Initial Mass Function Variation in two Elliptical Galaxies using Near-Infrared Tracers
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Initial Mass Function Variation in two Elliptical Galaxies using Near-Infrared Tracers
R. Elliot Meyer, Suresh Sivanandam,
1, 2 and Dae-Sik Moon Department of Astronomy & Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON, M5S 3H4, Canada Dunlap Institute for Astronomy & Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON, M5S 3H4, Canada (Received 2019 January 15; Accepted 2019 March 19)
Submitted to ApJABSTRACTUsing integral field spectroscopy, we demonstrate that gravity-sensitive absorption features in thezJ-band (0.9–1.35 µ m) can constrain the low-mass stellar initial mass function (IMF) in the cores oftwo elliptical galaxies, M85 and M87. Compared to the visible bands, the near-infrared (NIR) is moresensitive to light from low-mass dwarf stars, whose relative importance is the primary subject of thedebate over IMF variations in nearby galaxies. Our analysis compares the observed spectra to thelatest stellar population synthesis models by employing two different methods: equivalent widths andspectral fitting. We find that the IMF slopes in M85 are similar to the canonical Milky Way IMF witha median IMF-mismatch parameter α K = 1 .
26. In contrast, we find that the IMF in M87 is steeperthan a Salpeter IMF with α K = 2 .
77. The derived stellar population parameters, including the IMFslopes, are consistent with those from recent results in the visible bands based on spectroscopic andkinematic techniques. Certain elemental abundances, e.g. Na and Fe, have dramatic effects on theIMF-sensitive features and therefore the derived IMF slopes. We show evidence for a high [Na/H] ∼ I absorption features. The high Na abundancemay be the result of a recent galactic merger involving M85. This suggests that including [Na/H]in the stellar population model parameters is critical for constraining the IMF slopes in M85. Theseresults confirm the viability of using NIR absorption features to investigate IMF variation in nearbygalaxies. Keywords: galaxies: elliptical and lenticular, cD, galaxies: evolution, galaxies: abundances, galaxies:stellar content, stars: luminosity function, mass function INTRODUCTIONThe functional form of the initial mass function (IMF)has far reaching implications in our understanding ofthe stellar component of galaxies, galaxy formation andevolution, and in the interpretation of observed galac-tic properties. It has been traditionally assumed thatthe IMF of extragalactic stellar populations follows thesame functional form as measured in the Milky Way(MW) (Salpeter 1955; Kroupa 2001; Chabrier 2003;Bastian et al. 2010). Recently, measurements of theIMF in early-type galaxies (ETGs) have called this as-sumption into question (van Dokkum & Conroy 2010;
Corresponding author: R. Elliot [email protected]
Treu et al. 2010; Spiniello et al. 2012; Conroy & vanDokkum 2012b; Cappellari et al. 2012; La Barbera etal. 2013). These studies have suggested that the IMFbecomes increasingly ‘bottom-heavy,’ meaning a largerfraction of low-mass ( < (cid:12) ) stars, in ETGs with highercentral velocity dispersions ( σ v ), higher alpha elementabundances ([ α /Fe]), or increasing metallicity ([Z/H])(Mart´ın-Navarro et al. 2015). This variation has alsobeen measured in the bulges of some massive spiralgalaxies (Dutton et al. 2013; Parikh et al. 2018).There are two general methods that have beenadopted to constrain the IMF of unresolved stellarpopulations. The first method relies on either galac-tic dynamics (e.g., Cappellari et al. 2012; Li et al. 2017)or gravitational lensing (e.g., Treu et al. 2010; Smith,Lucey, Conroy 2015; Collier, Smith, Lucey 2018) to a r X i v : . [ a s t r o - ph . GA ] M a r constrain the galactic mass and therefore the stellarmass-to-light (M/L) ratio. These measured (M/L) arethen compared to those derived from stellar populationmodels to infer a mass excess that would be indica-tive of a variable IMF. The second method uses severalsurface-gravity sensitive absorption features (e.g. Na I µ m, Ca II Triplet 0.86 µ m, Wing-Ford band (FeH)0.99 µ m) along with stellar population synthesis (SPS)to fit the IMF directly from the integrated galaxy spec-trum (e.g., van Dokkum & Conroy 2012; Spiniello etal. 2012; La Barbera et al. 2013; Alton, Smith, & Lucy2017; Zieleniewski et al. 2016). Both these methodshave independently found evidence for IMF variationsin galaxies, strengthening the overall argument for theexistence of some effect. However, different studies haveidentified discrepancies between the IMFs measured forparticular galaxies (Smith 2014), on the existence ofIMF variation (Smith & Lucey 2013; Smith, Lucey,Conroy 2015), or the cause of the variation (La Bar-bera, Ferreras, & Vazdekis 2015). Reconciling thesediscrepancies requires additional confirmation based onevidence from new or expanded methods.Constraining the IMF using gravity sensitive featuresis enticing as it directly probes the galactic stellar popu-lations. They help break the degeneracy arising over therelative contribution of dwarf and giant stars with sim-ilar effective temperatures to the integrated light. Ab-sorption features, however, are highly sensitive to stellarpopulation parameters such as age, star formation his-tory, and elemental abundances (Conroy & van Dokkum2012, hereafter CvD12a). This requires either additionalfeatures, full spectral modelling, or broader spectral cov-erage to more reliably constrain these population param-eters.A majority of studies that have employed SPS have fo-cused on using absorption features in the visible bands(up to 1.0 µ m). Few studies have extended further intothe NIR, with notable exceptions (e.g. Alton, Smith, &Lucy 2017, hereafter ASL17). There are advantages toexploring the NIR, relative to the visible bands, for usein constraining the IMF, including its increased sensi-tivity to light from faint, low-mass dwarfs. The spec-tral intensity of M dwarfs, which tend to dominate thestellar mass of galaxies regardless of the shape of theIMF, peaks in the range of 0.8–1.2 µ m (Rajpurohit etal. 2013). In addition, a significant percentage of thelight emitted by late type M dwarfs, i.e. M ≤ . (cid:12) , isemitted in the NIR. According to the CvD12a models,there are numerous gravity-sensitive absorption featuresin the zJ-band (0.9 – 1.35 µ m) that vary by 1% or morebetween a Kroupa (MW-like) and bottom-heavy IMF.These features are: the Wing-Ford band (FeH) at 0.99 µ m, a Ca I line at 1.13 µ m, a Na I line at 1.14 µ m, a K I Doublet at 1.17 µ m, a K I line at 1.25 µ m, and a Al I line at 1.31 µ m.In this paper we present a pilot study on constrainingthe IMF of nearby ETGs using the above set of zJ-bandgravity sensitive features. For this, we observed the in-nermost cores of two nearby ETGs. Recent spatiallyresolved studies of nearby ETGs have found indicationsthat the IMF slopes in these galaxies vary radially (Sarziet al. 2017; van Dokkum, Conroy, Villaume, et al. 2016;La Barbera, et al. 2016; Mart´ın-Navarro, La Barbera,Vazdekis, et al. 2015). These studies suggested thatthe bottom-heavy IMF may be localized in the cores ofmassive ETGs while the IMF becomes more MW-like atlarger radii. Galactic cores are, therefore, ideal locationsfor investigating variations in the IMF. We compare ourobserved spectra to the latest version of the Conroy &van Dokkum (2012) models (Conroy et al. 2018, here-after C18). Our analysis adopts two standard methods:equivalent width (EW) measurement and spectral fittingbased on a Markov Chain Monte Carlo (MCMC) tech-nique, and we conduct a detailed comparison betweenthe results from the two methods.This paper is organized as follows: we provide thedetails of our observations and data reduction proce-dure, the measured equivalent widths, the MCMC simu-lations, and discussion in § § §
