Pixel Scale and Orientation of PHARO. II.

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1 Pixel Scale and Orientation of PHARO. II. Stanimir A. Metchev Caltech 3Sep, Introduction An initial determination of the PHARO plate scale is presented in White(2002, Memo I) foronecassringangle,usingasinglebinarystarforcalibrationobservedonjun23,2002. Below I present a continuation of this investigation, and study the dependence of the plate scaleandthepositionangleofthedirectionnorthonthearraywithboth(x,y)positionon the array, and cass ring angle, using several calibration binaries observed on different nights. 2. Observations Calibration binary star observations were performed during two runs on May 10 11, and July with the Palomar 200-inch telescope using PALAO + PHARO, for the purpose of determining the pixel scale on PHARO at the f/29.91 focal ratio. The calibration binaries were selected from the 6th Catalogue of Visual Binaries, so as to have the largest possible separations( 1 ;tominimizetherelativeimportanceofcentroiding)and/oraccurately determined orbits(grade 1; to minimize uncertainties arising from the orbital solution of the binary). A summary of the observations and the orbital parameters of the observed binary calibrators is presented in Table 1. The observations were conducted mostly under strong winds or heavy cirrus conditions: factorswhichshouldnotaffecttheastrometryhowever.theseeingwas1 2 ink s,andthe airmass ranged between 1.0 and 1.3 for all calibration binary observations. The AO loop rateswerebetween500hz1500hz.duetoproblemswithachievingaolockonbrightstars during the July run, focus offloading from the secondary was turned off. All binaries wereobservedwiththeh,k s orbrγfiltersinpharowithannd0.1%ornd1.0%filter insertedinfrontofthearraytokeepthestarsfromsaturatingintheshortestexposures (1.8s). Due to the poor conditions, the AO correction was sometimes inadequate, resulting in poor images. These were excluded from the subsequent analysis, for which we have chosen

2 2 imagesinwhichadiffraction-limitedcoreoffwhm= pixwasclearlyvisible.The Strehlratioswereestimatedtobebetween10and60%,varyingonatimescaleofminutes. Eachbinarystarwasditheredacrossthearraytosamplethepixelscaleandthearray orientation in a number of locations. Five-point dither patterns were used for the purpose of sky-subtraction. Usually the 5-point dithers were done at 5 locations: at the center of the array(wheremostofthesciencetargetsareimaged),andineachofthe4pharoquadrants. DuringtheJuly15-16run,theprocedurewasrepeatedatall4orientationangles(333.5 N-up,E-left;63.5 N-left,E-down;153.5 N-down,E-right;and243.5 N-right,E-up) ofthecassring,tocheckfordependenceonthecassringangle. 3. Analysis The relative positions of the binary components were obtained using the IRAF/APPHOT task CENTER, employing the gauss centering algorithm. The gauss algorithm determines thecentersbyiterativelyfittinga1dgaussianfunctionalongboththexandyaxeswithin aspecifiedboxsize,usingafixedfwhmvalue. Basedonvisualinspectionsoftheradial fitstothediffractioncoresofthebinarycomponents,weadoptedafwhmvalueof3.7pix (0.093 )forthek s andbrγimages,and2.7pix(0.068 )fortheh-bandimages. Thebox sizewasset10pix,and8pix,respectively,inaccordancewiththerecommendedvalueof FWHM. The measured separations and orientations were then compared to the predicted values(from the orbital solution at this epoch; using the FORTRAN program ORBITSNICE)todetermineboththepixelsizeandtheringangleoftrueNorth. To obtain the uncertainties in the pixel scale and in the north direction for observation, theerrorinthemeanofthemeasurements(σ mean )wasaddedinquadraturetotheerror inthesemi-majoraxis(a;normalizedtothemeasuredseparation),ortotheerrorinthe longitude of the ascending node(ω), respectively. Note however that the uncertainties in a and Ω provide only an approximate estimate of the uncertainty in the relative position of the binary. WDC and WDC have grade 4 orbits, and, by definition, do not have published uncertainties in the orbital parameters. These are however longer-period binaries(table 1), and we thus expect that the relative positions of the components in them are known relatively accurately nonetheless.

