PPM: Positions and Proper Motions

Table name:      PPM
Records:         326518
Spectral Band:   OPT
Kind of Object:  Star
Mode:            Proper Motion,Astrometry 
PreView:            
Coordinates:     J2000

Reference

Bastian J., Roeser S. 1990

Description

The idea of this Introduction to PPM is to deliver a short explanation together with the catalogue itself. It should not be understood as a detailed description of the work performed in the construction of PPM. This will be given in a forthcoming paper (Bastian and Roeser, 1990).

Fields

  
Name        Type   Meaning                                                 
  
ppm           i    PPM star number 
sao           i    SAO star number
hd            i    HD star number   
agk3          c    AGK3 star number
name          c    Durchmusterung star number
sp            c    Spectral type
mag           i    Visual magnitude (99.9 if unknown)
r_a           i    Right ascension for epoch + equinox J2000, FK5
dec           i    Declination for epoch + equinox J2000, FK5   
e_pos         f    Standard position error, in arcsec 
pma           f    Annual proper motion (mu)_(alp) (arcsec/yr)
pmd           f    Annual proper motion (mu)_(del) (arcsec/yr)
e_pma         f    Mean error on (mu)_(alp) (arcsec)
e_pmd         f    Mean error on (mu)_(del) (arcsec)
ep_ra         i    Weighted mean epoch for RA in years since 1900
ep_dec        i    Weighted mean epoch for Dec in years since 1900 
notes         c    Notes with the following meaning:
                   
 
                   P  problem case,  preferably  not  to  be  used  as  
                      astrometric reference star.                       
                   C  a critical remark on this object is given in the  
                      List  of Critical Remarks, it should not be used  
                      as astrometric refe- rence star.                  
                   D  double  star,  preferably  not  to  be  used  as  
                      astrometric reference star.                       
                   H  member of the  High-Precision  Subset  (HPS)  of  PPM. 
                   F  member of FK5, high precision stars, mostly very  
                      bright stars.                                     
                   R  a remark  on this star  is given in  the List of  
                      Remarks on Individual Stars.                      
                     
Computed Fields                               
  
_ra           I    Right ascension for epoch + equinox B1950, FK4 
_de           I    Declination for epoch + equinox B1950, FK4             
_lii          I    Galactic Longitude  
_bii          I    Galactic Latitude

BUILD

In principle, the construction of PPM proceeded in the same way as for other astrometric compilation catalogues in the past: For each star, a mean position and a proper motion are derived from a number of measured positions (found in published source catalogues) by a least-squares adjustment. In detail, however, quite a number of new methods and concepts were used which greatly reduced the effort for this undertaking. PPM was constructed in several steps, each of which will now be explained very briefly.

Compilation of the star list.

The star list for PPM was constructed starting from the magnetic tape version of AGK3, which contains 181581 stars. All FK5 stars (Basic FK5 plus Bright Extension) north of -2.5 degrees declination were added, if not already included. In the course of the work six AGK3 stars had to be deleted (because they are non-existent) and five close companions to AGK3 stars were added. This gave the final list of 181731 stars.

Identification of stars in the source catalogues

The complete list of source catalogues is given in Chapter 3, below, along with an explanation of their abbreviations, with bibliographic references and some statistics.

The stars in each of the source catalogues were identified with the objects of the star list. This was done in a fully automatic process. Problem cases recognized in this process were investigated manually to detect typing errors in the source catalogues, to correctly identify double star components, to avoid the effect of grossly incorrect positions in the star list etc.

Prior to the identification of Astrographic Catalogue data (given as x,y plate coordinates originally) a rough plate reduction was performed, using published approximate plate constants.

Construction of a preliminary system of positions and proper motions.

A preliminary system of positions and proper motions is necessary to eliminate systematic deviations between the individual source catalogues. For this purpose we used AGK3, but with its positions and proper motions corrected to the system of NIRS (Corbin, 1978), the latter being regarded as a representation of the FK4 system. This correction was done using the systematic differences between AGK3 and NIRS given by Schwan (1985).

