The Black Hole in the Compact, High-dispersion Galaxy NGC 1271
Jonelle L. Walsh, Remco C. E. van den Bosch, Karl Gebhardt, Akın Yıldırım, Kayhan Gültekin, Bernd Husemann, Douglas O. Richstone
aa r X i v : . [ a s t r o - ph . GA ] J un D RAFT VERSION O CTOBER
8, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
THE BLACK HOLE IN THE COMPACT, HIGH-DISPERSION GALAXY NGC 1271 J ONELLE
L. W
ALSH , , R EMCO
C. E.
VAN DEN B OSCH , K ARL G EBHARDT , A KIN Y ILDIRIM , K AYHAN G ÜLTEKIN , B ERND H USEMANN , , AND D OUGLAS
O. R
ICHSTONE George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, and Department of Physics and Astronomy, Texas A&MUniversity, College Station, TX 77843, USA; [email protected] Department of Astronomy, The University of Texas at Austin, 2515 Speedway, Stop C1400, Austin, TX 78712, USA Max-Planck Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany Department of Astronomy, University of Michigan, 1085 S. University Ave., Ann Arbor, MI 48109, USA European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Garching, Germany Leibniz Institute for Astrophysics Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany
Draft version October 8, 2018
ABSTRACTLocated in the Perseus cluster, NGC 1271 is an early-type galaxy with a small effective radius of 2.2 kpcand a large bulge stellar velocity dispersion of 276 km s - for its K -band luminosity of 8 . × L ⊙ . Wepresent a mass measurement for the black hole in this compact, high-dispersion galaxy using observationsfrom the integral field spectrograph NIFS on the Gemini North telescope assisted by laser guide star adap-tive optics, large-scale integral field unit observations with PPAK at the Calar Alto Observatory, and HubbleSpace Telescope
WFC3 imaging observations. We are able to map out the stellar kinematics both on smallspatial scales, within the black hole sphere of influence, and on large scales that extend out to four times thegalaxy’s effective radius. We find that the galaxy is rapidly rotating and exhibits a sharp rise in the velocitydispersion. Through the use of orbit-based stellar dynamical models, we determine that the black hole has amass of (3 . + . - . ) × M ⊙ and the H -band stellar mass-to-light ratio is 1 . + . - . Υ ⊙ (1 σ uncertainties). NGC1271 occupies the sparsely-populated upper end of the black hole mass distribution, but is very different fromthe Brightest Cluster Galaxies (BCGs) and giant elliptical galaxies that are expected to host the most massiveblack holes. Interestingly, the black hole mass is an order of magnitude larger than expectations based on thegalaxy’s bulge luminosity, but is consistent with the mass predicted using the galaxy’s bulge stellar velocitydispersion. More compact, high-dispersion galaxies need to be studied using high spatial resolution observa-tions to securely determine black hole masses, as there could be systematic differences in the black hole scalingrelations between these types of galaxies and the BCGs/giant ellipticals, thereby implying different pathwaysfor black hole and galaxy growth. Subject headings: galaxies: elliptical and lenticular, cD – galaxies: individual (NGC 1271) – galaxies: kine-matics and dynamics – galaxies: nuclei – black hole physics INTRODUCTION
Over the past 15 years, it has become increasingly clearthat supermassive black holes are an essential component of agalaxy, as demonstrated by the correlations connecting blackhole masses and galaxy bulge properties (e.g., Kormendy &Richstone 1995; Ferrarese & Merritt 2000; Gebhardt et al.2000; Marconi & Hunt 2003; Gültekin et al. 2009; Kormendy& Ho 2013). Supermassive black holes are thought to regu-late galaxy properties and influence star formation via feed-back processes (Silk & Rees 1998; Fabian 1999), howeverthe black hole – bulge relations can also arise because of theinherent averaging associated with random galaxy mergers,without the need for the black hole to actively influence itshost galaxy (Peng 2007; Jahnke & Macciò 2011). Roughly 80dynamical black hole mass ( M BH ) measurements have beenmade to date (Kormendy & Ho 2013), almost exclusivelythrough the use of high angular resolution facilities such asthe Hubble Space Telescope ( HST ) and 8 -
10m ground-basedtelescopes with the aid of adaptive optics (AO). Despite thegrowing number of black hole mass measurements, the localblack hole mass census is highly incomplete. Gaining a morecomplete picture of black hole demographics and a deeper un-derstanding the mechanisms that drive black hole/galaxy evo-lution requires the secure measurement of many more blackholes, particularly those at the extremes of the black hole mass scale and in a wider range of galaxy types.With the goal of finding more objects suitable for futuredynamical black hole mass measurements, the HET MassiveGalaxy Survey obtained long-slit spectra of ∼ R e , be-low 3 kpc, a central stellar velocity dispersion larger than250 km s - , and K -band luminosities ∼ (5 - × L ⊙ .The HET spectra hint that these compact, high-dispersiongalaxies could host some of the largest black holes known( M BH > M ⊙ ), and that the black holes could weigh ahigh fraction of its host galaxy’s mass. Six example ob-jects were highlighted in van den Bosch et al. (2012), andorbit-based stellar dynamical models were calculated for onegalaxy, NGC 1277. In the case of NGC 1277, van den Boschet al. (2012) found a 1 . × M ⊙ black hole that is surpris-ingly 59% of the galaxy’s bulge mass, or 14% of the galaxy’stotal mass. While Yıldırım et al. (2015) infer a similar M BH from seeing-limited, large-scale integral field unit (IFU) data,Emsellem (2013) show a smaller black hole of a few billionsolar masses can also reasonably reproduce the observed HETlong-slit kinematics presented in van den Bosch et al. (2012). Obtaining secure black hole mass measurements for theother compact, high-dispersion galaxies found through theHET Massive Galaxy Survey is important for addressingquestions concerning the upper end of the black hole – hostgalaxy relationships. With the present sample of black holemass measurements, the slope, intrinsic scatter, and even theshape of the correlations for high-mass black holes are notwell established (e.g., McConnell & Ma 2013). Also, theblack hole mass – stellar velocity dispersion relation ( M BH – σ ⋆ ) and the black hole mass – bulge luminosity relation ( M BH – L bul ) are in direct conflict at the upper end, and make drasti-cally different predictions for the inferred number density ofthe most massive black holes (Lauer et al. 2007). Not onlyare the compact, high-dispersion galaxies from the HET sur-vey useful for filling in the poorly sampled high-mass end ofthe black hole relations, but also the mass estimates from M BH – σ ⋆ and M BH – L bul differ by a factor of at least three. Con-sequently, the galaxies are also useful for testing which ofthe correlations is more fundamental and a better predictor of M BH at the high-mass end of the scaling relations.While recent progress has been made in searching for, andrevising measurements for, black holes with masses largerthan 10 M ⊙ (Shen & Gebhardt 2010; Gebhardt et al. 2011;McConnell et al. 2011, 2012; van den Bosch et al. 2012;Walsh et al. 2010, 2013; Rusli et al. 2013), many of thesegalaxies are giant ellipticals or Brightest Cluster Galaxies(BCGs), which are often large (with R e >
10 kpc; e.g., DallaBontà et al. 2009), have cored surface brightness profiles, andare dispersion-supported showing little to no rotation. In con-trast, the compact, high-dispersion galaxies found through theHET survey are small, rapidly rotating, and generally exhibitcuspy surface brightness profiles. Such host galaxy environ-ments haven’t been extensively explored on the black hole –host galaxy relationships. Besides NGC 1277, only the com-pact galaxies NGC 1332 (Rusli et al. 2011), NGC 4342 (Cret-ton & van den Bosch 1999), NGC 4486B (Kormendy et al.1997), and M60-UCD1 (Seth et al. 2014) have dynamicalblack hole mass measurements, with NGC 1332 and NGC4342 being most like NGC 1277. For these galaxies, theblack hole mass measurements are in agreement with M BH – σ ⋆ given the intrinsic scatter of the relation, but are positiveoutliers from the M BH – L bul relation (Kormendy & Ho 2013).We note that there are uncertainties associated with the bulgeluminosity for NGC 1332 (see Kormendy & Ho 2013 for de-tails) and the black hole mass measurement for NGC 4486B(see Gültekin et al. 2009 for details). Also, tidal strippingis believed to be the cause of the over-massive black hole inthe ultracompact dwarf galaxy M60-UCD1 (Seth et al. 2014),and there is some debate as to whether NGC 4486B and NGC4342 have been stripped as well (e.g., Faber 1973; Bogdanet al. 2012; Blom et al. 2014). Nevertheless, additional sim-ilar galaxies need to be studied because there could be sys-tematic differences in the scaling relations between the com-pact, high-dispersion galaxies and the giant ellipticals/BCGs.If so, that would imply that the black holes in the two types ofgalaxies grew in different ways.While the compact, high-dispersion galaxies are unusual inthe present-day Universe, they are qualitatively similar to thetypical z ∼ z ∼ z ∼ z ∼ z > HST and AO-assisted IFU observa-tions to probe the region over which the black hole domi-nates the galaxy’s potential (the black hole sphere of influ-ence; r sphere = GM BH /σ ⋆ ), and IFU observations that samplethe large-scale stellar kinematics out to several effective radii.In this paper, we focus on measuring the mass of the blackhole for the first compact, high-dispersion galaxy for whichwe have completed AO IFU observations. NGC 1271 has notbeen widely investigated in the literature and is given an un-certain SB0 classification according to the NASA/IPAC Ex-tragalactic Database (NED). The galaxy is located within thePerseus cluster, at z = 0 . H = 70 . - Mpc - , a matter density of Ω M = 0 .
