Astronomy 101 Labs

Sarah Jane Schmidt

Summer 2010

These labs were used in my first Summer Astronomy 101 class in 2010. Each lab was started in class,and many of them were completed as homework. I drew heavily on these labs when I assembled exams.

While the text and the majority of figures are my own, many of these labs were based on those orig-inally authored by Julianne Dalcanton http://www.astro.washington.edu/users/jd/Astro101/

or those who have posted to the Astronomy 101 clearinghouse http://www.astro.washington.edu/courses/labs/clearinghouse/labs/labs.html.

Supplies

For most labs, you’ll need a calculator and a pen or pencil. Some labs require additional supplies:

• Lab 1:

– bright light

– styrofoam ball (that can be put on the end of a pencil to represent the moon)

• Lab 2:

– golf ball

– stopwatch

– string (for measuring the height of the ledge)

– yardstick

– ledge (∼10 meters works well)

• Lab 3:

– yardstick

• Lab 5:

– galaxy pictures

• Lab 6:

– balloon

– ruler

– marker that can write on balloon

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Contents

1 Moon Phases 31.1 Examining The Moon Phase Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Creating Your Own Moon Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Gravity 72.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Dropping Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.1 Measure the height . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 The Mass of the Earth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4 Experimental Error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Parallax 133.1 The Parallax of Your Eyes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.2 The Parallax of Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4 Color-Magnitude Diagram 214.1 Color and Magnitude on the H-R Diagram . . . . . . . . . . . . . . . . . . . . . . . . 234.2 Color Magnitude Diagrams of Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3 Making Your Own CMD’s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5 Galaxy Classification 315.1 Galaxy Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315.2 Classifying Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.3 Understanding the Spectra and Colors of Galaxies . . . . . . . . . . . . . . . . . . . . 35

6 Hubble Law 396.1 A Balloon Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396.2 Velocities of Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406.3 Distances to Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436.4 Measuring the Hubble Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

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1 Moon Phases

Intoduction

The moon is one of the most easily observed objects in the sky. The goal of this lab is to understandthe phases that we can observe.

1.1 Examining The Moon Phase Diagram

The moon is only visible to us because it reflects the light form the sun. The following illustrationshows how that creates patterns. Please answer the questions under the diagram.

1. What do the white parts of the Earth and the Moon represent?

2. What about the black parts?

3. What does it mean if the moon is full?

4. What does it mean if there is a new moon?

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1.2 Creating Your Own Moon Phases

For this part of the lab, you will need:

• a pen or pencil

• a partner

• a bright light

• a styrofoam ball

Stick the point of your pen or pencil into the styrofoam ball as a handle. The ball will representthe moon and the bright light will imitate sunlight. One partner will hold the moon in placewhile the other partner will stand in place of the Earth and rotate.

Hours in the Day

Position the ”Earth” and the ”Moon” so that the moon is full. Be sure to hold the moon highenough so that ”Earth” doesn’t block the light of the ”Sun.” In order to simulate a day, thepartner imitating the Earth should spin once, to the left (counterclockwise).

The amount you rotate corresponds to a time. When you face the Sun, it is noon. When thesun is just rising, it is 6 am.

5. Below, draw a circle. Label the direction of the Sun, and then label where you would be facingat noon, midnight, 3, 6, and 9 am and pm. It’s probably best if you check this before you moveon.

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Table 1. The rise and set times of the Moon (for All the Phases, below)

Moon Phase Rise time Highest point Set time

New Moon Noon

Waxing Crescent 3 pm 9pm

First Quarter Noon

Waxing Gibbous 3 am

Full Moon Midnight

Waning Gibbous 9 pm 3 am

Third Quarter noon

Waning Crescent 3 am

New Moon Noon

Full Moon

Position the ”Moon” so that it’s full. Be sure that the shadow from the ”Earth” doesn’t blockthe light reflecting off of the Moon.

6. If the Sun rises at 6 am, when does the Moon set?

7. When does the Moon rise?

All the Phases

Over the course of the month, the moon will complete an orbit around the Earth. Simulate thephases in the chart above, and fill in the rise and set times. If you recognize a pattern, you canfill in the rest appropriately.

8. In the space below, draw and label a waxing crescent and a waning crescent. What looksdifferent about them, and why?

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Eclipses

There are two kinds of eclipses:

• Solar Eclipse: A solar eclipse is when the moon moves directly in front of the Sun andblocks its light.

• Lunar Eclipse: A lunar eclipse is when the Earth blocks Sunlight from reaching theMoon.

9. Based on the definitions above, what phase is the Moon in during a solar eclipse? Why?

10. Based on the definitions above, what phase is the Moon in during a lunar eclipse? Why?

11. There is a lunar eclipse on Saturday. What phase is the moon in now?

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2 Gravity

Intoduction

In this lab, we will measure g and use it to calculate the mass of the Earth.

2.1 Background

The Gravitational Constant

The acceleration due to gravity that we feel at the Earth’s surface is always known as lower case g.The force felt on an object due to gravity can be written as:

Fg = mg (1)

Where Fg is the force due to gravity and m is the mass of the object.

The value of g depends on the mass of the Earth and the distance from the center of the Earth, aswell as the universal gravitational constant, G. Another way of writing the force felt on an objectdue to gravity is:

Fg =GMm

R2(2)

Where the upper case M is the mass of the Earth, the lower case m is the mass of the object, andR is the distance to the center of the Earth.

