TECH OBSERVA ASTRON 1
TECH OBSERVA ASTRON 1 AST 3722C
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This 23 page Class Notes was uploaded by Ms. Adrian Buckridge on Friday September 18, 2015. The Class Notes belongs to AST 3722C at University of Florida taught by Staff in Fall. Since its upload, it has received 18 views. For similar materials see /class/206982/ast-3722c-university-of-florida in Astronomy at University of Florida.
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Date Created: 09/18/15
Techniques of Observational Astronomy M The Effect of the Earth39s Atmosphere Introduction Ground based astronomy is heavily in uenced by the Earth39s atmosphere In addition to the interruption of observations by clouds the atmosphere affects the wavelengths that can be observed the resolution that can be achieved the accuracy of position and brightness measurements and it introduces lines both absorption and emission into spectra Absorption and Scattering Extinction Absorption and scattering in the Earth39s atmosphere is usually called by astronomers extinction There are three main sources 1 molecular scattering This is Rayleigh scattering and thus goes as 11ambdaA4 2 scattering by dust and aerosol particles haze essentially wavelength independent 3 molecular band absorption Ozone cuts off the UV oxygen and H20 bands show up in the IR beyond 7000A Typical Atmospheric Absorption 09 09 08 08 0 07 05 05 E C 2 a g 05 05 a o g 04 M S 03 03 02 02 I 01 01 r I l 0 300 350 400 450 500 550 500 550 700 50 800 Wavelength nm The plot shows typical curves for Rayleigh dust and ozone absorption as well as the passbands for the frequently used U ultraviolet B blue V visual R red and I infrared astronomical lters The actual amount of absorption depends on how much atmosphere is in the beam airmass Note that in the blue and especially in the ultraviolet the potential for loss is very high Ultraviolet observations from low altitude observamnes are usually not useful Note also Lhatthe absorption m the V yellowrgreen L mm 1 NH wavelength S Zenilhal Ellinclinn n mamquot m p May 1an fans 1975 a e 15mm Emmimu minimum E a n Fimxv 1 s 1 Ceylihmmn m nun L mem hu iugc mum t minLLiuu mm A NuwAhsuhnu 39 Sk and New 0e 0 Km Peak National Obs Rosemary Hm Obs Airmass For For m r l n w l manta usually terrned secZ wherezls the zenrth angle orzenrth dstanee The thckness h ean be set to umty one atrrnass at the zentth so x52z The plane parallel approxlmatlon ls sutTrerentforrnostpurposes for z lt 60 Beyond 75 rtrs where z ls the apparent not true zenrth dstanee x see 7 0 0018167 see 7 1 e 0 002875 see 71 2 e 0 0008083 secx 71 Refraction The atmosphere refracts bands the path ofllghtrays passlng through rt Thls has the effect apparent slze andloeauon seelng and serntrllatron Assumlng aplanerparallel umF rw t to be approxlmately t 004 tan z where 2M5 the true zenth dstanee The apparent L i e I the apparent zenth dstanee as one looks eloser and eloser to the honzon The resultthat rno e rnrnutes laterthan rnrght be expeeted and an extended object e g the sun or moon wlll appear attened when vlewed near the hon This image also illustrates the effect of dispersion which may result in the 39 visible for a brief instant at the upper limb ofthe sun Second Order Effects of the Atmosphere Dispersion Dispersion is the variation in refraction as a function ofwavelength A star viewed at a large zenith distance may appear elongated by this effect The figure illustrates what may be seen where z is the zenith angle and r is the seperation between the blue and red images the assumed star size here is 1quot Clearly this effect can become a problem for astrometry position measurement as well as spectroscopy where some ofthe wavelengths of interest may not even pass through the spectrograph entrace aperture 39green ash 2 0 an 45 50 75 I amquot 035quot manquot 104quot z24quot A A R V V v 9 Tracking Rate Because refraction is a function of zenith distance a star39s diumal motion will vary with time For precise tracking telescopes must compensate for this variation Edward Skinner King developed an algorithm for such compensation which results in the King Tracking K 143607 040 cot tandcost cos 39 i 056 In ain Joust us am e5 b r on 5 where Kis the tracking rate in minutes of solar time per revolution dis the declination is the latitude and t is the hour angle Seeing and Scintillation A demonstrauon ofthe effects of astronomxcal smug the atmospheric turbulence which 15 the most kmds of optical observations from the ground This frame compar 5 M74 NG M74 4 1 such as dust structures Photo from 13111 ch1 Umversxty ofAlabama T1 1 a Salzgeber Another sct of uotcs on seemg Here 15 a site that redwts seem m North Amenca ces Henden ct a1 CCD Phammevy Apnl 11 1999 Ch 4 on class I OM Romamshm An Introductmn ta Aspuuumtmz Phammevy Usmg CCD s August 23 2000 cu 7710180 class CDVROM Interesting Links h 1 at a site run by Lcs Cow1c1 lastrevxsed 914200412 48 PM Techniques of