PSIWA - GALAXIES AND COSMOLOGYpersonal.psu.edu/wnb3/psiwa/workbook-final-2005.pdf · cool stars - the red giants, which are generally old stars. The formation of stars in a galaxy

GALAXIES AND COSMOLOGY

Penn State Inservice Workshop in AstronomyNiel Brandt

Department of Astronomy and AstrophysicsThe Pennsylvania State University

Originally prepared by Daniel Weedman Digital conversion by Jessie Hart

Table of Contents:

Introduction

Excercise 1: Size of the Milky Way Galaxy and Distance to Nearby Galaxies Excercise 2: Diameters & Distances of Messier Galaxies Excercise 3: Estimating the Distance to the Local Supercluster Excercise 4: Estimating the Distance to the Coma Cluster Excercise 5: The Hubble Deep Field - North Excercise 6: The Hubble Law Excercise 7: The Cosmic Microwave Background Excercise 8: The Most Distant Objects in the Universe

Conclusion

Supplemental: Accurate Distance to M100 and the Local Supercluster Supplemental: A Distant Galaxy Seen Through A Lens Supplemental: Galaxies in the Young Universe

INTRODUCTION

Astronomy is an incredibly comprehensive subject, requiring you in principle to have total knowledge of life, the Universe, and everything. Presumably, most of you already have a head start by having some knowledge of astronomy based on your own teaching or prior workshops. This workshop investigates in more detail those parts of astronomy dealing with our efforts to understand the fundamental nature of the Universe - the subject of cosmology. New discoveries are being made all the time that are relevant to this. Much of this course emphasizes images from the Hubble Space Telescope to demonstrate the most important frontier research topics relevant to galaxies and cosmology.

Astronomy is an observational science. That means we learn from what we see. This is an important skill, to be an astute observer, and is applicable to many more uses in life than astronomy. An objective of this workshop is to give you experience in doing this which you can pass on to your own students. Various images will be shown in the lectures to illustrate or simulate things in the Universe. Specific guides to Web sites will be used as supplements for all of the topics covered. For supplementary work in this and all other areas of astronomy, an extensive collection of color images for various topics along with explanatory material can be found on the WWW under "Astronomy Picture of Day".

http://antwrp.gsfc.nasa.gov/apod/astropix.html

Photographs from the Hubble Space Telescope are under "Hubble Space Telescope Public Pictures" at

http://hubblesite.org/newscenter/

A continuing orientation to NASA's missions in space science, including recent press releases, is accessible at

http://www.hq.nasa.gov

Our workshop will give you details and scientific experience in understanding what we know about galaxies and cosmology, and how we know it. In preview, this knowledge

is summarized below:

Stars in the Universe are grouped into huge collections called galaxies, each of which can possess hundreds of billions of stars, all remaining together in the Galaxy because of their mutual gravity. Our Sun lives in one of these, called the Milky Way Galaxy because the most conspicuous manifestation of our own Galaxy is the "Milky Way" that we see in the sky. Our Galaxy is a spiral galaxy which, if seen from afar, would be characterized by a huge spiral pattern that outlines the Galaxy's disk. Surrounding this disk shaped region containing the spiral arms is a larger, more spherical volume called the halo. Stars in galaxies have different characteristics depending on whether they are in the disk or in the halo, with the key difference being that the oldest stars are in the halo and the youngest in the disk. You can observe this for yourself in various images that are shown, because the disk is characterised by the bright blue stars in the spiral arms. These are identifiable with the places where stars are being born. Conversely, the characteristic color of the halo is the yellowish tint that is the signature of bright but cool stars - the red giants, which are generally old stars.

The formation of stars in a galaxy only happens in the spiral arms of the disk because that is where hydrogen and dust, the raw materials for the stars, have collected. Depending on the amount of such material still present, galaxies can have dramatically different appearances. Spiral galaxies are classified according to the relative conspicuousness of their spiral arms relative to their haloes. You will see many beautiful examples of different types of galaxies. The most numerous galaxies are the elliptical galaxies, which come in all sizes from the smallest galaxies to the largest, and which do not have spiral arms. This means that elliptical galaxies do not have any young stars; they look much like the isolated halo of a spiral galaxy would look if the spiral arms were removed. Galaxies which do not fit either the spiral or elliptical categories are called irregulars. Many are small "shreds" of material with so little stars and gas that gravity has not been able to organize their shape. Other irregulars are gigantic systems whose shapes have been grossly distorted by collisions with other galaxies. As one astronomer described these, "After two cars collide, you do not have a new type of car. You have a wreck."

The most important irregular galaxies are samples of the small "shreddy" kind called the Large and Small Magellanic Clouds, unfortunately for you being visible only from the southern hemisphere. These are important because they are the closest galaxies outside our Milky Way Galaxy. Moving on out, beyond these, the next galaxy

encountered is the magnificent spiral galaxy in Andromeda, the most distant object (at about 2 million light years) visible to the unaided human eye. The Milky Way Galaxy, the Andromeda Galaxy, and another spiral galaxy called M33 provide the major constituents of the small group of galaxies in which we dwell, called for obvious reasons the Local Group. Containing several other small elliptical and irregular galaxies, the Local Group is an outlying clump of galaxies belonging gravitationally to a much larger and more distant collection - the Local Supercluster.

Bizarre things are seen happening to galaxies. Sometimes, because of collisions or other triggers, extraordinarily violent but brief episodes of star formation and death occur. These are called starbursts. In other cases, a mysterious source of energy in the very center of a galaxy can shine with luminosity output exceeding by thousands of times the light from all the stars in a galaxy. These incredible events in the cores, or nuclei, of galaxies are the quasars, which can be so luminous that some quasars are the most distant objects seen in the Universe. Not only can tremendous energy be produced, but much of it is squirted out in one direction, in huge jets or beams of energy. How can this happen? Nobody knows in detail, although we now have good evidence that accreting supermassive black holes are involved. The galactic menagerie has many names, names given in consequence of the historical accidents of their discovery. You will learn some of these by name in our various exercises.

