A massive, quiescent, population II galaxy at a redshift of 2.1
Mariska Kriek, Charlie Conroy, Pieter G. van Dokkum, Alice E. Shapley, Jieun Choi, Naveen A. Reddy, Brian Siana, Freeke van de Voort, Alison L. Coil, Bahram Mobasher
aa r X i v : . [ a s t r o - ph . GA ] D ec LETTER
A massive, quiescent, population II galaxy at aredshift of 2.1
Mariska Kriek , Charlie Conroy , Pieter G. van Dokkum , Alice E. Shapley , Jieun Choi , Naveen A. Reddy , Brian Siana ,Freeke van de Voort , Alison L. Coil , Bahram Mobasher Unlike spiral galaxies such as the Milky Way, the majority of thestars in massive elliptical galaxies were formed in a short periodearly in the history of the Universe. The duration of this forma-tion period can be measured using the ratio of magnesium to ironabundance ([Mg/Fe]) , which reflects the relative enrichment bycore-collapse and type Ia supernovae. For local galaxies, [Mg/Fe]probes the combined formation history of all stars currently in thegalaxy, including younger and metal-poor stars that were addedduring late-time mergers . Therefore, to directly constrain the ini-tial star-formation period, we must study galaxies at earlier epochs.The most distant galaxy for which [Mg/Fe] had previously beenmeasured is at a redshift of z ≈ . , with [Mg/Fe] = 0 . +0 . − . . Aslightly earlier epoch ( z ≈ . ) was probed by stacking the spec-tra of 24 massive quiescent galaxies, yielding an average [Mg/Fe]of . ± . . However, the relatively low signal-to-noise ra-tio of the data and the use of index analysis techniques for bothstudies resulted in measurement errors that are too large to al-low us to form strong conclusions. Deeper spectra at even earlierepochs in combination with analysis techniques based on full spec-tral fitting are required to precisely measure the abundance pat-tern shortly after the major star-forming phase ( z > ). Here wereport a measurement of [Mg/Fe] for a massive quiescent galaxy ata redshift of z = 2 . , when the Universe was 3 billion years old.With [Mg/Fe] = 0 . ± . , this galaxy is the most Mg-enhancedmassive galaxy found so far, having twice the Mg enhancement ofsimilar-mass galaxies today. The abundance pattern of the galaxyis consistent with enrichment exclusively by core-collapse super-novae and with a star-formation timescale of 0.1 to 0.5 billion years– characteristics that are similar to population II stars in the MilkyWay. With an average past star-formation rate of 600 to 3,000 so-lar masses per year, this galaxy was among the most vigorous star-forming galaxies in the Universe. We observed the galaxy COSMOS-11494 with the near-infraredmulti-object spectrograph MOSFIRE on the
Keck I Telescope . Itwas also observed by two other programmes , and so we incorpo-rated these publicly available archival data. COSMOS-11494 was se-lected from the 3D-HST survey . With a stellar mass M given by log M/M ⊙ = 11 . ± . , COSMOS-11494 is among the most mas-sive galaxies at its redshift, and it has a very low star-formation rate ofless than . M ⊙ / yr (see Methods). Similarly to the typical massive,quiescent galaxy at this redshift, it is smaller than its local counterpartsof the same mass, with an effective radius of 2.1 kpc . The MOS- Department of Astronomy, University of California, Berkeley, CA 94720, USA Departmentof Astronomy, Harvard University, Cambridge, MA, USA Astronomy Department, Yale University,New Haven, CT, USA Department of Physics & Astronomy, University of California, Los Angeles,CA 90095, USA Department of Physics & Astronomy, University of California, Riverside, CA 92521,USA Center for Astrophysics and Space Sciences, University of California, San Diego, La Jolla,CA 92093, USA λ ( µ m)0102030 a J H K b VJH660 680 700 720 740 760rest-frame λ (nm)1015202530 e H α TiO KK
480 500 520 540 560 5802025 F λ ( - e r g s - c m - n m - ) d H β MgI FeI FeI FeI FeI FeI HH
380 390 400 410 420 430510152025 c H η H ζ CaII H ε H δ CaI CH JJ Figure 1:
Photometry, image and MOSFIRE spectrum ofCOSMOS-11494. a,
Multi-wavelength spectral energy distribution(black circles) and best-fitting stellar population model to only the pho-tometry (grey line). b, HST colour (V, J, and H) image. c-e,