3 3 4. Results 4.1. Pixel Scale The measured average pixel scales for all observations and the respective cass ring orientations are listed in Table 2. The nominally predicted pixel scale mas/pix(hayward etal.2001)is3.4σlowerthantheunweightedaverage(25.218±0.035mas/pix)ofallthe pixelscalemeasurements. Thecurrentresultisconsistentatthe1σlevelwiththeonein MemoI(25.168±0.034;White2002). AsfoundinMemoI,Figures1 4showthatthereisapositionaldependenceofthepixel scaleonthearray. Thelocationofeachmeasurementissetasthemid-pointbetweenthe binary star components, and the size of the symbol corresponds linearly to the measured value.thevariationsacrossthearrayforasinglebinaryandcassringangleareoftheorder oftensofσ mean,andappearlinearlycorrelatedwiththexandycoordinatesinadiagonal fashion across the array for each cass ring angle. The sense of the correlation is preserved betweenthejun23,2002(figure1)andjul16,2003(figure4)observationsofthesame binary(wdc )ataringangleof63.5. Itis,however,notpreservedbetween the Jul 15 and 16, 2003 observations of two different calibration binaries, WDC (Figure3)andWDC (Figure4),atallcassringangles. OnthenightsofJul15and16,2003,thepixelscaleexperimentwasperformedat allcassringangles. ItisapparentfromFigures3and4thatthesenseofthepixelscale variations depends on the cass ring angle: it is approximately orthogonal for cass ring angles at90 toeachother(bestexpressedinfigure3). However,forcassringanglesat180 to eachother,thepixelscaledependenceon(x,y)positiononthearrayisnearlythesame. Planarleast-squaresfitstothedependenceofthepixelscaleπ(x,y)onxandyare listedintable3forallobservations. Thecoefficientsa 0,a 1,a 2 areall>99.5%significant (comparedtoamodelinwhichthecorrespondingcoefficientissetto0). Fromcorner to corner, these relations predict a variation in the pixel scale of 0.30 mas/pix. The uncertainties in the semi-major axes of the binaries are not included in the listed errors for thea 0,a 1,a 2 parameters(theywouldcontributeonlytotheerrorofa 0 ) Ring Angle TheringangleofNorthis ±0.108 basedonanunweightedaverageofall measurements 3.4σhigherthanthevaluefoundinMemoIfromthemeasurementof WDC at a single cass ring angle. We confirm that the north direction, similarly

4 4 tothepixelscale,isdependentonthepositiononthearray,andonthecassringangle (Figures 5 8). Onceagain,wefindthatthedependenceofthenorthdirectiononxandyisrepeatable for observations of the same binary(wdc ) conducted at a cass ring angle of 63.5 ayearapart(figures5and8),however,itisnotrepeatablebetweentheobservations ofwdc andwdc takenanightapart(figures7and8. Also, there does not seem to be a one-to-one correspondence between the sense of the dependence ofthenorthdirectionacrossthearrayη(x,y)andthecassringangle(asfoundforthepixel scale, as well). Least-squaresfitstothisdependencearelistedinTable4.Thecoefficientsa 0,a 1,a 2 are > 99.5% significant except where the errors in the coefficients are comparable(within a factor of2)totheirvalues,inwhichcasethesignificanceis 80%.TherelationslistedinTable4 predictavariationof 0.5 ofthenorthdirectionacrossthearray.theuncertaintiesinthe longitudesoftheascendingnodesωofthebinariesarenotincludedinthelistederrorsfor thea 0,a 1,a 2 parameters(theywouldcontributeonlytotheerrorofa 0 ). 5. Discussion The unrepeatability of the plate scale and north angle positional dependences between thenightsofjul15and16,2003,indicatesthatastrometricobservationsneedtobedone onanightlybasis,ifanabsoluteaccuracyofbetterthan±0.15mas/pixand±0.25 are desired across the full PHARO field. It is possible that the greater uncertainty in the orbital solution of WDC (a grade 4 orbit), compared to that of WDC (grade1),maybethecauseofthiseffect(althoughi mnotcertainhow),sincetheresults for WDC alone are somewhat more repeatable: to within 0.20 mas/pix in the platescale,andtowithin 0.1 intheringangle. Ontheotherhand,iftheobserved night-to-night discrepancies are real, it is very probable that any rotation of the Cass ring mayhavearandomeffectontheplatescaleandnorthangleorientation(possiblydueto loose connections?). I have written a script cal binary in the macros directory on ezra2 that performs a5-pointditherpatternat5locationsonthearray,andtakes251.8-secexposuresand about15mintocompleteforasinglecassringorientationangle.havingtorunthisforall orientation angles will take a significant amount of time, although may be an appropriate activity for lapses of heavy cirrus. Another alternative is to take second epoch observations of candidatebinariesonlyatonecassringangle,andrunthe calbinary scriptonacalibration

5 5 binaryonlyforthatoneangle. Onecouldthusavoidrotatingthecassringwhenprecise astrometry is required, to minimize unwanted random effects. A further experiment to determine whether cass ring rotations affect the pixel scale in a randomwayistoreturntothesamecassringsettingandperformthebinarystarexperiment several times over the course of the night, on a single calibration binary. However, there are othereffectsthatwillalsolikelyaffectthesenseofthepixelscaledependenceonethe(x,y) position, most notably the orientation of the f/29.91 focal plane with respect to the horizon. Thatis,thesameresultmaynotbeattainableatdifferenthourangles. Hence,itmay not be possible to improve the accuracy of atrsometric measurements with PHARO beyond ±0.15 mas/pix. REFERENCES Close, L. M., et al. 2003, ApJ, 599, in press(astro-ph/ ) Hale,A.1994,AJ,107,306 Hartkopf,W.I.,Maso,B.D.,&MacAlister,H.A.1996,AJ,111,370 Hayward,T.L.,Brandl,B.,Pirger,B.,Blacken,C.,Gull,G.E.,Schoenwald,J.,&Houck, J.R.2001,PASP,113,105 Pourbaix, D. 2000, A&AS, 145, 215 Scardia, M Astron. Nachr. 300, 307 White, R. 2002, Pixel Scale and Orientation of PHARO Determined from the Binary Star HD (Memo I) ThispreprintwaspreparedwiththeAASL A TEXmacrosv5.2.