There is an awesome and humbling mystery associated with galaxies. Their gravity can be measured by the motions of stars and gas in the Galaxy, thereby determining the force controlling the stars and gas. There is way too much gravity. The amount of gravity associated with galaxies is at least ten times as much as should be associated with the stars and gas we can see in galaxies. Where is the rest arising from? The source is hypothesized to be the totally invisible and fundamentally mysterious Dark Matter, most of which seems to be associated with the haloes of galaxies. Dark Matter is the ultimate embarrassment to astronomers, because we can only study in detail the stuff we can see.

How did the Universe begin? Did the Universe come from nothing? Was there anything here before the Universe? Are there other universes? Will the Universe ever end?

Anyone who has ever asked these questions is asking about cosmology. Trying to understand the history and nature of the entire Universe, or cosmos, has been a

fundamental goal of all thinking humans. Although originally in the realm of philosophy and religion, cosmology has now become a science. A scientific theory is an idea that not only explains known phenomena, but can produce predictions about how new measurements or experiments will turn out. The more precise the prediction, the stronger the theory is considered to be. While our current theories of cosmology are not as strong as many other astronomical theories, they are scientific, because the theories make predictions which can be compared with new astronomical observations.

Cosmology is our attempt to understand the overall structure, history, and future of the entire Universe. That is a big subject. The first steps depend on measuring the distances to some galaxies, as will be illustrated with the exercises. The techniques often follow common sense - that similar things look smaller or fainter the further away they are. For measuring distances in the Universe, the distance indicators usable to the greatest possible distances are the giant elliptical galaxies, and you will see examples of these which are so many billions of light years away that they fade to nearly invisible dots.

Once distances to galaxies are known, an extraordinary observational result is found when the recession velocities of these galaxies are measured using redshift in the spectrum. The two quantities distance and velocity increase in proportion to one another. All cosmological theories depend upon this observation that the distance to a galaxy is proportional to the velocity with which it is moving away from us, as measured by the redshift. This velocity-distance relation is also called the Hubble Law, and it is the single most important item in cosmology. The Hubble Law is an observation which you will reproduce with your own measurements. The interpretation of this observation is that the Universe is expanding. We have no other way conceptually to explain this observation other than to conclude that the Universe is continuously growing larger. Furthermore, by comparing the velocities with which galaxies are separating to the distances apart they have achieved, we can calculate with simple arithmetic how long it has taken the Universe to grow to its present size. This length of time is taken to be the age of the Universe, and you will determine a rough estimate of that age based on measurements you make. (The best answer we have today is that the Universe is about 13.7 billion years old.) Recent detailed studies of the expansion rate of the Universe, utilizing observations of supernovae in distant galaxies, indicate that the Universe's expansion is accelerating. The reason for this acceleration is poorly understood, and a mysterious entity termed Dark Energy is currently believed to provide the necessary cosmic repulsion. Studies of this putative Dark Energy are currently at the forefront of observational cosmology.

The fundamental postulate of current cosmological theories is that the entire Universe began at a specific instant, with a violently explosive event giving rise to all of the matter and energy now in the Universe. That was an incredible moment, when the entire Universe was compressed into an extraordinarily hot and dense spot and all matter and energy came into existence, not to mention time and the structure of space. This sounds like it was quite a thrill, and it is celebrated by calling this event the Big Bang. It would be hard to believe something like that could actually happen if we didn't have evidence. The Big Bang was originally conceived in the 1930's when the observations were made which indicated that the Universe is expanding. If the Universe is now expanding, it is reasonable to conclude that it was once much smaller. The theory of the expanding Universe stated, therefore, that the Universe began expanding from a single, very condensed beginning. A prediction of this theory is that the energy of the explosion required to set the Universe into motion might still be observable. In 1964, energy was observed coming from throughout the Universe; this energy is seen as a feeble glow called the cosmic microwave background radiation. The glow was originally detected using radio receivers sensitive to the wavelengths of microwaves - the same wavelengths utilized by radar or by microwave ovens. Is this glow the remaining energy from the Big Bang? NASA's Cosmic Background Explorer (COBE) and Wilkinson Microwave Anisotropy Probe (WMAP) were designed to provide the answer by measuring the properties of the microwave background radiation much more precisely than could be done with receivers on Earth.

One of the predictions of a Big Bang cosmology is that the energy remaining from the Big Bang must be at a single temperature. This is because the Universe should have cooled uniformly as it expanded after the Big Bang, when the temperature was originally millions of degrees. By now, the Universe should have cooled so much that the temperature is just a few degrees above absolute zero. COBE determined that the temperature of the Universe is 2.726 degrees above absolute zero. This is a very precise temperature; there are no spectral irregularities which would indicate contamination by radiation from a different temperature. This important result means that the temperature measured arose from a single explosion, at a single time, rather than from several different events in the Universe. Also, the precision of the temperature indicates that nothing has happened in the Universe, other than uniform cooling, to alter the glow produced by the explosion of the Big Bang. All of these observations agree with the predictions of the Big Bang theory.

Another prediction of the theory is that the background radiation should be nearly the same brightness in all directions, with only very small deviations. This is because the Big Bang filled the entire Universe, so the leftover radiation should still fill the entire Universe and be seen no matter where we look. If a loudspeaker were connected to a microwave receiver, we would hear a uniform hiss of static from the sky, and COBE and WMAP found that this hiss is almost exactly the same everywhere to a precision exceeding one hundredth of one percent. This matches the precision expected from the Big Bang. In fact, the precision of the measurements is so good that it can be used to test the predictions of a refinement on the Big Bang theory. This refinement is the theory of inflationary cosmology, which attempts to utilize theories from high energy physics and quantum mechanics to ask in more detail just what happened during the instant of the Big Bang. A corollary of this theory is both exciting and philosophically daunting: that our Universe may be one random fluctuation among many, so that universes come and go in some vast, overarching fabric of spacetime.

