ASTROMETRIC CALIBRATION OF THE ADONIS ADONIS / SHARPII+ / NICMOS 3
DEVICE IN USE AT ESO 3.60M TELESCOPE

Introduction

The purpose of this work is to realize an astrometric calibration of the Adonis / SharpII+ / Nicmos 3 device in use at ESO 3.60m telescope, La Silla, Chile. The first step of this calibration has been performed on the basis of a single near-infrared image (SK filter) of a part of the Trapezium cluster in the Orion nebula. This image was obtained on September 26, 1999 using the 50 mas/pixel configuration of the Adonis system by F. Marchis and D. Le Mignant (coronographic technical night).

At this time (December 2001), 46 images has been performed by the Adonis team during technical nights in 1999 (09-26, 10-25, 12-02), 2000 (01-04, 03-16, 11-10, 12-13) and 2001 (02-16, 02-21, 10-25, 12-11) using the 35, 50 and 100 mas/pixel configurations of the device. The figure shows the heliocentric position (X, Y) of the earth at the dates of observation in the mean J2000 equator of DE405 (postscript version). The direction of the star theta Orion is also shown. At this time, half of the Earth's orbit has been covered but it needs more observation to get a reasonable statistical sample of data. The images are divided up as follows: 14 images at 100 mas/pixel, 18 images at 50 mas/pixel and 14 images at 35 mas/pixel, all in the SK broadband (2.154 ± 0.323).

Two images (100 and 50 mas/pixel) in the H broadband (1.643 ± 0.353) has also been realized the 30th October 2001.

The goal of this work is to test the feasibility of using such a calibration in order to perform the astrometric reduction of an astronomical observation without enough stars (less than 3) to realize a standard astrometric reduction with a 6 parameters plate constant model. It is usually the case in small fields of view like those proposed by Adonis where sometimes only one or two reference stars are observable.

A possible application of this calibration is, for example, the astrometric reduction of observations of the Uranian and Neptunian natural satellites systems performed in october 1999 at ESO 3.60m telescope by Descamps et al. (ESO proposal 64.S-0289, 1999). An other application could be the determination of astrometric positions of an asteroid of special interest (for example (216) Kleopatra) in the case where only one or two catalogued stars are present in (or near) the field of view. Otherwise, it could be apply to galactic or extragalactic object observations for which astrometry is in demand. 

Another goal of this work is to study the behavior (optic and mechanics) of the receptor over seasons and meteorological conditions. As a result it will be possible to realize a valuation on the stability of the scale factors and of the orientation of the Adonis device for the different configurations in use.

Finally, this work will be usefull to improve the astrometric positions and the proper motions of some stars (30 more or less at this time) of the center part of the Trapezium cluster.

Images and reference data

The images used for this work are centered near theta₁ Orion in the Trapezium cluster in the Orion nebula:

Astrometric data of theta₁Orion

Name	theta1 Orion  HIP 26221 ; TCC 068
J2000 position (ICRS)	RA = 5h 35m 16s.4655  De = -5o 23' 22".905
Trigonometric parallax	-1.85 mas
Proper motion  (ICRS, epoch 1991.25)	µRA = -0.924 mas/yr  µDe = +0.130 mas/yr
V magnitude	5.13

The wavefront analysis is performed by the RETICON wavefront sensor using this bright star. To avoid light saturation on the detector, we used, sometimes, a 1.0" diameter coronagraph and an integration time of 4s*20 frames in the SK broadband.

The SK filter used for the observation is centered at 2.154 µm with a bandwidth of 0.323 µm and a peak of transmission of 91%. The H filter is centered at 1.643 µm with a bandwidth of 0.353 µm and a peak of transmission of 82%.

The meteorological conditions (see picture) of each observation can be retrieve by the La Silla - MeteoMonitor.

The images used for the project are presented hereafter. The theoretical orientation of each image is regarded as close to zero (the x axis is almost parallel to the Earth equator).The theoretical scale factors and the size of the fields of view are indicated.

