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Subsections

5 The solutions

The new solutions are presented in Tables 1-7 with a layout close to that of the Hipparcos Catalogue for the relevant columns. For each Hipparcos entry there are one line (Table 1) or two lines (all the other tables). In the latter case the first line reproduces the Hipparcos solution as it appears in the Catalogue, while the second line gives the corresponding values from the new processing. Only the second line appears in Table 1.
  
Table 1: Stars with no Hipparcos astrometric solutions. In Tables 1-7, column numbers follow the field designation of the published Hipparcos Catalogue


\begin{tabular}
{\vert r\vert rr\vert r\vert rr\vert rrrrr\vert rr\vert r r r rr...
 ....6 & 1.9 & 1.4 & 1.8 & 21 & 4.04 & TYC & & & & & \\ [3pt]
 \hline
 \end{tabular}

The column headers are self-explanatory and the Hipparcos field is indicated in the last row of the header, so that the detail explanation can be found in the Introduction to the Hipparcos and Tycho Catalogues. The column labelled Sce indicates the source of the new information that has been found and which motivated the reprocessing. It has the following meaning:

The column F1 gives the percentage of rejected observations while F2 is the goodness-of-fit of the astrometric solution to the accepted observations. For a Gaussian distribution of the residuals, F2 follows a standard normal law of zero mean and unit variance so that values of F2 less than 2-3 are typical for a good fit.

Each table, or group of two tables for the largest, refers to a single category of re-examined solutions listed in Sect. 3. No star appears in more than one table.

5.1 Stars with no Hipparcos solutions

Among the 263 entries with no astrometric solution, a certain number already appear in the Catalogue notes with a solution derived after the Catalogue was finalized with absolute and/or relative parameters different from those appearing in the standard layout. These entries have not been re-examined and consequently are not included in the accompagnying table. The 13 genuine new solutions from this subset are given in Table 1. Most were recognized as overlooked double stars, or known double stars with unsatisfactory relative solutions such that the astrometric parameters could not be derived.
  
Table 2: New component solutions for stars flagged C in Field 61 of the main Catalogue


\begin{tabular}
{\vert r\vert rr\vert r\vert rr\vert rrrrr\vert rr\vert r r r rr...
 ... 0.57 & LAM & 346 & 3.689 & 0.010 & 3.60 & 0.06 \\ [3pt] 
 \hline
 \end{tabular}


  
Table 3: Hipparcos solutions with time dependent proper motions (stars flagged G in field 61 of the Hipparcos Catalogue)


\begin{tabular}
{\vert r\vert rr\vert r\vert rr\vert rrrrr\vert rr\vert r r r rr...
 ... & 1.22 & SS2 & 168 & 20.759 & 0.029 & 2.50 & 0.10 \\ [3pt]
 \hline\end{tabular}

Specific comments

$\bullet$ HIP 1338: While the Tycho Catalogue was the basic source for the relative astrometry, a similar separation was found in the Digitized Sky Survey and in recent ground based observations.

  
Table 4: Suspected doubles (HIP $< 60\,000$) flagged S in field 61 of the main Catalogue


\begin{tabular}
{\vert r\vert rr\vert r\vert rr\vert rrrrr\vert rr\vert r r r rr...
 ...-$0.22 & TYC & 266 & 16.824 & 0.054 & 2.95 & 0.10 \\ [3pt] 
 \hline\end{tabular}


  
Table 5: Suspected doubles (HIP $\gt 60\,000$) flagged S in field 61 of the main Catalogue

The Hipparcos solution given here can be considered as reliable. The residuals remain fairly large which can be attributed to the photometric variability detected from the Hipparcos data. The astrometric parameters are found to agree with the Tycho solution, but both the parallax and proper motions are more accurate.

$\bullet$ HIP 18045: The SS2 has been used to search for a star close to the position given in the Hipparcos Input Catalogue. The Hipparcos target was about 20 arcsec from the actual star and consequently the signal recorded was weak and highly variable according to the detector pointing and too far away from the true value to allow a convergence of the software. However the SS2 position was good enough as starting values and the iteration converged to an acceptable solution. A note in the Hipparcos Catalogue indicates that TYC 6451-1246-1 ($\alpha= 57.854\,289,\, 
\delta =
-25.929\,220$) could be the corresponding star. In fact this is very likely a spurious solution (nothing seen in the SS2 there) while TYC 6451- 122-1 is within 20 mas of our solution and with comparable magnitude (allowing for the attenuation effect due to the pointing offset). The new solution provides a reliable parallax and proper motion with standard errors of about 3 mas.