4, and §
5, respectively,followed by a summary and our conclusions in § OBSERVATIONS AND DATA REDUCTIONWe chose two galaxies, M85 and M87, from the vanDokkum & Conroy (2012) (hereafter vDC12) targetsample that were shown to have highly contrasting, cen-tral IMFs. Selected parameters for the targets can befound in Table 1. Conroy & van Dokkum (2012b) (here-after CvD12b) concluded that M85 has a MW-like IMFwhile M87 has a Salpeter type. M87 has also been thesubject of IMF variation analysis using SPS in ASL17and Sarzi et al. (2017) and dynamical modelling in Old-ham & Auger (2017), all of which have found a Salpeter-like or steeper IMF. Furthermore, these two galaxies areon opposite ends of both the IMF– σ v and IMF–[ α /Fe]distributions in CvD12b. They are therefore suited asexemplary targets for observational analysis of stellarpopulations with contrasting IMFs.2.1. Observations
We carried out seeing-limited, integral field spectro-scopic observations of M85 and M87 with the Near-Infrared Integral Field Spectrometer (NIFS; McGregoret al. 2003) on the 8-meter Gemini North Telescope aspart of the
GN–2015A–Q–47 programme. M85 was ob-served on May 8th, 27th, and 30th, 2015 while M87 wasobserved on June 2nd and 5th, 2015. The observationswere made using the zJ–filter and both the z-band (0.94–1.15 µ m) and the J-band gratings (1.15–1.33 µ m), re-spectively. This provided an effective spectral coverageof 0.94–1.33 µ m. These bands have spectral resolvingpowers in the range of ∼ ∼ (cid:48)(cid:48) × (cid:48)(cid:48) mapped by 29 image slices, anda pixel scale of 0. (cid:48)(cid:48)
103 and 0. (cid:48)(cid:48)
04 across and along theslices, respectively.The targets were observed with a repeated target–sky–target nodding sequence. The z- and J-bands for M85 aswell as the J-band for M87 were observed for 8 × × × × Data Reduction
The obtained NIFS data were primarily reduced usinga suite of python / iraf reduction scripts provided bythe standard Gemini NIFS pipeline. The pipeline scriptsperform flat fielding, sky subtraction, spatial distortioncorrection, wavelength calibration, and spectral cubeextraction. Additional data processing such as atmo-spheric absorption (telluric) correction and uncertaintyestimation were accomplished with custom python rou-tines.Atmospheric absorption in the galaxy spectra was cor-rected for using the spectrum of a A0V telluric star ob-served at a similar airmass as the galaxy observations.Before being applied to the galaxy spectrum, the tel-luric star spectrum was first corrected for intrinsic A0Vstar absorption features, such as the strong Paschen se-ries lines, following the method outlined in Vacca et al.(2003). This method employs a template Vega spectrumthat is scaled to match the observed A0V star absorp-tion features.In order to remove the telluric features from the galaxyspectra, the telluric standard spectrum was aligned withthe respective galaxy spectrum using 7 telluric regionsthat appear in both spectra. This was necessary as thewavelength solutions provided by the NIFS pipeline werenot precise enough for the atmospheric features to bealigned across the observed bandpass. The telluric fea- tures were then removed by dividing the galaxy spectraby the corrected telluric standard spectrum.The Na I µ m feature is located in a region ofstrong telluric absorption at the end of the NIFS z-band.The above telluric correction method was repeated onthis feature in isolation so as to further reduce the effectsof atmospheric absorption on the feature profile.M87 has a strong, central active galactic nucleus(AGN) that likely contaminates the measured absorp-tion features (Alton, Smith, & Lucy 2017; Sarzi et al.2017). Two strong emission features were identified inthe final M87 spectrum: a [S III ] + P (cid:15) feature at ∼ µ m, and a weaker [Fe II ] feature at ∼ µ m. The [Fe II ]feature intersected with the K I µ m feature in theEW index measurement bands. It was removed fromthe M87 spectrum with a gaussian profile fit; however,the residual effects significantly reduced our confidencein the measurement of the K I µ m feature. Wetherefore excluded this feature from our analysis of theobserved M87 spectrum.In addition to the line emission, continuum emissionfrom the AGN also likely contaminated the observedM87 spectrum. ASL17 used Hubble observations ofM87 to measure the level of AGN contamination to thespectrum continuum level. They estimated an approx-imately 15% contribution to the total M87 continuumlevel. Since the field of NIFS is almost identical to thatof the KMOS field in their study, we consider the effecta 15% continuum correction would have on our IMFmeasurements in § §
3) are shaded: the blueshaded regions are the continuum bands, and the ma-genta regions are the measurement bands. The spectralresolution of the M87 spectra was halved (R ∼ ∼ µ m) is 71 and 61 for M85 andM87, respectively. EQUIVALENT WIDTH ANALYSIS
Table 1.
Selected galaxy parameters of the target sample.Galaxy RA DEC T exp (min) z σ (km s − ) [Mg/Fe] [Fe/H] α K (1) (2) (3) (4) (5) (6) (7) (8) (9)M85 (NGC 4382) 12:25:24.1 +18:11:29 40 (Z), 40 (J) 0.0024 170 0.11 -0.02 0.63M87 (NGC 4486) 12:30:49.4 +12:23:28 30 (Z), 40 (J) 0.0043 370 0.33 -0.16 1.90 Note —(1) Target galaxy (2) Right ascension (3) Declination (4) Total exposure time (5 min exposures) (5)Redshift from Smith et al. (2000) (6) Velocity dispersion averaged in the central 3 (cid:48)(cid:48) from Emsellem et al.(2004) (7)–(9) From CvD12b; α K = (M/L) K /(M/L) K,MW is the ‘IMF-mismatch’ parameter (see § Wavelength ( ˚A) . . . . . R e l a t i v e F l u x FeH Ca I Na I K I a&b K I 1.25 Al IPa β Na I
M85M87
Figure 1.
Fully collapsed and reduced spectra for both M85 (solid blue line) and M87 (solid red line). The spectra werenormalized by dividing by a high-order polynomial for clarity. The absorption features that we measure in this paper arelabelled and highlighted (Table 2). The equivalent width continuum bands are shaded in blue and the measurement bands areshaded in magenta. The emission feature seen in the M87 spectrum at 9500 ˚A is a [S
III ] + Pa (cid:15) composite feature from thecentral AGN. This line was not removed from the spectrum as it does not affect the measurement of any of the IMF-sensitivefeatures.
Table 2.