Date (m/d/y)	Image (FITS format)	Filter	Scale factor  (mas/px)	Field of  view (")	Compressed format
09/26/1999	tco_990927_0958_redavg	SK	50	12.8	gzip
10/25/1999	mst_991026_0854_redavg	SK	100	25.6	gzip
-	mst_991026_0900_redavg	SK	50	12.8	gzip
12/02/1999	kgb_991203_0245_redavg	SK	100	25.6	gzip
01/04/2000	stp_000115_0316_redmed	SK	35	9	gzip
-	stp_000115_0321_redmed	SK	50	12.8	gzip
-	stp_000115_0324_redmed	SK	100	25.6	gzip
-	stp_000115_0337_redmed	SK	35	9	gzip
-	stp_000115_0339_redmed	SK	50	12.8	gzip
03/16/2000	mst_000317_0024_redmed	SK	100	25.6	gzip
-	mst_000317_0027_redmed	SK	50	12.8	gzip
-	mst_000317_0032_redmed	SK	35	9	gzip
-	mst_000317_0035_redmed	SK	35	9	gzip
-	mst_000317_0038_redmed	SK	50	12.8	gzip
11/10/2000	mst_001110_0451_redmed	SK	100	25.6	gzip
-	mst_001110_0452_redmed	SK	100	25.6	gzip
-	mst_001110_0454_redmed	SK	50	12.8	gzip
-	mst_001110_0503_redmed	SK	35	9	gzip
-	mst_001110_0507_redmed	SK	35	9	gzip
-	mst_001110_0511_redmed	SK	50	12.8	gzip
12/13/2000	fma_001213_0517_redmed	SK	100	25.6	gzip
-	fma_001213_0519_redmed	SK	50	12.8	gzip
-	fma_001213_0523_redmed	SK	35	9	gzip
-	fma_001213_0526_redmed	SK	35	9	gzip
-	fma_001213_0530_redmed	SK	50	12.8	gzip
02/16/2001	kjb_010216_0155_redavg	SK	100	25.6	gzip
-	kjb_010216_0156_redavg	SK	100	25.6	gzip
-	kjb_010216_0157_redavg	SK	100	25.6	gzip
-	kjb_010216_0208_redavg	SK	100	25.6	gzip
-	kjb_010216_0213_redavg	SK	50	12.8	gzip
-	kjb_010216_0214_redavg	SK	50	12.8	gzip
-	kjb_010216_0222_redavg	SK	35	9	gzip
-	kjb_010216_0228_redavg	SK	35	9	gzip
02/21/2001	mst_010221_0048_redavg	SK	50	12.8	gzip
10/25/2001	stp_911025_0703_redavg	SK	50	12.8	gzip
-	stp_911025_0706_redavg	SK	50	12.8	gzip
-	stp_911025_0711_redavg	SK	35	9	gzip
10/30/2001	hm_H_011030_0923_56_cln	H	100	25.6	gzip
-	hm_H_011030_0927_55_cln	H	50	12.8	gzip
12/11/2001	koe_911211_0212_redavg	SK	50	12.8	gzip
-	koe_911211_0214_redavg	SK	50	12.8	gzip
-	koe_911211_0215_redavg	SK	50	12.8	gzip
-	koe_911211_0218_redavg	SK	100	25.6	gzip
-	koe_911211_0220_redavg	SK	100	25.6	gzip
-	koe_911211_0222_redavg	SK	100	25.6	gzip
-	koe_911211_0224_redavg	SK	35	9	gzip
-	koe_911211_0226_redavg	SK	35	9	gzip
-	koe_911211_0228_redavg	SK	35	9	gzip

As an example, the field of view of the first image of the project is available in GIF format (click on the image for a better resolution). The scale factor is here 50 mas/px and the field of view is 12.8'' x 12.8''. The brighter star, theta Orion, is masked by a coronograph to avoid light saturation.

Astrometric data of the reference stars used for this calibration are taken from M. J. Mc Caughrean and J. R. Stauffer, "High resolution near-infrared imaging of the trapezium: a stellar census", Astron. Journal, vol.108, no. 4, 1994 (hereafter referred to as CS), and are presented below.

The column RC indicate if the star is known to have a radio source counterpart. The column NP indicates the number of star positions measured until now. An ASCII version of the data used for this work is available here. This figure (or its postscript version) shows the K' magnitude of the stars.

Reference stars (except TCC068) in the core of the Trapezium cluster used for the calibration (From Mc Caughrean et al., AJ vol. 108, no 4, 1994).

