UNIVERSITY OF SURREY DEPARTMENT OF PHYSICS

Level 1: Experiment 2B

THE HUBBLE CONSTANT AND RADIO

1 AIMS

1.1 Physics This experiment consists of a pair of computer simulations that mimic ‘virtual’ telescopes. The first part of the experiment simulates a robotic optical telescope equipped with a spectrometer to examine the spectra of and to measure their apparent magnitudes, whilst the second part simulates a radio telescope to measure the MHz frequency signals from neutron . The specific aims of the two parts of the experiment are as follows: Part 1: Hubble Constant and Red-Shift Measurements. Spectrometer data is used to measure the spectra of light emitted from galaxies, and their apparent magnitudes. Using Pogson’s law you will determine their distances from the Earth. From the spectra you will use the Doppler Effect to determine their velocities. At the end of the first part of this experiment you should be able to: l Understand how the position of an object in space can be determined by a co- ordinate system based on a sphere, and understand the as a unit of astronomical distance. l Understand how stellar magnitudes can be used to estimate astronomical distances. l Calculate a value for the Hubble constant and the rate at which the is expanding. l Estimate the age of the universe and assess some of the problems in obtaining a reliable estimate. Part 2: Pulsar Radio Astronomy. The periodic radio signals received from pulsars are examined, and the period of the signal is measured. By studying the variations in the arrival time of pulsar signals as a function of the signal frequency, the dispersion of electromagnetic radiation travelling through space is measured. From these dispersion measurements, the distance of a typical pulsar can be calculated. At the end of this part of the experiment you should be able to: l Understand the nature and mechanism of pulsar signals from neutron . l Measure the period of a pulsar signal and show that the signal strength varies as a function of radio frequency. l Understand the effect of dispersion in the propagation of pulsar signals, and use this effect to measure the distance of a typical pulsar from earth.

Last updated on 4/2/05 by PJS Experiment 2B - Hubble Constant and Pulsars 1.2 Skills The particular skills you will start to acquire by performing this experiment are: l The ability to use a realistic computer simulation. l Appreciate the use of optical and radio telescopes to acquire spectra and radio signals, and how this data can be used to determine stellar and extragalactic distances. l Researching the scientific methods for measuring stellar and pulsar distances and the latest findings on the expansion and age of the universe.

PART1: THE HUBBLE CONSTANT - REDSHIFT RELATIONSHIP

2. INTRODUCTION AND THEORY

The instructions for using the computer simulation are contained in Appendix A. There are some terms and expressions however that you may be unfamiliar with. These are explained below:

2.1 The Celestial Coordinate System

Right Ascension and . This is a celestial coordinate system similar to the terrestrial system of longitude and latitude with the earth situated at the centre of a .

Declination (symbol d or Dec) is analogous to latitude and is the angular distance of a celestial object above or below the celestial equator. It is measured in degrees, seconds and minutes of arc as shown in Figure 1. Right Ascension (symbol RA or a) is analogous to terrestrial longitude and is the angular distance between the hour circle though an object and the hour circle through the vernal equinox. RA is usually measured in hours, minutes and seconds.

In this way the position of a celestial object can be uniquely specified by its RA and Dec as shown in Figure 1.

Figure 1: The terrestrial coordinate system of longitude and latitude (left), and the celestial coordinate system of Right Ascension and Declination (right).

Page 2 of 18 Experiment 2B - Hubble Constant and Pulsars 2.2 Absolute and Apparent Magnitudes – Pogson’s Law & Stellar Distances

The scale on which stars are rated is based on a convention first devised by Hipparchus. They are classified by by rating the brightest stars that can be seen with the naked eye as magnitude 1.0, and the faintest as magnitude 6.0. Later, with the invention of the telescope and for consistency, it became necessary to assign to some stars a magnitude brighter than 1.0. Hence is magnitude 0 and , magnitude -1.4. The has an apparent magnitude of -26.74! It is important to understand that the more negative the apparent magnitude, the brighter the star appears. Or conversely, the larger the magnitude (more positive), the fainter the star appears. To understand why this is so we need to note two things:

The human eye perceives equal ratios of brightness at equal intervals. For example, if you tried to compare the relative brightness of a 100W and 200W light bulb at the same distance, then the 200W bulb would not appear twice as bright as the 100W bulb. What you would observe however, is that the difference in brightness between the 100W and the 200W bulb will appear the same as the difference in brightness between a 200W and a 400W bulb.

