arXiv:astro-ph/9907003v1 1 Jul 1999 ayn eeso eal,i scerta oefundamental some that clear in is (albeit it studied detail), dSphs kinematics of Galactic internal levels varying nine their all had now Although have 1990). apply strictly 1983; not (Milgrom does possi- gravity the Newtonian & “low-acceleration which and/or a in Klessen occupy regime” 1995) Pryor 1989; diffuse these & Miller that Piatek bility & cf. (Kuhn 1998; field Kroupa tidal Galactic the inta Shglxe r neoe ndr ao fmass of conclu- halos dark the in enveloped to ∼ are Kor- alternatives galaxies dSph & remaining that Hill Pryor sion The & 1996; Aaronson Annan 1990). & mendy (Olszewski, lumi- Gilmore viable distributions most Hargreaves, appear velocity 1996; the longer non-isotropic binary of no and as — atmospheres such the dSph — nous in galaxies pulsations these high stars, the of for dispersions samples, explanations velocity velocity alternative radial several acquisition expanded that the greatly suggest and of dSphs, analysis Galactic and the to belonging ants dark massive that in evidence embedded are of con- halos. galaxies piece dispersions dSph compelling Mateo velocity Galactic 1995; most anomalous the single al. These the et Vogt 1998). stitute 1994; al. al. et et Hargreaves 1993; al. oiydseso nterne61 ms km 6-13 range the in dispersion locity eotda nxetdylreitra eoiydisper- s velocity km 6.5 internal who kinematics of large (1983), internal sion Aaronson unexpectedly their of galax- an of work known pioneering reported Studies faintest the the with . began among the are in Way ies Milky the to rpittpstuigL Nov using Journal, typeset Astrophysical Preprint the in publication for Accepted un okhsntol ofimdti eutbthses- has but Subse- result this stars. confirmed carbon that only tablished three not has for work velocities quent radial on based ogtr oioigo h ailvlcte frdgi- red of velocities radial the of monitoring Long-term h iedafshria dp)glxe belonging galaxies (dSph) spheroidal dwarf nine The 5 1 3 2 4 2 arneLvroeNtoa aoaoy iemr,C 945 CA Livermore, Laboratory, National Livermore Lawrence aionaIsiueo ehooy alSo 0-4 Pasa 105-24, Stop Mail Technology, of Institute California eateto srnm,81Dnio ulig Universit Building, Dennison 821 Astronomy, of Department Fellow Fairchild M. Sherman twr bevtr,Uiest fAioa usn Z857 AZ Tucson, Arizona, of University Observatory, Steward × 10 7 ms km ml ubro tr aigmaue eoiis u etestimat best signifi Our the velocities. is although measured II , having And the stars of of number face small the across gradient velocity aaisadi ossetwt h rsneo asv akhl nA in halo dark massive a of presence headings: the Subject with consistent is and galaxies ailvlcte aigamda rcso of precision median a having velocities radial wr peodlglx nrmd I(n I.W n weighted a find We II). (And II spheroidal dwarf M h ihRslto cel pcrmtro h ekItlsoeha telescope I Keck the on Spectrometer Echelle Resolution High The ⊙ − Mtoe l 93 r eeehaigby heating severe are 1993) al. et (Mateo NENLKNMTC FTEADOEAI WR PEODLGA SPHEROIDAL DWARF II ANDROMEDA THE OF KINEMATICS INTERNAL every 1 − n eta eoiydseso of dispersion velocity central a and M/L 1 A 1. T aatcdp aayhsacnrlve- central a has galaxy dSph Galactic o h rc Shglx:aresult a galaxy: dSph Draco the for E tl mltajv 04/03/99 v. emulateapj style X INTRODUCTION a rc C Patrick V cetdfrpbiaini h srpyia ora,Nov Journal, Astrophysical the in publication for Accepted 20 = AdoeaII) (Andromeda aais wr aais ieaisaddnmc aais individu galaxies: — dynamics and kinematics galaxies: — dwarf galaxies: . 9 − +13 ot ˆ 10 . . e ´ 9 1 M 1 , 2 − ⊙ ai Mateo Mario , 1 /L ( e.g. V, ⊙ ute et Suntzeff , hsvlei iia otoeo eea aatcdafspheroidal dwarf Galactic several of those to similar is value This . me 019 issue. 1999 10 ember ea A91125 CA dena, σ ABSTRACT 3 ≃ 0 fMcia,AnAbr I48109 MI Arbor, Ann Michigan, of y 21 dadW Olszewski W. Edward , 50 9 = ms km 2 1 . 3 − +2 cie nVg ta.(95.Attlo 9sprt aper- separate af- 29 although of object, total program each A for (1995). extracted were al. tures et Vogt in scribed excellent. were run the exposure. lamp throughout each comparison conditions after Th-Ar and Observing with before 3600s, immediately taken were spectra stars II And all tdt 1 to ited n 0.0 and nfis re,teeage ile pcrlcvrg of coverage spectral a yielded angles these 4480 order, first in mlyd dutdt anstigo 2.4 of setting gain a to adjusted 2 employed, binned 1024 was of tele- area detector I 14-15 Keck The the of on 1994) nights Echelle scope. Resolution al. the And et High Vogt the (HIRES; for on using Spectrometer 1998 spectra obtained October Echelle were 15-16 and II. giants And member in 50 II giants for red spectroscopy candidate intermediate-resolution and tometry ailvlcte o ee e insi n Iobtained II And in telescope. giants I Keck red nine the on seven based with for II And velocities of radial kinematics internal by the this dominated of analysis In are dSphs that dynamics. Galactic arguments non-equilibrium of motions vitiate internal high would a (vanthe of dispersion kine- isolated detection velocity a the relatively 1993), central for is al. K¨onig target galaxy et 1972; promising Bergh this den a Since is study. II) matic (And II Andromeda unanswered. remain questions rs-ipre n rtn nlswr xdat fixed were angles grating and cross-disperser td fCo´,Oe&Chn(99 h present who (1999) Cˆot´e, Cohen of & Oke study 2 − . . 