STRUCTURE AND FORMATION OF cD GALAXIES: NGC 6166 IN ABELL 2199^*

To distinguish between competing theories about the origin of cD galaxies (Section 8), a particularly powerful diagnostic is their internal kinematics. Does the velocity dispersion profile $\sigma (r)$ increase to the cluster velocity dispersion as one looks farther out into the part of the halo that encompasses many non-central cluster members? Is the systemic velocity of the halo similar to that of the central galaxy or is it similar to that of the cluster as a whole? Are these velocities ever different? This subject has a long history, and partial answers to these questions have been known for several decades.

2.1.1. Systemic Velocities

2.1.2. Velocity Dispersion Profiles

We obtained spectra at three slit positions (Figure 1) along and near the major axis of NGC 6166 with the 9.2 m HET and Low Resolution Spectrograph (LRS: Hill et al. 1998). The slit width was $1\buildrel{\prime\prime}\over{.} 5$, the reciprocal dispersion was 116 km s⁻¹pixel⁻¹, and the resolution expressed as a velocity dispersion was ${\sigma }_{\mathrm{instr}}=125$ km s⁻¹. The slit positions had exposure times of 8 × 900 s ("center," with NGC 6166 centered well inside the slit), 4 × 900 s ("offset" position along the major axis, centered on the bright, elongated galaxy NGC 6166A visible in Figure 1), and 6 × 900 s + 1 × 800 s ("alternate" position offset by 115 from the major axis but on the other side of the center, positioned to miss star and galaxy images). All individual exposures were taken on different nights. The standard star spectrum used is a combination of HD 74377 and HR 2600 which reproduces line strengths of massive elliptical galaxy spectra well and minimizes template mismatch. In any case, the kinematics were measured with Bender's (1990) Fourier correlation quotient method, which is designed to eliminate template bias. Errors were calibrated with Monte Carlo simulations.

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Figure 2 shows an unsharp-masked version of the sum of the best spectra along the central slit position (white line in Figure 1). By dividing out the brightness profile of the galaxy, we can see absorption lines and qualitatively judge S/N from the center out to the largest radii. The strongest lines in NGC 6166, Mg b, Na D, and Hβ, are visible all the way to the companion galaxy on the slit. Even Fe λ 5270 Å and 5335 Å are visible quite far out (see also Figure 3). They are used in Section 6 to measure [α/Fe] overabundance out into the part of the halo where the velocity dispersion is large. Most important, Figure 2 already shows that all lines except Na D get very wide in the cD halo of NGC 6166.

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The Na D line is narrow at all radii and shows little gradient in velocity. It gives a dispersion of ${\sigma }_{\mathrm{Na}\ {\rm{D}}}\simeq 300$ km s⁻¹ at all radii. We assume that the line is produced by interstellar gas and do not include it in the wavelength region from redward of the iron lines to blueward of Hβ that we use for V and σ measurements. Dust is seen near the center in Figure 8. There may be a more smoothly distributed ISM at larger radii, as suggested also by the fact that Hβ absorption in our spectra is significantly weaker than even a very old stellar population would show. However, it is not obvious that its kinematics should be a simple as we measure with the Na D line. Interpretation of this line in the context of the X-ray gas halo of the galaxy is beyond the scope of this paper.

The offset and alternate slit positions yielded poorer spectra. We discard one spectrum taken with too much moonlight, so the alternate slit position has only six good spectra. Of these, one is fainter than normal by ∼14% and two more are fainter by ∼23%, presumably due to clouds. (The observations are queue-scheduled, so we cannot personally monitor the observing conditions. However, we checked that the galaxy was centered on the slit. Seeing is relatively unimportant.)

Offset sky spectra were taken after all NGC 6166 exposures. For the center slit position, these were cleaned of bad pixels and averaged to give high S/N and then used for all sky subtractions. Each spectrum was individually sky-subtracted before the spectra were added. The sky subtraction of the central slit spectra is good (Figure 2). However, for the other two slit positions, most sky spectra could not be used for sky subtraction because too many night sky emission lines changed in strength in the short time between exposures. For the offset sky positions, the sky was measured as far from the galaxy as possible; since even the NGC 6166 end of the slit is far from the galaxy (Figure 1), these sky spectra should be essentially free of galaxy light. However, for the alternate slit position, sky spectra taken from the galaxy images do subtract a little halo light. For this reason—as well as problems with moonlight and with clouds—the alternate slit position does not reach as far out as the primary slit position illustrated in Figure 2. In addition, we found that we got the best results to the largest radii in the alternate slit position by using only the four best spectra.

Figure 3 shows sample spectra for five radial bins in NGC 6166 and for the optimized template star. This binning is used in Section 6 to measure line strengths for the Mg b and Fe lines. Reliable line strength measurements are possible out to the bin at $r=59\prime\prime$. Velocity dispersions are easier—they are measureable for the $r=87\prime\prime$ bin and for several others at large radii in the center, alternate, and offset slit positions.

The summed center, alternate, and offset spectra were reduced with the Fourier correlation quotient program of Bender (1990). This gives velocity V, velocity dispersion σ, the higher-order Gauss–Hermite coefficients h₃ and h₄, and nonparametric line-of-sight velocity distributions (LOSVDs). At some radii near $r\sim -12\prime\prime$ (see Figure 2), the LOSVDs show a main peak at the systemic velocity of NGC 6166 and smaller peak in its wings associated with another of the multiple nuclei. We omitted the corresponding velocity bins from the LOSVD fit. Since neither the center nor the radii where σ starts to climb are affected, this cleaning does not affect our conclusions. However, many published V and σ measurements show contamination from the multiple nuclei.