On Hipparchus’s scale, the flux (W.m-2) coming from stars of the 1st magnitude was about 100 times greater than that from stars of the 6th magnitude. A difference of 6 - 1 = 5 magnitudes therefore, corresponds to a flux ratio of 100. This means that a magnitude difference of 1 corresponds to a flux ratio of (100)1/5 or 2.512. Pogson in 1856, formulated Hipparchus somewhat subjective scale into a precise mathematical law: æ f ö ç 2 ÷ m2 - m1 = -2.5logç ÷ (1) è f1 ø

where m1 and m2 are the apparent magnitudes of star 1 and star 2, respectively and f1 and f2 are the received flux from star 1 and star 2, respectively.

We can see that equation (1) is sensible if we note that the minus sign ensures that magnitudes are a measure of faintness. If f2 < f1 (star 2 is fainter than star 1) then the flux ratio is < 1 and the log of the ratio is negative. So m2 - m1 is positive and the fainter star has the larger magnitude as expected. The multiplier 2.5 is a scaling factor that ensures that a flux ratio of 100 corresponds to a magnitude difference of 5. e.g. if f2 / f1 = 1/100 then m2 - m1 = 5.

We can now use Pogson’s law to derive an scale and use it to estimate stellar distances.

Suppose you could place all the stars at a fixed distance from the earth. The differing distances would not then be a factor in how bright the stars appeared. Instead, the differences in magnitude would be only due to differences in and as such, these values would be absolute.

Astronomers use a standard distance of 10 for absolute magnitude comparison. See Appendix C for explanation of the parsec (pc). The magnitude that a star would have 10pc from the earth is thus defined as its absolute magnitude.

If a star has a Luminosity L with an absolute magnitude M then assuming that the luminosity is radiated uniformly over the area of a sphere, the flux received at the earth if the star is at a distance r is

Page 3 of 18 Experiment 2B - Hubble Constant and Pulsars L f = (2) 4pr 2

Let f10 be the flux the star would have at a distance of 10pc. Then from Pogson’s law,

2 2 2 2 m - M = -2.5 log (f / f10) where f10 = L / (4p.10 ) so f/f10 = 10 /r = (10/r) .

We can thus write Pogson’s law as: 2 æ10 ö m - M = -2.5logç ÷ = -5log10 + 5log r è r ø or m - M = 5log r - 5 (3)

In the experiment you will use equation (3) by measuring the apparent magnitude m and assuming a value for the absolute magnitude M in order to calculate r. For the purposes of the experiment, the absolute magnitude of all galaxies that you will observe is assumed to be -22. Note that we are measuring visual magnitudes as opposed to bolometric magnitudes. i.e. the magnitude measured over all wavelengths of the electromagnetic spectrum. Pogson’s law is a reasonable one, since with the exception of very hot and very cool stars, most is emitted in the visual part of the spectrum.

2.3 Doppler shift of the H & K lines of Ca

The Doppler effect is something you should be familiar with. We use the relation:

Dl V = r (4) l0 c

where Dl = lobserved - l0 where l0 is the wavelength observed in the laboratory and Vr is the of the .

The H and K lines of Ca are prominent spectral absorption lines of ionised calcium from stars with surface temperatures similar to the sun. The K line (393.4nm) and the H line (396.8nm) are easily observable in galaxies. Note that the spectrometer measures the wavelength in angstroms (1 Angstrom = 1Å = 10-10m).

By measuring lobserved for each of the K and H lines you can use equation (4) to calculate the radial velocity in each case.

You should take the average of the two values you have calculated for your measure of the radial velocity of the galaxy.

2.4 Hubble’s Law

It the early part of the 20th Century it was noticed that all the galaxies except those relatively nearby, showed redshifts in their spectra. Edwin Hubble (1899 - 1953) plotted their distances against their radial velocities. He found that the further a galaxy was from the , the faster

Page 4 of 18 Experiment 2B - Hubble Constant and Pulsars it was moving away. This was the first direct evidence that the universe was expanding. Could it be due to a gigantic explosion in the past?

Hubble expressed this as Hubbles's Law:

Vr = H 0d (5)

where H0 is the Hubble Constant. The Hubble Constant also gives us information about the age of the universe. To see this note that H0 = Vr/d. Now if we take the reciprocal of H0 from equation (5) we can see that this is simply a measure of “how long the universe has been travelling for” or its current age.

3 MAKING THE MEASUREMENTS

Follow the instructions as given in the student manual. In particular you should:

A Familiarise yourself with operating the telescope and moving it around the sky. Watch out for authors!

B Make sure that the spectrometer slit is centred on the brightest section of the galaxy. This will minimise your integration time. Make sure you count for a period that gives you at least a signal to noise ratio of 10.

