The motivation for this project extends from a long-standing need for accurate angular diameters for (roughly) main sequence stars. I selected the target list by aiming to meet several criteria, described below in detail. As discussed in the Introduction, several sources indicate that at least a 2% accuracy on the measured angular diameter is needed to refine the effective temperature scale to better than 1%, because TEFF ∝θ1/2. This limit will also
allow us to calibrate color-temperature relations to a high degree of accuracy, and enable us to extend our knowledge to large populations of stars throughout the Galaxy. For this project, we aim to measure the angular diameter of a star to better than 4%, only to arrive at a sample that is large enough for an initial analysis; however, most of the stars observed will be sufficiently resolved down to the 2% level.
2.1.1 Resolution Limits
How accurately one can measure the angular diameter of a star depends on how far down the visibility curve you are able to sample. The visibility function of a single star is expressed as:
V = 2J1(x)
x , (2.1)
where
where B is the projected baseline, θ is the angular diameter of the star, and λ is the wave- length of observation. By knowing the λ and B utilized in a given observation, we can estimate the optimum resolution range resulting from the accuracy with which we can mea- sure the object visibility. For instance, assuming that we can readily measure the visibility of a star to 5% (McAlister, private communication), by evaluating Equation 2.1, we find that we must sample down to a visibility of V=0.55 to obtain better than 4% accuracy on the measured angular diameter of a star. To ensure that we will reach the resolution limit for our observations, we set the cutoff to obtain a visibility of 0.55 for CHARA’s third longest baseline (S2/E1=302.2m). Thus, the limiting resolution that meets this criteria is θ = 0.65 mas in K band and θ = 0.50 mas in H band. By binning the spectral types and taking the nominal values for linear diameters for the stars from Cox (2000), the maximum distance for each spectral type bin is found (Figure 2.1).
I did not rely on assigned spectral types for stars because often it is difficult to find agreement from one catalogue to the next. Instead, in the HIPPARCOS Catalogue query, the ranges in spectral types were sampled by (B−V) color indices, and luminosity classes were sampled by restricting the apparent V magnitudes of the stars to only admit roughly main sequence stars (Cox 2000). These sample criteria are listed in Table 2.1.
2.1.2 Instrumental Limits
In this project, the instrumental limits for observing are restricted only by the target dec- lination, which must be greater than −10◦. Stars approaching this declination suffer from baseline foreshortening. This is where the maximum projected baseline will never reach the full 330m on the longest S1/E1 baseline. Another factor in observing low-declination objects
10 20 30 40 50 Distance (pc) 0.0 0.5 1.0 1.5 2.0
Angular Size (mas)
A0 A5 F0 F5 G0 G5 K0
Figure 2.1: Angular Size Versus Distance:Plot of angular size of star by spectral type versus distance. The shaded region indicates distances where the star becomes too unresolved inH-band to achieve the goal of better than 4% accuracy on the angular diameter measurement. For example, we can observe a G0 dwarf to 20 pc using our adopted experimental setup.
is that they do not remain at their highest elevations for very long. Stars that are observed at lower than ≈30◦ degrees elevation are thought to have calibration problems because one is observing through too much airmass, and seeing effects are more apparent at these low elevations. Additionally, the calibrator observed is likely to have a very different airmass, even if one is chosen to be very nearby, and these values change frequently when the objects are rising/setting. Last but not least, a very good reason not to observe a star too far south (and at low elevation) is that you are doomed to be glaring through the exhaust pipe of Los Angeles, which lies in the southern direction from Mount Wilson Observatory.
Magnitude limits are not a factor because of the resolution requirements set by the goals of the project (θ > 0.50 mas for better than 4% accuracy in H-band). These are set by the distances of the target stars, and their predicted linear sizes. For instance, an A0 star has an absolute magnitude MV = 0.65, so at the maximum distance of 33 pc it has an apparent
magnitude ofmV = 3.2. For the late end of the sample, a K0 star has an absolute magnitude
MV = 5.9, so at the maximum distance of 16 pc this star has an apparent magnitude of
mV = 6.9. These translate into apparent K magnitudes of mK = 3.2 and mK = 5.0 for the
A0 star and the K0 star, respectively (assuming (V −K)A0 = 0.0 and (V −K)K0 = 1.96;
Cox 2000). Very conservative limits for observing with the CHARA Classic beam combiner require a K magnitude to be brighter than 7, much fainter than these values. This fact also gives some relief in finding suitable calibrators for the target stars, which are preferred to be of similar spectral type as the object, but must also be an unresolved source (i.e., farther and dimmer).
Figure 2.2 shows the relationship between a star’s angular diameter as a function of effective temperature and observed K magnitude in a graphical representation. This uses the results from Code et al. (1976) where the angular diameters and effective temperatures are measured for eleven luminosity class V and IV stars1. For example, a K = 5 mag star
with a temperature of ∼4000 K will have an angular diameter of ∼0.5 mas.