UNVEILING THE σ-DISCREPANCY IN INFRARED-LUMINOUS MERGERS. I. DUST AND DYNAMICS^*,†

The optical spectra presented here are reanalyzed from the work presented in RJ06a. Briefly, the observations were obtained with the Echellete Spectrograph and Imager (ESI; Sheinis et al. 2002) at the W.M. Keck II 10 m observatory. A 05 slit width was used, with a slit length (spatial axis) of 20''. ESI has a fixed resolution of 36.2 km s⁻¹ or R ∼ 8300. The position angle (P.A.) of the slit was rotated to correspond to the major axis of each galaxy as determined from K-band images. The data were reduced using the Image Reduction and Analysis Facility (IRAF)² developed by the National Optical Astronomy Observatories. The reduction of the data and spectral extraction method used for both the central 1.53 h⁻¹ kpc diameter aperture and multiple apertures extracted along the spatial axis of the galaxy remain unchanged from RJ06a and Rothberg & Joseph (2006b, hereafter RJ06b). A log of the observations can be found in Table 3 of RJ06a. An aperture of diameter 1.53 h⁻¹ kpc was selected to match the size used in P98 and to remain consistent with the works of Jorgensen et al. (1995) and Smith et al. (1995) which brought a large body of spectroscopic data onto a common system.

Once the one-dimensional, flux-calibrated spectra were extracted, the processing differed from that of RJ06a and RJ06b. Observations longward of 0.89 μm are affected by strong H₂O telluric absorption. Telluric corrections were applied to objects with redshifts of z ⩾ 0.02 using normalized spectrophotometric standards with the TELLURIC task in IRAF. σ_○, rotation curves (V(r)), and σ-curves were measured using continuum normalized spectra. The continuum for each object was normalized by fitting a second-order Legendre polynomial to specific wavelength regions, rather than a fifth-order spline3 fit to the entire order (as in RJ06a and RJ06b). Five regions were used for the fitting corresponding to those defined in Cenarro et al. (2001) as continua for the calcium triplet: (0.8474–0.8484 μm, 0.8563–0.8577 μm, 0.8619–0.8642 μm, 0.8700–0.8725 μm, and 0.8776–0.8792 μm). The choice to use specific wavelength regions and a low-order polynomial was made to avoid distorting the shape of the CaT absorption lines. Finally, rather than using IRAF to interpolate over bad pixels caused by imperfect background subtraction, which can also alter the shape of the CaT absorption lines, bad pixel masks were created to be used with the new version of the IDL pixel-fitting routine VELOCDISP used to measure velocity dispersions in RJ06a,b. An error spectrum was also generated for each object and was used in fitting σ. The error spectrum was computed using the variance array generated by IRAF, which takes into account the gain and read-noise of the array, and the polynomial fit used in the continuum normalization.

GNIRS

Near-IR observations centered on the 2.29 μm CO feature were also obtained with the NIRSPEC spectrograph (McLean et al. 1998) on the W. M. Keck II 10 m telescope. Briefly, the observations were made in the echelle mode using a slit width of 0432 (dispersion) and a slit length of 24'' slit (spatial). This gives a resolution of R ≃ 12 km s⁻¹ or R ≃ 25,000. The P.A. of the slit was aligned with the photometric K-band major axis of each galaxy. The reduction of the data and spectral extraction method used for the central 1.53 h⁻¹ kpc diameter aperture remain unchanged from RJ06a. A log of the observations can be found in Table 3 of RJ06a.

Once the one-dimensional spectra were extracted, the processing differed from that of RJ06a. The spectral shape of the data was restored by multiplying the object spectra by a blackbody of T = 9300 K, corresponding to that of an A0V star (telluric standard) using the IRAF task MK1DSPEC. Like the GNIRS data, the continuum was then normalized by fitting a second-order Legendre polynomial to specific wavelength ranges redward of the CO feature. Since the wavelength range of the NIRSPEC data is smaller than that of the GNIRS data, only two continuum regions were used for normalization, 2.2745–2.2775 μm and 2.2885–2.2915 μm. This normalization is different than that employed in RJ06a. In that paper, a first-order Legendre polynomial was fitted over the entire spectrum blueward of the ¹²CO (2,0) band head, including the Mg i absorption feature at 2.2814 μm. The wavelength range used for analysis is λ = 2.274–2.302 μm, which is larger than that used in RJ06a. An error spectrum was generated for each object in the same manner as was done for the ESI and GNIRS observations.

Two sets of additional σ_○ were obtained from the literature to supplement the observations. The first set consists of σ_○,CO for six merger remnants (NGC 3256, NGC 4194, Arp 193, AM 2055 − 425, NGC 7252, and IC 5298) as is noted in Table 5. The second set consists of optical and near-IR σ_○ for the comparison sample of elliptical galaxies, and are listed in Table 6.

In order to reduce possible errors introduced by measurements of kinematic properties made with different aperture sizes, the σ_○ of the comparison sample of ellipticals and σ_○,CO of merger remnants taken from the literature, were corrected to a common aperture diameter of 1.53 h⁻¹ kpc (34 diameter circular aperture at the distance of Coma). This is the same aperture diameter used to measure σ_○ in the merger remnants (and the E0 NGC 5812). As noted in P99, Jorgensen et al. (1995) and Smith et al. (1997) explored aperture effects in early-type galaxies and found that σ scales with aperture size as

$$\begin{equation} {\log \;\frac{\sigma (d)}{\sigma (d_{\circ })} = \alpha \; \log \;\frac{d}{d_{\circ }}}, \end{equation} \tag{ 1 }$$

where the aperture diameter d_○ = 1.53 h⁻¹ kpc and d is defined by

$$\begin{equation} {\it d}\; \simeq \; 1.025\;\times \;2\;{\sqrt{\frac{xy}{\pi }}} \; \times \; {\it n} \end{equation} \tag{ 2 }$$

x and y are the slit width and spectral extraction aperture, respectively, in arcseconds, n is the number of parsecs in 1'' for the galaxy, and α = 0.04 on average. Jorgensen et al. (1995) and Smith et al. (1997) both used this algorithm to attempt to bring spectroscopically derived measurements onto a common system. The same standard aperture of 1.53 h⁻¹ has been adopted here. These corrections were not employed by SG03, nor in RJ06a for literature sources, but are used here. Table 6 shows the corrected σ_○,CaT and σ_○,CO for the comparison sample of elliptical galaxies. The errors shown in Table 6 come from the various sources cited for the kinematic measurements.