C You should record measurements from at least 2 galaxies in each galaxy cluster. This should give you about 10 sets of measurements.

D For each measurement record:

(i) The name of the object being observed (ii) Its apparent magnitude (iii) The photon count (iv) Integration time (v) Wavelength of the K and H lines (vi) Intensity (vii) Signal to noise ratio

Note monitor must be set to finder when changing field.

Page 5 of 18 Experiment 2B - Hubble Constant and Pulsars 4 ANALYSIS

Answer the following questions:

(i) On the tracking display of the robot telescope, North & South are in their normal positions yet East & West are reversed. Why is this? (Hint: think about the observer’s position in relation to the celestial sphere).

(ii) Using equation (3) calculate r for each set of measurements. Calculate Dl for each of the K -1 and H lines and use equation (4) to calculate each galaxy’s radial velocity Vr in km.s by

taking the average of each value of Vr that you calculate for the K and H lines.

(iii) Plot a graph of Vr against r for the values you have obtained. Remember that r is measured in parsecs.

(iv) From the slope of your graph, determine a value for the Hubble Constant in km.s-1.Mpc-1 and an error in your value. Hence determine the current age (and error) of the universe.

(v) Equation (3) was used on the assumption that the light from distant galaxies is not attenuated during its passage to earth. In reality starlight has to pass through interstellar gas and dust clouds in the Milky Way where absorption may take place. Intergalactic absorption may be considered negligible. Equation (3) then becomes

M = m + 5 - 5log r - AV d (6)

where AV is the interstellar absorption factor and d is the distance (in pc) over which

absorption occurs. A typical value for AV within line of sight of the galactic plane of the Milky Way, is 0.002 magnitudes pc-1. The Sun lies out to towards the edge of the galactic disc and a realistic value for d might be 150 pc. Using equation (6) and two sets of values of m calculate an average revised value of r based on an absorption distance of 150 pc.

(vi) From your answer to (v) calculate a revised value of H0 and hence a revised estimate of the age (and error) of the universe.

(vii) Compare your answers to (vi) with your answers to (iv). Does the effect of interstellar absorption have a significant effect on your values of the Hubble Constant and the age of the universe?

(viii) Values for the Hubble Constant of between 50 and 100km.s-1.Mpc-1 have been measured.

What are the implications of a relatively high value of H0 for the age of the universe and theories of galaxy and ? (Hint: look at reference [4]).

Page 6 of 18 Experiment 2B - Hubble Constant and Pulsars Part 2: PULSAR MEASUREMENTS WITH A RADIO TELESCOPE

5. NEUTRON STARS AND PULSARS Many of the most massive stars, astronomers believe, end their lives as neutron stars. These are bizarre objects so compressed that they consist entirely of neutrons, with so little space between them that a star containing the mass of our sun occupies a sphere no larger than about 10 km. in diameter, roughly the size of Manhattan Island. Such objects, one would think, would be extremely hard, if not impossible, to detect. Their surface areas would be several billion times smaller than the sun, and they would emit so little energy (unless they were impossibly hot) that they could not be seen over interstellar distances. Astronomers were therefore quite surprised to discover short, regular bursts of radio radiation coming from neutron stars—in fact it took them a while before they realized what it was they were seeing. The objects they discovered were called pulsars, which is short for “pulsating radio sources.” The discovery of pulsars was made quite by accident. In 1967, Jocelyn Bell, who working for her Ph.D. under Anthony Hewish in Cambridge, was conducting a survey of the heavens with a new radio telescope that was designed specifically to look for rapid variations in the strengths of signals from distant objects. The signals from these objects varied rapidly in a random fashion due to random motions in the interstellar gas they pass through on their way to earth, just as stars twinkle randomly due to motions of air in the earth’s atmosphere. Bell was surprised one evening in November, 1967 to discover a signal that varied regularly and systematically, not in a random fashion. It consisted of what looked like an endless series of short bursts of radio waves, evenly spaced precisely 1.33720113 seconds apart. The pulses were so regular, and so unlike natural signals, that, for a while, Bell and Hewish tried to find some artificial source of radiation—like a radar set or home appliance—that was producing the regular interference. It soon became clear that the regular pulses moved across the sky like stars, and so they must be coming from space. The astronomers even entertained the idea that they were coming from “Little Green Men” who were signalling to the earth. But when three more pulsating sources were discovered with different periods (all around a second in length) and signal strengths in different parts of the sky, it became clear that these “pulsars” were some sort of natural phenomenon. When Bell and Hewish and their collaborators published their discovery, in February 1968, they suggested that the pulses came from a very small object - such as a neutron star - because only an object that small could vary its structure or orientation as fast as once a second. It was only about six months after their discovery that theoreticians came up with an explanation for the strange pulses: they were indeed coming from rapidly spinning, highly magnetic, neutron stars. Tommy Gold of Cornell University was the first to set down this idea, and, though many details have been filled in over the years, the basic idea remains unchanged. We would expect neutron stars to be spinning rapidly since they form from normal stars, which are rotating. When a star shrinks conservation of angular momentum causes the star to spin faster. Since neutron stars are about 100,000 times smaller than normal stars, they should spin 100,000 times faster than a normal star. Our sun spins once very 30 days, so we would expect a neutron star to spin about once a second. A neutron star should also have a very strong magnetic field, magnified in strength by many orders of magnitude over that of a normal star - because the shrunken surface area of the star concentrates the field. The magnetic field, in a