27 and a cosmological constant of Ω Λ = 0 .
73. TheSloan Digital Sky Survey g - i color is 1.6 and absolute r -bandmagnitude is -20.8 for the galaxy. Long-slit spectra of NGC1271 were obtained through the HET Massive Galaxy Survey,and the reported [N II ]/H α and [O III ]/H β emission-line ratiosmeasured within a 3 . ′′ M BH – host galaxy rela-tionships, and summarize our findings. OBSERVATIONS
For NGC 1271, we obtained imaging observations with the
HST
Wide-Field Camera 3 (WFC3) in order to measure thegalaxy’s surface brightness distribution. We also acquiredspectra with the Near-infrared Integral Field Spectrometer(NIFS; McGregor et al. 2003) on the 8.1m Gemini North tele-scope assisted by the ALTtitude conjugate Adaptive optics forthe InfraRed (Herriot et al. 2000; Boccas et al. 2006) system.The NIFS data is important for constraining M BH , as it re-solves the black hole sphere of influence. We also acquiredlarge-scale spectra with the Postdam Multi Aperture Spec-trograph (PMAS; Roth et al. 2005) in the Pmas fiber PAcK(PPAK; Verheijen et al. 2004; Kelz et al. 2006) mode at the3.5m telescope at Calar Alto Observatory. Although long-slitspectroscopic observations along the galaxy major axis havebeen previously made using the HET, measuring a large-scale,two-dimensional (2D) velocity field is preferable over a sin-gle slit observation for constraining the stellar mass-to-lightratio and the stellar orbital distribution. Hence, we use thePPAK IFU observations in place of the major-axis HET mea-surements. Below we describe the WFC3, NIFS, and PPAKobservations and data reduction methods. HST
Imaging
We observed NGC 1271 with
HST
WFC3 and theIR/F160W filter under program GO-13050. The observationwas composed of three dithered full array exposures of 450s, and four dithered subarray exposures of 1.7 s, leading to atotal integration time of 1354 s. The short subarray exposureswere chosen to ensure the nucleus would not become satu-rated. The flattened, calibrated images were corrected for geo-metric distortions, cleaned, and combined using AstroDrizzle(Gonzaga et al. 2012). Since the exposures were dominatedby galaxy light, we found that the standard AstroDrizzle skysubtraction overestimated the background flux. We thereforemanually measured the background level in each of the im-ages. For the full array images, we measured the flux from thecorners of each image, while for the subarray exposures wemeasured the flux difference between the sky-subtracted fullframes and the subarray frames. With the background leveldetermined, the exposures were combined to produce a super-sampled image with a spatial resolution of 0 . ′′
06 pixel - . Notonly is the HST image suitable for determining the luminousdistribution on near the black hole, but due to the small sizeof NGC 1271, we were also able to measure the luminosityout to larger galaxy scales, extending to ∼ R e (adopting aneffective radius of 5 . ′′
6, or 2.2 kpc, measured from a singlecomponent Sérsic fit to the
HST
F160W image; see Section8.2).
NIFS Spectroscopy
The NIFS laser guide star (LGS) AO observations were ac-quired over three nights, on 2012 Dec 27, 2012 Dec 29, and2013 Jan 8, in queue mode under program GN-2012B-Q-51.We used the H + K filter and the K grating with a central wave-length of 2.2 µ m to obtain spectra over a 3 ′′ × ′′ field-of-viewand a spectral resolution of R ∼ R = 17 . ′′ away from the galaxy wasused as the tip-tilt reference. In addition, we observed the tip-tilt star to monitor the PSF during each of the three nights andthe A0 V stars HIP 10559 and HIP 22842 for telluric correc-tion.The data were reduced using IRAF tasks within the Gem-ini/NIFS package version 1.11, utilizing the example NIFSprocessing scripts . The reduction included sky subtraction,flat fielding, interpolation over bad pixels, cosmic-ray clean-ing, and spatial rectification and wavelength calibration usingRonchi mask and arc lamp exposures. The spectra were thencorrected for telluric features, using an A0 V star spectrum,after interpolating over the Br γ absorption line and dividingby a black body with a temperature of 9480 K. Next, a datacube was produced, having x and y spatial dimensions, each IRAF is distributed by the National Optical Astronomy Observatory,which is operated by the Association of Universities for Research in Astron-omy under cooperative agreement with the National Science Foundation with a scale of 0 . ′′
05 pixel - , and one spectral dimension, λ ,using a common wavelength range and sampling for the in-dividual science exposures. The relative spatial positions be-tween the data cubes were determined by summing along thewavelength axis and cross-correlating the resulting flux maps.The offsets were used to align and combine the 12 individualexposures, generating the final data cube of the galaxy. Datareduction of the PSF star observations followed a similar pro-cedure. PPAK Spectroscopy
The PPAK observations of NGC 1271 were acquired as partof a campaign to obtain large-scale spectroscopy of the com-pact, high-dispersion galaxies. The observations, data reduc-tion, and kinematic measurements for NGC 1271 will be pre-sented in Yıldırım et al. (in prep), but follow closely the PPAKobservations for two other compact, high-dispersion galax-ies described in Yıldırım et al. (2015). For completeness, webriefly review the pertinent information below and in Section4.2.The wide-field IFU observations were taken over threenights, from 2013 Jan 4-6, using the V500 grating to pro-vide coverage of 4200 - ∼
850 at 5000 Å. We used three dithers to fully sample the331 2 . ′′ ′′ away from the center ofthe instrument field-of-view, were used to measure the sky.During each of the three nights, two 1200 s science exposureswere taken at each of the three dither positions, leading to atotal of 6 hours of on-source integration. The data reductionfollowed the procedure adopted for the Calar Alto Legacy In-tegral Field Spectroscopy Area Survey. The main steps in-cluded bias subtraction, flat-fielding, cosmic ray cleaning, ex-traction of spectra, wavelength calibration, sky subtraction,and flux calibration using spectrophotometric standard stars.Spectra from the three pointings were then combined and re-sampled into a data cube, followed by a correction for dif-ferential atmospheric refraction. We note that the line spreadfunction is measured as a function of wavelength and fiber po-sition from arc lamps during the wavelength calibration step,and then homogenized to a common value prior to the extrac-tion of the PPAK kinematics. The details of these steps arediscussed at length by Sánchez et al. (2012) and Husemannet al. (2013) and we refer the reader to those publications foradditional information. CONSTRUCTING THE LUMINOUS MASS MODEL
We generated a luminous mass model for NGC 1271 by pa-rameterizing the
HST
WFC3 F160W image as the sum of 2DGaussians using the Multi-Gaussian Expansion (MGE) for-malism (Monnet et al. 1992; Emsellem et al. 1994). The MGEmethod is able to reproduce a wide range of galaxy surfacebrightness profiles and allows for an analytic deprojection todetermine the intrinsic luminosity density. Here, we use theimage decomposition package Galfit (Peng et al. 2010) be-cause it takes into consideration an error map during the fitand allows for the detailed examination of model residuals,but we utilize the implementation of Cappellari (2002) to de-termine suitable starting parameter values for the initial runwith Galfit. When constructing the MGE model, we accountfor the WFC3 PSF, which we adopt from van der Wel et al.(2012). This PSF was generated with Tiny Tim (Krist & Hook F IG . 1.— Isophotes of the MGE model (red) are compared to the HST