7 6 1 h aawr eue namne dnia ota de- that to identical manner a in reduced were data The stenaeto h Shglxe soitdwt M31, with associated galaxies dSph the of nearest the As e in ebr fAdI eeslce rmthe from selected were II And of members giant Red ms km o ee e insblnigt h isolated the to belonging giants red seven for 2.1. < ∼ ◦ ′′ epciey ic h rs ipre a used was disperser cross the Since respectively. , . − λ< λλ 15 1 2. betSlcinadHRSSpectroscopy HIRES and Selection Object hr a eeiec o radial a for evidence be may There . × ac fti euti o u othe to due low is result this of cance × o h lblms-olgtrtoof ratio mass-to-light global the for e ∼ enrda eoiyof velocity radial mean BEVTOSADREDUCTIONS AND OBSERVATIONS 7 04pxl.Asnl edu mlfirwas amplifier readout single A pixels. 1024 me 019 issue. 1999 10 ember ′′ . 6900 ihteC ekr xouetmsfor times Exposure decker. C5 the with 0 4 dII. nd n ..Cook K.H. and enue omauenine measure to used been s .Teetac pruewslim- was aperture entrance The A. ˚ 5 × Letter v ,gvn neffective an giving 2, LAXY r al –188 = epeetan present we , e − 1 AU The /ADU. ± 3 I V − 0 pho- . 05 ◦ 2 Andromeda II ter some experimentation it was decided to use only eight dashed lines show the major and minor axes of the galaxy, ◦ orders in measuring radial velocities (i.e., those spanning where we have estimated a position angle of θ0 = 160±15 ˚ the range 4848 <∼ λλ <∼ 5413 A). Eleven high-S/N spectra for the major axis of the galaxy based on a visual inspec- for seven different IAU radial velocity standard stars were tion of Figure 2 of Caldwell et al. (1992). The ellipse also obtained during the two night run. These spectra indicates the geometric mean King-Michie core radius of ′ were reduced in a similar manner to those of the And II rc = 1.86 (see §3.2), where e ≡ 1 − b/a = 0.3 (Cald- program stars and were used to create a master template well et al. 1992). The seven stars having measured radial as described in Vogt et al. (1995). Radial velocities for velocities are found in the same quadrant of the galaxy, And II red giants were then derived by cross-correlating although five of these objects lie within one core radius their spectra against that of the master template. of the galaxy’s center while the two remaining stars are A critical step in deriving mass-to-light ratios from ra- located considerably further out, at radii of 4.′65 and 6.′00. dial velocity measurements is the proper determination of In the upper and right panels of Figure 2, we plot the he- the velocity uncertainties. This is best done empirically, liocentric radial velocities for the seven stars as a function using repeat radial velocity measurements (preferably ob- of perpendicular distance from the major and minor axes, tained during separate observing runs). We have combined respectively. Interestingly, the two most distant stars both −1 the 34 velocities of 14 stars given in Vogt et al. (1995) have radial velocities of vr >∼ −180 km s , whereas the and Mateo et al. (1998) with additional velocities for four velocities of the five stars near the center of the galaxy fall −1 stars (including two And II members) obtained during this in the range −197 <∼ vr <∼ −188 km s . This fact, along run. All velocities were obtained using identical intrumen- with the galaxy’s rather high ellipticity, suggests that rota- tal setups and similar reduction procedures using IRAF.6 tion might, at least in part, be responsible for the high ve- We express the velocity uncertainty of each measurement locity dispersion measured for And II. Such a result would as be surprising since only one Galactic dSph galaxy (Ursa σv = α/(1 + RT D), (1) Minor) is known to be rotating, and even in this case, the rotation is dynamically unimportant: v /σ ∼ 0.5 where R is a parameter which measures the height of rot,0 0 T D (Hargreaves et al. 1994; Armandroff, Olszewski & Pryor the cross-correlation peak relative to the local noise in the 1995). In the next section, we discuss the possible effects cross-correlation function, and α is a constant which must of rotation on the derived mass-to-light ratio for And II. be determined empirically (Tonry & Davis 1979). Based on our sample of repeats, we adopt α = 12.0 which is slightly lower than, but consistent with, the values of 14.9 3.2. Mass-to-Light Ratio and 13.4 found by Mateo et al. (1998) and Cook et al. We have estimated the mass-to-light ratio of And II in (1999) using smaller samples. It is, however, inconsistent two different ways. First, we have fit an isotropic, single- with the value of 26.4 given in Vogt et al. (1995) although mass King-Michie model to the V -band surface bright- the difference is due primarily to a single discrepant ness profile given in Caldwell et al. (1992), asssum- (Leo #23) which was discarded since it was found to con- 2 ing E(B − V ) =0.062 mag, AV = 3.1E(B − V ) and tribute nearly half of the total χ for the sample. We D = 660 kpc (Cˆot´eet al. 1999b). The parameters of conclude that that equation 1 with α = 12.0 closely re- this model are given in Table 2, along with other fun- flects our true velocity errors, and refer the reader to Cˆot´e damental parameters for And II. Both the radii used in et al. (1999a) for a full discussion of the determination of the fit and those quoted in this table are geometric mean α. radii. The tabulated (1σ) uncertainties in these param- The results are summarized in