Column 8 in Table 7 shows the computed values of log L_IR for the merger remnants and the comparison sample of ellipticals. L_IR is defined as the total flux from 8–1000 μm (see Table 1; Sanders & Mirabel 1996) using the four IRAS passbands (12, 25, 60, and 100 μm). In cases where there is no detection in one or more IRAS bands, the 3σ rms is used for computing L_IR. The sources for the fluxes are listed in Table 7.

Figure 1 shows a comparison between optical (CaT) and near-IR (CO) σ_○ for a larger sample of merger remnants than in RJ06a, including LIRGS (left) and non-LIRGs (center). The overplotted dashed line represents unity (σ_○,optical = σ_○,IR). The figure includes merger remnants which were found to lie on or very close to the FP in RJ06a. Figure 1 also includes a sample of 23 elliptical galaxies (right) to test whether they show any indications of a discrepancy similar to those seen in SG03. The optical velocity dispersions (σ_○,optical) of the comparison sample of ellipticals come from both the CaT and the Mg Ib line (λ ∼ 5200 Å). Table 6 notes which absorption lines are used for each elliptical galaxy. Dressler (1984) and Barth et al. (2002) compared the two different absorption features and found σ_○ matched within the errors. Major differences arose only when there was evidence of star formation in the Mg Ib region.

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Every attempt was made to remove as many systematics as possible which might cause differences between the optical and IR σ_○ for the merger remnants. All of the optical and near-IR observations (2/6 LIRGs, 6/8 non-LIRGs) used the same P.A. for the slit. The slit widths in the dispersion direction were similar (05, 0432, 03 for ESI, NIRSPEC, and GNIRS, respectively). The same 19 template stars were used to derive σ_○ and the extraction aperture (spatial axis) remained the same for all observations. The σ_○ obtained from the literature were corrected to a common aperture size as noted in Section 4.1.1. Unfortunately, the P.A.s most of observations from the literature were not published. The one published P.A. is for AM 2055 − 425, which was −45° compared with −35° used for the CaT observations.

If the optical and infrared are probing the same stellar populations and the same mass profiles, then the slope should be unity, within the observational errors. A double weighted least-squares (dwlsq) fit (Press et al. 1992) has been made to the data to compare with a slope of unity. This method of fitting the data is required because there is no true independent variable. A simple least-squares fit or any variation which assumes independent and dependent variable will not produce a meaningful result, as there is no implied causation between one σ_○ and the other (see Feigelson & Babu 1992 for a detailed discussion). The only underlying assumption is that the slope should be unity if σ_○ for each stellar line is measuring the same thing. Measurement errors for each variable must be taken into account. The dwlsq fits for the data in each panel (left to right) are

$$\begin{eqnarray} \;\;\;{\rm LIRG\;merger\;remnants:}\;\; \sigma _{\circ,{\rm CO}} &=& -0.33^{(\pm 0.10)}\;\sigma _{\circ, {\rm optical}}\nonumber \\ && +\; 208.96^{(\pm 21.40)}, \end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray} {\rm non\hbox{-}LIRG\;merger\;remnants:}\;\; \sigma _{\circ,{\rm CO}} &=& 0.77^{(\pm 0.07)}\;\sigma _{\circ, {\rm optical}}\quad\nonumber \\ && +\; 37.04^{(\pm 17.37)},\; \end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray} \;{\rm comparison\;ellipticals:}\;\; \sigma _{\circ,{\rm CO}} &=& 0.97^{(\pm 0.04)}\;\sigma _{\circ, {\rm optical}}\nonumber \\ && +\; 2.89^{(\pm 11.04)}. \end{eqnarray} \tag{ 5 }$$

The above fits indicate that for elliptical galaxies, σ_○ measured at optical and near-IR wavelengths produce virtually the same result over a wide range of luminosities. Moreover, with the exception of NGC 5812, these observations were made with varying P.A.s and different templates. The LIRGs show a very poor fit, while the non-LIRGs show a smaller, but statistically significant offset from unity. These results strongly suggest that the σ-discrepancy is related to the galaxy type. The result for "pure" elliptical galaxies is important because it confirms what SG03 argued, namely, that the S0's in their sample were the dominant cause for the discrepancy between σ_○,optical and σ_○,CO. The result also confirms more rigorously for the first time, that optical and near-IR σ_○ probe the same dynamics in elliptical galaxies, and can be used interchangeably.

Cox et al. (2006) used numerical simulations to study the kinematic structure of gas-rich, equal mass merger remnants. The simulations included a treatment for radiative cooling, star formation, and feedback from supernovae. Their results showed that the youngest populations had the largest rotation, thus making it possible to identify different aged populations based on V(r). If the CaT and CO are tracking two distinct stellar populations, then their V(r)'s should differ significantly, if they are tracking the same population, then they should match. The deep GNIRS observations allow, for the first time, such a comparison to be made in merger remnants. Figures 2 and 3 show a comparison between CaT and CO derived V(r)'s (Figure 2) and σ as a function of radius (Figure 3) for six non-LIRG merger remnants observed with GNIRS. The filled circles in both figures represent CaT measurements, the open circles in both figures represent CO measurements. The dotted vertical lines in each panel, taken together, represent the width of the 1.53 h⁻¹ kpc diameter aperture used to extract σ_○. A qualitative comparison between the CaT and CO measurements in Figures 2 and 3 suggests that for most of the merger remnants, the CaT and CO track each other closely. The non-LIRG merger remnants show very similar V(r) and σ(r).

