POSSII IMAGES ASTROMÉTRIC REDUCTION Reduction methods and their influence on Theta and Rho measures...

POSSII IMAGES POSSII IMAGES ASTROMÉTRIC ASTROMÉTRIC

REDUCTIONREDUCTION

Reduction Reduction methods and their influence methods and their influence on Theta and Rho measureson Theta and Rho measures

Ignacio NovalbosIgnacio Novalbos

O.A.N.L. BarcelonaO.A.N.L. Barcelona

O.A.N.L. Barcelona 2010O.A.N.L. Barcelona 2010

ORIGIN ORIGIN AND AND

OBJECTIVEOBJECTIVE


Relative astrometry of new pairs discovered on POSSII platesRelative astrometry of new pairs discovered on POSSII plates

OAGOAG CCommon ommon PProper roper MMotion otion WWide ide PPairs airs SSurveyurvey

ORIGIN ORIGIN


OBJECTIVEOBJECTIVE

Knowing which astrometric reduction Knowing which astrometric reduction method / software method / software get the most get the most

accurate, when we measured on images accurate, when we measured on images from the POSSII-Jfrom the POSSII-J , which usually , which usually present saturation for stars with present saturation for stars with

magnitude <12.magnitude <12.


METHODOLOGYMETHODOLOGY


METHODOLOGYMETHODOLOGY- Selection of pairs from the Catalog of Rectilinear Elements - Getting POSS II images of each pair - Get the time of each plate from the FITS header - From the linear elements and using a linear regression we calculate the values for "x" and "y"- From the rectangular coordinates we calculate polar coordinates (theta and rho), correcting the theta value for the quadrant - We evaluate the accuracy of calculations by plotting “x / y “ vs epoch and " theta / rho” vs epoch, adjusting the values to a linear fit and analyzing the R-squared value- We confirm the accuracy of the estimates for theta and rho with the residuals obtained from the ephemerids calculated and those of the CRE -We calculate the calibration constants for each of the plates from Astrométrica +USNO A2.-Relative astrometry is obtained for each pair with different astrometric reduction methods-We evaluate and compare the results


PAIRS SELECTIONPAIRS SELECTION


CATALOGCATALOG

CCatalog atalog RRectilinear ectilinear EElements v. 2009.2 lements v. 2009.2 (1176 pairs)(1176 pairs)


SELECTION CRITERIASELECTION CRITERIA

- Pairs with Mag V>11 for both components. (61 Pairs = 5,2%)- Pairs with Mag V>11 for both components. (61 Pairs = 5,2%)

- Pairs with DEC between -20º y +20º. (15 Pairs = 1,3%)- Pairs with DEC between -20º y +20º. (15 Pairs = 1,3%)

- Pairs with residuals <1º PA and < 0,5” Sep. (7 Pairs = 0,6%)- Pairs with residuals <1º PA and < 0,5” Sep. (7 Pairs = 0,6%)

- Pairs with rho >10” . (6 Pairs) - Pairs with rho >10” . (6 Pairs)

- - Pairs with historical measurements Pairs with historical measurements N >5 . (6 Pairs) N >5 . (6 Pairs)