WFC3 F160W image (top) and to the inner 3 . ′′ × . ′′ q ′ ) was required to belarger than 0.25. Due to the degeneracy associated with fittinga large number of Gaussians, we chose to restrict q ′ > . EXTRACTING THE STELLAR KINEMATICS TABLE 1MGE P
ARAMETERS j log I j (L ⊙ , H pc - ) σ ′ j ( ′′ ) q ′ j (1) (2) (3) (4)1 6.074 0.073 0.252 4.778 0.175 0.833 4.786 0.399 0.564 4.183 0.765 0.775 3.172 1.838 0.666 3.756 2.018 0.267 3.391 4.306 0.258 3.054 5.857 0.389 2.474 8.876 0.4910 1.879 12.946 0.7211 0.889 24.772 0.99 N OTE . — The component number is listed in column (1), the cen-tral surface brightness, using a galactic extinction of 0.085 and a solarabsolute magnitude of 3.33, is provided in column (2), the dispersionalong the major axis is given in column (3), and the axis ratio is pre-sented in column (4). The components all have of a position angle of - . ◦ and projected quantities are denoted with primed variables. From the NIFS and PPAK data cubes, we measured theline-of-sight velocity distribution (LOSVD) as a function ofspatial location. The LOSVD was described using the firstfour Gauss-Hermite (GH) moments: the radial velocity ( V ),the velocity dispersion ( σ ), and h and h , which describethe LOSVD’s asymmetric and symmetric deviations from aGaussian. High signal-to-noise (S/N) spectra, typically & σ uncertainties. During the Monte Carlo runs, thepenalization term was set to zero to produce realistic errors. NIFS Kinematics
We measured the stellar kinematics from the three pri-mary K -band CO bandheads [(2 - CO, (2 - CO, and(4 - CO] in 127 spatial bins by using pPXF to fit the wave-length region between 2 . - . µ m. We made use of theNIFS Spectral Template Library v2.0 (Winge et al. 2009),which contains 28 stars observed using the NIFS IFU withthe K grating and H + K filter. The library includes spectraltypes ranging from G8 - M5 giant stars, K3 - M3 supergiants,and a G8 II star.We first created an optimal stellar template by fitting a highS/N spectrum, constructed by adding together all spectra inthe galaxy data cube. This optimal template was composedof six stars, and was dominated by M5 III, M3 III, and K3Iab stars that make up 37%, 26%, and 21% of the total flux,respectively. Next, we measured the GH moments in each spatial bin with pPXF by keeping the relative weights of thestars that make up the template fixed, but allowing the co-efficients of a second degree additive Legendre polynomialand a second degree multiplicative Legendre polynomial tovary. Such polynomials are needed to account for differencesin the optimal stellar template and the galaxy spectra shape,as the continuum of the stars in the NIFS Spectral TemplateLibrary has been previously removed. The kinematics werein good agreement with those measured when fitting a newoptimal stellar template to each spatial bin and fitting onlytwo GH moments. Finally, we bi-symmetrize the kinematicsusing the machinery presented van den Bosch & de Zeeuw(2010). Since the dynamical models are only able to pro-duce symmetric kinematics, this step is commonly performed(e.g., Gebhardt et al. 2003; Cappellari et al. 2006; Onken et al.2014) in order to reduce the noise in the observations. Withthe symmetrization routine, the systematic offsets in the oddGH moments, such as the galaxy’s recession velocity, are re-moved as well.From the NIFS data, we find that the galaxy is rotatingquickly, with stars reaching velocities of ±
226 km s - . Thereis also a sharp peak in the velocity dispersion, which risesfrom 205 km s - at a radius of ∼ ′′ to 396 km s - at the cen-ter. The map of h is anti-correlated with the velocity map,while h shows a slight increase at the center. The S/N in eachspatial bin (measured as the ratio between the median value ofthe spectrum and standard deviation of the pPXF model resid-uals) ranged between 33 and 96 with a median value of 66.Therefore, we were able to place excellent constraints on thekinematics, with median errors over all spatial bins of 7 kms - , 9 km s - , 0 .
02, and 0 .
02 for V , σ , h , and h , respectively.We present example spectra and fits with pPXF at three dif-ferent locations within the NIFS data cube in Figure 2 and thebi-symmetrized NIFS kinematics in Table 2. PPAK Kinematics
We measured the stellar kinematics in 268 spatial bins overa wavelength range of 4200 - β , Mg Ib , and Fe5015 lines. During the fit with pPXF, we masked sky featuresand emission lines and included a 15th degree additive poly-nomial. The kinematics were extracted using the Indo-U.S.Library of Coudé Feed Stellar Spectra (Valdes et al. 2004),and the optimal stellar template was dominated by G9 V, G9III, K0 III, and A0p stars. As a final step, we bi-symmetrizethe kinematics and subtract off the systematic offsets in theodd GH moments using the procedure in van den Bosch & deZeeuw (2010).The kinematics from the PPAK data were measured out to ∼ ′′ , or ∼ R e . The large-scale kinematics exhibit featuresthat are similar to the measurements made from the high spa-tial resolution NIFS data. In particular, the stars show rotationwith velocities of ± - from 102 km s - at radius of ∼ ′′ , andthere is a h - V anti-correlation. The difference in the peakvelocity dispersions measured from the PPAK and NIFS datacan be attributed to the very different spatial resolutions of thetwo data sets. Typical errors on the PPAK kinematics for V , σ , h , and h are 8 km s - , 12 km s - , 0.04, and 0.05. We presentexample fits to the galaxy spectra at several spatial locationsin Figure 3 and provide the bi-symmetrized PPAK kinematicsin Table 3.NGC 1271 has an uncertain SB0 classification according to F IG . 2.— Shown in the top, middle, and bottom panels, respectively, areexample NIFS spectra extracted from three spatial locations: a single spaxellocated near the nucleus, a bin containing five spaxels at an intermediate dis-tance from the galaxy center, and one of the outermost bins composed of 28spaxels. Overplotted in red is the optimal stellar template convolved with thebest-fitting LOSVD. The model residuals are shown in green, and have beenshifted by an arbitrary amount. NED, but we do not see an obvious bar feature in the
HST
F160W image or in the PPAK/NIFS kinematics. N-body sim-ulations have shown that common kinematic signatures asso-ciated with bars include a “double-hump” feature in the rota-tion curve and an h - V correlation over the projected lengthof the bar (Bureau & Athanassoula 2005). Instead, even theunsymmetrized kinematics clearly show a smooth increase inthe radial velocity from the southeast side of the galaxy tothe northwest side, and that h is anti-correlated with V , as isexpected for axisymmetric systems. MEASURING THE PSF
The PSF of the NIFS and PPAK observations are importantinputs into the stellar dynamical models. In order to estimatethese quantities, we convolve the MGE model presented inSection 3 with the sum of two concentric, circular 2D Gaus-sians in order to match the collapsed NIFS and PPAK datacubes. The PSF is parameterized by the dispersion and rela-tive weight of each Gaussian component. We find dispersionsof 0 . ′′
16 and 0 . ′′
43 with relative weights of 0.61 and 0.39, re-spectively, for the NIFS PSF, while the PPAK PSF can bedescribed with dispersions of 1 . ′′
52 and 5 . ′′
45 with relativeweights of 0.82 and 0.18. In addition, the comparison be-tween the