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A more quantitative comparison between the CaT and CO measurements was made. A Kuiper two-tailed test was used to quantitatively compare the distributions of the CaT and CO measurements. It is a modified version of the two-tailed Kolmogorov–Smirnov (K–S) test developed by N. H. Kuiper which is sensitive to changes at the tail ends of the distribution (Kuiper 1962; Press et al. 1992). Like the K–S test, the Kuiper test probes the null hypothesis that the two distributions in question arise from the same population. It is a non-parametric test that makes no assumptions about the form of the parent distribution. The only assumption is that the two distributions are continuous. While, the K–S test is useful for detecting shifts in the probability distribution, it has difficulty detecting spreads in the distribution. Such spreads are most noticeable at the tails of the distribution (Press et al. 1992). Both the K–S and Kuiper two-tailed tests require that each distribution have a minimum of four valid data points. The test is used to determine whether the null hypothesis can be rejected within specific confidence levels (Stephens 1970, 1974). In this case, the null hypothesis is that the CaT and CO V(r) and σ(r) match over the same spatial radius for each merger remnant. With one exception (σ(r) in NGC 5018 at the 0.025 confidence level), the null hypothesis could not be rejected in any galaxy for either V(r) or σ(r).

The left panel in Figure 1 clearly demonstrates a σ-discrepancy in LIRGs, while in the center panel, the non-LIRGs show a slight discrepancy. To explore this result further, a new parameter, σ_frac, is defined and will be used for the remainder of the paper:

$$\begin{equation} \sigma _{\rm frac} = \frac{\sigma _{\circ,{\rm Optical}} - \sigma _{\circ,{\rm CO}}}{\sigma _{\circ,{\rm Optical}}}, \end{equation} \tag{ 6 }$$

where σ_Optical = σ_CaT for the merger remnants. Figure 4 is a plot of L_IR versus σ_frac for all of the merger remnants (left) and the comparison sample of ellipticals (right). The symbols in Figure 4 are the same as in Figure 1. The dotted horizontal line in both panels represents σ_frac = 0. The dashed diagonal line in the left panel of Figure 4 represents a least-squares fit to the data. In order to test for the presence of a correlation between L_IR and σ_frac for the mergers and ellipticals, a Pearson Correlation Test was used. This tests the degree of linear correlation between two sets, ranging from r = −1 to +1, (perfect negative or anti-correlation to perfect positive correlation). The results show a correlation coefficient of r = 0.77 for the merger remnants, and r = 0.06 for the ellipticals. Of course, correlation does not equal causation, but it may point at important physical processes which drive the mismatch. A least-squares fit to the data for merger remnants yields

$$\begin{equation} \sigma _{\rm frac} = 0.17^{\pm 0.04}\;{\rm log}\;L_{\rm IR}\; - \; 1.67^{\pm 0.44} \;\;\; ({\rm log}\;L_{\rm IR} \ge 9.5). \end{equation} \tag{ 7 }$$

This provides a method to predict the approximate σ-discrepancy in other LIRGs and ULIRGs.

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SG03 compared the dust masses of their sample of early-type galaxies with the differences in optical and near-IR σ, to test whether the presence of dust was correlated with the differences in σ. While they were unable to find any correlation, they did postulate that the presence of dust around the cold stellar component in S0 galaxies may shield the disk component from detection at optical wavelengths. Figure 5 (top) shows a comparison between σ_frac and the estimated dust mass (M_dust) for the sample of merger remnants (top, left) and elliptical galaxies (top, right). The symbols are the same as in Figure 1. The dust masses were computed using the approximation given in Hildebrand (1983) and Thuan & Sauvage (1992):

$$\begin{eqnarray} M_{\rm dust} ({\it M}_{\odot }) & = & 9.59\;\times 10^{-1} \; S_{\rm 100} \; D^{2} \nonumber \\ && \times \left[\left(9.96\frac{S_{\rm 100}}{S_{\rm 60}}\right)^{1.5} -1\right]\; {\it M}_{\odot }, \end{eqnarray} \tag{ 8 }$$

where S₆₀ and S₁₀₀ are the IRAS flux densities at 60 and 100 μm in Jy, respectively, and D is the distance in Mpc. This equation assumes the far infrared emission originates from dust with an emissivity law ∝ λ⁻¹ at λ ⩽ 200 μm and a temperature derived from the 60 and 100 μm IRAS color, T_d, given by Sauvage (1997):

$$\begin{equation} T_{\rm d} \; = \; \frac{95.94 \,{\rm K}}{\ln \left[(1.67)^{4}\;\frac{S_{\rm 100}}{S_{\rm 60}}\right]}. \end{equation} \tag{ 9 }$$

However, Goudfrooij & de Jong (1995) noted that there is likely a contribution from hot circumstellar dust to the 60 and 100 μm flux from Mira type stars. The corrections to the 60 and 100 μm flux densities are

$$\begin{equation} S_{\rm 60}\; ({\rm Corrected})\; = S_{\rm 60}\; -\; 0.020\; S_{\rm 12}, \end{equation} \tag{ 10 }$$

$$\begin{equation} S_{\rm 100}\;({\rm Corrected})\; = S_{\rm 100}\; -\; 0.005\; S_{\rm 12}, \end{equation} \tag{ 11 }$$

where S₁₂ is the 12 μm IRAS flux density. In cases where there is no detection in one or more IRAS bands, the 3σ rms is used as an upper limit and plotted as such in Figure 5 (top). The diagonal dashed line plotted in Figure 5 (top, left) is a least-squares fit to the data:

$$\begin{equation} \sigma _{\rm frac}\; = \; 0.21^{\pm 0.08}\; M_{\rm dust}\; - 1.06^{\pm 0.48}. \end{equation} \tag{ 12 }$$