Inflationary cosmology represents the beginning of efforts to produce a theory that might eventually explain how the Big Bang happened. This theory states that in the first fraction of a second immediately after the Big Bang, the young Universe expanded at a much more rapid rate than at later times. Inflationary cosmology predicts just how uniform the Universe became, and predicts that slight irregularities remained after this rapid "inflation". These irregularities are quite small, only about 1/100,000 of the average background intensity, analogous to seeing 1-inch waves on an ocean 2 miles deep, but COBE and WMAP were able to detect them. Did these same irregularities subsequently condense and become the gigantic clusters of galaxies seen today? How did the smooth early Universe turn into the Universe of today, irregularly filled with galaxies? Answering these questions with current theories requires the same spectre that raised its ugly head earlier, the presence of overwhelming amounts of Dark Matter and Dark Energy in the Universe.

So much for the past. What we must know to predict the future of the Universe is how much matter and energy are in it, including Dark Matter and Dark Energy. Until we know this, we cannot decide if the Universe will expand forever or will someday stop expanding, reverse, and reunite to generate a new Big Bang and another universe. The alternatives - continued expansion or not - are described in terms of open universe vs. closed universe.

Cosmology has almost become an embarrassment. We need a mysterious attractive

force (Dark Matter) along with a mysterious repulsive force (Dark Energy) in order to have a consistent theory of the Universe. This is not a satisfactory situation.

In learning and teaching cosmology, it is easy to become frustrated with the ambiguity

of our current explanations. On the other hand, it is intellectually stimulating to realize

that you can understand how far human minds have gone toward answering the

Ultimate Questions. I hope, by the conclusion of this workshop, that you will be

enthusiastic about passing this stimulation on to your own students.

EXERCISE 1: SIZE OF THE MILKY WAY GALAXY AND DISTANCES TO NEARBY GALAXIES

This exercise is a beginning toward orienting students to the extraordinary scale of perspective needed to comprehend the Universe. The variety of steps required to do this utilizes the concept of making scale maps and the concept of using ratios to describe these scales. The calculations which are listed in this exercise step through the entire Universe, starting with the Solar System.

We can begin with something, made as small as possible, that represents our star, the Sun. It is good to make it big enough that the Earth can be shown in scale size compared to the Sun. The Sun is about 1,000,000 miles in diameter. The Earth is about 10,000 miles in diameter.

a. Take the Sun to be 1 meter in diameter. Draw an Earth which is approximately the correct size relative to the model used for the Sun. Explain your calculations.

The distance from the Earth to the Sun is about 100,000,000 miles (100 million, or 108 in "scientific notation" because there are 8 zeros in the number).

b. Determine how far away your Earth drawing must be from the model Sun to represent correctly the distance between Earth and Sun. Explain your calculations.

The star Vega is the brightest in the night sky in summer and fall. It is at a distance of about 30 light years. The star Polaris, easy to find any time of year, is about 800 light years away; Polaris can be seen at such a great distance because it is a supergiant star. In round numbers, stars you can readily see with your unaided eye are not likely to be more than 1000 light years away. Light traveling to Earth from the closest star, our Sun, only requires 500 seconds to make the trip. In the context of the 3-D scale model of the Galaxy that has been described, the fact to be emphasized is the small size of the volume in that galaxy which contains virtually all of the stars visible to the human eye.

c. Using your scale model of the Solar System in b., how far would you have to go to draw to correct scale the distance of Vega? Explain how you determined this result. Suggest something or some place that might be located at the approximate distance of Vega on your scale map.

All of the stars we can see in the sky are part of our Milky Way Galaxy, a typical spiral galaxy of diameter about 100,000 light years. The Sun is located about 2/3 of the way

out from the center toward one side.

d. Sketch a spiral galaxy like the Milky Way and draw a circle at the approximate location of the Sun whose radius is the distance from the Sun to Polaris.

In later exercises, you will see how distances to other galaxies are determined. Looking ahead, we can add the most important nearby galaxies to a scale map of our part of the Universe. This will illustrate how sizes of galaxies compare to distances between them and how empty most of space really is.

The closest spiral galaxy to our own is the Andromeda Galaxy, M31. It is about 2,000,000 light years away and is about the same size as our Milky Way Galaxy. You have included a copy of a photograph of M31 which shows its angular size in the sky.

e. Sketch to correct scale model galaxies showing the sizes and separations of the Milky Way Galaxy and M31.

The Milky Way Galaxy is an outlying member of a huge group of galaxies called the Local Supercluster, at whose center are numerous galaxies, two of which (M100 and M87) you will later learn to be particularly important. M100 is a spiral (color it blue because its light is dominated by bright, young, blue stars); M87 is a giant elliptical (color it orange because its light is dominated by bright red giant stars). Both are about 100,000 light years in diameter. These galaxies and the center of the Local Supercluster are at a distance of about 50,000,000 light years.

f. Sketch to correct scale a map showing the sizes and separation of the Milky Way Galaxy and M31, and the galaxies M87 and M100 (take these two to be about 3,500,000 light years apart from each other). M31 is in roughly the opposite direction from the Milky Way Galaxy compared to M87 and M100.

EXERCISE 2: DIAMETERS & DISTANCES OF MESSIER GALAXIES

Late in the 18th century, a few years after the United States began, a Frenchman named Charles Messier (knowing little and caring less about the newly created nation) was irritated in his comet hunting. (His last name is pronounced "messy-eh") He was irritated because his observations were confused by fuzzy looking blobs seen in his telescope that looked like the fuzzy blobs of comets, but weren't. Once and for all, he decided to write down the locations of all these fuzzy blobs so he would quit being confused and could get on with what he thought would make him famous, which was

finding comets. The catalog of fuzzy objects, still known by their "M" numbers, now contains the most famous galaxies and nebulae in the sky. But who ever heard of a "Messier's Comet"?

Find the Messier catalog at http://www.seds.org/messier/index.html.

a. Record the distances and angular diameters for M31, M51, M65, M74, M81, and M104. (Note that distance is given in thousands of light years so that, for example, a distance of 37000 means 37,000,000 or 37 million light years. Angular diameter is given in arcminutes, abbreviated " ' ") Record the angular diameter as determined from the longest axis in order to accomodate tilted spiral galaxies.

b. Use your M31 photo to illustrate what is measured by the angular diameter you record.

c. Plot a graph including the six galaxies showing the angular diameter on the vertical axis and the distance on the horizontal axis. Comment on what this result shows.

