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Some notes on Tycho photometry and its use


Section Director's Note


This item was contributed by Mark Kidger and he points out that this is unpublished research and therefore copyright and requests that anyone wishing to use the information quotes the source and requests permission prior to publication.


1.0       What is Tycho photometry?


Tycho was an instrument on the Hipparcos satellite launched in 1989. Tycho was a scanning star-mapper that was less precise than main instrument – although still extremely precise compared to most ground-based measurements – but that allowed somewhat fainter stars to be measured in two colours, roughly approximating to the B and V bands. The Tycho-2 catalogue, the most recent and definitive, includes 2 539 913 stars (about 60 per square degree of sky) and is almost complete to magnitude V=11.


Although typically an individual Tycho measurement had rather large errors, Tycho took many tens of measures – on average one hundred and thirty – thus the uncertainty in the final Tycho magnitude is normally about a factor of ten better than the standard deviation of the measures for any star.


Note that only the Tycho-2 catalogue should be used. Previous Tycho photometry suffered from some difficulties, as is logical in such a vast undertaking and these have had to be ironed-out progressively with time.


2.0       The problem


Although Tycho photometry is stated to be “rather close” to the Johnson system, even the most cursory use of the data shows that, especially in B, there are large differences between the Johnson system and Tycho-2 magnitudes. Despite the fact that Tycho-2 magnitudes are listed to three places of decimals, that is, millimagnitude precision, the difference between the Tycho-2 magnitude and Johnson-scale photometry can be more than 0.5 magnitudes in B and 0.2 magnitudes in V. This effect means that uncorrected Tycho-2 photometry may be highly misleading. However, the exact correction to apply has been subject to considerable discussion.


My student, Fabiola Martín-Luis and I are using Tycho photometry in a calibration programme to make a precise calibration of stars for the 10-m Gran Telescopio CANARIAS (GTC). This programme has required us to compile accurate visible and near-infrared photometry for a large number of stars, both from our own observations at Teide Observatory (Tenerife) and el Roque de los Muchachos Observatory (La Palma).


This programme has required us to understand Tycho photometry and its relationship to the standard photometric systems. We have compared Tycho-2 photometry with observations of some 500 stars observed in BVRI on multiple nights at the two observatories using the 1-m Jacobus Kapteyn Telescope (JKT) and the 0.82-m IAC-80 Telescope (IAC-80). All our observations were calibrated against Landolt stars, the accepted standard for visible photometric calibration. On a typical night we observed some sixty Landolt stars of a wide range of colours to calibrate our photometry.


We have previously established that our photometry is very close indeed to the standard Johnson system of photometry. We call our photometric system (purely for internal use), the Johnson-FML system that, here, is abbreviated to “FML” (or, on the axes of some plots, to “FM”).


The results of our study are presented below. 



When we represent uncorrected Tycho-2 photometry against FML photometry we see two important effects: first, the slope of the line is clearly less than unity, in other words, Tycho magnitudes are consistently fainter than FML photometry; second, there is an evidence increase in the photometric dispersion to fainter magnitudes.


These two tendencies are clearly seen in both bands, although they are especially strong in B. Note too how, at B>8, the stars seem to separate into two bands in the plot, with the upper band appearing to follow the line of BTycho = BFML and the second band of Stars showing BTycho > BFML.



By B=13 the least squares fit to the photometry shows that BTycho » BFML + 0.7, so the differences are very important.


A similar effect is seen in V, although the trend is not so marked. Note how, for the brightest stars, it appears that VTycho = VFML, just as, in B, for the brightest stars we see that BTycho = BFML. This effect is extremely misleading and, as we will see, is due to the fact that our bright stars are, for instrumental reasons, all of spectral type A[1]. Note that in the plot below “V30” refers to the filter number in the JKT database. This allows us to identify the filter’s exact profile and chacteristics as several V filters with slightly different transmission profiles were available to users. We used this same filter in each observing run.




The plot of (B-V)FML against (B-V)Tycho gives us some valuable hints about Tycho’s photometric behaviour, as well as the biases in our sample of stars, which can give rise to misleading results in this, or any other study. It also shows that a few stars have wildly inaccurate photometry: this can be due to misidentification of the star when cross-correlating between our star list and the Tycho catalogue, or to problems with the photometry (usually with the faintest stars observed by Tycho). Note how our sample of stars splits into two well-separated groups in the colour-colour plot. One group shows (B-V) £ 0.35 and the second,  (B-V) ³ 1.0. This separation is logical as the stars that we have selected for calibration are mainly of spectral types A(0-5)V and K-MIII; these groupings of colour indices reflect the normal colours for stars of these spectral types, the former white or slightly yellow, the latter orange or red.


