The Baryonic and Dark Matter Properties of High Redshift Gravitationally Lensed Disk Galaxies
P. Salucci, A. M. Swinbank, A. Lapi, I. Yegorova, R. G. Bower, Ian Smail, G. P. Smith
aa r X i v : . [ a s t r o - ph ] A ug Mon. Not. R. Astron. Soc. , 000–000 (0000) Printed 7 November 2018 (MN L A TEX style file v2.2)
The Baryonic and Dark Matter Properties of HighRedshift Gravitationally Lensed Disk Galaxies
P. Salucci , A. M. Swinbank , A. Lapi , I. Yegorova ,R. G. Bower , Ian Smail , G. P. Smith Astrophysics Sector, SISSA/ISAS, Via Beirut 2-4, I-34014 Trieste, Italy ICC, Department of Physics, Durham University, Durham School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT ∗ Email: [email protected]
ABSTRACT
We present a detailed study of the structural properties of four gravitationally lenseddisk galaxies at z = 1. Modelling the rotation curves on sub-kpc scales we derive thevalues for the disk mass, the reference dark matter density and core radius, and theangular momentum per unit mass. The derived models suggest that the rotation curveprofile and amplitude are best fit with a dark matter component similar to those oflocal spiral galaxies. The stellar component also has a similar length scale, but withsubstantially smaller masses than similarly luminous disk galaxies in the local universe.Comparing the average dark matter density inside the optical radius we find that thedisk galaxies at z = 1 have larger densities (by up to a factor of ∼
7) than similardisk galaxies in the local Universe. Furthermore, the angular momentum per unitmass versus reference velocity is well matched to the local relation, suggesting thatthe angular momentum of the disk remains constant between high redshifts and thepresent day. Though statistically limited, these observations point towards a spirals’formation scenario in which stellar disks are slowly grown by the accretion of angularmomentum conserving material.
Key words: galaxies, rotation curves, galaxies, gravitational lensing, galaxy clusters,Integral Field Spectroscopy, Gravitational Arcs: Individual
It has long been known that the kinematics of spiral galaxiesdo not show Keplerian fall-off in their rotation curves, butrather imply the presence of an invisible mass componentin addition to the stellar and gaseous disks (Rubin et al.1980; Bosma 1981; Persic & Salucci 1988). In the local Uni-verse, observing the distribution of star light and mappingthe gaseous component through H i it has been possible tobuild up a picture of the how the baryonic component of diskgalaxies is distributed and how this relates to the underlyingdark matter component (e.g. Persic et al. 1996). Tracing theevolution of galaxy mass from high-redshift up to the presentday is only truly reliable if we can observe the same compo-nents at early times. A pioneering study was performed byVogt et al. 1996 where a handful of rotation curves (RC’s)of objects at z ∼ . > ∼
1) galaxies are much fainter and havesmaller angular disk scale lengths than galaxies observed at low redshift, therefore obtaining the spatial information re-quired for detailed studies is beyond the limits of currenttechnology. Indeed, mapping the internal properties and dy-namics of both the stellar and gaseous components of galax-ies at high redshift is one of the main science drivers for thenext generation of ground and spaced based telescopes atmany wavelengths (e.g. ELT, NGST, ALMA).One way to overcome this problem is to use the nat-ural amplification caused by gravitational lensing to boostthe size and flux of distant galaxies which serendipitouslylie behind massive galaxy clusters. This technique is ex-tremely useful since we are able to target galaxies whichwould otherwise be too small and faint to ensure a suffi-ciently high signal-to-noise spectroscopy in conventional ob-servations. As such, gravitational lensing has been exten-sively used to make detailed studies of distant galaxies: fora galaxy at z =1 with an amplification factor ten, an angularscale of 0.6 ′′ can correspond to < ∼ c (cid:13) Salucci et al. by Integral Field Spectroscopy (which produces a contiguous two dimensional velocity map at each point in the targetgalaxy). This allows a clean decoupling of the spatial andspectral information, thus eliminating the problems arisingfrom their mixing in traditional long-slit observations. It istherefore much easier to identify and study galaxies withregular (bi-symmetric) velocity fields.In this paper, we present a detailed study of fourrotation curves extracted from disk galaxies which havebeen observed through the cores of massive galaxy clus-ter lenses. These targets are taken from the recent workof Swinbank et al. (2003, 