The instrumental velocity dispersion was measured in our reduced spectra to be ${\sigma }_{\mathrm{instr}}=125$ km s⁻¹, easily adequate for the galaxy dispersions σ ≳ 300 km s⁻¹ studied in this paper.

The kinematics are listed in Table 1 and shown in Figure 4.

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Table 1.  Fourier Correlation Quotient Kinematic Measurements of NGC 6166

Radius	V	$\epsilon (V)$	σ	$\epsilon (\sigma )$	h3	$\epsilon ({h}_{3})$	h4	$\epsilon ({h}_{4})$	S/N
(arcsec)	(km s−1)	(km s−1)	(km s−1)	(km s−1)					(Å−1)
−29.55	−36	17	416	30	−0.080	0.037	0.219	0.037	32
−2.79	−2	3	294	5	0.010	0.011	0.054	0.011	110
−0.97	4	3	298	4	0.012	0.010	0.022	0.010	112
0.43	1	4	301	5	0.037	0.011	0.031	0.011	109
2.04	−3	3	311	5	0.007	0.010	0.050	0.010	116
5.09	4	3	302	5	0.012	0.011	0.053	0.011	111
9.87	−2	5	330	7	0.008	0.013	0.081	0.013	89
16.57	−17	6	362	9	−0.012	0.016	0.106	0.016	75
26.15	−38	13	448	20	0.037	0.026	0.129	0.026	45
37.65	−44	18	495	29	−0.003	0.033	0.144	0.033	36
51.88	−17	36	574	46	0.000	0.057	0.036	0.057	21
66.07	−90	70	732	96	0.003	0.086	0.069	0.086	14
82.62	−49	87	853	76	0.064	0.093	−0.105	0.093	13
106.8	29	118	886	111	0.297	0.121	−0.083	0.121	10
−87.85	−56	285	986	336	...	...	...	...	7
−64.12	−63	86	606	102	...	...	...	...	13
−47.67	−31	45	474	53	...	...	...	...	20
−33.57	−50	23	419	28	...	...	...	...	34
−22.99	−34	16	352	19	...	...	...	...	41
−17.59	−37	14	363	16	...	...	...	...	50
−9.60	−24	7	273	9	...	...	...	...	69
−7.01	−4	7	277	9	...	...	...	...	70
−4.90	−14	7	279	8	...	...	...	...	80
−3.02	−5	5	284	6	...	...	...	...	98
−1.61	−1	7	297	8	...	...	...	...	84
−0.67	4	7	310	8	...	...	...	...	89
0.04	−1	7	307	8	...	...	...	...	85
0.51	−3	7	310	8	...	...	...	...	83
0.98	6	8	299	9	...	...	...	...	74
1.68	7	6	306	7	...	...	...	...	98
3.09	12	5	295	6	...	...	...	...	111
4.97	12	7	286	9	...	...	...	...	72
7.32	15	6	282	8	...	...	...	...	83
105.0	−125	153	841	180	...	...	...	...	11

Note. The columns list radius with negative radius on the NE side of the center, velocity V with respect to the systemic velocity and its estimated error $\epsilon (V)$, velocity dispersion σ and its estimated error $\epsilon (\sigma )$, and the h₃ and h₄ Gauss–Hermite moments of the line-of-sight velocity distribution (LOSVD) and their respective errors $\epsilon ({h}_{3})$ and $\epsilon ({h}_{4})$, and the signal-to-noise ratio for the binned spectrum. When no values of h₃ and h₄ are given, then the LOSVDs were fitted with Gaussians. The first block of results are for the center slit position; the second block is for the alternate slit position; and the third block is for the offset slit position.

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The systemic velocity of NGC 6166 is 206 ± 39 km s⁻¹ higher than the velocity 9088 ± 38 km s⁻¹ of 494 cluster galaxies (Lauer et al. 2014). Here we use our measure of the systemic velocity of NGC 6166, ${V}_{\mathrm{cD}}=9294\pm 10$ km s⁻¹. It is consistent within errors with values in Zabludoff et al. (1993) and in Coziol et al. (2009). Other, inconsistent published measurements may be affected by contamination by the multiple nuclei. Using our ${V}_{\mathrm{cD}}$, NGC 6166 moves at $(0.25\pm 0.05)\sigma$, typical of the values found by Lauer et al. (2014).

If the cD halo consists of tidal debris, then we expect that its systemic velocity should shift toward that of the cluster at the radii where σ rises toward the cluster value. Figure 4 shows that the velocity at large radii does decrease from ${V}_{\mathrm{cD}}$ toward the cluster velocity. The average of the large-radius points is only ∼ −70 km s⁻¹. Still, the inner cD halo of NGC 6166 is more nearly at rest within the cluster than is the central galaxy.

The measurement of the velocity difference between the cD halo and the cluster is more difficult that the measurement that the halo σ is a factor of ∼3 larger than the central σ of NGC 6166. NGC 6166's peculiar velocity is only 25% of the cluster σ, twice as big as the error bars in the V measurements. (The V and σ errors are comparable; see Table 1.) Moreover, some halo stars that are nearest to NGC 6166 may be pulled slightly toward the galaxy velocity. So the V comparison is more difficult and less obviously successful than the σ comparison. But we do see a shift in halo V toward the cluster velocity on both sides of the center. This supports our picture that the halo stars were stripped from many cluster galaxies.

Figure 5 compares our kinematic results on NGC 6166 with published dispersion profiles. Carter et al. (1999) and Kelson et al. (2002) observed much of the rise in σ to the cluster value. However, our observations are the first to reach deep enough to see σ for the intergrated starlight in a cD halo rise all the way to the cluster dispersion in any galaxy cluster.

