3.1 The Photomultiplier The key to the operation of the photomultiplier is called the photoelectric eæect, discovered in 1887 by H. Hertz. When light

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1 Photoelectic Photometry Lab 1 Objectives To learn how to make precise measurements of stellar brightnesses, and how the Earth's atmosphere aæects our ability to measure brightness. 1. Learn how to measure stellar brightness with a photoelectric photometer 2. Get good familiarity with the celestial sphere 3. Analysis of data, estimation of errors 4. Learn about Standards in measurement and calibration 5. Learn how the atmosphere eæects starlight that passes through it 2 Skills Required This is an advanced lab because it requires some knowledge of observing èso that the team is eæcient enough to get all the required dataè, and will require extensive data analysis. The equipment used in this lab is very easy to use. Skills used: æ Polar Alignment of telescope, use of setting circles æ Ability to ænd things using star charts æ Statistical Analysis æ Spherical Trigonometry æ Understanding Sidereal time, Hour Angle, Airmass æ Linear Least Squares æts 3 Background Photometry is a quantitative way to measure the brightness of a star. Photometry is important in photography, astronomy, and illumination engineering. Instruments used for photometry are called photometers. Light waves stimulate the human eye in diæerent degrees, depending on the wavelength of the light. Because it is diæcult to make an instrument with the same sensitivity for diæerent wavelengths as the human eye, photometers need special colored ælters to make them respond like the human eye. Photometry is very important in astronomy because it gives the astronomer a direct measure of the energy output of stars, or of the amount of light reæected èor scatteredè by surfaces of planets and other small bodies. Colors, or measurements of the amount of light through ælters centered at diæerent wavelengths can give information on the temperatures of stars. 1

2 3.1 The Photomultiplier The key to the operation of the photomultiplier is called the photoelectric eæect, discovered in 1887 by H. Hertz. When light strikes a metal surface, electrons are released, the number released being proportional to the intensity of the light. Electrons are bound to the metal by electric forces, and light with suæcient energy can liberate the electrons. The way a photometer works is that light enters the instrument and strikes the photocathode èmade of a metal chosen so that optical light exceeds the threshold for release of the electronsè. For typical materials the quantum eæciency is about 10è, meaning for every 100 incident photons, only 10 electrons are released. In order to get enough electrons to measure as a current, the photocathode is places in a multiplier tube. A series of dynodes are kept at electric potentials less negative than the photocathode, thus the released electrons are accelerated and travel toward the dynode. The impacts of the electrons on the dynode release about 4-5 times as many electrons, and these are accelerated to another dynode at an even less negative potential. This process is repeased many times until there is a large cascade of electrons which can be measured at the last dynode called the anode. At the end of the multiplication chain, 1 initial electron can deliver about 4 æ electrons at the anode! Figure 1: Diagram of a photomultiplier, from N. Giæn 4 Experiment In this lab you will measure the brightness of some variable stars, and fully calibrate them. Figure 2 shows an example of an unusual type of variable star, called an R Coronis Borealis star. It varies irregularly in brightness í usually being very bright, but occasionally growning faint. For this type of star, dust in the star's atmosphere condenses out occasionally and blocks the starlight. The star gets bright again when the star heats up and vaporizes the dust or blows it oæ. We will report our brightnesses in the standard V èvisualè and R èredè astronomical magnitude system. Magnitudes arose historically from the ancient greeks who listed the brightest stars in the sky as having ëærst importance" or ærst magnitude. The next brightest as having ësecond importance" or second magnitude. The eye is actually a logarithmic detector, and this system as been formalized such that each magnitude diæerence is a factor of 2.5 in brightness. We will be measuring an electric current or counts èphotonsè per second, C, from the star, and this has to be converted into a magnitude èmè system. This is done with the following equation: 2

3 Figure 2: Data on R Coronis Borealis from mid 1966 through mid m =,2:5 logècè è1è 4.1 Eclipsing Binaries Eclipsing Binaries are a type of variable star system which is not varying intrinsically. Instead the apparent brightness variation is caused by the geometry èas viewed from earthè of a pair of orbiting stars. As one star passes in front of another the starlight dims. There will be 2 eclipses each period, and the eclipse with the greatest light loss will be called the primary eclipse. This occurs when the hotter, brighter star is blocked from view. The light curves are important to study becuase they contain information about the star's sizes, their shapes, mass exchange, and star spots. Information about speciæc eclipsing binary systems in Table 1 are listed below: æ The AW UMa system is probably either a triple or quadruple star system. The masses of the primary stars are M 1 = è1.79æ0.14èm æ, and M 2 = è0.143æ0.011èm æ. The third star has an apparent mass of M 1 = è0.85æ0.13èm æ. æ æ Lib is a chemically peculiar close contact binary star system. æ The star 68 Herculis èu Herculis, HD , SAO 65913è is a Beta Lyrae type eclipsing binary. It was discovered to be variable by J. Schmidt in 1869, and was found to be an eclipsing binary in 1909 by Baker. The maximum magnitude of the system is about 4.7 and the minima alternate between about 5.0 and 5.4. Figure 3 shows a set of observations made by Phil McJunkins ètexas A&M Univ.è and Dan Bruton èaustin State Univ.è. 3