Name	RC	J2000 position		K' mag.	NP
		RA = 5h 35m	De = -5o23'
TCC 033		15s.537	15".84	13.10	4
TCC 034		15s.559	29".69	13.50	8
TCC 039	x	15s.728	22".63	9.31	20
TCC 040		15s.768	10".06	6.77	1
TCC 041		15s.760	38".43	11.61	1
TCC 042	x	15s.792	26".74	10.02	23
TCC 043		15s.801	12".14	11.40	4
TCC 045	x	15s.821	14".45	5.87	14
TCC 046	x	15s.834	22".61	8.92	22
TCC 047	x	15s.842	25".67	10.97	23
TCC 050		15s.899	38".12	12.46	1
TCC 051		15s.961	22".82	13.20	21
TCC 054	x	16s.063	24".42	13.30	27
TCC 056		16s.069	07".24	7.53	1
TCC 057	x	16s.072	27".91	12.90	28
TCC 058		16s.093	23".15	13.60	23
TCC 059		16s.100	14".33	11.58	14
TCC 060		16s.129	06".96	6.43	1
TCC 062		16s.221	19".07	12.26	32
TCC 063	x	16s.284	16".70	9.55	16
TCC 065	x	16s.324	22".74	12.20	4
TCC 066		16s.326	25".40	12.40	26
TCC 068		16s.462	23".03	4.41	16
TCC 070		16s.612	16".22	10.77	16
TCC 071		16s.649	28".90	12.60	39
TCC 072		16s.720	25".28	9.01	40
TCC 073	x	16s.745	16".54	9.05	16
TCC 074	x	16s.764	28".05	10.90	39
TCC 075	x	16s.832	26".13	13.00	7
TCC 077	x	16s.844	26".30	12.60	40
TCC 082	x	17s.977	37".14	9.28	3
TCC 084	x	17s.062	34".13	7.91	14
TCC 087		17s.248	16".69	5.85	11

One should remark that differences for the star TCC 068 between the Hipparcos position and the CS one are 52.5 mas in RA and 125 mas in De (i.e.. the Hipparcos position is toward north-east from the CS one). It is consistent with position errors mentioned by CS in their paper. As far as we know, the proper motions of all stars used in this work have not been determined neither by CS nor by anyone. So we should wait for significant differences between catalogued positions and those determined in this work.

Methodology

The method of calibration consists in doing the astrometric reduction of the field of stars using a classical 6 parameters plate constants determination which, in this case, materialize the linking function between the celestial and the CCD frame: 

xi  =  A + B x + C y
eta =  D + E y + F x

where A, B, C, D, E, F are the plate constants (printed, respectively, as A(1), A(2), A(3), B(1), B(2), B(3) in the astrometric result files) and (x, y) and (xi, eta) depict, respectively, the CCD and the celestial frame (tangent plane perpendicular to the optical axis of the telescope). In this way, the constants A and D can be associated to the offset between the "true" center of the celestial frame and the intersection of the optical axis and the celestial sphere in the tangent plane; B and E can be associated to the scale factors along the x and y axis respectively; C and F can be associated to the orientation of x and y axis in comparison, respectively, with the Earth equator (RA axis) and with the direction of the celestial north pole (Dec axis). This description is available as long as the field of view is small enough to neglect non-linear deformation. Thus, one can calculate the orientation angle:

theta = atan (C / E)

and the scale factors:

f_x = B / cos(theta)
f_y = E / cos(theta)

The radiometric and cosmetic treatments of the image were performed by F. Marchis using a pipeline based upon the eclipse software. The photocenter positions of the stars on the CCD receptor were obtained using the ESO-Midas 97NOV software and a special script (named ccdphot) developed by P. Descamps and based on a bidimensional gaussian stellar profile model and full aperture photometry. Since the beginning of 2001, the CCD star positions are measured using an IDL's program, centro, developped by P. Descamps and J. Berthier on the base of Moffat-Gaussian stellar profile model and sky background fit. Finally the astrometric reduction was performed with the Priam software developed at the Institut de Mécanique Céleste (Fienga and Berthier, 1999). It is still under validation and in restricted access (it should be available by the year 2002).

The astrometric reduction is performed in a topocentric apparent frame (true equator; equinox of the date) and includes a correction for the atmospheric refraction. As this angular deviation could not be approximated by a bijective model, we used two types of models: the first one to compute observed positions (affected by refraction) of objects from their theoretical positions (without refraction); the second one to inverse the process. For the first step, we choose to use the mapping function model of Yan (Yan, 1996, Yan and Ping, 1995) which writes the offset in zenithal distance induced by the atmospheric layers using a rational fraction shape. For the second step, we use the model developed by Stone (Stone, 1996) which is based on the classic Laplace refraction law (see for example, Kovalevsky, 1990). The physical atmosphere model is the same in the two cases and is materialized by the Owens formula for the refractive index (Owens, 1968). The impact of using 2 different refraction laws in the reduction process has been studied and it appears that, by composing these two corrections, the bijectivity of the process is assured at a good level of accuracy (Berthier and Fienga, 1997).

