IS THERE A BLACK HOLE IN NGC 4382?^*

Measuring black hole masses precisely requires spectra with high spatial resolution. Thus, most precise black hole mass measurements come from observations using the Hubble Space Telescope (HST), though adaptive optics techniques are showing promise (e.g., Krajnović et al. 2009; Nowak et al. 2010; Gebhardt et al. 2011) and mass measurements using maser observations are ramping up (Kuo et al. 2010). We observed Ca ii triplet absorption from NGC 4382 with the Space Telescope Imaging Spectrograph (STIS) on HST set with the G750M grating and a 52'' × 02 slit. The medium-dispersion grating, as opposed to the low-dispersion G750L grating, is necessary in order to get the spectral resolution high enough to recover line-of-sight velocity distributions (LOSVDs) with sufficient precision. The slit was set at a width of 02 to optimize the signal-to-noise ratio as core ellipticals have relatively low central surface brightness and widening the slit as far as possible allows as short an observation as possible. The slit was positioned along a position angle of P.A. = 48° east of north close to the photometric major axis position angle of P.A. = 30° as determined from HST/Wide Field Planetary Camera 2 (WFPC2) observations (see Section 2.3 below; Lauer et al. 2005; Kormendy et al. 2009). We obtained 16 exposures at five dither positions for a total of exposure of 18,794 s. The STIS CCD has a 1024×1024 pixel format, a readout noise of ${\sim} 1 e^-\ \mathrm{pix{\rm el}}^{-1}$, and a gain of 1.0 without on-chip binning. The spectra spanned a wavelength range of 8257–8847 Å, and our wavelength solutions revealed a reciprocal dispersion of 0.554 Å pixel⁻¹, and the spatial scale was 005071 pixel⁻¹ for G750M at 8561 Å.

The STIS data reduction was done with routines developed for this purpose (Pence 1998; Pinkney et al. 2003) following the standard pipeline: raw spectra were extracted from the multi-dimensional FITS file, and then a constant fit to the overscan region was subtracted to remove the bias level. The STIS CCD has warm and hot pixels that change on timescales of about a day. These pixels require that the subtraction of dark current be accurate, which we accomplished by using the iterative self-dark technique (Pinkney et al. 2003). After flat fielding and dark subtraction, spectra were shifted vertically to a common dither, combined, and rotated. One-dimensional spectra were then extracted using a bi-weight combination of rows. Near the galaxy center, we adopted a 1 pixel wide binning for maximum spatial resolution. These data-reduction methods are similar to those in Pinkney et al. (2003), which the interested reader may consult for details.

LOSVDs were extracted from reduced spectra as described in Gültekin et al. (2009b). Each galaxy spectrum is a convolution of the intrinsic spectrum of stars observed in the aperture with the LOSVD of those stars. We deconvolved the observed galaxy spectrum using the template spectrum composed from standard stellar spectra using a maximum penalized-likelihood method (Gebhardt et al. 2003; Pinkney et al. 2003). We present Gauss–Hermite moments of the extracted velocity profiles in Table 1 and Figure 1. Although it is common practice to communicate velocity profiles with Gauss–Hermite moments, we use LOSVDs binned in velocity space for our modeling described below in Section 3.

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Ground-based velocity information was obtained from archival data using the Spectrographic Areal Unit for Research on Optical Nebulae (SAURON),⁸ an integral-field spectrograph unit mounted on the William Herschel Telescope in La Palma (Bacon et al. 2001). As the SAURON instrument and observations were designed to measure and characterize the internal kinematics of the selected galaxies (de Zeeuw et al. 2002), the data are excellent for our purposes. In its low-resolution mode, the instrument has a field of view of 33 × 41'' with 094 pixels, each of which provides a spectrum with FWHM = 4.2 Å spectral resolution. This spectral resolution corresponds to σ_instr = 108 km s⁻¹ at 4950 Å, near the center of the 4800–5380 Å wavelength range. The data were taken on 2001 March 14 in two pointings, each consisting of four exposures of 1800 s each under FWHM =27 seeing (Emsellem et al. 2004).