Table 1, which gives for eters have been determined by fitting King-Michie mod- each star the ID number, V magnitude, (V −I) color, pro- els to each of 100 simulated data sets generated from the jected galactocentric distance, position angle, heliocentric original model and using the uncertainties in the observed Julian date and RT D. The final two columns give the in- surface brightness profile (see Fischer et al. 1992). In- dividual and mean heliocentric radial velocities. Finding tegrating the isotropic model over all radii gives a total charts for the program stars may be found in Cˆot´eet al. +0.73 6 luminosity of LV = (2.95−0.50) × 10 LV,⊙ for And II. (1999b). Based on the seven radial velocities given in Table 1, we +3.1 −1 3. ANALYSIS find a scale velocity of vs = 10.8−3.0 km s and a sys- temic velocity of v = −185.4±3.5 km s−1 for this model. Mean Velocity, Velocity Dispersion and the 0 3.1. These values correspond to a central velocity dispersion Possibility of Rotation +2.7 −1 +13.9 of σ0 = 9.3−2.6 km s and M/LV = 20.9−10.1M⊙/LV,⊙, Using the velocities given in Table 1, we find vr = which we adopt as our best estimate for the global mass- −1 −1 −188.1 ± 2.8 km s and σmle = 7.1 ± 2.1 km s using to-light ratio for And II. Note that if the sample is limited the Pryor & Meylan (1993) maximum-likelihood estima- to just the five stars with r < rc, this estimate drops to +1.9 tors for the weighted mean radial velocity and intrinsic M/LV = 2.0−1.3M⊙/LV,⊙, demonstrating that the high velocity dispersion. For comparison, the bi-weight esti- mass-to-light ratio found here is due to the large velocity mates (Beers, Flynn & Gebhardt 1990) for the systemic residuals of the two outermost stars. velocity and velocity dispersion are vr,bw = −188.5 ± 3.6 As a check on the above mass-to-light ratio, we have −1 −1 km s and σbw =8.3 ± 1.0km s , respectively. also used the tensor virial theorem to estimate the mass of The large panel of Figure 2 shows the location our seven And II, explicitly including the possible effects of rotation. program stars with respect to the center of And II. The Naturally, with a sample of only seven radial velocities, 6IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under contract to the National Science Foundation. Cˆot´eet al. 3 the exact form of the rotation law (if any) is hopelessly Might this be the case for And II? Following Mateo et al. under-constrained. Our goal here is simply to explore the (1993), we calculate for each dE/dSph galaxy possible effects of ordered motions on the inferred velocity a “stability index”, X = log10(ρV,0/ρGal), where ρV,0 ∼ dispersion and, hence, on the derived mass-to-light ratio. µV,0/2rc is the central density of the dSph galaxy (de- In the right and upper panels of Figure 2 we show the termined from the observed surface brightness profile and rotation-corrected velocities for the seven And II members an assumed mass-to-light ratio of M/LV = 2M⊙/LV,⊙) assuming that, over the region spanned by these stars, the and ρGal is the mean density of the host galaxy interior galaxy is rotating as a solid-body about the minor and to the position of each satellite. The latter values have major axes, respectively. The virial mass is then given by been calculated assuming logarithmic potentials for M31 and the Milky Way having circular velocities of vc = 260 2r −1 M = (v2 +3σ2) (2) and 220 km s , respectively. The results of this exercise G rot,0 0 are shown in the upper panel of Figure 3. For And II, we −3 find ρ =0.012 ± 0.003M⊙ pc and X ∼ 2.1, meaning where v is the mass-weighted rotation velocity, σ is V,0 rot,0 0 that the internal baryonic mass density in And II is ∼ 120 the mass-weighted velocity dispersion and r is the har- times greater than the average enclosed mass density (i.e., monic radius (e.g., see Meylan & Mayor 1986). The and baryons). Evidently, tides are unlikely to rotation-corrected velocities (i.e., the open circles in Fig- play an important role in driving the internal kinematics ure 2) are then used to derive σ , approximating the den- 0 of And II.7 sity profile by the isotropic King model discussed above (which assumes that mass traces light). In the two cases 3.3.3. Dark Matter of solid-body rotation about the major and minor axes, the derived mass-to-lights ratios are M/LV = 63 and The lower panel of Figure 3 shows the global mass-to- 19M⊙/LV,⊙, respectively. If rotation is neglected (i.e., the light ratios of Local Group dE/dSph galaxies (data from uncorrected velocities are used), then the virial mass esti- Mateo 1998) plotted as a function of their absolute mag- mator gives M/LV = 22, in agreement with the preceding nitude. Clearly, And II is consistent with the established results. trend between mass-to-light ratio and integrated luminos- ity (Kormendy 1987). In addition, the mass-to-light ratio 3.3. Discussion found here is consistent, at the 1.2σ level, with the sug- gestion (Mateo et al. 1993; Mateo 1998) that all dE/dSph We now discuss the implications of the mass-to-light galaxies studied to date consist of luminous components ratio of And II presented here, concentrating on three having M/LV = 2M⊙/LV,⊙ which are embedded in dark possible interpretations: (1) Modified Newtonian Dynam- 7 matter halos of mass M ∼ 2 × 10 M⊙, as indicated by the ics (MOND); (2) non-equilibrium dynamics; and (3) dark dashed line in Figure 3. matter.