Page 7 of 18 Experiment 2B - Hubble Constant and Pulsars pulsar, is tilted at an angle to the axis of rotation of the star (see Figures 2a and 2b).

Figure 2: The pulse is ‘on’ when the earth receives radio waves (left) and the pulse is ‘off’ when the magnetic axis of the pulsar is tilted away from the earth (right). According to this model the rapidly spinning, highly magnetic neutron star traps electrons and accelerates them to high speeds. The fast-moving electrons emit strong radio waves which are beamed out like a lighthouse in two directions, aligned with the magnetic field axis of the neutron star. As the star rotates, the beams sweep out around the sky, and every time one of the beams crosses our line of sight (basically once per rotation of the star), we see a pulse of radio waves. Today over a thousand pulsars have been discovered, and much more is known about them than in 1967. The pulsars seem to be concentrated toward the plane of the Milky Way galaxy, and lie at distances of several thousand parsecs away from us. This is what we’d expect if they are the end products of the evolution of massive stars, since massive stars are formed preferentially in the spiral arms which lie in the plane of our galaxy. Except for a few very fast “millisecond” pulsars, the periods of pulsars range from about 1/30th of a second to several seconds. The periods of most pulsars increase by a small amount each year—a consequence of the fact that as they radiate radio waves, they lose rotational energy. Because of this, we expect that a pulsar will slow down and fade as it ages, dropping from visibility about a million years after it is formed. The faster pulsars thus are the youngest pulsars (except for the “millisecond pulsars, a separate type of pulsars, which appear to have been spun up and revitalised by interactions with a nearby companion.) To an observer, a pulsar appears as a signal in a radio telescope; the signal can be picked up over a broad band of frequencies on the dial (In this exercise, you can tune the receiver from 400 to 1400 MHz). The signal is characterised by short bursts of radio energy separated by regular gaps. Since the period of a pulsar is just the length of time it takes for the star to rotate, the period is the same no matter what frequency your radio telescope is tuned to. However, the signal appears weaker at higher frequencies. The pulses also arrive earlier at higher frequencies, due to the fact that radio waves of higher frequency travel faster through the interstellar medium, a phenomenon called interstellar dispersion. Astronomers exploit the phenomenon of dispersion, to determine the distance to pulsars. In this exercise, you will learn how to operate a simple radio telescope, and then use it to investigate the periods, signal strengths, and distances of several representative pulsars.

Page 8 of 18 Experiment 2B - Hubble Constant and Pulsars 6. MEASURING THE DISTANCE OF PULSARS From observations of distribution of pulsars in the sky we can see that pulsars are strongly concentrated along the Galactic plane, indicating that they populate the disk of our Galaxy. Direct measurements of the distances to pulsars are notoriously difficult to obtain – the details of these techniques are outside the scope of this experiment. In the absence of a direct measurement, the distances to most pulsars can be estimated from an effect known as pulse dispersion, which arises from the fact that the group velocity of the pulsed radiation through the ionised interstellar medium is frequency dependent. Pulses emitted at higher radio frequencies travel faster through the interstellar medium, arriving earlier than those emitted at lower frequencies. You’ll be able to see this small effect using our radio telescope, since you can receive signals at up to three wavelengths simultaneously, and can compare the arrival times on the three graphic displays. Experimental observations have been used to derive a phenomenological expression relating the delay Dt between two signals at different frequency to the distance of the pulsar. For a high frequency signal f1 (MHz) and a low frequency signal f2 (MHz), Dt (seconds) can be expressed as:

2 2 ææ 1 ö æ 1 ö ö Dt = 4.15´10-3 ´ çç ÷ - ç ÷ ÷ D n çç f ÷ ç f ÷ ÷ e èè 2 ø è 1 ø ø where D the pulsar distance is in parsecs, the frequencies f1, f2 are in MHz, and ne the interstellar electron density has the value of 3x104 m-3. Using this expression the distance of a pulsar can be measured from the difference in arrival time of a pulse at two different frequencies.