1. Put those two equations together to write g in terms of G, M , and R:

2. Does the acceleration due to gravity (g) depend on the mass of the object being accelerated?

Acceleration of a Dropped Object

When something is dropped from a height, the amount it falls is given by the equation:

h =1

2g × t2 (3)

Where h is the distance moved and t is the time it takes for the object to drop. We will measureboth the height and time it takes to drop to derive g.

3. Rearrange the equation to write g in terms of h and t:

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2.2 Dropping Objects

For this subsection of the lab, you will need:

• A golf ball (or similarly heavy, small object)

• A stopwatch

• A height of at least 4-5 meters

• A string and ruler, or other method of measuring height

It’s recommended that you work with at least one other person. When you measure the heightand drop the golf ball, it’s easier to have someone at the top of the drop and another personat the bottom.

2.2.1 Measure the height

First, select a place to drop your ball, and measure the height. One method is to use a pieceof string long enough to reach from the top to the bottom, and then measure the length of thestring.

4. What is the height you will drop from? (in meters)

We also need to characterize our measurement error. You should think about whether or notyou stretched your string at any point, how big your ruler was compared to the string, and howfinely you could measure the string compared to the ruler.

5. With this in mind, estimate how close your measured height is to the actual height: (in meters)

You can calculate the percent uncertainty by dividing the uncertainty by the total measurement.The percent uncertainty is a good way of figuring out how exact your measurement is.

6. What is your percent uncertainty for the height measurement?

Timing the Drop

In order to make sure you’ve timed the drop of the ball well, you will need to drop it 20 timesfrom the height, using the stopwatch to get the precise time. This minimizes some of the errorsthat have to do with stopping and staring the stopwatch at the right time. Be careful to dropthe ball from the exact height you measured, and to drop the ball rather than throw it.

Use the table on the top of the next page to record the time for each of the 20 drops.

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Drop # Time (s) Drop # Time (s) Drop # Time (s)

1 8 15

2 9 16

3 10 17

4 11 18

5 12 19

6 13 20

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Table 2 Time For Ball Drop

The time we will be using to measure gravity is the average of the 20 drop times that yourecorded. To find the average, add together all the times you measured and divide by 20.

7. What is the average of the drop times?

One way to estimate the error is by using the range of measurements. We’re going to find theerror in time (∆t) from the highest measured time (thigh) and the lowest measured time (tlow):

∆t =thigh − tlow

2(4)

8. What is your ∆t?

9. What is your percent uncertainty in the time?

Calculating g

10. Use your measured h and t to calculate g:

Many different experiments have measured g precisely at g = 9.8ms2

.

11. Calculate the difference between this number and your value of g:

The difference between the two numbers is due to errors in the measurement of h and t.

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12. Which error had a larger effect on the result, ∆h or ∆t (hint: compare their percent uncertain-ties)?

Next, we are going to use the errors in the measurement of h and t to calculate the range ofpossible values of g. We’re going to define:

tmax = t+ ∆t tmin = t− ∆t (5)

hmax = h+ ∆h hmin = h− ∆h (6)

So then the upper and lower values of g will be:

gmax =2hmaxt2min

gmin =2hmint2max

(7)

13. What are your upper and lower values for g?

14. Is the real value of g between your calculated gmin and gmax?

15. What does it mean if the real value of g isn’t within your range of possible g?

2.3 The Mass of the Earth

For this subsection, you’ll need to know the universal gravitational constant, G, and the radiusof the Earth, R.

• G = 6.67 × 10−11 m3

kgs2

• R = 6.38 × 106m

The reason we are giving you the value for R and using it to calculate M (instead of the otherway around) is because R is much easier to measure than M . The radius of the Earth can bemeasured with a few observations and some geometry. The mass is much harder to measuredirectly.

In problem number 1, you wrote g in terms of M , R, and G.

16. Rewrite that equation so it’s for M in terms of the other numbers and constants:

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17. Calculate a value for M using your g:

18. Use your gmin and gmax to calculate an Mmin and Mmax:

19. Calculate the real value of M using the real value of g = 9.8ms2

.

20. How does it compare to your value of M (calculate the difference)?

21. Is the real value of M between your Mmin and Mmax?

22. Do you think this experiment is a reliable way to calculate the mass of the Earth?

2.4 Experimental Error

23. List 5 things that made your measurement of g more uncertain:

24. Pick two items from your list above, and describe how you could change the experiment toreduce the amount of error:

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3 Parallax

Intoduction

Distances in astronomy

Distance is very tough to measure in astronomy. We can’t use a ruler or a meter-sitck (or a light-year-stick) to simply measure a distance. We also can’t travel to distant stars, measuring our speedand the time it takes to make the journey.

Within our solar system, the distances between objects have been precisely measured by radar rang-ing. We send sound waves out to other objects, then record the amount of time it takes for themto bounce off of them and return to us. This method is precise, and it’s the reason we know thedistance between the Earth and the Sun.

Radar ranging is impossible outside our own solar system. As sound waves travel longer distances,they become weaker. We would need a very powerful radar in order to send strong enough signals toreach another star. The method is also impractical for stars - we would need to wait years in orderfor the sound waves to return to us.

We focus on parallax because it is the only direct determination of distance we have for objectsoutside out solar system. We use it in order to help us determine the distances to even more distantobjects, using methods we’ll discuss in detail over the next few weeks.

Parallax

The parallax method allows us to determine the distance to stars through geometry. We take advan-tage of the Earth’s orbit to observe nearby stars shifting against the background of far away stars.This shift is the star’s parallax. The diagram below shows the Earth at two positions in its orbitaround the Sun. The dotted line shows its view of the nearby star against the background stars.

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In order to measure a star’s parallax, we take an observation (picture) of the star at one side of ourorbit, then wait until we are on the other side of the sun and take another observation.