Reduction of source catalogues to the preliminary system

Zonal systematic deviations as well as magnitude and colour-dependent systematic deviations between each of the source catalogues and the preliminary system were determined and eliminated. For Astrographic Catalogue zones we performed second-order plate reductions, using the preliminary system as reference. The resulting star positions were further corrected for magnitude- and colour-dependent deviations and for effects of higher-order distortion ("coma").

Determination of weights for the source positions

In a least-squares adjustment weights have to be assigned to the individual measurements, according to their mean errors. Magnitude-dependent mean errors of the positions were determined for each source catalogue. For Astrographic Catalogue zones this was achieved by investigating the differences between positions of the same star measured on different (overlapping) plates. For Yale and AGK1 zone catalogues the differences between the source positions and a preliminary version of PPM (Roeser and Bastian, 1988) were investigated. For the Carlsberg Meridian Circle catalogues (CMC 1985-1988) the differences to FK4 were investigated by R. Bien (1988). For AGK3R the mean errors given by Eichhorn (1974) were used.

Least-squares adjustment

A standard weighted least-squares adjustment of the mean positions and proper motions was performed for each star - separately for right ascensions and declinations. Automatic tests for unduly large scatter among the measurements (based on the chi-square sum) and automatic elimination of obvious outliers (based on appropriately normalized individual residues) were implemented. All stars having bad chi-square sums beyond a certain significance limit, but still not showing obvious outliers, were marked as "problem cases" (see flag 'P' in column 19.1 of the printed catalogue). This occurred in about 950 cases.

Manual treatment of difficult cases

The automatic outlier elimination deleted about 5500 measured coordinates (out of more than 2 million). Tight restrictions, however, were imposed on this automatic process in order to avoid spuriously "good" results. This created about 800 "difficult cases" that were treated manually. A majority of these turned out to be coarse errors in AGK3, the rest was caused by errors in other source catalogues, mixed-up double star components etc. For about 180 objects no satisfactory solution could be found. These were added to the "problem cases" of step 6, giving a total of 1120 PPM stars with flag 'P'.

Another group of stars was subject to manual checks: Those AGK3 stars not found in any source catalogue except AGK2 and AGK3 (about 60 cases). We checked these for coarse errors of AGK3 by locating the stars on Palomar Sky Survey prints - with a precision of a few arcsec. In most cases they were found at the predicted positions. Nine cases were indeed caused by errors in both AGK2 and AGK3. We kept the data for these nine objects, but marked them as severe problem cases (see flag 'C' in column 19.1 of the printed catalogue).

Transformation from the preliminary to the final system

The positions and proper motions derived so far were transformed from the preliminary system (described above) to the new IAU (1976) coordinate system, as defined by FK5. This step had two major parts: First, a transformation from the preliminary system to a presumably better representation of the FK4 system was performed. Then a standard transformation from the FK4 system (B1950) to the FK5 system (J2000).

The first part became necessary because of the discovery of two sorts of systematic deviations between the preliminary system and the FK4 system:

Uncorrected atmospheric dispersion in the original AGK2 and AGK3 positions had caused a strong colour-dependent and declination-dependent systematic error. This was corrected. No other colour or magnitude equations were applied to the preliminary system. In other words: The colour and magnitude system of PPM is identical to that of AGK3 (except for the dispersion effect, of course).
In the course of the work we found indications for zonal errors of our preliminary proper motion system. Therefore we did not keep this for the final system of PPM. Instead we constructed a a new system of positions and proper motions from the systems of AGK3R (unchanged) and the CMC catalogues (after transformation to the FK4 system).

The transition from FK4 system to FK5 system followed exactly the same procedure as was used in the construction of FK5 (Fricke et al., 1988).

More details on the construction and properties of the system of PPM will be given by Roeser (1989).

Introduction of FK5 data for FK5 stars

For the stars contained in FK5 Part I (the Basic Fundamental Stars) and in FK5 Part II (the Bright Extension Stars), PPM gives the original FK5 data. These were introduced by simply copying them from the machine-readable version of FK5.

Provision of cross-references and auxiliary data

In addition to the astrometric data PPM gives cross-references to other star catalogues, magnitudes, spectral types and a number of flags for each star.