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The Carter et al. (1999) data are not shown in Figure 5, because they did not publish a table of their results. Their outermost measurements at radii of 30''–36'' are $\sigma \simeq 390$, 361, and 438 km s⁻¹. These are consistent with our results and with Kelson's. (However, Carter et al. 1999 derive velocities that increase as r increases; they interpret this as "modest major-axis rotation." Kelson et al. 2002 also see "systematic rotation [$V/\sigma \approx 0.3$] in the intracluster stars beyond 20 kpc." We do not see rotation; rather, the halo velocity decreases toward the cluster velocity on both sides of the center.)

Tonry (1984, 1985) measured the multiple nuclei of NGC 6166 but did not reach far enough out to see an outward increase in σ. Similarly, Fisher et al. (1995) and Loubser et al. (2008) measured only a slight outward drop in σ in the main body of the galaxy.

Figure 5 illustrates the most important result in this paper: The velocity dispersion in NGC 6166 increases outward to a weighted mean of $\sigma =865\pm 58$ km s⁻¹ for the four data points at $r=83\prime\prime$–$107\prime\prime$. This equals the velocity dispersion $\sigma \;=819\pm 32$ km s⁻¹ for 454 galaxies in Abell 2199 (Lauer et al. 2014). The rise in σ to the cluster velocity dispersion is consistently implied by all three of our slit positions. This result is the strongest evidence that the cD halo of NGC 6166 is made of stars that have been accreted in minor mergers or stripped from cluster galaxies by dynamical harassment.

Our standard picture of the nature of cD halos and the way in which we identify cD galaxies are based in large part on photometry of NGC 6166 and other cD galaxies by Oemler (1976). Oemler's procedures and conclusions were later made quantitative by Schombert, as discussed below. But the iconic, two-component structure suggested by Oemler's photometry of cDs—particularly NGC 6166—firmly cemented in our minds the notion that cDs consist of an elliptical-galaxy-like central body plus a photometrically distinct, shallower-surface-brightness halo that is not present in normal giant ellipticals. Oemler's profile of NGC 6166—augmented by Hubble Space Telescope (HST) photometry to improve the central spatial resolution—is shown in Figure 6.

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The clearly two-humped profile in Figure 6 decisively quantifies Morgan's description of his visual impression of two-component structure. Other cDs in Oemler (1976), in Schombert (1986, 1987, 1988), and in other papers from the same era behave similarly. The picture of cD halos that has been in our minds ever since is made still more concrete using modern profile analysis machinery by decomposing the profile into two Sérsic (1968) functions. Several recent papers have done this and suggested that the inner components are normal ellipticals whereas the cD halos have exponential profiles (Seigar et al. 2007; Donzelli et al. 2011). In fact, the Sérsic–Sérsic decomposition in Figure 6 requires that the cD halo have $n\simeq 0.77$, between an exponential (n = 1) and a Gaussian (n = 0.5) in its outer cutoff. A worrying hint is that the inner profile has n = 1.62, smaller than we have found for any other elliptical (KFCB). Note that, in making this fit, we have been very conservative about excluding the inner, shallow-power-law core (see Kormendy et al. 1994; Lauer et al. 1995, and KFCB for the definition of cores and Gebhardt et al. 1996; Kormendy 1999 , and Lauer et al. 1995 for a demonstration that they are features of the unprojected and not just the projected profiles). We also omit the central active galactic nucleus (AGN) from the fit. About 2/3 of the light of the profile in Figure 6 is in the cD halo.

The ideas summarized above were made more quantitative by Schombert (1988). Schombert (1986, 1987) measured average surface brightness profiles of non-first-ranked ellipticals as functions of galaxy absolute magnitude M_V in seven M_V bins from −17 to −22.5 (he used ${H}_{0}=50$ km s⁻¹ Mpc⁻¹). Schombert (1988) then used these template profiles to define cD galaxies. First, the template profile is found that best matches the inner profile of the candidate galaxy over the largest possible radius range. If this profile fits all of the candidate galaxy to within the scatter seen among the individual profiles that were used to make the template, then this galaxy is an ordinary elliptical. In contrast (Figure 1 in Schombert 1988; cf. Figure 6 here), if the galaxy in question has a giant outer halo above the template profile fitted to the inner parts, then the galaxy is a cD and the integrated difference between its observed profile and the best-fitting template is the cD halo. This definition is similar in spirit to one used by Oemler (1976) but has the advantage of allowing the profiles of ellipticals to depend on luminosity. And it has the virtue of being nonparametric—it does not depend on describing the inner profile with an analytic fitting function.

The profile decomposition shown in Figure 6 is nothing more nor less than Schombert's procedure in parametric form, using Sérsic functions for the inner and outer components. Much experience in recent years has shown that Sérsic functions are excellent fits to elliptical-galaxy profiles (see KFCB for data and review) and hence also to Schombert's template profiles. However:

We find a problem with our canonical picture of cD halos (Section 3.2 ). The photometry shown in Figure 6 is in error. Our composite profile measurements of NGC 6166 are very well fitted by a single Sérsic function at all radii outside the central core. In contrast to our kinematic results, there is no photometric hint of two-component structure.

We have measured the V- and I-band surface brightness profiles of NGC 6166 using CCD images from four ground-based telescopes and four cameras (WFPC1 PC, WFPC2 WF, ACS, and NICMOS2) on HST. Parameters of the images are listed in Table 2. This section discusses the V-band profile.

The central profile is from an HST WFPC1 measurement by Lauer et al. (1995), from our measurement of an HST WFPC2 F555W image (GO program 7265; D. Geisler, P. I.), and from our high-resolution (Gaussian dispersion radius ${\sigma }_{*}=0\buildrel{\prime\prime}\over{.} 32$) V-band image from the Canada–France–Hawaii Telescope (CFHT) Cassegrain camera. The CFHT observing run is discussed in KFCB . The three images give independent V-band zeropoints that agree (fortuitously) to much better than ±0.01 mag arcsec⁻². The three zeropoints have been averaged.