1. How long does it take the Earth to get from one side of its orbit to the other?

2. How far apart are these two positions?

3.1 The Parallax of Your Eyes

In order to complete this subsection, you will need a meterstick, someone to work with, a pencil (orpen), and about 10 meters of space to walk around in.

Distance to a Pencil

We’ll start by comparing the parallax for a pencil to its distance.

• Hold, or have your partner hold, the meter stick horizontally (parallel to the floor) so that oneend is nearly touching between your eyes, and the other end is sticking straight out away fromyou.

• Have your partner hold a pencil up at 50cm (halfway down the meterstick).

• While they hold it there, look at the pencil through one eye at a time. Pay careful attentionto how much the pencil appears to be moving against the background.

• Once you have done that a few times, ask your partner to move the pencil to the end of themetersitck. Again, look at the pencil through one eye at a time, noting how much the fingerappears to be moving against the background.

The changing position of the finger, which you just observed, is analogous to the picture of parallaxfrom the page before.

3. How big was the shift at one meter compared to the shift at 50 cm (circle one)?

half as much twice as much

4. We could also say that the parallax is inversely proportional to the distance of the object fromthe observer. Based on that statement, what’s the equation that relates the distance, d, to theparallax, θ?

d ∼ θ d ∼ 1θ

Check to be sure your answers to #3 and #4 are consistent with each other.

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5. Below, draw a diagram which shows how the parallax of the pencil is similar to the parallax wemeasure for stars. Be sure to label your eyes, the pencil, and the background and what theyrepresent on the previous drawing.

Testing Your Eyes

To complete this subsection, you’ll measure how effective your eyes are at measuring parallax.

• Begin with you and your friend standing 1-2 meters apart. Look at your friend first with oneeye, and then the next. If you see your friend shift against the background, then ask them totake a big step back.

• Repeat this process until you can no longer see your parter shift against the background. Usethe meterstick to measure the distance between the two of you when your

• In order to be sure this is the right distance, repeat this process three times.

6. Enter each of the three distances in the table below.

try 1 try 2 try 3

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7. What is the average of the three distances that you measured?

8. Based on the range of the distances you measured, how accurate do you think this method isfor testing the ability of your eyes to detect parallax?

9. What is the main source of error in measuring the distance?

10. How well could your partner measure the distance? If your maximum parallax distance isdifferent, why do you think that is?

3.2 The Parallax of Stars

In this subsection, we’ll work with parallax shift as it applies to stars.

The Parsec

Just as we discussed two weeks ago, we measure distances and sizes on the sky in arcseconds andarminutes. These measurements led astronomers to define a unit of distance that’s known as theparsec. A parsec is defined as the distance of a star that has a parallax of one arcsecond.

So with distance (d) in parsecs and parallax (θ) in arcseconds:

d =1

θ(8)

11. Calculate the distance to a star that has a parallax of 2 arcseconds.

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12. If the diagram below was drawn to represent our view of star that’s a parsec away, label theblack arrows with the following (note that the diagram is not to scale):

• a parsec

• an AU

• an arcsecond

13. How many light-years are there in one parsec?1 light-year = 9.46 ? 1015 meters1 parsec = 3.09 ? 1016 meters

14. How many AU are there in one parsec?1 AU = 1.5 x 1011 meters

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Calculating Distances From Parallax

Below are four different fields of stars. In each one, the background stars are black. Each nearbystar (in grey) is shown from either end of Earth’s orbit.

15. The tick marks around each panel are a ruler that measures tenths of arcseconds. Use them tomeasure the shift between each star, which you should fill into the table below.

16. Use the parallax of each star to calculate its distance.

star parallax (arcseconds) distance (parallax)

star 1

star 2

star 3

star 4

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17. Which star had the farthest distance? Is its shift larger or smaller than the rest?

18. The smallest parallax angle we can measure is around 0.01 arcseconds. How far is that, inparsecs?

19. What is that in light-years?

You’ve already calculated that a parsec is much bigger than an AU. Now we want to check howit compares to much larger distances.

20. The distance to the center of the Galaxy is about 25,000 light-years. How much larger is thatthan the maximum parallax distance?

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4 Color-Magnitude Diagram

Introduction

On Tuesday, we learned about the H-R diagram. Today we’ll use some applications of what welearned to derive the distances to and ages of some clusters. First, we need to go over some termsand equations that we’ll be using throughout the lab.

The Magnitude System

Magnitudes are numbers that astronomers use to talk about brightness. The system originated with”naked eye” astronomers, who could only use their eyes to classify the brightness of each star. Theseearly astronomers labeled the brightest stars with the number 1, the next brightest stars were 2, andso on through 6 or 7.

As technology advanced, astronomers stared using telescopes, photographic plates, and now CCD’s- but the magnitude system stuck. After we measure the amount of energy that is reaching us froma star, we convert the information back into the magnitude system.

The magnitudes and fluxes of two objects are related by:

M1 −M2 = −2.5 log(f1f2

) (9)

where M1 and M1 are the magnitudes, and f1 and f2 are the fluxes. There are two important thingsto remember about the magnitude system as we work through the lab.

• Magnitudes are backwards. The objects which we see the most light from have the smallestmagnitudes, while the objects that we see less light from have larger magnitudes.

• Magnitudes are not linear. A star with a magnitude of 2 is not twice as bright as a star witha magnitude of 4. This is useful when comparing the brightnesses of drastically different stars.