OBJECT PAIRSOBJECT PAIRS

WDS ID R.A. DEC. N V1 V2

CATALOG RECTILINEAR ELEMENTS EPHEMÉRIDS

Époch theta +/- rho +/-

00384+0130 BAL 947 00 38 23,51 +01 30 11,8 13 11,10 11,24 2010.0 216,6 0,3 18,973 0,118

07140-0101 BAL 781 07 13 56,15 -01 01 26,6 5 12,15 12,22 2010.0 8,8 0,7 11,859 0,139

14165+0145 H N 1AC 14 16 27,24 +01 45 17,4 8 11,36 11,98 2010.0 144,1 0,2 30,377 0,128

17226+0410 BAL2891 17 22 33,51 +04 09 51,7 10 11,39 11,53 2010.0 20,2 0,2 22,285 0,219

22166+0147 HJ 3102 22 16 36,91 +01 47 28,1 9 11,09 11,40 2010.0 179,3 0,6 14,628 0,202

23514+0225 HJ 3220 23 51 25,97 +02 24 55,4 12 11,35 11,41 2010.0 11,1 0,5 36,371 0,277


IMAGESIMAGES


POSS II-JPOSS II-J


OBSERVATORYOBSERVATORY

Anglo-Australian Observatory Anglo-Australian Observatory


TELESCOPETELESCOPE

UK Schmidt Telescope


PLATESPLATES

BAL 947 STScI_POSS2UKSTU_Red_00-38-24.00_+01-30-00.0

BAL 781 STScI_POSS2UKSTU_Red_07-13-56.19_- 01-01-24.8

H N 1AC STScI_POSS2UKSTU_Red_14-16-30.00_+01-45-00.0

BAL2891 STScI_POSS2UKSTU_Red_17-22-36.00_+04-10-00.0

HJ 3102 STScI_POSS2UKSTU_Red_22-16-36.00_+01-47-00.0

HJ 3220 STScI_POSS2UKSTU_Red_23-51-24.00_+02-25-00.0


STScI IMAGESSTScI IMAGES

BAL 781BAL 781


IMAGES ÉPOCHIMAGES ÉPOCH


EPHEMERIDSEPHEMERIDS

CALCULATION CALCULATION


LINEAR ELEMENTSLINEAR ELEMENTS

DD X0,,,,,,,,, XA,,,,,,, Y0,,,,,,,,, YA,,,,,,, T0,,,,,, RHO0,,, THETA0

+/-,,,,,,,, +/-,,,,,, +/-,,,,,,,, +/-,,,,,, +/-,,,,, +/-,,,, +/-,,,

BAL 947-2.664223 -0.021999 -1.384188 0.042342 1617.387 3.002 297.45

0.193818 0.000583 0.206333 0.00062 0.01 0.197 3.89

BAL 7815.310282 0.007829 -1.887678 0.022025 2456.369 5.636 70.43

0.382692 0.000751 0.358334 0.000704 0.01 0.38 3.67

H N 1AC-5.918252 0.047859 15.575843 0.018185 1513.899 16.662 200.8

0.307658 0.000696 0.324397 0.000734 0.02 0.322 1.07

BAL 2891-6.116268 0.053455 -5.465692 -0.059818 1751.713 8.203 311.78

0.063766 0.00032 0.251954 0.001265 0.01 0.174 1.35

HJ 3102-7.107194 -0.018479 6.003492 -0.021876 2404.232 9.303 229.81

0.25092 0.000513 0.333161 0.000681 0.009 0.288 1.86

HJ 322021.087496 -0.028467 -13.20597 -0.045457 1515.297 24.881 57.94

0.471982 0.001176 0.371912 0.000927 0.039 0.446 0.93


COORD. TRANSFORMATION COORD. TRANSFORMATION

We calculate the rectangular coordinates replacing in:

x = xa * (t-t0) + x0y = ya * (t-t0) + y0

From “x y” we obtain the polar coordinates replacing in:

rho = Raiz(x^2 + y^2)theta = arctg (-y/x)

Starting from the linear elements:

(x0,y0,t0) (rho0,theta0,t0)


LINEAR REGRESSIONLINEAR REGRESSION

BAL 947

Correction

270º

Catalog Ephemerids

theta rho

Époch (T) x y theta theta rho theta rho O-C O-C

2010.0 -11.30131639 15.23983165 53.44068498 216.56 18.973 216.6 18.973 -0.04 0.000

2009.5 -11.29031689 15.21866065 53.42926971 216.57 18.949

2009.0 -11.27931739 15.19748965 53.41782603 216.58 18.926

2008.5 -11.26831789 15.17631865 53.40635383 216.59 18.902

2008.0 -11.25731839 15.15514765 53.39485300 216.61 18.879

2007.5 -11.24631889 15.13397665 53.38332343 216.62 18.855

2007.0 -11.23531939 15.11280565 53.37176503 216.63 18.832

2006.5 -11.22431989 15.09163465 53.36017767 216.64 18.808

2006.0 -11.21332039 15.07046365 53.34856126 216.65 18.784

2005.5 -11.20232089 15.04929265 53.33691569 216.66 18.761

2005.0 -11.19132139 15.02812165 53.32524084 216.67 18.737 216.7 18.738 -0.03 -0.001

2004.5 -11.18032189 15.00695065 53.31353660 216.69 18.714


LINEAR FIT “x”LINEAR FIT “x”