Observational Astronomy M Basic Astronomical Photometry Reference Romanishin Ch 3 which I follow closely in much of this The purpose of astronomical photometry is to determine the brightness of an object or a region of an extended object In fact all astronomical photometry is a form of spectrophotometry the determination of the ux from the object in some region of the electromagnetic spectrum In this context flux is the energy received per second per unit area per unit frequency or wavelength interval F 3 5391 cmg Hzl in frequency units F1erg 51 cm i in wavelength units A quotspectrumquot is the variation in ux as a function of frequency or wavelength over some range of frequency or wavelength For the remainder of this discussion we will assume that we are looking at spectra as a function of wavelength since that is most common usage for visible light True spectrophotometry passes the incoming radiation through a dispersing element diffraction grating or prism Filter photometry measures the ux in fairly broad wavelength regions using typically glass lters This can be considered low resolution spectrophotometry The process sequence is radiation leaves object passage through interstellar andor interplanetary medium passage through Earth39s atmosphere unless observed with spaceborne instrument passage through optics of telescope passage through dispersing element or filter photons incident on detector response from detector recorded The observed spectral energy distribution can be altered at each of these stages Usually an observer attempts to process the data in order to estimate the distribution at the top of the atmosphere This processing is nontrivial and usually is done via a differential measurement rather than as an absolute measurement Differential vs Absolute Photometry Absolute Photometry To do absolute spectrophotometry we would need to know the absolute sensitivity of the detector in output units per ux unit the absolute transmission of the dispersing element or lter the absolute transmission or re ection of every element in the telescope and unless observed with spaceborne instrument the absolute transmission of the Earth39s atmosphere In practice it is nearly impossible and certainly not routine to do such absolute calibration of a system Changes in conditions due to dust accumulation aging or deterioration of surface etc would have to be known at all times Even if the telescope system was well calibrated the Earth39s atmosphere is not What to do Differential photometry If we can observe a star of known characteristics nearly adjacent to our program object in position and time we can assume that the both objects are effected in the same fashion by the system and hence that the characteristics of the program object can be determined by their ratio or difference relative to the quotcomparisonquot star In practice nearly all filter photometry is differential although this is possible only because a few astronomers have developed a system of suitable comparison stars through absolute photometry Practical Approach to Differential Photometry make observations of the program object and at least one comparison star any observation of an object will include also quotskyquot in the vicinity of the object make the necessary measurements to allow subtraction of the sky from the object measurements calculate the ux from the program object in units of the ux from the comparison star use the known ux or magnitude of the comparison star to get the ux or magnitude of the program object Standard Magnitude and Color Systems In the visual region of the spectrum astronomers use a logarithmic system of ux measurement called magnitudes The magnitude system has its roots in a system of describing star brightnesses that goes back to the astronomer Hipparchus 2200 years ago Today the system is specified algorithmically by 1 39 m2 2395 10310 1fo Since optical astronomers still frequently refer to stars and observations of stars in units of magnitude it is useful to have a few magnitude terms committed to memory Note that the magnitude system is an inverse system in that brighter objects have algebraically smaller values and that very bright objects have negative magnitudes Brightest Faintest Full moon Venus Limit at HST limit naked eye naked eye 46m scope stars stars l5 About 65 127 Up to 745 About 19th About 30th Frequently we think in terms of magnitude differences which are equivalent to ux or brightness ratios Mag diff 1 25 5 075 01 IFluX ratio 254 10 100 2 01 There are a number of magnitude systems related to the wavelength regions involved In most cases colors de ned as a difference in magnitudes are also used in the description of a stars characteristics The standard system in the visible region of the spectrum is the JohnsonCousins UBVRI system Stellar characteristics are frequently plotted in terms of a colormagnitude diagram V vs B V or a colorcolor diagram UB vs BV The wavelength coverage of a standard UBVRI filter set