A procedure is described for calculating the brightness of stars in a band that does not coincide with the bands of their observation. As an example, we took the calculation for the navigation catalog of the star sensor. We present a way to reduce the orientation error by increasing the accuracy of determining the position of the photocenter of the star image on the radiation receiver - a charge-coupled matrix device. The most difficult is the accounting of the shadow signal. First, the rates of thermogeneration strongly depend on temperature. Second, the scatter of average values of thermogeneration rates in individual elements is many times greater than the random scatter (noise) in each of them. Thirdly, in addition to "normal" elements in the charge-coupled matrix device there are "hot" elements, the rates of thermogeneration in which are tens to hundreds of times higher than in "normal" elements and may have a different dependence on temperature.
The problem of recalculating the star magnitudes of navigation catalogs arises when creating any
sensor, since an input (source) catalog is required, complete up to a certain star magnitude in the
sensitivity band of the sensor, and direct observations of stars in the photometric bands used in these
instruments are usually absent. For the SAI star sensor, the recalculation problem is even more
important, since during its operation this sensor uses information on the brightness of the stars. Because
of this, the accuracy of calculating the magnitudes in the sensitivity band of the silicon charge-coupled
device (CCD) (panchromatic band) should be high [
For the calculation, we used data from the Tycho-2 [
where
catalog [
and , and the 2MASS catalog, in three near-IR bands J, K, H. Due to the fact that the
accuracy of measuring the brightness of bright stars in these catalogs is rather low, for such stars we
used photometric data from the WBVR catalog of the SAI MSU [
The catalog creation procedure included the following steps:
Primary cleaning of catalogs: elimination of variables and close binaries; Mutual identification of catalog stars, identification and elimination of identification errors; Exclusion of stars with abnormal color indices. The appearance of such color indices is associated either with the anomalous properties of the star or its variability (due to nonsimultaneous brightness measurements in the bands included in the color index), or with errors in measuring the brightness of stars in at least one band. Such stars are not suitable for conversion to other spectral bands; The next step for calculating the brightness of stars - the central one in the procedure - is the construction of a reduction polynomial (or a system of polynomials for various calculation cases) based on the color indices of the stars. The constructed polynomial must satisfy a number of conflicting requirements: to provide small residual deviations of the stars and, at the same time, have sufficiently low degrees. The polynomial system is required when using stars for which measurements in the catalogs are not present in all photometric bands.
The reduction polynomials were constructed according to the following scheme: systems in the original catalogs and for the model interstellar extinction magnitude using the formula: where - magnitude of the star in the stripe of the star sensor; spectrum to the Z band;
- color indices of stars from the source catalog; K - number of bands in the photometric system of the original catalog;
- the magnitude of the star in the band of the original catalog, which is closest in position in the N - the order of the polynomial used;
- polynomial coefficients. approximation with the required accuracy. coefficients of the polynomials
.
The order of the polynomial was limited to N = 3, which turned out to be quite sufficient for Using the nonlinear least squares method (the Marquardt - Levenberg method), the values of the After finding the coefficients, an analysis of their significance was carried out; insignificant coefficients were discarded. Then the next iteration was carried out. Usually 6-10 iterations are enough (depending on the number of bands in the source catalog) to determine the significant terms of the polynomials.
2,51 - power irradiance spectral density (PISD); – PISD stars; – stars Vega; - monochromatic interstellar absorption coefficient with optical depth X; - response curve of the receiving equipment in the i-th spectral band. (1) (2) with known PISD were carried out for a random set of values of the parameter X.
To correctly simulate the influence of interstellar reddening, the calculations of for each star
Reducing polynomials were compiled in the form of the dependence of the magnitude of the star in
the stripe of the device Z on the color indices of the selected source catalog:
according to
2,6155
2,2947
6,0792
6,1329
there is only one color index (
), while the 2MASS survey catalog has only two: (J-H), (H-K) [
The combination of these catalogs makes it possible to obtain in this way a large number of magnitudes of stars in the Z band for stars identified in both catalogs.
As an example of a photometric polynomial for determining the magnitude of a star in the Z band The photometric characteristics were verified by comparing the Z values obtained from different source catalogs. For this, a list of common stars of the WBVR catalogs of the SAI MSU, Tycho-2, Uc, Bc, Vc, Rc, Ic Kuzins, UBVRI Johnson, JHK 2MASS was compiled. The prepared polynomials for these stars were used to calculate the values of Z. To check the reliability of the polynomials, the differences in the values of Z were plotted, calculated from different sources. For example, Figure 1 and 2 show the dependences of such differences on the color index and the magnitudes of the stars. (3)
Analysis of the graphs shows that the value of the standard deviation of the difference in magnitudes is 0.027m, the spread of values slightly increases in the region of red stars. The average value for 320 common stars is 0.0018m, that is, there is practically no dependence either on the color index or on the magnitude.
Similar plots have been built for other photometric catalogs. In the presence of measurements of the star in different catalogs, we took the weighted average value of Z.
The problem of recalculating the stellar magnitudes of navigational catalogs arises in the creation of any sensor, because we need an input (original) catalog, complete to a certain stellar magnitude in the sensitivity band of the sensor, and direct observations of stars in the photometric bands used in these devices are usually absent.
The presented method can be adapted to different spectral bands and input catalogs. In the work [
This work was carried out within the framework of the state assignment of the Ministry of Education and Science of the Russian Federation on "Conceptual modeling of the information and educational environment of human capital reproduction in a digital economy" 121102600069-2.
This work was performed within the framework of the state assignment of the Ministry of Education and Science of Russia on the topic "Development of new methods of autonomous navigation of spacecraft in outer space" 121102600068-5.
This study was supported by the Russian Federation State Task No 0555-2021-0005.