2006). They were observed withthe Gemini-North Multi-Object Spectrograph Integral FieldUnit (GMOS IFU) . We concentrate on the galaxy dynamicsas traced by the [O ii ] λλ i disks in galaxies atthese early times would be wellcome, such observations willhave to wait for future instrumentation (e.g. ALMA).In this paper we use nebular emission lines to probe thekinematic of the galaxies. We extract one-dimensional rota-tion curves from the velocity fields to infer the distributionof stellar and dark matter components. Finally, we compareour results with similarly luminous disk galaxies in the localUniverse. Through-out this paper we use a cosmology with H = 72 km s − , Ω = 0 . = 0 . t = 13 . Gyr . Our sample comes from observations of six gravitational arcsin Swinbank et al. (2006). In order to avoid possible biases,the targets were selected only to be representative of galax-ies in the distant Universe and no attempt was made toselect galaxies with relaxed late-type morphology. We did, Programme ID: GN-2003A-Q-3. The GMOS observations arebased on observations obtained at the Gemini Observatory, whichis operated by the Association of Universities for Research in As-tronomy, Inc., under a cooperative agreement with the NSF onbehalf of the Gemini partnership: the National Science Founda-tion (United States), the Particle Physics and Astronomy Re-search Council (United Kingdom), the National Research Council(Canada), CONICYT (Chile), the Australian Research Council(Australia), CNPq (Brazil) and CONICET (Argentina).
Properties of the galaxies
Arc z M D r ρ R opt v h (10 M ⊙ ) ( kpc ) (10 − g cm − ) ( kpc ) ( km s − )A2390 0.912 0.40 3.1 1.4 8.3 151RGB1745 1.056 0.18 4.2 0.37 9.6 104A2218 1.034 1.70 5.8 0.64 7.7 166Cl2236 1.116 0.12 1.4 3.2 5.4 101 Table 1.
Derived structural parameters from the RC mass mod-elling. Error bars for M D are shown in 2, while the uncertaintiesin r , v h , R opt ≡ . R D and ρ amount to 30%, 15%, 15%, 40%respectively. however, require that arcs were resolved in both spatial di-mensions so that a two dimensional velocity field could beextracted from the IFU data. This restricted our selectionto galaxies with moderate magnification. From the sampleof six galaxies, four galaxies appear to have (relaxed) bi-symmetric velocity fields with late-type morphologies andcolours. The rotation curves from these four galaxies ap-pear regular and we therefore restrict our analysis to thesearcs. We stress that the morphology, colours and velocityfields of the four galaxies in this sample all strongly sug-gest these galaxies are consistent with late type spirals (seeSwinbank et al. (2006)). From our optical/near-infrared imaging, we constrain thespectral energy distribution (SED) of each galaxy. Since thearcs usually lie with a few arcs-seconds of nearby brightcluster galaxies, we calculate the magnitude of the arcs invarious pass-bands by masking the arc and interpolating thelight from the nearby cluster members. The background lightis then removed and surface photometry in different bandsis obtained.Using the cluster mass models the arcs are recon-structed to the source-plane and the geometry and disk-scaleparameters of the disks are measured. This is achieved byfitting ellipses to an isophote of the galaxy image using amodified version of the idl gauss2dfit routine which fitsan exponential profile to the two-dimensional light distribu-tion. From this, the ellipticity, the inclination and luminosi-ties and the disk scale lengths are obtained (see Table 2 and3 in Swinbank et al. (2006)). These latter are also reportedbelow in Table 1.
In Fig. 1 we show the one dimensional rotation curves of thegalaxies in our sample. These are extracted by sampling thevelocity field along the major axis cross section. The zero-point in the velocity is defined using the center of the galaxyin the reconstructed source plane image. The error bars forthe velocities are derived from the formal 3 σ uncertainty inthe velocity arising from Gaussian profile fits to the [O ii ]emission in each averaged pixel of the datacube. For themass modelling analysis we folded the rotation curves onthe kinematical center to ensure that any small-scale kine-matical sub-structure is removed. c (cid:13) , 000–000 ass Decomposition of z=1 Giant Luminous Arcs Figure 1.
Filled circles represent the IFU rotation curves having enough data to allow the coaddition of the kinematics of the recedingand the approaching arm, red and blue open circles represent the rotation curves along each arm in the other cases. The dark-matterand stellar components are shown with long dash and short dash lines, whilst the model circular velocity is shown with a solid line.
