|:: Introduction :: Images and reference data :: Methodology :: :: Astrometric results ::|
|:: Graphics and discussion :: Conclusion :: References :: Contact ::|
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.
The images used for this work are centered near theta1 Orion in the Trapezium cluster in the Orion nebula:
HIP 26221 ; TCC 068
|J2000 position (ICRS)||RA = 5h 35m 16s.4655
De = -5o 23' 22".905
|Trigonometric parallax||-1.85 mas|
(ICRS, epoch 1991.25)
|µRA = -0.924 mas/yr
µDe = +0.130 mas/yr
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
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.
|Name||RC||J2000 position||K' mag.||NP|
|RA = 5h 35m||De = -5o23'|
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.
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:
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:xi = A + B x + C y
eta = D + E y + F x
and the scale factors:theta = atan (C / E)
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).fx = B / cos(theta)
fy = E / cos(theta)
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).
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).
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.
The different values obtained for the scale factors, plotted against time, are presented in the following figures:
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.
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.
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
|function of the time
(Sep. 1999 to Dec. 2001)
The two following figures show the histogram and the cumulative histogram of the distribution of the RA and Dec errors:
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
|Histogram of distribution|
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.
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
|function of the time
(Sep. 1999 to Dec. 2001)
and these show their distributions:
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|
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
|function of the time
(Sep. 1999 to Dec. 2000)
Their distributions are presented below:
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.
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:
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.
|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|
|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|
|J. Berthier, IMCCE, Paris, France|
|F. Marchis, Univ. of Berkeley, California, USA|
|P. Descamps, IMCCE, Paris, France|