Finally, the astrometric positions of the stars are expressed in a topocentric astrometric J2000 frame (mean equator; equinox of J2000.0) and are cleared of the refraction effect. The reference system of these positions is based on the FK5 and CS positions of stars of which the reference frame is based on the Jones and Walker absolute reference frame (1988), which probably derives from the absolute frame of Fallon (1975).

Astrometric results

The CCD measured positions (in pixels) of the stars, the observational conditions and the astrometric results for each observation are available hereafter in the table. The reference frame of each image is constructed on the basis of some stars of the CS catalogue (NRS is the number of reference stars in the frame).

Date (m/d/y)	Measures	NRS	Conditions	Results
09/26/1999	tco_990926_0958.mes	7	tco_990926_0958.cnd	tco_990926_0958.sol
10/25/1999	mst_991025_0854.mes	20	mst_991025_0854.cnd	mst_991025_0854.sol
-	mst_991025_0900.mes	7	mst_991025_0900.cnd	mst_991025_0900.sol
12/02/1999	kgb_991202_0245.mes	20	kgb_991202_0245.cnd	kgb_991202_0245.sol
01/04/2000	stp_000104_0316.mes	5	stp_000104_0316.cnd	stp_000104_0316.sol
-	stp_000104_0321.mes	7	stp_000104_0321.cnd	stp_000104_0321.sol
-	stp_000104_0324.mes	20	stp_000104_0324.cnd	stp_000104_0324.sol
-	stp_000104_0337.mes	8	stp_000104_0337.cnd	stp_000104_0337.sol
-	stp_000104_0339.mes	10	stp_000104_0339.cnd	stp_000104_0339.sol
03/16/2000	mst_000316_0024.mes	22	mst_000316_0024.cnd	mst_000316_0024.sol
-	mst_000316_0027.mes	6	mst_000316_0027.cnd	mst_000316_0027.sol
-	mst_000316_0032.mes	5	mst_000316_0032.cnd	mst_000316_0032.sol
-	mst_000316_0035.mes	8	mst_000316_0035.cnd	mst_000316_0035.sol
-	mst_000316_0038.mes	10	mst_000316_0038.cnd	mst_000316_0038.sol
11/10/2000	mst_001110_0451.mes	22	mst_001110_0451.cnd	mst_001110_0451.sol
-	mst_001110_0452.mes	21	mst_001110_0452.cnd	mst_001110_0452.sol
-	mst_001110_0454.mes	9	mst_001110_0454.cnd	mst_001110_0454.sol
-	mst_001110_0503.mes	4	mst_001110_0503.cnd	mst_001110_0503.sol
-	mst_001110_0507.mes	8	mst_001110_0507.cnd	mst_001110_0507.sol
-	mst_001110_0511.mes	9	mst_001110_0511.cnd	mst_001110_0511.sol
12/13/2000	fma_001213_0517.mes	22	fma_001213_0517.cnd	fma_001213_0517.sol
-	fma_001213_0519.mes	9	fma_001213_0519.cnd	fma_001213_0519.sol
-	fma_001213_0523.mes	5	fma_001213_0523.cnd	fma_001213_0523.sol
-	fma_001213_0526.mes	8	fma_001213_0526.cnd	fma_001213_0526.sol
-	fma_001213_0530.mes	9	fma_001213_0530.cnd	fma_001213_0530.sol
02/16/2001	kjb_010216_0155.mes	23	kjb_010216_0155.cnd	kjb_010216_0155.sol
-	kjb_010216_0156.mes	23	kjb_010216_0156.cnd	kjb_010216_0156.sol
-	kjb_010216_0157.mes	23	kjb_010216_0157.cnd	kjb_010216_0157.sol
-	kjb_010216_0208.mes	23	kjb_010216_0208.cnd	kjb_010216_0208.sol
-	kjb_010216_0213.mes	7	kjb_010216_0213.cnd	kjb_010216_0213.sol
-	kjb_010216_0214.mes	7	kjb_010216_0214.cnd	kjb_010216_0214.sol
-	kjb_010216_0222.mes	4	kjb_010216_0222.cnd	kjb_010216_0222.sol
-	kjb_010216_0228.mes	4	kjb_010216_0228.cnd	kjb_010216_0228.sol
02/21/2001	mst_010221_0048.mes	9	mst_010221_0048.cnd	mst_010221_0048.sol
10/25/2001	stp_011025_0703.mes	7	stp_011025_0703.cnd	stp_011025_0703.sol
-	stp_011025_0706.mes	7	stp_011025_0706.cnd	stp_011025_0706.sol
-	stp_011025_0711.mes	4	stp_011025_0711.cnd	stp_011025_0711.sol
10/30/2001	hmH_011030_0923.mes	19	hmH_011030_0923.cnd	hmH_011030_0923.sol
-	hmH_011030_0927.mes	7	hmH_011030_0927.cnd	hmH_011030_0927.sol
12/11/2001	koe_011211_0212.mes	8	koe_011211_0212.cnd	koe_011211_0212.sol
-	koe_011211_0214.mes	6	koe_011211_0214.cnd	koe_011211_0214.sol
-	koe_011211_0215.mes	6	koe_011211_0215.cnd	koe_011211_0215.sol
-	koe_011211_0218.mes	15	koe_011211_0218.cnd	koe_011211_0218.sol
-	koe_011211_0220.mes	18	koe_011211_0220.cnd	koe_011211_0220.sol
-	koe_011211_0222.mes	18	koe_011211_0222.cnd	koe_011211_0222.sol
-	koe_011211_0224.mes	4	koe_011211_0224.cnd	koe_011211_0224.sol
-	koe_011211_0226.mes	4	koe_011211_0226.cnd	koe_011211_0226.sol
-	koe_011211_0228.mes	4	koe_011211_0228.cnd	koe_011211_0228.sol