The stellar kinematics data are provided as Gauss–Hermite moments for each lenslet position on the galaxy. The Gauss–Hermite moments from each lenslet were converted into LOSVDs. The data from each quadrant of the galaxy were combined into one, changing signs of the odd moments as necessary. We binned the data into four position angles (0°, 20°, 30°, and 70° east of the major axis) with seven radial bins and one position angle (45° east of the major axis) with six radial bins for a total of 34 LOSVDs from ground-based data.

To incorporate errors in the Gauss–Hermite moments in our data set we created 10⁴ Monte Carlo realizations of LOSVDs for each SAURON lenslet. As described in Gültekin et al. (2009b), Gauss–Hermite moments corresponding to unphysical negative values are assigned a value of zero with a conservative uncertainty. For each spatial bin, we took the median LOSVD of all realizations at a given velocity and the standard deviation as the error, which dominated the individual measurement errors. The Gauss–Hermite moments of the LOSVDs are presented in Figure 1 as a function of radius along with our STIS data. These measurements agree well with the ground-based kinematics from Fisher (1997).

The profiles were binned into 13 equal bins in velocity from −500 to 500 km s⁻¹ about the systemic velocity covering the range of velocities measured. Using the ground kinematic data, we compute an effective stellar velocity dispersion, defined as

$$\begin{equation} \sigma ^2_e \equiv \frac{\int _{0}^{R_e} ({\sigma (r)^2 + V(r)^2}) I(r) dr}{{\int _{0}^{R_e} I(r) dr}}, \end{equation} \tag{ 3 }$$

where R_e is the effective radius, I(r) is the surface brightness profile (see Section 2.3 below), and V(r) and σ(r) are the first and second Gauss–Hermite moments of the LOSVD. Using a non-parametric method of integrating the brightness and ellipticity profile, Kormendy et al. (2009) find R_e = 102 ± 6''. From the ground-based velocity profile, we find an effective stellar velocity dispersion of σ_e = 182 ± 5 km s⁻¹.

The high-resolution photometry of the central regions of NGC 4382 comes from WFPC2 observations on HST using filters F555W (V) and F814W (I). The observations, data reduction, and surface brightness profiles (including Nuker profile fits) are detailed by Lauer et al. (2005). Surface brightness profiles are also available at the Nuker web page.⁹ The wide-field data that we use are literature data from ground observations on the 1.2 m telescope of the Observatoire de Haute-Provence with point-spread function (PSF) FWHM =312 originally obtained by Michard & Marchal (1994). The ground data are B-band data, which we have color-corrected with B − V = 0.9, determined by requiring the space data and ground data to match where they overlap in the spatial direction. Figure 2 shows the surface brightness profiles of the space and ground data along with our adopted, combined surface brightness profile for our modeling.

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Since our modeling efforts began, a superior ground-based photometric data set became available (Kormendy et al. 2009). The data come from several different instruments. Inside of 1'', it is the same WFPC2 F555W data that we use. Starting at 1'', the profile is an average of WFPC2 and Advanced Camera for Surveys data as well as two different cameras on the Canada–France–Hawaii Telescope. At the largest radii, the data come from the McDonald 0.8 m telescope, which has a wide field of view. We plot it in Figure 2 for comparison. The agreement inside of R < 15'' is striking. At large radii, there is a small but systematic deviation from our adopted surface brightness profile. This is almost certainly due to the different colors used and is likely evidence of a slight color gradient starting outside of R > 100''. At these large radii, the smaller PSF of the Kormendy et al. (2009) data set does not have a large advantage, and the extremely wide coverage—out to R = 625''—is not used since our kinematic profiles only go out to R = 30''.

The first of these assumptions, constant mass-to-light ratio, is unlikely to be far from reality. Using XMM-Newton and Chandra data, Nagino & Matsushita (2009) study the gravitational potential as revealed by X-ray emission from the interstellar medium, assumed to be in hydrostatic equilibrium and spherically symmetric. Within ~2 kpc, about the outer extent of our data, they find a constant B-band mass-to-light ratio consistent with a potential dominated by stellar mass. Over the range of 02 < r < 10'' (≈0.2–1 kpc) NGC 4382 has a shallow V  −  I color gradient d(V  −  I)/dlog (r) = +0.006  ±  0.003, i.e., growing bluer with decreasing radius, with V − I = 1.108  ±  0.001 at r = 1'' (Lauer et al. 2005). While the sign of the color gradient is unusual, the magnitude is small enough to dismiss worries about changing stellar population in the galaxy.

