4.3 Prototype Evaluation

The prototype needed to produce good quality data, results that were not of a publishable standing would have proven that it was necessary to improve the quality of the PL. The main result of the work presented in this section is the derivation of the first high quality main sequence for an open cluster (see Figure 4.6), all the way down to the hydrogen burning limit. In accordance with the critical test set for this data the results have been published in Steele and Howells (2001a,b).

4.3.1 Scientific Background

Low mass stars have low effective temperatures (<5000K).This means that their atmospheres can contain large numbers of molecular species. Therefore their spectra are dominated by absorption bands which are hard to model due to the vast number of transitions that must be incorporated. In addition molecular recombination in the interior leads to convection penetrating deeply into the optically thin atmospheric layers. Because of these effects, the grey-approximation (constant opacity) is no longer valid below 5000K (Chabrier et al., 1996; Saumon et al., 1994). This means that modelling low mass objects requires a correct description of the non-ideal effects in the interior as they affect the equation of state, a derivation of accurate atmospheric models, and a consistent (non-grey) boundary condition between the atmosphere and the interior.

Such models are now being developed by various groups (Baraffe et al., 1998; Saumon et al., 1995) and are being tested against empirical HR diagrams for nearby stars (see Monet et al., 1992) with known parallaxes. A problem with this approach is that metallicity and age variations in the nearby star sample can confuse the HR diagrams, making their comparison with isochrones from the models difficult. To overcome this problem the first high quality main sequence for an open cluster all the way down to the hydrogen burning limit (recall that members of an open cluster will all have the same metallicity, distance and age) is derived. In the past this approach has been limited by a lack of membership information making the construction of an HR diagram solely from crowded CCD frames difficult. However for Praesepe the proper motion study of (Hambly et al., 1995) (HSHJ95) provides a high quality membership list all the way from 0.8 to 0.13M.

4.3.2 Observations

Observations were carried out at the Jacobus Kapteyn Telescope (JKT), La Palma on the nights of 1999 February 17-23 using the 1024x1024 pixel TEK4 CCD detector. During that time interval 5.5 out of the possible 7 nights were photometric, and it is observations from those 5.5 nights that are presented here. The filters employed were R_h, I_h and (Z_rgo). Due to observing time constraints it was not possible to observe the whole HSHJ95 catalogue. Therefore all objects in the magnitude range 11<R_59F <19 (note R_59F is the photographic R magnitude scale) and with RA (1950) < 8^h37^m30^s (corresponding to HSHJ95 catalogue number <315) were observed. In addition the first nine objects of the HSHJ95 catalogue in the magnitude range 19 <R_59F <20 were also observed.

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It should be noted that during the reduction it was found that data for a number of objects were corrupted (generally in only one filter). There was no apparent correlation between time of observation and/or the magnitude of the objects observed and the corruption. In order to produce a homologous set of observations, we chose to disregard such objects even when they had good magnitudes in the other filters. In total therefore, RIZ magnitudes for 218 objects out of 515 are presented in Table 4.1.

4.3.3 Model Fitting

Figures  4.4 & 4.5 present (I,R-I) and (R,R-Z) colour magnitude diagrams of the cluster. The main sequence is immediately apparent in both diagrams.

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Figure 4.6 re-plots the cluster members evident in Figure 4.4 along with the theoretical isochrone of Baraffe et al. (1998) for solar metallicity and an age of 1Gyr. It should be noted that in re-plotting Figure 4.4 those points deemed not to be part of the cluster, due to their distance from the observed main sequence, were removed. Praesepe has a well determined and uncontroversial distance. Hipparcos derives a distance modulus of m - M = 6.24 (Mermilliod et al., 1997), in agreement with fits to the upper main sequence by Mermilliod et al. (1990) who derive m - M = 6.20 and Hauck (1981) who obtains m - M = 6.26. The cluster is also sufficiently old (~ 1 Gyr) that the lowest mass stars have reached the main sequence.

The theoretical isochrone is a good fit, with the high mass end matching well. However the low mass end diverges at approximately 0.45 M  with the model being too blue. This effect was also noted by Baraffe et al. (1998) and attributed to an unknown source of optical opacity. Also to be noted is that a recent paper by Pinfield (2002) publishes data which reproduces the results shown here.

In an effort to ascertain if there is an observed binary sequence obvious in the data two additional lines are also plotted. These lines are generated by first calculating a best fit line to the data. The equation of this line is,

(4.3)

These additional two lines are then offset from this fit in the ordinate axis. They are separated by 2.5log ₁₀(2) (as the light comes from a binary object). Since there appears to be more points below the best fit the offsets are; the solid cluster sequence line equals the polynomial +0.25 and the dotted binary sequence equals the polynomial -0.50.

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