Table 7 lists the computed T_d and M_dust for the merger remnants and elliptical galaxies. Thuan & Sauvage (1992) and Sauvage (1997) warn that IRAS is mainly sensitive to dust in the temperature range 25–30 K. M_d will be underestimated if there is a substantial cold dust component (T ∼ 10 K). The elliptical galaxies show practically no correlation. The computed values in Table 7 are presented to give an approximation for the dust temperatures and masses, and are far from absolute. Figure 5 (top, left) shows a moderately strong correlation between M_dust and σ_frac for the merger remnants.

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Figure 5 also shows a comparison between the 1.49 GHz (20 cm) continuum flux densities and σ_frac for the merger remnants (bottom, left) and ellipticals (bottom, right). The 1.49 GHz luminosities are computed using the relation from Yun et al. (2001).

$$\begin{equation} {\rm log} \; {\it L}_{\rm 1.49 \,GHz} \; = \; 20.08 \; + \; 2 {\rm log}\, {\it D} \; + {\rm log}\; S_{\rm 1.49\,GHz}\;\; ({\rm W \,Hz}^{-1}), \end{equation} \tag{ 13 }$$

where D is the distance in Mpc and S is the flux density in Jy. The computed luminosities are listed in Table 7. Yun et al. (2001) demonstrated a linear correlation between the 60 μm luminosity and 1.49 GHz radio luminosity of slope nearly unity. Using data from the IRAS 2 Jy Survey (Strauss et al. 1990, 1992; Fisher et al. 1995) and the NRAO VLA Sky Survey (NVSS; Condon et al. 1998), they derived a method for estimating the SFR from 1.49 GHz flux measurements. Thus, the 1.49 GHz flux can also be used as a proxy for detecting the presence of strong star formation in galaxies with large amounts of dust. The 1.49 GHz flux is most sensitive to stellar populations t < 10⁸ yr (see Condon (1992) for a more detailed review). The computed luminosities in Table 7 are based on measurements from the NVSS or higher resolution surveys for the merger remnants (Condon 1987; Condon et al. 1990; Moellenhoff et al. 1992; Smith & Kassim 1993). Where possible, the higher resolution data are used in Table 7 as noted. The integrated fluxes used to compute L_1.4 GHz for most of the merger remnants were taken from the central regions of the resolved galaxies. The dashed diagonal line in the bottom, left panel is the least-squares fit to the points, given by

$$\begin{equation} \sigma _{\rm frac}\; = \; 0.17^{\pm 0.04}\; {\rm log}\;L_{\rm 1.49 \,GHz}\; - 3.59^{\pm 1.02}. \end{equation} \tag{ 14 }$$

Also shown in each panel of Figure 5 is the Pearson correlation coefficient, which indicates a strong correlation between L_1.49 GHz and σ_frac. The ellipticals show no correlation.

Figure 6 is a two panel figure which shows the I-band FP from Scodeggio et al. (1997; dotted line left panel) and the K-band FP from Pahre et al. (1998b; dotted line right panel). The I-band FP has been corrected to H_○ = 75 km s⁻¹ Mpc⁻¹. Overplotted in both panels are LIRG merger remnants (open circles), non-LIRG merger remnants (filled circles), and the comparison sample of ellipticals (open diamonds). Due to the limitations of available I-band data, the same merger remnants and ellipticals do not appear in both panels. All LIRGs, 20/23 ellipticals, and 3 non-LIRG merger remnants (NGC 4194, NGC 5018, NGC 7252) are overplotted on the I-band FP. The left panel in Figure 6 presents the position of merger remnants on the I-band FP for the first time.

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Qualitatively, the difference between the location of LIRGs on the I- and K-band FPs is striking. The LIRGs show virtually no offset from the I-band FP and have a dynamic range similar to that of the elliptical galaxies. Yet in the K band, the LIRGs are clustered together and offset from the FP. Most non-LIRGs show less deviation from the FP in both panels, with the exception of two remnants (NGC 4194 and NGC 7252) on the K-band FP.

Quantitatively, the mean of the residuals (ΔFP), or average offset, of the LIRG merger remnants from the I-band FP is −0.05 dex, compared with −0.58 dex for the K-band FP. The non-LIRGs have an average offset of 0.02 dex in the I band and −0.28 dex in the K band. Excluding the two outliers, NGC 4194 and NGC 7252 in the K band, reduces this to −0.17 dex. These two merger remnants have the brightest L_IR of the non-LIRGs. For comparison, the average offsets of the ellipticals from the I-band and K-band FP are −0.004 and −0.07 dex, respectively. Figure 7 plots the I-band (top) and K-band (bottom) FP residuals (ΔFP) against L_IR for the merger remnants (left) and elliptical galaxies (right). The Pearson correlation coefficient was used to test whether a relation exists in any of the four panels. The only strong correlation is an anti-correlation between the K-band ΔFP and the L_IR of the merger remnants. The more IR-luminous the merger remnant, the larger the offset from the FP. A least-squares fit to the data yields

$$\begin{equation} \Delta {\rm FP}_{\rm K}\;= \; -0.25^{\pm 0.04}\;{\rm log}\; L_{\rm IR}\; +\; 2.29^{\pm 0.52}\;\;\; ({\rm log}\;L_{\rm IR} \ge 9.5). \end{equation} \tag{ 15 }$$

The best-fit line is shown in Figure 7 (dashed line in bottom left panel). This fit should provide an estimate of the offset of a LIRG/ULIRG from the K-band FP for objects lacking kinematic or photometric observations. The effect is not seen in ellipticals at either wavelength nor in merger remnants in the I band. The negligible anti-correlation seen in the I-band panels is driven by one point in both plots.