Filters

We’ve mentioned filters briefly before, but now we’ll be a little more specific. When we take data,we use a filter to block out most wavelengths of light, and only allow the portion of the spectrum weare interested in to get to our detector.

The graph on the next page shows the three different thermal emission spectra from the light activitya few weeks ago. Most graph is shaded grey, expect for the wavelengths that the B and V filters letthrough.

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200 300 400 500 600 700 800 900Wavelength (nm)

0

2

4

6

8

10

12

14

Re

lative

In

ten

sity

B V

200 300 400 500 600 700 800 900

0

2

4

6

8

10

12

14

T = 4000 K

T = 6000 K

T = 8000 K

1. Which of the thermal emission spectra emits more of its flux in the B filter than the V filter?

2. Which of the thermal emission spectra emits more of its flux in the V filter than the B filter?

Absolute and Apparent Magnitudes

The difference between absolute and apparent magnitudes is similar to the difference between abso-lute and apparent brightness. Apparent magnitude, like apparent brightness, is the amount of lightwe see, usually within a specific filter. The amount of light that we detect in the wavelengths allowedby the V filter is the apparent V magnitude.

The absolute magnitude is a little different. We define it as the magnitude that a star would be ifit was at 10 parsecs. When we discuss absolute magnitudes, we use a capital M, with the filter asa subscript. The absolute V magnitude is known as MV . For the rest of the lab, it’s important toknow how the difference between the magnitudes relates to distance, which begins with:

MV − V = −2.5 log(fabsfapp

) MV − V = −2.5 log(L

4π(10 pc)24πd2

L) (10)

And results in:d = 10

V −MV +5

5 (11)

where V is the apparent V magnitude, MV is the absolute V magnitude, and d is the distance, inparsecs.

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Color

The last piece of the puzzle we need to know about is color. We’re used to color as a qualitativeword or image, but when astronomers discuss color it’s a number. Color is the difference betweenthe magnitudes in two filters, or the ratio of the fluxes in each of the two filters.

For today, it’s enough to know that smaller, or negative, numbers are bluer, while larger numbersare redder. The color we’ll be working with is B − V .

4.1 Color and Magnitude on the H-R Diagram

The diagram below shows B − V color, absolute magnitude, temperature, and luminosity for about20,000 stars from the Hipparcos Survey. The Hipparcos Survey measured parallaxes of about 150,000stars in addition to their B and V apparent magnitudes. Because the survey measured both distanceand apparent magnitudes, we have calculated absolute magnitudes for all those stars.

While the B − V and MV are measured quantities, the luminosity and temperature given are ap-proximate, in order to related back to the diagrams we’ve already examined.

−0.5 0.0 0.5 1.0 1.5 2.0(B−V) color

20000 7500 5000 4000 2500Temperature (K)

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10

5

0

−5

MV: absolu

te V

magnitude

10−4

10−2

1

102

104

Lum

inosity (

tim

es the S

un’s

Lum

inosity)

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Before we move on to working with clusters, there are a few questions about the H-R diagram of theHipparcos stars:

3. The diagram shows both the main sequence and some red giants, as well as a few white dwarfs.Draw a line through the main sequence.

4. What is the absolute V magnitude (MV ) of the Sun? What is its B − V color?

5. What is the approximate temperature of a main sequence star with a B−V of 1.5? How abouta main sequence star with a B − V of −0.1?

The table below gives the approximate B − V colors and lifetimes for different spectral types alongthe main sequence.

Spectral Type B − V color Main Sequence Lifetime (years)O -0.35 106

B -0.16 107

A 0.13 5 × 108

F 0.42 5 × 109

G 0.70 1010

K 1.18 7 × 1010

M 1.63 1011

6. Use the B − V colors given to label spectral types along the main sequence.

4.2 Color Magnitude Diagrams of Clusters

The Color Magnitude Diagram (CMD) of a cluster is interesting because we can assume that all thestars in the clusters are both the same distance from us, and the same age. This means that we canuse the CMD, compared with nearby stars, to derive the ages and distances of the clusters.

7. Clusters are nearly spherical in shape, and should have some depth. Why can we assume asinge distance for the whole cluster?

8. Why can we assume that each cluster contains stars of the same age?

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−0.5 0.0 0.5 1.0 1.5 2.0(B−V) color

22

20

18

16

14

Appare

nt V

Magnitude

NGC 1261

Above is the CMD of NGC 1261, a globular cluster.

Measuring Distance From A CMD

9. We’ll start with a B−V of 0.55. What’s the average apparent V magnitude of the stars in thecluster with that color?

10. Using the diagram of the Hipparcos stars, what is the absolute magnitude of a B − V=0.55star along the main sequence?

11. Use the distance formula (given on the second page of the lab) to calculate the approximatedistance to that star.

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We can’t really estimate the distance to the cluster from measurements to just one star. Inorder to make sure we have accurate results, we need to use a few stars and average the results.Later in the lab, you’ll have a few charts like the following to fill in. I’ve completed a few moreentries for NGC 1261.

B − V color apparent Vmagnitude

absolute Vmagnitude

distance (pc)

0.5 21.75 4.5 2.81 ×104

0.45 20.5 3.5 2.51 ×104

0.4 19.75 3.25 1.99 ×104

12. Calculate the average of the three distances from the table, and include the distance you foundon the previous page.

Age From a CMD

Earlier, you explained why we can assume that all the stars in a cluster are the same age. This isuseful to us because we know exactly which stars are leaving the main sequence, because the mainsequence ends. The majority of the stars in the cluster turn around and populate the red giant branch.