Page 9 of 18 Experiment 2B - Hubble Constant and Pulsars

7. MAKING THE MEASUREMENTS Open the Radio Telescope program using the ‘Radio Astronomy of Pulsars’ icon on the desktop. A Familiarise yourself with the controls used to steer the Radio Telescope and the operation of the Radio Receiver – as described in Appendix B. B Point the telescope at pulsar 0628-28 (from the Hot-List) and set the radio receiver to 600 MHz. Measure the pulsar period by averaging over 10 pulsar peaks. Estimate the error in your value of the period, using an estimate of the cursor precision on the screen. C Investigate how the period of the pulsar varies as a function of frequency. Tabulate the pulsar period over ~8 values of the radio receiver frequency in the range 400 – 1400 MHz, and plot a graph of your data. Comment on the variation in the signal strength with radio frequency. You may wish to look at some other pulsars from the Hot List, such as 2154+40, 0740-28, and 0531+21 (Crab Nebula). Generally speaking the rotation of a pulsar slows down as it ages, so a period measurement allows a crude ranking of age of different pulsars. D To investigate the interstellar dispersion, display 2 radio receiver channels, both set initially at 400 MHz (use the add channel button when the receiver is off) and with the Horizontal Seconds set to 4. Increment the frequency of the second channel f2 in 100 MHz steps up to its maximum value, whilst keeping the frequency of the first channel f1 constant at 400 MHz. Tabulate the time difference Dt between the signals as a function of frequency f2. Include an estimate of the error in Dt. You may find that at high frequencies the intensity of the peaks becomes too weak for an accurate measurement. Experiment with increasing the Horizontal Seconds control to a higher value – the integration time of the detector increases and the peaks become smaller. Why is this not useful for your measurements of small time differences? Using the dispersion expression on the previous page for the time difference Dt as a function of f1 and f2, choose a suitable graph with which you can demonstrate the linearity of this expression. Plot this graph using the data from your table. Do you consider the error in your X-axis values or in your Y-axis values to be the most significant? Add error bars to the points if appropriate. Comment on the graph’s linearity, and hence the validity of the interstellar dispersion formula over a range of frequencies. E To measure the pulsar distance D, it is necessary to acquire three simultaneous signals at three different frequencies. Open a third radio channel, and set the three channels to 400 MHz, 600 MHz and 800 MHz (with a Horizontal Seconds value of 4 s). Click on the record button to save the data to disk. Switch the receivers on and let the them scan five or six times (only the first four scans are saved). Switch the receiver off and click OK to the dialogue boxes. Save the data file to your network (H:\) drive or to a floppy disk for subsequent analysis in SigmaPlot or Excel.

Page 10 of 18 Experiment 2B - Hubble Constant and Pulsars

8. PULSAR DISTANCE DATA ANALYSIS

The Radio Telescope data files are saved as ASCII files (with a default file name .PLR) that can be imported into SigmaPlot or Excel. The first few lines of a typical data file for 3 channels of data looks like this: (the ! comments have been added to the file later)

'0628-28',100,2 ! name of pulsar, telescope aperture (m), number of receivers (0-2) 400.00,600.00,800.00 ! frequencies of the 3 traces (MHz) 1.000,1.000,1.000 ! receiver gains 51920.11465512,0.01000 ! start time (JD – 2,400,000), time interval DT between points (sec) 2.000,5.000,6.108 ! first data points (at time T0) 2.000,3.000,2.422 ! second data points (at time T0+ DT) 2.000,0.000,3.000 ! etc… 1.000,1.000,3.422 0.000,1.523,4.422 0.000,3.090,2.000 0.000,1.000,0.000 Note that the data points start from Row 5 onwards, and the time interval between points is given in Row 4. Import1 the data into your preferred spreadsheet, and display the 3 traces as line graphs. Label the graphs carefully (eg. with the time interval between points) and print them out to put in your laboratory notebook. 2 2 æ 1 ö æ 1 ö ç ÷ ç ÷ Use the data from the graphs to extract values of T2 - T1 and ç ÷ - ç ÷ , and hence the è f 2 ø è f1 ø pulsar distance D. With the three frequencies you will be be able to extract three pairs of these values, leading to three separate measurements of D. Estimate the error on the values of D that you calculate. Comment on the consistency of your three measurements of the pulsar distance, and quote an average value, with an error.