Similar in resolution to the CFHT Cassegrain image is a g image from the CFHT MegaCam. We also include photometry of an r image from SDSS; it is used over a larger radius range to derive the I-band profile in the next subsection, but it is used here to help to tie together small and large radii, and it helps to measure the ellipticity and PA profile. The outer profile is obtained using a g-band image from the Wendelstein Observatory's new 2 m Fraunhofer Telescope and a V-band image from the McDonald Observatory 0.8 m telescope. The latter profile reaches $r=416\prime\prime$, where $\mu =27.28$ V mag arcsec⁻². The V-band profile of NGC 6166 is similar in accuracy and limiting surface brightness to the data in KFCB .

Figure 7 shows the raw profiles. Three kinds of profiles are shown. Most are based on isophote fits as in Bender (1987 ), Bender & Möllenhoff (1987), and Bender et al. (1987, 1988). The algorithm fits ellipses to the galaxy isophotes; it calculates the ellipse parameters surface brightness, isophote center coordinates ${X}_{\mathrm{cen}}$ and ${Y}_{\mathrm{cen}}$, major and minor axis radii, ellipticity , and position angle PA of the major axis. Radial deviations of the isophotes from the ellipses are expanded in a Fourier series in the eccentric anomaly ${\theta }_{i}$,

$$\begin{eqnarray}&&{\rm{\Delta }}{r}_{i}=\underset{k=3}{\overset{N}{\displaystyle \sum }}\left[{a}_{k}\mathrm{cos}(k{\theta }_{i})+{b}_{k}\mathrm{sin}(k{\theta }_{i})\right].\end{eqnarray} \tag{ 1 }$$

The most important parameter is a₄, expressed in the figures as a percent of the major-axis radius a. If ${a}_{4}\gt 0$, the isophotes are disky-distorted; large a₄ at intermediate radii would indicate an S0 disk. If ${a}_{4}\lt 0$, the isophotes are boxy. The importance of these distortions is discussed in Bender (1987, 1988 ), Bender et al. (1987, 1988, 1989, 1994 ), Kormendy & Djorgovski (1989 ), Kormendy & Bender (1996), KFCB , Kormendy (2009), and below.

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Some profiles were measured using Lauer's (1985) program profile in the image processing system VISTA (Stover 1988). The interpolation algorithm in profile is optimized for high spatial resolution, so it is best suited to our high-S/N images of the core of NGC 6166. The isophote calculation is Fourier-based, so it not well suited to measuring the outer parts of NGC 6166, where masking of other galaxies in the cluster results in very incomplete isophotes.

Finally, as discussed further below, we use a major-axis, $(0\buildrel{\prime\prime}\over{.} 2-)$two-pixel-wide cut profile to verify that the ellipse fitting was not adversely affected by the companion galaxies.

Seriously discrepant data in the profiles at small radii (usually because of inadequate spatial resolution) and at large radii (usually because of spatial variations in sky brightness) were pruned out before final averaging. Two additional complications require discussion.

• 1.  
  Three additional cluster galaxies lie in projection close to the center of NGC 6166 (e.g., Minkowski 1961; Burbidge 1962; Tonry 1984, 1985). Profile calculations need to correct for the light of these galaxies. Lauer (1986; see also Lachièze‐Rey et al. 1985) decomposed the four galaxies using ground-based images and concluded that the two large companions are relatively undistorted, consistent with the hypothesis that they are not strongly interacting with NGC 6166. It was already known that the brighter two companions differ in velocity from NGC 6166 by −1520 km s⁻¹ and +570 km s⁻¹ (e.g., Minkowski 1961); these velocity differences are consistent with true separations that are similar to the projected ones, but they do not clearly establish a close physical relationship. We follow Lauer and assume that NGC 6166 itself is not affected by the companions. We therefore calculate its profile by masking out the companions.
• 2.  
  There is patchy dust absorption near the galaxy center. We take this into account next.

Figure 8 illustrates both problems. The top image shows isophotes at average major-axis radii of $7\buildrel{\prime\prime}\over{.} 9$, $11\buildrel{\prime\prime}\over{.} 7$, $18\buildrel{\prime\prime}\over{.} 6$, and $24\buildrel{\prime\prime}\over{.} 9$. Above the center, all contours except the one at $24\buildrel{\prime\prime}\over{.} 9$ are substantially affected by the closest companion. Various strageties were used to correct for the companions. For some profiles, the companions were masked; for others, contaminated pixels were replaced by pixels from the opposite side of the galaxy center. The same strategy was used on the dust contamination; the most reliable results were obtained by interpolating through the dust in the right-hand quadrants and then replacing the most strongly affected pixels in the left quadrants by pixels from the opposite side of the center. All these procedures are somewhat vulnerable, because isophote fitting requires many pixels that need correction. So, as a check on the isophote fitting, we derived a major-axis cut profile along the vertical line in Figure 8. The cut is 2 pixels = $0\buildrel{\prime\prime}\over{.} 2$ wide in the F555W WF image. The lower part of Figure 8 shows that the cut is minimally affected by dust (a few pixels were corrected). More importantly, we used pixels only from the bottom half of the image at radii where the top half is affected by the companions shown and only from the top half of the image at much larger radii where a companion not illustrated in the figure begins to be important.

