A New Low Mass for the Hercules Dsph: the End of a Common Mass Scale for the Dwarfs? the Astrophysical Journal Letters, 706(1):L150-L154

Adén, D; Wilkinson, M I; Read, J I; Feltzing, S; Koch, A; Gilmore, G F; Grebel, E K; Lundström, I (2009). A new low mass for the Hercules dSph: the end of a common mass scale for the dwarfs? The Astrophysical Journal Letters, 706(1):L150-L154. Postprint available at: http://www.zora.uzh.ch

University of Zurich Posted at the Zurich Open Repository and Archive, University of Zurich. Zurich Open Repository and Archive http://www.zora.uzh.ch

Originally published at: The Astrophysical Journal Letters 2009, 706(1):L150-L154. Winterthurerstr. 190 CH-8057 Zurich http://www.zora.uzh.ch

Year: 2009

A new low mass for the Hercules dSph: the end of a common mass scale for the dwarfs?

Adén, D; Wilkinson, M I; Read, J I; Feltzing, S; Koch, A; Gilmore, G F; Grebel, E K; Lundström, I

Posted at the Zurich Open Repository and Archive, University of Zurich. http://www.zora.uzh.ch

Originally published at: The Astrophysical Journal Letters 2009, 706(1):L150-L154. A new low mass for the Hercules dSph: the end of a common mass scale for the dwarfs?

Abstract

We present a new mass estimate for the Hercules dwarf spheroidal (dSph) galaxy, based on the revised velocity dispersion obtained by Adén et al. The removal of a significant foreground contamination using newly acquired Strömgren photometry has resulted in a reduced velocity dispersion. Using this new velocity dispersion of 3.72 ± 0.91 km s-1, we find a mass of M 300 = 1.9+1.1 -0.8 × 106 M sun within the central 300 pc, which is also the half-light radius, and a mass of M 433 = 3.7+2.2 -1.6 × 106 M sun within the reach of our data to 433 pc, significantly lower than previous estimates. We derive an overall mass-to-light ratio of M 433/L = 103+83 -48[M sun/L sun]. Our mass estimate calls into question recent claims of a common mass scale for dSph galaxies. Additionally, we find tentative evidence for a velocity gradient in our kinematic data of 16 ± 3 km s-1 kpc-1, and evidence of an asymmetric extension in the light distribution at ~0.5 kpc. We explore the possibility that these features are due to tidal interactions with the Milky Way. We show that there is a self-consistent model in which Hercules has an assumed tidal radius of rt = 485 pc, an orbital pericenter of rp = 18.5 ± 5 kpc, and a mass within rt of $M_{{\rm tid},r_t}=5.2_{-2.7}^{+2.7} \times 10^6\,M_\odot$. Proper motions are required to test this model. Although we cannot exclude models in which Hercules contains no dark matter, we argue that Hercules is more likely to be a dark-matter-dominated system that is currently experiencing some tidal disturbance of its outer parts. The Astrophysical Journal, 706:L150–L154, 2009 November 20 doi:10.1088/0004-637X/706/1/L150 C 2009. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

A NEW LOW MASS FOR THE HERCULES dSph: THE END OF A COMMON MASS SCALE FOR THE DWARFS?

D. Aden´ 1, M. I. Wilkinson2,J.I.Read2,3, S. Feltzing1,A.Koch2,G.F.Gilmore4, E. K. Grebel5, and I. Lundstrom¨ 1 1 Lund Observatory, Box 43, SE-22100 Lund, Sweden 2 Department of Physics and Astronomy, University of Leicester, University Road, Leicester LE1 7RH, UK 3 Institute for Theoretical Physics, University of Zurich, Winterthurerstrasse 190 8047, Switzerland 4 Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, UK 5 Astronomisches Rechen-Institut, Zentrum fur¨ Astronomie der Universitat¨ Heidelberg, Monchhofstr.¨ 12-14, 69120 Heidelberg, Germany Received 2009 June 26; accepted 2009 October 6; published 2009 November 4

