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3.3 Detection Regimes in Perspective

The differences between observations in the optical and near-infrared are sufficiently great that they warrant discussion. In this section, we will discuss the relative merits of optical (0.4 - 0.9 µm) and near-infrared (1.0 - 2.5 µm) observations of Cepheids. To accomplish this, we will consider, in turn, the wavelength dependence of observables, factors affecting the detected signal, and factors contributing to the noise.

3.3.1 Wavelength Dependence of Observables

Panoramic detectors used in the optical (0.4 - 0.9 µm) and the near-infrared (1.0 - 2.5 µm) are unity gain devices which produce a single electron for every detected photon. A blackbody at an effective temperature of 5500 K - typical of longer period Cepheids - has a slowly varying photon spectral density from the V bandpass (0.5 µm) out to K (2.2 µm). (We will come back to this fact again when we discuss the signal.) However, the near-infrared spectra of stars of this effective temperature are strongly distorted by the H- opacity minimum at 1.6 µm, centered on the photometric H bandpass. The effect of this opacity minimum is to allow radiation characteristic of a hotter source function to escape, and consequently a Cepheid will appear approximately 20% brighter at 1.6 µm than predicted by a blackbody spectrum scaled to, say, a V magnitude. (A second and less important effect which works in the same direction is the smaller amount of limb-darkening in the near-infrared.)

One consequence of the H- opacity feature is the near constant H - K color of Cepheids (and for that matter, RR Lyrae stars) through their pulsation cycle. Since the H - K index varies extremely slowly in this temperature regime, a useful value for the total absorption for bandpasses in the 1 - 2.5 µm regime may be estimated on the basis of the H - K index at one phase point.

During pulsation, both the effective temperature and radius of a Cepheid vary. Since the relative change in radius rarely exceeds 5% in Cepheids (except for the longest period stars), the areal change is only of order 10%. Therefore, the large lightcurve amplitudes observed in the optical are primarily a reflection of the changes in surface brightness during the pulsation cycle, due to the changes in effective temperature. This variation is illustrated in Figure 2, where the relative number of photons at minimum and maximum effective temperature are easily compared. For detection of variation, a short wavelength bandpass such as B or V is indicated, whereas for measurement of mean lightcurve characteristics, a long wavelength bandpass such as I, J, H, or K is advantageous.

Figure 2. In this diagram, the photon spectral density of a blackbody at 6000 K (solid line) and 5000 K (dashed line) is illustrated. These effective temperatures represent the range encountered during the pulsation of a typical 10-day Cepheid. The positions of the B, V, I, J, H, and K bandpasses are indicated. The number of detected photons from sources of these effective temperatures is proportional to the area under the curve for each bandpass. Wider bandpasses and higher quantum-efficiency detectors in the near infrared are particularly advantageous for the cooler and brighter long-period Cepheids. The increased near-infrared flux due to the lower H- opacity is not shown in this diagram.

Other well-known advantages of longer wavelength observation are the smaller total absorption, reduced sensitivity to flux redistribution due to metallicity, and reduced sensitivity to possible photometric contamination by an upper main-sequence companion.

3.3.2 Signal

Earlier, the slowly varying photon spectral density for Cepheid stars was described. If, for the purposes of this discussion, we take it to be constant, then the number of detected photons will vary as the throughput of the atmosphere and telescope optics, the width of the bandpass, and the quantum efficiency of the detector. It is not widely appreciated that the near-infrared is competitive with or superior to, say, the I (0.8 µm) bandpass in each of these respects.

The popular notion is that near-infrared transparency is quite poor. In fact, this is only true between the bandpasses! The total atmospheric absorption in the J, H, and K bandpasses rarely exceeds 0.2 mag and the extinction coefficient is typically 0.04-0.10 mag/airmass for these bandpasses, which is the same range expected for photometry at I. (The near-infrared extinction curves are non-linear, so quoting extinction coefficients alone would be slightly misleading [Manduca and Bell 1979].)

The bandwidths of the J, H, and K filters are typically 0.3 - 0.35 µm, compared to 0.2 µm at I and 0.08-0.10 µm at B or V. Furthermore, the quantum efficiency of thinned CCDs at I is typically 30-35%, whereas quantum efficiencies greater than 60% over the J, H, and K bandpasses can be realized with HgCdTe detectors. The reflectivity of aluminum is 93-96% in the 1.0-2.5 µm region compared to 86% at I.

Optical CCD chips continue to outperform near-infrared detectors in terms of field size, and this optical advantage is likely to remain for the immediate future.

3.3.3 Noise

Far and away the biggest disadvantage for ground-based near-infrared work is the high (and variable) sky brightness, primarily due to emission bands of the OH- radical. The surface brightness of the sky climbs toward the red throughout the bandpasses of interest, being 19.2, 14.8, 13.4, and 12.6 mag arcsec-2 for the I, J, H, and K bandpasses, respectively (CFHT Observer's Manual 1990). Part of the K sky brightness value is undoubtedly due to the emissivity of the telescope optics, so the true K sky brightness may be as low as 14 mag arcsec-2. The V - K color of the night sky has been referred to as the ``Infrared Decade'' (Schechter, private communication). Since the emitting layer for this airglow is at an altitude of about 90 km, it is necessary to go to space to escape its effects. There is a break in the OH- band spectrum in the long wavelength side of the K bandpass, but this is just where thermal emission starts to become a problem. (It is possible that this break could be exploited from a cold site such as Antarctica.)

A second important contribution to the noise in the photometry is crowding of stellar images. The difference between long-wavelength optical and infrared photometry is not substantial with respect to crowding. The K-giant background against which Cepheids will be detected acts as a background having statistical fluctuations due to variations in the number of giant stars per pixel, but is significantly redder (V - K = 3.3) than the variables (V - K = 2.0). The effects of both crowding and sky noise are obviously reduced when the FWHM of the stellar images is small (i.e., good seeing conditions).

3.3.4 Bandpasses of Choice

For the near-field, optical ground-based photometry is likely to remain dominant for the foreseeable future, as a result of the lower sky surface brightness in this regime. However, due to the substantial advantages of the near-infrared (particularly when unconstrained by molecular atmospheric absorption, since a single 1-2.5 µm bandpass could then be used) in terms of number of detected photons, the most distant Cepheid moduli can be obtained in the near-infrared from space - possibly with the NIC second generation HST instrument.

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