4 4.2 Intrinsic Variable Stars Figure 3: Lightcurve of eclipsing binary 68 u Her. Intrinsic variables are stars which vary in brightness because of internal changes which can cause pulsations. Some of the pulsations can be very long èoverayearè while others can be short. For this lab we will select only short-period variables of the following types: æ æ Scuti stars í low amplitude, sinusoidal behavior with periods é 0.3 dy. æ Dwarf Cepheids í Amplitudes é 1 mag, periods é 0.3 day and can have asymmetric light curves. æ RR Lyrae stars í Similar the Dwarf Cepheids, with periods between 0.3 to 1.0 day. Below is a description of the intrinsic variable stars which might be observed during the lab. Below are some brief descriptions of the intrinsic variable stars included in this lab. æ The ç Bootes variable star is a rapidly rotating A-type dwarf star which has avery small periodicity è38 minè and probable low amplitude variation èthus is not our ærst choice for a targetè. This star possesses a circumstellar dust disk. æ V703 Sco is a post-main sequence red giant star, a dwarf Cepheid. æ X Sgr is a spectroscopic binary system with a cepheid variable star. The orbital period of the companion star is days. Note: the columns with 7UT, 8UT and 9UT show the airmass and altitude of the objects as a function of time. 4

Table 1: Candidate Variable Stars Name æè2000è æè2000è æv Type Per Epoch 7UT 8UT 9UT AW UMa 11:30:04 +29:57:53 WUMa 6.8-7.1 0.43 38044.782 1.4è46 1.8è33 2.9è20 ç Boo 14:16:10 +51:22:02 æsct 6.5-7.1 0.267 39370.

5 Table 1: Candidate Variable Stars Name æè2000è æè2000è æv Type Per Epoch 7UT 8UT 9UT AW UMa 11:30:04 +29:57:53 WUMa è46 1.8è33 2.9è20 ç Boo 14:16:10 +51:22:02 æsct è58 1.2è54 1.4è47 æ Lib 15:00:58 í08:31:08 EAèSD è61 1.1è61 1.2è53 68 u Her 17:17:20 +33:06:00 ælyr è52 1.1è64 1.0è73 V703 Sco 17:42:17 í32:31:23 RRLyr è24 1.8è33 1.6è40 X Sgr 17:47:34 í27:49:50 æcep è32 1.4è44 1.2è52 W Sgr 18:05:01 í29:34:48 æcep è è42 1.3è Open Clusters Open clusters are groupings of stars which physically reside in the same place in space èi.e. they are all at approximately the same distance from the earthè, and formed at the same time. Because they are at the same distance from us, their apparent relative brightnesses are the same as their absolute relative brightnesses. The one main diæerence between the stars will be their masses. Stars are gaseous balls, and would collapse under their own self gravity, ifitwere not for the outward pressure from the hot interior gases where the thermonuclear reactions are taking place. The more massive stars burn their fuel faster, in order to keep high enough pressure to counteract gravity. We learned in the lecture on light and radiation that hotter stars are also bluer stars. If we plot a diagram of temperature èor colorè versus the brightness of a star in a cluster, we will see that the stars do not fall randomly on the plot. We can use this type of plot, called a Hetzspring-Russell diagram, to determine the age of the cluster of stars. This type of plot was ærst developed independently in by E. Hertzsprung and H. N. Russell. Figure 4: Schematic HR Diagram. The diagonal line of stars is called the main sequence, where stable H-fusion occurs. As a star runs out of fuel in its core, it begins to collapse and will eventually heat up enough to start the fusion of He. At the end of the H-burning stage, the star moves oæ the Main Sequence. Also, prior to the beginning of H-burning, while the star is still forming, it will move 5