To quantify the effect of deviations from constant mass-to-light ratio on estimates of black hole mass, we note that when the black hole kinematic influence is barely resolved, M_BH and are anti-correlated (Gebhardt & Thomas 2009; Schulze & Gebhardt 2011). Thus, if there were unaccounted systematic effects such as a radial gradient in , it would increase the uncertainty in M_BH. We can easily estimate the magnitude of the effect since it is linear with . That is, a 30% change in will result in at most a 30% change in M_BH inference. Based on the radial color gradient analysis above, the magnitude of any radial gradient must be small, a couple of percent at most. Thus, the total systematic uncertainty in M_BH is less than a couple of percent.

The second of these assumptions, axisymmetric mass distribution, is potentially violated. Note that the counter-rotating "kinematically decoupled core" (KDC) found in the OASIS data does not necessarily imply deviations from axisymmetry (McDermid et al. 2004). As can be seen from the images of the galaxy (Figures 6 and 7), the change in ellipticity near the center ( = 0.6 at r ≈ 02) to the outer regions ( = 0.2 for r > 1'') may demonstrate that this system is, overall, triaxial (Chakrabarty 2010). Modeling a truly triaxial system requires a triaxial code (van den Bosch & de Zeeuw 2010), but the case for triaxiality is not straightforward because inside of 02, the ellipticity decreases again (Lauer et al. 2005).

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An alternative interpretation of the two-dimensional photometry is that there are two peaks in surface brightness at the center of the galaxy with projected separation 025 (Lauer et al. 2005). Such a double nucleus appears to be similar to the double nucleus in M31 (NGC 0224; Lauer et al. 1993), which Tremaine (1995) explained as the result of a projection of a central eccentric disk of stars that is stable only in the presence of a massive dark object, such as a black hole.

This interpretation is born out in the unsymmetrized STIS spectroscopy (Figure 8). There is a prominent increase in the velocity dispersion at the location of the secondary surface brightness peak R ≈ 04. This would be expected for an eccentric stellar disk.

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An eccentric disk cannot be modeled by our orbit superposition code, which forces axisymmetry. In order to estimate the error introduced by forcing axisymmetry, we compared the mass that would be obtained by treating an eccentric disk as though it were a circular orbit. We use the mass estimator 〈v²_xy〉 averaged over the orbit, where v_x is the line-of-sight velocity and y is the distance from the center of light of the orbit on the sky. This is a suitable surrogate for our modeling. We then compare the value of the estimated mass assuming an elliptical orbit to the mass inferred when assuming a circular orbit with the same semi-major axis. Treating an elliptical orbit as though it were a circular orbit produces an error in the black hole mass that depends on the orbit's eccentricity and orientation. For an eccentricity of 0.60, the error in the black hole mass estimate caused by ignoring the eccentricity varies from −15% to +7%. Orbits with smaller eccentricity produce smaller errors. Given the statistical uncertainties in our M_BH estimate, we can safely ignore this systematic uncertainty.

A consequence of our assumption of axisymmetry is that we are only sensitive to the presence of a black hole at the center of the galaxy. There are two potential issues. The first is whether an existing black hole is located at the center; the second is whether the STIS slit was positioned to allow measurement of any central black hole. We consider both of these.

Because NGC 4382 is a recent merger (see Section 4.3), a relevant question is whether any black hole in the galaxy is located at the center, a requirement for detection with our method. The timescale for a black hole to sink to the center of a galaxy depends on where it starts its descent and in what orbital configuration. In a purely tangential orbit at ~20 kpc, it would take longer than a Hubble time to rest at the center, but a radial orbit at ~100 pc would take less than ~50 Myr. In the most likely case, before the merger, there would be a black hole in the primary galaxy. Following the merger, it is unlikely that it would have traveled farther than ~100 pc, and we can expect any such black hole to be at the center now.

Since the center of NGC 4382 is morphologically complex and we have not found strong evidence for a black hole at its center, it is important to determine that the slit was positioned in such a way that the central kinematics could be determined. From the STIS acquisition camera image (Figure 6), it can be clearly ascertained that it does so. This image comes from the STIS acquisition image taken just before the slit and dispersive element were added. We have subtracted a symmetric model for NGC 4382 in order to show the non-symmetric features. The red box shows the location of the slit, and the red cross shows the center position of the galaxy.