9. REFERENCES

1) C.R. Kitchin, Astrophysical Techniques, (Adam Hilger, Bristol, 1991) 2nd Ed. This contains more information on the stellar magnitude scale. 2) C.W. Allen, Astrophysical Quantities, (Athlone Press, London, 1973). Data on interstellar absorption coefficients may be found on p 263. 3) W.J. Kaufmann, Universe, (W.H.Freeman & Co, New York, 1987) 2nd Ed. Discussion on stellar may be found on p. 345. 4) W.L. Freedman et al, Nature 371, 757 - 762 (1994).

1 To import data into SigmaPlot, you must first rename the Radio Telescope data file using Windows Explorer so that the file extension is .DAT instead of .PLR – this will allow SigmaPlot to ‘see’ the file. Then from SigmaPlot choose the Import option from the File menu, set the Rows control to 5, and click on Analyse. Then select Import and check that the 3 traces of data have been correctly assigned to 3 columns in the spreadsheet. It is a good idea to then give each column a name to identify the frequency of the data set – right click on the top of each spreadsheet column to set the Column Title. Page 11 of 18 Experiment 2B - Hubble Constant and Pulsars APPENDIX A: Using the Hubble – Redshift Telescope.

The software for the CLEA Hubble Redshift Distance Relation laboratory exercise puts you in control of a large optical telescope equipped with a TV camera and an electronic spectrometer. Using this equipment, you will determine the distance and velocity of several galaxies located in selected clusters around the sky. From these data you will plot a graph of velocity (the y-axis) versus distance (the x-axis). How does the equipment work? The TV camera attached to the telescope allows you to see the galaxies, and “steer” the telescope so that light from a galaxy is focused into the slit of the spectrometer. You can then turn on the spectrometer, which will begin to collect photons from the galaxy. The screen will show the spectrum—a plot of the intensity of light collected versus wavelength. When a sufficient number of photons are collected, you will be able to see distinct spectral lines from the galaxy (the H and K lines of calcium), and you will measure their wavelength using the computer cursor. The wavelengths will be longer than the wavelengths of the H and K lines measured from a non-moving object (397.0 and 393.3 nanometers), because the galaxy is moving away. The spectrometer also measures the apparent magnitude of the galaxy from the rate at which it receives photons from the galaxy. So for each galaxy you will have recorded the wavelengths of the H and K lines and the apparent magnitude. Familiarise yourself with the operation of the telescope, using the following commands: 1. Open the Hubble Redshift program by double clicking on the Hubble Redshift Icon (pink). Click on Log in... in the MENU BAR and enter student names if you wish (omit the lab table number). Click OK when ready. 2. The title screen of exercise appears. In the MENU BAR, the only available (bold-faced) choices are to start or to quit, click on Start. The Hubble Redshift Distance Relation program simulates the operation of a computer- controlled spectrometer attached to a telescope at a large mountain-top observatory. It is realistic in appearance, and is designed to give you a good feeling for how astronomers collect and analyse data for research. The screen shows the control panel and view window as found in the “warm room” at the observatory. Notice that the dome is closed and tracking status is off. 3. To begin the experiment, first open the dome by clicking on the dome button. The dome opens and the view we see is from the finder scope. The finder scope is mounted on the side of the main telescope and points in the same direction. Because the field of view of the finder scope is much larger than the field of view of the main instrument, it is used to locate the objects we want to measure. The field of view is displayed on-screen by a CCD camera attached on the finder scope. (Note that it is not necessary for astronomers to view objects through an eyepiece.) Locate the Monitor button on the control panel and note its status, i.e. finder scope. Also note that the stars are drifting in the view window. This is due to the rotation of the earth and is very noticeable under high magnification of the finder telescope. It is even more noticeable in the main instrument which has even a higher magnification. In order to have the telescope keep an object centred over the spectrometer opening (slit) to collect data, we need to turn on the drive control motors on the telescope. 4. We do this by clicking on the tracking button.