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Figure 9 shows that the average V-band composite profile is robustly determined. We have enough different data sets with different problems (e.g., non-flatness of the sky brightness) so that agreement among data sets reliably identifies problem points. They are pruned. Near the center, the profiles that are corrected with Lucy–Richardson deconvolution (Lucy 1974 ; Richardson 1972)—i.e., the ones from Lauer et al. (1995) and from the CFHT Cassegrain camera—agree with the much higher-resolution WF profile. In fact, since the V-band cut profile is most free of dust effects, it is used at radii near 1'' in preference to the Lauer et al. (1995) data. (The difference is only a few hundredths of a mag arcsec⁻²—see Figure 11.) Most important: The major-axis cut profile agrees with the isophote fit profiles to ≲0.02 V mag arcsec⁻². The success of this check is important to our confidence in the final profile.

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The average V-band photometry is tabulated in Table 3.

An I-band composite profile is derived in Figure 10, albeit from few sources. We need it primarily as another check of the V-band profile, including the ellipticity and position angle. The central profile and VEGAMAG zeropoint are from an HST ACS F814W image (GO program 9293; H. Ford, P. I.). It helps that dust is less important at I band. However, we can go further: the availability of an ACS F475W image (GO program 12238, W. Harris, P. I.) allows us to make a dust-corrected image, as follows.

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First, the F475W g-band image was rotated and registered to ∼0.2 pixel accuracy with the F814W I-band image. Then a dust-corrected I-band image was derived using the procedure described in Nowak et al. (2008 , Appendix A) and summarized here. In the following, f_g and f_I are the F475W and F814W surface fluxes per square arcsecond; no subscript indicates magnitudes or fluxes as observed, a subscript "0" refers to an extinction-corrected quantity. From the relation,

$$\begin{eqnarray}&&{A}_{I}\equiv I-{I}_{0}=\alpha E(g-I),\end{eqnarray} \tag{ 2 }$$

where A_I is the I absorption and $E{(g-I)\equiv (g-I)-(g-I)}_{0}$ is the reddening in the color $(g-I)$, it follows that:

$$\begin{eqnarray}&&{f}_{I,0}=\displaystyle \frac{{f}_{I}^{\alpha +1}}{{f}_{g}^{\alpha }}\displaystyle \frac{{f}_{g,0}^{\alpha }}{{f}_{I,0}^{\alpha }}.\end{eqnarray} \tag{ 3 }$$

If the stellar population gradient in the inner regions of NGC 6166 is negligible, then ${f}_{g,0}{/f}_{I,0}$ ≈ constant and thus:

$$\begin{eqnarray}&&{f}_{I,0}\propto \displaystyle \frac{{f}_{I}^{\alpha +1}}{{f}_{g}^{\alpha }}.\end{eqnarray} \tag{ 4 }$$

The parameter α is determined by

$$\begin{eqnarray}&&\alpha ={({A}_{g}/{A}_{I}-1)}^{-1}\approx 1.0,\end{eqnarray} \tag{ 5 }$$

where we have assumed a standard extinction curve to obtain the numerical value for the filters considered here (e.g., Savage & Mathis 1979).

The correction is not perfect, because it is based on the assumption that all of the dust is in a screen in front of the image. In NGC 6166, most of the dust is near the middle of the galaxy, in front of only about half of the stars. Then Equation (5) overcorrects for the dust. Better results are obtained if we adopt a smaller value for α (a value of 0 would imply no correction). After some experimenting, we adopt $\alpha =0.6$, which yields the smoothest appearance of the isophotes. Explicitly,

$$\begin{eqnarray}&&{f}_{{I},\mathrm{dust}-\mathrm{corrected}}={f}_{{I},\mathrm{observed}}^{1.6}/{f}_{{g},\mathrm{observed}}^{1.6}\end{eqnarray} \tag{ 6 }$$

The residual dust contamination is small.

Then the brown circles in Figure 10 are derived from the dust-corrected image using Bender's isophote fitting program. The red points are derived using VISTA profile on the dust-corrected image after 80 iterations of Lucy–Richardson deconvolution and after further cleaning of dust as discussed in Section 3.2. These profiles agree essentially perfectly.

A final check is possible using an HST NICMOS2 F160W image (GO program 7453, J. Tonry, P. I.). There is no star in the field of view, so we do not attempt point-spread function (PSF) deconvolution. But dust is essentially unimportant. The core profile calculated from this image also agrees very well with the I-band results, when PSF blurring is taken into account. In particular, the F160W profile confirms that the core profile is cuspier at red wavelengths than it is in V band.

Figure 11 illustrates our Section 3.3 conclusion: The core profile of NGC 6166 is cuspier at red wavelengths than it is in V band. We suggest that the difference is caused by V-band absorption over the entire central arcsec of the galaxy. Clear hints of widespread, low-level absorption are visible in Figure 8.

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It is difficult to measure the power-law cusp slope far inside the profile break radius ${r}_{{b}}=2\buildrel{\prime\prime}\over{.} 41$ (Lauer et al. 2007). The reason is that the nuclear source is spatially resolved and has an unknown profile. Whether it consists of stars or an AGN or some combination, we cannot subtract it robustly. However, the shallowest I-band slope at $r\sim 0\buildrel{\prime\prime}\over{.} 5$ to $1\buildrel{\prime\prime}\over{.} 0$ corresponds to a Nuker function (Lauer et al. 1995) $\gamma \simeq 0.13$. This agrees with $\gamma =0.12$ obtained in Lauer et al. (2007 ; any correction for the nuclear source is not discussed). Previous estimates, $\gamma =0.08$ (Lauer et al. 1995) and $\gamma =0.081$ (Byun et al. 1996), were determined from the Lauer et al. (1995) V-band PC1 profile shown in Figure 11. Our V-band cut profile is even flatter than Lauer's profile—it is less affected by patchy dust—so our composite V-band profile is even less cuspy than $\gamma \simeq 0.08$.