You can transform angular diameters of things into actual diameters if you know the distance. The concept is to imagine a circle centered on you, and the distance to the

thing is the radius of the circle. The circumference of a circle in arcminutes is 360o x 60' = 21,600', because there are 60' in each degree.

The circumference of a circle in the same numbers you measure actual distance is 2·Pi·r, and r in this case is the distance from you to the thing. So these ratios are equal:

thing's actual diameter = thing's angular diameter 2·Pi·r 21,600

d. Determine the average actual size of the galaxies listed, deducing diameter in light years. Comment on how this compares to the diameter previously stated for our Milky Way Galaxy.

EXERCISE 3: ESTIMATING THE DISTANCE TO THE LOCAL SUPERCLUSTER

M100 (Image is .67 x .67 degrees)

The images you have are from the research-quality Palomar Sky Survey Photographs of that part of the sky which includes the center of the Local Supercluster. This is in the direction of the constellation Virgo, so it is also sometimes known as the Virgo Cluster. A scale is shown giving the angular diameter for portions of these images. You can determine galaxy diameters by scaling their diameters to the scale of the entire photo.

a. Using the photo, locate the galaxy M100 and any edge-on spiral. Measure the diameter of these two galaxies on the photo, measuring to the faintest visible extent of the galaxies. Convert your measured diameters into arcseconds.

These galaxies resemble what our Milky Way Galaxy would look like at the distance of the Virgo Cluster. Your objective is to determine the distance to the Local Supercluster, assuming that galaxies 15 and 16 have in the average this same diameter. I can help with the geometrical concepts needed, but a simple way to deduce them is to think of the distance to these galaxies as the same as the radius of a circle which is centered on our Galaxy and goes out to those galaxies. The circumference is 2·Pi·r, for r the

required distance. The circumference is also 360o·60' ·60" = 1,296,000 arcseconds. You have measured the diameter of galaxies 15 and 16 and can determine what fraction of the circle they represent. You can also assume their diameter in light years so you can determine the circle's circumference in light years. From that, you can determine r.

b. Determine the distance to galaxies 15 and 16 in the center of the Local Supercluster, as measured in light years. State the source of your assumption about their actual diameters.

Supplemental exercise: Accurate distance to M100 and the Local Supercluster

EXERCISE 4: ESTIMATING THE DISTANCE TO THE COMA CLUSTER

Based on studies of Cepheids, the distance to M100 and the other galaxies in the Local Supercluster considered correct by most astronomers is approximately 50 million light

years. Even with HST, Cepheids cannot be observed at greater distances. But galaxies keep going. As galaxies get further away, precise and direct measurements of their distances become difficult because the measurements have to be based on assumptions of uniformity regarding the entire galaxy. The simplest such assumption would be that all galaxies of the same type (such as spirals or giant ellipticals) have the same actual size. In this case, the apparent size (that is, the diameter the galaxy appears to have) would decrease in proportion to increasing distance. Using the simple assumption that all spiral galaxies have the same actual diameter, we will estimate the distance to the next large cluster of galaxies: the Coma Cluster.

Begin with another image of the spiral galaxy M100 in the Local Supercluster obtained by HST. Find this image by going to: http://hubblesite.org/newscenter/There is a search utility at this WWW site. You are looking for a supplementary image associated with the press release "Cepheid Variable Star in Galaxy M100."

M100

a. The full width of an HST photo is 160 arcseconds. Estimate the full diameter of M100 in arcseconds based on the HST photo, explaining your calculations and assumptions.

NGC 4881

Now find an image of the galaxy NGC 4881 on the WWW site. This is a picture of part

of the Coma Cluster of galaxies. It is beautiful because it shows, in one picture, all of the different kinds of galaxies, arranged together in the sky so that their relative sizes can be estimated. Note a giant elliptical, a dwarf elliptical, a spiral, and an irregular.

b. Sketch an image of the cluster showing the location of a giant elliptical, a dwarf elliptical, a spiral, and an irregular galaxy.

c. Measure the diameter of the largest spiral galaxy in your image, giving your answer in arcseconds.

d. Using your measurements of galaxy size, estimate the distance to the Coma cluster, explaining the proportionalities and assumptions used to achieve this distance estimate.

EXERCISE 5: THE HUBBLE DEEP FIELD - NORTH

Perhaps the most dramatic image from the Hubble Space Telescope has been one of the faintest pictures ever taken of the Universe. This is the Hubble Deep Field - North, which reveals galaxies of many different types, out to distances exceeding 10 billion light years (allowing us to see such galaxies as they were when the Universe was less than 1/3 of its present age). It also shows in dramatic perspective how many galaxies there are. We will use slides of these images to make the following calculations, but you can reproduce them using images on the WWW.

To learn how the HDF-N was obtained and to see detailed close ups, go to:

http://www.stsci.edu/ftp/science/hdf/hdf.html

Go to pretty pictures.

Read the Press Release Text

To see the full picture, go to Images on the right, and view Full WFPC2 Mosaic.

Go back to Images and click on Sample Galaxies from the Hubble Deep Field

WFPC2

a. Draw a sketch of the entire HST WFPC2 image showing where the three enlarged images are found.

b. Estimate the distance to the spiral galaxy in the lower left hand corner using the principles and assumptions of previous exercises.

c. Pick out and locate in a sketch of the HDF-N examples of elliptical and irregular galaxies.

The width of the HDF-N is 160 arcseconds. There are 60 arcseconds in one arcminute. There are 60 arcminutes in one degree. Consequently, there are 3600 square arcseconds in one square arcminute and 3600 square arcminutes in one square degree. There are about 41,000 square degrees in the entire sky.

d. Counting a sample of galaxies in part of the HDF-N, estimate how many galaxies would be visible to HST in the entire Universe.

It took approximately 10 days to obtain the photograph of the HDF-N.

e. Determine how many years it would take for HST to obtain photographs like the HDF-N that cover the entire sky.

EXERCISE 6: THE HUBBLE LAW

Until now, the exercises have mostly concentrated on the techniques used to estimate galaxy distances and, by consequence, galaxy sizes. Cepheid variables were first used to do this in the 1920s. Humans have had since then some concept of the immense sizes and distances of galaxies. The next steps were equally dramatic, allowing knowledge of galaxies to be used to study overall characteristics of the Universe itself. In this exercise, you will discover an extraordinary property of the Universe that Edwin Hubble discovered in the 1930s.