3.3.1. Modified Newtonian Dynamics The authors thank Phil Fischer for useful discussions, and the referee, Tad Pryor, for his prompt and helpful Milgrom (1983, 1995) has argued that dSph galaxies oc- comments. PC acknowledges support provided by the cupy a “low-acceleration regime” in which Newton’s sec- Sherman M. Fairchild Foundation. MM was partially sup- ond law deviates from the standard r−2 law. For isotropic ported by grants from the NSF during the course of this velocity dispersion tensors, the MOND virial mass is given research. EWO was partially supported by NSF grants by AST 92-23967 and AST 96-19524. 81 − M = σ4(Ga ) 1 (3) 4 0 0 where G is the gravitational constant, σ0 is the central line- −8 −1 of-sight velocity dispersion and a0 =1.2 × 10 cm s is +2.7 the MOND acceleration constant. Adopting σ0 = 9.3−2.6 km s−1 (the central velocity dispersion of the isotropic +0.73 6 King-Michie model) and LV = (2.95−0.50)×10 LV,⊙ gives +4.8 M/LV = 3.2−2.3M⊙/LV,⊙ for the MOND mass-to-light ratio, which is consistent with the mass-to-light ratios of Galactic globular clusters. We conclude that MOND pro- vides an adequate description of the internal kinematics of And II, without requiring the presence of a dark halo.