"x"/epoch

y = -0.022x + 32.917

R2 = 1

-11.40

-11.30

-11.20

-11.10

-11.00

-10.90

-10.80

-10.70

-10.60

1975.0 1980.0 1985.0 1990.0 1995.0 2000.0 2005.0 2010.0 2015.0


LINEAR FIT “y”LINEAR FIT “y”

"y"/epoch

y = 0.0423x - 69.868

R2 = 1

13.80

14.00

14.20

14.40

14.60

14.80

15.00

15.20

15.40

1975.0 1980.0 1985.0 1990.0 1995.0 2000.0 2005.0 2010.0 2015.0


LINEAR FIT “theta”LINEAR FIT “theta”

theta/epoch

y = -0.0246x + 266.04

R2 = 0.9996

216.50

216.60

216.70

216.80

216.90

217.00

217.10

217.20

217.30

217.40

1975.0 1980.0 1985.0 1990.0 1995.0 2000.0 2005.0 2010.0 2015.0


LINEAR FIT “rho”LINEAR FIT “rho”

rho/epoch

y = 0.0471x - 75.631

R2 = 1

17.40

17.60

17.80

18.00

18.20

18.40

18.60

18.80

19.00

19.20

1975.0 1980.0 1985.0 1990.0 1995.0 2000.0 2005.0 2010.0 2015.0


ESTIMATED EPHEMERIDSESTIMATED EPHEMERIDS

Époch (T) Ephemerids

Plates x y theta Correction º theta rho

BAL 947 1987.5 -10.806338887 14.2871366460 52.90 270 217.10 17.914

BAL 781 1990.0 1.659079099 -12.1594552250 82.23 90 7.77 12.272

HN 1AC 1994.0 17.058901759 24.3064796850 -54.94 90 144.94 29.695

BAL 2891 1997.0 6.995548585 -20.1382697660 70.84 90 19.16 21.319

HJ 3102 1990.5 0.538159628 15.0542932320 -87.95 90 177.95 15.064

HJ 3220 1987.5 7.645293199 -34.6709017710 77.56 90 12.44 35.504


CALIBRATION CALIBRATION CONSTANTSCONSTANTS


18:43:33 - USNO-A2.0: 154 Records read (22.8' x 22.8')18:43:33 - USNO-A2.0: 154 Records read (22.8' x 22.8') Center Coordinates: RA = 00h 38m 24.00s, De = +01° 30' 00.0"Center Coordinates: RA = 00h 38m 24.00s, De = +01° 30' 00.0"18:43:34 - Object List for Image 1 (BAL 947 STScI_POSS2UKSTU_Red_00-38-24.00_+01-30-00.0~1.fits): 18:43:34 - Object List for Image 1 (BAL 947 STScI_POSS2UKSTU_Red_00-38-24.00_+01-30-00.0~1.fits): 753 Detections (75 Stars, 75 Ref. Stars, 0 Movers)753 Detections (75 Stars, 75 Ref. Stars, 0 Movers)18:43:34 - Astrometry of Image 1 (BAL 947 STScI_POSS2UKSTU_Red_00-38-24.00_+01-30-00.0~1.fits): 18:43:34 - Astrometry of Image 1 (BAL 947 STScI_POSS2UKSTU_Red_00-38-24.00_+01-30-00.0~1.fits): 75 of 75 Reference Stars used: dRA = 0.36", dDe = 0.41"75 of 75 Reference Stars used: dRA = 0.36", dDe = 0.41" X = +3.035090985E-6 +4.942446179E-6*x' +1.451099745E-8*y'X = +3.035090985E-6 +4.942446179E-6*x' +1.451099745E-8*y' Y = -3.718054588E-6 +1.501028067E-8*x' -4.946326400E-6*y'Y = -3.718054588E-6 +1.501028067E-8*x' -4.946326400E-6*y' Origin: x0 = 441.0, y0 = 441.0Origin: x0 = 441.0, y0 = 441.0 Center Coordinates: RA = 00h 38m 23.96s, De = +01° 29' 59.2"Center Coordinates: RA = 00h 38m 23.96s, De = +01° 29' 59.2" Focal Length = 3033.7mm, Focal Length = 3033.7mm, Rotation = 0.17°Rotation = 0.17° Pixel Size: 1.02" x 1.02",Pixel Size: 1.02" x 1.02", Field of View: 15.0' x 15.0' Field of View: 15.0' x 15.0' 18:43:34 - Photometry of Image 1 (BAL 947 STScI_POSS2UKSTU_Red_00-38-24.00_+01-30-00.0~1.fits): 18:43:34 - Photometry of Image 1 (BAL 947 STScI_POSS2UKSTU_Red_00-38-24.00_+01-30-00.0~1.fits): 70 of 75 Reference Stars used: dmag = 0.41mag70 of 75 Reference Stars used: dmag = 0.41mag