Return to the Messier Catalog which you used before. Find the catalog at http://www.seds.org/messier/index.htmlClick on image icons to view the catalog.

a. Record the distances of these galaxies (the first five of which you have already done): M31, M51, M65, M74, M81, M104, M87, M77, M66, M64, M82, M33. Record any notes or questions you have about particular galaxies that you wish to ask about in class. Allow space to add the other numbers needed from item b., below.

Your next use of the WWW utilizes a site normally only used by professional astronomers when we need comprehensive data on a particular galaxy. But you only need one little piece of the data. Go to the "NASA Extragalactic Database" at

http://nedwww.ipac.caltech.edu/

Look under "Objects" and click on By Name.

In Object Name box, type the galaxy name (for example, type M31 with no spaces). Leave other parameters as set. Click on "Submit Query"

You will see a data box with a lot of information. The number under z or km/s is the radial velocity of the galaxy as measured in kilometers per second and should show values in the range of a few hundred to a little over a thousand. This is a measure of the speed with which that galaxy is receding from our Milky Way Galaxy.

The "redshift" of a galaxy is denoted by the symbol z. This is defined as the shift in the wavelength of light divided by what the wavelength of that light should be. For example, typical spectral lines from a galaxy are lines of hydrogen. The strongest hydrogen line in the visible spectrum is supposed to be at a wavelength of 650

nanometers. If this line is observed at a longer (redder) wavelength, the spectrum has been "redshifted" because of the motion of the galaxy away from us. For example, if the line is observed at 680 nanometers, the amount of wavelength shift is 680-650 = 30 nanometers. The redshift parameter z would then be z = 30/650 = 0.046. The redshift can be transformed into velocity if the velocities are small compared to the speed of light. This transformation is given by velocity = (speed of light)·(z). The speed of light, also denoted as c, is 300,000 km per second. The galaxy in our example, therefore, has velocity = (300,000)·(0.046) = 13,800 km per second away from us.

An alternate way to define redshift z is to use the ratio of the observed wavelength of the light to the wavelength it is supposed to be. From the definition of z, this ratio is mathematically equivalent to (1+z). In our example, the observed wavelength is 680 nanometers. It is supposed to be at 650 nanometers. This yields that (1+z) = 680/650 = 1.046.

b. Record the number under z or km/s for your galaxy. Return to "NED Home" and repeat until you have recorded the velocities for all 12 galaxies for which you have distances.

c. Make a graph displaying velocity and distance. Plot velocity on the vertical axis. This graph is known as the "Hubble Diagram". Comment on what it shows you.

d. Determine the value of the average ratio velocity/distance. This ratio is called

the "Hubble Constant". As you will learn in class, its value leads to an estimate of the age of the Universe.

You have reproduced for yourself the data which imply that the Universe is expanding.

Such data are all we have to estimate the age of our entire cosmos. By measuring how

fast galaxies are moving apart, and how far apart they have become, we can determine

how long they have been moving. This length of time is taken to be the age of our

Universe.

EXERCISE 7: THE COSMIC MICROWAVE BACKGROUND

By inference, the expansion of the Universe implies a beginning for that expansion. The time calculated for the duration of the expansion is taken as the age since that beginning. This is a deduction based on what we think the Universe was doing up until now but provides no direct evidence for the beginning. As we attribute the beginning to the "Big Bang" and assume that all of the present-day stuff of the Universe was in existence starting with the Big Bang, it is no surprise that we think the Universe was a very hot, dense place in its early years. The cosmic microwave background shows us energy left over from those early years, and this observable energy is taken as direct evidence for a very hot early Universe, the kind of Universe expected after the Big Bang. You will now see this energy as seen by NASA's Cosmic Background Explorer satellite.

Go to the Home Page of the Cosmic Background Explorer (COBE): http://lambda.gsfc.nasa.gov/product/cobe/.

Go to DMR (Differential Microwave Radiometer).Go to DMR Images.Go down to the last image, read the paragraph by it, and click on the image to see it in full.

The two circles show "fish-eye" views of the Universe, the first as would be seen looking away above the top side of our Milky Way Galaxy (North Galactic Hemisphere) and the second looking away below the bottom side (South Galactic Hemisphere). The color scale shows departures from the average and goes from coldest (bluest and blackest - to extremes of 100 millionths of a degree colder than average, or -100 microKelvin) to hottest (reddest, to extremes of 100 millionths of a degree hotter than average, or +100 microKelvin; 100 millionths of a degree is the same as 100 times

10-6, or 10-4 degrees). These departures from the norm are what is called "anisotropy"; something that is perfectly smooth and even is "isotropic".

Keep in mind that the average temperature of the background on which these anisotropies are found is 2.726 degrees K.

a. Sketch or reproduce the pictures and choose on one of the maps both a cold spot and a hot spot. Show on your reproduction which ones you pick.

b. What is the temperature of your hot spot? What is the temperature of your cold spot? In a percentage or ratio sense, how much hotter is the hot spot than the average? How much colder is the cold spot than the average?

c. Make an analogy to departures from perfection on the surface of a very smooth, very deep ocean. For the deepest ocean (about 35,000 feet deep), how high would a wave have to be for its height to correspond to the "hottest" departure from average?

d. Keeping in mind that each "fish-eye" view covers 180 degrees of angle across the sky, about how far apart are the cold and hot spots you picked?

The parameter (1+z) represents the factor by which wavelengths are stretched, or enlarged, because of redshift. This stretching arises because the Universe is expanding. In the most fundamental sense, (1+z) is a description of the amount of enlargement of the Universe - how much it enlarged between the time a galaxy produced light and the time (now) when we see that light. (1+z) is our most fundamental cosmological parameter, because many characteristics of the Universe depend on this enlargement factor.

The temperature of the energy in the Universe, as this temperature was in the past, increases in direct proportion to (1+z). For example, a galaxy seen having (1+z) = 3 would be seen at a time when the Universe was 3 times hotter than today.