3.3.2. Non-Equilibrium Dynamics: Tides One possible explanation for the high central velocity dispersions of dSph galaxies is that these objects are not in dynamical equilibrium as a result of time-dependent os- cillations caused by the tidal field of the host galaxy (e.g., Kuhn & Miller 1989; Cuddeford & Miller 1990) or outright tidal disruption (Kroupa 1997; Klessen & Kroupa 1998). 7Although M33 is ∼ 2× nearer (in projection) to And II, its influence is negligible compared to that of M31 due to its much lower mass −1 (e.g., vc ∼ 80 km s according to Figure 3 of Zaritsky, Elston & Hill 1989). 4 Andromeda II

Table 1 Radial Velocities for Red Giants in Andromeda II

ID V (V − I) R θ HJD RT D vr vr (mag) (mag) (′) (deg) 2440000+ (kms−1) (kms−1) And II-5 21.89 1.72 1.36 243 11101.8579 3.97 –192.3±2.4 –192.6±1.6 11101.9021 4.45 –192.8±2.2 And II-32 21.82 1.81 0.72 221 11101.9499 5.05 –188.1±2.0 –188.1±2.0 And II-22 21.65 1.69 4.65 195 11101.9961 3.41 –180.1±2.7 –178.7±1.8 11102.0407 4.05 –177.6±2.4 And II-4 21.91 1.62 0.53 250 11102.7910 7.08 –188.9±1.5 –188.9±1.5 And II-11 21.94 1.63 1.61 200 11102.8367 4.97 –194.8±2.0 –194.8±2.0 And II-36 22.05 1.78 1.29 181 11102.9153 4.12 –197.3±2.3 –197.3±2.3 And II-26 21.82 1.66 6.00 191 11103.0083 4.11 –176.4±2.3 –176.4±2.3 Cˆot´eet al. 5