The cluster age is assumed to be the main sequence lifetime of the highest mass star still on the mainsequence. In order to find the age of the cluster, you need to identify the approximate location ofthat star or stars. We call this the ”main sequence turn off” because the stars that are done burningtheir hydrogen are turning off of the main sequence.

For NGC 1261, that seems to be at B − V = 0.4, where the dashed line is shown over the CMD.

13. Using the table on page 4, find the approximate main sequence lifetime of a star of B − V =0.4.

That lifetime is equal to the age of NGC 1261!

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4.3 Making Your Own CMD’s

On the next page are V and B − V data for three different star clusters. On the page after, thereare graphs for each of the three clusters. Your tasks are to:

• Put all the data onto the graph for the appropriate cluster.

• Fill in the table with the B − V color, apparent V magnitude, absolute V magnitude andcalculated distance from three different parts of the main sequence.

• Average the three distances to get a final distance.

• Draw a vertical line through the main sequence turn off.

• Fill in the B − V color of the main sequence turn off in the space provided below the table.

• Find the age of the cluster and write it below the table.

You are welcome (but not required) to use the blank space below for calculations. The main reasonfor the blank page is so that the data and graphs are not on two sides of the same page.

Also, there are some additional questions on the back page!!

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M 45

V B − V14.4 1.287.6 0.1211.6 0.8411.9 0.908.6 0.357.9 0.204.2 -0.1015.8 1.4414.8 1.476.8 0.028.3 0.3613.5 1.189.5 0.4714.0 1.232.9 -0.0912.8 1.1614.0 1.319.1 0.4710.1 0.5610.3 0.623.6 -0.085.1 -0.0814.4 1.4711.1 0.766.2 -0.0513.1 1.2215.0 1.5515.5 1.3612.5 1.0711.8 0.86

M 12

V B − V19.7 0.7419.0 0.6719.2 0.7018.8 0.6518.5 0.6418.4 0.6318.2 0.6418.0 0.6617.8 0.7217.7 0.7517.4 0.8316.4 0.8815.2 0.9514.3 1.0412.7 1.4119.4 0.7218.7 0.64

47 Tuc

V B − V19.6 0.7620.6 0.9821.0 1.0521.0 0.9621.6 1.2322.0 1.3122.2 1.2322.6 1.3323.0 1.4517.6 0.5317.7 0.5818.0 0.5718.4 0.6018.8 0.6519.1 0.6919.8 0.8320.1 0.8820.4 0.9321.4 1.1021.6 1.2013.5 1.1015.5 0.8212.0 1.4512.6 1.2512.9 1.1414.0 0.9914.0 0.6914.0 0.7914.0 0.5914.9 0.8516.2 0.7316.6 0.7316.9 0.7017.0 0.5817.2 0.51

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−0.5 0.0 0.5 1.0 1.5 2.0(B−V) color

20

15

10

5

0

Ap

pa

ren

t V

Ma

gn

itu

de

M45

B − Vcolor

apparent Vmagnitude

absolute Vmagnitude

distance

Average distance is:

Turn off B-V is:

Age of cluster is:

−0.5 0.0 0.5 1.0 1.5 2.0(B−V) color

20

18

16

14

12

Ap

pa

ren

t V

Ma

gn

itu

de

M12

B − Vcolor

apparent Vmagnitude

absolute Vmagnitude

distance

Average distance is:

Turn off B-V is:

Age of cluster is:

−0.5 0.0 0.5 1.0 1.5 2.0(B−V) color

25

20

15

10

Ap

pa

ren

t V

Ma

gn

itu

de

47 Tuc

B − Vcolor

apparent Vmagnitude

absolute Vmagnitude

distance

Average distance is:

Turn off B-V is:

Age of cluster is:

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14. Which of the clusters is the oldest?

15. Which cluster is the most distant?

16. Look back at the CMD for NCG 1261. Why does the main sequence seem to end around B−V= 0.4 and exclude the most numerous stars?

17. We need to be able to see the main sequence turn off in order to find both the age and thedistance to the star cluster. For a cluster that’s 1010 years old, what is the absolute magnitudeof the turn-off?

18. If the faintest apparent magnitude we can see using modern telescopes is around V=28, thenhow far is the farthest cluster of 1010 years that we can us the CMD method on?

19. The center of the galaxy is approximately 8.5 ×103 pc away. How does that compare to theapproximate limiting distance for CMD distances that you found in the previous question?

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Name:

5 Galaxy Classification

Introduction

We briefly discussed galaxies at the beginning of the quarter, but now it’s time to study them indetail. On a basic level, galaxies are large collections of stars, gas, and dust. There’s a large range inthe size of galaxies (108 to 1012 stars) and a very large range in morphology, or shape and appearance.Some galaxies are nearly spherical, some are disk-like, and some are blotchy collections of materialseemingly assembled at random.

In this lab you will explore the morphology and classification of galaxies by examining both theirimages and their spectra.

5.1 Galaxy Morphology

Galaxy Features

Above are a cartoon and image of a galaxy. Note that the images are inverse - the white parts areempty space, while the grey and black trace the light we detect. The following galactic featureslabelled:

• bulge: A higher concentration of stars, gas, and dust at the center. The bulge sometimescontains a supermassive black hole.

• disk: The surface of the galaxy, where most of the matter is located. In the images above, weare viewing the entire disk from the top, not the side.

• spiral arms: These are more highly concentrated matter than the surrounding disk.

• clumps: There are areas where there’s a lot of gas and dust which are usually associated withstar formation.

• foreground star: In many images of galaxies, stars in our own galaxy are between us and thegalaxy in the center of the image.