The microwave background radiation that we see today originated when the Universe was approximately 3000 degrees K, because at that temperature the matter thinned out enough (as hydrogen atoms formed) that the light could escape and go on its way.

e. Determine the redshift z at which the microwave background radiation originated.

The distance back in time to which we observe a galaxy, or anything else in the Universe, is called the "look-back time." This is how far into the past we are seeing. It is equivalent to the distance to the object as measured in light years, because we see something as it was when the light left it. Look-back time is expressed as a fraction of the age of the Universe, using the (1+z) parameter. Transforming (1+z) into look-back time requires an assumption about whether the Universe has always been enlarging at

the same speed. (If it was expanding faster in the past, it did not take as long to reach its present size, so our estimate of the age of the Universe from the Hubble constant would be too long.)

If we assume that the expansion rate of the Universe has not changed since it began, then

Look-back time = (Age of Universe) · (z/(1+z)).

That is, the ratio z/(1+z) is a measure of the proportion of the Universe's past into which we are observing for a galaxy with a particular value of (1+z). (Need an example? Take the United States to be 222 years old (in the year 1998). If we looked back into history to an event in 1860, we would be "looking-back" 138 years, the look-back time. We would be looking back a fraction of 138/222 of the entire history. This fraction is 0.62. If there were a historical equivalent of z/(1+z), it would be 0.62 in this case.) The age of the Universe which has passed until that galaxy is seen would then be the total age of the Universe minus the look-back time. (In the historical example, this would be the age of the nation up until the event seen in 1860, which would be 84 years. You can determine for yourself that this elapsed age is the same as the total age until now - 222 - minus the look-back time.) From our calculations, we have previously deduced an expansion time of the Universe that gives an age of about 13.7 billion years. This means we will consider that

Look-back time = (13.7 billion) · (z/(1+z))

and that the elapsed age of the Universe up until a galaxy is seen is

Age of the Universe = 13.7 billion - [13.7 billion · (z/(1+z))]

f. Determine how long the Universe had existed at the time the microwave background radiation which we now see was released.

The length of time you calculate in (f) would be the maximum time that a beam of light or any other transfer of information could have traveled through the Universe up until the background radiation was released, because nothing can travel faster than light. The maximum distance covered by any information transfer in the Universe up until that time would then be the age of the Universe times the maximum travel speed, the speed of light. That is, your answer to (f) expressed as light years would be the maximum distance between any two objects in the Universe that could possibly have "communicated" in the time allowed since the Universe began.

If this calculation is made for the time at which the cosmic microwave background was produced, we find that portions of the Universe which could possibly have had time to communicate with each other were separated by less than 10 degrees in angular size on the sky. Look at your COBE maps. 10 degrees is a very small distance compared to the 180 degrees that each map extends across the sky. So how could parts of the Universe so far apart "know" they were supposed to be at the same temperature, when they could not possibly have had time to exchange any information or energy?

This contradiction between the size within which things would have had time to mix together in the early Universe and the actual observed uniformity of the entire Universe is a fundamental mystery of cosmology. It is called the "horizon" problem. When confronted with a mystery, the scientific approach is to attempt a solution based on inventing a new idea for explanation that goes beyond the old ideas that created the mystery. Trying to explain this mystery has given rise to an entirely new idea of how the Universe formed, a theory called "inflationary" cosmology. The implications of this theory are drastic. The most intriguing implication is that our Universe is only one among many - but it's ours!

The proportionalities you deduced in parts (b) and (c) for the temperature irregularities seen by COBE also apply to the anisotropies, or irregularities, in the distribution of matter in the early Universe. The hot material emitting the background radiation was of slightly differing density. The thicker material cannot be seen quite as far back in time, because you can't see through thick stuff as easily, so the thicker material is seen at a colder (more recent) temperature. The opposite is true for the thinner stuff. This means that COBE also shows that irregularities in the distribution of matter in the Universe were very small at the time the background radiation was released.

Yet, galaxies are great concentrations of matter compared to the totally empty space in

between them. Astronomers are still working to understand in detail how the evenly filled Universe at the time it was 3000 degrees subsequently coalesced into the galaxies. Somehow, the very small irregularites had to become greatly concentrated. We believe that gravity was the main agent for making this happen.

The most distant galaxy yet observed has z of approximately 6.5.

g. Determine how much time was available between the time of the release of the cosmic microwave background, at which time the matter and energy in the Universe was distributed with nearly perfect smoothness, and the time of existence for this earliest galaxy we have seen in the Universe.

h. Draw a timeline for the Universe, showing the elapsed history from the Big Bang until now, indicating the times of release of the cosmic microwave background, the time at which we see the earliest galaxy, and the time at which our Sun and Solar System formed (4.6 billion years ago).

Your answer for the time span between the production of the cosmic microwave

background and the time of the first galaxy seen is the maximum time allowable for the

transformation of the Universe from an evenly filled space of energy and matter to a

space filled with galaxies. The intervening time period remains a great mystery of the

Universe. Somehow, galaxies formed. How?

NASA's Wilkinson Microwave Anisotropy Probe (WMAP), launched in 2001, has advanced cosmic microwave background studies even further by making the most precise maps yet of this radiation. See http://map.gsfc.nasa.gov for details.

EXERCISE 8: THE MOST DISTANT OBJECTS IN THE UNIVERSE

In order to understand the formation of things, we would like to see it happening. You know from the previous exercise that some mysterious events occurred in the early years of our Universe, whereby the evenly distributed hot material that produced the microwave background radiation condensed to form galaxies. If this had not happened, our Galaxy would not be here, our Sun would not be here, our planet would not be here - and we would not be.

Our vision is penetrating further and further. This exercise shows you pictures of some of the most distant things ever seen by humans.

First, look again at the Hubble Deep Field - North field to see some of the most distant objects known in that picture. Go to http://www.stsci.edu/ftp/science/hdf/hdf.html.Go to pretty picturesGo to Sample Galaxies from the Hubble Deep Field

In the top picture, find the bluish, stretched-out galaxy underneath the small elliptical near the top of the picture and about one third of the way across the picture from the left edge. This galaxy is now known to have a redshift of z = 2.8.

a. Sketch the location of this galaxy in the picture and determine its distance in light years (which is the same as the look-back time to this galaxy). Use our

regular assumption that the Universe is 13.7 billion years old. How old was the Universe at the time this galaxy is seen?