The O-C of the star positions, differences between observed (i.e. reduced) and calculated (from CS catalogue) positions are grouped together in a single file: Calib_run.sol.omc.

Graphics and discussion

Scale factors:

The different values obtained for the scale factors, plotted against time, are presented in the following figures:

35 mas/px scale postscript version x y mean value (mas/px) 35.35 34.12 stand. dev. (mas/px) 0.70 0.37

50 mas/px scale postscript version x y mean value (mas/px) 49.44 49.58 stand. dev. (mas/px) 0.36 0.20

One can conclude that, in the limit of more or less 0.5 mas, the scale factors are stabled and closed to the theoretical ones, except for the 100 mas/px scale factor which presents a systematic offset of 1.4 ± 0.2 mas/px. Hence, an error of 1.1% to 1.4% is made on distance measurements between stars in the field of view. If the theoretical scale factors are used instead of the real ones, it leads, in the worst case (diagonal of the frame), to an accuracy better than 180 mas for the 35 mas/px scale, 200 mas for the 50 mas/px scale and 500 mas for the 100 max/px scale.

100 mas/px scale postscript version x y mean value (mas/px) 98.63 98.60 stand. dev. (mas/px) 0.17 0.18

Orientation:

The different values obtained for the CCD frame orientation, plotted against time, are presented in this figure (postscript version). As expected, the orientation angle of the CCD frame is closed to zero, between ± 0°.5, except for the 03/16/2000 run for which it is about -1°. Whitout this run, the mean orientation angle is -0.20° ± 0°.29.

Errors on the reduced star positions:

When applying the constant plates model on CCD measured star positions, the errors induced from the reduction process are calculated. They represent the accuracy of the reduced positions and take into account the errors arising from the observation (i.e. on x and y, given by the CCD measurement uncertainties), the errors on the estimation of the constant plates (computed by least squares) and the errors on the reference star positions (mean errors of the stellar catalogue), defined, here, as the truncation error of the coordinates values, i.e. 15 mas in right ascension and 10 mas in declination (the accuracy on star positions given by CS in their catalogue is 50 mas for most stars, 60 mas for the fainter stars and about 200 mas for the faint stars close to a bright one like TCC065).

