The Globular Cluster M 80
3.3 The Observations and Data Analysis
3.3.1 The Ultraviolet Data
The UV survey described in Dieball et al. (2010) and Section 3.1 required a single, deep image for each filter, so individual images taken using each filter were com-bined to give master images. By contrast, the individual images were needed to search for variability. For the variability study, a total of 48 FUV images were used, all obtained using the ACS in the Solar Blind Channel (SBC). These consisted of 32 images taken with the F165LP filter in four consecutive orbits, and one orbit (eight images) with each of the F150LP and F140LP filters. A further eight images were taken in one orbit using the F250W filter with the ACS/HRC. The images were all taken at the same pointing. Table 3.7 gives an overview of the UV data.
The 32 F165LP images, obtained within a 5.5 hour period, were used in the search for variable sources. Any source that was detected in enough images to be reliably investigated for variability should have been detected in the master image, meaning that source detection was not necessary; I was able to simply use the cat-alogue created using the master images, as described in Section 3.1.2. I used the FUV source catalogue as input to daophot (Stetson, 1991) running under IRAF in order to perform photometry on each individual F165LP image. The same param-eters as described in Section 3.1.2 were used, but I kept the position of the input coordinates fixed (rather than using recentring routines).
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For each source I derived a reduced χ2 value relative to a constant brightness model. Theχ2value evaluates how well set of measurements matches the expected values. It is given by
where Oi is an observed value,µ is the expected or model value,σi is the error on the measured value and n is the number of degrees of freedom. In this case,µ is the weighted mean of the source’s magnitude measurements,σiis the error given in the daophot output, and n= (number of measurements − 1).
In principle, this value reflects the likelihood that a source’s magnitude does not change over the 32 measurements. However, the photometric errors produced by daophot (σ in the equation above) tend to be overestimated for faint sources and underestimated for bright sources. As shown in Figure 3.9, this causes the reduced χ2 value to decrease monotonically towards fainter (mean) magnitudes, as the photometric error increases. One cannot, therefore, simply assume that any source with a reducedχ2value above a certain limit must be varying.
Instead, I compared the reducedχ2value for each source to its mean FUV mag-nitude (see right panel of Figure 3.9) and looked for sources whoseχ2 was signifi-cantly larger than that of other sources of comparable brightness. The red line in the right panel of Figure 3.9 indicates theχ2values above which I expect to find 0.1%
of sources (for simplicity, this selection line was produced by assuming that theχ2 value at a given magnitude is Gaussian distributed), equating to 2 expected outliers in the catalogue of 2345 sources. There were three sources which had χ2 values higher than this line, and these sources are highlighted in Figure 3.9. As shown in the left panel of Figure 3.9, the photometric errors of these sources (red points) give no indication that they are remarkable compared to other sources of similar brightness. The χ2 value, at least for sources 2234 and 2324, are not exceptional compared to the catalogue as a whole; it is only when one plots theχ2value against magnitude that they begin to stand out. The three outlying sources were investi-gated in further detail, along with two previously known variable sources, T Sco (see Section 3.1.5.1) and DN 1 (Section 3.1.5.2). Table 3.8 gives their positions and magnitudes, and, in Figure 3.10, the parts of the master FUV and NUV images that include the five sources investigated in this section are shown.
One of the outlier sources, TDK 1, showed the strongest evidence of brightness variations. Figure 3.11 shows the FUV image of TDK 1 when it is brightest (left) and faintest (right).
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Figure 3.9: Left: the photometric error increases towards fainter magnitudes. In-set: the three variable sources (red points) do not appear to be remarkable in the plot of magnitude versus photometric error. Right: reduced χ2 value for each source in the FUV catalogue, compared to its mean magnitude. The most signif-icantly variable sources are highlighted. Note that χ2 was determined using the actual magnitudes (in STMAG), but they are plotted on a log scale. The blue line shows the medianχ2 in the magnitude bins of width 0.5 magnitude. The red line indicates the cut-off; sources above this line were investigated for variability. Also marked (cyan points) are the two known variable sources, T Sco and DN 1.
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Figure 3.10: Portion of the combined FUV (top) and NUV (bottom) image show-ing the five variable sources discussed in this section. North is up and East is to the left.
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Table 3.8: Positions of the variable sources TDK 1, 2 and 3, as well as DN 1 and T Sco. The first column is the source name, followed by the FUV ID number. Columns 3 and 4 give the source position in RA and DEC coordinates. Columns 5 to 8 give the FUV and NUV magnitudes and corresponding photometric errors as derived from daophot. Column 9 gives the ID number of the optical counterpart taken from Piotto et al. (2002), followed by the optical magnitudes (as reported by Piotto et al. 2002) in columns 10 and 11. Note that the magnitudes given are calculated from the master image in each filter and are thus subject to variability intrinsic to the source.
1 2 3 4 5 6 7 8 9 10 11
ID IDFUV RA DEC FUV σFUV NUV σNUV IDpiotto Bpiotto Vpiotto
[hh:mm:ss] [deg:mm:ss] [mag] [mag] [mag] [mag] [mag] [mag]
1 2817 16:17:02.104 -22:58:29.23 18.209 0.014 18.045 0.005 2710 16.217 16.360 2 2238 16:17:02.164 -22:58:33.24 19.981 0.032 19.703 0.011 2172 19.015 19.028 3 2324 16:17:02.861 -22:58:32.65 18.593 0.016 17.403 0.003 1450 16.594 16.226 DN 1 1387 16:17:02.176 -22:58:38.59 22.578 0.120 21.869 0.055 * * * T Sco 2129 16:17:02.818 -22:58:33.94 15.444 0.005 19.247 0.008 * * *
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Figure 3.11: The variable source, TDK 1, at the brightest (left) and the faintest (right) that was seen in the FUV observations. North is up and East is to the left.
Note that the difference in brightness shown between the left and right images is an underestimate of the actual variation: the high state magnitude is an underes-timate of the peak brightness, due to a gap in the data at this point; the low state magnitude is not the true low state, as the source was still growing fainter when this observation occurred.