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Figure 8 presents the FP in a different projection, separating the photometric and kinematic observables. The top panel is the I-band FP and the bottom panel is the K-band FP. The symbols are the same as in Figure 1. The advantage of this projection is that it directly compares the distribution of optical and infrared σ_○ along the x-axis. Again, this shows the clustering of the LIRGs in the K band, while at I band, the merger remnants show a dynamic range similar to that of the elliptical galaxies along the FP. Moreover, the "pure" I-band and K-band FP presentations of the properties of the merger remnants in Figures 6 and 8 explain the apparent contradiction between the results in RJ06a and earlier IR studies. The properties of the merger remnants plotted on the K-band FP in RJ06a are a "hybrid" of K-band photometry and optical σ_○. In the case of elliptical galaxies, combining optical σ_○ and K-band photometric properties makes little difference, but for IR-bright merger remnants, the differences are significant.

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The results presented in the previous section suggest that the distributions of both mass and luminosity of (primarily) LIRG merger remnants derived from K-band observations are different when compared with those of elliptical galaxies, yet are similar to those of elliptical galaxies when derived from I-band observations. While the presence of young stellar populations has been known for some time to affect the observed luminosities of merger remnants in the near-IR, they also influence the kinematic properties measured in the near-IR. Figure 9 shows a comparison between M and M/L in the I band (left) and K band (right) for the merger remnants and elliptical galaxies. The symbols are the same as in Figure 1. The vertical dotted line in both panels indicates the mass of an m* galaxy. The masses shown in Figure 9 are total virial M_dyn of each galaxy calculated using

$$\begin{equation} {\it M}_{\rm dyn} = \kappa \; {\frac{\sigma _{\circ }^2 \; r_{\rm eff}}{G}} \end{equation} \tag{ 16 }$$

(Proveda 1958; Fish 1964; Rood et al. 1972; Tonry & Davis 1981; Binney 1982; Bacon et al. 1985; Richstone & Tremaine 1986; Mathews 1988; Bender et al. 1989), where r_eff is from a de Vaucouleurs profile fit and G is the gravitational constant. The constant κ used is 6.0 (Michard 1980), rather than the canonical 9.0, which assumes σ does not vary over the galaxy. Michard (1980) showed that κ actually varies as a function of geometry, inclination, observational factors, and rotational component. Taking into account the use of σ_○ and the spread of such values in elliptical galaxies, Michard (1980) concluded that a value of κ = 6.0 is most appropriate. The total L in the I and K bands are extrapolated using 〈μ〉_eff and assuming a de Vaucouleurs profile. Thus, the total light is 2π 〈I_eff〉 R_eff² (Binney & Merrifield 1998; Milvang-Jensen & Jørgensen 1999). Neither is corrected for extinction.

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In the I band, the M_dyn of the merger remnants span nearly the same range as the elliptical galaxies. Almost all of the mergers have masses ∼ several-m*, while at K band there is a clear bifurcation between LIRGs and non-LIRGs, with the exception (again) of NGC 4194 and NGC 7252, which have the brightest L_IR of the non-LIRGs. The LIRGs straddle the m* line in the K-band panel, while the non-LIRGs overlap with the elliptical galaxies. A Kuiper two-tailed test was used to test whether the distributions of the properties of the merger remnants and elliptical galaxies are similar. The null hypotheses tested in this section are that the I-band and K-band properties (M/L and M_dyn) of the merger remnants and elliptical galaxies come from the same population. In the I band, the null hypothesis cannot be rejected for any comparison between LIRG or non-LIRG merger remnants and the elliptical galaxies. In the K band, the null hypothesis cannot be rejected when comparing the properties of non-LIRG merger remnants to elliptical galaxies. However, in the K band, the null hypothesis can be rejected at the 0.01 confidence level for LIRG and elliptical M_dyn and at the 0.15 confidence level for LIRG and elliptical M/L.

Figure 9 also compares the evolution of M/L at I band and K band for a single-burst population using the stellar population models from Maraston (2005, hereafter M05). A single-burst model was selected based on numerical simulations of Mihos & Hernquist (1996) and because the sample selection criterion of a single (coalesced) nucleus indicates that the major burst has already occurred or is ongoing. Gas-rich mergers may undergo smaller bursts due to earlier tidal passages and interactions, but the spiral response of the disks to interactions is not very effective at driving gas to the center. It is during the final coalescence that the bulk of the gas is funneled to the barycenter of the merger, producing a peak in the SFR 1–2 orders of magnitude more than the pre-interaction rate over a timescale of ∼50 Myr.

The vector in each panel includes the age of the population at a given M/L. The vectors reflect changes only in M/L, not mass, and their positions in Figure 9 do not reflect any information about mass. The "twists" present in both (but strongest at K band) reflect real double values in M/L at certain ages. The model shown assumes solar metallicity and a Salpeter initial mass function (IMF). Changing from solar to either half or twice solar metallicity causes only a slight shift (<0.1 dex) up or down in M/L at both wavelengths. Using a Kroupa IMF shifts the M/L vector down by 0.3 dex and shrinks the "twist" slightly in the K-band vector at t ∼ 0.2–0.4 Gyr.