MOS-FIRE spectrum in three wavelength intervals (J, H, and K; black), cor-responding to the coloured areas in a . The gray shaded regions repre-sent the 1 σ uncertainty on the flux. The best-fitting stellar populationmodel used to derive the age and abundance pattern is shown in red.FIRE rest-frame optical spectrum, the multi-wavelength spectral en-ergy distribution and Hubble Space Telescope ( HST ) colour image of COSMOS-11494 are shown in Figure 1.Here we measure the stellar abundance pattern of COSMOS-11494from the MOSFIRE rest-frame optical spectrum with our absorptionline fitter ( alf ) code (see Methods). For our default model we adopta two-component stellar population, for which the age of both compo-nents and the slope of the stellar initial mass function (IMF) are freeparameters. To enable comparison with previous work , we also fit1 .0 0.2 0.4 0.6 0.8 1.00.00.20.40.60.81.0 M ( M O • )24681012 A ge ( G y r) a : r ed m e r ge r s M ( M O • )-0.5-0.4-0.3-0.2-0.10.00.1 [ F e / H ] b M ( M O • )0.00.20.40.60.8 [ M g / F e ] c M ( M O • )-0.20.00.20.40.6 [ C a / F e ] d -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1[Fe/H]0.00.20.40.60.8 [ M g / F e ] e Figure 2:
Age and abundance patterns of COSMOS-11494 in comparison to lower-redshift quiescent galaxies. a,
Stellar population age, b, [Fe/H], c, [Mg/Fe], and d, [Ca/Fe] versus stellar mass. e, [Mg/Fe] versus [Fe/H]. The black dashed line represents a chemical evolution model fordifferent star-formation timescales in Gyr. In all panels, the black and grey filled squares represent COSMOS-11494 for the two-component andsingle-age model, respectively, the coloured symbols represent low-redshift galaxies binned by mass and redshift, and the small black plusesare nearby galaxies . Error bars are 1 σ . The red arrows represent the simple evolutionary model (see main text).the spectrum with a single-age model and a Kroupa IMF.For the default model we find [Fe / H] = − . ± . , [Mg / Fe] =0 . ± . , [Ca / Fe] = 0 . ± . and an age of . ± . Gyr.The best-fitting mass-to-light ratio (
M/L ) is consistent with the
M/L assuming a Kroupa IMF ( ( M/L ) / ( M/L
Kroupa ) = 0 . ± . ), al-though the error is large because of the insufficient S/N of the spec-trum and the lack of rest-frame near-infrared coverage. We also fit thismodel with λ restframe < ˚A excluded, and find similar values.For the single-age model we find similar abundance ratios as for thetwo-component model, but the modelled age is 1 Gyr younger. Thisdifference is expected, because younger stellar populations have lower M/L and so have larger weights in the fit.In Figure 2 we compare the spectral modelling results ofCOSMOS-11494 with those of galaxies at . < z < . and ofa sample of nearby massive galaxies . All galaxies are fitted withthe alf code. Figure 2 illustrates that COSMOS-11494 is more Mg-enhanced than similar-mass galaxies at lower redshift, with [Mg/Fe]about 0.3 dex higher. [Ca/Fe] is also higher compared to the values forlower-redshift massive galaxies.To interpret the abundance pattern of COSMOS-11494, we showa chemical evolution model in Figure 2e, which assumes a SalpeterIMF , a constant star-formation history over a given timescale, a core-collapse and a type Ia supernova yield model ; we also adopt apower-law delay-time distribution of the from t − for type Ia super-novae that occured between 0.1 and 13 Gyr . The star-formation timescale decreases along the curve, with the highest value of [Mg/Fe]corresponding to the shortest timescale of 0.1 Gyr. The relatively lowFe abundance in combination with the high [Mg/Fe] favours a shortstar-formation timescale of around . Gyr. Therefore, this model im-plies that COSMOS-11494 has experienced very little enrichment bytype Ia supernovae.However, the best-fitting timescale strongly depends on the as-sumed delay time of prompt type Ia supernovae. This parameter ispoorly constrained in models and depends on the type Ia progenitormodel ; for the double degenerate scenario the lifetime can be as shortas about 0.1 Gyr, whereas for a single degenerate scenario it can be ashigh as about 0.5 Gyr . However, the delay times of prompt type Iasupernovae inferred from observations are as short as . Gyr , andso 0.5 Gyr may be a conservative upper limit. The assumed IMF af-fects the chemical evolution model as well, and a flatter IMF results ina longer timescale. Finally, the adopted chemical evolution model de-pends on the core-collapse supernova yields , and other yield modelswere unable to reproduce the observed high [Mg/Fe] in combinationwith the observed [Fe/H] . Nonetheless, individual stars with sim-ilarly high [Mg/Fe] and [Fe/H] values as COSMOS-11494 have beenidentified in the bulge of the Milky Way , which supports the validityof the adopted yield model . Taking into account all uncertainties onour chemical evolution model, we estimate a star-formation timescaleof ∼ . − . Gyr.Ca, which is also produced and returned to the interstellar medium2 ick indices < F e > t gal =2 Gyr [Mg/Fe]=0.00.3 0.5-0.33 0.00 0.35 t gal =4 Gyr z=2.1 galaxyz=1.6 stackz=1.4 galaxy Figure 3:
Abundance pattern of COSMOS-11494 in comparison toother high-redshifts galaxies.