Equivalent width index names and definitions.Index Feature (˚A) Blue RedContinuum (˚A) Continuum (˚A)FeH 0.99 9905–9935 9855–9880 9940–9970Ca I I I a 1.17 11680–11705 11667–11680 11710–11750K I b 1.17 11710–11750 11793–11810 11765–11793K I I Equivalent Width Measurements In §
1, we identified seven gravity-sensitive absorptionfeatures in the zJ-band that vary by greater than 1% be- tween stellar populations with a bottom-heavy IMF andthose with a MW-like IMF. The EW index definitionsfor these features are identical to those given in CvD12a,Kin17, and Smith, Lucey, Carter (2012) and are listed inTable 2. All seven features increase in strength for stel-lar populations with a higher percentage of dwarf starsthan giants. Any giant star sensitive features in the zJ-band vary weakly with respect to the IMF so they werenot included in the following analysis due to the highS/N required to accurately measure the effects of theIMF.We defined fiducial models from C18 for each galaxyin order to provide a standard comparison to the mea-sured indices. The stellar ages and metallicities of thefiducial models closely match those measured within a R e /8 radius for M85 (5.0 Gyr Age, [Z/H] = 0.0) andM87 (13.5 Gyr Age, [Z/H] = 0.2) in McDermid et al.(2015). The observed NIFS fields for both galaxies werefully contained within a R e / R e / Adopted Stellar Population Models
In the following analysis, we make use of two groupsof synthetic simple stellar population models from C18:one group that varies the IMF while holding other stellarpopulation parameters (e.g. age, metallicity) constant,and another group of ‘response functions’ for individ-ual elemental abundances (e.g. [Na/H], [Fe/H], [Ca/H],[K/H], etc). These models are computed by combin-ing observed stellar spectra from the MIST (Choi et al.2016) and Extended IRTF (Villaume et al. 2017) spec-tral libraries, with the theoretical response functions.Both groups of models are subdivided into sets withfixed metallicities ranging from [Z/H] = –1.5 to +0.2and stellar ages from 1.0 to 13.5 Gyr. The former groupof models are used to characterize the IMFs of M85 andM87 and the latter to infer the effects of possible abun-dance variations.The group of models with variable IMF slopes followsa broken power law for the IMF functional form. Thepower law is split into three mass intervals with expo-nents ( x i ): x : 0 . ≤ M/M (cid:12) < . x : 0 . ≤ M/M (cid:12) < . x : 1 . ≤ M/M (cid:12)
The x and x exponent values range from 0.5 to 3.5in steps of 0.2. The IMF slope for stellar masses above1.0 M/M (cid:12) , x , is static and identical to the KroupaIMF value of 2.3. We refer to ‘X’ as a single slope IMF Table 3.
Measured IMF-sensitive index strengths.Line EW S/N a EW S/N a M85 M85 M87 M87FeH 0.99 0 . ± .
08 81 0 . ± .
11 67Ca I . ± .
07 73 0 . ± .
15 50Na I . ± .
24 53 0 . ± .
50 28K I a 1.17 0 . ± .
07 84 0 . ± .
09 95K I b 1.17 0 . ± .
06 100 0 . ± .
14 64K I . ± .
11 67 –Al I . ± .
18 45 0 . ± .
25 59 a Mean S/N within the index feature band defined inTable 2. exponent, equivalent to an IMF where x and x areequal, i.e. a Salpeter IMF is defined as X = 2.3, and abottom-heavy IMF as X ≥ Constraints on the IMF from Individual LineIndices
We compare the observed EW indices for both M85and M87 to those measured from the broadened fidu-cial models in Figures 4 and 5. The indices are plottedas a function of the two low-mass IMF exponents, x and x , with the black and red contours marking linesof constant model index and the observed index, respec-tively. Also included for reference are Kroupa, Salpeter,and bottom-heavy (X = 3.0) IMFs shown as the blue,magenta, and green star symbols, respectively.In Figures 4 and 5, the observed index strength ofsome of the features, e.g., FeH and Na I µ m, showdiscrepancies in their favored IMF slopes, making it dif-ficult draw consistent conclusions regarding the IMFslopes in either galaxy. A likely explanation for thesediscrepancies is the strong degeneracy between the ef-fects of the IMF and other stellar population parame-ters, such as elemental abundances and stellar ages, onthe measured index strengths (Conroy & van Dokkum2012). This indicates that a simple analysis based ongeneral stellar population parameters available in theliterature is inadequate for constraining the IMF; con-sequently, we need a more rigorous analysis that takesthe effect of the varying abundance ratios into accountto more effectively constrain the IMF. Below, we con-duct an investigation into the effects of varying elemen-tal abundances on the measured index strengths for eachobserved feature. This investigation is used to interpretthe results of a more thorough study of the IMFs of theobserved galaxies in § . . . . . FeH . . . Ca I . . . . . . . . . Na I . . . K Ia . . . . K Ib . . . . . K I 1.25 . . . . . . Al I
Wavelength ( ˚A) R e l a t i v e F l u x M85Bottom HeavyKroupa
Figure 2.
The seven observed IMF-sensitive absorption features from the observed M85 spectrum (solid blue lines). The dashedlines are fiducial models with a stellar age of 5.0 Gyr and solar metallicity. Models with Kroupa and bottom-heavy IMFs areseen as the green and red dashed lines, respectively. The model spectra have been been broadened to match the central velocitydispersion of M85. The blue and red shaded areas correspond to the EW bandpass regions and the magenta shaded areascorresponds to the feature index measurement region (see Table 2). The grey shaded regions correspond to a 68.3% confidencelevel in the spectral intensity. . . . . FeH . . . . . Ca I . . . . . . . . . . . . . Na I . . . K Ia . . . K Ib . . . . . K I 1.25 . . . . . . Al I
Wavelength ( ˚A) R e l a t i v e F l u x M87Bottom HeavyKroupa
Figure 3.
Same as Figure 2. The fiducial models for M87 have a stellar population age of 13.5 Gyr and [Z/H] = 0.2. The EWbandpass regions for the K I . . . . . . . . . . . . FeH . . . . . Ca I . . . . . . Na I . . . . . . . . . . . . K Ia . . . . . . . . . . . . . . . . . . . K Ib . . . . . . . . . . . . K I 1.25 . . . . . . . . . . . . Al I x x Figure 4.
Model EW index strengths for each of the seven absorption features measured in the M85 spectrum, relative tothe IMF power-law exponents, x and x , measured from the fiducial models. The black and red contours represent lines ofconstant index strength and the observed index strength, respectively. Kroupa, Salpeter, and bottom-heavy IMFs are markedas blue, magenta, and green stars, respectively. The grey regions represent the the index–space covered by the measured indexstrength within a 68.3% confidence level. The strengths of individual indices are inconclusive regarding the best fit IMF slopes. . . . . . . . . . . . . FeH . . . . . . Ca I . . . . Na I . . . . . . . . . . . . . K Ia . . . . . . . . . . . . . . . . . . . K Ib . . . . . . . . . . . . K I 1.25 ∗ . . . . . . . . . . . . Al I x x Figure 5.
Same as Figure 4 for the indices measured from the M87 spectra. Note that the uncertainties are large enough tocover the majority of the index–space for many of the M87 absorption features. This makes drawing a conclusion regarding thebest-fit IMF slopes difficult with the index strengths. (*The KI 1.25 feature is presented for comparison purposes but is notincluded in the analysis below.)