Page 12 of 18 Experiment 2B - Hubble Constant and Pulsars The telescope will now track in sync with the stars. Before we can collect data we will need to do the following: (a) Select a field of view (one is currently selected). (b) Select an object to study (one from each field of view). 5. To see the fields of study for tonight’s observing session. Click once on the change field item in the MENU BAR at the top of the control panel. The items you see are the fields that contain the objects we have selected to study tonight. An astronomer would have selected these fields in advance of going to the telescope by: (a) Selecting the objects that will be well placed for observing during the time we will be at the telescope. (b) Looking up the RA and DEC of each object field in a catalog such as Uranometria 2000, Norton’s , etc. This list in the change field menu item contains 5 fields for study tonight. You will need to select one galaxy from each field of view and collect data with the spectrometer (a total of 5 galaxies). To see how the telescope works, change the field of view to Ursa Major II at RA 11 hour 0 minutes and Dec. 56 degrees 48 min. Notice the telescope “slews” (moves rapidly) to the RA and DEC coordinates we have selected. The view window will show a portion of the sky that was electronically captured by the charge coupled device (CCD) camera attached to the telescope. The view window has two magnifications (see Figure 2 on next page): Finder View is the view through the finder scope that gives a wide field of view and has a cross hair and outline of the instrument field of view. Spectrometer View is the view from the main telescope with red lines that show the position of the slit of the spectrometer. 6. Locate the Monitor button in the lower left hand portion of the screen. Click on this button to change the view from the Finder Scope to the Spectrometer. Using the Spectrometer view, try moving the telescope ‘manually’ to any galaxy. Do this by ‘slewing’, or moving, the telescope with the mouse and the N, S, E or W buttons. Place the arrow on the N button and click on the left mouse button. To move continuously, press and hold down the left mouse button. Notice the red light comes on to indicate the telescope is slewing in that direction. As in real observatories, it takes a bit of practice to move the telescope to an object. You can adjust the speed or slew rate of the telescope by using the mouse to press the slew rate button. (1 is the slowest and 16 is the fastest). When you have positioned the galaxy accurately over the slit, click on the take reading button to the right of the view screen. The more light you get into your spectrometer, the stronger the signal it will detect, and the shorter will be the time required to get a usable spectrum. Try to position the spectrometer slit on the brightest portion of the galaxy. If you position it on the fainter parts of the galaxy, you are still able to obtain a good spectrum but the time required will be much longer. If you position the slit completely off the galaxy, you will just get a spectrum of the sky, which will be mostly random noise. 7. When collecting data from the object we will be looking at the spectrum from the galaxy in

Page 13 of 18 Experiment 2B - Hubble Constant and Pulsars the slit of the spectrometer. Typically a spectrum of the galaxy will exhibit the characteristic H & K calcium lines which would normally appear at wavelengths 3968.847 Å and 3933.67 Å, respectively, if the galaxies were not moving. However, the H & K lines will be red shifted to longer wavelengths depending on how fast the galaxy is receding. Photons are collected one by one. We must collect a sufficient number of photons to allow identification of the wavelength. Since an incoming photon could be of any wavelength, we need to integrate for some time before we can accurately measure the spectrum and draw conclusions.

The more photons collected, the less the noise in the spectrum, making the absorption lines easier to pick out. To initiate the data collection, press start/resume count. To check the progress of the spectrum, click the stop count button. The computer will plot the spectrum with the available data. An integration time of 30s is probably the minimum required for a bright galaxy. 8. Clicking the stop count button also places the cursor in the measurement mode. Using the mouse, place the arrow anywhere on the spectrum, press and hold the left mouse button. Notice the arrow changes to a cross hair and the wavelength data appears in the lower right area of the window. As you hold the left mouse button, move the mouse along the spectrum. You are able to measure the wavelength and intensity at the position of the mouse pointer.

Page 14 of 18 Experiment 2B - Hubble Constant and Pulsars APPENDIX B: The Radio Telescope Controls

Familiarise yourself with the operation of the Radio Telescope and Radio Receiver by completing the following exercises: 1. Click File on the menu bar, select Run and then the Radio Telescope option. · The window should now show you the control panel for the CLEA radio telescope. A view screen at the centre shows the telescope itself, a large steerable dish, which acts as the antenna to collect radio waves and send them to your receiver. · The Universal Time (UT) and the local sidereal time for your location are shown in the large digital displays on the left. (See Figure 1) · The coordinates at which the telescope is pointed, Right Ascension (RA) and Declination (Dec), are shown in the large displays at the bottom. 2. Just below and to the right of these coordinate displays is a button labelled View. Click on the View button, and screen in the centre will show you a map of the sky, with the coordinate lines labelled. · A yellow square shows you where the telescope is pointed. 3. You can steer the telescope around the sky by clicking and holding down the N-E-S-W buttons at the left side of the window. Try it, and watch the square move, showing that the telescope is moving around the sky. · The coordinate readouts will also move. · You can change the pointing speed of the telescope by resetting the slew rate button at the lower left. Try setting it to 100, and see how much faster you can move the telescope around the sky. 4. You can move the telescope in two other ways: · by clicking on the set coordinates button at the bottom of the screen · by selecting objects from the Hot-List pull-down menu on the menu bar at the top of the window. 5. The telescope has a tracking motor designed to keep it pointed at the same spot in the sky as the earth turns. Right now the motor is off, and, even if you are not moving the telescope with the N-E-S-W buttons, you will see the Right Ascension display changing, because the rotating earth is causing the telescope to sweep the sky. You should turn on the tracking motor to remedy this. Just below the time displays on the left hand side of the screen is a button labelled Tracking. If you click on it, you will see the word on appear next to the button, and you will notice that the Right Ascension display stops changing. The telescope will now track any object it is pointed at. 6. Point the radio telescope to Pulsar 0628-28, by selecting this pulsar from the Hot List. The telescope will move to the required coordinates. 7. Now turn on the radio receiver. Click on the Receiver button in the upper right of the telescope control window. · A rectangular window will open which has the controls for your receiver on the right, and a graphic display of the signal strength versus time on the left.