We show the Lick indices h Fe i andMg b for COSMOS-11494, a z ≈ . quiescent galaxy observed with VLT /X-Shooter, and a stack of z ≈ . quiescent galaxy spectra ob-served with Subaru /MOIRCS. Error bars are 1 σ . We also show gridsbased on SPS models for a range of range of values of [Z/H] and[Mg/Fe]. The dark and light grey grids are for galaxy ages of 2 Gyrand 4 Gyr, respectively.through core-collapse supernovae, also shows a strong enhancementwith respect to Fe; the difference compared to low-redshift analoguesis even more extreme than for Mg. This differential evolution of Caand Mg with time is unexpected, because both elements are formedin massive stars, but metallicity-dependent core-collapse-supernovayields might explain the differences .When combining the star-formation timescale and the best-fittingstellar mass, we find an average past star-formation rate of (600–3,000) M ⊙ /yr. The single-age best-fitting SPS model sets a lower limiton the formation redshift of z > . For the two-component model wefind an average formation redshift of z = 12 +9 − . The inferred star-formation rate and formation epoch are consistent with the propertiesthat were derived for the most active galaxy found so far, HFLS3 .This dusty sub-millimetre galaxy has a star-formation rate of 2,900 M ⊙ /yr and a redshift of z = 6 . , and so could be similar to thestar-forming progenitor of COSMOS-11494.COSMOS-11494 seems to be more Mg-enhanced than z ≈ . galaxies in previous work. However, because different methods havebeen used in these studies, systematic differences may occur, andthe derived values cannot be directly compared . For a more di-rect comparison to previous studies, we use the Lick indices h Fe i (=[Fe5270+Fe5335]/2) and Mg b . For the z = 1 . galaxy, the spec-trum was not deep enough to measure the two Fe lines needed to deter-mine h Fe i . Instead, we calibrated h Fe i for two other iron lines (Fe4388and Fe5015) using a set of SPS models , and derived h Fe i from these(marginally detected) lines for the z = 1 . galaxy. Figure 3 shows themeasurements in comparison to a grid of SPS models for a range ofmetallicities ([Z/H] = − . , . , . ) and [Mg/Fe] values (0.0, 0.3,0.5).For COSMOS-11494 the [Mg/Fe] ≈ . implied from the Lickindices is consistent with the modelling results. This value illustratesthat COSMOS-11494 – which probes an earlier epoch than previouswork – is indeed more Mg-enhanced than the quiescent galaxies in theother studies. Furthermore, our high S/N spectrum results in the mostrobust abundance pattern measurement for a distant galaxy so far. Al-though the two different approaches to derive the abundance pattern give consistent results for COSMOS-11494, for distant galaxies, thefull spectral modelling approach is strongly preferred over the approachinvolving Lick indices (Methods).The high [Mg/Fe] of COSMOS-11494 compared to lower-redshiftquiescent galaxies of similar mass suggests that this galaxy, and possi-bly other distant quiescent galaxies, do not passively evolve into quies-cent early-type galaxies today. A similar conclusion was drawn fromthe small sizes of distant quiescent galaxies compared to their localanalogs , and in the past several years it has become apparent that dis-tant quiescent galaxies grow in mass and size by accreting primarilysmaller galaxies . This inside-out growth by late-time mergers withless-massive galaxies predicts a decline in [Mg/Fe], because lower-mass galaxies are less Mg-enhanced In Figure 2 we explore this scenario by showing the predicted pathof COSMOS-11494 for a simple evolutionary model. We assume thatthe galaxy grows by red minor (1:10) mergers with smaller, less Mg-enhanced quiescent galaxies with [Mg/Fe] = 0 . , [Fe/H] = − . ,and [Ca/Fe] = 0 . , and that the mass nearly doubles between z =2 . and the present day following the mass evolution d(log M ) / d z = − . . Therefore, we assume no evolution in [Mg/Fe] and [Ca/Fe]at lower masses. If the abundance ratios for these galaxies would behigher at earlier times as well, then the predicted evolution would beless strong. To estimate the evolution in galaxy age for the mergermodel, we assume that the age is proportional to M . , as was foundfor z < . galaxies .Figure 2 shows that the merger model can substantially decrease[Mg/Fe] and [Ca/Fe], and increase [Fe/H]. However, there are severalcaveats to our simple model comparison. First, the . < z < . measurements are derived by fitting a single-age model, and so are sen-sitive to low levels of recent star formation. Second, we assume thatthe accreted stars are well-mixed with the in-situ population. However,simulations of galaxy formation show that the added material is mostlydeposited in the outskirts of the galaxy , and so the net evolution dueto mergers – in the central parts targeted by the spectrographs – maybe less. Third, it is unlikely that the descendent of COSMOS-11494 isa typical massive, quiescent galaxy today. The star formation in manylow-redshift quiescent galaxies is quenched at later times, resulting inlonger star-forming periods and, hence, lower [Mg/Fe]. Therefore, thedescendant of COSMOS-11494 presumably resides in the tail of thelow-redshift distributions. Finally, the model does not include possiblelate-time star formation or mergers with star-forming galaxies, whichwould also result in a decrease in [Mg/Fe] with time.More spectra of quiescent galaxies at high redshifts are needed tomeasure the evolution of the slope and the intercept of the age − M and[Mg/Fe] − M relation. These measurements could eventually discrim-inate between different evolutionary scenarios, and the amount of mix-ing of stars after galaxy mergers . In combination with more accuratesupernova progenitor and yield models, and therefore improved chem-ical evolution models, these measurements will also provide uniqueinformation on the star-formation histories of the most massive galax-ies and their possible role in the reionization of the Universe at z > .We expect that observations with NIRspec on the James Webb SpaceTelescope will revolutionize this field within the next five years, withfuture ultra-deep observations with MOSFIRE paving the way.
1. Matteucci, F. Abundance ratios in ellipticals and galaxy formation.
Astron.Astrophys. , 57–64 (1994).2. Trager, S. C., Faber, S. M., Worthey, G. & Gonz´alez, J. J. The StellarPopulation Histories of Early-Type Galaxies. II. Controlling Parameters ofthe Stellar Populations.
Astron. J. , 165–188 (2000).3. Thomas, D., Maraston, C., Bender, R. & Mendes de Oliveira, C. TheEpochs of Early-Type Galaxy Formation as a Function of Environment.
Astrophys. J. , 673–694 (2005). . Conroy, C., Graves, G. J. & van Dokkum, P. G. Early-type Galaxy Arche-ology: Ages, Abundance Ratios, and Effective Temperatures from Full-spectrum Fitting. Astrophys. J. , 33 (2014).5. van Dokkum, P. G. et al.
The Growth of Massive Galaxies Since z = 2 . Astrophys. J. , 1018–1041 (2010).6. Lonoce, I. et al.
Old age and supersolar metallicity in a massive z ∼ . early-type galaxy from VLT/X-Shooter spectroscopy. Mon. Not. R.Astron. Soc. , 3912–3919 (2015).7. Onodera, M. et al.
The Ages, Metallicities, and Element Abundance Ra-tios of Massive Quenched Galaxies at z ≃ . . Astrophys. J. , 161(2015).8. McLean, I. S. et al.