Wing-Ford Band (FeH 0.99 µ m) The FeH 0.99 µ m feature is widely included in IMFvariation studies (e.g. van Dokkum & Conroy 2012; Al-ton, Smith, & Lucy 2017; Vaughan et al. 2018) due toits low-sensitivities to a stellar population’s age and α –element abundance (Conroy & van Dokkum 2012). It isthe only molecular feature in the measured set of sevenfeatures. According to the C18 models, the strengthof this index is primarily sensitive to [Fe/H] and has anegative relationship with [Na/H]. The latter relation-ship originates from the role of Na as a major electrondonor in cool stars. A high Na abundance encouragesthe dissociation of the FeH molecule in stellar atmo-spheres (CvD12a; ASL17; Smith, Lucey, Carter 2012;Vaughan et al. 2018).The observed index strength of the FeH 0.99 µ m fea-ture is 0.39 ± ± ± σ v (McConnell et al. 2016), or spectral contamina-tion from the central AGN.3.3.2. Calcium Feature (Ca I µ m) The Ca I µ m feature is the weakest IMF-sensitivefeature in our set. The strength of the Ca I µ mindex is strongly sensitive to [Ca/H] but it is not affectedby variations in [Na/H], unlike other IMF indicators inboth the visible and NIR bands (Smith, Lucey, Carter2012). We measured a Ca I index strength of 0.20 ± ± I index strength in M87may be the result of a low Ca abundance, as found inASL17 for a set of similarly massive ETGs. 3.3.3. Sodium Feature (Na I µ m) The Na I µ m feature is the most dwarf star sensi-tive feature in the zJ-band according to the C18 models.In addition, the models indicate that the index strengthhas a strong, negative relationship with [Fe/H], similarto the relationship between FeH and [Na/H].The measurement of this index is complicated by itslocation within a densely populated band of telluric wa-ter absorption lines for low-redshift galaxies.We measured a very strong Na I µ m index in bothobserved galaxies, 1.33 ± ± I µ m index strength isgreater than expected for a MW-like IMF as measuredin CvD12b. Reconciling this index strength with thefiducial model strength for a Kroupa IMF (0.72 ˚A) wouldrequire either a significantly enhanced [Na/H], a higher[Z/H], a more bottom-heavy IMF, or a combination ofthese effects. If we compare the measured index strengthwith a stellar population model with [Z/H] = +0.2 dexinstead of solar metallicity, the index strength is insteadmarginally consistent with a Kroupa IMF.Our measured Na I µ m index in M87 is consistentwith a Salpeter-like IMF, albeit with very high uncer-tainties (Figure 5). As previously mentioned, the cen-tral [Na/H] in M87 has been measured to be significantlygreater ([Na/H] > I µ m index despite a close fit to theoverall spectrum and a predicted Salpeter-like IMF.3.3.4. Potassium K I Features
We use two K I features in our NIFS data for con-straining the IMF of M85: a doublet feature (K I a andK I b) at 1.17 µ m and a feature at 1.25 µ m. The indexstrengths of the doublet feature are strong in M85, sug-gesting the IMF slopes of M85 are similar to a SalpeterIMF. The strength of the 1.25 µ m index, on the otherhand, favors a more MW-like IMF than Salpeter. Notethat in the doublet, the K I b index provides tighter con-straints on the IMF than the K I a index as the formeris more sensitive the changes in the IMF slope than thelatter.This discrepancy in the favored IMF slopes of the twoK I features is seen to a lesser degree in ASL17 wherethe measured central index strengths of the doublet areconsistent with steeper IMFs than the 1.25 µ m index.This effect may be related to the high sensitivity of the1.25 µ m feature to variations in [ α /H] as the strength ofthis feature can be dramatically weakened as [ α /H] in-creases due to changes in the local continuum behaviour(ASL17). We find that the discrepancy in the favoredIMF slopes from the two K I features is reduced if weinstead adopt a [Z/H] = +0.2 dex model. This is sug-gestive that an increased metallicity, or an increased Kabundance, may also be responsible for the discrepancies(see ASL17).For M87, the strengths of the K I doublet indices bothfavour Salpeter-like IMFs which is consistent with theIMFs observed in the center of the galaxy by CvD12b.As mentioned in § I µ m linein our analysis of M87 due to AGN effects.3.3.5. Aluminum Feature (1.31 µ m) We measure an Al I feature at 1.31 µ m that hasnot been well explored for use in constraining the IMFslopes of integrated stellar populations. This feature wasfirst identified as IMF-sensitive in CvD12a, and ASL17included measurements of the index strength in theirstudy of the IMF of massive ETGs. We measure anAl I index strength of 1.11 ± ± x – x index space forthis feature.3.4. Comparison to Reported Index Strengths
ASL17 measured the index strengths of all seven fea-tures listed in Table 2 for M87. In order to compare ourindex strengths to those measured in ASL17 we scale ourmeasurements to a common σ v = 230 km s − . ASL17did not report central index strengths for FeH and Ca I µ m so we instead compare to their measurementsat R e /3. We find that our index strengths are gener-ally consistent with those in ASL17 with the exceptionof the Na I µ m index. We measure a scaled indexof 1 . ± .
65 ˚A compared to their index strength of2 . ± .
26 ˚A. This discrepancy is likely a result of thelower S/N of our z-band spectrum for M87 as well ascomplications with the index measurement due to thedense telluric absorption around this feature.Smith, Lucey, Carter (2012) measured the Ca I µ m index strength in a sample of Coma cluster ETGswith similar σ v to M85 ( >
100 km s − ). Our measuredstrength in M85 is consistent with their mean measure-ment of 0.279 ± I µ m index strength of approximately 1.0 in Table 4.
Additional line index bandpass definitions.Index Feature (˚A) Blue RedContinuum (˚A) Continuum (˚A)Na I β low σ v ETGs, which is also consistent with the strengthof our measured index in M85. SPECTRAL FITTING ANALYSISWe now describe our method for fitting the observedspectra of M85 and M87 to the C18 models. We con-struct a set of adjusted models to account for abundanceratios variations in Na, Fe, Ca, and K by scaling theC18 models with fixed ages and [Z/H] by the theoreticalelemental response functions. Specifically, we fit theseadjusted C18 models to the observed feature spectralbands defined in Table 2 while allowing for variable stel-lar population parameters: the age, [Z/H], IMF slopes,and the aforementioned elemental abundances. We fitthe feature spectral bands to the models, in contrast tofitting broader spectral bandpasses as in CvD12b, in or-der to characterize the effectiveness of this particular setof features for constraining the IMF. In addition, fittingthe feature bands allows for a comparison with the sim-ilar extragalactic IMF analysis in the NIR presented inASL17. 4.1.
Additional Features
The seven features discussed in this paper are weaklysensitive to stellar population ages in the range of 7–13.5 Gyr (Kin17). The index strengths vary by a muchgreater amount ( ≤ ∼ β (Pa β ) feature at 1.28 µ m. The Pa β feature is highlysensitive to the stellar population age, similar to theclassical Lick H β feature employed to constrain stellarages in stellar population studies in the visible bands(e.g. McDermid et al. 2015).Furthermore, many of the features in Table 2 are sen-sitive to variations in the Na abundance (see § I . . . . . . . Pa β M85 . . . . . . . Na I 1.27 M85
Age: 3 Gyr, [Na/H]: 0.6 dexAge: 3 GyrAge: 13.5 Gyr . . . . . . . Pa β M87 . . . . . . Na I 1.27 M87
Age: 13.5 Gyr, [Na/H]: 0.6 dexAge: 3 GyrAge: 13.5 Gyr
Wavelength ( ˚A) R e l a t i v e F l u x Figure 6.