are plotted at httpwwwastrou eduNoliverast3722lecturesBasicPhotomfiltersetshtm These are the filters installed at the 046m and 076m telescope at Rosemary Hill Observatory References Lists of standard stars httn39 sofa astro ntoledn edn SOFA 39 yhtml This page is maintained by John P Oliver39 write me at oliverastrou ealu This material is being made available to vou subject to a varietv 0f caveats This page was last edited 1142004 1146 AM Techniques of Observational Astronomy M Basic Telescopes Telescope Mounts the telescope mount allows the telescope to point anywhere in the sky and to track stars as they rise and set Balancing Proper balance is important if the telescope is to track the stars in all parts of the sky without drifting Polar alignment It is necessary that an equatorial mount be closely aligned on the pole to ensure accurate tracking Mounts Polaris k zenlth J h Equtorial Munt Altazimuth Mount Equatorial Mount two axes a polar axis is aligned with the Earth39s axis allowing diurnal tracking a perpendicular declination axis 0 advantage one axis diurnal tracking 0 disadvantage asymetry to gravity Zenith The bendmg of the deehnanon axis of a German Equatona mount ano emg causing trackmg and pointing errors a snmxlarproblem occurs with thfkkaM wnltn d mount may bend the bendmg ls eonstant an be eonnpensated by neahgnnnent othe tube or optics Altaznnutn Mount tw ax s an aznnutn axis angned with the zenith aperpendmular altde axis antage symetneal to gummy duadvant k1 eldrotauon mnnm path of star near zenith An anlmauon ofthe altazlmth mounted GTc Tracking and Pointing the posrtron of eaeh axls ls read outto the eomputer by angle eneoders Tracklng ean be throughthe zenlth The result ls a dead zone near the zenlth for altazlmuth mounts A y affects only pornung andnot traelnng Rotation of Field e g n rm no t mount Consrder the ease oftxacklng a star that passes nearthe zenrth as the zenrth ls 180 whleh mustbe rotated at the eoneetrate to eompensate forfleldrotatlon Equatorial Mounts Asymetrio Equatorial Mounts 2 German Equatorial Modi ed German English Equatorial erman Mourrt Most frequently usedforrefracnng teleseopes Mustbe reversed to observe on both sldes ottlre mendlan Mo G M n far errd the tube can clear the prervutlrout the ueedto rever Engllsh Mourrt Must be reversed to observe on botlr sldes ofthe mendlan Full support for both errds oftlre polar axls may restuet use ueartlre pole Syrnetrioal Equatorial Mounts Fork Mount Yoke Mount Horseshoe Yoke Fork Mourrt most frequently usedforre ecnng teleseopes To reach pole tube must clear for Yoke Mourrt Added support forpolar axls Cannot reach pole Horseshoe Yoke Mourrt Allows reachmg pole whlle provldmg support at both errds of polar axls Palomar 5m Horseshoe Yoke prime focus cage Lick 3m fork mount fork mount v m t r The Lick Observatory Crossley 091m English Equatorial 1n spete othe great dlfflculty en Worklng wetle tnes teleseope tlee 0 91m crossley esults Thls was probably due to tlee great effort expended by ets users andtlee almost perfeetmaten oflts pnme focus speetrograple to ets opteeal system Balancing an Equatorial Telescope ll 0 w h s y Thls ean only be tlee ease lfthe orthogonal axes enterseet and tlee eenter ofmass lees at tlee enterseeuon poent i Z e i gt4 A laquot quot Cl m I T l ayaelable for tnes task axes Balanee tlee tube en tlee y dereeuon Thls balanee es frequently d You may have to mount xed we g C Polar axes Balanee wetle eounterweeglet at end ofDec axes D Polar axes Thls balanee es frequently negleeted You may have to mount xed weeglnts ee negleete General nntes To testbalanee you mustbe able to let tlee seope move freely about tlee releyant axes Thls may requlre releaslng tlee motor Tu nrw ml wleates done for large seopes Tne basee seope and permanent equepment ean be carefully balaneed uslng e be balaneed by slldmg weeglnts en poseteons A and C Polar Axis Alignment pole Mesalegnmentwell eause a starto dnftln botn deelenateon and nglet aseenseon Drift Alignment p Ntthtth po1e onzon wrth appropnate srgn ehanges Kthe teleseope polar axrs rs ultedtowards the south from the true pole the teleseope wru be fouowrng apath takmg rt south ofthe equator andthe star thus th wru appearto dnftnorth True Pole Pornt the startowards the south at a star at about 0 deehnauon Kthe teleseope polar axrs rs ultedtowards the east from the true pole the teleseope wru be folio apath takmg rtnorth ofthe equator andthe star thus the star wru appearto dnft south True Pole Analysis Atthe eelestaal equator 0 deebnataon the x motion is 15 per hour or 15 per mmute the der at any given deelmatton is then xn 15 hour 1539t minute 39n ccs5 X The y dn xs then given by my xgta11aaulrL 5 811 These equations ean be solved forthe polar alt angles alpha and beta Lm pmp base and the pier 77115 page 15 mamtamed by John P 77 male 1 madz av OIwer39 Wale m2 at a11v2rgsvau 2du 1an12 m all sub 110 a v a cavems Thxs page was last edued September 30200310 32 AM Techniques of