ABSTRACT We present a new mass estimate for the Hercules dwarf spheroidal (dSph) galaxy, based on the revised velocity dispersion obtained by Aden´ et al. The removal of a significant foreground contamination using newly acquired Stromgren¨ photometry has resulted in a reduced velocity dispersion. Using this new velocity dispersion ± −1 = +1.1 × 6 of 3.72 0.91 km s , we find a mass of M300 1.9−0.8 10 M within the central 300 pc, which is also the = +2.2 × 6 half-light radius, and a mass of M433 3.7−1.6 10 M within the reach of our data to 433 pc, significantly lower = +83 than previous estimates. We derive an overall mass-to-light ratio of M433/L 103−48[M/L].Ourmassestimate calls into question recent claims of a common mass scale for dSph galaxies. Additionally, we find tentative evidence for a velocity gradient in our kinematic data of 16 ± 3kms−1 kpc−1, and evidence of an asymmetric extension in the light distribution at ∼0.5 kpc. We explore the possibility that these features are due to tidal interactions with the Milky Way. We show that there is a self-consistent model in which Hercules has an assumed tidal radius of +2.7 6 = = ± = × rt 485 pc, an orbital pericenter of rp 18.5 5 kpc, and a mass within rt of Mtid,rt 5.2−2.7 10 M . Proper motions are required to test this model. Although we cannot exclude models in which Hercules contains no dark matter, we argue that Hercules is more likely to be a dark-matter-dominated system that is currently experiencing some tidal disturbance of its outer parts. Key words: galaxies: dwarf – galaxies: formation – galaxies: fundamental parameters – galaxies: individual (Hercules) – galaxies: kinematics and dynamics

1. INTRODUCTION may be incorrect. In Aden´ et al. (2009), we showed that the mean velocity of the Hercules dSph is embedded in the foreground Dwarf spheroidal (dSph) galaxies are believed to play an dwarf star velocity distribution. We used the Stromgren¨ c1 important role in the formation and evolution of much more lu- index to weed out the foreground dwarf stars. This index is minous galaxies (e.g., Gallagher & Wyse 1994). dSphs are char- able to clearly identify red giant branch (RGB) stars redder acterized by their low surface brightness, low total luminosity, than the horizontal branch, enabling a separation of RGB stars and spheroidal shapes that are consistent with their pressure- in the dSph galaxy and foreground dwarf stars. By weeding supported stellar kinematics (e.g., Grebel et al. 2003). out the foreground contaminants, we found that the dispersion Knowledge of dSph masses is essential for comparison with for Hercules is reduced from 7.33 ± 1.08 km s−1 to 3.72 ± cosmological simulations of galaxy formation. Good mass 0.91 km s−1. In this Letter, we explore the consequences of this estimates help us to establish whether the paucity in the number finding. of observed systems (a few tens) to the number of predicted In Section 2, we derive a new mass for Hercules and show satellite halos (several thousands) represents a fundamental that it is not consistent with a common mass scale for the dSphs. failure of our cosmological model (e.g., Moore et al. 1999), or In Section 3, we investigate the possibility of a velocity gradient whether it is simply telling us that galaxy formation is inefficient in the kinematic data of Hercules. In Section 4, we discuss on small scales (e.g., Read et al. 2006a). Recent studies have the relative importance of tides and dark matter in Hercules. suggested that the dSph galaxies share a common mass within Section 5 summarizes our conclusions. a certain radius (Walker et al. 2007, 2009; Strigari et al. 2008). If confirmed, this would be an important clue to the processes 2. MASS ESTIMATE FROM THE SPHERICAL JEANS that regulate the formation of the lowest luminosity galaxies. EQUATIONS All mass estimates implicitly assume that contamination of −1 the kinematic sample by foreground stars or unbound tidal We use the velocity dispersion, σv = 3.72 ± 0.91 km s tails is negligible, and that the system is in (or close to) virial (Aden´ et al. 2009), to constrain the mass of the Hercules dSph. equilibrium. Since the mass of an equilibrium stellar system is We assume that the system is in dynamical equilibrium, is proportional to its velocity dispersion squared, an overestimate spherically symmetric, has an isotropic velocity distribution, of the velocity dispersion will result in an inflated mass estimate. and a flat velocity dispersion profile.6 With these assumptions, The assumption of virial equilibrium may be called into question the Jeans equation for the mass distribution (Equation (4.215) if the system is tidally disrupting (Oh et al. 1995; Kroupa 1997; Klimentowski et al. 2007;Munoz˜ et al. 2008). The recently discovered Hercules dSph (Belokurov et al. 6 Note that Wolf et al. (2009) and Walker et al. (2009) find that their mass 2007), with an ellipticity of e ∼ 0.5 (Coleman et al. 2007), estimates at the half-light radius are insensitive to a wide range of mass models and velocity anisotropy parameterizations, so our results should not be is an example of a galaxy in which assumptions of equilibrium sensitive to these assumptions.

