightness. How many times brighter is a magnitude + 1 star compared to a magnitude + 6 star?

3. Extrapolate the magnitude system beyond positive numbers: what would be the magnitude of a star 100 times brighter than a magnitude + 3 star? Briefly defend your answer.

4. Suppose you are told a star has a magnitude of zero. Does that make sense? Does this mean the star has no brightness?

Table 4-1. Magnitudes vs. Factors of Brightness

Difference Multiplicative In Magnitude Factor in Brightness

1 2.52 2 6.25 3 16 4 40 5 100 6 ? 10 ? 11 ? 15 ? 5. Star A has a magnitude of 0 and star B has a magnitude of + 6. How much brighter is star A compared to star B? To answer this, perform the following steps. Hint: Refer to Table 4-1 above.

(a) What is the difference in magnitudes?

(b) Note that 1 + 5 = _____

(c) Remember, magnitudes are additive while brightnesses are multiplicative. So to find how much brighter A is compared to B,

Note that _____ x _____ = _____

6. Star C has a magnitude of -5 and is 1 million times brighter than star D. What is the magnitude of star D? Briefly defend your answer.

Part #2: Absolute magnitudes & distances

Astronomers talk about star brightnesses in one of two ways:

 Apparent magnitude: How bright a star appears to be  Absolute magnitude: How bright a star really is.

1. Recall that luminosity is the term used by astronomers to discuss a star’s intrinsic brightness. Which of the above ideas refers to a star’s luminosity?

2. Recall that flux is the term used by astronomers to discuss the amount of light detected from a star. Which of the above ideas refers to a star’s flux?

The two different types of magnitudes are related by trigonometric parallax, a method used to determine distances to nearby stars (see Figure 4-1):

Figure 4-1. A nearby star appears to shift position, compared to a distant star background; due to the orbit of the Earth around the Sun.

The distance unit called the parsec (pc) is the distance at which an object shows a parallax of one arcsecond. It is also 3.26 Light Years, or 26 trillion miles. For convenience sake, astronomers define an object’s absolute magnitude to equal its apparent magnitude as seen from a distance of 10 pc. 3. Star E has an apparent magnitude of + 2 and star F an apparent magnitude of + 3. Which star looks brighter? Which star actually is brighter?

4. Star G has an absolute magnitude of + 2 and star H an absolute magnitude of + 3. Which star looks brighter? Which star actually is brighter?

5. Star I has an absolute magnitude of + 1 and an apparent magnitude of -1. Is star I closer than 10 pc, further than 10 pc, or exactly 10 pc away? Briefly defend your answer.

6. Star J has an absolute magnitude of + 1 and an apparent magnitude of + 4. How far away is it? To answer this, perform the following steps, showing work when necessary. Hint: Also refer to Table 4-1 above.

(a) Is star J further than, closer to, or equal to 10 pc distant?

(b) What is the difference in magnitudes?

(d) Recall that light acts as an inverse square law. To help find distance, calculate the square root of the multiplicative factor:

(e) Finally, multiply this result by 10 pc to get the distance to star J: