COSMOS FAQs & Facts - Hipparcos

A. Hipparcos is an acronym for HIgh Precision PARallax COllecting Satellite. Appropriately the proununciation is also very close to Hipparchus, the name of a Greek astronomer who lived from 190 to 120 BC. By measuring the position of the Moon against the stars, Hipparchus was able to determine the Moon's parallax and thus its distance from the Earth. He also made the first accurate star map which lead to the discovery, when compared with other data from his predecessors, that the Earth's poles rotate in the sky, a phenomenon referred to as the precession of the equinoxes.

The concept of using the data recorded by the star mappers for astrometric and photometric observations was conceived by Erik Høg, a Danish astronomer involved with the Hipparcos mission. It was fitting that the catalogue which resulted from the star mappers should then be named after Tycho Brahe, a 16th century Danish astronomer, who produced the first 'modern' star catalogue (1602).

Q2. Please explain the catalogues in the context of some other recent catalogues that I've heard about which make use of the Hipparcos and Tycho data, in particular the ACT and the TRC. [Aug 99]

Details provided by Ronnie Hoogerwerf, Sterrewacht Leiden (August 1999)
At the end of the 19th century photographic plates, for the first time, could be produced and used in a systematic and reliable way. This led the astronomical community to propose the 'Carte du Ciel' project: an enormous international effort to 'map the heavens' (see, e.g., Eichhorn 1974; Debarbat et al. 1988; Urban & Corbin 1998). The main goal was to make an astrometic catalogue consisting of all stars brighter than about photographic magnitude m=11 mag with positional accuracies better than 0.5 arcsec (this part of the project was called the Astrographic Catalogue). The second goal was to produce charts with the relative positions of all stars down to 14 magnitude (the Carte du Ciel). This second part of the project was never completed due to the enormous amount of time and costs needed to reproduce and distribute these plates. The first project was completed. The entire sky was imaged on photographic plates. To reduce problems with plate defects, each sky area was observed twice by overlapping plates. This major undertaking was distributed over 20 observatories, each of which observed part of the sky (subdivided according to Declination). The observatories used the same type of telescope to ensure that the plate scale would be identical for all plates. In total, 22,660 plates were exposed. The plates were developed, measured, and the stellar positions recorded (in millimeters), along with the known plate corrections and the equations needed to convert millimeters into Right Ascension and Declination. Typographical errors in these publications were published separately. These publications together with their corrections are known as the Astrographic Catalogue (AC).

Tycho: The Tycho instrument functioned as the star mapper for the Hipparcos satellite: it recorded all stars passing the field of view. These measurements were reduced to obtain positions, proper motions, parallaxes, and broad band photometry for 1,058,332 stars. The errors in the astrometric parameters (about 20 mas/yr) are typically 20 times the errors in the Hipparcos Catalogue. However, the TYC positions are still better than in any other catalogue of comparable size. A re-analysis of the raw data is currently being carried out and will result in a new Tycho Catalogue (TYC2) (Hoeg 1997) containing about 2.5 million stars; it will become publicly available in the first half of the year 2000.

AC2000 & ACT: The AC2000 (Astrographic Catalogue 2000) (Urban et al. 1998b) is the result of a new reduction of the AC conducted at the USNO. Magnitude and positions are provided for 4,621,836 stars in the Hipparcos reference system (ICRS, see ESA 1997, Vol. 1, Section 1.2), with a median epoch of 1904. The AC2000 has been combined with TYC (median epoch J1991.25) to obtain proper motions based on the position difference between both catalogues; the average epoch difference is about 90 years. These proper motions are recorded in the ACT (Urban et al. 1998a). The TYC stars were matched to the AC2000 stars by propagating the Tycho positions to the AC2000 epoch, taking into account the TYC proper motions. An area of 15 arcsec radius was then searched around the propagated TYC position for AC2000 stars (see Urban et al. 1998 for details). In total 97.5 per cent TYC stars were unambiguously matched to an AC2000 entry. Some TYC stars were considered problematic and discarded if they were indicated to be part of close multiple systems, or if the positions had extremely low astrometric quality. After the cross-identification, proper motions were computed using the differences in position and epoch. The proper motions were brought from the mean epoch of the AC2000 and TYC to the epoch J2000 (Fricke 1963). In total, the ACT contains positions and proper motions for 988,758 stars (average error in the proper motion of 2.4 mas/yr and better than 3.5 mas/yr for 80 per cent of the stars, positional accuracies adopted from the Tycho Catalogue).

TRC: The TRC is the European equivalent of the ACT. Its construction also required a re-reduction of the AC, putting the AC onto the Hipparcos reference system, and combining the resulting position with those in the TYC. The TYC stars were propagated to the AC epoch without using proper-motion information; the relatively large proper-motion errors might degrade the stellar position instead of improving it. The propagated TYC positions were then matched to stars in the AC using a maximum search window of 180 mas/yr × dT, where dT is the epoch difference between the TYC and the AC. Consequently, high proper motion stars are not included in the TRC. Doubtful identifications were, if possible, resolved using magnitude information in the two catalogues. Stars with uncertain photometry or astrometry have not been included in the TRC. The TRC proper motions were constructed using the TYC and AC positions. On top of the random error an additional 1.6 mas/yr was added (in quadrature) to account for residual systematic effects. The TRC contains 990,182 stars (average error in proper motion of 2.4 mas/yr, positional accuracy of 25-45 mas). Details of the construction of the TRC are given in Kuzmin et al. (1999).

References:
Debarbat S., Eddy J.A., Eichhorn H.K., Upgren A.R., 1988, Mapping the Sky: Past Heritage and Future Directions, IAU Symp. 133
Eichhorn H.K., 1974, Astronomy of Star Positions. Frederick Ungar, New York
Hoeg E., 1997, ESA SP-402, 25
Kuzmin A., Hoeg E., Bastian U., Fabricius C., Kuimov K., Lindegren L., Makarov V.V., Roeser S., 1999, A&AS, 136, 491
Urban S.E., Corbin T.E., 1998, Sky & Telescope, Vol. 95, No. 6, p. 40
Urban S.E., Corbin T.E., Wycoff G.L., 1998a, AJ, 115, 2161
Urban S.E., Corbin T.E., Wycoff G.L., Martin J.C., Jackson E.S., Zacharias M.I., Hall D.M., 1998b, AJ, 115, 1212

Q3. Why doesn't the Hipparcos website allow interrogation according to various important cross-identifiers: BD, or CD for example? [Dec 97]

A. Cross identification of stars is frequently complicated by the angular precision or resolution of earlier catalogues, or errors propagated in these identifiers through the literature. Some identifiers are included within the fields of the machine-readable version of the Hipparcos and Tycho Catalogues, but they should be considered more "for information". If you know a particular star identifier, use the CDS SIMBAD facility to find the corresponding HIP number - these identifiers are maintained and updated. Or use the position of the star to search the catalogue.

Q4. I've found a couple of cases where the cross-reference given for a HIP star is different to that given for the corresponding TYC star. What is going on? [Dec 97]

A. This is a good example of the previous problem. The HIP and TYC catalogues were cross-referenced to other catalogues independently. Sometimes, there is no obvious answer as to which is "correct". See SIMBAD!

A. This could be done, but things get a little messy due to the different angular resolutions of the two catalogues, and the fact that a HIP number may embrace a double or triple system, for which the components are separately listed in the Tycho Catalogue. We suggest you proceed as follows: use the HIP number to find the position of the object. Search at this position, with a radius suitable to include multiple components (say 30 arcsec). All relevant TYC objects will be returned.

[In the Celestia 2000 CD-ROM, the HIP window provides the TYC number of any TYC entry in common with the HIC entry, and vice versa.]

A. It may be worth you taking a look at Volume 3 of the published catalogue, ESA SP-1200, describing the catalogue construction, and especially Chapter 20 "Verification of Parallaxes" and Chapter 22 "Analysis of Double Star Results". Basically, we do not expect the parallaxes to be significantly perturbed by (detected or undetected) binarity, unless the orbital period is close to one year, in which case the photocentric motion may confuse the shift in the system's apparent position due to parallax. ASCII Discs 5 and 6 (in Volume 17) provide the intermediate astrometric data necessary to carry out a rigorous re-analysis of the astrometric data, taking into account subsequent ground-based information on orbital parameters of specific objects. To our knowledge this has not been carried out for these objects. So some suspicion is always appropriate, but we are not aware of specific errors confirmed by a thorough analysis.

Q7. In a recent paper accepted in MNRAS "The Lutz-Kelker bias in trigonometric parallaxes" by R.D. Oudmaijer et al, they state in the Abstract "This statistical effect, the so-called Lutz-Kelker bias, causes measured parallaxes to be too large." And later "We find that there is indeed a large bias affecting parallaxes, with an average and scatter comparable to predictions." Does this mean that all the Hipparcos parallaxes are biased? [Jan 98]

A. Yes and no. Not in the simple sense that there is some "mistake" in the catalogue that with hindsight could or should have been fixed. Lutz-Kelker bias, and the bias in quantities *derived* from the measured parallaxes, are well-known effects which are not disputed. These effects should be considered in any rigorous discussion of derived quantities, see, for example, two papers in the Hipparcos-Venice '97 Proceedings, ESA-SP 402: Luri & Arenou "Utilisation of Hipparcos data for distance determinations: error, bias and estimation", page 449; and Brown et al "Some considerations in making full use of the Hipparcos Catalogue", page 63. But there are several issues involved, as detailed below by Hans Schrijver (98-02-02):

The answer to the question whether trigonometric parallaxes are biased is in some sense a matter of perspective. The astrometrist asks the question: given a real parallax, what is the expectation of the measured parallaxes? The astrophysicist, on the other hand, poses the question: given a measured parallax, what is the expectation of the real parallax? Perhaps not surprisingly, this will lead to some different answers.

I think one can distinguish three areas where bias can play a role:

(1) The observational area. Given a star with real parallax pi_0, what will the distribution of measured parallaxes be for a given sigma_pi? Most people agree that the Hipparcos measurements show a nice, almost Gaussian distribution around pi_0. This in strong contrast with ground based measurements where the problem of determination of the zero point (correction from relative to absolute parallaxes) easily leads to a bias.

(2) Bias related to transformation to other physical quantities (distances, absolute luminosities). This is caused by the transformation of the distribution of observed parallaxes to the distribution of the desired quantity by applying the Jacobian of the transformation. This is illustrated in Figures 1 and 2 of Luri & Arenou ("Utilisation of Hipparcos data for distance determinations: error, bias and estimation", Hipparcos-Venice '97 Proceedings, ESA-SP 402, 449). It is my strong impression that many people think that this effect is the Lutz-Kelker one (for example, van Leeuwen, Space Science Reviews, 81, 361); it is not, however: see (3).

(3) Biases related to the question: given a measured parallax pi, what is the distribution of real parallaxes pi_0? The answer to this question (i.e., the expectation of pi_0) depends critically on the distribution (in distance, luminosity, etc.) of the sample of stars that may contribute to the measurement. In the Lutz & Kelker paper, building on the ideas of `Statistical Astronomy' (Trumpler & Weaver 1953), the authors show that for a uniform distribution of stars, without any constraint on luminosities, the measured trigonometric parallaxes are strongly biased towards the observer (i.e., too large), depending on the relative measurement error. Although their results are certainly much too pessimistic for the general case, we must assume that parallaxes will, in principle, always have a bias in this sense, the magnitude of which can be very different from case to case.

I think the general message to the users must be (and I think we all agree about that): use the parallaxes, especially those with lower precision with great care. The method proposed by Luri & Arenou (in their Section 5) represents a valid approach to this problem (taking into account all available information about the star sample). Although from their introduction one gets the impression that only the bias of category (2) is treated, in the end their method seems quite general.

It is mainly the bias described under (3) that is addressed in the paper by Oudmaijer et al. It is the effect that is to be taken into account by the astrophysicists making use of the data. And in this area, the trigonometric parallax is as much a `derived physical quantity' as all the others.

A. Feast & Catchpole specifically formulated the problem to avoid biases in the luminosities. We can only leave it to the refereed literature to make the position clearer in due course.

A. The Hipparcos observations and data analysis was carried out in such a way that any systematic parallax shifts should be common to all stars. There is good evidence that a *global* shift does not seem to be present [see for example Volume 3 of the printed catalogue, Chapter 20 on verification of the parallaxes]. The Hipparcos Catalogue documentation does not address explicitly possible systematic offsets occurring at small angular scales, although the general effects of correlations on such scales is discussed. What little we know presently is mostly implicit in the discussion of the NDAC-FAST consortium differences given in Chapter 16 and 17 of Volume 3. Hard facts are seemingly: (1) that there is no significant *global* offset; and (2) that the quoted standard errors are not significantly underestimated, again on a global scale. This is what is proven in Chapter 20 and in many subsequent applications of the data. But it still leaves room for spatial correlations - which in a single experimental realisation are seen as systematic errors on small scales. We don't know what the spatial correlations are, but values of up to 0.2-0.3 over a few degrees in bad (ecliptical) regions may not be unrealistic, given the correlations of the FAST/NDAC differences. This would correspond to an expected (rms) level of systematics that is of the order of (1.5 mas)*sqrt(0.25) = 0.75 mas, if the typical error of the individual parallax is 1.5 mas. In Figure 16.34 (Volume 3) it is shown that NDAC/FAST differences could easily be 2 mas when averaged in 2*2 deg fields in the ecliptic region. Even if the merging reduces the systematics by a factor 2 there could still be remaining effect at the 1 mas level in 2*2 deg areas. So the behaviour reported is probably consistent with our knowledge of the catalogue, although whether this is the correct, or complete, explanation here will probably require further investigations. It would be interesting, for example, to look at the separate NDAC and FAST parallaxes for the Pleiades stars. At the same time, the Pleiades is not the only cluster showing results discrepant with pre-Hipparcos predicted parallaxes.

Q10. So what evidence is there that the astrometric data for individual objects are reliable?

A. Astrometry (positions, proper motions, or parallaxes) having a demonstrated accuracy comparable to that of Hipparcos at the individual object level are strictly limited. This of course makes it very difficult to quantify the Hipparcos errors from an external perspective - a problem common to all experiments. However, VLBI results provide one such source, and these have supplied confidence in the overall positional quality (see ESA SP-1200, Volume 3, Chapter 18, especially Table 18.1), as well as in the individual parallaxes (Chapter 20, Table 20.1 and Figure 20.2). Independent distance estimates have also been obtained for three Hyades orbital binaries, with parallax values (in mas) as follows:

HIP	Hipparcos	Torres et al	Reference
20087	18.25+/-0.82	17.9+/-0.6	Ap.J., 1997, 474(256)
20661	21.47+/-0.97	21.44+/-0.67	Ap.J., 1997, 479(268)
20894	21.89+/-0.83	21.22+/-0.76	Ap.J., 1997, 485(167)

To our knowledge other individually-reliable distance determinations are less easy to compare directly with the Hipparcos results. However, we will be pleased to update this according to any new information supplied.

Q11. How about the existence of comparable quality astrometric data in conflict with the Hipparcos results?

A. One of the most significant tests is presumably the Hubble Space Telescope FGS results on the following Hyades cluster objects, reported by a large collaboration (van Altena et al, Ap.J., 1997, 486, L123). Here are the FGS-based parallaxes (in mas) and proper motions (in mas/yr), compared with the Hipparcos determinations:

HIP	pi(FGS)	pi(HIP)	mu_a(FGS)	mu_a(HIP)	mu_d(FGS)	mu_d(HIP)
20563	15.4/0.9	19.35/1.79	105.0/0.9	112.72/2.48	-14.1/0.8	-33.20/1.99
20850	16.6/1.6	21.29/1.91	78.9/1.3	106.16/1.57	-16.7/1.5	-17.59/1.18
21123	16.5/0.9	23.41/1.65	106.6/1.1	105.81/1.60	-16.2/3.0	-30.97/1.25
21138	15.7/1.2	15.11/4.75	102.5/1.4	100.76/4.54	-14.0/1.4	-23.42/3.21

There are clearly major differences, evident at the level of several times the combined standard errors. Either there is something wrong with the Hipparcos values, or with the Hubble Space Telescope values (or both). Both have been subjected to significant calibration effort, and both claim comparable accuracies with the FGS values being typically more precise (formal standard error) than the Hipparcos ones. Such results do indicate the huge challenge of performing astrometry at the mas level. A detailed evaluation of these specific conflicting results would certainly be valuable.

Q12. How do I get more details of objects shown in the Millennium Star Atlas? For example, how do I get the period and other details of the variable objects shown in the Atlas?

A. There are two easy ways. Either use the web catalogue search facility to get details of objects in a given area close to that of the object you're interested in. It should be straightforward to track the object down from that.

Q13. Why does the Millennium Star Atlas show distances in light-years, when the rest of the Hipparcos Catalogue works in milliarcsec and its related reciprocal, the parsec?

A. Most of the Hipparcos and Tycho Catalogue material is primarily of use to professional astronomers, who tend to prefer use of the parsec as the unit of distance measurement. The Millennium Star Atlas should serve the professionals, but we hope it will have great value for the amateur astronomer. Sky & Telescope know that from their correspondence, the light-year is more welcomed. We felt the use of the light-year was therefore preferable in this context. If an accurate distance (and error) estimate is needed, the user will have to extract these data from the main catalogue in any case.

A. The two stars are HIP 42762, V="11.83," parallax="64.56+/3.92;" and HIP 42748, V="9.62," parallax="74.95+/13.82." The brighter star has an abnormally large error on its parallax. Hipparcos flags it as suspected non-single. It shows the importance of looking at all of the information, including the uncertainties - of course, it was not practical to show these in the Atlas.

Q15. What can amateur astronomers contribute to follow-up observations now that the Hipparcos and Tycho Catalogues are available?

A. A huge amount! A large number of new variables have been discovered, and many of these reveal interesting features in their light curves that require follow-up observations. For example, there are many new eclipsing binaries for which only a single minimum has been observed by Hipparcos. These need additional ground-based observations to pin down their period. We refer interested observers to the web pages of the AAVSO for more details.

A. The Hipparcos and Tycho Catalogues are purely observational - radial velocities were not acquired by the satellite, and attempts to undertake a coordinated radial measurement programme from the ground, such that they could be included in the final catalogue, were unsuccessful. In any case the published catalogues were not intended as an opportunity to create a wider stellar data base. For this, users should resort to the extensive facilities provided by the CDS; in particular updated radial velocities can be found through SIMBAD.

A. We had (at least) three options:

(a) to introduce a new identifier corresponding to this new catalogue, following general catalogue construction traditions. This had numerous benefits throughout the mission preparation and data analysis phase, but also led to a unique number for each object, a simple classifier which could be referred to uniquely, and a convenient form of connection between the main catalogue, its various annexes, and throughout the documentation;

(b) drop all identifiers, and use only the object's position at some specified epoch and within some specified reference system. This would have been logical (and is an approach used in other surveys). It was considered, but it would probably have been widely criticised for a number of reasons, well-known to those who have reflected on the problem. In any case, this solution would have been equally guilty of renaming well-known stars with yet another designation;

(c) we are left with the approach presumably implicitly recommended in the above remarks by Griffin et al: to use identifiers from the HD Catalogue, for example. However, such identifiers are not available for a large number of objects in the catalogue (they have the additional inconvenience for a printed catalogue of being only tolerably correlated with the object's right ascension). So, presumably, they would need to be supplemented by identifiers from, say, DM. Since these are also not available for all objects (and are subject to numerous errors, including those propagated through the literature) they would presumably, in turn, need to be supplemented by SAO numbers, or by Gliese numbers, or by LHS/LTT numbers; or by whatever identifier you believe constitutes the object's "well-known" designation. In practice, the Input Catalogue allocated 8 fields for these major cross-identifiers. The Hipparcos project felt it inappropriate to allocate the same (or other) fields to reproduce these cross-identifiers, which are unrelated to the Hipparcos mission, and which (again) cannot easily be searched in a printed catalogue. The problem might have been circumvented if we'd not chosen to print the Hipparcos Catalogue (the identifiers could have been built - and frozen - into the machine-readable version) but we believe this would have made the catalogue less easy to access and use.

There is another complicating factor, which is that a Hipparcos entry is not necessarily a (single) star: thus the fact that a HIP entry is recognized as a double star is more efficiently conveyed by the use of a HIP number than it could be by manipulating the HD number(s) of the star(s). And in the words of Daniel Egret of the CDS: "As a data center we are certainly supportive of the strategy chosen by the Hipparcos project, which implied giving a running number to all Hipparcos entries: this is very valuable to help us provide a pointer to Hipparcos data in the databases."

Meanwhile, to get a feeling for how well-known the stars "renamed" by Hipparcos actually are, and to illustrate the problem of cross-identifications, try a little test. Enter the SIMBAD data base using Griffin et al's reference, HR 51565/6. SIMBAD returns "This identifier is not correctly written: HR 51565". In this case the authors were evidently refering to HD 51565/6 - a typo, and there are all-too-many of them in the literature!

Q18. Can you explain the standard errors that you give with the catalogue measurements? [Mar 98]

A. The Hipparcos & Tycho Catalogues adopt the following formal definition of the "Standard Error", as given in Appendix A (Glossary) of Volume 1:

Standard error: estimated errors are given following the recommendations of the `ISO Standards Handbook 3: Statistical Methods', where the standard error is defined as: `the standard deviation of an estimator; the standard error provides an estimation of the random part of the total estimation error involved in estimating a population parameter from a sample.'

In practice, the characterisation of the random part of the error assumes specific properties of the error distributions, viz. that they are normal (Gaussian) distributed. This is explained in Section 1.5.2 (Error Propagation) of Volume 1:

In Section 1.2.8 a standard model of stellar motion was introduced, and other, more complex models are discussed in Section 2.3. The numerical fitting of such a model to observational data generally results in an estimate both of the parameter vector a and of its covariance matrix C . With n free parameters, these are expressed respectively as matrices of dimension n ×1 and n × n .

[From a statistical viewpoint, a and C jointly provide a complete specification of the fitted model and its uncertainties only in the context of linear estimation and normal (Gaussian) error distributions. The estimation problems encountered in the Hipparcos and Tycho data analyses are seldom strictly linear, and sometimes strongly non-linear, and the error distributions are in practice never Gaussian. Perhaps the most dramatic consequence of non-linearity is the possible existence of grid-step errors, which in unfortunate cases may result in positional errors of the order of an arcsec while the formal standard errors remain in the milliarcsec range. Additional statistics provided in the catalogue, such as the rejection rate and goodness-of-fit (Fields H29-30), provide some indication of the sometimes abnormal behaviour of data, but in practice no complete characterisation of the fit is possible. Nevertheless, in the vast majority of cases a and C provide an extremely useful approximation to complex reality.]

The resulting probability levels can be assessed from standard tables of the normal probability integral (see, e.g. tabulations in Ambramowitz & Stegun). Thus, for example, on the assumption that the errors are normally distributed, the probability that the true quantity falls between ± 1 sigma is 0.6827, the probability that it falls between ± 2 sigma is 0.9545, etc.

The caveats noted above should be kept in mind in drawing astrophysical conclusions from these formal probabilities.

The same definitions indeed apply to all other astrometric parameters throughout the Hipparcos and Tycho Catalogues.

van Leeuwen, F. et al. (2007), MNRAS, 379, 723 (link to ADS abstract and paper)

Feast M.W. and Catchpole R.M. (1997), MNRAS, 286, L1-L5 (link to ADS abstract and paper)

Q20. I am trying to understand double stars in Hipparcos and Tycho. In particular, HIP 717: it has two components (A and B) in the DMS Annex, with a "good" solution (DC5="Qual=A"). But, in Tycho it has only one entry. Furthermore, its MultFlag (T49) is equal to 'Y' (investigation for duplicity carried out on Tycho data, no indication of duplicity was found), but its CCDM component identifier (T51) is equal to 'AB'. So, is this source indeed a double or not? There are 3541 stars like this one in Tycho. In those cases, does the TYC MultFlag overrule the HIP DMS Annex?

A. Answer provided by F. Arenou.
Assessing whether a source is double or not is always a problem. It depends on the resolution of the instrument, the angular separation between components, and their magnitude difference. Due to the better capabilities of Hipparcos, it is not exceptional that it may have detected a star as double, whereas Tycho has not.

The field H59: C indicates the duplicity. The separation and magnitude difference are precisely measured (H64-H67). The field H57: 1 indicates that there is only one entry for the 2 (H58) components because they were not separated enough to get individual astrometry for each component. Instead of considering one flag overruling the other, this may show that Hipparcos could resolve the system while Tycho did not succeed.

However, a firm answer can only come from a detailed analysis star per star, and may need complementary observations.

Q21. I have a question about the Bradley effect (light aberration) in which the apparent position of stars oscillates with the amplitude of 20.6" during the year, due to the velocity of the Earth around the Sun. 1 - Is it correct to say that "exactly" the same effect (apparent oscillation) exists in the observed position of all planets? 2 - Is it also correct to say that this apparent oscillation of 20.6" also appears in the apparent position of the Moon and even in the precise position of the Earth satellites? I realize that since all these objects (planets, moon and Earth's satellites) are all submitted to the Bradley effect, this is undistinguishable on the star background, since the aberration of light (the Bradley effect) can be observed only if we use absolute coordinates.

A. The precise definition of directions in astronomy is a complicated one, and requires consideration of the relativistic motion of the light source (e.g. a star or planet) and of the observer (e.g. on Earth), and a precise definition of the reference frame in which the measurements are made (e.g. with respect to the Solar System Barycentre). Classical stellar aberration (as first detected by Bradley) is the non-relativistic (i.e. Newtonian) expression for the direction to a source as seen by a moving observer (e.g. the Earth). When calculated to first order in (1/c), allowing for the Earth's orbital eccentricity, and referring to the standard astronomical reference epoch of J2000.0, the constant of aberration is 20.495...arcsec. The position of a distant object therefore oscillates with this amplitude (due to the circular component of the Earth's orbital motion) during the year, as you note.

The only complication when considering a more nearby object (whether it is a planet, the Moon, or a satellite) is that the source itself has a significant motion. It is the velocity of the observer relative to the velocity of the source that is relevant. As in the case of stellar aberration, a simple first order expression for the "proper direction" can be obtained by neglecting relativistic and higher order terms. The correction in direction due to the relative motion between source and observer is known as planetary aberration.

As a specific example, if the source and observer move with the same relative transverse velocity, the aberration term is zero.

If you wish to go into more details, several specialist books could be consulted, of which "Vectorial Astrometry" by C.A. Murray (Adam Hilger) can be recommended.

Q22. I would like to calculate a flux or irradiance from the magnitudes in the Hipparcos and Tycho catalogs, but I can't find a zero magnitude flux in the documentation. What are the zero magnitude fluxes for both the Hipparcos V and the Tycho VT magnitude scales? Or better yet, where in the documentation are these numbers?

A. Equation 1.3.23 on p58 of The Hipparcos and Tycho Catalogues, Volume 1 (Section 1.3) is what you need.

Q23. How far away (pc or ly) was, or what was the smallest parallax for, the most distant star measured by the Hipparcos satellite? I have seen varying numbers - one ESA publication stated that it was 1000 ly while I've seen various astronomy professors say it was on the order of 3000 ly. For whatever maximum distance is correct, can I assume that Hipparcos pretty much mapped all the stars within that distance from the Earth - i.e., the number in the Hipparcos catalogue plus the number in the Tycho catalogue? I suppose if I knew how to search the Hipparcos and Tycho catalogues, I could determine this answer, but I thought I'd ask anyway.

A. Let's talk in terms of angles (a parallax of 1 milliarcsec means a distance of 1000 pc). You will find very small values of the parallax in the catalogue, e.g. 0.1 milliarcsec which formally would mean a distance of 10,000 pc. There are even negative parallaxes, which physically means nothing. The important point is also the accuracy of these estimates. If we measure 0.1 milliarcsec, and the accuracy is 1 milliarcsec, it doesn't mean that we have really determined a distance of 10,000 pc. So there is not really a simply answer to your question "what is the maximum distance measured"... it depends on the accuracy you are happy to accept. Many workers say that they only want to work with distances accurate to say 10%. For a typical measurement accuracy of 1 milliarcsec, this will mean stars with parallaxes greater than 10 milliarcsec, i.e. stars within just 100 pc of the Sun. If you're happy with distance accuracies of 20%, our measurements extend out to around 200 pc. But not every star out to these distances was measured by Hipparcos, so the catalogue is certainly not complete to these distances.

Q24. I noticed there is now a Tycho-2 catalogue which contains information on something like 2.5 million stars. Were all of these 2.5 million stars mapped by Hipparcos, and if so, why did the number increase from 1 million in the original Tycho catalogue?

A. Recall that there were two separate instruments on the satellite. One gave the Hipparcos Catalogue of 120,000 stars. The second gave the Tycho Catalogue. Hipparcos observed only those stars we'd included in a starting catalogue, while Tycho made detections of any signal above a certain level. At the time the catalogues were published, the Tycho detection level was set such that the Tycho 1 catalogue contained about 1 million stars. Thereafter, a more careful analysis led eventually to fainter stars being detected, eventually leading to the 2.5 million stars.