Note also that the stars with a colour index close to zero are the ones that show (B-V)FML = (B-V)Tycho, while the red stars show (B-V)FML >> (B-V)Tycho. This demonstrates that there is a strong colour term in the photometry.


3.0       Questions and solutions


3.1       Question 1


Is Tycho photometry on the same photometric scale as Johnson-FML, or is there a slope and/or zero point correction required to transform Tycho photometry to the Johnson system?


We need to solve the equation


VFML = a * VTycho + b + c* (B-V)                                                                                 (1)


And demonstrate that a = 1 and that b = 0.


3.2       Solution


We selected a simple of stars with a colour index of zero and looked at the trend on the magnitude-magnitude diagram, comparing Tycho-2 photometry with FML. The stars selected all had a colour index in the range –0.05 £ (B-V)FML £ +0.10.



Note that to magnitude 10 Tycho º Johnson-FML. At fainter magnitudes the Tycho photometry can have very large errors, leading to significant dispersion. The presence of a few faint stars with large photometric errors means that the least squares fit has a slope that is not exactly unity, but it is evident that it is extremely close to unity and that the brighter stars are tightly clustered around a line of slope unity.


When the fainter stars are neglected in the fit, the least squares regression fit has a slope of unity that, within the errors, passes through the origin. In other words, we can state with a high degree of confidence that, in equation (1), a = 1 and b = 0 and that we can treat the correction of Tycho-2 photometry as requiring only a colour transformation to place it on the standard Johnson photometric system.


3.3       Question 2


What is the colour transformation required to convert Tycho-2 photometry to the Johnson system and how should it be applied?


We can now simplify equation (1) to


VML = VTycho + c* (B-V)


Calculate the value of “c” and ensure that it is a simple linear term.


3.4       Solution


This we do in two steps. First, we select a sample of stars with the same magnitude and look at the correction between the difference in magnitude Tycho-FML and the colour index. The selected stars had magnitudes from 8.9 < V <. 9.1, giving more than 40 stars, all with good photometry and a range of colour index up to (B-V) = +2.2.



In both B and V we can see that the Tycho-FML difference is strongly correlated with the colour index. The dependence is much stronger between (B-V)Tycho and BTycho-BFML with the steeper slope typical of a detector with low blue sensitivity[2] and also shows greater dispersion because the reddest stars are very faint for Tycho to observe in B and thus have large photometric errors. In contrast, V shows a smaller dispersion, but also weaker colour correlation. Note that in neither case does the least squares fit pass through the origin.


We find that:


VFML = VTycho - 0.032 - 0.0833 * (B-V)Tycho




BFML = BTycho + 0.056 - 0.3006 * (B-V)Tycho


When we make the same plot with the full data set we find almost identical fits to the data but, logically, as some of the stars are rather faint, a much greater dispersion and a population of outliers.



For the full simple of stars we find fits that are virtually identical to the reduced, magnitude-limited sample:


VFML = VTycho - 0.016 - 0.0741 * (B-V)Tycho




BFML = BTycho + 0.064 - 0.2983 * (B-V)Tycho


These two relations are our definitive transformations for the Tycho photometry.


The fact that the regression lines of both the magnitude-limited and complete sample of stars are – to within the errors – identical, also serves as a check that the transformation from Tycho to Johnson-FML depends only on the colour index and not on the magnitude of the star.


Now we invert the process and apply to derived colour correction to the Tycho photometry to check that it corrects both the dispersion and the slope of the magnitude-magnitude diagram.


In B the change in the plot before and after correction is considerable. We see that the regression line slope in the corrected plot is close to unity and that the dispersion is small to B=12. Unfortunately though, as can be seen, the presence of some much fainter stars with a large dispersion skews the fit slightly and makes it flatter than unity.



In V the improvement to the fit is even greater and the slope differs from unity by less than 0.5%. This relationship is seen to describe the magnitude accurately in the range from 5 < V < 12.5 with an acceptable dispersion.




4.0       Conclusions


  • Tycho-2, as published, is not corrected for colour transformation.


  • When corrected, it is in the standard Johnson system.


  • The colour term is large and is especially important in B, but should not be neglected in V.


  • There is a simple correction so transform Tycho ® Johnson.


VFML = VTycho - 0.016 - 0.0741 * (B-V)Tycho


Ø      And


BFML = BTycho + 0.064 - 0.2983 * (B-V)Tycho


  • However, this correction depends on (B-V)Tycho colour index and thus is a hostage to its reliability. For the fainter and redder stars where the error is (B-V)Tycho is large there will be a correspondingly large error in the transformation of the magnitude to the Johnson scale. In extreme cases, for fainter and redder stars, the total uncertainty in the transformed magnitude may be >0.3 magnitudes.


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[1] We cannot observe bright red stars, as they would saturate the detector in the red bands.

[2] In other words, a detector that shows a strong fall in quantum efficiency towards the blue.