$\bullet$ HIP 27464: This is probably an optical pair (different proper motions in the Tycho solutions). The solution agrees with TYC 4098-5-1.

$\bullet$ HIP 31132: The observation target was 7 arcsec from the star and the proper motion in right ascension and declination were so far from the true values that no convergence was possible. A dedicated setting in the software overcame this problem and yielded a good solution in terms of standard errors but with a questionable goodness-of-fit.

$\bullet$ HIP 34226: A binary with components of similar brightness which accounts for the very large standard errors.

  
Table 6: Stochastic solutions (HIP $< 60\,000$) flagged X in field 61 of the main Catalogue

The two components appear as TYC 1899-1444-1 and 1899-1444-2, but the Hipparcos solution lies somewhere in between. With a separation less than 2 arcsec the two components were hardly discernible with the Tycho detection system.

$\bullet$ HIP 41884: Solution at 30 mas from TYC 4862-794-1, but large pointing offset (15 arcsec) due to a poor position in the Input Catalogue.

$\bullet$ HIP 81402: The initial separation and position angle were taken from the Input Catalogue and confirmed by Tycho. The Hipparcos solution for the relative astrometry is excellent. However the large standard errors in the astrometric parameters are a consequence of the very small magnitude difference between the two components.

$\bullet$ HIP 81694: Orbital double star not resolved as double by Tycho. The target was at 18 arcsec from the actual star position and is responsible for the instability of the signal and the large standard errors.

$\bullet$ HIP 86405: No new input data were used but the case by case processing allows a better control of the outliers and more observation were a priori rejected.

5.2 Stars with new component solutions

Table 2 corresponds to solutions of double stars published in the Hipparcos Catalogue and in the Double and Multiple Systems Annexe C. In all of these cases we have found that the relative astrometry of the double was wrong by one or several grid-steps or, in two cases, that a single star solution fitted the data much more satisfactorily. Thanks to new ground based observations or again from the two Digitized Sky Surveys it was possible to determine a more reliable separation and position angle and to solve the grid-step ambiguity unresolved by Hipparcos.

The improvement in the final astrometric solution shows up clearly in the number of rejected observations, the quality of the goodness-of-fit and/or the standard error. The solutions refer to the primary components of the double systems. In general the astrometric solutions are not very different from that of the Catalogue, primarily because the double stars involved generated a weak deviation from the single star signal and the absolute astrometry was not too sensitive to an error in the separation of the two components. However the multiplicity data given here supersede the Hipparcos values.


  
Table 7: Stochastic solutions (HIP $\gt 60\,000$) flagged X in field 61 of the main Catalogue

Specific comments

$\bullet$ HIP 8035: The relative astrometry of the Hipparcos Catalogue is proved wrong by subsequent ground based observations. Using this constraint the standard error of the separation concluded from the Hipparcos data is greatly improved. The new astrometric solution fits the data more closely.

$\bullet$ HIP 13725: The FAST solution retained for the final publication was subsequently considered as very doubtful. In addition no companion was seen on SS1 or SS2 with separation larger than 5 arcsec. While this do not preclude this star to be a close binary, we think that in this case the magnitude difference should be larger than 4, with a negligible influence on the Hipparcos signal. A single star solution is then preferable and yields an excellent fit.

$\bullet$ HIP 38479: The recent ground based observation shows clearly that the Hipparcos position of the secondary is wrong by exactly one grid-step. The final fit is obtained with no observation rejected, although the goodness-of-fit is not as good.

$\bullet$ HIP 44488: The recent ground based separation (12 arcsec) is definitely incompatible with the SS1 image taken 40 years ago with $\rho = 19$ arcsec. The new Hipparcos solution is however excellent and leaves no room for a different separation. One may hypothesize that the system is in fact an optical binary comprising a distant star and a faint and nearby fast moving star. Additional observations, old or new, should help resolve the problem.

$\bullet$ HIP 69736: The Input Catalogue gives this system a separation of $4\hbox{$.\!\!^{\prime\prime}$}2$and a magnitude difference $\Delta m =4$. From the Digitized Sky Survey a much larger separation should be adopted, which eventually leads to a better astrometric solution. The system is actually triple, and the largest separation corresponds to the two brightest components.