The figures hereafter present different kind of visualization of the distribution of the errors, for a total of 33 stars and 555 positions (see Tab. above for the detail of each star).

function of the star number (TCC 0xx)	function of the time (Sep. 1999 to Dec. 2001)
postscript version	postscript version

The two following figures show the histogram and the cumulative histogram of the distribution of the RA and Dec errors:

Histogram	Cumulative histogram
postscript version	postscript version

We see that most of the errors (more that 95%) are smaller that 50 mas in both RA and Dec. These errors are minimized by the fact that we choose, for the reference star positions accuracy, the truncation error of the coordinates values (15 mas in RA and 10 mas in Dec). In the reality, the errors should be greater. However, defined as it is, the errors reflect the uncertainties of the CCD measurements combined with the astrometric reduction. And we see that for some stars, this uncertainty is systematically greater than 20 mas (stars TCC 34, 59, 62, 63, 70, 77, 87 especially). Let compare these results to the x and y CCD measurement uncertainties, presented in the following figures (regardless of the scale factors):

function of the star number (TCC 0xx)	Histogram of distribution
postscript version	postscript version

We see that the mean accuracy of the CCD measurements is 0.12 ± 0.1 pixel in x and 0.19 ± 0.2 pixel in y; It can reach 0.4 pixel and sometimes, in the worst case, 0.6 to 0.8 pixel, that is to say 12 to 80 mas for the 100 mas/px configuration. For the stars quoted previously, there is no exception: the accuracy of their position measurements is equivalent that for other stars.

Residuals of the reference star positions:

The residuals of the astrometric fit for each reference stars are expressed as differences between apparent stars positions (i.e. expressed in a true frame) given by ephemeris calculation and the one calculated applying the plate constants model (i.e. the reduced star positions). The following figures show the values of the residuals:

function of the star number (TCC 0xx)	function of the time (Sep. 1999 to Dec. 2001)
postscript version	postscript version

and these show their distributions:

Histogram	Cumulative histogram
postscript version	postscript version

We see that the residuals are between ± 80 mas for about 90% of the values. This explains the values of the reduced star position errors (see above), ± 50 mas for 95% of the values, while the CCD measurement uncertainties and the reference star position errors are smaller.

We also see that it seems to exist a period of variation of the right ascension and of the declination residuals, with a period more longer for the second one so that we could not have detected it before. We will realize a frequency analysis of the residuals to determine the period and the amplitude of these variations and we will try to point out the reasons of this in a close futur...

The graphic showing the residuals in function of the star number allows us to detect the stars for which the residuals are worst that ± 50 mas in RA and De: TCC062, TCC066, TCC071, TCC084. We see also that for the stars TCC043, TCC051, TCC059 the residuals are not good in right ascension only, whereas it is in declination for the stars TCC042, TCC074. The only position of TCC082 is also not accurate because the star is very close to the border of the field (see frame stp_000115_0324). The following figure (residuals in function of the K' magnitude) shows that the residuals of the faint stars (K' mag. > 11) are more dispersed than the residuals of the bright ones, with an exception: the star TCC084 (K' mag. = 7.9). A reason to this should arise from the photocenters determination, and more precisely from the form of the stellar profiles. It has been demonstrated (Descamps, 2000) that, in some case, and especially in adaptive optic, the stellar profile is not well modelized by a gaussian function which can't fit a surplus of energy in the wings of the profile. In this case, a modelization based on a combination of a MOFAT and a gaussian functions fits much better the stellar profile. The difference between the measured photocenter positions can reach 1 pixel.

We should now do again the astrometric reduction without those stars as reference stars and without stars such as TCC065 (because of their low accuracy CCD measurement) to improve the results of this work. We'll try to do it in a close futur...

Residuals function of the K' magnitude

postscript version

O-C of the star positions:

On top of the calibration, the astrometric positions of the reference stars are calculated to validate the process. They are expressed in a J2000 astrometric topocentric frame at the date of observation. The resulting O-C, i.e. the differences between the positions determined here and those ones calculated by the ephemeris, are presented below:

function of the star number (TCC 0xx)	function of the time (Sep. 1999 to Dec. 2000)
postscript version	postscript version

Their distributions are presented below:

Histogram	Cumulative histogram
postscript version	postscript version

As we see it before for the residuals, it seems to exist a periodic variation of the O-C in right ascension and in declination. Quantitatively, 95% of the O-C are smaller than 85 mas in right ascension and than 100 mas in declination, while the accuracy of CS catalogue star positions is 50 mas for most stars, 60 mas for the fainter stars and about 200 mas for the faint stars close to a bright one like TCC065. The O-C vector maps show also that the O-C vectors are oriented in all the directions, as it is confirmed by the following figures.