Observational Astronomy AST3722C Basic Statistics We use statistics to analyze a set of observations in order to evaluate just what we can conclude from those data Imagine we have a collection of data 445 450 450 455 455 455 460 465 465 455 455 45 45 455 455 45 45 445 445 44 44 435 435 1 2 3 4 5 5 7 a 9 Important characteristics Mean the average value 4556 l x I I N Median The individual value from the collection such that 12 the observations are less and 12 are greater 455 Note that the median must be extracted from the dataset not simply calculated Mode The most frequently occurring value seldom of interest 455 Why is the median sometimes useful Imagine a different data set 445 450 450 455 455 455 460 465 87 a D MUbLTme DNmnomwnmm Mean 5006 Median 455 so the median is unaffected by a single very low or very high outlier ie a point that is way out of the main group of points How do we get an estimate of how good are data are Simple Deviation dz XI x Mean Deviation 7 1 d i 2 ix x N 1 l 39 the Nl re ects the loss of one degree of freedom if we had a single data point mean deviation would be meaningless Varianc e 2 1 7 2 0 34209 1 Standard Deviation quotroot mean square deviationquot or mm or sigma i 1 2 a iizfxfx 0rd V N I V N 7 I which is a bener estimator for random errors than mean deviation How repeatablereliable are our values The mm deviation tells us something about the expected value of a single observation If the data are normally distributed 68 ofthe poinm will lie within i1 sigma 95 ofthe poinm will lie w39 2 sigma 997 ofthe points will lie within i3 sigma Usually we accept a variation as statistically signi cant only if it is more than 3 sigma from e mean Standard deviation of the mean How reliable is our estimate of the mean The imfionin the metal is given by 2161 7 f NW 7 1 This is an estimator of the quality of the mean Value and it I ainerl hv 39 oints Note that to improve the quality of the data by a factor of ten would require one hundred samplings of the data The W n in the mem sometimes called rtde errof is the appropriate value to use to draw error barf on a plot of mean values 1 1027051 9374577 9291529 1022656 1105028 9293493 1048264 1029943 9352754 1080685 1004486 6660202 2106141 mean std dev std err 2 9699768 8722317 1024426 1127647 1119835 1173313 7816412 9765819 1109502 8913299 1004649 1292402 4086935 3 1061652 8487374 1076497 1082898 1112649 1179858 8874805 1028124 1070592 9885192 1033701 1009143 3191189 4 1067639 927521 9848607 9323228 1105721 1000187 1213331 9612005 862086 8494068 9904276 1123548 3552972 Kinds of data collections Normal or Gaussian distributions Most experimental results should follow this distribution Mean Median Mode Standard Deviation 498 493 561 102 Frequency Histogram DFvKuency Poisson 0r counting rate distributions Data collections where a value can never be less than 0 may have a Poisson distribution An example is photon statistics the number of photons that can arrive at a given moment can be 0 1 2 etc but never less than 0 Mean Median Mode Standard Devi ation 5022 5 4 2213688 Frequen Hisimgram H nn c 7 Lnil c z e 7x 0639 Q Bin The counts accumulated in a CCD pixel will have a Poisson distribution The standard deviation of a Poisson distribution is given by O V N so if you have 10000 counts in a pixel the error will be i100 SignaltoNoise ratio 0 Have we taken enough data 0 How much longer should we observe For Poisson statistics c total received counts Signal Noise SN nags c 10 316 32 0413 S N Z 7 Z J 100 1000 100 0114 c 1030 3162 316 0035 10300 10300 1030 0011 103000 31623 3162 0033 Linear Least Squares or Regression analysis Assume a straight line t to some data Dlte T F RFoas 1802 374 29584 01002 533 28922 11302 59 2m 123101 528 29162 mun 2202 622 28513 NEW 28400 35 4D 45 50 55 BB 55 Assume a straight line t to some data Let y focus value X temperature Llnear Least Squares Flt j abx Ayi jgti or yi abxi Ayi yi a bxi this is the equation of condition lets minimize the sum of the squared deviations N 0M 0M M A 2 to m1n1m1ze M let 2 0 4 6a ab i 2Na2bei 22yi 0 a i 7bei2 20in Zinyi 0 b 2xi x i 2 y a bc 26quot x The errors can be estimated from The mean square deviation of the j 1 points from the fit is gt f If we set A if T 739 h 1 N07quot W II CF t en U 39 I Linear Least Squares Fit ZQBUD zssun 294cm Coa cie39ts Sfarxhtd Error 292nm Intercept 3111957 37071 gt Slope 45991 691 29 QBEDD 254nm 235nm Interpretation At 0 F the focus will be about 31000 The change in focus with temperature is about 740 counts per degree Correlation Coef cient It is useful to look at the correlation coefficient rho between x and y A correlation coefficient of 0 means that x and are not correlated a value of 1 means the quantities are positivelynegatively correlated n y av Thispage39 39 39 quot JothOliver39 39 quot quot J This material is bemg39 made available to you subiect ta avariegu at caveats This page Was last edited 10252004
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