HST image and the collapsed data cubes allows forthe center of the NIFS and PPAK apertures to be defined. Thecore of the NIFS PSF is larger than expected for AO obser-vations (e.g., Krajnovi´c et al. 2009; Seth et al. 2014), whichis likely the result of using a fairly faint, off-axis tip-tilt star.In Section 7.1, we test the effect of our assumed NIFS PSFon the inferred black hole mass by instead estimating the PSF
TABLE 2NIFS K
INEMATICS x ( ′′ ) y ( ′′ ) V (km s - ) ∆ V (km s - ) σ (km s - ) ∆ σ (km s - ) h ∆ h h ∆ h (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)-0.027 0.022 -8.879 7.817 396.368 10.793 0.017 0.016 0.029 0.017-0.027 -0.028 -38.385 6.554 394.762 8.844 0.017 0.014 0.033 0.0180.055 0.022 37.125 5.608 395.394 7.818 -0.015 0.012 0.031 0.0150.055 -0.028 11.045 6.073 392.972 8.368 -0.001 0.012 0.029 0.014-0.077 -0.003 -45.778 6.763 392.601 9.207 0.026 0.014 0.028 0.017 N OTE . — Table 2 is published in its entirety in the electronic edition of ApJ. A portion is shown here for guidance regarding itsform and content. Columns (1) and (2) are the x and y Voronoi bin generators, measured relative to the galaxy center. Columns (3)- (8) provide the bi-symmetrized NIFS kinematics and errors. The position angle is 141.14 ◦ , measured counter-clockwise from thegalaxy’s major axis to x . F IG . 3.— Shown in the top, middle, and bottom panels, respectively, are example PPAK spectra extracted from three spatial locations. Overplotted in red is theoptimal stellar template convolved with the best-fitting LOSVD, and the gray shaded boxes denote the wavelength regions excluded during the spectral fitting,due to the presence of emission lines or sky lines. The model residuals are shown in green, and have been shifted by an arbitrary amount.TABLE 3PPAK K INEMATICS x ( ′′ ) y ( ′′ ) V (km s - ) ∆ V (km s - ) σ (km s - ) ∆ σ (km s - ) h ∆ h h ∆ h (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)-0.063 -0.208 -28.540 4.759 296.999 6.723 0.010 0.013 0.027 0.016-0.063 0.792 18.003 4.564 294.131 6.221 -0.013 0.013 0.025 0.0160.937 -0.208 60.969 4.491 282.870 5.858 -0.030 0.013 0.035 0.017-1.063 -0.208 -85.825 4.277 278.884 5.984 0.043 0.012 0.036 0.017-0.063 -1.208 -60.969 4.491 282.870 5.858 0.030 0.013 0.035 0.017 N OTE . — Table 3 is published in its entirety in the electronic edition of ApJ. A portion is shown here for guidance regarding itsform and content. Columns (1) and (2) are the x and y Voronoi bin generators, measured relative to the galaxy center. Columns (3)- (8) provide the bi-symmetrized PPAK kinematics and errors. The position angle is 140.71 ◦ , measured counter-clockwise fromthe galaxy’s major axis to x . from NIFS observations we acquired of the tip-tilt star itself. ORBIT-BASED MODELS
Black hole masses are often measured from stellar kine-matics by constructing dynamical models based upon theSchwarzschild superposition method (Schwarzschild 1979),and here we use the three-integral, triaxial Schwarzschildcode of van den Bosch et al. (2008). This technique findsa self-consistent distribution function from the observableswithout any assumptions about the orbital anisotropy. In themodel, the black hole, the stars, and dark matter all contributeto the galaxy’s gravitational potential. The stellar potential isdetermined by deprojecting the observed surface brightnessassuming a viewing orientation and a stellar mass-to-light ra-tio ( Υ ) that is constant with radius. We then generate a rep-resentative orbit library in the potential, and the orbits arenumerically integrated while keeping track of their intrinsicand projected properties. During the modeling, the effects ofthe PSF and aperture binning are taken into account. Finally,we assign weights to each orbit such that the superpositionmatches the observed kinematics and total light distribution.We calculate many models varying the parameters of inter-est ( M BH , Υ , the viewing orientation parameters, and the darkmatter halo parameters), and the best-fit model is the one withthe lowest χ . Application to NGC 1271
For NGC 1271, we adopt a (nearly) oblate axisymmetricshape, with an intermediate to long axis ratio of 0.99. Weassume axisymmetry given that NGC 1271 looks highly flat-tened and exhibits rapid rotation, and we do not find any evi-dence for kinematic twists. With this assumption, the inclina-tion angle ( i ) is the only viewing orientation parameter neededto describe the galaxy’s intrinsic shape. In our final model, weadopt i = 83 ◦ (where i = 90 ◦ corresponds to an edge-on view).The MGE description of NGC 1271 presented in Section 3 in-cludes a couple of flat Gaussian components, which can onlybe deprojected for angles 77 . i . ◦ . Therefore, we choseto run models at a fixed inclination angle that lies midway be-tween the extremes. Our choice of inclination angle is furthersupported by a nuclear dust disk that appears highly inclinedin an HST
WFC3 F814W image. While the F814W imageclearly shows a regular dust lane, the F160W image and the K -band NIFS data cube used in our analysis do not appear tobe significantly affected by dust. In addition, the NGC 1271models include a spherically symmetric dark matter halo fol-lowing a Navarro-Frenk-White (NFW) form (Navarro et al.1996). The parameters describing the NFW halo are the con-centration index ( c ) and the fraction of dark matter ( f DM ),where f DM ≡ M DM / M ⋆ and M DM is the halo virial mass and M ⋆ is the stellar mass. Hence, our models have four free pa-rameters: M BH , Υ H , c , and f DM .We began by calculating models on a coarse grid thatspanned a wide range of values before generating models ona smaller, more finely sampled grid focused around the mini-mum χ . Ultimately, our final model grid contained 21 M BH values, 31 Υ H values, 8 c values, and 20 f DM values withlog( M BH / M ⊙ ) ∈ [9 . , . Υ H ( Υ ⊙ ) ∈ [0 . , . c ∈ [2 , f DM ∈ [50 , . ′′
003 to 100 ′′ , and 8 angularand 8 radial values at each energy. We note that triaxial orbitfamilies (e.g., box orbits) continue to be included in our or-bital libraries because we are running a triaxial Schwarzschild code in the axisymmetric limit. Moreover, we employ adithering method, in which 125 orbits with adjacent initialconditions are bundled together, to establish a smooth dis-tribution function when constructing Schwarzschild models.Thus, the galaxy models are made with 696,000 orbits. Themodels were fit to the observed NIFS and PPAK kinematics,where 4 GH moments were measured in a total of 395 bins,resulting in 1580 observables. MODELING RESULTS
The results of the final model grid are summarized in Fig-ure 4, which shows the χ as a function of M BH , Υ H , c , and f DM after marginalizing over the other three parameters. Wefind best-fit values of M BH = 3 . × M ⊙ , Υ H = 1 . Υ ⊙ , c = 16, and f DM = 50 (corresponding to M DM = 5 . × M ⊙ ).The comparison between the observed NIFS kinematics andmodel predictions is shown in Figure 5 and the comparisonbetween the PPAK data and model predictions is displayed inFigure 6. The model is an excellent match to the observedkinematics, and is able to reproduce the sharp increase in thevelocity dispersion and the slight peak in h at the nucleus.The χ per degree of freedom ( χ ν ) is 0.3. If the unsym-metrized kinematics are used instead, the best-fit model has χ ν = 1 . M BH and Υ H that are consistent within thefinal uncertainties given below in Section 7.1.As can be seen in Figure 4, we are able to place strongconstraints on M BH and Υ H . By searching for the rangeof M BH , or Υ H , values that caused the minimum χ to in-crease by 1 and 9, we estimate the 1 σ and 3 σ model fittinguncertainties. We find M BH = (3 . + . - . ) × M ⊙ (1 σ ) and M BH = (3 . + . - . ) × M ⊙ (3 σ ), as well as Υ H = 1 . + . - . Υ ⊙ (1 σ ) and Υ H = 1 . + . - . Υ ⊙ (3 σ ). In contrast, the dark haloparameters are not well constrained, and the c and f DM val-ues are highly uncertain. Specifically, the marginalized χ curve for c is unconstrained at the upper end, with c > σ level. Although the best-fit value for c is at the maxi-mum value considered in our final model grid, previous runsusing coarsely sampled grids showed no sign of convergencefor large values of c . Similarly, the marginalized χ curve for f DM is essentially flat, and all f DM values sampled by our grid(50 ≤ f DM ≤ σ . The best-fit valuefound for f DM is the minimum value considered in our finalgrid, but we also ran models without a dark halo and found asignificantly worse fit, such that the χ increased by 123 rela-tive to the best-fit model with a dark halo. Thus, a dark halo isrequired to match the observed kinematics, but its propertiescannot be pinned down with the current datasets and we donot present any further details associated with the dark haloparameters. Error Budget