MOSFIRE, the multi-object spectrometer for infra-red exploration at the Keck Observatory. In
Society of Photo-Optical In-strumentation Engineers (SPIE) Conference Series , vol. 8446 of
Societyof Photo-Optical Instrumentation Engineers (SPIE) Conference Series (2012).9. Belli, S., Newman, A. B., Ellis, R. S. & Konidaris, N. P. MOSFIRE Absorp-tion Line Spectroscopy of z > Quiescent Galaxies: Probing a Periodof Rapid Size Growth.
Astrophys. J. Let. , L29 (2014).10. Kriek, M. et al.
The MOSFIRE Deep Evolution Field (MOSDEF) Sur-vey: Rest-frame Optical Spectroscopy for ∼ . ≤ z ≤ . . Astrophys. J. Supp. , 15 (2015).11. Skelton, R. E. et al.
Astrophys. J. Supp. , 24 (2014).12. Momcheva, I. G. et al.
The 3D-HST Survey: Hubble Space TelescopeWFC3/G141 grism spectra, redshifts, and emission line measurementsfor ∼ , galaxies. ArXiv e-prints (2015).13. van de Sande, J. et al.
Stellar Kinematics of z ∼ Galaxies and theInside-out Growth of Quiescent Galaxies.
Astrophys. J. , 85 (2013).14. Conroy, C. & van Dokkum, P. Counting Low-mass Stars in IntegratedLight.
Astrophys. J. , 69 (2012).15. Choi, J. et al.
The Assembly Histories of Quiescent Galaxies since z =0 . from Absorption Line Spectroscopy. Astrophys. J. , 95 (2014).16. Kroupa, P. On the variation of the initial mass function.
Mon. Not. R.Astron. Soc. , 231–246 (2001).17. Conroy, C. & van Dokkum, P. G. The Stellar Initial Mass Function in Early-type Galaxies From Absorption Line Spectroscopy. II. Results.
Astrophys.J. , 71 (2012).18. Salpeter, E. E. The Luminosity Function and Stellar Evolution.
Astrophys.J. , 161 (1955).19. Kobayashi, C., Umeda, H., Nomoto, K., Tominaga, N. & Ohkubo, T.Galactic Chemical Evolution: Carbon through Zinc.
Astrophys. J. ,1145–1171 (2006).20. Nomoto, K., Thielemann, F.-K. & Yokoi, K. Accreting white dwarf modelsof Type I supernovae. III - Carbon deflagration supernovae.
Astrophys. J. , 644–658 (1984).21. Maoz, D., Mannucci, F. & Brandt, T. D. The delay-time distribution of TypeIa supernovae from Sloan II.
Mon. Not. R. Astron. Soc. , 3282–3294(2012).22. Kobayashi, C. & Nomoto, K. The Role of Type Ia Supernovae in Chem-ical Evolution. I. Lifetime of Type Ia Supernovae and Metallicity Effect.
Astrophys. J. , 1466–1484 (2009).23. Thielemann, F.-K., Nomoto, K. & Hashimoto, M.-A. Core-Collapse Su-pernovae and Their Ejecta.
Astrophys. J. , 408 (1996).24. Woosley, S. E. & Weaver, T. A. The Evolution and Explosion of MassiveStars. II. Explosive Hydrodynamics and Nucleosynthesis.
Astrophys. J.Supp. , 181 (1995).25. Fulbright, J. P., McWilliam, A. & Rich, R. M. Abundances of Baade’sWindow Giants from Keck HIRES Spectra. II. The Alpha and Light OddElements.
Astrophys. J. , 1152–1179 (2007).26. Riechers, D. A. et al.
A dust-obscured massive maximum-starburstgalaxy at a redshift of 6.34.
Nature , 329–333 (2013).27. Worthey, G., Faber, S. M., Gonzalez, J. J. & Burstein, D. Old stellar pop-ulations. 5: Absorption feature indices for the complete LICK/IDS sampleof stars.
Astrophys. J. Supp. , 687–722 (1994).28. Thomas, D., Maraston, C. & Bender, R. Stellar population models of Lickindices with variable element abundance ratios. Mon. Not. R. Astron.Soc. , 897–911 (2003).29. van Dokkum, P. G. et al.
Confirmation of the Remarkable Compactnessof Massive Quiescent Galaxies at z ∼ . : Early-Type Galaxies Didnot Form in a Simple Monolithic Collapse. Astrophys. J. Let. , L5–L8(2008).30. Naab, T., Johansson, P. H. & Ostriker, J. P. Minor Mergers and theSize Evolution of Elliptical Galaxies.