The cuspiness of the central profile affects no conclusions of this paper. But it will be important to use the appropriate, dust-free profile if in future we obtain stellar kinematic data that allow a dynamical search for a supermassive black hole.

Our profile measurements in Figures 9 and 10 do not show the two-component structure that is so obvious in Figure 6. We believe that the Oemler (1976) profile is in error; the most likely reason is the difficulty of correcting for the many cluster galaxies that overlap the cD halo. Modern ellipse-fit software copes more robustly with incomplete isophotes.

A single Sérsic (1968) function fits the complete profile of NGC 6166 outside the cuspy core. Both this result and the Sérsic index, n = ${8.3}_{-0.6}^{+1.0}$ in V band or ${7.8}_{-1.0}^{+1.4}$ in I band, are completely normal for core-boxy-nonrotating ellipticals. Figure 12 compares NGC 6166's profile shape with the sample of elliptical galaxies studied by KFCB . They found that n ranges from 5.4 ± 0.3 to 9 ± 1 for their core ellipticals (red profiles in Figure 12). NGC 6166 is virtually indistinguishable from these galaxies; indeed, many core ellipticals have shallower outer profiles $\mathrm{log}I(r/{r}_{{b}})$ than does NGC 6166. It is especially interesting to contrast NGC 6166 with M87. M87 is by all arguments a more marginal cD than NGC 6166. But a Sérsic fit to its overall profile gives $n={12}_{-1}^{+2}$, larger than $n\simeq 8$ in NGC 6166. Plausible allowance for a cD halo in M87—i.e., exclusion of the outermost profile points—gave a marginally better fit with $n={9}_{-1}^{+2}$, consistent with our fit to NGC 6166 but with only a little extra light in the cD halo of M87. Such a halo is less—not more—obvious in NGC 6166.

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A two-component, Sérsic–Sérsic decomposition is allowed by our data (Section 4), but the fit is not significantly better than the one-component decomposition. There is no reason to believe that we detect two components from photometry alone.

This is a surprising result. We plan but have not yet carried out similar photometry of other cD galaxies. We therefore do not know that the present results on NGC 6166 apply more generally to all cD galaxies. Nevertheless:

We arrive at an ironic situation: The spectroscopy results resoundingly confirm our standard picture that the cD galaxy NGC 6166 in Abell 2199 has an outer halo that consists of debris from member galaxies. The halo stars are dynamically controlled by the cluster, not the central galaxy, and they have the kinematics (i.e., more nearly the systemic velocity and the velocity dispersion) of the other galaxies in the cluster, even when the cD is dynamically colder and in motion with respect to the sea of background stars. But the supposedly much easier task of recognizing the presence of a cD halo from two-component structure in the surface brightness distribution turns out to fail dramatically in the nearest, most prototypical cD galaxy, NGC 6166.

Is it possible to recognize cD galaxies by photometry alone? A photometric technique is desirable, because spectroscopy to look for an outward rise in velocity dispersion is expensive. Our results suggest a partial answer: The cD nature of NGC 6166 can be recognized via quantitative differences in structural parameters and parameter correlations. This helps but is not entirely satisfactory. Parameter distributions for cD galaxies and non-cD ellipticals overlap. There may be physics in this. The physical differences between cDs and core-boxy-nonrotating ellipticals may be smaller than we have thought. Figures 13 and 14 illustrate these points.

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Figure 13 compares the brightness profile of NGC 6166 to the Virgo cluster elliptical galaxies. Radii are plotted in kpc. NGC 6166 has a larger and fainter core than any elliptical in Virgo, including M87. And its outer profile is shallower and it reaches larger radii than that of any elliptical in Virgo, including M87. Quantitatively, the extreme cD NGC 6166 is distinguishable from normal core ellipticals. However, the marginal cD M87 (see KFCB ) overlaps with other core ellipticals in its profile properties.

Figure 14 compares the structural parameters of NGC 6166 with parameter correlations from KFCB and from Kormendy & Bender (2012). These are projections of the "fundamental plane" correlations (Djorgovski & Davis 1987; Dressler et al. 1987; Faber et al. 1987; Djorgovski et al. 1988; Djorgovski 1992; Bender et al. 1992, 1993), between the effective radius r_e that encloses half of the light of the galaxy, the effective brightness ${\mu }_{{e}}$ at r_e, and (in this case) total absolute magnitude.

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NGC 6166 parameters are based on an assumed distance of D = 130.8 Mpc (NASA/IPAC Extragalactic Database "NED" D(Local Group) for cluster Abell 2199 and the WMAP five-year cosmology parameters, Komatsu et al. 2009). NGC 6166 is plotted twice in Figure 14 :

To get the less extreme point, we integrate the brightness and ellipticity profiles (that is, the two-dimensional isophotes) to the outermost data point in Figure 9, i.e., $r=416\prime\prime$ where ${\mu }_{V}=27.28$ V mag arcsec⁻². This gives V = 11.75, ${M}_{V}=-23.86$, ${r}_{{e}}=71\buildrel{\prime\prime}\over{.} 2=45.2$ kpc, and ${\mu }_{{e}}=23.76$ V magarcsec⁻². Galactic absorption corrections are from Schlegel et al. (1998). This point in Figure 14 is consistent with a slight extrapolation to higher luminosity of the correlations for other ellipticals.