6 toward the main sequence as the core heats up. Star clusters will have stars of diæerent masses, hence stars at diæerent stages of evolution, and by making a HR diagram, we can estimate the age of the cluster. Figure 5: Schematic HR Diagram for clusters of ages 1 million years, 100 million years and a globular cluster billion years old. Table 2: Candidate Open Clusters Name Constell æè2000è æè2000è Mag Size ë 0 ë 7UT 8UT 9UT NGC 6231 Sco 16:54.0 í41: è23 2.1è28 1.9è31 M6 Sco 17:40.4 í32: è25 1.8è34 1.6è40 NGC 6475 Sco 17:53.9 í34:49 2.4è24 1.8è33 1.6è Standard Stars While we can accurately measure the brightness of celestial objects with our photometer, to be useful scientiæcally, we have to put our measurements on a standard scale. Not all devices will produce the same C for the same objects because of diæerences in quantum eæciency of the detector, etc. In order to put things into a standard scale, we measure stars of known brightness, called standars. Below are some stars we will use as standards. Note: Some of the ëstandard" stars are actually listed as variablesè!è. These are ok for our project since the magnitude of variation is so small that we will not detect it èæ Leo: æv = 0.07 mag; æ Vir: æv = 0.05 magè. 4.5 Procedure Follow the procedure outlined below to obtain calibrated data on your object. æ Set up telescope, and align the ænder æ As soon as Polaris is visible, polar align the telescope 6

7 Cat è Name Name2 Table 3: Standard Stars Spec æè2000è æè2000è V R Comment 3982 æ Leo Regulus B8V 10:08:22 +11:58: Var? 4033 ç UMa HD89021 A2IV 10:17:06 +42:54: í 4534 æ Leo HD A3V 11:49:04 +14:34: Var æ Scuti Com 13:11:52 +27:52: æ Crv HD B8III 12:15:48 í17:32: Var Vir HD G5V 13:28:26 +13:46: í 5056 æ Vir Spica B1V 13:25:12 í11:09: í Var SA :45:21 +00:47: Boo 14:15:40 +19:10: Oph 16:37:09 í10:34: æ Find one of the bright stars in the standards list using a ænding chart ènorton'sè and set the telescope setting circles and turn on tracking æ mount the photometer, and ænd your object and center in the photometry aperture and focus the telescope. æ Take 10 sets of measurements of the standard star you select and record the time èuniversal Time, UT í which is the time in Greenwich = HST + 10 hrè. Each measurement will be a reading of the count rate of the star, followed by a measurement of the blank sky next to the star. Be sure to note the exposure time and gain for both on logsheets provided. æ Go to your program object and do a set of measurements. æ Try to get at least 3 measurements of your standard star at diæerent times - i.e. telescope positions at diæerent elevations èa low and high elevationè. The standard star will be used to measure the amount of atmospheric extinction. æ If you are observing a cluster, you must get observations in two ælters. 5 Data Reduction 5.1 Means and Errors If we make a measurement of the brightness of a star, we expect our measurement will be approximately equal to its brightness, but not exactly equal. Because of random errors, if we make a second measurement, it will be diæerent from the ærst, but also approximately equal to the brightness of the star. With a large number of observations, we expect that on average the measurements will be distributed around the correct value. The standard deviation is a measure of how much scatter there is in the data, and gives us an estimate of how well we know the number. The formal deætitions of mean and standard deviation, ç, are: 7

8 x = 1 N X xi è2è ç 2 = 1 N, 1 X èxi, xè 2 è3è where N is the number of data points Spherical Trigonometry When we are considering coordinate systems in the night sky, on the celestial sphere, we need to explore a new mathematical area called spherical trigonometry, because we are dealing with angles on a spherical surface. A spherical triangle is the intersection of 3 arcs. If the sides of a spherical triangle are labeled a, b, and c, and the opposite angles A, B, and C, then we have 2 important rules which are relevant to astronomical coordinate systems: the law of sines: and the law of cosines: sinès 1 è sinèa 1 è = sinès 2è sinèa 2 è = sinècè sinèa 3 è cosès 1 è = cosès 2 è cosès 3 è + sinès 2 è sinès 3 è cosèa 1 è è4è è5è Figure 6: Spherical Traingle. 5.2 Calculating Airmass The starlight that reaches our telescope has passed through the Earth's atmosphere, and as it does so some of the light is lost due to scattering and absorbtion. The more atmosphere it passes through, the more light islost. When a star is at our zenith, or on the meridian, it will pass through the least amount of atmosphere, but on the horizon it will pass through more atmosphere, and more light is lost. If we are going to make precise measurements of stellar brightness, we need to correct for the amount of light which is lost, and this will depend upon where in the sky the star is. The measure of how much atmosphere the light is passing through is called the airmass, ç. Airmass is given by the following formula: ç = secèzè = ësinèçè sinèæè + cosèçècosèæè cosèhaèë,1 Here, ç is the latitude of the observing site, æ is the declination of the object and HA is the hour angle of the object. This formula derives from the law of cosines in spherical trigonometry. 8 è6è