The third of these assumptions, dynamical equilibrium, is the most important. Our analysis, like any dynamical analysis of this kind, does not handle large deviations from dynamical equilibrium. Schweizer & Seitzer (1992) found a high fine structure index in NGC 4382 of Σ = 6.85, defined as

$$\begin{equation} \Sigma = S + \log (1 + n) + J + B + X, \end{equation} \tag{ 4 }$$

where S is a visual estimate of the strength of the most prominent ripples with range S = 0–3, n is the number of detected ripples, J is the number of jets, B is a visual estimate of the maximum boxiness of isophotes, with range B = 0–3, and X = 0 or 1 indicates the absence or presence of an X-structure, respectively (Schweizer et al. 1990).

Lauer et al. (2005) consider NGC 4382 to be an excellent candidate for a recent merger based on its high value of Σ, one of the three-highest non-merging in the Schweizer & Seitzer (1992) sample, the KDC mentioned above, and the galaxy's blue average V  −  I color. Kormendy et al. (2009) note that the strong fine-structure features are also seen in the gri Sloan Digital Sky Survey (SDSS) image and interpret this as evidence that the galaxy has recently merged but has not fully relaxed.

The fine structure index, however, is sensitive to gas-rich minor mergers that are unlikely to disturb the entire galaxy or the central parts of the galaxy from an equilibrium condition. Additionally, fine structure may be a poor measure of recent gas-poor major mergers (van Dokkum 2005; Tal et al. 2009). In the case of NGC 4382, the fine structure appears to be "Malin shells," which can be the result of gas-poor, primarily stellar, mergers (Malin & Carter 1980; Quinn 1984). As a core elliptical this galaxy is expected to be a mostly gas-poor merger (Lauer et al. 2007b; Kormendy et al. 2009).

The virialization time at the center of the galaxy is much shorter than at the outer regions where the Malin shells are at apopause and may persist for ~10⁸ yr so that virialization proceeds from the inside out. It is thus not likely to affect the inner portions of the galaxy important for our study (Navarro 1990). As a final comment on the evidence of recent merger activity, we note that Chung et al. (2009) investigated NGC 4382 for signs of interaction motivated by the ~35 kpc projected distance from NGC 4395. They found no signatures of interaction in H i or other wavelengths.

So, we urge caution against overinterpretation of our kinematics modeling, but for the remainder of this discussion, we take our results at face value while considering their implications.

Resolving the sphere of influence of the black hole is desireable but not necessary for measuring the mass (Gültekin et al. 2009c). As the sphere of influence is more and more poorly resolved, the uncertainties in mass increase until the estimate of black hole mass is consistent with zero or even negative (e.g., NGC 3945, Gültekin et al. 2009b). Using our measured effective velocity dispersion of σ_e = 182  km s⁻¹, the black hole mass predicted from the M–σ relation is M_BH = 8.8 × 10⁷ M_☉. From Equation (1) the predicted sphere of influence for this object at a distance of 17.9 Mpc has radius 013 or diameter 026. The central resolution element of our STIS spectroscopy is 02 across the slit and 005 along the slit. Thus, the projection of the predicted sphere of influence fits entirely inside of the central resolution element. Based on our best-fit mass estimate of M_BH = 1.3 × 10⁷ M_☉, the radius of the sphere of influence is 003 (diameter 006), where the velocity dispersion is 145  km s⁻¹. The diameter of the actual sphere of influence is thus about the size of the pixel but 3.3 times smaller than the slit width. At such low resolution, it is typical to find an upper limit to the mass of the black hole, as we have here. The 1σ upper bound to the black hole mass is M_BH = 6.5 × 10⁷ M_☉, which has a sphere of influence radius 013, the same as the predicted sphere of influence.

Our modeling reveals that the kinematic observations are consistent with no black hole in NGC 4382 at about the 1σ level. If there were, in fact, no black hole in NGC 4382, it would be one of only two early-type galaxies with upper limits on their black hole mass below that predicted by the scaling relations. The other is NGC 3945, but the double bars in that galaxy may prevent reliable black hole mass estimation (Gültekin et al. 2009b). Given that our mass measurement does not completely rule out the presence of a black hole, we consider whether NGC 4382 is a unique object or merely lies along the low-end tail of the distribution of black hole masses for a given host galaxy property.