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The Hubble Sequence

Astronomers have developed many different ways to classify galaxies, but one specific scheme, knownas the Hubble Sequence, has been in use for decades. This cartoon shows how the main propertiesof galaxies vary along the Hubble Sequence.

The ”E” stands for elliptical, the ”S” for spiral, and ”Irr” for irregular. The number ”0” is placed aftera spiral galaxy that is nearly an elliptical galaxy, and the letters ”a” through ”d” indicate differentcharacteristics in sprial galaxy shape. When we talk about galaxy types we use a short-hand: E, S0,and Sa are early-types, and Sc, Sd, and Irr are late-types.The Hubble type of a galaxy is based on the presence and variation of around four different features,which we’re asking you to identify:

1. The size of the bulge compared to the disk. Which end of the sequence has larger bulges?Which end has larger disks?

2. The presence or absense of spiral arms. Which galaxies have spiral arms? Which havenone?

3. The tightness of the spiral arms. How tight or loose are the arms in each of the types?How does it change through the spiral part of the sequence?

4. The clumpiness of the spiral arms. Which galaxies have more clumps? Which ones haveless?

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5.2 Classifying Galaxies

This subsection of the lab will involve the 30 pages of galaxy images that are provided. They weretaken from the Sloan Digital Sky Survey. Each page has three parts - a large image of the galaxywith an inverse color scale, a small image that’s a normal color scale, and the galaxy spectrum.

Galaxy Images

Sort through the images and set aside those that already have a classification. Arrange those imagesin order of their types on the Hubble Sequence (from early-types to late-types) so that you can lookat each of them. Some of them have classes like Sab or Scd which are intermediate Hubble types -Sab goes between Sa and Sb, while Scd would go between Sc and Sd.

Before we classify the rest of the galaxies, there are two things you should look at:

• Bars: Some of the galaxies have a feature near their center known as a bar. Like spiral arms,a bar is a feature near the center that has more gas, dust, and stars than the area around it.For example, galaxies #6 and #12 both have an Sc classification, but #6 has a bar while #12doesn’t.

• Orientation: Some of the galaxies are viewed at different angles than others. For example,galaxy #17 looks like it’s edge on - we’re viewing the disk from the side rather than on top.#24 is nearly the same type, but looks different because we can see it face-on.

The Hubble type of each galaxy should be based only on the large inverse image on the page. Theother image is faded, small, and not detailed. .

5. Fill in the table below with the classification for each of the unclassified galaxies. Compareeach image to the galaxies that are already classified, and be careful to look at the propertieswe listed on the previous page: the size of the bulge compared to the disk and the presence,tightness and clumpiness of the spiral arms

6. For each galaxy, decide whether it has a bar or not and fill in that column of the table.

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Galaxy # Classification Bar? Spectrum

1 S0/Sa

2

3

4 E/S0

5

6 Sc

7

8 S0

9 E

10 Irr

11 Scd

12 Sc

13

14

15

Galaxy # Classification Bar? Spectrum

16 Sab/Peculiar

17 Sb

18

19

20

21 Sd/Irr

22

23

24 Sbc

25 E

26

27

28

29 Sb

30 Sa

7. How many of the galaxies have bars?

Galaxy Spectra

We’ll now turn our attention to the spectra of the galaxies and classify them into three categories:

• red: If the spectrum peaks to the right, or at longer wavelengths than 500 nm, then we willclassify them as ”red.” Galaxy # 24 is a good example of a red spectrum.

• blue: If the spectrum peaks to the left, or at longer wavelengths than 500 nm, then we willclassify them as ”blue.” Galaxy # 21 is a good example of a blue spectrum.

• emission: If the spectrum is dominated by emission lines, then we will classify them as ”emis-sion.” Galaxy # 18 is a good example of an emission spectrum.

Of course, the galaxy spectra are more complicated than that. Don’t worry too much about borderlinecases - some galaxies are in between red and blue, or in between blue and emission.

8. Go through each of the galaxies, and write a classification spectrum based on their spectrumin the table above.

9. Once you’ve completed that, count the numbers of galaxies of each Hubble type that are red,blue, and emission. Write those counts in the table below.

E or E/S0 S0 or S0/Sa Sa or Sab Sb or Sbc Sc or Scd Sd or Sd/Irr Irregular

red

blue

emission

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For the following questions, don’t worry about the few galaxies that seem to be exceptions. Answerbased on the average properties of the galaxies.

9. Are the emission line galaxies late-type or early-type?

10. In general, are the blue galaxies more often early-type or late-type?

11. In general, are the red galaxies more often early-type or late-type?

5.3 Understanding the Spectra and Colors of Galaxies

The spectra of the galaxies show a combination of all the light that’s emitted from both the starsand the gas that the galaxies contain. We can use that fact to figure out why some galaxies mightlook more red and blue, and where those emission lines come from.

The Ages of Stars

First, we’ll look at two diagrams:

40000 20000 10000 4000 2000Temerature (K)

10−4

10−2

100

102

104

106

Lum

inosity

40000 20000 10000 4000 2000Temerature (K)

10−4

10−2

100

102

104

106

Lum

inosity

These diagrams should resemble the color magnitude diagrams of clusters, except that they are interms of temperature and luminosity instead of color and magnitude.

12. Which of the diagrams represents an older cluster? How do you know?

When we are looking at the light in a galaxy spectrum, it’s similar to looking at the light of hundredsor millions of these clusters added together. To interpret the galaxy spectra, we need to figure out

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which stars contribute the most to the luminosity.