Astrophys. J. Let. , L178–L182(2009).
Acknowledgements
M. K. acknowledges discussions with J. Greene andE. Quataert. The data presented in this paper were obtained at the W. M.Keck Observatory, which is operated as a scientific partnership among theCalifornia Institute of Technology, the University of California and the NationalAeronautics and Space Administration. The Observatory was made possibleby the generous financial support of the W.M. Keck Foundation. The authorswish to recognize and acknowledge the very significant cultural role and rev-erence that the summit of Mauna Kea has always had within the indigenousHawaiian community. We are most fortunate to have the opportunity to con-duct observations from this mountain. We acknowledge support from NSFAAG collaborative grants AST-1312780, 1312547, 1312764, and 1313171and archival grant AR-13907, provided by NASA through a grant from theSpace Telescope Science Institute. C.C. acknowledges support from NASAgrant NNX13AI46G, NSF grant AST-1313280, and the Packard Foundation.
Correspondence
Correspondence and requests for materials should beaddressed to M. K. (email: [email protected]).
Author Contributions
M. K., P. G. v. D. & C. C., wrote the primary Keck pro-posal. M. K. & C. C. led the interpretation. M. K. wrote the reduction pipeline,reduced the data, determined the stellar mass, measured the Lick indices,and wrote the text. C. C. developed the SPS model, fitted the spectrum, andderived the chemical evolution model. M. K., P. G. v. D., J. C., F. v. d. V.,and N. A. R. did the observations. All authors contributed to the analysis andinterpretation. ETHODS
Best-fitting model to the photometry.
To derive the stellar massof COSMOS-11494, we fit the broadband photometry with the flexi-ble stellar population synthesis (SPS) models . We assume a de-layed exponential star formation history of the form SFR ∝ t e − t/τ and the dust attenuation law from Kriek & Conroy . We adoptthe Chabrier stellar IMF to facilitate direct comparison with lower-redshift studies .The error bar on the stellar mass is completely dominated by sys-tematic uncertainties. We estimate this uncertainty by varying theSPS model , dust attenuation law , parameterization of the star-formation history, and the scaling of the broadband spectral energy dis-tribution. We do not vary the IMF, as it can be approximated by asimple offset in the stellar mass. A Kroupa IMF would have resultedin a similar stellar mass as for the Chabrier IMF, whereas a SalpeterIMF would have resulted in a stellar mass a factor of 1.6 higher. Spectral fitting.
Parameters are estimated from the rest-frame op-tical spectrum with the alf code. This code combines librariesof isochrones and empirical stellar spectra with synthetic stellar spectracovering a wide range of elemental abundance patterns. The code fitsfor C, N, O, Na, Mg, Ca, Ti, V, Cr, Mn, Fe, Co, Ni, redshift, velocitydispersion, and several emission lines. The stellar population age andIMF are free parameters as well, and multiple stellar population com-ponents are allowed. When fitting a two-component model, the agerepresents the mass-weighted average age of the two separate compo-nents. The ratio of the model and data are fitted by a high order polyno-mial to avoid potential issues with the flux calibration of the data. Thefitting is done using a Markov chain Monte Carlo algorithm . Lick indices versus full spectral modelling.