In the bottom picture, find the little nest of four dots near the bottom of the picture and about one-fourth of the way across the picture from the right edge. This nest of objects is thought to be a galaxy in the process of birth and is now known to have a redshift of z = 3.2.

b. Sketch the location of this galaxy in the picture and determine its distance in light years (which is the same as the look-back time to this galaxy). Use our regular assumption that the Universe is 13.7 billion years old. How old was the Universe at the time this galaxy is seen?

Go to other pictures for the Hubble Space Telescope at http://hubblesite.orgUse the Search feature on the site to search for "cl1358." Find the image dated July 30, 1997 (http://hubblesite.org/newscenter/newsdesk/archive/releases/1997/25/)Read the caption.Go to Full Press Release Text.

c. Sketch the larger of the 3 pictures and show where in this picture is found the enlargement in the upper right hand box that contains the distant galaxy. Understand what you are seeing in the context of the caption. Read the press release text and record the value of redshift z that is mentioned for this galaxy.

Determine its distance in light years and how old the Universe was at the time this galaxy is seen. Comment on the color of this galaxy compared to the ones you saw in (a) and (b). Think about what this color might mean.

Return to http://hubblesite.org.Search for "Galaxies in the Young Universe 12/6/1994." View the image and read the caption.

d. Sketch the box in the image which has the greatest enlargement, labeling the galaxy and the quasar as described in the caption. Record the redshift z of each one from the last paragraph of the caption. Determine the distance in light years for both the galaxy and the quasar. What strikes you as most extraordinary about the quasar compared to all of the galaxies you have seen in this exercise?

CONCLUSION: WHAT DO WE DO NOW?

You have now studied some of the most intriguing mysteries of our Universe. Those of us whose profession is to wonder about these mysteries have plans for addressing them. One comprehensive compilation of plans is found within the description of NASA's strategy for missions to gather more crucial observations. A general orientation to the scientific themes within the NASA Space Science program and access to detailed information about all NASA science missions is maintained and updated at

http://www.hq.nasa.gov.

You and your students can find links here to about anything they might ever need for

exploring topics on their own, because NASA has become sensitized to the importance of public and student understanding of scientific discovery.

Studying these sources will allow you and your students to understand the missions and discoveries that will continue to come over the next 20 years which will give new insights, and perhaps cause new scientific revolutions. Teaching is at the frontier of stimulating a revolution in public understanding of the Universe!

The End

SUPPLEMENTAL: ACCURATE DISTANCE TO M100 AND THE LOCAL SUPERCLUSTER

In Exercise 3, you estimated the distance to M100 based upon the assumptions that it was about the size of our Galaxy and that you could measure the diameter of a galaxy with reasonable precision. We will have to return to these assumptions once more in Exercise 5, but M100 actually is close enough that its distance can be measured much more precisely.

Some galaxies, including M100, are close enough that individual stars can be seen within them. Enough is known about a few of these stars that their true luminosities are known. If the luminosity of an object is known, its distance can be deduced from the brightness it appears to have. The most important kind of stars for such a study are Cepheid variable stars. Luminosities of these stars can be determined from the rate at which they pulsate, or vary in light. If Cepheids can be found in a galaxy, their luminosities can be determined from their variability characteristics, and the distance to the galaxy containing the star can be measured. Your first exercises are to find some Cepheid variable stars in M100. You will use photographs obtained with the Hubble Space Telescope.

Go to: http://www.astro.northwestern.edu/labs/m100/m100.html

Read measuring cosmic distances in "Table of Contents." Continue to a color view of M100.

a. Draw a sketch of the positions of the four "chips" which combine together to produce an HST image. Show the dimensions of the image in terms of arcminutes and arcseconds (each of the "pixels" in the image is 0.1 arcseconds wide)

Continue to The HST images of M100 used for the Cepheid Hunt.

b. Click on one of the WF chips, then click to get a magnified view, and measure the width of that view in arcseconds, remembering that the individual pixels you see are 0.1 arcsecond wide.

Continue to Looking for variable phenomena. Read and understand the concept of "blinking" the images. Continue to Classifying variable phenomena on HST images. Continue to Hunting Cepheids.

Ignore the instruction about the lab sheet. Follow the demonstrations through the point of clicking on grid 47 and examining this grid. Note what happens when you find a real Cepheid. The technical information about the Cepheid (light curve, etc.) is not in the required scope of the exercise we are doing, but we will discuss it briefly. It is this technical information that allows astronomers to deduce how far away is that Cepheid, and therefore how far away is the galaxy M100 which contains that Cepheid. Your job will be to find another Cepheid variable star so you will get some idea of how

astronomers do this. Continue to determining the physical parameters of each Cepheid, but you may ignore this section if you wish and continue past it to begin your own Cepheid hunt

d. Pick any grid or grids you wish to examine. Work until you have found at least 2 Cepheids. For each one, draw a sketch of the grid image showing the Cepheid location and write down the grid number of the Cepheid that you found.

You have reproduced much of the process in which many astronomers have invested major effort with the Hubble Space Telescope, all toward the single objective of determining an accurate distance to the Local Supercluster. After 8 years of effort, in the spring of 1999, this "Key Project" with HST was finished. The results for the distances to 18 galaxies, based on 800 Cepheids, gave a "definitive" value for distances, supposedly accurate to 10%. You can see a discussion of this result in the Astronomy Picture of the Day (http://antwrp.gsfc.nasa.gov/apod/astropix.html), clicking into "Archive" and scrolling to May 27, 1999. As soon as this was announced, another "definitive" result using a completely independent technique yielded distances about 25% less. Oh well.) This distance is so crucial because determining an accurate distance to galaxies is the key to determining the age of the Universe, as you will see soon. (Astronomers calculate this age by using a parameter called the "Hubble Constant", which is a ratio of velocity to distance. For the Cepheid Key Project, the deduced value of H is 70 km/s/Mpc (kilometers per second per Megaparsec). You will learn later how this relates to age.)