The number of points on the two diagrams doesn’t accurately represent how common the types ofstars are. For every one star that’s between 10 and 150 solar masses, we’ve learned that there areabout 200 stars between 0.08 and 0.5 solar masses.

13. A star between 0.08 and 0.5 solar masses should have a luminosity of about 10−3 times theSun’s luminosity. How luminous are 1000 stars with that luminosity?

14. If there are 1000 stars between 0.08 and 0.5 solar masses, how many should there be between10 and 150 solar masses?

15. How luminous are the massive stars?

16. Circle the most luminous stars in each of the diagrams.

17. What color should the combined spectrum of older stars be? What spectrum should thecombined spectrum of younger stars be?

18. Based on their colors, should early-type galaxies have younger or older stars? What aboutlate-type galaxies?

The ages of the stars in the galaxies only sometimes relate to the age of the galaxy. They instead tellus something different - how recently stars have formed in that galaxy. A galaxy could have formedlong ago and recently some event has provoked star formation. Galaxies of the same age could havedrastically different spectra and colors, while galaxies of different ages and similar recent historiescould have more similar spectra and colors.

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Recent Star Formation

While the ages of stars indicate how recent star formation has happened, there is a more directindication of how emission lines form.

Emission lines trace gas that’s been heated by recently formed stars. Think of the picture we lookedat of the Eagle Nebula - the massive O star that’s recently formed is heating a large gas cloud whereother stars are forming. The emission lines from a similar gas cloud are what’s readily apparent inthe galaxies that you classified as emission spectra.

19. In the space below, draw the scenario where an observer would see an emission line spectrumfrom a region that is forming stars.

20. Are your emission spectra galaxies and blue galaxies of similar Hubble types? Does that makesense?

21. Look again at the spectra for galaxies #19 and #20. They seem to be both blue and have someemission lines. What do you think is happening in those galaxies?

22. Look again at the spectra for galaxies #16, #22, and #30. Their spectra have a few emissionlines, but look red. What do their pictures have in common? Form a hypothesis about whytheir spectra could be red despite the emission lines.

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Name:

6 Hubble Law

Introduction

The Hubble Law is the foundation of modern cosmology. It describes the expansion of the universe,in terms of the relationship between the distances to galaxies and the rate at which they appear tobe moving away from us. The Hubble Law can be summarized by this equation:

v = Ho × d (12)

where Ho, the Hubble constant, relates the apparent velocity of each galaxy, v, to its distance, d. Ho

is a measurement of the rate of the expansion of the universe. Our goal for this lab is to measureand understand Ho, the Hubble constant.

6.1 A Balloon Universe

For this subsection of the lab, you will need a balloon, a ruler and something to write on the balloonwith. The balloon will represent the expanding universe. Blow up the balloon a little bit, hold itclosed and draw three galaxies on it. Two of the galaxies should be closer to each other, and onefarther away, like this:

Make sure your galaxies are small in size compared to the balloon and compared to the space betweenthem. Hold the balloon closed while you make the first measurement.

1. What is the distance between galaxies A and B? Distance between galaxies A and C?

Now, blow up the balloon for five seconds. Tie the balloon closed while you make your secondmeasurement.

2. What is the distance between galaxies A and B? Distance between galaxies A and C?

3. How much did the distance change between galaxies A and B? When you consider the balloonwas expanding for 5 seconds, what is their velocity of expansion?

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4. How much did the distance change between galaxies A and C? And what is their velocity ofexpansion?

We can measure a Hubble constant for our balloon - we have a distance between galaxies, and avelocity.

5. Using the total current distance between galaxies A and C and their velocity of expansion,what is Ho for your balloon? Be sure to include the units.

6. What is 1/Ho, the age of your balloon universe? It should be larger than 5 seconds. Why?

7. The Ho you measure from the other pair of galaxies should be the same. Why? How can thegalaxies have different velocities but the same rate of expansion?

6.2 Velocities of Expansion

We’ll now move on to the measurements that will allow us to calculate the Hubble constant for thereal universe. In order to measure the velocities of a sample of galaxies, we measure the redshift oflines in their spectra.

On the next page, there are spectra of 6 galaxies. Each of the spectra show the region surroundinga prominent Hydrogen emission line, which is known as Hydrogen Alpha, or Hα. The rest wave-length of Hα is λrest = 6562.8A, and its wavelength is shown below each of the spectra. Note thatthe A symbol stands for the unit called an Angstrom. An angstrom is a unit of measure used forwavelengths and small distances. One angstrom is equal to ten nanometers.

Some of the spectra have more than one emission line. In eachspectrum, Hα is the largest emissionline.

8. Draw a vertical line through the peak of each of the Hα emission lines.

9. Look at where each of the lines you drew falls in comparison to the rest wavelength of Hα.Which galaxy should have the largest redshift? Which should have the smallest?

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10. Measure the wavelength of the peak of the Hα emission line in the spectra for each of thegalaxies. Write your results in the table on the next page.

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Galaxy Hα (A) z v (km/s)

NGC 1832

NGC 2903

NGC 3147

NGC 3471 6610

NGC 3623 6565

NGC 3627

NGC 4631 6575

NGC 5548

NGC 6217 6590

NGC 6643

We can now use our observed Hα wavelengths to calculate the redshift of each galaxy, which isrepresented by the letter z. The equation for z is:

z =λobs − λrest

λrest(13)

Where λrest is the rest wavelength of Hα (6562.8A) and λobs is the observed wavelength - which youjust filled into the table for each galaxy.