$\bullet$ HIP 71867: There is no double possible with that separation in the image of the Digitized Sky Survey. The single star solution is excellent and left no room for improvement with a double star model.

$\bullet$ HIP 76435: Triple system from the Tycho Catalogue. The separation used here is for the detached components which yields a better fit to the Hipparcos data.

$\bullet$ HIP 79902: The Hipparcos relative astrometry with $\rho = 
16$ arcsec is not seen in the Digitized Sky Survey. On the other hand the solution using the Input Catalogue value of $3\hbox{$.\!\!^{\prime\prime}$}3$ or the new ground based observation leads to a much better fit.

5.3 The acceleration solutions

We have re-examined systems which were solved in the Hipparcos standard solution with the extended single star model, allowing for a time dependent proper motion. Most of the acceleration solutions published in the Hipparcos Catalogue (2622 in total) are of good quality and were not reconsidered in this work. As for the other groups we focussed only on the questionable solutions. It happens that among those classified as doubtful (360 with a goodness-of-fit larger than three), very few appear in our data base of detected or suspected binaries, which means that no new processing could be attempted. Finally quite often the separation we found from the FAST data was too small and could not be confirmed or rejected from the Digitized Sky Survey.

These facts account for the very small yielding in this group, since only four new solutions are proposed, all based on actual detection of a companion in images of the Digitized Sky Survey. The subsequent Hipparcos solutions for the separations given here have fairly good standard errors and the final astrometric fits are all of good quality. Given the separations and the distance it is unlikely that the acceleration proposed in the Hipparcos Catalogue should be real, unless the primary is also a close astrometric binary.

$\bullet$ HIP 23266: The new solution has a much better fit to the data than the published solution, but with larger standard errors due to the error propagation from the double star model. The difference between the old and new proper motion is much larger than the expected statistical error, although the double star signal is very weak with $\Delta m =3.5$. However the acceleration components in the published solution are large (respectively 40 and -9 mas/yr2) and not fully independent of the first order term.

5.4 The suspected doubles and multiples

This group comprises a set of solutions for entries detected as non single from the Hipparcos data and for which no definitive solution for the separation, position angle and magnitude difference was possible without ambiguity at the time of the Catalogue publication. In general, for this specific group of stars, NDAC and FAST concluded their processing with two very different solutions with no external way to decide if at least one was correct. The abscissa were eventually processed as for single stars, leaving a non negligible scatter in the residuals due to the imperfection of the model.

The new solutions are given in Table 4 (HIP $< 60\,000$) and Table 5 (HIP $\gt 60\,000$). There are no Hipparcos data in the multiplicity columns and the second line of each entry gives the relative astrometry derived from the Hipparcos observations and using the approximate $\rho$ and $\theta$ provided by the quoted source. The change in the goodness of fit is the best indication of the improvement in the solutions and at the same time confirms to some extent the relative astrometry and photometry. When the double star has magnitude difference less than 1.5 the change is spectacular.

Due to the error propagation in the double star model, the standard error of the astrometric parameters are usually larger than with the single star model although the goodness-of-fit is much improved by allowing for the duplicity.

$\bullet$ HIP21000: This is the most striking case of this group with a distance twenty times larger and a much smaller proper motion in the new solution. This star appears as a double system in the Input Catalogue with $\rho = 4\hbox{$.\!\!^{\prime\prime}$}4$. It was processed with the single star model in Hipparcos because FAST and NDAC could not agree on the relative astrometry of the system. With the confirmed separation it is clear that the double star model is better, even though the standard errors are larger because of the small magnitude difference. All the 15 observations were used with no rejection.

5.5 The stochastic solutions

This is the largest single group of doubtful solutions in the Hipparcos Catologue and is in fact a mixture of various categories. All the new solutions presented in Table 6 (HIP $< 60\,000$) and Table 7 (HIP $\gt 60\,000$) follow from the discovery of updated multiplicity parameters which proved sufficient to reprocess the double star data. Without exception the final goodness-of-fit statistics are all acceptable (the Hipparcos values for F2 were conventionally set to zero in the Catalogue). The main interest of these new solutions lies in the derivation of accurate parameters for the relative astrometry of the double systems and the more reliable parallaxes that are subsequently obtained.


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