CALIBRATION CONSTANTSCALIBRATION CONSTANTS


CALIBRATION CONSTANTSCALIBRATION CONSTANTS

Astrométrica + USNO-A2 A B

A.Rotatión "/pixel R.A. DEC. R.A. DEC.

BAL 947 +0,17 1.02 00 38 23.550 +01 30 13.49 00 38 22.735 +01 29 57.24

BAL 781 +0.08 1.01 07 13 56.190 -01 01 28.34 07 13 56.209 -01 01 11.87

HN 1AC -0.09 1.01 14 16 27.162 +01 45 16.16 14 16 28.470 +01 44 52.06

BAL 2891 -0.18 1.01 17 22 33.550 +04 09 52.26 17 22 34.013 +04 10 12.43

HJ 3102 -0.09 1.01 22 16 36.915 +01 47 32.43 22 16 36.924 +01 47 12.75

HJ 3220 +0,13 1.02 23 51 25.990 +02 24 54.78 23 51 26.404 +02 25 29.42


ASTROMETRYASTROMETRY


ABSOLUTE ASTROMETRYABSOLUTE ASTROMETRY

Astrométrica + USNO A-2Astrométrica + USNO A-2


RecToPolRecToPol


RecToPolRecToPol

Efemérides RecToPol O-C

theta rho theta rho theta rho

BAL 947 217.10 17.914 216.95 20.332 0.16 2.418

BAL 781 7.77 12.272 0.99 16.472 6.78 4.200

HN 1AC 144.94 29.695 140.86 31.071 4.07 1.376

BAL 2891 19.16 21.319 18.95 21.326 0.20 0.007

HJ 3102 177.95 15.064 179.61 19.680 1.65 4.616

HJ 3220 12.44 35.504 10.16 35.191 2.28 0.313

Desv. Estándar 2.54 1.945


fv FITS VIEWER v 4.1.4fv FITS VIEWER v 4.1.4


fv FITS VIEWER v 4.1.4fv FITS VIEWER v 4.1.4

Efemérides fv O-C


BAL 947 217.10 17.914 217.83 17.917 0.72 0.003

BAL 781 7.77 12.272 6.88 12.641 0.89 0.369

HN 1AC 144.94 29.695 144.69 30.052 0.24 0.356

BAL 2891 19.16 21.319 18.75 21.558 0.40 0.239

HJ 3102 177.95 15.064 177.58 15.106 0.37 0.042

HJ 3220 12.44 35.504 12.80 35.570 0.36 0.066

Desv Estándar 0.25 0.163


ALADíN + “Dist”ALADíN + “Dist”


ALADíN + “Dist”ALADíN + “Dist”