Much manual labour went into the provision of cross-references. They were determined by different methods, ranging from direct cross-identification (based on positions only) to simply copying historic work done by others (in the cases of catalogues having low positional accuracy such as DM and HD). Cross-references are given explicitly for four catalogues: Bonner Durchmusterung (abbreviated DM), SAO Catalogue, Henry Draper Catalogue (HD) and AGK3. Three more cross-references are given implicitly by flags (see columns 19 of the printed catalogue): Flag 'F' in column 19.4 denotes the stars contained in FK5 (Parts I and II). Flag 'H' in column 19.3 indicates stars that are contained in AGK3R and/or one of the CMC catalogues. The double star flag 'D' (column 19.2) was created by cross-referencing PPM with the Catalogue of Components of Double and Multiple Stars (Dommanget, 1988).

The magnitudes and spectral types were copied either from AGK3 or from FK5, see Chapter 8 for details.

Various sorts of auxiliary information are given in the List of Critical Comments and in the List of Remarks (Chapters 5 and 6),

PROPERTIES

Random Errors

The table below shows a summary of the error budget of PPM. Each line of the table gives the following data for the particular set of stars indicated: The number of stars in the set, the average number of source positions per star, the average of the mean epochs (for right ascension and declination), the average of the mean errors of proper motion (for right ascension and declination) and the average of the mean errors of position at epoch 1990 (again for right ascension and declination). Units are seconds of arc and seconds of arc per century, respectively. At the bottom of the table the corresponding values for AGK3 and SAOC are given for comparison (a more complete comparison of PPM with SAOC, AGK3 and the - future - HIPPARCOS catalogue is given by Roeser and Bastian (1989), Fig. 3).

                            Error budget of PPM                             
   
  set of stars       No.   No. mean    epochs  mean  err.  mean    err.     
                   stars  obs.                 prop. mot.  pos.    1990     
   
  PPM, all stars  181731   6.2 1931.5  1930.7  0.43  0.42  0.27    0.27     
  PPM, HPS stars   31841   7.8 1950.3  1948.0  0.24  0.25  0.12    0.12     
  PPM, FK5 stars    1365   --- 1954.2  1945.2  0.08  0.10  0.04    0.05     
   
  AGK3            181581   2.0 1945    1945    0.95  0.95  0.45    0.45     
  SAOC, north     133000   2.0 1930    1930    1.5   1.5   0.9     0.9

Three subsets of PPM are shown in the table: The first line refers to the entire catalogue, the last line to the 1365 FK5 stars and the second line to the High-Precision Subset (HPS) of PPM. This subset will be briefly discussed now.

PPM essentially was constructed by combining AGK3 with early-epoch catalogues. So the mean epochs of PPM are quite early and the present-day accuracy is dominated by the accuracy of the proper motions. Therefore it would be highly desirable to have a repetition of AGK3 at present epoch. This not being available, we decided to introduce the Carlsberg Meridian Circle (CMC) catalogues, nos. 1 to 4. (CMC 1985 -1988). In addition we introduced AGK3R because of its higher accuracy compared to AGK3. The High-Precision Subset of PPM is defined as the set of PPM stars for which either CMC or AGK3R observations are available. Its superior precision in present-day positions is mainly due to the fine work done at the Carlsberg Meridian Circle.

Note that (on average) more than 6 measured positions are available per star. This redundancy allowed us to discover (and avoid) a large number of coarse errors in the source catalogues. It ensures that PPM contains very few coarse errors. For 1064 PPM stars the redundancy was not sufficient to resolve discrepancies between the source positions. They carry the 'P' flag mentioned above.

Source Catalogues

More than 1.1 million source positions (i.e. right ascensions and declinations) were used for the construction of PPM. The following table lists the various groups of source catalogues used and the total number of positions derived from each group. More information on the catalogues as well as bibliographic references are given in the book by Eichhorn (1974), except for the CMC catalogues.

		     Source Catalogues                              
	 
	 Astrographic Catalogue zones      466 278                  
	 AGK3                              181 581                  
	 AGK2                              181 581                  
	 AGK1                              141 146                  
	 Yale zone catalogues               80 574                  
	 Gyllenberg, 1926                   11 498                  
	 Prager, 1923                        8 602                  
	 
	 CMC 1, 2, 3, 4                     25 656                  
	 AGK3R                              20 581                  
	 
	 Total                           1 117 497

Systematic Errors

We did our very best to ensure that PPM is on the system of FK5. Such a goal, however, can be reached to a certain accuracy only. We estimate that the residual systematic deviations between PPM and the FK5 system have a typical size of 0.05 arcsec for the positions at mean epoch and of 0.2 arcsec per century for the proper motions.