The more extreme point is derived by extending the profile to $r\simeq 2000\prime\prime \sim 1.3$ Mpc using the overall Sérsic fit and keeping the outer ellipticity constant at the last observed value. The limiting surface brightness is 30.9 V mag arcsec⁻²; this is an "integration to infinity" similar to those discussed in KFCB . Then V_T = 11.35, ${M}_{VT}=-24.27$, ${r}_{{e}}=162\prime\prime =103$ kpc, and ${\mu }_{{e}}=25.27$ V mag arcsec⁻². Within the scatter, this point is consistent with a larger extrapolation of the correlations for normal ellipticals. It deviates slightly from linear correlations in having larger r_e and fainter ${\mu }_{{e}}$, but slightly curved fits to normal ellipticals would not show NGC 6166 as deviant.

We conclude that NGC 6166 is more extreme than the ellipticals in the combined sample in Figure 14 in the sense expected for a cD: it has larger effective radius and fainter effective brightness. In this sense, the cD structure is recognizable quantitatively in the parameter correlations.

cD and non-cD galaxies overlap in parameter distributions (Schombert 1986, 1987). And yet, the cD NGC 6166 is qualitatively different from non-cD ellipticals, even brightest cluster galaxies. This is important, because cD and brightest cluster galaxies are often considered to be equivalent. But NGC 6166 is surrounded by an immense halo of stars that are controlled dynamically by the cluster potential, not by the central galaxy. Isolated ellipticals cannot have such halos, and observations of velocity dispersion profiles in non-cD core ellipticals show no rise in σ at large radii (e.g., Kronawitter et al. 2000; Proctor et al. 2009; Weijmans et al. 2009; Foster et al. 2011; Raskutti et al. 2014).

We conclude (1) that cD structure is real and distinct from non-cD ellipticals but (2) that it is difficult to recognize the difference photometrically. Extreme structural parameters help (Figure 14). But in less extreme cases—and, to be certain, even in NGC 6166—velocity dispersion data are required to identify cluster halos reliably. The fact that cD classification is difficult is our problem, not the galaxy's.

Are cD halos made of stars that rain out of cooling flows in hot gas (see Fabian et al. 1991; Fabian 1994 for reviews)? This idea was entertained in the heyday of the cooling-flow problem, when we observed large amounts of X-ray-emitting, hot gas in clusters but could not measure temperature profiles. Absent heating processes, hot-gas cooling times near the centers of many clusters and individual galaxies are short. In clusters, 10²–10³ ${M}_{\odot }$ yr⁻¹ of baryons should rain out of the hot gas, presumably by star formation. To escape detection, the initial mass function would have to be truncated above ∼1 ${M}_{\odot }$ (Fabian et al. 1991). We have never directly observed such star formation in any environment (Bastian et al. 2010).

This possibility is now regarded as a non-starter. The main reason is that we now can measure gas temperature profiles, and we find that temperatures decrease only modestly to a floor at ${kT}\sim 1$ keV. In particular, we do not see the strong emission lines from Fe xvii that would be our signal that gas has cooled below 0.7 keV (see Fabian 2012 for review). So the cooling flow problem has morphed into a different question: what keeps the gas hot? At least three heating processes are hard to avoid. Most popular is heating by AGN feedback (Fabian 2012; Kormendy & Ho 2013; Heckman & Best 2014 provide reviews). Also, gas from the cosmological web that falls into objects with masses $M\gt {M}_{\mathrm{crit}}\sim {10}^{12}$ ${M}_{\odot }$ accelerates so much that a shock forms where it impacts the static intergalactic or intracluster medium; this heats the hot gas from the outside inward (Birnboim & Dekel 2003; Kereš et al. 2005; Dekel & Birnboim 2006, 2008). This is an aspect of ${M}_{\mathrm{crit}}$ quenching of star formation. Finally, dying stars eject large amounts of mass into the intracluster medium at the kinetic temperatures of stars in galaxies and galaxies in clusters (e.g., Ostriker 2006). All three mechanisms are likely to be important. In this picture, episodic cooling fuels the AGN and switches it on long enough to allow it to keep the center of the hot gas hot (Fabian 2012). Small amounts of star formation may be connected with these events, and small amounts of star formation are seen in brightest cluster galaxies (e.g., Liu et al. 2012). But no compelling argument suggests that large amounts of star formation occur in clusters at radii where we see cD halos. Also, our observation that the cD halo of NGC 6166 is α element enriched precludes the idea that prolonged, in situ star formation made a significant fraction of the light that we see in the halo.

Do cD halos originate as an integral part of the formation of the central galaxy? For example, could a specialized history of galaxy mergers make both the central and halo parts of a cD galaxy together?

Our phrasing is somewhat different from the question that dominated work on brightest cluster galaxies (BCGs) in the 1970s–1990s (see Tremaine 1990 for a review). Then, the emphasis was on observational hints that BCGs in general (i.e., including but not limited to cDs) are inconsistent with statistical expectations based on the luminosity functions $\phi (L)$ of fainter galaxies in the cluster. If $\phi \propto {L}^{\alpha }\mathrm{exp}(-L{/L}^{*})$ with characteristic luminosity L^* (Schechter 1976), then BCGs with $L\sim 10\;{L}^{*}$ are statistically too bright to be drawn from the populations of other galaxies in the clusters (see Figure 1 in Binggeli 1987 for an evocative illustration). In many papers, cDs and non-cD BCGs were discussed together. Given the observation that cD halos are approximately as bright as or brighter than the central parts of the galaxies (e.g., Seigar et al. 2007), this essentially ensures that BCGs as a class will look especially luminous (Tremaine & Richstone 1977).

As some authors have done since the beginning of this subject, we differentiate between the main bodies of cDs and their halos. In NGC 6166, we separate them operationally as having σ $\simeq \;300$ and $\sigma \;\sim \;832$ km s⁻¹, respectively. How the main bodies of BCGs form and how cD halos form may be separate questions.