Efemérides Aladín O-C


BAL 947 217.10 17.914 217.08 17.914 0.02 0.000

BAL 781 7.77 12.272 7.68 12.310 0.09 0.038

HN 1AC 144.94 29.695 144.92 29.736 0.02 0.041

BAL 2891 19.16 21.319 19.24 21.388 0.08 0.069

HJ 3102 177.95 15.064 177.90 14.992 0.05 0.072

HJ 3220 12.44 35.504 12.50 35.570 0.06 0.066



REDUC & SURFACEREDUC & SURFACE


REDUCREDUC

Efemérides Reduc O-C


BAL 947 217.10 17.914 217.21 17.824 0.11 0.090

BAL 781 7.77 12.272 7.91 12.208 0.14 0.064

HN 1AC 144.94 29.695 144.78 29.787 0.16 0.092

BAL 2891 19.16 21.319 19.35 21.408 0.19 0.089

HJ 3102 177.95 15.064 177.83 15.158 0.12 0.094

HJ 3220 12.44 35.504 12.47 35.522 0.03 0.018



SURFACESURFACE

Efemérides Surface O-C


BAL 947 217.10 17.914 216.69 17.750 0.41 0.164

BAL 781 7.77 12.272 7.29 11.890 0.48 0.382

HN 1AC 144.94 29.695 145.01 29.295 0.07 0.400

BAL 2891 19.16 21.319 18.90 21.238 0.26 0.081

HJ 3102 177.95 15.064 178.14 15.389 0.19 0.325

HJ 3220 12.44 35.504 12.71 35.906 0.27 0.402



RESULTSRESULTS


O-C THETAO-C THETA

RecToPol fv Aladín Reduc Surface

BAL 947 0.16 0.72 0.02 0.11 0.41

BAL 781 6.78 0.89 0.09 0.14 0.48

HN 1AC 4.07 0.24 0.02 0.16 0.07

BAL 2891 0.20 0.40 0.08 0.19 0.26

HJ 3102 1.65 0.37 0.05 0.12 0.19

HJ 3220 2.28 0.36 0.06 0.03 0.27


O-C THETAO-C THETAResiduos theta

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

5.50

6.00

6.50

7.00

7.50

BAL 947 BAL 781 HN 1AC BAL 2891 HJ 3102 HJ 3220

RecToPol

fv

Aladín

Reduc

Surface


O-C THETA (2)O-C THETA (2)Residuos theta

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00


fv

Aladin

Reduc

Surface


O-C RHOO-C RHO


BAL 947 2.418 0.003 0.000 0.090 0.164

BAL 781 4.200 0.369 0.038 0.064 0.382

HN 1AC 1.376 0.356 0.041 0.092 0.400

BAL 2891 0.007 0.239 0.069 0.089 0.081

HJ 3102 4.616 0.042 0.072 0.094 0.325

HJ 3220 0.313 0.066 0.066 0.018 0.402


O-C RHOO-C RHO

Residuos rho

0.0000.2000.4000.6000.8001.0001.2001.4001.6001.8002.0002.2002.4002.6002.8003.0003.2003.4003.6003.8004.0004.2004.4004.6004.8005.000


RectoPol

fv

Aladin

Reduc

Surface


O-C RHO (2)O-C RHO (2)

Residuos rho

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0.400

0.450


fv

Aladin

Reduc

Surface


STANDARD DEVIATIONSTANDARD DEVIATION O-C O-C THETA/RHOTHETA/RHO

0.00

0.50

1.00

1.50

2.00

2.50

3.00

theta 2.54 0.25 0.03 0.05 0.15

rho 1.950 0.163 0.028 0.030 0.137



CONCLUSIONSCONCLUSIONS The largest deviations correspond to the results obtained with The largest deviations correspond to the results obtained with

"RecToPol" which almost certainly is due to the low precision of "RecToPol" which almost certainly is due to the low precision of Astrometrica in estimating the centroid for star-saturated images.Astrometrica in estimating the centroid for star-saturated images.

Residuals derived from measurements made with the software "fv" are Residuals derived from measurements made with the software "fv" are 10 times better than those obtained from the absolute astrometry and 10 times better than those obtained from the absolute astrometry and we can accept them within the error margins normally allowed.we can accept them within the error margins normally allowed.

The measurements made with "Surface" improve even those obtained The measurements made with "Surface" improve even those obtained with "fv" and show theta and rho residuals in the order of tenths.with "fv" and show theta and rho residuals in the order of tenths.

The two softwares / methods that presents the lowest residuals between The two softwares / methods that presents the lowest residuals between observed and calculated ephemerids (and therefore the greatest observed and calculated ephemerids (and therefore the greatest accuracy available) are “Reduc" and the tool "Dist" from Aladin.accuracy available) are “Reduc" and the tool "Dist" from Aladin.


THE REASON? THE REASON?

We conclude that eye and brain working We conclude that eye and brain working in concert, we always give more in concert, we always give more accurate results than any other accurate results than any other synthetic method based on synthetic method based on mathematical calculations. The high mathematical calculations. The high precision of “Reduc", similar to that precision of “Reduc", similar to that achieved manually with "Dist", we are achieved manually with "Dist", we are pretty sure that is due to the "human pretty sure that is due to the "human component " that we put into the component " that we put into the software when we mark the photocentric software when we mark the photocentric star manually.star manually.

POSSII IMAGES ASTROMÉTRIC REDUCTION Reduction methods and their influence on Theta and Rho measures...

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