Based on the M–σ relation (M_BH/M_☉  =  10^8.12(σ_e/200 km s⁻¹)^4.24; Gültekin et al. 2009c), the mean logarithmic black hole mass for a galaxy with σ = 182 km s⁻¹ is log (M_BH/M_☉) = 7.95, corresponding to M_BH = 8.8 × 10⁷ M_☉. The scatter in the M–σ relation is lognormal with standard deviation ₀ = 0.31 ± 0.06 for the population of ellipticals. Taking the scatter into account, the 68% confidence interval of black hole mass is M_BH = 4.0 × 10⁷ to 1.8 × 10⁸ M_☉, which is consistent within our 1σ mass estimate.

To calculate the mass expected from the M – L relation (M_BH/M_☉ = 10^8.95(L_V/10¹¹ L_{☉, V})^1.11; Gültekin et al. 2009c), we must first find the luminosity of the bulge. The total luminosity of the galaxy may be obtained from M_V = −22.54 ± 0.05 (Kormendy et al. 2009) using log (L_V/L_{☉, V}) = 0.4(4.83 − M_V) (cf. Verbunt 2008). Given that we are adopting the more modern classification of E2, this galaxy is "all bulge," and so the luminosity is L_V = 8.9 × 10¹⁰ L_{☉, V}. The mean logarithmic mass for such a galaxy is log (M_BH/M_☉) = 8.89 or M_BH = 7.8 × 10⁸ M_☉. Taking the ₀ = 0.38 ± 0.09 scatter in the relation into account, the 68% confidence interval in mass is M_BH = 3.0 × 10⁸ to 2.1 × 10⁹ M_☉. The lower limit of this range is more than a factor of 2 larger than our 3σ upper limit for the black hole mass. In this sense, the black hole mass is anomalously low.

In order to be consistent with the M–σ relation but low according to the M – L relation, NGC 4382 cannot lie on the mean Faber & Jackson (1976) L–σ relation. In fact, core galaxies with M_V = −22.54 have a mean logarithmic velocity dispersion corresponding to σ = 253 km s⁻¹, compared to our measured value of σ_e = 182 km s⁻¹.

The stellar mass of the bulge is M_* = L_VV = 3.3 × 10¹¹ M_☉. This is consistent with g- and z-band model magnitudes, which give M_* = 4.0 × 10¹¹ M_☉ (Bell et al. 2003; Gallo et al. 2010). Thus, M_BH/M_* = 3.9 × 10⁻⁵ compared to the standard 1.3 × 10⁻³ value (Kormendy & Gebhardt 2001). Using the 3σ upper mass bound, the ratio is M_BH/M_* = 4.2 × 10⁻⁴, still a factor of 3 lower. In Section 4.6, we discuss how our value of _V may be wrong because we do not include a dark matter halo in our modeling, but this is only likely to result in a small (5%–10%) decrease in _V (Gebhardt & Thomas 2009; Schulze & Gebhardt 2010).

Like many other early-type galaxies, NGC 4382 has a flat luminosity core. It has been argued that the cores are scoured out by the inspiral of black holes during galaxy mergers (Begelman et al. 1980; Ebisuzaki & Makino 1995; Faber et al. 1997; Volonteri et al. 2003a, 2003b; Milosavljević & Merritt 2003; Lauer et al. 2007b; Kormendy & Bender 2009). This process ejects stars on elongated orbits and leads to tangentially biased stellar distribution functions (See Figure 5). The galaxy's core can be described by its stellar mass "deficit," the mass in stars ejected from what was previously a power-law profile. The most recent numerical simulations on black hole mergers find that for nearly equal masses, the mass deficit should scale with the total mass of the binary (Merritt 2006), but for mass ratios far from unity, the mass deficit should scale with the mass of the secondary (Sesana et al. 2008).