As mentionedin the main text, for COSMOS-11494 the [Mg/Fe] ≈ . im-plied from the Lick indices is consistent with the modelling results.The metallicity measurements also agree between the two methods:our best-fitting values for [Mg/Fe] and [Fe/H] imply [Z/H] = 0 . (=[Fe/H]+0.94[Mg/Fe] ), which is consistent with the model shownin Figure 3 for the best-fitting age of 2.5 Gyr. For the z ≈ . in-dividual galaxy and the z ∼ . stack, the abundance patterns arebased on the Lick indices, and so by construction they should be closerto the grid points. This is indeed the case for z ≈ . individualgalaxy with a [Mg/Fe] of . +0 . − . and a [Z/H] of . +0 . − . . Forthe derived age of 4 Gyr the two Lick indices are consistent with themodel grid. However, the individual Fe lines yield very different andinconsistent results when calculating h Fe i . For the z ≈ . galaxystack , the derived [Mg/Fe] = 0 . +0 . − . , [Z/H] = 0 . +0 . − . andlog (age / Gyr) = 0 . +0 . − . are less consistent with the derived val-ues based on all Lick indices, though the error bars are large.Although the two different approaches to derive the abundance pat-tern agree well for COSMOS-11494, the full spectral modelling ap-proach is strongly preferred over the appraoch involving Lick indices.The rest-frame optical spectrum of z > galaxies has been shiftedto near-infrared wavelengths. The many skylines at these wavelengthsin combination with the relatively lower S/N of the spectra of distantgalaxies result in large error bars on the measurement of a single fea-ture. Lick indices are integrated measurements and do not take intoaccount wavelength-dependent features within the bandpass. There-fore, skylines will severely complicate their measurement because af-fected wavelengths are not down-weighted. Furthermore, skylines re-sult in non-Gaussian and correlated noise properties, and so error barson Lick indices are usually underestimated. Consequently, Lick indicesare much more prone to systematic errors. The discrepancies betweenindividual Lick indices and the derived stellar abundance pattern basedon all Lick indices for the two lower-redshift measurements further il-lustrate this point. By modelling the full spectrum, we use many more features and can better deal with the larger uncertainties in regions af-fected by skylines. Code availability.
The data reduction package used to pro-cess the raw MOSFIRE data will be made public in the com-ing year at http://astro.berkeley.edu/˜ mariska. To derive the stel-lar mass, we used the flexible SPS models which are available athttps://github.com/cconroy20/fsps and the SPS fitting code
FAST ,which is publicly available at http://astro.berkeley.edu/˜ mariska/fast/.The spectral fitting code alf that was used to derivethe abundance pattern is not publicly available, but the un-derlying model components are available for download fromhttp://scholar.harvard.edu/cconroy/sps-models. Data availability.
The one-dimensional original and binnedspectrum shown in Figure 1 and corresponding 1 σ uncertainties,as well as the best-fitting model spectrum are available as SourceData. The binned spectrum is constructed by first masking wave-lengths affected by skylines and poor atmospheric transmission, andthen taking the median of the flux of ten non-masked consecu-tive pixels. The photometric data points shown in Figure 1 aremade available by the 3D-HST collaboration (catalog version v4.1)at http://3dhst.research.yale.edu/Data.php. The abundance pattern forCOSMOS-11494 for both the two-component and single-age model, asshown in Figure 2, is also available as Source Data.
31. Conroy, C., Gunn, J. E. & White, M. The Propagation of Uncertaintiesin Stellar Population Synthesis Modeling. I. The Relevance of UncertainAspects of Stellar Evolution and the Initial Mass Function to the DerivedPhysical Properties of Galaxies.
Astrophys. J. , 486–506 (2009).32. Conroy, C. & Gunn, J. E. The Propagation of Uncertainties in StellarPopulation Synthesis Modeling. III. Model Calibration, Comparison, andEvaluation.
Astrophys. J. , 833–857 (2010).33. Kriek, M. & Conroy, C. The Dust Attenuation Law in Distant Galaxies:Evidence for Variation with Spectral Type.
Astrophys. J. Let. , L16(2013).34. Chabrier, G. Galactic Stellar and Substellar Initial Mass Function.
Publ.Astron. Soc. Pac. , 763–795 (2003).35. Bruzual, G. & Charlot, S. Stellar population synthesis at the resolution of2003.
Mon. Not. R. Astron. Soc. , 1000–1028 (2003).36. Maraston, C. Evolutionary population synthesis: models, analysis of theingredients and application to high-z galaxies.
Mon. Not. R. Astron. Soc. , 799–825 (2005).37. Cardelli, J. A., Clayton, G. C. & Mathis, J. S. The relationship betweeninfrared, optical, and ultraviolet extinction.
Astrophys. J. , 245–256(1989).38. Calzetti, D. et al.
The Dust Content and Opacity of Actively Star-formingGalaxies.
Astrophys. J. , 682–695 (2000).39. Foreman-Mackey, D., Hogg, D. W., Lang, D. & Goodman, J. emcee: TheMCMC Hammer.
Publ. Astron. Soc. Pac. , 306–312 (2013).40. Kriek, M. et al.
An Ultra-Deep Near-Infrared Spectrum of a CompactQuiescent Galaxy at z = 2 . . Astrophys. J. , 221–231 (2009)., 221–231 (2009).