At this point, visibilities for two fringe packets have been obtained, but which visi- bility represents the target and which represents the calibrator is still unknown. The magnitudes of these two components of the system are helpful in resolving this dis- crepancy. Any two fringe packets within the field of view of the CHARA Array (1 arcsecond) will have an effect on each other’s visibility due to the magnitude difference between the two objects, even if the two objects are not observed within the same delay scan (ten Brummelaar, private comm.). The ratio of the visibilities between two objects is affected as follows:
V1,corr V2,corr =βV1,obs V2,obs (3.7) βwide = 100.4∆Kwide (3.8) ∆Kwide =K1−K2 (3.9)
where V1,corr and V2,corr are the corrected visibilities of the brighter and fainter com-
ponents of the wide orbit, respectively, V1,obs and V2,obs are the observed visibilities
that were derived above from fringe-fitting, andK1 and K2 are the magnitudes of the
components. Further details on the derivation of Equation 3.7 are given in Appendix A. From these equations, it can be deduced that the larger the magnitude difference between the components, the larger the visibility ratio between the bright and faint components. For this reason, the larger packet is generally assumed to be the brighter
component. The MSC is consulted to determine whether the brighter component is the target or the calibrator. The MSC presents onlyV-magnitudes for the individual components, so spectral types andV −K values from Cox (2000) are used to convert these toK-magnitudes. If spectral types are not available for all components, theV
magnitudes are used to determine whether the calibrator or target is brighter. Gen- erally, the spectral types of the stars in a given system are not so different that one component would be brighter than the other in V but dimmer in K. In cases where the magnitudes appear to be roughly equal inK according to the MSC, two separate sets of data are produced, one for each of the two scenarios. Orbit fits, which will be discussed in detail later, are performed on both sets of data.
In theory, one could use the wide orbit’s position angle along with the baseline orientation to determine the relative identities of the fringe packets on a given night. Consider the configurations in Figure 3.10. The middle baseline position is completely perpendicular to the position angle of the binary. According to equation 2.2, this will produce a separation of zero between the two fringe packets. Two other baselines positions are displayed, one on either side of the perpendicular position. Both of these baselines will produce a non-zero separation between the fringe packets, but the orientations of the packets on the delay scan will be opposite. In other words, the baseline for which the angle T1OI (where O is the origin) is acute produces a fringe packet for component I at a position of higher delay than the fringe packet for component II. The baseline for which angle T1OI is obtuse will then produce a
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fringe packet for component I at a position of lower delay than the fringe packets for component II. Because the CHARA Array records the position of the dither mirror for all data points, it would be obvious in the data reduction process which fringe packet is located at higher delay and which one is located at lower delay. It should be noted that this method only gives the relative identities (I and II) of the packets, not the absolute identities (target and calibrator). If the same system was observed on a different night, where the binary position angle and baseline orientation have completely changed, it would be theoretically possible to determine which packet in the new configuration would correspond to I and which would correspond to II. It would not, however, be possible to determine whether I represented the target or the calibrator. One would have to try both possible scenarios.
A method of using the baseline orientations and binary position angles has been developed by ten Brummelaar (private comm.). For every epoch of observation, the difference in the angles, δ = θ −ψ, is calculated. Then, because the baseline orientation angle is only defined between 0◦
and 180◦
, 2π is added to any value of δ
less than−180◦ and subtracted from any value greater than 180◦. Then, all values of
|δ| <90◦ are considered to have one orientation of the fringe packets, and all values
of |δ|>90◦
have the opposite. This method was tested on the system V819 Her, an object in which the packet identities are obvious due to the large magnitude difference between the target and calibrator. Unfortunately, this method did not produce the expected results for V819 Her. This may be due to some inherent difference in the
Figure. 3.10: Identifying fringe packets. I and II represent two stars in a binary system with a certain position angle measured from North to East. Three different baselines are plotted against the binary. The middle baseline position angle is perpendicular to the binary position angle, while the other two baselines are slightly displaced from the middle one.
way data are processed between CHARA’s three general sets of baselines (S-E, S-W, E-W), especially in regard to how positions of higher delay relate to the positions of the components on the sky. Because the use of baseline orientations failed to produce consistent results, the method of assigning the larger fringe packet to the higher flux component is always used.
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