These numbers do not hold, however, for a few special groups of objects: The very blue stars (spectral types B2 and earlier), the very faint stars (fainter than about 12 in photographic magnitude) and the very bright stars (brighter than about 7, but not in HPS or FK5). Because these groups are very small by number it was neither possible to check our preliminary system to the desired accuracy, nor could we correct the individual source catalogues to this system with the desired accuracy. So we just do not know anything about possible systematic errors for these small groups.

Another possible systematic error stands out clearly from our data, but still cannot be removed. It is a magnitude equation in right ascension, affecting stars fainter than about 10.5 mag (photographic). It shows up as a systematic difference between PPM and the CMC catalogues (remember that, by definition, the magnitude dependence of the proper motion system of PPM is that of AGK3. The CMC catalogues were transformed to that system before inclusion into PPM). It has a mean value of about 0.08 arcsec for stars between 10.6 and 11.0 mag, and 0.15 arcsec for stars fainter than 11.0 mag. The cause of this systematic difference cannot be identified with existing astrometric data. Therefore it cannot be removed in a reasonable way. More details will be given by Roeser (1989).

Some Statistics

PPM contains 131502 SAOC stars, which corresponds to almost 99 percent of all SAOC stars in the celestial region covered by PPM. It contains 85357 HD stars, corresponding to about 70 percent of all HD stars in the region. There are 16031 double star flags ('D'), 1120 problem cases ('P' flags), 22 critical comments ('C' flags) and 228 less important remarks ('R' flags). The 'R' flags refer to peculiar DM designations and variable star designations mostly.

REFERENCES

Bastian, U., Roeser, S. (1990): in preparation
Bien, R. (1988): private communication
Bystrov, N.F., Polozhentsev, D.D., Potter, Kh.I., Zalles, R.F., Zelaya, J.A. and Yagudin, L.I. (1989): On the FOKAT catalog. Astron. Zh. 66, 425.
CMC (1985-1988): Carlsberg Meridian Catalogue La Palma, Numbers 1 to 4. Copenhagen University Observatory, Royal Greenwich Observatory and Real Instituto y Observatorio de la Armada, San Fernando.
Corbin, T. (1978): The proper motions of the AGK3R and SRS stars. IAU Colloquium No. 48, Eds. F.V Prochazka and R.H. Tucker, 515.
Dommanget, J. (1988): in HIPPARCOS, Scientific Aspects of the Input Catalogue Production II, Proceedings of a Colloquium held at Sitges, Spain, 1988, eds. J. Torra and C. Turon, page 191.
Eichhorn, H. (1974): Astronomy of Star Positions, Frederick Ungar Publ. Co., New York.
Fricke, W., Schwan, H., Lederle, T. (1988): Fifth Fundamental Catalogue (FK5). Part I. The Basic Fundamental Stars. Veroeff. Astron. Rechen-Institut Heidelberg Nr.32. IAU (1976): IAU Transaction XVI B, Reidel Publ., Dordrecht 1977.
Lieske, J. (1979): Precession matrix based on IAU(1976) system of astronomical constants, Astron. Astrophys. 73, 282.
Lopez, C. (1987): The Proper Motions of AGK3 Stars. IAU Colloquium No. 100, Fundamentals of Astrometry, Beograd, Sep. 8-11, 1987, in press.
Murray, C.A. (1983): Vectorial Astrometry, Adam Hilger Ltd., Bristol, UK.
Roeser, S. (1989): The System of PPM. IAU Symposium No. 141, Inertial Coordinate System on the Sky, Leningrad, Oct. 17-21, 1989
Roeser, S. and Bastian, U. (1988): A New Star Catalogue of SAO Type, Astronomy and Astrophysics, Suppl. Ser. 74, 449
Roeser, S. and Bastian, U. (1989): Compilation of the PPM Catalogue, in: Star Catalogues, A Centennial Tribute to A.V. Vyssotsky, eds. A.G.D. Philips, A.R. Upgren, L. Davis press, Schenectady, N.Y., 1989
Roman, N.G. and Warren, W.H. (1984): Documentation for the Machine-Readable Version of the SAO Star Catalogue, Version 1984, National Space Science Data Center, Greenbelt, Maryland
Schwan, H. (1985): The systems of the positions and proper motions in star catalogues AGK3, AGK3RN, and N30. Astron. Astrophys. 149,50.
Smith, C.A., Corbin, T.E. Hughes, J.E., Jackson E.S., Khrutskaya, E.V, Polozhentsev, A.D., Poloshentsev, D.D, Yagudin, L.I., Zverev, M.S. (1989): The SRS catalog of 20488 star positions.