11. The observed wavelength of Hα for the galaxy NGC 3471 is given in as λ = 6610A. Calculatethe redshift of NGC 3471 and show your work below:

12. Calculate the redshifts of all 10 galaxies, and fill them into the table.

We can calculate velocity from redshift by multiplying the redshift, z, by the speed of light, c:

v = z × c (14)

In this lab, we want our final velocities to be in units of km/s, so use the speed of light in the sameunits:c = 3 × 105km

s

13. Use your redshifts to calculate the velocity of each of the galaxies listed in the table above.

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6.3 Distances to Galaxies

Distance is a difficult quantity to measure for galaxies. Astronomers often use ”standard candles”to measure these distances - objects which have bright, well known luminosities. We can measurethe apparent brightness of a standard candle, and then use the inverse square law to calculate thedistance. In this lab, we are going to use a slightly simpler but less accurate method that involves”standard rods.”

A standard rod is a an object which has a well known size. We can measure the angular size of theobject on an image, and then compare that to the object’s real size in order to calculate a distanceto the object. To find the distances to galaxies, we are going to assume that all spiral galaxies haveapproximately the same diameter.

14. Based on what we talked about in class, do you think this is an accurate assumption?

15. Would it be more or less accurate if we tried to use the standard rod assumption with ellipticalgalaxies? What about irregular galaxies?

On the next page are pictures of six galaxies. We are going to measure their diameters in order tocalculate their distances. The first thing we need to do is figure out the image scale - it’s the sameon every image. The scale bar on galaxy NGC 4631 is one milli-radian in length. As a reminder, aradian is a unit that we use to measure angles. A milli-radian is one thousandth of a radian, just likea millimeter is one thousandth of a meter.

16. What is the length of the scale bar on NGC 4631 in cm?

17. Also use your ruler to measure the diameters of each of the galaxies and fill in the first columnof the table. You should measure the diameter at the widest part of each galaxy.

18. Why do we measure the diameter at the widest part of the galaxy?

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44

Galaxy diameter (cm) diameter (mrad) distance (Mpc)

NGC 1832 2.9

NGC 2276

NGC 3034 9.9

NGC 3147 2.9

NGC 3245

NGC 4631

NGC 5248

NGC 5548

NGC 6217

NGC 7469 0.8

Next we need to convert our measurements into milliradians. To convert we’ll need to use theequation:

diameter in milliradians =1 milliradian

length of scale bar in cm× diameter in cm (15)

because the scale bar represents one milliradian, and all the images are on exactly the same scale.

19. Convert the diameter of NGC 1832 from cm to milliradians and show your work below:

20. Convert the other 9 diameters from cm into milliradians and fill the results into the table.

To estimate the distances, we will take advantage of the concept of angular size.

distance =actual diameter

angular diameter(16)

For each of these galaxies, we are using an estimated actual diameter of 22 kiloparsecs. You won’tneed to convert units to fill in the table. We are dealing with units of 10−3 radians and 103 parsecs.If we plug that into the standard rod distance equation, we get:

distance =103 parsecs

10−3 radians= 106 parsecs (17)

Or a million parsecs, which we call a megaparsec and abbreviate Mpc.

21. Calculate the distance to NGC 1832 and show your work in the space below:

22. Calculate the distances to all 10 galaxies, and fill in the last column of the table.

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6.4 Measuring the Hubble Constant

Below is a table of distances and velocities. The entries that are blank should correspond to thevalues that you calculated using the spectra for velocities and the galaxy images for distance. Theentries that are filled in were calculated using the same method.

Galaxy Distance (Mpc) Velocity (km/s)

NGC 1832

NGC 1357 42.4 2075

NGC 2276 2229

NGC 2775 22.2 1298

NGC 2903 11.4

NGC 3034 91

NGC 3147

NGC 3227 25.4 1003

NGC 3245 1067

NGC 3368 19.6 772

NGC 3471 49.2

NGC 3516 48.5 2402

NGC 3623 9.6

NGC 3627 10.4

NGC 3941 27.2 740

NGC 4631

NGC 4775 38.4 1555

NGC 5248 765

NGC 5548

NGC 6181 34.7 2204

NGC 6217

NGC 6643 23.1

NGC 6764 36.2 2058

NGC 7469 4602

23. Fill in the blank entries on the table using the values you calculated values for v and d.

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24. Plot all the values for v and d, both your calculated and the ones provided, onto the graphbelow.

0 20 40 60 80 100 120Distance (Mpc)

0

1000

2000

3000

4000

5000

6000

Velo

city (

km

/s)

The data should fall on some sort of a line (with scatter). We need to fit a line to the data to calculateour value for the Hubble constant.

25. Using a ruler, draw a line through the data. You line should have about half the points aboveit, and half below it. Your line should also go through 0,0. Those are the distance andrelative velocity of the Milky Way Galaxy, and we are sure of those.

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Next we need to calculate the slope of our line, which should be the Hubble constant.

26. What velocity is your line at when it hits a distance of 60 Mpc?

27. The slope of your line, the Hubble constant, will be that velocity divided by 60 Mpc. What isyour Hubble constant? Be sure to include the units.

28. The real value of the Hubble constant is more about Ho = 71km/sMpc . How different is the value

that you obtained?

29. One major source of uncertainty is the distances based on the galaxy sizes. If you measureda smaller than actual diameter, this would lead to a smaller than actual Hubble constant.Explain why that’s the case.

30. List three other possible sources of uncertainty in your measurement of the Hubble constant.

31. What is the age of the universe (1/Ho) that you calculate from your Hubble constant? Convertyour answer to years.1 Mpc = 3.09 ×1019 km1 year = 3.16 ×107 s

32. How does your calculated age compare to the actual age of the universe?

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