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Appendix A: Impact of crowding and photometric errors

In this section, we briefly discuss the major biases and sources of errors in our photometric analysis that could potentially affect the results.

Appendix A.1: Crowding and blending

Since the Spitzer-IRAC pixel size is relatively large (~1.2′′ pixel^-1), it is possible that more than one star actually falls in it. Hence blending due to crowding is an obvious worry near cluster centers. However, as discussed in Origlia et al. (2010), our approach of combining the relatively low-resolution IRAC photometry with high-resolution near-IR photometry (in some cases also supported by HST photometry) has been designed to minimize this problem.

In fact, the most common cases of two relatively bright giants falling within the 8 μm PSF, thus potentially mimicking spurious dusty stars, should be easily identified in the higher resolution near-IR images. Hence, to avoid any spurious detection of color excess due to blend, for each candidate dusty star in the surveyed GCs, we directly inspected a 5″ × 5′′ high-resolution and deep K band sub-image centered on it. If we identified star(s) within the PSF and with comparable brightness (well within an order of magnitude, the exact value depending on their distance from the target) at 8 μm as well as in the K band (given that stars with pure photospheric emission have (K − 8)₀ ≈ 0), the target star was rejected as a dusty candidate and not included in the final samples of dusty giants shown in Figs. 2 and 3. In addition, in a few suspect cases we performed the same procedure using HST images in the F814W band, as already done in Origlia et al. (2010). This provides the most solid evidence that the IR excess is not due to blends.

As stated in Sect. 4, we performed artificial star experiments to estimate the degree of completeness of our Spitzer and near-IR catalogs. These experiments have also been used to evaluate the fraction of expected blending due to crowding (either cluster or field stars), from a statistical approach. We found that this fraction is always below 5%, and in agreement with the values estimated by the direct inspection of high-resolution near-IR and HST images.

Appendix A.2: Unresolved background

We emphasize that the main source of background noise in the Spitzer images of our GCs is neither zodiacal light (also tabulated in the header of the fits images) nor unresolved galaxy emissions, but, as a matter of fact, unresolved stellar light (a few to several times the zodiacal light at 8 μm and fully dominant at shorter wavelengths). In the observed clusters, zodiacal light at 8 μm ranges between 4 and 8 el s^-1 (i.e., between 5 and 10 MJy sr^-1, in perfect agreement with the very recent estimates by Krick et al. 2012)⁵, while the unresolved stellar background ranges between 10 and 40 el s^-1. These background levels correspond to Vega magnitudes ranging between 11.5 and 13.5 at 8 μm. The large majority of the stars sampled in our survey are still brighter than the background, especially those we target as candidate dusty stars, and only the lower RGB sequence in the most distant clusters is fainter than the unresolved background. However, even these fainter stars are always many times brighter than the background noise. The PSF fitting procedure we used (see Sect. 2) also provides a local estimate of the background level, hence possible contamination and local variations by diffuse light is accounted for and automatically subtracted from the computed instrumental magnitudes.

Appendix A.3: Photometric errors

To properly quantify the photometric errors, we define the S/N as the ratio between the signal of the star in el s^-1 (background subtracted) and the square root of the total (star+background) signal in el s^-1, multiplied by the square root of the on-source integration time (in sec). In all clusters, the faintest stars that we measured always have S/N> 15 and those with color excess always have S/N> 100 in all Spitzer bands. This implies that pure dust emission (which is always >30% of the total light at 8 μm) has always been detected at S/N> 30 and we can thus firmly exclude that the 8 μm flux in excess of the photospheric emission is due to background fluctuations. In summary, we obtain that random photometric errors of the stars we reliably measured are always less than 10% (i.e., <0.1 mag) in all Spitzer bands. Such relatively small random errors are not surprising, given that the final on-source integration time in each filter of our Spitzer observations has been quite long, ranging between 1000 and 2700 s. Our complementary near-IR photometry also has very small (typically <0.03 mag) random errors (see Valenti et al. 2004, 2004b, 2007 for details). Zero points calibrations in both the near-IR and Spitzer bands are uncertain by a few percent.

Appendix A.4: 47 Tuc: a test-bench target

An optimized photometric reduction and overall random errors well below <0.1 mag both in the near- and mid-IR bands are mandatory in order to safely detect small color excesses. A clear example of how large photometric uncertainties in both pass-bands can lead to misleading results is offered by the case of 47 Tuc. Indeed, our finding of dusty stars down to about the HB level Origlia et al. (2007, 2010) has been questioned by McDonald et al. (2011) and Momany et al. (2012). However, an accurate comparison of the datasets has shown that their claims were mostly a consequence of an insufficient accuracy of their near- and mid-IR photometry.

In fact, the photometry by McDonald et al. (2011) has larger photometric errors at any given magnitude than that presented in Origlia et al. (2010). Indeed, by comparing the CMDs in Figs. 1 and 2 of Origlia et al. (2010) with the CMDs in Fig. 12 of McDonald et al. (2011), one can clearly see that the color scatter in the latter is significantly larger than in the former. Moreover, McDonald et al. (2011) made an extensive use of 2MASS photometry in the inner region, which is less accurate and likely affected by blending because of its lower resolution than the data used by Origlia et al. (2007). In fact, by comparing the K-band and 8 μm photometry for a subsample of candidate dusty stars in common between Origlia et al. (2007) and McDonald et al. (2011, see their Fig. 13), one finds that 8 μm photometries differ by about +0.1 mag only, while K-band photometries differ by about −0.3 mag, implying average 0.2 mag = bluer (K − 8)₀ colors for the dusty stars in McDonald et al. (2011). This indicates that the main discriminant between the two analyses is the K band, not the Spitzer photometry. The bluer K − 8 colors and the overall larger errors of McDonald et al. (2011) photometry largely prevent the detection of color excesses (a few tenths of a magnitude) as measured by Origlia et al. (2007).

Similar arguments apply to the Momany et al. (2012) photometric survey of 47 Tuc using the mid-IR imager VISIR at the VLT. While VISIR has an optimal, high spatial resolution, unfortunately its sensitivity is insufficient to probe small color excesses along the RGB in GCs. Indeed, Fig. 3 and Table 2 of Momany et al. (2012) show that about two magnitudes below the tip their photometric error rapidly increases from 0.1

up to 0.3 mag. Such errors are comparable with (at 1−2σ level) if not exceeding, the majority of color excesses measured by Origlia et al. (2007). This is not surprising, in fact even at an 8 m-class telescope and with the use of narrow band filters, the thermal background is still so high and variable that it is very difficult to obtain accurate, deep photometry from the ground (as required for this scientific goal) compared to a space facility like Spitzer.

© ESO, 2014