Discussion:

Those results may be improved, first, by removing the worst stars as reference stars and by doing again the astrometric reduction of the frames. But, without further investigation, it is pure speculation to try to determine the origin of the residuals and the O-C and their periodic variations. First, a study should be done to answer the 2 questions:

• What is the link between the two reference frames? The reference frame of the CS positions is based on the Jones and Walker absolute reference frame (1988), which probably derives from the absolute frame of Fallon (1975), while our reference frame is based on the FK5 and CS positions of the stars.

• Are we sure that we compare the same kind of positions? No description of the type of the star coordinates is given in the CS paper except the "J2000.0 coordinates" label.

Another source of improvement should be to pay much attention to the astrometric CCD measurements. As we have already say it, we have studied the quality of the usual gaussian adjustment of stellar profiles and has showed that, especially with adaptive optic images, the tails of the stellar profiles was not always satisfactorily modeled so that (x,y) star photocenter positions could be shifted up to one pixel, depending on the star behavior (for example a faint star close to a bright one like TCC065) (Descamps, 2000). This means that we should measure again some of the star positions to obtain more reliable results.

Remark:

the study of the stars proper motion in a large part of the Trapezium cluster by JW (1988) shows that, in general, they are smaller than ±4 mas/year. But since the collection of plates used by JW to determine the proper motions has been realized in 1960 and 1961, and even if CS have take into account the stars proper motions to realize their astrometric reference frame, uncertainties on proper motions and nearly 30 years of proper motion can introduce large corrections (tenth of mas). It's why it could be interesting to start a work to try to calculate the star proper motions on the base of our astrometric positions and CS ones (the time span between the positions is about 10 years...).

Conclusion

This work allows us to conclude that it is possible to use such a calibrating field to determine the scale factor (in the limit of more or less 1 mas) and/or the orientation factor (in the limit of ±0°.5) in order to reduce the number of unknowns in astrometry. It is stressed that, as long as this ongoing project is not completed, the calibration parameters derived here are valid only for these particular nights of observation. Meanwhile, if a user is in demand of calibration parameters to reduce its new observation, an image of this (or of a larger) part of the Trapezium cluster should be performed and reduced (we can provide the reduction, contact the authors).

It will be of great interest to regularly observe the Trapezium cluster core to improve the near-infrared coordinates of stars and to complete the valuation on the stability of the scale and orientation factors of the Adonis / SharpII+ / Nicmos3 device in the different configurations proposed to observers (100, 50 and 35 mas/pixel).

Also, a special work should be undertaken to reckon the proper motion (and the velocity dispersion inside the cluster) of all the stars of the central part of the cluster. This may improve the astrometric calibration. And it is another reason to carry on the observations of the Trapezium cluster with ADONIS.

References

Berthier and Fienga, 1997	J. Berthier and A. Fienga, "Comparaisons d´expressions de la réfraction astronomique", Journées scientifiques du Bureau des longitudes, 1997
Caughrean and Stauffer, 1994	M. J. Mc Caughrean and J. R. Stauffer, "High resolution near-infrared imaging of the trapezium: a stellar census", Astron. Journal, vol. 108, no. 4, 1994
Descamps, 2000	P. Descamps, private communication, 2000
Fallon, 1975	F. Fallon, PhD. thesis, University of Florida, Gainesville, 1975
Fienga and Berthier, 1999	A. Fienga and J. Berthier, "Principe de réduction d´images astrométriques", Note scientifique et technique du Bureau des longitudes, S063, 1999
Jones and Walker, 1988	B. F. Jones and M. F. Walker, "Proper motions and variabilities of stars near the Orion nebula", Astron. Journal, vol. 95, no. 6, 1988
Kovalevsky, 1990	J. Kovalevsky, "Astrométrie moderne", Springer-Verlag Berlin Heidelberg, 1990
Owens, 1968	...
Stone, 1996	R. C. Stone, "Accurate method for computing atmospheric refraction", Publications of the Astronomical Society of the Pacific, 108, 1996
Yan, 1996	H. Yan, "A new expression for astronomical refraction", Astron. Journal, vol. 112, no. 3, 1996
Yan and Ping, 1995	H. Yan and J. Ping, "The generator function method of the tropospheric refraction corrections", Astron. Journal, vol. 110, no. 2, 1995

Contact:

J. Berthier, IMCCE, Paris, France

F. Marchis, Univ. of Berkeley, California, USA

P. Descamps, IMCCE, Paris, France

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