The formal model fitting uncertainties quoted in the previ-ous section are the statistical errors associated with the dy-namical models, however systematic effects can have a sig-nificant impact on the inferred black hole mass and mass-to-light ratio. In this section, we evaluate some common sourcesof uncertainty that are not already incorporated into the statis-tical errors, such as those associated with the assumed form ofthe dark matter halo, the adopted inclination angle, the num-ber of orbits used in the models, the NIFS PSF model, detailsassociated with the extraction of the NIFS kinematics, and thesymmetrization of the input kinematics. F IG . 4.— The plots summarize the results of the stellar dynamical models run with i = 83 ◦ and an NFW dark matter halo. The χ is shown as a function of M BH (top left), Υ H (top right), c (bottom right), and f DM (bottom left) after marginalizing over the other three parameters. The red point denotes the best-fitmodel, and the dashed line depicts where minimum χ has increased by 9, which corresponds to the statistical 3 σ uncertainties. The uncertainty in M BH and Υ H due to systematic effects is significantly larger than that statistical 1 σ error (see Section 7.1). Thus, we do not plot the statistical 1 σ confidence level, as it is notrepresentative of the range of possible parameter values. The M BH and Υ H parameters are well constrained despite the large uncertainties associated with thedark halo parameters. Dark Matter Halo : Previous work has clearly shown thatthe dark halo could be an important component in the stel-lar dynamical models due to the degeneracy between the darkhalo and stellar mass-to-light ratio, which in turn is also de-generate with the black hole (e.g., Gebhardt & Thomas 2009;Schulze & Gebhardt 2011; Rusli et al. 2013). If r sphere is spa-tially well resolved, then the degeneracy between the blackhole and mass-to-light ratio can be mitigated, and the exclu-sion of a dark halo will have minimal impact on the inferred M BH . In contrast, if r sphere is not very well resolved and a darkhalo is not included in the stellar dynamical models, then Υ will be artificially elevated to account for the missing massat large radii. Since Υ is taken to be constant with radius, asmaller M BH is then required to fit the observed central kine-matics.When generating a grid of models without a dark halo forNGC 1271, and assuming i = 83 ◦ to match our fiducial modelpresented in Section 7, we measure M BH = 1 . × M ⊙ and Υ H = 1 . Υ ⊙ . In other words, the inferred M BH is underesti-mated by a factor of ∼ M BH = 2 . × M ⊙ and Υ H = 1 . Υ ⊙ .Moreover, we tested how the assumed shape of the dark haloaffects M BH . Our fiducial model was calculated assuminga spherical NFW halo, but another common form is a halowith a cored logarithmic potential (Binney & Tremaine 1987;Thomas et al. 2005), given by ρ DM ( r ) = V c π G r c + r ( r c + r ) . (1)The parameters V c and r c are the asymptotic circular velocityand radius within which the dark matter density is constant.Thus, the halo from a logarithmic potential yields smallerdensities at small radii compared the the NFW halo. We con-structed models with a dark halo from a cored logarithmic po-tential, sampling 9 . ≤ log( M BH / M ⊙ ) ≤ .
2, 0 . ≤ Υ H ≤ . Υ ⊙ , 100 ≤ V c ≤
700 km s - , and 1 ≤ r c ≤
32 kpc. We recov-ered similar results to the models with an NFW halo, namelythat M BH = 3 . × M ⊙ and Υ H = 1 . Υ ⊙ , correspondingto a 7% increase in M BH and a 4% decrease in Υ H comparedto the fiducial model. Although the black hole mass is sen- F IG . 5.— The bi-symmetrized NIFS kinematics for NGC 1271 (top) are compared to the best-fit model predictions (bottom), where M BH = 3 . × M ⊙ and Υ H = 1 . Υ ⊙ . The same scaling, shown by the color bar on the right with the minimum and maximum values given at the top of the maps, is used to plot thedata and model. The NIFS observations show that the galaxy is rapidly rotating with a peak in the velocity dispersion at the nucleus. An anti-correlation between h and V is found, as is expected for galaxies with axial symmetry. The blue-shifted side of the radial velocity map corresponds to the southeast side of thegalaxy.F IG . 6.— The bi-symmetrized PPAK kinematics (top), which extend out to about 4 R e , are shown along with the predictions from the best-fit stellar dynamicalmodel (bottom); see Figure 5 for description. Kinematic measurements are missing from x ∼ - ′′ , y ∼ ′′ and from x ∼ ′′ , y ∼ ′′ due to the presence offoreground objects, which were masked before extracting the kinematics. The southeast side of the galaxy has blue-shifted radial velocities. sitive to the inclusion of a dark halo in the stellar dynamicalmodels, the form of the halo has a small impact on M BH . Forthis reason, being unable to constrain the dark halo parame-ters is not a concern for the purposes of this paper, as longas reasonable halos are sampled over when constructing theorbit-based models. Inclination Angle : All of the models presented in this pa-per assume an axisymmetric shape with an inclination angleof i = 83 ◦ . However, we also ran a grid of models that sam-pled 13 inclination angles from 77 to 89 ◦ . This correspondsto the range of angles for which the MGE model in Section3 can be deprojected. It is computationally expensive to cal-culate a model grid that samples over M BH , Υ H , i , c , and f DM simultaneously, so we instead varied the first three parame-ters while sampling over five NFW halos. The five dark haloswere those with the lowest χ from the model grid at the be-ginning of Section 7, and the halos span a range of c and f DM values (8 ≤ c ≤
16 and 50 ≤ f DM ≤ M BH = 3 . × M ⊙ , which is within 10% ofthe best-fit value in Section 7, and Υ H = 1 . Υ ⊙ , which is thesame as the best-fit value in Section 7. Moreover, the best-fitinclination angle was i = 87 ◦ , however the angle was not wellconstrained. All angles between 79 ◦ and 89 ◦ were allowedwithin the 3 σ statistical uncertainties. Such behavior is notsurprising, and other stellar dynamical work have also foundit difficult to infer the inclination angle from 2D line-of-sight0kinematics (Krajnovi´c et al. 2005; van den Bosch & van deVen 2009). Number of Orbits : The fiducial model presented in Sec-tion 7 was calculated using orbits that covered 29 equipoten-tial shells with 8 angular and 8 radial values at each energy.When accounting for the orbital dithering, this translates intoa total of 696,000 orbits. We also tested the effect on M BH and Υ H when the number of orbits is about doubled, such that37 equipotential shells with 10 angular and 10 radial valuesat each energy are used. Again 125 orbits with adjacent start-ing positions were bundled together, resulting in 1,387,500orbits. Due to a large increase in computational time for asingle model, we constructed a model grid that samples over M BH , Υ H , and the top five NFW halos from Section 7. Wefound no change in the best-fit M BH or Υ values compared tothe fiducial model. NIFS PSF : The NIFS PSF was measured by comparing theMGE model of the