6 6 Fig.1. PositionaldependenceofthepixelscaleforthenightofJun23,2002(fromMemo I).ThebinaryWDC wasobservedatangleof63.5. Thepointsizeindicates the pixel scale, decreasing linearly from the largest value(25.31 mas/pix) to the smallest one (24.93 mas/pix).

7 7 Fig.2. SameasFigure1above,forWDC (leftpanel;cassringat63.5 )and WDC (rightpanel;cassringat243.5 ).Thecompassarrowscorrespondtothe directionsnandeonthearray,withecounter-clockwisefromn.

8 8 Fig.3. PositionaldependenceofthepixelscaleforthenightofJul15,2003.Thebinary star WDC was observed at all 4 nominal cass ring angles.

9 9 Fig.4. SameasFigure3,butforJul16,2003,andWDC

10 10 Fig. 5. PositionaldependenceofthenorthdirectionforthenightofJun23,2002(from MemoI).ThebinaryWDC wasobservedatacassringangleof63.5. The point size indicates the position angle of north decreasing linearly from the largest value ( )tothesmallestone( ).

11 11 Fig. 6. SameasFigure5,butforWDC (leftpanel;cassringat63.5 )and WDC (rightpanel;cassringat243.5 ).

12 12 Fig. 7. Positionaldependenceoftheangleofnorthforeachofthe4cassringangles. WDC ; Jul 15, 2003.

13 13 Fig.8. SameasFigure7,butforJul16,2003,andWDC

14 14 Table 1. Observed binaries Binary Date ρ P.A. a Ω P WDC Reference (WDC) (UT) (year) (arcsec) (degree) (arcsec) (degree) (years) grade May 10, ± ± ± Jul 15, Jun 23, ± ± ± Jul 16, May 11, References. 1. Hartkopf(1996); 2. Scardia(1979); 3. Pourbaix(2000); 4. Hale(1994) Table 2. Average pixel scale and north direction Date Binary Cassring Scale a North a Measurements (UT) (WDC) (degrees) (mas/pix) (degrees) (#) Jun 23, ± 0.034(0.083) ± 0.099(0.093) 28 May 10, ± 0.041(0.059) ± 0.19(0.049) 25 May 11, (0.015) (0.074) 20 Jul 15, (0.057) (0.082) (0.030) (0.100) (0.060) (0.077) (0.040) (0.104) 55 Jul 16, ± 0.030(0.035) ± 0.099(0.105) ± 0.031(0.054) ± 0.099(0.098) ± 0.030(0.019) ± 0.101(0.053) ± 0.031(0.053) ± 0.098(0.084) 25 unweighted average ± 0.035(0.110) ± 0.108(0.341) 11 predicted b c a The1σerrorforthepixelscaleandthenorthdirectionincludestheerrorinthemeanofthemeasurements, andtheerrorinthesemi-majoraxis(normalizedtothebinaryseparation),orintheascendingnodeofthe binary, respectively. The quantities in parentheses represent the observational scatter. b Haywardetal.(2001). c Daycrewsetting.

15 15 Table3. Pixelscaleπ(x,y)=a 0 +a 1 x+a 2 ymas/pix Star Date Cassring a 0 a 1 a 2 Measurements WDC UT deg mas/pix 10 4 mas/pix mas/pix 2 # May 10, ± ± ± May 11, ± ± ± Jul 15, ± ± ± Jul 15, ± ± ± Jul 15, ± ± ± Jul 15, ± ± ± Jul 16, ± ± Jul 16, ± ± Jul 16, ± ± Jul 16, ± ± Table4. Northangleη(x,y)=a+bx+cydegrees Star Date Cass ring a b c # meas WDC UT deg deg 10 4 deg/pix 10 4 deg/pix May 10, ± ± ± May 11, ± ± ± Jul 15, ± ± ± Jul 15, ± ± ± Jul 15, ± ± ± Jul 15, ± ± ± Jul 16, ± ± ± Jul 16, ± ± ± Jul 16, ± ± ± Jul 16, ± ± ±

September 2008 LGS Science Observing Plan 9/18/08 v1.1, A. Bouchez

1. General Procedures September 2008 LGS Science Observing Plan 9/18/08 v1.1, A. Bouchez We should attempt to complete highest priority observing programs first, before proceeding to lower priority programs.