AST 104 Lab 8: Hubble Deep Field & The Fate of the Universe

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1 Name: SUID: AST 104 Lab 8: Hubble Deep Field & The Fate of the Universe Introduction: One of the most revered images in all of Astronomy is the so called Hubble Deep Field image. Part of the Hubble Telescope s mission was to use its telescopic power to observe distant objects that were previously beyond our ability to see. So, after some minor mishaps involving a bad mirror and some recalibration, the Hubble Telescope was aimed at a typical patch of sky, which was devoid of many bright sources within the Milky Way Galaxy, so that most if not all of the image would be of distant objects, such as galaxies. Your TA should have the resulting image on display. The image is beautiful, not only for its diverse array of colors and shapes, but for what it reveals about our Universe. The fraction of the sky this represents is incredibly small (You ll see just how small in section 1), and yet even within this tiny fraction of the sky, we see many, many galaxies, each with its billions upon billions of stars, each of which with the possibility for many planets. It s humbling in a way to see just how small our corner of the Universe really is. However, more can be drawn from this image than poetry and existential epiphanies; this image is enough to make a prediction for the very fate of the Universe itself. This lab will walk you through how, first by familiarizing you with the use of angular distances to make measurements of the sky, and then by deducing how many galaxies exist in our Universe, and then using that result to determine what fate has in store for our Universe.

2 Part 1: Angular Measurement: You are likely familiar with the idea of measuring lengths and distances using a ruler or similar device, obtaining a measurement in units of length such as inches or meters. But this way of measuring isn t useful for measuring things we see in the sky. Instead we measure such things in terms of angles; we state lengths as the angle the object makes in the sky. You can imagine finding the angle of the Moon by extending your arm so that you point to the bottom of the moon, and the raising your arm until you point to the top. The angle your arm swept through is the angular measurement of the Moon. We ll be using measurements like this throughout the lab, so we ll familiarize you with them by exploring just how small the Hubble Deep Field image really is, first by comparing it to the familiar Moon, and then to the sky as a whole. 1.) A degree is subdivided into smaller units (In much the same way that feet are divided into the smaller inches); 1 Degree contains 60 arc-minutes, and 1 arc-minute contains 60 arc-seconds. The diameter of the Moon measured in degrees is about. 5 o. What is the Moon s diameter in arc-minutes? Moons Diameter: arc-minutes. 2.) The area of a circle in terms of its diameter is A = 1 4 πd2, where D is the diameter. What is the area of the Moon in arc-minutes^2? Moon s Area: arc-minutes^2.

3 3.) At each table should be a printout of a small section of the Hubble Deep Field image (Specifically, the top left corner). This image represents roughly 1/13 th of the total image, and is approximately a square with length of.6 arc-minutes. Thus, its area is.36 arc-minutes^2. Based on this, how many times can this small section fit inside the area of the moon in the sky? The Hubble Deep Field image can fit in the area of the Moon times! 4.) Based on these answers, do you think the section of the Hubble Deep Field image on the printout represents a large portion of the sky?

4 Part 2: The Number of Galaxies in the Universe When the astronomers controlling the Hubble Telescope selected the region of the sky to point the telescope at, they intentionally chose a typical region of the sky. Thus, it makes sense to assume that what is true for this part of the sky ought to be true for everywhere in the sky. We will use this fact to estimate the number of galaxies in the Universe 1.) We can think of the sky as a sphere that encapsulates the Earth, where what we see is the interior surface of that sphere. Thinking of the sky this way, we can deduce the radius of this sphere to be about 57.3 degrees. Convert the number to arc-minutes, and then find the area of the sky in arc-minutes using the formula A = 4πr 2. (Note: You should consider using scientific notation for the rest of this lab. The numbers get quite messy otherwise!) The Area of the sky is arc-minutes^2. 2.) How many of the Deep Field Image sub-sections would we need to cover the entire sky? Consider using scientific notation. We would need Deep Field images to cover the entire sky.

5 3.) Carefully count the number of galaxies in the printout of the small piece of the Hubble Deep Field image. Number of galaxies in Deep Field Image sub-section: galaxies. 4.) Using your answers to questions 2 and 3, find a way to estimate the total number of galaxies in the Universe. It is worth noting how impressive this number is, both because of how many galaxies this reveals to be in the Universe, and because such an estimate was obtained from a single image! Number of galaxies in the Universe: galaxies! Part 3: The Fate of the Universe Now that we have an estimate for the number of galaxies in the Universe, it s time to estimate the mass density of the Universe (The amount of mass divided by the volume). This number is of vital importance; this single number can tell you the eventual fate of the entire Universe! 1.) The Milky Way Galaxy is a fairly typical galaxy, neither noticeably bigger nor noticeably smaller than most other galaxies. We can therefore assume that its mass of 3*10 45 g is the average mass of a galaxy in the Universe. Using this value and your estimate for the number of galaxies in the Universe, determine an estimate for the total mass of the Universe. Total mass of the Universe: grams.

6 2.) We now need an estimate for the volume of the Universe that we can see. If we assume that the farthest galaxy we ve been able to see, at 13 billion light-years away, is at the edge of the (observable) Universe, then the radius of the Universe is also 13 billion lightyears, which in centimeters is 1.235*10 28 cm. Since the volume of a sphere is V = 4 3 πr3, what is the volume of the Universe in cm^3? Volume of the Universe: cm^3. 3.) The mass density can be found by taking the total mass and dividing by the total volume. What, then is the mass density of the Universe? Mass density of the Universe: g/cm^3. 4.) Gravity extends to the outer reaches of the Universe. Because all the galaxies in the Universe attract all the other galaxies in the Universe it is possible that the gravitational pull of all the galaxies will eventually reverse the Hubble expansion. If this happens the galaxies will begin to fall back together and will lead to a Big Crunch. Astronomers estimate this will happen if the mass density of the Universe is g/cm^3. This is known as the critical density. Compare the value you obtained for the mass density of the universe with the critical density. If your estimate is correct what is the fate of the Universe?

7 Part 4: Additional Questions 1.) During the course of this calculation, we made several assumptions. Each assumption we make impacts the accuracy of our result. List as many such assumptions as you can, and comment on a.) Whether you think this assumption was reasonable and b.) How much you think this affected our result. You should find at least 3 such assumptions! 2.) Based on your answer to question 1 above, do you think your answer for the fate of the Universe is still reasonable?

8 3.) Suppose astronomers discovered large clumps of dark matter outside of galaxies, and spread throughout the Universe. Would this dark matter have been included in our estimate for the mass of the Universe? What effect, if any, would this discovery have on our estimate for the mass density of the Universe?