HST image to the collapsed NIFS datacube. While this approach is commonly used in black holemass measurement work (e.g., Krajnovi´c et al. 2009; Sethet al. 2010; Walsh et al. 2012), estimation of the PSF fromAO observations is notoriously difficult due to the constantlychanging quality of the AO correction and the combination ofdata cubes from multiple nights. Therefore, we also estimatedthe PSF in a different manner in order to assess how stronglythe adopted NIFS PSF affects M BH . Utilizing the NIFS obser-vations of the tip-tilt star, we fit the sum of four concentric,circular 2D Gaussians to the collapsed NIFS data cube usingGalfit. We found that the PSF is best described by Gaussianswith dispersions of 0 . ′′
04, 0 . ′′
08, 0 . ′′
21, and 0 . ′′
43 with relativeweights of 0.08, 0.36, 0.26, and 0.30. A four-component PSFmodel provided a significantly better fit to the collapsed datacube than a simpler two-component model, and the residualsbetween the four Gaussian model and the data have a standarddeviation of just 9% out to a radius of 1 ′′ . The PSF is typicalof what one would expect from the Gemini AO system (e.g.,Gebhardt et al. 2011; Onken et al. 2014), and the quality of theAO correction is better than that implied by the PSF adoptedin the fiducial model. This is not completely surprising asthe NIFS observations of the star used the star itself for tip-tilt corrections, whereas the observations of the galaxy weremade off-axis, using the star for guiding. Nonetheless, cal-culating stellar dynamical models using this better PSF andcomparing to the results using the poorer PSF should coverthe range of possible black hole masses due to the uncertaintyin the NIFS PSF. We calculated models using the new four-Gaussian PSF and further assumed that the center of the NIFSspaxel with the largest flux coincides with the galaxy nucleus.We varied M BH and Υ H , while sampling over the top fiveNFW halos from Section 7, and found M BH = 2 . × M ⊙ and Υ H = 1 . Υ ⊙ . Therefore, the black hole mass and mass-to-light ratio change by 10% and 4% compared to the fiducialvalues in Section 7. Measuring the NIFS Kinematics:
We measured the NIFSkinematics with pPXF using a second degree additive Leg-endre polynomial and a second degree multiplicative polyno-mial to correct for shape differences between the LOSVD-broadened optimal stellar template and the observed galaxyspectrum. We selected this continuum correction because itwas one of the simplest models that still provided a good fitto the data, and produced kinematics that were in good agree-ment with those measured using combinations of degree 0 - - K -bandNIFS observations from the Gemini archive of stars that arepart of the NIFS Spectral Template Library and two stars ob-served under program GN-2010A-Q-112. These twelve starsare K0 - M5 giants, a K5 supergiant, and an M0 supergiant.We reduced the observations following the main procedureoutlined in Section 2.2, with the additional steps of extractinga one-dimensional spectrum, rebinning to a common wave-length range and sampling, and shifting the stars to rest. Withthis new template library, we are able to obtain good fits to thegalaxy spectra using low-order polynomials with pPXF.In order to examine possible effects on M BH and Υ H dueto uncertainties associated with the choice of the pPXF poly-nomial degree, we fit dynamical models to the NIFS kine-matics extracted using the new stellar template library and anadditive constant, along with the PPAK kinematics presentedin Section 4.2. We sampled over M BH , Υ H , and the top fiveNFW halos from Section 7, finding M BH = 2 . × M ⊙ and Υ H = 1 . Υ ⊙ . This corresponds to a change of 20% and4% from the best-fit black hole mass and mass-to-ratio fromthe fiducial model. These results are likely representative ofa maximum change in best-fit parameter values, as using thisparticular continuum correction with the new stellar templatelibrary resulted in the largest number of bins with kinematicsinconsistent at the 1 σ level (all bins were consistent at the 2 σ level) compared to the NIFS kinematics from Section 4.1. Symmetrizing the Kinematics:
The NIFS and PPAK kine-matics were bi-symmetrized prior to using them as inputs intothe stellar dynamical modeling code. We used the methodoutlined in van den Bosch & de Zeeuw (2010), which aver-ages the measurements of a GH moment in a four-fold sym-metric manner around the minor and major axes. During theaveraging of the measurements for a single GH moment, thekinematic error of the bin and the fraction of flux a spaxel con-tributes to that bin are taken into account. Such modificationsto the input kinematics and their errors are a common way inwhich to reduce observational noise, and often kinematics arebi-symmetrized in order to obtain reasonable results from anaxisymmetric modeling code and are point-symmterized foruse with a triaxial modeling code. However, symmterizationroutines are never perfect, as discussed in van den Bosch &de Zeeuw (2010). We therefore tested how symmetrizationaffects M BH and Υ H by running additional models with kine-matics that were point-symmetrized. We find that the blackhole mass increases to 3 . × M ⊙ , or by 20% of the fidu-cial value, and the H -band mass-to-light ratio decreases to1 . Υ ⊙ , or 4% of the fiducial value from Section 7. Summary:
We derive the final range of black hole massesand mass-to-light ratios for NGC 1271 by adding in quadra-ture the formal model fitting 1 σ uncertainty from Section 7and the additional sources of systematic uncertainty above.Ultimately, we determine that M BH = (3 . + . - . ) × M ⊙ and Υ H = 1 . + . - . Υ ⊙ . The dominant source of systematicsfor NGC 1271 are those associated with the continuum-correction model used to extract the NIFS kinematics and the1symmetrization of the kinematics. Both affect M BH and Υ H atthe 20% and 4% level, respectively. Other Considerations
In addition to examining possible sources of systematic un-certainty and incorporating the effects into the final error bud-get, we ran other tests to assess the robustness of the NGC1271 M BH measurement. We describe these tests below. Nuclear Dust Disk:
A dust disk is present at the center ofNGC 1271, and is visible in the F814W WFC3 image. How-ever, dust doesn’t appear to be significant in the near-infraredimaging and in the NIFS data cube. We tested constructinga new MGE of the F160W image after excluding the dustdisk by using the F814W image as guide for generating themask. We ran dynamical models using the modified MGE,following the procedure in Section 6.1 and sampling over thetop five NFW halos from Section 7. We found best-fit val-ues of M BH = 3 . × M ⊙ and Υ H = 1 . Υ ⊙ , which is wellwithin the final uncertainties adopted for NGC 1271 discussedin Section 7.1. Stellar Mass-to-Light Ratio Variation:
Our dynamical mod-els assume that Υ H remains constant with radius. In order todetermine whether there is an obvious change in stellar popu-lation, we generated an MGE of the F814W image followingthe methods described in Section 3. During the fit, we maskedout the nuclear dust disk and foreground objects in the F814Wimage, and we accounted for the PSF using a bright, isolatedstar in the image. From the MGE models of the F814W andF160W images, we don’t see evidence for color gradients,finding that the color changes by at most 0.16 mag from 0 . ′′ ′′ .Although NGC 1271 exhibits a fairly uniform color, wefurther examined dynamical models that are fit to only theNIFS kinematics. Given the limited radial extent of the NIFSkinematics, which extend out to a radius of ∼ ′′ , or ∼ M BH = (3 . + . - . ) × M ⊙ and Υ H =1 . + . - . Υ ⊙ (1 σ uncertainties). We show contours of χ asa function of black hole mass and mass-to-light ratio for thisNIFS-only model grid in Figure 7. PPAK Kinematics:
When measuring the stellar kinematicsfrom the PPAK data, we masked out spectral regions con-taining possible emission lines and sky residuals, as can beseen in Figure 3. In order to verify that our choice of a spec-tral mask does not bias the kinematic measurements and in-ferred black hole mass, we decreased the number and widthof the excluded wavelength regions. We ran dynamical mod-els using the modified PPAK kinematics while sampling overthe top five dark matter halos in Section 7. We measured M BH = 3 . × M ⊙ and Υ H = 1 . Υ ⊙ , which is within thefinal uncertainties given for NGC 1271 in Section 7.1.Also, the observed velocity dispersion of the PPAK kine-matics presented in Section 4.2 drops below the instrumen-tal resolution in many of the spatial bins located & ′′ awayfrom the nucleus. While care was taken to homogenize theline spread function to a common value such that there wasno variation with wavelength or fiber position, measuring dis-persions well below the instrumental resolution is a difficulttask. We therefore also tested the effect on M BH and Υ H whenexcluding the spatial bins in which the dispersion was below150 km s - . When calculating dynamical models that fit to F IG . 7.— Contours of χ are shown as a function of black hole mass and H -band mass-to-light ratio for the case when dynamical models are fit to justthe NIFS kinematics. At each gray point a model was calculated, and the redsquare denotes the best-fit model. The red contour and two black contourssignify where χ has increased by 1, 4, and 9 from the minimum. Thus, thevertical lines show the 1 σ uncertainties on M BH and the horizontal lines givethe 1 σ uncertainties for Υ H when marginalizing over the other parameters. the adjusted PPAK kinematics and that sample over the topfive dark matter halos in Section 7, we find no change fromthe best-fit values presented in Section 7. DISCUSSION
NGC 1271 harbors a black hole with M BH = (3 . + . - . ) × M ⊙ and has a stellar mass-to-light ratio of Υ H =1 . + . - . Υ ⊙ . We note that the final uncertainty on the blackhole mass we use is comparable to the formal 3 σ statisticaluncertainty. Some (Cappellari et al. 2009; Krajnovi´c et al.2009; Emsellem 2013) have suggested 3 σ statistical errorsshould be used in place of 1 σ errors as a conservative wayin which to account for the effect of unknown systematics on M BH . With a black hole mass of 3 . × M ⊙ and adopting276 km s - for the bulge stellar velocity dispersion (see Sec-tion 8.2), r sphere = 0 . ′′
44. Thus, the NIFS observations haveresolved the black hole sphere of influence. Below we dis-cuss the galaxy’s orbital structure and place the galaxy on the M BH - host galaxy relations. Orbital Structure
In addition to determining the mass of the black hole inNGC 1271, the Schwarzschild models provide informationabout the galaxy’s orbital structure. Using our best-fit modelin Section 7, we show the ratio σ r /σ t as a function of radiusin Figure 8. The tangential velocity dispersion is defined as σ t = ( σ φ + σ θ ) /
2, and ( r , θ, φ ) are the usual spherical coor-dinates. We find that NGC 1271 is roughly isotropic at allradii covered by our kinematic measurements, deviating by atmost 30% from σ r /σ t = 1, but we observe a trend in which σ r /σ t declines at radii outside the black hole sphere of in-fluence. As expected, short-axis tube orbits dominate in thisoblate system, making up more than 85% of the orbits at allradii. Long-axis tube orbits, which are important for triaxialand prolate systems, are negligible, while the fraction of box2 F IG . 8.— NGC 1271’s orbital structure, as inferred from the best-fit dy-namical model, is shown. The anisotropy (top) and orbit type (bottom) aredisplayed with radius over the range covered by the NIFS and PPAK kine-matic measurements. The horizontal dashed gray line denotes the isotropiccase and the vertical dot-dashed gray line shows the black hole sphere ofinfluence. NGC 1271 is roughly isotropic at all radii and is dominated byshort-axis tube orbits as is expected for oblate systems. orbits increases at small radii but still make up only 15% ofthe orbits near the nucleus.Furthermore, we use our best-fit stellar dynamical model toexamine the mass distribution as a function of average radius, ¯ r , and spin, ¯ λ z , of the orbits, where ¯ λ z = ¯ J z × ( ¯ r / ¯ σ ). Here, ¯ J z is the average angular momentum along the z -direction and ¯ σ is the average second moment of the orbit. NGC 1271 showsseveral dynamical components, as can be seen in Figure 9,including a clear non-rotating bulge (with - . < ¯ λ z < . ¯ λ z ∼ . < ¯ λ z < . Black Hole – Host Galaxy Relations
Although the dynamical decomposition from the best-fitstellar dynamical model presented above can be used to placeNGC 1271 on the M BH – bulge relationships, we follow themore common approach of carrying out a photometric de-composition to determine the galaxy’s bulge luminosity andbulge effective radius. Using Galfit, we find a single Sérsiccomponent fit is an insufficient description of the galaxy, withthe percent difference between the model and data reachingas high as 60%. The fit is significantly improved with theaddition of one or two other Sérsic components, and in thelater case the percent difference between the model and datais under 15%. In Table 4, we present the best-fit parametersof Galfit models with one, two, and three Sérsic components,as well as the F160W luminosity for each component. Thethree-component model provides the best match to the HST image, but it is difficult to unambiguously identify a “bulge”component because the components all have rather low Sér-sic indices. Therefore, we conservatively assume that the in-nermost component of the three-component model providesa lower limit on the bulge luminosity and effective radius,while the innermost component of the two-component modelgives an upper limit. This yields a K -band bulge luminosity F IG . 9.— The mass distribution is plotted as a function of average spin andradius of the orbits for the region covered by our kinematics measurements.The dynamical decomposition utilizes the orbital weights from our best-fitstellar dynamical model and shows distinct non-rotating bulge ( - . < ¯ λ z < .
2) and rotating ( ¯ λ z > .
2) disk components.TABLE 4G
ALFIT M ODELS
Component m H L H ( L ⊙ ) R e ( ′′ ) n q ′ (1) (2) (3) (4) (5) (6)1 10.72 7.7 × × × × × × N OTE . — Column (1) shows the Sérsic component number, column (2) provides theF160W apparent magnitude in the Vega system, not yet corrected for galactic extinction,column (3) gives the luminosity after a correction of 0 .
085 for galactic extinction andassuming an absolute solar magnitude of 3 .