SUPPLEMENTAL: A DISTANT GALAXY SEEN THROUGH A LENS

World's Most Powerful Telescopes Team Up With a Lens in Nature to Discover Farthest Galaxy in the Universe

Full press release text:

An international team of astronomers has discovered the most distant galaxy found in the universe to date, by combining the unique sharpness of the images from NASA's

Hubble Space Telescope with the light-collecting power of the W. M. Keck Telescopes — with an added boost from a gravitational lens in space.

The results show the young galaxy is as far as 13 billion light-years from us, based on an estimated age for the universe of approximately 14 billion years. This would place the galaxy far back in time during the "formative years" of galaxy birth and evolution, less than a billion years after the birth of the universe in the Big Bang.

The detailed image shows that bright dense knots of massive stars power this object. Due to the firestorm of starbirth within it, the galaxy is intrinsically one of the brightest young galaxies in the universe, blazing with the brilliance of more than ten times our own Milky Way.

"We are fascinated to be witnessing the very early stages of the construction of what could well become a massive galaxy like our own Milky Way," says Garth Illingworth of the University of California, Santa Cruz. "This object is a pathfinder for deciphering what is happening in young galaxies, and offers a rare glimpse of the powerful events that transpired during the formation of galaxies."

"We were excited by the possibility that we may have found a unique example of a galaxy in formation at the time of the earliest quasars," said Marijn Franx of the University of Groningen in the Netherlands.

Predicted by Einstein's theory of general relativity, gravitational lenses are collections of matter (such as clusters of galaxies) that are so massive they warp space in their vicinity, allowing the light of even more-distant objects to curve around the central lens-mass and be seen from Earth as greatly magnified.

The object is so far away, observing it in such detail would tax the capabilities of both Hubble and Keck without the magnification of the gravitational lens, provided by a foreground cluster of galaxies that is much closer to us at five billion light-years.

Due to a rare and fortunate alignment of the young galaxy behind the foreground cluster, astronomers gain a magnified view that is five to ten times better than Hubble alone can yield for an object at such a great distance. A telltale sign of the lensing is the smearing of the remote galaxy's image into an arc-shape by the gravitational influence of the intervening galaxy cluster.

The smeared image of the galaxy stood out because of its unusual reddish color. "Such magnified galaxies had been observed before, but never with such a color. The special color of the galaxy in the arc is due to absorption by the matter in the universe between us and the galaxy, and suggested to us that it was at a great distance," says Franx.

The suspected remoteness of the lensed object was confirmed when the team of astronomers made spectroscopic observations with one of the twin 10-meter Keck telescopes on Mauna Kea, HI, to measure its redshift, and therefore its distance, based on the shifting of its light towards the red end of the visible light spectrum. The resulting high redshift (z=4.92) corresponds to a very early era when the universe was just beginning to form galaxies.

Though candidates for still more distant objects have been proposed, they have not been confirmed spectroscopically. The previous most-distant known object was the quasar PC1247+34 (z=4.90).

"Based on this image we can begin to make some conclusions about the early growth of galaxies," says Illingworth. "The knots show that starbirth happens in very tiny regions compared with the size of the final galaxy." This helps clarify the astronomer's view of the formation of galaxies as occurring within a cauldron of hot gas, with knots of intense star formation, strong winds, and "mergers" — collisions of the dense star-forming knots.

Using Keck's spectroscopic capabilities, the astronomers have also, for the first time, been able to measure the motions of the gas within such a distant galaxy. The observations reveal gas flowing at nearly 500,000 miles per hour (200 km/sec), presumably accelerated by energy from supernova explosions going off like a string of firecrackers.

"The strong winds that we observe suggest that galaxies may lose a lot of material when they are young and thereby enrich the empty space around them," says Franx. "Many astronomers had speculated about the existence of such winds in such distant galaxies, and we now have an object where we can see them directly. It is striking that the most distant galaxy found to date is also the one that provides us the most detailed picture of events in such distant galaxies."

Release Date: 12:00AM (EDT) July 30, 1997 Release Number: STScI-1997-25

Contact:

Don SavageNASA Headquarters, Washington, DC(Phone: 202/358-1547)

Tammy JonesGoddard Space Flight Center, Greenbelt, MD(Phone: 301/286-5566)

Ray VillardSpace Telescope Science Institute, Baltimore, MD(Phone: 410-338-4514)

Andrew PeralaW.M. Keck Observatory, Kamuela, HI(Phone: 808/885-7887)

SUPPLEMENTAL: GALAXIES IN THE YOUNG UNIVERSE

[left] This image of a small region of the constellation Sculptor, taken with a ground-based photographic sky survey camera, illustrates the extremely small angular size of a distant galaxy cluster in the night sky. Though this picture encompasses a piece of the sky about the width of the bowl of the Big Dipper, the cluster is so far away it fills a sky area only 1/10th the diameter of the Full Moon. The cluster members are not visible because they are so much fainter than foreground stars.

[center] A NASA Hubble Space Telescope (HST) image of the farthest cluster of galaxies in the universe, located at a distance of 12 billion light-years. Because the light from these remote galaxies has taken 12 billion years to reach us, this image is a remarkable glimpse of the primeval universe, at it looked about two billion years after the Big Bang. The cluster contains 14 galaxies, the other objects are largely foreground galaxies. The galaxy cluster lies in front of quasar Q0000-263 in the constellation Sculptor. Presumably the brilliant core of an active galaxy, the quasar provides a beacon for searching for primordial galaxy clusters.

The image is the full field view of the Wide Field and Planetary Camera-2, taken on September 6, 1994. The 4.7-hour exposure reveals objects down to 28.5 magnitude.

[right]This enlargement shows one of the farthest normal galaxies yet detected, (blob at center right) at a distance of 12 billion light-years (redshift of z=3.330). The galaxy lies 300 million light-years in front of the quasar Q0000-263 (z=4.11, large white blob and spike on left side of frame) and was detected because it absorbs some light from the quasar. The galaxy's spectrum reveals that vigorous star formation is taking place.

Credit: Duccio Macchetto (ESA/STScI), Mauro Giavalisco (STScI), and NASA