The rotation curves of local spiral galaxies imply the pres-ence of an invisible mass component, in addition to the stel-lar and gaseous disks. The paradigm is that the circularvelocity field can be characterized by: V = V D + V H + V HI (1)where the subscripts denote the stellar disk, dark haloand gaseous disk respectively. From the photometry wemodel the stellar component with a Freeman surface den-sity (Freeman 1970):Σ D ( R ) = M D πR D e − R/R D (2)where R D is the disk lenght-scale, while R opt ≡ . R D canbe taken as the ”size” af the stellar disk, whose contributionto the circular velocity is: V D ( x ) = 12 GM D R D (3 . x ) ( I K − I K ) (3)where x = R/R opt ≡ R/ (3 . R D ) and I n and K n are themodified Bessel functions computed at 1 . x . In small spiralsthe H i disk is an important baryonic component only for R > R D , i.e. outside the region considered here. It is plausiblethat in similar objects also at high redshifts, inside R D ,the H i gas contributes to the gravitating baryonic mass bya very small amount, residing at larger radii and it slowlyinfalls forming the stellar disk.For the dark matter component we take a sphericalhalo for which V H ( R ) = G M H ( < R ) /R . Following theobservational scenario constructed in the local Universe(Persic & Salucci 1988; Salucci & Burkert 2000) we assumethat it has the Burkert (1995) density profile (see alsoSalucci et al 2007): ρ ( R ) = ρ r ( R + r ) ( R + r ) , (4) where r is the core radius and ρ the effective core density.It follows that: M H ( R ) = k (cid:20) ln (cid:16) Rr (cid:17) − tan − (cid:16) Rr (cid:17) + 12 ln (cid:18) R r (cid:19)(cid:21) (5)with k = 6 . ρ r and of course V H ( R ) = GM H ( R ) /R Wenote that the adopted velocity profile is a quite general: itallows a distribution with a core of size r , converges to theNFW profile at large distances and, for suitable values of r can also mimic the NFW or a isothermal profile, over thelimited region of galaxy which is mapped by the rotationcurves.The mass model has three free parameters: the diskmass M D , the core radius r , and the central core density ρ .The observations extend out approximately (2 − R D , have10-60 independent measurements with an observational er-ror of 3% −
10% in their amplitude, of 0.05-0.2 in their slopes dlogV /dlogR . The error in the estimate of the disk inclina-tion angles is negligible with respect to the above. These er-rors are (understandably) higher than those associated withthe best quality local RC’s and make it difficult to constrainthe halo density profile ρ ( R ). However, they are sufficientlysmall to yield a reliable value for the halo mass, the aver-age density inside a reference radius, (which we chose to be R ≡ R D so that < ρ > ≡ M H ( R ) / (4 / πR ) and the diskmass and a reasonable estimate of the ”core radius”.By reproducing the observed rotation curves with themodels given by equations 1-5 we derive the best fit param-eters for each galaxy and overlay the resulting mass modelonto each rotation curve in Fig. 1. In Table 1 we report themain structural parameters: the disk mass, the halo core ra-dius, ρ , the optical radius R opt and v h ≡ V H ( R opt ), i.e. thehalo contribution to circular velocity at the optical radius.In all our rotation curves the amplitude and the pro-file of the stellar disk contribution can not reproduce the c (cid:13) , 000–000 Salucci et al.
Figure 2.
Left: disk mass (in solar units) versus reference velocity (in km/s ) compared with the z =0 relation ( solid line) and with thisscaled down by 0.6 dex ( dashed line). Middle: average dark matter density (in g cm − ) versus reference velocity compared with the z =0relation ( solid line). Right: disk angular momentum per unit mass j (in km/s kpc units) versus disk mass compared with the z =0 relation( solid line). The uncertainties on the local relations are: 0.15 dex in j , 0.2 dex in log M D and 0.3 dex in log < ρ > . observed RC rise between 1.5 R D and the last measuredradius. This strongly suggests evidence for the presence, at z ≈
1, of a dark matter component of mass comparableto that found for local disk galaxies with similar V opt (seeFigures 2, 8 and 9 of Persic, Salucci & Stel, 1996). We de-rive disk masses ranging between 1 × M ⊙ to 2 × M ⊙ for galaxies with reference velocity V opt between 100 km s − and 200 km s − . These disk masses are smaller by a factor2-4 than those of the local spirals with the same referencevelocity which are shown to follow Inner Baryon Dominance(see Salucci & Persic, 1999). The high redshift stellar disksare sub-maximal disks. Forcing a maximal disk even in the”weak” implementation of Persic and Salucci (1990) leadsto unacceptable fits of our high-z RC’s.The best fit values for r is of the order of ∼ . R D ,which is larger than usually compatible with a NFW pro-file, although the error-bars on our data preclude any strongstatement.Since the gravitational lens model affects the source-plane reconstruction of the galaxies, we must test for theeffect that this has on the resulting rotation curves. Wereconstruct the galaxies using the family of lens modelsthat inhabit the ∆ χ contour corresponding to 1 σ confi-dence interval relevant to each cluster. For example, themodel of RGB 1745 has five free parameters, and the lensmodeling uncertainties are therefore derived by consider-ing models within the ∆ χ =5 .