The Pa β and Na I µ m features from theobserved M85 (top row) and M87 (bottom row) spectra. Theobserved spectrum (solid blue line) is compared to modelspectra for a stellar population with 3 and 13.5 Gyr ages(dotted lines) and one with an enhanced [Na/H] = 0.6 dex(black line). The [Na/H] enhanced model has a stellar ageof 3 Gyr for M85 and 13.5 Gyr for M87. The model M85spectra assume a Kroupa IMF while the model M87 spectraassume a bottom-heavy IMF. The model spectra have beenbroadened to match the velocity dispersion of each galaxy.The grey shaded regions correspond to a 68.3% confidencelevel in the spectral intensity. The vertical shaded regionscorrespond to the EW index measurement bands as in Figure2. µ m feature, which is the most IMF-sensitive of the sevenfeatures. Due to the importance of [Na/H] in constrain-ing the IMF slopes in this analysis, we define a new EWindex for the Na I feature at 1.27 µ m. The Na I µ m feature provides an independent constraint on theNa abundance that is not sensitive to variations in theIMF slopes (Smith 2015).The EW index measurement bands for both featuresare defined in Table 4. The spectral bands are designedto have similar band widths (20–30 ˚A) and total widths( ∼
100 ˚A) as the seven features in Table 2. Profiles of theobserved Pa β and Na I µ m features for both galax-ies can be seen in Figure 6 alongside stellar populationmodels with ages of 3 and 13.5 Gyr and [Na/H] = 0.6for illustration purposes. The models in the figure as-sume either Kroupa or bottom-heavy (X = 3.0) IMFs forthe M85 and M87 spectra, respectively, although neitherfeature is significantly sensitive to the IMF slopes. ThePa β feature, in the left column, is clearly sensitive to thestellar population age with the observed M85 and M87spectra being better described by models with youngerand older stellar populations, respectively. In the right Table 5.
Model Parameterpriors for the MCMC ensem-ble sampler.Parameter Prior LimitsAge 1.0–13.5[Z/H] –0.25–0.2 x a x a [Na/H] –0.5–0.9[K/H] –0.5–0.5[Ca/H] –0.5–0.5[Fe/H] –0.5–0.5 a The IMF slope exponentsare limited to incrementsof 0.2 as in the Conory18models. column, the Na I µ m feature is highly sensitive tothe Na abundance with the observed feature profiles forboth galaxies more closely aligned with the Na enhancedmodels. Furthermore, Pa β has a minor sensitivity to[Ca/H] while both features have minor sensitivities to[Fe/H]. 4.2. MCMC Model Overview
The model parameters are estimated with the pub-licly available emcee routine (Foreman-Machey, et al.2013), a Markov-Chain Monte-Carlo ensemble samplerthat characterizes the posterior probability distributionsof a particular model provided observed data and uncer-tainties. Our implementation of this routine maximizesa log-likelihood function, ln p ( D | θ, σ ) = − (cid:88) i (cid:104) D i − M i ( θ ) σ i (cid:105) (2)where D i is the observed spectrum at the i th wavelengthelement, θ are the input model parameter values listedin Table 5, M i ( θ ) is the adjusted C18 model, and σ i isthe measured uncertainty in the spectral intensity.Each MCMC simulation consists of 512 ‘walkers’ eachof which explore the posterior distributions, p( θ | D, σ ),of the model input parameters over 4000 steps or a to-tal of 2 . × samples. The final 1000 samples ofeach walker are kept for the following analysis while thepreceding 3000 samples are discarded as a standard pa-rameter ‘burn-in’ phase.The MCMC model input parameters and their priorsare listed in Table 5. We impose uniform, ‘top–hat’, dis-tributions for the priors of the input parameters in order1to avoid any potential bias to the ensemble sampler. Theinitial model parameters for each walker are chosen atrandom from within the these distributions. We splitthe input parameters into two groups: a base set andan extended set. The base set of parameters consists ofthe stellar population age, metallicity ([Z/H]), and thetwo IMF slopes x and x . In contrast, the extendedset adds four elemental abundance ratios to the baseset: [Na/H], [Fe/H], [Ca/H], and [K/H]. We fit the ob-served feature bands (Tables 2 and 4) of M85 and M87to both sets of model parameters in order to assess theeffects of fitting abundance variations on the IMF slopeconstraints.In order to calculate the log-likelihood (Equation 2)we first create ‘adjusted models’ by scaling and broad-ening the models from C18 as a function of the inputabundance ratios and the known velocity dispersion ofM85 and M87 (Table 1), respectively. The log-likelihoodis then calculated by comparing the feature bands be-tween the observed spectra and the ‘adjusted model.’The feature bands are normalized with the same methoddetailed in § ± § ± ± Results: MCMC Spectral Fitting
Table 6 presents the ‘best-fit’ model parameters forM85 and M87, as constrained by the final 1000 like-lihood samples of the MCMC walkers, including thestellar population ages, metallicities, IMF slopes, abun-dance ratios, and ‘IMF-mismatch’ parameters ( α K ). α K is a common measure that relates the constrained (M/L)in the K-band to the (M/L) measured from the modelsassuming a MW–like IMF. This parameter is described in more detail in § th percentile level) of the posterior distri-butions, and the 16 th and 84 th percentile levels are givenas the uncertainties in the median. Table 6 provides thebest-fit results for both the extended and base set ofmodel parameters, and demonstrates that the exclusionof the individual abundance ratios has a significant effecton the measured IMF slopes in M85. This discrepancyis further discussed in § x and x , have very broad dis-tributions in both figures, indicating that it is diffi-cult to constrain the exact power-law shape of the IMFwith our data. These broad distributions may also bedue to the high-degree of co-variance between the indi-vidual IMF slopes which results in an unusual best-fitIMF functional form in M85, x = 1.98 +0 . − . and x =1.47 +0 . − . , where the IMF slope is shallower in the rangeof 0 . ≤ M/M (cid:12) < . M/M (cid:12) . The best-fit IMF slopes in M87, x = 2.74 +0 . − . and x = 2.70 +0 . − . ,are consistent with a super–Salpeter IMF. Despite thebroad distributions of the IMF slopes, we find contrast-ing IMFs in M85 and M87 with the former favouring amore MW-like IMF and the latter more bottom-heavyIMFs.We measure best-fit ages for M85 and M87 of 3.65 +1 . − . Gyr and 11.59 +1 . − . Gyr, respectively. The measuredages agree with previous measurements of 3.84 ± ± ≥ ± β line in the MCMC model analysis hasa dramatic effect on the measured best-fit ages. Thiseffect is discussed in more detail in § +0 . − . dex and0.02 +0 . − . dex for M85 and M87, respectively. For M85,the measured metallicity is close to the recent measure-ment of [ Z/H ] ∼ .
32 in the galactic core (Ko et al.2018). Similar to the measured age of M87, the metallic-ity posterior distribution for M85 peaks strongly at theC18 model maximum of [Z/H] = 0.2 dex, which suggeststhat the metallicity is greater than the median value.2
Table 6.