When their halos are inventoried separately, it is much less obvious that the main bodies of cDs are unusual enough to imply formation physics that is different from that of other cluster galaxies. The new observations in this paper do not speak strongly to this issue, and we do not discuss it in detail. Ways in which the main body of NGC 6166 is not unusual are the subject of Sections 3.2–3.5. Except for its unusually large and low-surface-brightness core (discussed in the previous section), the main body of NGC 6166 is rather like M87 (a marginal cD) but also like the other giant-core-boxy ellipticals in the Virgo cluster. Quantitative differences (Section 3.6) are mainly due to the cD halo of NGC 6166. However, we note here one additional observation that does imply something special about cD-like galaxies:

Prototypical of a compelling but mysterious phenomenon, M87 has an unusually large number of globular clusters for its galaxy luminosity. Harris & van den Bergh (1981) introduced the specific globular cluster frequency S_N as the number of globulars per unit absolute magnitude M_V = −15 of galaxy luminosity. Measurement of S_N is tricky for many reasons (e.g., galaxy distances are uncomfortably large, so we see less deeply into cluster luminosity functions than we would like), but the conclusion that ${S}_{N}\sim 10$ is factors of several larger for M87 and for some other BCGs (e.g., NGC 1399: Hanes & Harris 1986; Harris & Hanes 1987; NGC 3311: Harris 1986; see Harris et al. 2013 for the most recent summary) has withstood the test of time. The number of globular clusters in NGC 6166 is ${N}_{\mathrm{GC}}=17,000\pm 4000$ (Harris et al. 2013). With respect to the absolute magnitude of the main E-like part of NGC 6166, this implies that ${S}_{N}\simeq 12$. If instead we normalize ${N}_{\mathrm{GC}}$ by the total luminosity including the cD halo, then ${S}_{N}\sim 4$. This is still slightly higher than the canonical number of 1 ± 1 (full scatter for almost all objects) for L^* ellipticals (Harris et al. 2013, Figure 10). In this sense, NGC 6166 is consistent with the behavior of other, similar-luminosity systems (see the Harris paper). As discussed, for example, in Burkert & Tremaine (2010), this is one indication that the early evolution of the objects that later assembled into these BCGs (some of which are clearly cDs and others of which are just giant ellipticals) was already special. This theme of an early, special environment in which NGC 6166 and its cD halo formed was discussed here in Section 7.

Our observations are most consistent with the now favored picture that cD halos are constructed by stellar-dynamical processes that are inherent to cluster evolution. The main body forms by the usual hierarchical clustering and galaxy merging, especially in smaller group precursors to present-day, rich clusters. In the process, violent relaxation splashes some stars to large radii. But the cD halo is added as a result of cluster-related processes such as the stripping of stars off of member galaxies by dynamical harassment and the cannibalism and destruction of dwarf galaxies in minor mergers. This picture was originated by Gallagher & Ostriker (1972) and by Richstone (1975, 1976) and has now been greatly elaborated in many papers, both observational (see the earlier papers on cluster background light and, e.g., Bernstein et al. 1995; Gonzalez et al. 2005; Arnaboldi et al. 2012; Montes & Trujillo 2014) and theoretical (e.g., Dubinski 1998; Murante et al. 2004, 2007; De Lucia & Blaizot 2007; Puchwein et al. 2010; and Cui et al. 2014).

Our observations (1) that the cD halo of NGC 6166 is more nearly at rest in Abell 2199 than is its central galaxy and (2) that this halo has the same velocity dispersion as the cluster galaxies support the idea that it consists of stars that were liberated from cluster members. The high velocity dispersion implies that the cD halo is controlled by cluster gravity. It is only by convention—and not because this is physically meaningful—that we call it the halo of NGC 6166.

On the other hand, the outer parts of NGC 6166 and the ICL merge seamlessly such that the brightness profile outside the central core is well described by a single Sérsic function with index $n\simeq 8$. In this sense, NGC 6166 qualitatively resembles other core-boxy-nonrotating elliptical galaxies such as those studied in KFCB and emphasized in the SAURON/Atlas${}^{3{\rm{D}}}$ series of papers (see M. Cappellari 2015, in preparation for a review). The Sérsic $n\gt 4$ halos of core-boxy-nonrotating ellipticals that are not BCGs manifestly belong to the galaxy:their velocity dispersions generally decrease monotonically outward.

This blurs the distinction between cDs and giant elliptical galaxies. Perhaps they are more similar than we thought. The central puzzle about both kinds of galaxies is why $n\gt 4$. In contrast, many numerical simulations of major mergers of two similar galaxies robustly show that the scrambled-up remnants of the stars that were already present before the mergers have Sérsic profiles with $n\sim 3\pm 1$ (e.g., van Albada 1982; Mihos & Hernquist 1994; Springel & Hernquist 2005; Naab & Trujillo 2006; Hopkins et al. 2009a, 2009b). These are precisely the Sérsic indices observed for coreless-disky-rotating ellipticals, which are thought to be formed in wet mergers during which starbursts grew the central extra light components (see Kormendy 1999 and KFCB for observations and review and Hopkins et al. 2009a for the most detailed simulations).

Maybe the main difference between cDs and core-boxy-nonrotating (but not cD) ellipticals is the degree to which clusters are dynamically old enough to have liberated enough stars from individual galaxies to make a detectable intracluster population. It may also matter whether the large-n halos formed in subgroups such that the central galaxy controls their dynamics or conversely in high-σ, rich clusters at radii controlled by the cluster rather than the central galaxy. An important goal of future work is to explore the reasons why cD galaxies and core-boxy-nonrotating ellipticals look so similar when their halo velocity dispersions point to significant differences in formation histories.