Table 2 Observed and Derived Parameters for Andromeda II

Quantity Symbol Value Units Reference

+100 Distance D 660−85 kpc 4 True Distance Modulus (m − M)0 24.1±0.3 mag 4 Reddening E(B − V ) 0.062±0.010 mag 3 +0.23 Absolute Magnitude MV −11.40−0.19 mag 2,5 +0.47 Core Radius rc 1.89−0.37 arcmin 2,5 +91 362−71 pc 2,5 +1.12 Half-Mass Radius rh 3.27−0.50 arcmin 2,5 +216 627−96 pc 2,5 +11.4 Tidal Radius rt 13.8−4.5 arcmin 2,5 +2.19 2.65−0.86 kpc 2,5 +0.37 Concentration c 0.87−0.25 2,5 Ellipticity e 0.3 2 Position Angle θ0 160±15 deg 2,5 −2 Central Surface Brightness µV,0 24.75±0.12 mag arcsec 2,5 +0.50 −2 4.43−0.47 LV,⊙ pc 2,5 +0.73 6 Integrated Luminosity LV (2.95−0.50) × 10 LV,⊙ 2,5 −1 Maximum Likelihood Mean Velocity v0 −188.1 ± 2.8 kms 5 −1 Biweight Central Velocity vr,bw −188.5 ± 3.6 kms 5 −1 Maximum Likelihood Dispersion σmle 7.1±2.1 km s 5 −1 Biweight Velocity Dispersion σbw 8.3±1.0 km s 5 King-Michie Model +3.1 −1 Scale Velocity vs 10.8−3.0 km s 5 +2.7 −1 Central Velocity Dispersion σ0 9.3−2.6 km s 5 +13.9 Mass-to-Light Ratio M/LV 20.9−10.1 M⊙/LV,⊙ 5 +1.9 Mass-to-Light Ratio (r < rc, N∗ = 5) 2.0−1.3 M⊙/LV,⊙ 5 Virial Theorem Mass-to-Light Ratio (no rotation) 22 M⊙/LV,⊙ 5 a Mass-to-Light Ratio (minor axis rotation) 19 M⊙/LV,⊙ 5 b Mass-to-Light Ratio (major axis rotation) 63 M⊙/LV,⊙ 5

References for Table 2: (1) K¨onig et al. (1993); (2) Caldwell et al. (1992); (3) Schlegel, Finkbeiner & Davis (1998); (4) Cˆot´e, Oke & Cohen (1999b); (5) This paper aMass-to-light ratio found using radial velocities corrected for solid-body rotation around the galaxy’s minor axis (e.g., see the right panel of Figure 2). bMass-to-light ratio found using radial velocities corrected for solid-body rotation around the galaxy’s major axis (e.g., see the upper panel of Figure 2). 6 Andromeda II

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Fig. 1.— Cross-correlation function for Andromeda II-5 obtained using our master radial velocity template. The Tonry-Davis RTD value for this cross correlation is RTD = 4.45, slightly lower than the average of RTD = 4.58 for the nine measurements given in Table 1. 8 Andromeda II

Fig. 2.— (Large Panel) Distribution of unresolved objects in the vicinity of Andromeda II. Red giants having one or more measured radial ′ ′ velocities are indicated by the large triangles. The core radius of Andromeda II is indicated by the ellipse, which has rc = 1.89, a = 2.26 and b/a = 0.7 (Caldwell et al. 1992). The dashed lines indicate the minor and major axes of the galaxy. (Upper Panel) Radial velocities for Andromeda II members plotted against distance along the photometric minor axis (filled circles). The dotted-line indicates the weighted least-squares fit to the points. The open circles show the rotation-corrected velocities, assuming solid-body rotation about the major axis. (Right Panel) Same as previous panel, except for the case of solid-body rotation about the photometric minor axis. Cˆot´eet al. 9

Fig. 3.— (Upper Panel) Stability index, X, for Local Group dE/dSph galaxies plotted against V -band absolute magnitude (circles). The 12 total of the Milky Way is assumed to be 1 × 10 M⊙. The mass of M31 is taken to be twice this value. (Lower Panel) Global V -band mass-to-light ratio for Local Group dE/dSph galaxies, plotted against V -band absolute magnitude (circles). The dashed line indicates the expected relation for dwarfs consisting of luminous components having M/LV = 2M⊙/LV,⊙ which are embedded in dark matter halos of 7 mass M ∼ 2 × 10 M⊙.