Acknowledgements

Generations of careful and patient observers and plate measurers have laid the base for the present work. Compared to their labour all other efforts that went into the preparation of PPM - inclu- ding our own - are small.

We gratefully acknowledge the help of Hamburger Sternwarte (C. de Vegt and H. M. Steinbach) and of Observatoire de Strasbourg (D. Egret and A. Fresneau) in providing the raw Astrographic Catalogue on punched cards. Several tons of cards were moved with the help of many hands in Strasbourg. Also we thank T. Corbin of US Naval Observatory for providing a magnetic tape containing part of the Strasbourg punched data already.

Heidelberger Druckmaschinen AG is gratefully acknowledged for technical help in the reading of the punched cards.

We thank the CMC group at La Palma for giving the CMC 4 catalogue to us prior to publication.

Last but not least we have to thank many people at our institute, especially E. Roehl and E. Mueller for careful checks and completion of the Astrographic Catalogue data, M. Erbach, M. Fleischer and T. Lederle for much valuable information on source catalogues, H. Schwan for many fruitful discussions and for his data on systematic differences between several catalogues, R. Bien for the determination of weights for the CMC catalogues and H. Bernstein for advice on mathematical statistics. Finally we want to thank R. Wielen, director of ARI, for giving us the opportunity to do this work.

USAGE

PPM gives positions for a standard epoch (J2000) and a standard coordinate system (mean equator and equinox for J2000 in the new IAU (1976) system of astronomical constants).

To apply PPM as astrometric reference at a different observational epoch, but still in the J2000 coordinate system, proper motions must be taken into account. For most purposes a simple linear formula (position difference equals epoch difference times proper motion) is sufficient. But note that this procedure will give inaccurate results close to the pole. Better formulae are given e.g. by Murray (1983) and in the introduction to FK5.

To apply PPM as astrometric reference for a different equator and equinox, but still in the IAU (1976) system of astronomical constants, precession has to be taken into account. The relevant formulae and numerical values are given e.g. by Lieske (1979) and in the introduction to FK5.

Note that simply precessing from J2000 to B1950 will still not give results in the old (FK4) astronomical coordinate system. This differs from the new IAU (1976) system by a correction to the precessional constant, a correction to the position of the vernal equinox, by the treatment of elliptical aberration and by complicated zonal corrections. All this adds up to several tenths of an arcsec in position and a few tenths of an arcsec per century in proper motion.

Application of proper motion and precession still gives mean positions. In order to derive apparent positions for PPM objects one has to apply nutation, aberration, stellar parallax, and relativistic light-bending, in addition (see e.g. Murray, 1983). For most practical uses of PPM these effects can be ignored. But PPM contains a small number of stars with fairly large paral- laxes. They are not indicated in the catalogue.

For each star PPM gives mean errors for right ascension and declination at their respective mean epochs T. Standard error propagation calculus can be used to calculate the mean error of a PPM position for an epoch t different from the mean epoch: Denoting the mean error of one coordinate at mean epoch by E(T), the mean error of proper motion by E(PM), the mean error of position at epoch t is given by

E(t)^2 = E(T)^2 + E(PM)^2 * (T-t)^2

Using more PPM stars in an application will usually give better results because of the partial cancellation of the purely accidental errors of the PPM data. However, this improvement will never get beyond the systematic errors of PPM, as discussed in the previous chapter.

Applications demanding utmost accuracy rather than high star density should use HPS stars only.