9 5.2.1 Hour Angle and Sidereal Time The ærst step to computing how much atmosphere the starlight has passed through is to calculate what is called the hour angle, HA. The observer's meridian is an imaginary great circle passing through the zenith èpoint directly overheadè and the North Celestial Pole èncpè. The star will be at it's highest elevation above the horizon when it crosses the meridian. The HA is an angular measure from the intersection of the celestial meridian and the celestial equator westward along the celestial equator. The units of measure are in hours rather than degrees. There are 24 hours in a circle of 360 æ. For example, for an object on the celestial meridian, HA=0. For an object on the W horizon HA=6 and on the E horizon HA=-6. We don't have to measure this angle, we can calculate it. HA = ST, æ where æ is the right ascension of the object and ST is the sidereal time. Greenwich mean time is regulated by the motion of the Sun. One solar day is the time between two successive passages of the sun overhead. However, during the day the sun is moving along its orbit around the sun, so to reach the same place in the sky, the earth has to rotate a little bit farther than 1 full rotation. Another type of day is called the sidereal day, and this is the time between two successive passages of a star overhead. The solar day is 24 hours, but the sidereal day will be slightly shorter, 23 h 56 m. This is why the stars rise 4 min earlier each day. There are about solar dyas in a year, and during this time the Earth makes rotations about its axis. Greenwich mean time nad Greenwich sidereal time agree at one instant every year at the autumnal equinox è9è22è. The formal deænition of Sidereal time, ST, is that it is the Hour Angle of the Vernal Equinox. Attached to the back of the lab is a table of sidereal times for Greenwich England at 0UT on each day for the TOPS workshop. 5.3 Extinction Coeæcients í Least Squares Fits For small to moderate airmasses, there is a simple linear relationship between the brightness or apparent magnitude m obs of an object and its airmass. If you plot mag versus airmss, the slope of the line will equal the extinction coeæcient, k: m i = m obs, kç Because of random errors, all the points won't fall exactly on a straight line. Ideally we want to have the best straight line that represents the data. This is computed by computing the sum of the diæerences between the æt line and the data and minimizing this. This technique is called least squares ætting. This is easy to do with a computer, but tedious with a calculator, so for the lab, we could just plot things on graph paper by hand and do an ëeyeball" æt. If you are interested, the equations for ætting a set of data, èx, y, çè for the slope, k and intercept b are: X xi y i X yi! k = 1 æ è X 1 b = 1 æ è X x 2 i X yi 9,X xi,x xi X xi y i! è7è è8è è9è è10è

10 where æ= X 1 X x 2 i,è Xxi! 2 è11è 5.4 Color Terms and Zero Points Finally, the last step in our data reduction is to take account of the fact that our instrument does not give us a calibrated number. We use the standard star measurements to convert our instrumental magnitudes, m i to a true magnitude. The true magnitude is given by: m = m i, kç + æèv, Rè+z Here æ is called the color term and z is a calibration zero point. If we rearrange this equation to: y = m, m i + kç = æèv, Rè+z we see that this is just the equation of a straight line with a slope of æ and intercept z for x-values of ëv-r". We know the colors and magnitudes of our standard stars, so we plot them and do another æt to get æ and z, our zero point. Once we know k, æ, and z we can plug these into our equation above to compute the true magnitudes from our instrumental magnitudes for our objects of unknown brightness. At this point, for variable stars, we will plot magnitude versus time, and for the clusters we will plot magnitude versus color as our ænal data product. è12è è13è 6 Follow-up and Further work If you would like to go the HOA sessions during rotation later you can use this software to help analyze the data. If you are really interested in pursuing this for your school, the photoelectric photometer is available from Optec, Inc., 199 Smith Street, Lowell, MI, 49331, è616è , FAX: è616è , At the TOPS workshop, you used the SSP-3, which costs $ èælters and carrying case are extraè. There are several good guide on how to do photometry for amateurs: æ Photoelectric Photometry of Variable Stars í A Practical Guide for the Smaller Observatory 2nd Ed., Ed. by Hall and Genet èavailable from Willman Bell, Inc., $24.95è. æ Astronomical Photometry, Henden & Kaitchuck, $ æ Software for Photometric Astornomy, Henden & Kaitchuck, $ There are numerous organizations where your data might be sent to make a real scientiæc contribution. The AAVSO è collects amateur photometry on variable stars for use by professional astronomers. 10

The Night Sky. The Universe. The Celestial Sphere. Stars. Chapter 14

The Night Sky. The Universe. The Celestial Sphere. Stars. Chapter 14 The Night Sky The Universe Chapter 14 Homework: All the multiple choice questions in Applying the Concepts and Group A questions in Parallel Exercises. Celestial observation dates to ancient civilizations