Page 15 of 18 Experiment 2B - Hubble Constant and Pulsars · The radio frequency the receiver is set to is displayed in the window near the upper right. It is currently set to 600 MHz. The receiving frequency can be altered using Freq. Controls. There are also buttons to control the horizontal and vertical scale of the graphic display. View the pulsar signal by clicking on the Mode button to turn the receiver on. The signal looks random, which is the background static, with an occasional brief rise in signal strength, which is the pulsar signal. Note the regular period of the pulsar signal. 8. Click on the Mode switch again to turn off the receiver. Note that it completes one scan of the screen before it stops. 9. Investigate the effect of varying the Vertical Gain and the Horizontal Scale. Choose a gain so that the pulsar signals are not clipped at the top of the screen. Note that for short values of the horizontal scale the pulsar signal amplitude is less – the telescope receiver has a shorter data collection time. For long time-scales the pulsar amplitudes are larger, and the vertical gain may need to be adjusted. Cursors can be set on the display by left and right clicks of the mouse button.

Page 16 of 18 Experiment 2B - Hubble Constant and Pulsars APPENDIX C: The (A.U.) and The Parsec

In order to understand how the parsec is used as a measure of distance we need to define another unit of distance that is used by astronomers called the Astronomical Unit A.U.

This is defined as the average distance from the Earth to the Sun and the accepted value is 1.50x1011m.

C.1 Stellar Parallax As the earth orbits the Sun, a star that is relatively close to the will appear to shift its Figure C1: The Parallax View. position with respect to the distant background stars as shown in Figure C1. The parallax, p, of the star is equal to the angular radius of the earth's orbit as seen from the star. Figure C2 illustrates the effect of stellar parallax. When the earth is in position (1) we take a picture of a nearby star. There will be many other stars on the picture, of course, as well as some very distant galaxies. On this picture (1), the star appears on the left side of the . A quarter of a year later, the earth has moved to position (2). We take another picture of the nearby star. In this picture (2) the star appears to Figure C2: Parallax observed from earth the right of the elliptical galaxy. The position of the galaxies themselves with respect to each other has not changed. The distances to them are so enormous that it makes no difference whatsoever from which position of the earth we look at them. The nearby star, however, is sufficiently close to observe a parallactic displacement. From Figure C1: (Radius of earth’s orbit / 2pd) = ( p/360°) so d = (360° x radius of earth’s orbit)/(2pp) (C1)

Page 17 of 18 Experiment 2B - Hubble Constant and Pulsars

We now convert 360° and p to seconds of arc to obtain d = [360 x 60 x 60 x radius of earth’s orbit)/(2pp(arcsec)] or d = [206,265 x (radius of earth) /p(arcsec)] Now the radius of the earth’s orbit is 1 A.U. and we define a new unit of distance called the parsec (pc) such that 1pc = 206,265 A.U. so that d(pc) = (206,265 (1 /206,265)) / p(arcsec) or d (pc) = 1 / p(arcsec) (C2) Equation (C2) is the fundamental definition: A parsec is the distance at which the observed parallax of a star is equal to 1 second of arc. It is now apparent why this unit is so useful to astronomers. Once the stellar parallax is measured then the distance of the star in parsecs is found by simply taking its reciprocal. Remember that 1 parsec = 206,265 A.U. = 206,265x1.50 x 1011m = 3.1x1016m.

Note. One thousand parsecs equals 1 kiloparsec (kpc); one million parsecs is 1 megaparsec (Mpc). The radius of the milky way is about 15kpc. The distance to the nearest galaxy (Andromeda) is about 680kpc.

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