Best-fit stellar population parameters for M85 and M87 including the Pa β and Na I µ m features.Galaxy Age (Gyr) [Z/H] x x [Na/H] [Fe/H] [Ca/H] [K/H] α K a M85 (Extended) 3.65 +1 . − . +0 . − . +0 . − . +0 . − . +0 . − . –0.03 +0 . − . –0.13 +0 . − . +0 . − . +0 . − . M85 (Base) 3.25 +0 . − . +0 . − . +0 . − . +0 . − . Fixed to [Z/H] 3.13 +1 . − . M87 (Extended) 11.59 +1 . − . +0 . − . +0 . − . +0 . − . +0 . − . –0.19 +0 . − . –0.24 +0 . − . +0 . − . +2 . − . M87 (Base) 11.60 +1 . − . –0.03 +0 . − . +0 . − . +0 . − . Fixed to [Z/H] 3.02 +2 . − . a Best-fit ‘IMF-mismatch parameter, see § The measured metallicity in M87 is consistent with theprevious measurement within R e /8 from McDermid etal. (2015).In addition to the IMF slopes, stellar populationage, and metallicity, we measure four abundance ratios,[Na/H], [Fe/H], [Ca/H], [K/H], in M85 and M87. Wefind evidence for a very high [Na/H] = 0.67 +0 . − . dex,and a reduced [Ca/H] of –0.13 +0 . − . dex in M85. In addi-tion, we measure a [Fe/H] = –0.03 +0 . − . dex and [K/H] =0.09 +0 . − . dex which are consistent with solar metallicity.We note that the measured [Ca/H] and [Fe/H], are pri-marily constrained by a single absorption feature. Theirbest-fit values are therefore susceptible to degeneracieswith other stellar population parameters (e.g. age andthe IMF slopes). The observed M87 spectrum is unableto provide strong constraints on the individual abun-dance ratios; however, including the abundance ratiosdoes not have a significant effect on the best-fit baseparameters in M87.The addition of the Na I µ m feature does notsignificantly affect the constrained Na abundance in ei-ther galaxy (see § I µ m feature exclusively(i.e. without the Na I µ m feature) the best-fit stel-lar population parameters, including [Na/H], remain un-affected. The consistency between the Na abundancesconstrained with either Na I feature supports the con-clusion that the stellar population in the core of M85has a significantly enhanced Na abundance.4.4. IMF-Mismatch Parameter
The individual IMF slopes, x and x , show a highdegree of correlation regardless of the set of features in-cluded in our spectral model fitting. This can be seenin Figures 7 and 8 by the consistently broad distribu-tions for the IMF slopes. To better quantify the IMFsof M85 and M87, we calculate the IMF-mismatch pa-rameter ( α K ) defined as, α K = (M / L) K / (M / L) K,MW (3) where (M/L) K is a mass-to-light ratio measured in theK-band, i.e. 2.03–2.37 µ m, and (M/L) K,MW is the K-band mass-to-light ratio assuming an underlying MW-like IMF. Note that a Kroupa IMF is adopted for theMW-like IMF here. The (M/L) values are corrected forthe remaining stellar mass at the best-fit age, includingremnants, following the MIST isochrones (Choi et al.2016).The IMF-mismatch parameter is a common measureused to describe the ‘bottom-heaviness’ of IMFs derivedfrom integrated stellar populations (e.g. La Barbera, etal. 2016; van Dokkum, Conroy, Villaume, et al. 2016;Sarzi et al. 2017). α K = 1.0 is representative of a MW-like IMF, while α K ∼ α K increases rapidly, rising to α K ∼ α K for both galax-ies calculated from models constructed with the best-fitages and metallicities (Table 6) and the posterior distri-butions of the two IMF slopes. The medians of the α K distributions for M85 and M87 are marked with greenand blue dashed lines, respectively. The median α K val-ues are presented in Tables 6 for each set of stellar popu-lation parameters. We find median α K of 1.26 +0 . − . and2.77 +2 . − . with the best-fit stellar population parametersin Table 6 for M85 and M87, respectively, indicatingthat the underlying IMFs are likely similar to a Kroupaand super-Salpeter IMF in those galaxies. DISCUSSION5.1.
Effect of the Stellar Age on the MeasuredParameters In § β fea-ture in the MCMC analysis had a dramatic effect on theconstrained stellar ages. Here we discuss some effects re-sulting from constraining the model parameters withoutthe Pa β and Na I µ m features described in § β feature from the MCMC simulation3 Age − . − . . . . [ Z / H ] [Z/H] . . . . . x x . . . . . x x − . . . . . [ N a / H ] [Na/H] − . − . . . . [ F e / H ] [Fe/H] − . − . . . . [ C a / H ] [Ca/H] . . . . . Age − . − . . . . [ K / H ] − . − . . . . [Z/H] . . . . . x . . . . . x − . . . . . [Na/H] − . − . . . . [Fe/H] − . − . . . . [Ca/H] − . − . . . . [K/H][K/H] Figure 7. ‘Corner plot’ of the MCMC output using the extended set of model parameters derived with the observed M85spectrum. The extended set of parameters include the Age, [Z/H], the two IMF slopes x and x , and four elemental abundanceratios [Na/H], [Fe/H], [Ca/H], [K/H]. The posterior distributions, calculated from the final 1000 samples of each of the 512MCMC walkers, are shown in the diagonal plots along with the 16 th , 84 th (green lines), and 50 th (red lines) percentiles. Belowthe posterior distributions are co-variance plots (contours) for each pair of parameters. The primary IMF constraint can beseen in the x – x co-variance plot. of the M85 spectra significantly increased the medianage from 3.65 +1 . − . to 7.88 +3 . − . Gyr. In contrast to theformer, a stellar age of 7.88 +3 . − . Gyr is inconsistent withrecent measurements of the stellar age in the core of M85from McDermid et al. (2015) and Ko et al. (2018). ForM87, the median stellar age increased from 10.23 +2 . − . to11.59 +1 . − . Gyr. This small adjustment was likely a con-sequence of the stellar age posterior distribution peaking at the maximum 13.5 Gyr regardless of the inclusion ofthe Pa β feature.Another important effect of excluding the Pa β andNa I µ m features from the MCMC simulations wasa significant decrease in the best-fit metallicity for M85.The decrease in the best-fit [Z/H] in M85, from [Z/H]= 0.17 +0 . − . in Table 6 to [Z/H] = 0.08 +0 . − . without theadditional features, was likely a consequence of the for-4 Age − . − . . . . [ Z / H ] [Z/H] . . . . . x x . . . . . x x − . . . . . [ N a / H ] [Na/H] − . − . . . . [ F e / H ] [Fe/H] − . − . . . . [ C a / H ] [Ca/H] . . . . . Age − . − . . . . [ K / H ] − . − . . . . [Z/H] . . . . . x . . . . . x − . . . . . [Na/H] − . − . . . . [Fe/H] − . − . . . . [Ca/H] − . − . . . . [K/H][K/H] Figure 8. ‘Corner plot’ of the MCMC output using the extended set of model parameters derived with the observed M87spectrum. The layout of this figure is identical to Figure 7. merly more tightly constrained, younger stellar popula-tion age. Younger stellar populations are dominated byhotter stars which have intrinsically weaker absorptionlines, thereby requiring a higher metallicity to accountfor the same feature strengths. As mentioned in § ∼ . +0 . − . derived forM87 without the two additional features was increasedby approximately 0.04 dex relative to the [Z/H] in Ta- ble 6. This slight increase was likely also a consequenceof the tighter constraints on the stellar population age= 11.59 +1 . − . Gyr in M87, as an older stellar popula-tion reduces the best-fit metallicity given constant indexstrengths.Excluding the Pa β and Na I µ m features fromthe MCMC simulations did not result in a significantchange in the best-fit IMF slopes, which was expecteddue to the low IMF sensitivity of these features outlinedin § α K K r oupa S a l pe t e r M87M85
Figure 9.
