arXiv:1104.3860v1 [astro-ph.CO] 19 Apr 2011 Submitted to the Astrophysical Journal Preprint typeset using L A T E X style emulateapj v. 11/10/09 A STELLAR VELOCITY DISPERSION OF A COMPACT MASSIVE GALAXY AT Z = 1.80 USING X-SHOOTER: CONFIRMATION OF THE EVOLUTION IN THE MASS-SIZE RELATION 1,2 Jesse van de Sande 3 ,Mariska Kriek 4 ,Marijn Franx 3 ,Pieter G. van Dokkum 5 ,Rachel Bezanson 5 ,Katherine E. Whitaker 5 ,Gabriel Brammer 6 ,Ivo Labb´ e 3 ,P aul J. Groot 7 ,Lex Kaper 8 Submitted to the Astrophysical Journal ABSTRACT Recent photometric studies have shown that early-type galaxies at fixed stellar mass were smaller and denser at earlier times. In this paper we assess that finding by deriving the dynamical mass of such a compact quiescent galaxy at z=1.8. We have obtained a high-quality spectrum with full UV-NIR wavelength coverage of this galaxy using X-Shooter on the VLT. We determined a velocity dispersion of 294±51 km s −1 . Given this velocity dispersion and the effective radius of 1.64±0.15 kpc (as determined from HST-WFC3 F160W observations) we find a dynamical mass of 1.7±0.5 × 10 11 M ⊙ . Comparison of the full spectrum with stellar population synthesis models indicates that the galaxy has a relatively young stellar population (0.40 Gyr) with little or no star formation and a stellar mass of M ⋆ ∼ 1.5 × 10 11 M ⊙ . The dynamical and photometric stellar mass are in good agreement. Thus, our study supports the conclusion that the mass densities of quiescent galaxies were indeed higher at earlier times, and this earlier result is not caused by systematic measurement errors. By combining available spectroscopic measurements at different redshifts, we find that the velocity dispersion at fixed dynamical mass was a factor of ∼1.8 higher at z=1.8 compared to z=0. Finally, we show that the apparent discrepancies between the few available velocity dispersion measurements at z > 1.5 are consistent with the intrinsic scatter of the mass-size relation. Subject headings: galaxies: evolution — galaxies: formation — galaxies: structure 1. INTRODUCTION In hierarchical structure formation models, the most mas- sive early-type galaxies are assembled last (e.g. Springel et al. 2005). This simple picture seems difficult to reconcile with recent studies showing that the first massive quiescent galax- ies were already in place when the universe was only ∼3 Gyr old (e.g., Labb´ e et al. 2005; Kriek et al. 2006; Williams et al. 2009). The recent discovery that these massive high-redshift galaxies still grow significantly in size (e.g., Daddi et al. 2005; Trujillo et al. 2006; van Dokkum et al. 2008), and mass (van Dokkum et al. 2010) elevates this apparent conflict. The observed compact high-redshift galaxies may simply be the cores of local massive early-type galaxies, which grow inside-out by accreting (smaller) galaxies (Naab et al. 2007; Bezanson et al. 2009; van der Wel et al. 2009), and thus as- semble a significant part of their mass at later times (see also Oser et al. 2010). At z > 1.2, the results may be interpreted incorrectly due to many systematic uncertainties. Firstly, sizes may have been underestimated, as low-surface brightness components might 1 Based on X-Shooter-VLT observations collected at the European Southern Observatory, Paranal, Chile. 2 Based on observations with the NASA/ESA Hubble Space Telescope (HST), obtained at the Space Telescope Science Institute, which is oper- ated by AURA, Inc., under NASA contract NAS 5-26555. 3 Leiden Observatory, Leiden University, P.O. Box 9513, 2300 RA Lei- den, The Netherlands. 4 Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA 5 Department of Astronomy, Yale University, P.O. Box 208101, New Haven, CT 06520-8101. 6 European Southern Observatory, Alonso de C´ ordova 3107, Casilla 19001, Vitacura, Santiago, Chile 7 Department of Astrophysics, IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands 8 Astronomical Institute Anton Pannekoek, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands have been missed (Mancini et al. 2010). However, recent work using stacking techniques (e.g. van der Wel et al. 2008; Cassata et al. 2010; van Dokkum et al. 2010), and ultra-deep HST-WFC3 data (e.g. Szomoru et al. 2010), demonstrated that radial profiles can now be measured with high accu- racy extending to large radii. Secondly, the stellar mass esti- mates suffer from uncertainties in stellar population synthesis (SPS) models, and the paucity of spectroscopic redshifts, and furthermore rely on assumptions regarding the initial mass function (IMF) and metallicity (e.g Conroy et al. 2009). Di- rect kinematic mass measurements, which are not affected by these uncertainties, are needed to confirm the high stellar masses and densities of these galaxies. Kinematic measurements have only recently become pos- sible for high-redshift galaxies. Using optical spectroscopy, Newman et al. (2010) have explored the epoch up to z ∼ 1.5. With near-infrared (NIR) spectroscopy these studies have been pushed to even higher redshift (Cenarro & Trujillo 2009). Using a ∼29hr spectrum of an ultra-compact galaxy at z = 2.2 obtained with GNIRS (Kriek et al. 2009), van Dokkum et al. (2009b) found a very high stellar velocity dispersion of σ = 510 +165 −95 km s −1 , confirming its high stel- lar density. However, this dispersion has a very large error. Onodera et al. (2010) used the MOIRCS on the Subaru tele- scope to observe the rest-frame optical spectrum of a less- compact, passive, ultra-massive galaxy at z = 1.82, but the low spectral resolution only allowed the determination of an upper limit to the velocity dispersion of σ< 326 km s −1 . With the lack of high-quality dynamical data at z > 1.5 there still is no general consensus on the matter of compact quiescent galaxies. Here we present the first high signal-to-noise ratio (S/N), high-resolution, UV-NIR spectrum of a z = 1.80 galaxy ob- served with X-Shooter (D’Odorico et al. 2006) on the VLT. Throughout the paper we assume a ΛCDM cosmology with