Kormendy & Bender (2009) included NGC 4382 in their study of the correlations between black hole mass and mass deficits. They estimated M_BH = 1.0 × 10⁸ M_☉ by assuming that it follows the Tremaine et al. (2002) M–σ relation, and they estimated _V = 8.3 by assuming that it follows _V∝L^0.36_V due to Cappellari et al. (2006). Using the photometry from Kormendy et al. (2009), they measured a luminosity deficit of 1.6 × 10⁸ L_{☉, V}. For their assumed values of M_BH and _V, NGC 4382 lies along the same correlation between M_BH and mass deficit as the rest of their sample (roughly M_deficit = 10 M_BH). Using the values for M_BH and _V we measure here, NGC 4382 appears to have a small black hole mass for its core mass deficit, but is consistent at the 1σ level. For our best estimate of the mass, M_deficit/M_BH = 45.6, and for the 1σ upper bound of the mass, M_deficit/M_BH = 9.1. Kormendy & Bender (2009) also found that the ratio of light deficit to total bulge luminosity (L_{V, deficit}/L_V = 1.8 × 10⁻³ for NGC 4382) scales with the ratio of black hole mass to bulge stellar mass. Using their empirical correlation and our measured value of M_BH/M_* predicts a ratio of L_{V, deficit}/L_V = 2.0 × 10⁻⁴. With our 1σ upper bound on M_BH, it predicts L_{V, deficit}/L_V = 1.7 × 10⁻³, consistent with the observed value within the total scatter of the relation. So, it appears that, in sum, the mass of any black hole in NGC 4382 is consistent with M–σ and core scaling properties but low based on M – L.

The low black hole mass does, however, clear up an apparent disparity in nuclear activity. The nuclear X-ray luminosity between 0.3 and 10 keV is less than L_X < 2.7 × 10³⁸ erg s⁻¹ (Sivakoff et al. 2003; Gallo et al. 2010). The core was also not detected in radio, typically considered a proxy for jet activity from an accreting black hole. With an X-ray limit and a radio detection, a black hole mass limit can be estimated (Gültekin et al. 2009a). Very Large Array observations at 8.4 GHz, however, did not detect any core radio emission with a 3σ upper limit of F_core < 0.11 mJy (Capetti et al. 2009). Capetti et al. (2009) note that it is concerning that a galaxy as large as NGC 4382 shows no sign of nuclear activity. Their argument is that, under the assumption that NGC 4382 hosts a M_BH ~ 10⁸ M_☉ supermassive black hole as would be expected from galaxy properties, the absence of nuclear activity in X-ray and radio bands indicates a failure of AGN activity to trace black holes. Even a small amount of ambient gas could produce enough radio emission to be visible for a large black hole. Our black hole mass estimate, however, indicates that it is more likely that NGC 4382 either has no black hole or a black hole that is far undermassive for its host galaxy properties. Therefore, the lack of any nuclear activity accurately traces the small or non-existent black hole in line with predictions for and existing observations of the AGN fraction in Virgo cluster galaxies (Volonteri et al. 2008; Gallo et al. 2008).

Although this work does not unambiguously detect a black hole, the mass-to-light ratio was determined precisely, _V = 3.74 ± 0.10 M_☉/L_{☉, V}, owing to the good coverage and high quality of the SAURON data. Unfortunately, NGC 4382 was not one of the galaxies modeled by Cappellari et al. (2006) so no direct comparison can be made. Note that we do not explicitly include a dark matter halo in our modeling. This is unlikely to affect our black hole mass results on account of the high spatial resolution provided by HST/STIS (Gebhardt et al. 2011). The stellar mass-to-light ratio, however, is likely to be affected by not including this component. While the inferred stellar mass-to-light ratio changed by a factor of 2 when including or omitting a dark matter component in the modeling for M87 (Gebhardt & Thomas 2009), the high spatial resolution in our data sets is likely to result in only a small (5%–10%) decrease in _V (Schulze & Gebhardt 2010). Galaxies with M_V = −22.54 have a mean mass-to-light ratio _V = 6.7 (Lauer et al. 2007a). Based on the scaling relation between _I and stellar velocity dispersion in ellipticals (Cappellari et al. 2006), the implied typical value for a galaxy with σ_e = 182 km s⁻¹ is roughly _V ≈ 5.3. The low value of _V in NGC 4382 compared to established ellipticals suggests ongoing star formation and would be expected for a recent merger.