IMF-mismatch parameter ( α K ) distributions de-rived with the best fit model parameters for M85 (orange)and M87 (blue) from Table 6. The green and blue dashedlines mark the medians of the M85 and M87 distributions,respectively. The solid vertical black lines mark the α K forKroupa (MW-like) and Salpeter IMFs. The best-fit α K foreach galaxy are clearly contrasting with M85 favouring aKroupa IMF and and M87 a super-Salpeter IMF. Impact of elemental abundances on the IMF
In Table 6, we presented the best-fit stellar popu-lation parameters for M85 and M87 when including(extended set) and excluding (base set) the elementalabundances from the MCMC simulations. There was asignificant discrepancy between the best-fit IMF slopesfor M85 when constrained by the base and extendedsets of model parameters. The former is best-fit by avery bottom-heavy IMF while the latter is best-fit by amore MW-like IMF. We investigated two possible ori-gins for this inconsistency: the exclusion of individualabundance ratios, i.e., [Fe/H], [Na/H], [Ca/H], [K/H],from the MCMC model parameters, and the removalof individual features (Table 2) from the fitting proce-dure. When the individual elemental abundances are ex-cluded, their values are fixed to the metallicity ([Z/H]),which does not account for the large deviations of certainelemental abundances such as the high best-fit [Na/H]in M85. Fixing the abundance ratios to [Z/H] may re-sult in the inconsistency between the IMF slopes whenderived with or without the elemental abundance ratios.Further MCMC simulations which excluded each of thefour line abundance ratios from the model parametersand/or excluded individual IMF-sensitive features fromthe fitting procedure were therefore conducted to inves-tigate this inconsistency. Excluding [Ca/H] and [K/H] from the model param-eters did not result in any meaningful differences in theresulting best-fit IMF slopes. In addition, excluding[Fe/H] resulted in only slightly shallower best-fit IMFslopes in M85. Individually excluding the FeH, Ca I ,K I , and Al I features from the fitting procedure alsohad no effect on the best-fit IMF slopes.The best-fit IMF slopes for M85 were significantlysteepened when [Na/H] was excluded from the modelparameters (i.e. fixing [Na/H] to [Z/H]). In this case, thebest-fit [Fe/H] was dramatically reduced in order to fitthe strong Na I µ m feature, as this feature strength-ens for lower Fe abundances (see § I µ m feature from the fitting procedure did not impactthe derived IMF slopes. In summary, we found that in-cluding [Na/H] in our model parameters was critical tothe interpretation of the strong Na I µ m feature inthe observed M85 spectrum.The best-fit IMF slopes for M87 did not exhibit thesame sensitivity to the Na abundance and the Na I µ m feature. This was likely a result of both the loweroverall S/N in the M87 spectrum and the weaker influ-ence of abundance variations on the spectra of high σ v galaxies.We note here that the strength of the Na I µ mfeature is known to be difficult to accurately predict withcurrent stellar population models. According to Smith(2015), the strength of this feature was often under-fitdespite a strong overall fit to the rest of their observedspectra. We obtained consistent results, however, when[Na/H] was constrained by either or both of the Na I µ m and Na I µ m features (see § I µ m feature is only visible at high [Na/H],increased our confidence in the high [Na/H] reported inTable 6 for M85.5.3. M87 AGN Correction
M87 is known to have a strong, central AGN that con-taminates the observed spectral continuum (see § I µ m line was excluded from our analysis ofthe stellar population properties in M87 due to a [Fe II]emission line from this AGN. We considered two possi-ble effects of accounting for the M87 AGN on the best-fitIMF slopes: excluding the K I µ m feature in ouranalysis of M85, and correcting the M87 spectrum foran estimated AGN continuum emission. For the former,we repeated the MCMC analysis of the M85 spectrum6while excluding the K I µ m feature and found thatthe best-fit IMF slopes are not significantly affected.To measure the effect of removing the AGN contin-uum, we repeated our analysis of M87 after subtracting apercentage of the linear continuum defined for each spec-tral feature in Table 2. We adopted the estimation fromASL17 that the AGN in M87 contributes approximately15% of the observed continuum level within the central3 (cid:48)(cid:48) . As expected, this correction resulted in a steepeningof the best-fit IMF slopes in M87 from a Salpeter-like(X ∼ ∼ Comparison to Previous IMF Results
The results presented in § α K = 0.63,which is shallower than the MW-like α K = 1.26 +0 . − . reported in Table 6. We note, however, that the α K distribution for M85 in Figure 9 peaks strongly at thelowest α K , suggesting that the α K for M85 is lower thanthe median. In M87, CvD12b found a super-SalpeterIMF with α K = 1.90 that is similar to our median α K =2.77 +2 . − . . Cappellari et al. (2013) measured the IMFs inM85 and M87 to be slightly steeper than a Kroupa IMFand slightly shallower than a Salpeter IMF, respectively,which is qualitatively consistent with our measurements.Our measurement of a super-Salpeter IMF in the cen-ter of M87 is similar to the results of Sarzi et al. (2017)and Oldham & Auger (2017). Using spectroscopy inthe visible bands, Sarzi et al. (2017) measured an IMFslope of approximately 2.9 in the core of M87 whichis consistent with both IMF slopes for M87 in Table6 of ∼ (cid:12) of approximately 2.5 in the core of M87 with a sophisticated dynamical modelconstructed from observations of M87 satellites.A novel result of this paper is the measurement of fourabundance ratios in M85, [Na/H], [Fe/H], [Ca/H], and[K/H], of which only [Fe/H] has prior reported mea-surements. vDC12 measured [Fe/H] = -0.02 dex inM85 which is consistent with our [Fe/H] measurementof − . +0 . − . dex in Table 6.We measured an exceptionally enhanced [Na/H] =0.67 +0 . − . dex in M85, which is typical of the cores ofold, massive ETGs (Spiniello et al. 2012). M85, how-ever, is known to have a young, counter-rotating, kine-matically decoupled core within the central 1 (cid:48)(cid:48) that mayhave formed from a recent, wet galaxy merger (McDer-mid et al. 2004; Terlevich, & Forbes 2002). This burstof star formation in the core of M85 may be the causeof the enhanced Na abundance. Na is injected into theinterstellar medium (ISM) by both the stellar winds ofmassive stars and by Type II supernovae, the latter has astrong, metallicity-dependent yield. Assuming our best-fit [Z/H] = 0.09 dex is accurate, the high Na abundancein M85 may be a result of this metallicity-dependentNa yield (Kobayashi et al. 2006). The Na enriched gasejected into the ISM from recently formed massive starsmay be accreted onto existing or still forming stars, dueto the high stellar density in the core of M85 (McConnellet al. 2016).Furthermore, we measured a strong Al I µ m in-dex in M85. Al and Na are produced in a similar fash-ion during the carbon burning phase of massive stars(Lecureur, Hill, Zoccali et al. 2007). Al also exhibitsthe same strong metallicity-dependent yield in Type IIsupernovae as Na. It is therefore possible that both thestrong [Na/H] and the high Al I index strength are aconsequence of the recent star formation in M85.Na is also produced as a product of hot bottom burn-ing in intermediate mass (3–8 M (cid:12) ) AGB stars (Vaughanet al. 2018). There is evidence that the Na yield fromthis process also increases with metallicity (Ventura etal. 2013). At ∼ +0 . − . dex for M87 (Table 6) is marginally con-sistent with recent measurements of a high [Na/H] = ∼ . σ v and metallicity (see § σ v (CvD12b). Recently,Parikh et al. (2018) measured correlations of varying de-grees between the low mass ( ≤ (cid:12) ) IMF slope andgalactic properties such as σ v , [Z/H], [Na/Fe], galacticradius, and stellar age in a sample of ∼
