Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Pointing Model for the Large Millimeter Telescope Computational Physics Project 2 Fitting a Pointing Model for the Large Millimeter Telescope About the LMT.... ● 50m diameter millimeter-wave telescope (32m completed) ● ● ● ● ● 75 microns RMS surface accuracy 1 arcsec relative pointing Focal plane array instrumentation Big single dish complement to ALMA Binational Collaboration ● ● Instituto Nacional de Astrofísica, Óptica, y Electrónica. (Mexico) UMass-Amherst (USA) Science Interlude.... AzTEC Image of M87 The debris disk of e Eridani. Deep LMT/AzTEC observations at 1.1 mm Starburst Galaxies approx. 1010 ly away Debris disk approx. 10 ly away The structure and dynamics of the debris disk is sensitive to planet formation process. LMT 1.1-mm Herschel 70-micron Brick Sgr B2 20 km/s cloud 50 km/s cloud Galactic Center with BoloCAM at 1.1mm (Courtesy John Bally/Jason Glenn) “Brick" in the CMZ An incredibly dense collection of gas and dust but with little star formation. Why? 0.45mm 3mm 1.1mm left: JCMT image of the 450 micron dust continuum emission; middle: ALMA image of the 3 mm dust continuum (e.g., Hand 2012; Rodrguez & Zapata 2013; Kaumann, Pillai & Zhang 2013; Longmore et al. 2013). Right: AzTEC image. Ultra Luminous IR Galaxy: Arp 220 LMT's Killer App Galaxy Evolution SubMM View Optical View Williams et al. 1997 Hughes et al. 1998 What are the “Submm Galaxies”? ULIRGs at high redshift? Ultraluminous infrared galaxies (ULIRGs): Dusty, LIR>1012LSolar High rates of Star Formation Gas rich interacting/merging Surace, Sanders, & Evans 1999 Spectral energy distribution: strong peak near 100 micron from warm dust Peak gets redshifted to 1 mm by z~10 Yun 2000 Observations of Distant Galaxies Age of Universe (GYr) 13.5 13.3 12.4 10.3 5.9 2.2 TODAY's LMT 5-sigma In 10 sqr arcmin Map with 2 hours Integration time Z Redshift 0.5 ● ● Continuum fux from dusty starbursts is almost independent of redshift In some models and cosmologies, objects get brighter with z. Atacama Cosmology Telescope Survey Bright Source Followup AzTEC Image Locates the source at high resolution Redshift Receiver Spectrum Determines the Redshift LMT: AzTEC & RSR Observations SPIRE 350um on AzTEC FWHM ~ 8” (3-20 minutes integration) Harrington et al. (in prep.) One or more CO line detected in 8/8 sources observed (15 to 30 minutes per source) Back to Project 2 Antenna Pointing ● ● The LMT is fully steerable, meaning that we can point and track any position on the sky. LMT moves in two directions: ● ● Azimuth – rotation about vertical axis. 0 Azimuth is towards the North. Position rotation towards the East from North. Elevation – rotation of the reflector structure about horizontal axis. 0 Elevation is towards the horizon. 90 degrees elevation is towards the zenith. Good Antenna Pointing is Needed to make Good Observations ● ● ● With 32m LMT, the radio beam is 8 arcseconds at 1.1 mm wavelength. We must point the antenna blindly with an accuracy that is a small fraction of this. Pointing is one of the most difficult technical challenges faced by large antennas ● Mechanical Misalignments ● Wind ● Thermal Distortions How do we achieve high accuracy? ● ● Main Solution is to create a Pointing Model. The model includes terms which account for all the mechanical misalignments which may be in the system. Examples: ● ● ● ● Azimuth Axis and Elevation Axis not perpendicular Axis encoders don't read zero precisely when antenna is pointer to zero. Antenna “sags” as elevation changes, resulting in pointing shifts Azimuth axis not perpendicular to ground. Physical Pointing Model ● ● Azimuth Offset ● Constant – Telescope Collimation (A1) ● Sin(El) – Axis Collimation (A2) ● Cos(El) – Azimuth Encoder Zero (A3) ● Sin(El) Sin(Az) – Antenna Tilt (A4) ● Sin(El) Cos(Az) – Antenna Tilt (A5) Elevation Offset ● Constant – Elevation Encoder Zero (E1) ● Cot(El) – Refraction (E2) ● Cos(El) – Bending (E3) ● Cos(Az) – Antenna Tilt (E4) ● Sin(Az) – Antenna Tilt (E5) Physical Pointing Model Azimuth Pointing Error is function of Azimuth and Elevation Elevation Pointing Error is function of Azimuth and Elevation Fitting the Model ● ● ● ● Make measurements of sources at known position and determine pointing errors. Observe pointing errors over the entire sky if possible. Fit pointing model to determine coefficients A1,A2,A3,A4,A5 and E1,E2,E3,E4,E5 To fit this linear model, we use the standard least squares approach described in class. Least Squares Solution (Az) Single Observation N Observations for the Fit Least Squares Solution: Project ● Step 1: Look at the Data ● ● ● ● See Project Description for link to data file and program to read data. Calculate Standard Deviation of Data before fit. Check distribution of errors. We think measurement error is should be about 1 arcseconds! Step 2: Fit the Data ● ● ● Review script given in Lecture on linear least squares fit. Modify to fit BOTH Azimuth AND Elevation pointing data. Give Parameter Estimates and estimate of errors. Project ● Step 3 – Assessing the Fit ● Compute the residuals to the model fit. ● Look carefully at residuals and address questions: ● – Have you improved the pointing errors by fitting the model? (Compare the model residuals to the standard deviation of the data before the fit.) – Are the residuals in Azimuth the same as the residuals in Elevation? – Do the residuals look like they follow a normal distribution? – Do points with larger measurement errors have larger residuals than ones with small errors? – Quantitatively, how likely is it that the residuals from the model arise from random measurement errors assuming that the standard deviation of measurement errors is about 1 arcsecond? – In a graph of the residuals versus Azimuth and Elevation, do you see any systematic trends that might indicate unmodeled effects? Conclusions? Do you think the antenna can point well enough to support observations with an 8 arcsecond beam? import importnumpy numpyasasnp np import importcsv csv Example Script flename flename=='PointingData.csv' 'PointingData.csv' f f==open(flename,'r') open(flename,'r') ##open openfle fle r r==csv.reader(f) ##create csv.reader(f) createcsv csvreader reader We use the csv module to read the data file since it is in “column separated variable” (csv) format. ##create createlists lists AzList AzList==[][] ElList ElList==[][] AzOffList AzOffList==[][] ElOffList ElOffList==[][] ##read readeach eachrow rowand andget getdata datafrom fromcolumns columns for forrow rowininr:r: AzList.append(eval(row[4])) AzList.append(eval(row[4])) ElList.append(eval(row[5])) ElList.append(eval(row[5])) AzOffList.append(eval(row[6])) AzOffList.append(eval(row[6])) ElOffList.append(eval(row[8])) ElOffList.append(eval(row[8])) Here we create empty python lists to receive the data. ##create createnumpy numpyarrays arrays az az==np.array(AzList) np.array(AzList) elel==np.array(ElList) np.array(ElList) azoff azoff==np.array(AzOffList) np.array(AzOffList) eloff eloff==np.array(ElOffList) np.array(ElOffList) Finally, we want numpy arrays with the data, since we will use these later for our least squares fitting routines. We convert the python lists to numpy arrays here. We read the file one row at a time. The data in the data file is a mixture of strings and floats, so we have to evaluate each entry in the table to get it to the correct data type.