Stellar population models from M05 were selected due to the starburst nature of merger remnants. The models in M05 are particularly sensitive to the presence of RSGs and thermally pulsing AGB (TP-AGB) stars. These populations contribute significantly (as much as 90% depending on metallicity) to the total near-IR luminosities of the starburst. The models include the presence of important molecular bands such as CN, TiO, C₂, H₂O in addition to the CO band heads. The presence of these bands can significantly affect M/L, colors, inferred stellar masses and ages. While the M05 models are not perfect in their ability to reproduce observed stellar populations, careful comparisons show them to provide significantly better matches than other available models in the near-IR for young populations.

The models reveal that in the I-band the M/L's of the merger remnants (both LIRG and non-LIRG) are dominated by stellar populations older than 5 Gyr. As noted above, they are statistically indistinguishable from the M/L of the elliptical galaxies. In the K-band, the same bi-modal distribution of the merger remnants seen in the FP figures appears here. The LIRGs (along with NGC 4194 and NGC 7252) have M/L consistent with a young starburst population (40–200 Myr) or an AGB/post-starburst population (400 Myr–1.5 Gyr). Because the luminosities have not been corrected for extinction, the age estimates should be viewed as qualitative comparisons only. More sophisticated age-dating of the stellar populations using a combination of stellar absorption and nebular emission lines will be presented in Paper II.

Figure 10 compares the M/L in I band (left) and K band (right) with σ_frac for the merger remnants (top) and elliptical galaxies (bottom). The symbols are the same as in Figure 1. In this figure, the σ-discrepancy is compared with M/L to test for a correlation using the Pearson correlation coefficient. No correlation exists for the elliptical galaxies at either wavelength. In the I band the LIRGs and non-LIRG remnants show no correlation. At K band, the merger remnants show a strong anti-correlation between M/L_K and σ_frac. Separating the two merger remnant populations gives a Pearson coefficient of −0.38 (moderate) for the non-LIRG merger remnants and −0.70 (strong) for the LIRGs. The dashed line in the upper left panel is the least-squares fit to that data:

$$\begin{equation} \sigma _{\rm frac}\; = \; -0.35^{\pm 0.10}\; {\rm log}\;\frac{M}{L_{\rm K}}\; + 0.05^{\pm 0.05}. \end{equation} \tag{ 17 }$$

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Figure 11 shows a comparison between the I-band and K-band surface brightness profiles of nine merger remnants from the sample: six are LIRGs and three are non-LIRGs. The profiles in Figure 11 were measured using elliptical isophotes, holding only the position of the nucleus fixed, allowing all other parameters to vary. The filled circles are the new I-band HST data, the open circles are K-band data first published in RJ04. Overplotted on each point are the 1σ errors. The data are plotted as a function of radius^1/4. The straight dashed diagonal lines are the de Vaucouleurs r^1/4 fits to the profiles. RJ04 established for the remnants shown in Figure 11 that their K-band profiles were well characterized by a de Vaucouleurs light profile. The I-band profiles are also well characterized by a de Vaucouleurs profile. The facts that both the non-LIRG and LIRG merger remnants follow r^1/4 profiles over large dynamic ranges and large spatial scales (well beyond 10 kpc in radius) in both the I and K bands and show evidence of strong tidal tails and shells, demonstrates that these objects are the products of major mergers (i.e., progenitor mass ratios between 1:1 and 4:1).

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The profiles of NGC 2623, Arp 193, AM 2055 − 425, and IC 5298 show a divergence between the I band and K band at radii ⩽ 1 kpc. The I- and K-band profiles of NGC 4194 and NGC 7252 run more or less parallel and are well fitted by an r^1/4 profile. NGC 7252 shows some evidence of an upturn or "excess light" in the I-band light profile at small radii, similar to the K-band discovery for other merger remnants in RJ04. However, the K-band data for NGC 7252 do not probe as far inward as the I-band data, so it may be possible that the K band shows the same or stronger upturn. However, at large radii, the I and K profiles are nearly parallel. NGC 5018 has nearly parallel I-band and K-band profiles. The results from NGC 1614 and NGC 3256 are less clear, but the latter does show a significant divergence beginning at r ∼ 2 kpc, and narrowing at smaller radii.

Another way to characterize the merger remnants is to compare the structural parameters in the I and K bands. The parameters a₄/a, , and P.A. are measured for each isophote as a function of linear radius, is shown in Figure 12 for the nine remnants. Overall the I-band and K-band structural parameters are very different from each other. With the exception of NGC 5018, the I band shows large variations in a₄/a, but very little variations in and P.A., whereas the K band shows evidence of twisty isophotes and large variations in ellipticity. The K-band shapes appear to be predominantly disky in the central regions (positive a₄/a). NGC 5018 shows little or no variation for a₄/a and P.A., however, does show a discrepancy within the central 1 kpc, and then a slight discrepancy at r > 10 kpc. NGC 7252 shows little variation between the I band and K band for the a₄/a and parameters, but the P.A.'s are very different. Figure 12 may indicate some structural evolution. NGC 5018 and NGC 7252 are the most advanced merger remnants shown; the latter is the last merger in the Toomre Sequence (Toomre 1977). These two merger remnants show less deviation between their I- and K-band structural parameters than the other merger remnants, consistent with their being in a transitional stage between mergers and ellipticals.

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Figure 13 plots (I − K) as a function of linear radius. The (I − K) values shown are derived from circular isophotes rather than the elliptical isophotes used to generate the surface brightness profiles shown in Figure 11. The choice to use circular isophotes to measure (I − K) profiles is based on the results in Figure 12. Nearly all of the remnants in Figure 12 show different I-band and K-band shapes. Thus, the shape of each elliptical isophote at I and K band is different, which means each isophote is measuring different spatial regions in the galaxy. The (I − K) color constrains information on both stellar and dust distribution.