89 contour. From each re-construction we extract the one-dimensional rotation curveand apply the analysis outlined above and find the maxi-mum variations are: ∆ log M D = 0 .
03, ∆ log < ρ > = 0 . V opt ) < ∼ − . Thus the uncertainties in the gravi-tational lens modelling is negligable compared to the uncer-tainties in the RC mass modelling.A cosmological significance of our result is evident inFig 2 where we compare the disk mass, the mean dark matterdensity within the optical radius and the angular momen-tum per unit mass, all as a function of reference velocity.These are compared to similar properties of the local ob-jects (Shankar et al. 2006). Figure 2 strikingly shows thathigh redshift spirals, modulo an offset of 0 . +0 . − . dex, areon the same logM D versus logV opt relationship found forlocal spirals arising from the systematic structural proper- ties of their mass distribution (Tonini et al. 2006), see also(Salucci et al. 1993) .In Fig 2, from the values of < ρ > , a quantity thatdifferently from ρ is weakly affected by the RC 1- σ fittinguncertainties, it is apparent that the DM halos of z = 1 diskgalaxies are denser by 0 . +0 . − . dex than those around sim-ilarly luminous z =0 spirals. The evidence that spiral disksat z =0 and z =1 have the same structural relationships isfurther supported by observations of the evolution of theTully-Fisher relation (which correlates the disk mass with V opt ). In our and in other independent samples (Swinbanket al 2006, , Vogt et al 1996, Bamford et al 2005) the galaxiesat z = 1 show a TF relation with a slope similar to that ofthe local TF, but with an offset compatible with that foundin the present work from the disk mass vs rotation velocity.This suggests that from z =1 to z =0, the stellar disk masses M D of a spiral has grown by a factor ∼ +1 − , that leads tojust a modest increase in the DM dominated quantity V opt .Further evidence that z = 1 disk galaxies are related topresent day spirals is provided by the relationship betweenangular momentum per unit mass ( j ) versus the referencevelocity, as shown in Fig. 2. This well theoretically moti-vated relation (e.g. (Tonini et al. 2006)) can be consideredas the imprint of the process of the formation of disks in-side dark matter halos related to the cosmological proper-ties of halo spin parameters. As Figure 2 shows, there ap-pears to be no evolution in this crucial relationship betweenthe the comological time at which we observe these spirals, z = 1 , t = 6 Gyr and the present time, z = 0 , t = 13 . Gyr .This agreement is remarkable: it establishes a link betweenlocal and high redshift disks, supporting the idea that theangular momentum remains constant during the evolutionof a disk system from high redshift to the present day.The kinematical estimate of the disk mass allows us toderive the mass-to-light ratios for our disk systems as a func-tion of luminosity and colour. In Fig. 3 we compare the diskmass and colour as a function of mass-to-light ratio com-pared to the relation in local spirals (Shankar et al. 2006).In order to compare directly with local relations, we considera simple passive evolution model for the luminosity evolu-tion. For a single stellar population the zero-point of thelocal relation is decreaed by a factor log (13 . /
6) which ac- c (cid:13) , 000–000 ass Decomposition of z=1 Giant Luminous Arcs Figure 3.
Left:
Mass-to-light ratio versus disk mass for the galaxies in our sample compared with the local disk galaxies from Shankar etal. (1996) (solid line). The average offset corresponds to an excess in luminosity by a factor four.