L150 No. 1, 2009 A NEW LOW MASS FOR THE HERCULES dSph L151

Table 1 Summary of Determination of Systemic Velocities, Velocity Dispersions, Masses, and Metallicities for the Hercules dSph

a Study Number of Stars vsys σMFurthest star M300 pc [Fe/H] − − (kms 1)(kms1)(M)(M)dex

Aden´ et al. (2009) 28 [RGB stars, c1 sel.] ··· ··· ··· ··· −2.35 ± 0.31 ± ± +0.5 × 7 +2.7 × 6 ··· This study 32 [Only Vrad sel.] 40.87 1.42 7.33 1.08 1.4−0.4 10 7.4−2.1 10 ± ± +2.2 × 6 +1.1 × 6 ··· This study 18 [RGB stars with Vrad]45.20 1.09 3.72 0.91 3.7−1.6 10 1.9−0.8 10

Notes. Columns: (1,2) number of stars in each study and a short description of how the stars were selected; (3,4) systemic velocities and velocity dispersions; (5) mass within the radius defined by the outermost RGB star in our study; (6) mass within the inner 300 pc; (7) mean metallicity. See Aden´ et al. (2009) for a full discussion of metallicities. a See Aden´ et al. (2009). in Binney & Tremaine 2008) becomes dν(r) ν(r) GM(r) σ 2 =− , (1) v dr r2 where r is the three-dimensional distance from the center of the galaxy, ν(r) is the de-projected stellar density profile, and M(r) is the enclosed mass. We use the exponential profile from Martin et al. (2008) to describe the stellar density profile. The de-projected exponential profile is given by Klimentowski et al. (2007) as (setting m = 1 in their Equation (4)) r −0.445 ν(r) = ν e−r/α, (2) 0 α where α is the exponential scale radius, related to the half- light radius as rh = 1.68 α, and ν0 is the central stellar density. Solving Equation (1)forM(r) using Equation (2) yields

r(r +0.445 α)σ 2 M(r) = v . (3) αG

+75 Using a half-light radius of 330− pc (Martin et al. 2008)we = 52 solve Equation (3)forr 433 pc, which corresponds to the Figure 1. Distribution of Monte Carlo mass estimates for Hercules. Solid line outermost member in our kinematic sample (Table 1). indicates the median from the Monte Carlo sampling. Dashed lines indicate the We estimate the error in the mass using 105 Monte Carlo 1σ limits from the Monte Carlo sampling. (a) Mass within the radius defined by realizations of the half-light radius, distance, and velocity the outermost RGB star in the kinematic sample, r = 433 pc. (b) Mass within dispersion of Hercules drawn from within the individual error the inner 300 pc. bars on each parameter. In this way, we obtain M433 = +2.2 6 3.7 × 10 M (Figure 1). The quoted errors are 1σ limits −1.6 observed dSphs. Our revised velocity dispersion implies a mass from the Monte Carlo sampling. Assuming a total luminosity +1.1 6 4 within the inner 300 pc (M )ofonly1.9 × 10 M.This of L = (3.6 ± 1.1) × 10 L (Martin et al. 2008), we find a 300 −0.8 = +83 indicates that Hercules falls considerably below this “common median mass-to-light ratio of M433/L 103−48 [M/L]. Aden´ et al. (2009) emphasize the importance of weeding mass scale” for dSphs. Since 300 pc is also approximately the out foreground contaminating dwarf stars. This is particularly half-light radius, this implies that Hercules also lies significantly vital for the Hercules dSph as its systemic velocity coincides off the Walker et al. (2009) enclosed half-light mass scaling with the bulk motion of dwarf stars in the Milky Way disk relation. in the direction of Hercules. Using the contaminated7 velocity To confirm that our result is not sensitive to our choice dispersion (Table 1), we would obtain a mass of 1.4+0.5 × of surface brightness profile, we have repeated our calcula- −0.4 = 7 tion using a Plummer profile with scale radius rpl 321pc 10 M, almost a factor of 4 larger than the uncontaminated (as used by Strigari et al. 2008). In this case, we find estimate. 6 M300 = 2.3 × 10 M in agreement with the mass calcu- 2.1. Hercules and the “Common Mass Scale” lated above. If instead we use our contaminated velocity dispersion and the exponential surface density profile, we obtain = +2.7 × 6 Strigari et al. (2008) speculate that the mass within a fixed M300 7.4−2.1 10 M which agrees with the value presented 7 radius, 300 pc, is approximately the same (∼10 M) in all the in Strigari et al. (2008). However, we note that Strigari et al. (2008) used a dispersion 7 Note that this “contaminated” dispersion has had its 3σ velocity outliers of 5.1 ± 0.9kms−1 (taken from Simon & Geha 2007) to obtain removed. Also, the initial candidate selection for the velocities was chosen their mass estimate. This is smaller than our contaminated value using color–magnitude diagram cuts. Even so, a significant fraction of of 7.33 ± 1.08 km s−1, yet they obtain a similar median mass foreground stars remain in this sample and are detected only through the use of − the Stromgren¨ photometry. to us. If we use a dispersion of 5.1 ± 0.9kms 1 as they do, we L152 ADEN´ ET AL. Vol. 706

2 Figure 2. (a) χ vs. the position angle. (b) Vrad vs. the semiminor axis distance. Figure 3. Spatial distribution on the sky of the stars identified as Hercules • The solid line indicates the least-squares fit. “ ” indicate members based on the members from both spectroscopy and photometry. “◦” indicate members based Stromgren¨ photometry (see Aden´ et al. 2009). on the Stromgren¨ photometry. “•” indicate members based on the Stromgren¨ photometry for which there are radial velocity measurements. The dashed line = +1.5 × 6 indicates the semiminor axis for the position angle of our detected rotation obtain a mass M300 3.6−1.2 10 M. This is just consistent axis. The solid ellipse represents the core radius and the dotted ellipse the inner with their determination within our mutual error bars. We note border of the field region of the Hercules dSph (Coleman et al. 2007). Solid that the median M300 will depend on the details of the mass lines outline the footprint of the WFC used to obtain the Stromgren¨ photometry. modeling procedure and so can be expected to differ between their study and ours (M. Walker 2009, private communication). − 0.38 km s 1. We obtain a reduced χ 2 of 3.89 for our 18 stars Additionally, we have repeated our calculation of the mass with 2 degrees of freedom. within 300 pc using a more recent estimate of the half-light Following Walker et al. (2008), we estimate the significance radius, r = 230 pc, by Sand et al. (2009). This half-light radius h of the velocity gradient using 105 Monte Carlo realizations. In is smaller and gives a mass that is ∼1.5 times more massive each realization, we sample the velocity and spatial distributions than the mass calculated using the half-light radius from Martin independently. Thus, we scramble the correlation between et al. (2008). velocity and position, while maintaining the original velocity 3. A VELOCITY GRADIENT IN HERCULES distribution and spatial positions. This is valid as long as the phase space distribution function of the stars is separable (which The presence of a velocity gradient in a dSph could either be implies that the velocity dispersion is independent of radius). We indicative of an intrinsic rotation, or a sign of tidal interaction determine the significance of the velocity gradient by computing with the Milky Way. In this section, we test for possible velocity the fraction of realizations that fail to produce a χ 2 as low as gradients in Hercules. the one calculated from the real data. We find a significance Assuming that the rotation around the semiminor axis (in the of the velocity gradient of 78% (1.23σ ). ellipse that describes the orientation of the dSph) is more likely than around the semimajor axis, we can define the “semiminor 4. DISCUSSION axis distance” dmi(θ) as the distance, perpendicular to the semiminor axis, between the axis and the star. For each of the 4.1. Galactic Tides in Hercules? 18 RGB stars with radial velocities, we calculate this distance In the previous section, we found tentative evidence for for different position angles θ. We then derive the gradient, k , rot a velocity gradient in the Hercules dSph. The peak-to-peak and zeropoint, m , by solving the following equation with a − v difference of ∼10 km s 1 within a radius of less than 1 kpc least-squares fit for each position angle, could be interpreted as the effect of Galactic tides (Read et al.

Vrad = krot × dmi(θ)+mv, (4) 2006b). Interestingly, Martin (2009) recently estimated the orbit of Hercules based on the assumption that its elongation is where Vrad is the radial velocity measurement for each star. The tidally induced and predicted a velocity gradient of at least least-squares fit to this function yields a χ 2 value for each θ 7kms−1 kpc−1 which is consistent with our observed gradient. (Figure 2(a)). Additionally, in Aden´ et al. (2009) we found that the spatial 2 ∼ The distribution enclosed by χmin + 1 corresponds to 1σ for distribution of the Hercules stars is asymmetric at 0.5 kpc. a normal distribution (Press et al. 1992). We use this to obtain There are three significant outlier stars to the south, but no the error in the position angle which minimizes χ 2. corresponding members at this distance in either the northern or − +18 We find a position angle of 35−23 degrees with a velocity western fields (Figure 3). These three stars are unambiguously gradient of 16 ± 3kms−1 kpc−1, and a zeropoint of 45.11 ± identified as RGB stars from the Stromgren¨ photometry. We No. 1, 2009 A NEW LOW MASS FOR THE HERCULES dSph L153

of the retrograde tidal radius of Hercules, i.e., rt ∼ 485 pc. If we assume further that the tidal radius of Hercules is set at the pericenter of its orbit, we can solve Equation (7) of Read et al. (2006c) to calculate the mass, Mtid, of Hercules as a function of its orbital pericenter, rp, for our assumed ranges of rs, γ , and ra.

We calculate both its mass within rt (Mtid,rt ) and its mass within 433 pc (Mtid,433) which can then be compared with our mass estimate based on the spherical Jeans equation (MSJ,433). The results of this calculation are given in Figure 4. The horizontal light gray band marks MSJ,433, the dark gray band marks Mtid,433

and the medium gray band marks Mtid,rt . The vertical solid and dashed lines mark the pericenters at which Mtid,433 = MSJ,433. The width of the tidal mass bands is due to the unknowns: rs, γ , and ra. However, to lowest order rt depends only on the mean density enclosed within it, and so these bands are narrow. For this reason, we obtain an estimate of both the orbital pericenter of Hercules (rp = 18.5 ± 5 kpc) and its mass within the tidal +2.7 6 = × radius (Mtid,rt 5.2−2.7 10 M ). The primary source of error on both of these quantities is our assumed tidal radius rt. Empirically, we derive scalings of r β r = 32 t kpc, (6) p 1 kpc Figure 4. Tidally determined mass for Hercules as a function of orbital pericenter = rp. We assume a retrograde tidal radius of rt 1 kpc for this calculation. The with β = 0.76 over the range rt = [0.4, 2] kpc, and horizontal gray band marks our mass estimate from the spherical Jeans equation MSJ,433 (see Section 2). The dark gray band marks our tidally determined mass α 6 rt within 433 pc Mtid,433 for Hercules. The medium gray band shows Mtid,rt , our = × Mtid,rt 24 10 M, (7) tidally determined mass within rt. The vertical solid and dashed lines mark the 1 kpc pericenters at which Mtid,433 = MSJ,433 (see Equation (6) for a formula giving the scaling of M with r ). tid,rt t with α = 2.1 over the same range. If we assume rt = 485 pc, we obtain a similar estimate of the now consider the possibility that the velocity gradient and the pericentric distance as that obtained by Martin (2009). positional outliers are evidence that Hercules is being tidally disrupted, and use this information to obtain a second mass 4.2. Is Hercules a Dark-Matter-Free System? estimate for the system. The tidal radius of a dSph depends on the potential of the host We have shown that our Hercules data are consistent with galaxy, the potential of the dSph, the orbit of the dSph within the presence of dark matter. We now consider whether models the host galaxy and the orbit of the stars within the dSph (e.g., without dark matter could also reproduce the data. Read et al. 2006c). We parameterize the Milky Way potential The most extreme scenario is that Hercules is disintegrating using the default model in Johnston et al. (2005), analyzed in the and its velocity dispersion arises solely due to the motion Galactic plane; and the Hercules potential using a generalized of its unbound member stars. If so, it will rapidly become Hernquist proﬁle (Hernquist 1990), unobservable (i.e., reach a lower surface brightness than the detection limit of the Sloan Digital Sky Survey (SDSS)). − − M(3 − γ ) r γ r γ 4 Hercules has a surface brightness of 27.2 ± 0.6 mag arcsec−2 ρ(r) = 1+ , (5) 3 (Martin et al. 2008). If the unbound stars are moving away 4πr rs rs s from Hercules at a velocity equal to the velocity dispersion −1 6 where M is the total mass, rs is the scale length, and γ is (3.72 ± 0.91 km s ), it would require only ∼200 × 10 years the central logarithmic cusp slope. We consider the ranges for the Hercules dSph to fall below the detection limit of SDSS −2 0.3