There are of course a number of procedural concerns that must be attended to in both calibrating and then applying the TRGB Method to extragalactic distance determinations. We briefly discuss the most important of these in this section. Some of these problems can be anticipated and dealt with in the design phases of the observing program (for example, crowding, signal-to-noise, etc.); some require careful post-processing (the removal of cosmic rays, background galaxies, etc.), or require complementary observations (to distinguish AGB stars, and deal with high-metallicity effects). Others will hopefully diminish in importance with additional time and effort (such as zero point uncertainties).
Until recently, the apparent magnitude of the TRGB was simply estimated by visual inspection of the color magnitude diagram. Lee, Freedman & Madore (1993) introduced a quantitative edge-detection method (the Sobel filter) to both identify the position and estimate the uncertainty of the TRGB observed luminosity. When this filter is convolved with the luminosity function, the output response function peaks where the discontinuity is the largest. Further refinements to this method have subsequently been introduced by Sakai, Madore & Freedman (1996a, b).
Normal globular clusters have asymptotic giant branch stars. These evolutionarily-advanced stars are found at magnitudes above and below the TRGB, loosely paralleling the red giant branch to the blue and exceeding the first ascent red giant branch stars at higher luminosities. In mixed-age populations intermediate-mass stars can also evolve up the AGB sequence populating those luminosity intervals above the TRGB with even brighter and often very much redder stars than normally found in old, metal-poor, pure Population II systems.
AGB stars can be a source of additive noise in the luminosity function near the TRGB, as they can be slightly brighter than MI ~ -4.0 mag. Fortunately, the AGB luminosity function is known to be flat and/or only rather slowly rising, thus making it extremely unlikely to be misidentified with the much more abrupt TRGB signature (when the edge-detection filter is passed through the luminosity function, it would respond more prominently to the pronounced discontinuity of the RGB tip). The AGB problem can also be minimized by observing the red giant branch population preferentially in the outermost halos of the galaxies where intermediate-age populations are less likely to be present. Furthermore, the added advantage of working in the lower-surface density halos is that crowding effects are also minimized.
Depending on the mix of Pop I and II, very massive stars can add contamination to the reddest portions of the CMD by contributing evolved supergiant stars. These objects are in proportion to the recent star formation rate and are spatially co-located with their immediate progenitors, the blue (plume) main sequence stars. Avoiding regions of easily identified active star formation reduces this contaminant effectively to zero. Nevertheless, these red supergiants are both rare (in comparison to TRGB stars) and show no characteristic discontinuity in their gradually increasing apparent luminosity function. They can add noise to the TRGB detection, but they are not likely to be mis-identified with it. This is especially true given that the blue population effectively predicts their presence and rough numbers.
At high metallicity (beyond [Fe/H] = -0.7 dex) bright stars suffer noticeable line blanketing even in the I-band (e.g., Bica et al. 1994). However, the effect is to make these high-metallicity tip stars fainter than their low-metallicity counterparts. This would be a problem (which could be calibrated in principle) for the determination of distances to pure, high-metallicity systems, but whether such ``pure'' systems do exist or even could exist is unlikely. In terms of detection thresholds, mixed-metallicity populations (that is, any system that has low-metallicity stars as the precursor population to the next generation of higher-metallicity red giants) would first reveal their (bluer, brighter) low-metallicity stars, and thereby define the jump in TRGB luminosity function at a magnitude corresponding to the low-metallicity calibration independent of the fainter (high-metallicity population) tip stars mixed in below.
Although the magnitude of the TRGB has been shown both observationally and theoretically to be extremely stable at MI ~ -4.0 mag, this stability has only been solidly demonstrated and calibrated in the metallicity range defined by Galactic globular clusters (i.e., -2.1 < [Fe / H] < -0.7 dex). At the higher metallicity end of this range, little data have been obtained to demonstrate whether the constancy of the TRGB magnitude prevails, or if not, how it changes in detail. Of course, one can reduce this uncertainty by restricting TRGB observations to the halos of galaxies where color gradients suggest lower metallicities. And, in practice, for most irregular galaxies, and the outer regions of spiral galaxies, the available lower-metallicity calibration will be sufficient.
Crowding will limit the discovery and the photometry in all TRGB applications. However, given even a rough estimate of the expected distance, the local surface brightness (in the halo) will predict the expected crowding at the magnitude corresponding to the tip. Using computer simulations, Madore & Freedman (1995) showed that the TRGB method could be applied out to 3 Mpc [(m - M) ~ 27.5 mag] from the ground, and from space at least a factor of four further in distance [(m - M) ~ 30.5 mag], being limited primarily by integration time rather than crowding in the latter case.
While this may seem to be a simple matter of combining aperture and integration time to reach the requisite signal-to-noise ratio, other factors preempt extended integration. Variable seeing is a critical issue for ground-based attempts to go to the limit of this method; while the limiting case of using HST encounters a variety of subtle but important issues relating to charge-transfer efficiency, fixed pattern noise, extensive cosmic ray removal, etc. when extremely long intergations are called for. Given these limitations, with its present detectors, HST may be considered to have an operating range of ~ 10 Mpc for applying the TRGB method; beyond that, extreme care should be taken in the acquisition, processing, and interpretation of the data.
Background galaxies as a source of noise can be dealt with in a variety of ways. First they can be resolved. In most cosmological models, galaxies are not expected to be much less than an arcsec for the magnitudes of interest in our applications, where I < 25 mag. Based on simple profile-fitting, galaxies can therefore be discriminated from stars and eliminated early in the analysis process. Very distant, point-like objects are not expected to have any abrupt discontinuity in their apparent luminosity function and could at worst contribute a ``background'' noise component which can be further reduced by color selection, eliminating the very bluest contaminants (certain quasars) and the very reddest (background ellipticals).
Careful planning and post-processing can deal with cosmic-ray events in the CCD images used to detect the TRGB. Median-filtering of multiple exposures, combined with image-profile fitting selection, set to reject ``sharp'' events can reduce cosmic-ray noise to an acceptable level of contamination.
The absolute magnitude of the TRGB rests on the globular cluster distance scale, which in turn depends on the calibration of the absolute magnitudes of the horizontal branch RR Lyrae stars. And that calibration, in form and zero point, is still controversial (see, for example, Sandage & Cacciari 1990, Renzini 1991, and Carney et al. 1992, for the full range of opinions). We have adopted the calibration of Da Costa & Armandroff (1990) which is MV (RR) = 0.17 [Fe / H] + 0.82 mag. As discussed in Walker (1992), Saha et al. (1992), and Freedman & Madore (1993), the fainter (MV (RR) ~ 1.0 mag) alternative calibration disagrees with the Cepheid distance scale to overlapping galaxies at the 0.2-0.3 mag level. Our currently adopted zero point is ~ 0.8 mag, and falls between the aforementioned extremes.