Right:
Mass-to-light ratio versus colorsrelations for our sample. The square box denotes the predicted colours from a Bruzual & Charlot single stellar population (see text fordetails). counts for the passive evolution of a single stellar populationfrom z = 1 to z = 0. As Fig. 3 shows the mass-to-light ratiosas a function of galaxy ( B − V ) colour are in broad agree-ment with predictions of a single stellar population which is ∼ Gyr old (Bruzual & Charlot 2003), although clearly pho-tometry at other wavelengths (such as rest-frame K-band)would allow a more detailed decomposition of the stellarpopultations in these galxies.
Figure 2 shows that at a radius corresponding to V opt thehigh redshift galaxies are significantly denser than compara-bly luminous local disk-galaxies: the average offset is about0.6 dex in log ( < ρ ) > . Although we can not exclude thatdynamical processes occur between z = 1 and z = 0 to re-duce the dark-matter density in the luminous regions, thisoffset is naturally explained if the halos embedding thesedisk galaxies formed at earlier times than the halos aroundsimilarly massive z = 0 spirals. In this framework we esti-mate the ratio between the virialization redshift of the localgalaxies and and that of the galaxies in our sample. Since ρ v ∝ ∆( z v )(1 + z v ) where ρ v and z v are average densityand redshift at virialization and ∆ v is known, for z = 1, z v = 1 .
7, which corresponds to t v = 6 Gyr .Assuming that our sample is a fair representation ofdisk galaxies at z ∼ z = 0 spirals, the following simple picture emerges:a present day spiral, with a given circular velocity, half-lightradius and the angular momentum per unit mass, at redshift1 had similar values for these quantities, but a smaller stellarmass: < M ⋆ ( t obs ) /M ⋆ ( t ) > ≃ .
3. This induces a scale forthe average SFR in the past 8 Gyr: ∼ . M ⋆ ( t ) / ( t obs − t ) ∼ M ⋆ ( t ) / (10 M ⊙ ) M ⊙ /yr . With these disks hav-ing an average age of 1 Gyr at z = 1 we can also derivean ”early times” average SFR ∼ . M ⋆ ( t ) / (1 Gyr ) ∼ M ⋆ ( t ) / (10 M ⊙ ) M ⊙ /yr which points towards a declin-ing SFR history.The marked increase of the luminosity per unit stellarmass in objects at high redshifts with respect to their localcounterparts has the simplest explanation in a passive evolu-tion of the starforming disks. Obviously, this simple picturerequires us to assume that the high redshift systems are thedirect counter-parts of similar rotation speed spirals at lowredshift. In this study, we have investigated the detailed propertiesof four disk galaxies at z = 1. These galaxies were observedat high spatial resolution thanks to the boost in angularsize provided by gravitational lensing by foreground massivegalaxy clusters and allow a much more detailed comparisonwith local populations than usually possible for galaxies atthese early times. Modelling the one-dimensional rotationcurves with those of Persic et al. (1996) we derive best fitparameters for the total dynamical mass, the core radius,the effective core density and the angular momentum perunit mass.The best fit model rotation curves to the data show thatthe amplitude and profile of the stellar disk componentcannot unambiguously reproduce the rise in the rotation curvewithout a dark matter component. Comparing the averagedark matter density inside the optical radius we find thatthe disk galaxies at z = 1 have larger densities (by up toa factor of ∼
7) than similar disk galaxies in the local Uni-verse. In comparison, we find that the angular momentumper unit mass versus reference velocity is well matched tothe local relation suggesting that the angular momentumof the disk remains constant between high redshift and thepresent day. Though statistically limited, these observationspoint towards a spirals’ formation scenario in which stellardisk are slowly grown by the accretion of angular momen- c (cid:13) , 000–000 Salucci et al. tum conserving material. Our result, also consistent withthe theoretical evolution of the angular momentum of disksfrom semi-analytic models from z =1 to z =0 which show themodest offset of ∆j < ∼ − for objects with circu-lar velocities between 50 and 300 km s − (Cole et al. (2000);Bower et al. (2006)). These reults provide an evolutionarylink between the disk systems we observe at redshift z ∼ i content of galaxies to z = 1, the exact relationbetween gas, stars and dark matter can be probed in muchmore detail. ACKNOWLEDGMENTS
We would like to thanks the anonymous referee for his/hersuggestions which improved the content and clarity of thispaper. We thank Carlton Baugh for providing the theoreticalevolution of disk mass in galaxies from galform . We alsothank Gigi Danese for useful discussions. AMS acknowledgessupport from a PPARC Fellowship, RGB acknowledges aPPARC Senior Fellowship and IRS and GPS acknowledgessupport from the Royal Society.
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