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Figure 13 shows a large (I − K) gradient at the centers of the merger remnants (radius ⩽ 1 kpc). At larger radii, the (I − K) color decreases for almost all of the mergers and approaches (I − K) = 1.99, which is the observed color in typical elliptical galaxies (Smith et al. 1997; Pahre et al. 1998a). The exception to this result is NGC 5018, which shows a nearly constant (I − K) ∼ 3, dropping only slightly at large radii.

Moving from one-dimensional color profiles to two-dimensional spatial maps of the central regions provides further insight into the activity occurring within the central regions of the merger remnants. Figure 14 shows (I − K) spatial maps of the central 10 kpc (diameter) for the nine merger remnants with I- and K-band data. The grayscale of each image has been calibrated to reflect the observed (I − K) values. To the right of each image is a grayscale bar showing the range of (I − K) values for each remnant. Over-plotted in each box is a rectangle representing the slit size and P.A. used to extract the σ_○,CaT. The CO slit widths for NGC 1614, NGC 2623, and NGC 5018 are slightly narrower (043, 043 and 03, respectively). The P.A.s of slits used for CO observations of NGC 3256, 4194, Arp 193, and IC 5298 are unknown. The P.A. and slit width used for the 1.6 μm CO observations of AM 2055 − 425 (Genzel et al. 2001) are also shown (dotted box). As noted earlier, the P.A. of the slits was aligned with the major axis of the galaxy as determined from K-band imaging. In some cases, this does not appear to line up with the structure seen in the (I − K) maps. The images in Figure 14 show strong, discrete structure in the central regions, compared to more uniform colors at radii ∼5 kpc. In some cases, there appears to be face-on spiral structure (NGC 1614, NGC 3256, NGC 7252, and IC 5298). NGC 5018 shows the same uniform colors seen in the one-dimensional profiles of Figure 13, with the exception of some dust lane structure near the nucleus. Arp 193 shows either a bar or edge-on disk which is bright in the K band but nearly invisible in the I band. The structures seen in NGC 2623, NGC 4194, and AM 2055 − 425 are less clear, but nonetheless indicate very red (I − K) colors in the central kiloparsec.

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The (I − K) color profiles shown in Figure 13 indicate the largest values are centered on the nuclear regions <1–2 kpc. The (I − K) colors are listed in Table 8. In this section, the (I − K) colors of the merger remnants are compared with stellar population models from M05 to attempt to constrain the ages of the central stellar population and the effects of dust. Figure 15 is a color–magnitude diagram (M_K versus (I − K)) for apertures of 1.53 h⁻¹ kpc in diameter, corresponding to the same spatial size as the σ_○ measurements. The dash-dotted line in both panels represents the evolution of a solar metallicity burst population assuming a Salpeter IMF from M05 with M = 10⁹ M_☉ (top) and M = 10¹⁰ M_☉ (bottom). Overplotted are the LIRG (open circles) and non-LIRG (filled circles) merger remnants. Also shown are extinction vectors for a foreground dust screen using the values from He et al. (1995) and mixed (dust and stars) from Thronson et al. (1990); Hunt et al. (1997). Ideally, Figure 15 can be used to estimate both the ages and mass of the central stellar population. A young burst (t < 20 Myr) would suggest a central mass ∼10⁹ M_☉, while an older burst (20 Myr < t < 1 Gyr) would imply a central mass ∼10¹⁰ M_☉. A factor of 10 in the mass of the burst population corresponds to a change of 2.5 mag in M_K. Thus, the lower limit to M_burst is 10⁹ M_☉, because M_K of the merger remnants would be brighter than a model with a smaller M_burst. Neglecting the theoretical prediction that the mass in the central few kpc is likely to reside in a rotating disk, the total mass budget within the central 1.53 h⁻¹ kpc can be estimated using σ_○,CaT from Table 5, assuming an isotropic velocity dispersion:

$$\begin{equation} {\it M}_{\rm dyn} \;=\; 2.32\;\times \;10^{5} \; \times \;{\it R}\,({\rm kpc})\; \times \sigma ^{2}_{\circ }\,({\rm km \; s}^{-1}) \; {\it M}_{\odot }, \end{equation} \tag{ 18 }$$

where R = 0.765 kpc (radius of the measurement of σ_○) and G is shown in galactic units. This gives an upper limit on the mass (neglecting extinction) of the merger remnants of M ∼ 10¹⁰–10^10.3 M _☉, because M_K of the merger remnants would be fainter than a model with a larger M_burst. This would be the total M_dyn within the central 1.53 h⁻¹ kpc, which would include young and old stars. Using this overestimate of the mass would still mean that the burst population is ⩽1 Gyr. Again, this leaves the LIRG merger remnants and NGC 4194 and NGC 7252 (two of the three non-LIRG remnants plotted in Figure 15) with ages consistent with either RSG or AGB stars. This range in starburst mass in merger remnants is consistent with the starburst masses estimated by Shier & Fischer (1998) for their sample of LIRGs.

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The (I − K) colors of the merger remnants are redder than the evolutionary tracks of the model. The reddest (I − K) colors occur for the young populations at 10 Myr and 0.9 Gyr, and for the older populations of ellipticals at around 10–15 Gyr. The Δ(I − K) between 10 Myr and 0.9 Gyr is 0.19, and between 0.9 Gyr and 15 Gyr is 0.22, which is negligible compared with the differences between the observed central colors of the merger remnants and the reddest colors attained in the starburst model. This implies that significant, albeit varied, reddening is present.