33, column (4) is the effective radius, column(5) gives the Sérsic index, and column (6) lists the projected axis ratio. of (1 . - . × L ⊙ when correcting for galactic extinc-tion using the Schlafly & Finkbeiner (2011) WFC3 F160Wvalue of 0 . H - K color of 0 . K -band solar absolute magnitude of 3 . . - . × M ⊙ when applying the best-fit mass-to-light ratio from our dy-namical models to the luminosities in Table 4. The corre-sponding bulge effective radius ranges between 0 . ′′ . ′′ . - . σ e , bul ) for three different bulgeeffective radii corresponding to the largest R e estimate fromthe Galfit decomposition, the smallest estimate of R e , and theaverage of the two. Additionally, some previous black hole3studies have chosen to exclude data within r sphere when de-termining σ e , bul because the stellar kinematics are under thedirect influence of the black hole in this region (e.g., Geb-hardt et al. 2011; McConnell & Ma 2013). When exclud-ing the region within r sphere , we find effective stellar velocitydispersions of σ e , bul = 272 km s - , σ e , bul = 276 km s - , and σ e , bul = 349 km s - , whereas when the region within r sphere isincluded we measure σ e , bul = 285 km s - , σ e , bul = 294 km s - ,and σ e , bul = 358 km s - , for bulge effective radii of 5 . ′′
2, 2 . ′′ . ′′
6, respectively. As a comparison, the HET MassiveGalaxy Survey reports a central velocity dispersion of 317 kms - (van den Bosch et al. 2015), which is the observed stellarvelocity dispersion within a 3 . ′′ M BH - σ ⋆ and M BH - L bul relations byKormendy & Ho (2013). For the purposes of placing NGC1271 on the M BH – σ ⋆ correlation, we use σ ⋆ = 276 km s - with uncertainties that include the σ e , bul measurements madefor bulge effective radii of 5 . ′′ . ′′ r sphere . When placing NGC 1271 on the M BH – L bul relation, we set the faint end of the bulge luminosity errorbar assuming the luminosity of the innermost component ofthe three-component Sérsic fit to the HST image and the highend of the error bar assuming the luminosity of the innermostcomponent of the two-component Sérsic fit. We adopt a K -band bulge luminosity of 4 . × L ⊙ , which is the midpointof the range of possible bulge luminosities.We find that NGC 1271 consistent with the M BH – σ ⋆ rela-tion, but is an order of magnitude above the black hole massprediction from the M BH – L bul correlation. In order to demon-strate that the black hole in NGC 1271 must be larger thanthat expected from M BH - L bul , in Figure 11 we present theNIFS observations of the velocity dispersion and h alongwith the predictions from the best-fitting model with a blackhole mass of 3 . × M ⊙ and a 4 . × M ⊙ black hole.The 4 . × M ⊙ black hole is expected from M BH – L bul when conservatively using the galaxy’s total K -band luminos-ity of 8 . × L ⊙ , which is derived from the single Sér-sic fit to the HST image, after correcting for galactic extinc-tion and assuming a H - K = 0 .
2. Clear differences betweenthe kinematic predictions and the observations can be seen byeye. The best-fit model with M BH = 3 . × M ⊙ is able tonicely reproduce the sharp rise in the velocity dispersion andthe slight peak in h at the nucleus, while the less massiveblack hole predicted from M BH – L bul fails to do so.NGC 1271 has an apparent ellipticity of ǫ = 0 . λ R ≡h R | V |i / h R √ V + σ i = 0 . R , V , and σ are the radius,velocity, and velocity dispersion and the brackets denote aluminosity weighted average (Emsellem et al. 2007). Usingthe dividing line between slow and fast rotators from theATLAS survey, such that fast rotators have λ R ≥ . × √ ǫ (Emsellem et al. 2011), NGC 1271 falls well within in thisfast rotator regime.NGC 1271 appears similar to the other compact galaxiesNGC 1277, NGC 1332, NGC 4342, NGC 4486B, and M60-UCD1. All six of these early-type galaxies have small sizes,are rotating, show large stellar velocity dispersions for theirluminosities, and have black holes that are too massive fortheir host galaxy’s bulge luminosity. The black holes, how- ever, are consistent with M BH – σ ⋆ given the intrinsic scatter ofthe relation. In the case of M60-UCD1, Seth et al. (2014) sug-gest that the ultracompact dwarf galaxy (UCD) was once thenucleus of a larger galaxy that has since been tidally strippedby the giant elliptical M60, whose center lies at a projecteddistance of just 6.6 kpc away from the UCD. While tidalstripping is a natural explanation for the presence of an over-massive black hole, in the case of NGC 1271, we do not seesigns of active stripping in the HST image. The isophotes ap-pear extremely regular, and no massive galaxies immediatelyneighbor NGC 1271 like in the case of M60-UCD1. NGC1271 is ∼
270 kpc in projection from the BCG of Perseus.Further evidence could come from counting the number ofglobular clusters, as the galaxy would be stripped of its glob-ular clusters first. While NGC 1271 appears not to have beenstripped with our current data, we cannot rule out an event inthe distant past.Interestingly, the behavior of the compact, high-dispersiongalaxies being consistent with M BH – σ ⋆ but being large pos-itive outliers on M BH – L bul could be in conflict with recentobservations of BCGs, which instead may hint that blackhole mass becomes independent of σ ⋆ at high black holemass while the M BH – L bul correlation remains unchangedat large luminosities (McConnell & Ma 2013; Kormendy &Ho 2013). Clearly, more compact, high-dispersion galaxiesand BCGs/giant ellipticals need to be examined. There couldbe systematic differences in the scaling relations between thetwo types of galaxies, thereby imply different mechanismsfor black hole growth. Since the compact, high-dispersiongalaxies like NGC 1271 look similar to the quiescent z ∼ CONCLUSION
To summarize, we obtained AO-assisted Gemini NIFS ob-servations of NGC 1271 to map out the stellar kinematics onscales comparable to the black hole sphere of influence, andlarge-scale IFU data with PPAK, which are useful for con-straining the galaxy’s stellar mass-to-light ratio and orbitaldistribution. Using an
HST
WFC3 H -band image along withthe spectral information, we constructed orbit-based stellardynamical models. We measure M BH = (3 . + . - . ) × M ⊙ and Υ H = 1 . + . - . Υ ⊙ . The quoted errors combine the 1 σ model fitting uncertainties with some common sources of sys-tematic uncertainty that affect stellar dynamical models. Theblack hole in NGC 1271 is at the upper end of the black holemass distribution ( M BH > × M ⊙ ). Yet, this compact,rapidly rotating galaxy, with a high stellar velocity disper-sion for its luminosity is very different from the giant ellip-tical galaxies and BCGs that are expected to harbor the mostmassive black holes in the Universe. Such host galaxy envi-ronments have yet to be widely explored on the M BH – hostgalaxy relations. With our mass measurement, we find thatthe black hole is too large for the galaxy’s K -band bulge lu-minosity of (4 . + . - . ) × L ⊙ , falling an order of magnitudeabove the expectation from the M BH – L bul correlation, butthe black hole mass is consistent with expectations from the M BH – σ ⋆ relationship assuming σ ⋆ = 276 + - km s - . Thisbehavior has also been observed in the few other compact4 F IG . 10.— NGC 1271 (red filled square) is shown on the black hole – host galaxy relations. The black hole/galaxy measurements (black and gray filled circles)and the fitted relations (dot dashed lines) are taken from Kormendy & Ho (2013). The compact galaxies that have existing dynamical M BH measurements aredenoted with the red asterisks. These galaxies are generally consistent with M BH – σ ⋆ but are positive outliers from M BH – L bul . Kormendy & Ho (2013) did notinclude the measurements shown in gray and light red when fitting the black hole scaling relations.F IG . 11.— The observed velocity dispersion (top) and h (bottom) measured from the NIFS data (left) is compared to predictions from the best-fit model with M BH = 3 . × M ⊙ (middle) and a model with a 4 . × M ⊙ black hole (right), which is the mass predicted from M BH – L bul when conservatively adoptingthe total galaxy luminosity. When generating the σ and h predictions for a 4 . × M ⊙ black hole, we sample over Υ H and the top five NFW dark halos fromthe model grid in Section 7, such that the combination of parameters produces a model with the lowest χ for a black hole mass of 4 . × M ⊙ . The data andmodel maps are plotted on the same scale, with the ranges given by the color bar to the right and the minimum and maximum values printed at the side of themaps. 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