400 ETGs. Ourbest-fit x slope for M85 and M87 is consistent withtheir IMF– σ v correlation. The Parikh et al. (2018) sam-ple, however, only includes galaxies with σ v <
200 kms − , so the comparison to our measured IMF slopes inM87 is only qualitative. Parikh et al. (2018) also foundthat the IMF in galaxies with high [Z/H] and [Na/Fe] areconsistent with a Salpeter IMF, which is only marginallyconsistent with the x slope measured for M85 in thispaper. In particular, they measured a very tight correla-tion between the IMF slope and [Z/H], which is inconsis-tent with our IMF slope in M85. A possible explanationfor this inconsistency is the lack of galaxies younger than5 Gyr in the sample studied by Parikh et al. (2018).The measurements of bottom-heavy IMFs in the coreof massive galaxies, as measured for M87 in this pa-per, and more MW-like IMFs in less-massive galaxieslike M85, implies that the conditions during the for-mation of these stellar systems were fundamentally dif-ferent. The cores of brightest cluster galaxies, such asM87, were likely formed in massive dark matter poten-tial wells and experienced an exceptionally dense starformation environment (Oldham & Auger 2017). Thestellar populations in the cores of these galaxies wouldtherefore be extremely old, as measured for M87 in Table6. In contrast, M85 is a much less massive galaxy witha younger stellar population, comparable to those in theMilky Way. The stars in the core of M85 likely formedin a significantly different environment than those inthe core of M87. Chabrier et al. (2014) examined thephysical basis for this type of IMF variation and deter-mined that the compressive turbulent motions found inextreme star formation environments can shift the char-acteristic mass of the IMF to a lower mass, resultingin a bottom-heavy IMF. This provides a consistent pic-ture for the origin of the observed IMF variation for M85and M87 in this paper, as a function of their contrastingformation histories. SUMMARY AND FUTURE WORKIn this paper, we have presented a study of the IMFsfor two ETGs, M85 and M87, with highly contrastingcentral velocity dispersions and [ α /Fe] using a set ofseven NIR, gravity-sensitive absorption features. This set of features have been relatively unexplored for thepurpose of measuring variations in the IMF from theintegrated light of extragalactic stellar populations. Tothat end, we compared the observed spectral regionsfor these features for both galaxies to stellar populationmodels described in C18.Our key conclusions are as follows: • Our measured feature indices and median α K forM85 and M87 are consistent with those foundin previous studies using both spectroscopic andkinematic techniques (e.g., Cappellari et al. 2013;Sarzi et al. 2017, vDC12, ASL17). • The EW index strengths of the seven IMF-sensitive features give inconsistent constraints forthe IMF slopes in both galaxies relative to fiducialmodels defined with previously measured stellarpopulation ages and metallicities. These incon-sistencies between the predicted IMF slopes andthe measured index strengths can be reconciled byassuming particular elemental abundance ratios,thereby underlining the necessity of consideringabundance variations when investigating the IMF. • The best-fit IMF slopes in M85, derived with theMCMC model fitting, are consistent with a MW-like IMF. However, the best-fit x slope is steeperthan the x slope which describes a unusual IMFfunctional form. This unusual IMF is likely a con-sequence of the high co-variance between the in-dividual IMF slopes. The median IMF-mismatchparameter, α K = 1 .
26, allows for a more definitiveinterpretation of a MW-like IMF in M85. • The best-fit IMF slopes in M87 are consistent witha super-Salpeter IMF. The median α K = 2.77 sup-ports our conclusion that the IMF in M87 is likelybetween a Salpeter and a bottom-heavy IMF. TheMCMC simulations were unable to constrain theindividual abundance ratios in M87 due to thelower S/N of the M87 spectrum than the M85spectrum. If the M87 spectral continuum is cor-rected for an estimated 15% additional continuumfrom the central AGN, the best-fit IMF slopessteepen to a bottom-heavy IMF. • We find a significantly enhanced Na abundance([Na/H] ∼ I features. This high[Na/H] may be a consequence of both the highmetallicity and the recent burst of star formationin the core of the M85. We conclude that, due to8 the high Na abundance, including [Na/H] in themodel parameters is critical to the interpretationof the IMF slopes in M85.This work adds to the growing body of evidence thatthe IMFs of ETGs vary as a function of fundamentalgalactic properties (e.g. σ v , [ α /Fe], [Z/H]) while alsoillustrating the viability of using NIR IMF-sensitive fea-tures as possible tools for investigating IMF variation.We are currently conducting a survey of nearby ETGsand the bulges of spiral galaxies using the recently com-missioned Wide Integral Field Infrared Spectrograph(WIFIS: Meyer et al. 2016; Sivanandam et al. 2018).Similarly to the NIFS spectrograph used in this work,WIFIS operates in the zJ-band and will be able to per-form a spatially resolved investigation of the IMF slopesout to large radii using this set of IMF-sensitive features.This survey will serve as a NIR companion to integralfield IMF variation studies in the visible bands such asthe MANGA (Bundy et al. 2014), CALIFA (S´anchez etal. 2012), and ATLAS3D (Cappellari et al. 2011) sur-veys. We anticipate that our analysis of the observedgalaxies in the WIFIS extragalactic survey will signifi- cantly contribute to our broader understanding of IMFvariation in nearby extragalactic objects.We thank C. Conroy and his group for the use of theirrecent stellar population models in this paper. DSMwas supported in part by a Leading Edge Fund fromthe Canadian Foundation for Innovation (project No.30951). Both DSM and SS were supported by a Dis-covery Grant from the Natural Sciences and Engineer-ing Research Council of Canada (NSERC). We thankthe anonymous referee for their helpful comments whichimproved the paper.This paper is based on observations obtained at theGemini Observatory, which is operated by the Associ-ation of Universities for Research in Astronomy, Inc.,under a cooperative agreement with the NSF on behalfof the Gemini partnership: the National Science Foun-dation (United States), the National Research Council(Canada), CONICYT (Chile), Ministerio de Ciencia,Tecnolog´ıa e Innovaci´on Productiva (Argentina), andMinist´erio da Ciˆencia, Tecnologia e Inova¸c˜ao (Brazil).The analysis in this publication made extensive useof the python modules NumPy (Van Der Walt et al.2011), AstroPy (Astropy Collaboration et al. 2013),SciPy (Jones et al. 2001), and Matplotlib (Hunter 2007).REFERENCES9