Figure 16 compares Δ(I − K), the change in (I − K) color between the central 1.53 h⁻¹ kpc diameter aperture and the last measured (I − K) isophote in the surface brightness profile of each merger remnant (the last plotted point in Figure 13), with σ_frac. The figure depicts the change in color due to the effects, primarily, of dust as a function of radius versus the σ-discrepancy. The Pearson correlation coefficient is also noted in Figure 16, and indicates a moderate correlation. The overplotted dashed line is a least-squares fit to the data:

$$\begin{equation} \sigma _{\rm frac}\; = \; 0.20^{\pm 0.03}\; \Delta (I-K)\; + 0.003^{\pm 0.003}. \end{equation} \tag{ 19 }$$

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In Section 5.2.2 and Figure 9, M/L_I and M/L_K were compared with population models to try to age-date the dominant populations in the central regions of the merger remnants. At K band, the mergers, in particular the LIRGs, were found to have M/L suggestive of significantly younger populations than at I band. However in Section 5.3.1 and in Figure 15, the effects of extinction were found to dominate the central I − K colors of the mergers. In this section, the near-IR colors are compared with the empirical colors of stars and stellar population models in an attempt to better constrain the populations in the central regions. Figure 17 is a (J − H) versus (H − K) color–color plot showing the non-LIRG (filled circles) and LIRG (open circles) merger remnants. The (J − H) and (H − K) colors for the merger remnants are listed in Table 8. The left panel compares the near-IR colors of merger remnants with empirical values of (J − H) and (H − K) of stars (Bessell & Brett 1988; Elias et al. 1985; Guandalini & Busso 2008). The right panel compares the merger remnants with a stellar population model from M05. The models show the evolution of a solar metallicity burst population, assuming a Salpeter IMF. The difference between solar and half or twice solar metallicities is that the latter tracks show no dispersion in (H − K) between 10 Myr and 1 Gyr. The "V"-shape of the tracks between those ages collapse to a single track and the (H − K) colors are indistinguishable at those ages. Overplotted on the stellar model in both panels are various ages of the populations. Also shown in both panels are extinction vectors for a foreground dust screen using the values from He et al. (1995) and mixed (dust and stars) from Thronson et al. (1990) and Hunt et al. (1997).

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The central aperture IR colors of the LIRGs place them beyond both the models and observed colors of RGBs and RSGs, but within the scatter of observed AGB stars. Mixed dust extinction is consistent with RSG intrinsic colors for the LIRGs, whereas a foreground dust screen is generally not. The IR colors of the non-LIRG merger remnants are much closer or overlap with the observed colors of stars. Several non-LIRGs align with the M05 model where the post-starburst (t > 1 Gyr) stellar populations reside.

Neither the empirical stellar tracks, nor the M05 model in Figure 17 appear capable of clearly identifying the ages or stellar types of the populations within the central 1.53 h⁻¹ kpc aperture. In general, the near-IR colors of the merger remnants are redder than the model or the observed colors of stars, although there is overlap with empirical observations of AGB stars for all of the mergers in Figure 17 (left). Based on the models of integrated colors, significant mixed extinction is suggested by the observed near-IR colors. Without an independent estimate of the extinction (and type of extinction), it is difficult to age-date the nuclear regions satisfactorily using only broadband JHK photometry. In addition, active galactic nuclei (AGNs) are known to have red IR colors, thus the contribution of an AGN might affect the broadband IR colors shown in Figure 17. However, it is unlikely that these mergers contain Type I (unobscured) AGNs. Neither the I- nor the K-band images show strong, bright central QSO-like point sources which overwhelm the host galaxy, typical of objects like Mrk 231 or Mrk 1014 (see Appendix A). Moreover, the ¹²CO band heads at 1.6 and 2.29 μm have EWs similar to red giants and in the case of the LIRGs, EWs akin to RSGs or AGBs (see forthcoming Paper II for further discussion). The presence of Type I AGNs is accompanied by strong non-thermal near-infrared continuum emission, resulting in weak EWs (e.g., Ridgway et al. 1994; Goldader et al. 1995; Oliva et al. 1999). This is not seen in the sample, nor are very broad hydrogen emission lines (v ⩾ 500 km s⁻¹) present. Spectroscopy should be able to resolve these issues clearly in three ways: (1) use specific spectral features, both absorption and emission, to age-date the populations; (2) use hydrogen emission lines and [Fe ii] (if present) to effectively constrain the amount of dust present; and (3) assess the presence of relative contribution of an AGN to the near-IR flux. Such spectroscopic analysis will be presented in Paper II.

If the central regions of the merger remnants are dominated in the IR by a star-forming, rotating stellar disk, this should also be reflected in the K-band isophotal shapes. The a₄/a parameter can be used to determine whether isophotes are disky (positive a₄/a) or boxy (negative a₄/a). Figure 18 compares the average a₄/a value within the central 1.53 h⁻¹ kpc with σ_frac (top) and the radio luminosity at 1.4 GHz (bottom). The average a₄/a value within the central 1.53 h⁻¹ kpc for each merger remnant is listed in Table 8. The top panel in Figure 18 demonstrates a weak correlation (r = 0.24) between disky isophotal shape and σ_frac. As the K-band continuum appears to be dominated by RSGs or AGBs for the merger remnants with largest σ_frac, this suggests these stars exist in a disky structure.

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The bottom panel in Figure 18 shows the a₄/a parameter plotted against L_1.4 GHz measured in a diameter of 1.53 h⁻¹ kpc. The horizontal line in this panel denotes the difference between radio loud and radio quiet emission. The merger remnants show a moderate correlation of r = 0.40, between L_1.4 GHz and a₄/a. The outlier is NGC 5018, which is rather radio quiet relative to other remnants (Moellenhoff et al. 1992). Excluding NGC 5018 (lower right point in bottom of Figure 18) increases the Pearson correlation coefficient to a strong correlation of r = 0.73. The 1.4 GHz emission plotted in Figure 18 is compact and measured within a region similar in size to that of the σ_○ observations and on roughly the same scales as those of theoretical predictions for disk formation. The presence of disky isophotes and its correlation, shown in Figure 18, with radio power are consistent with the presence of strong star formation occurring within a central disk.