THE DYNAMICAL MASSES, DENSITIES, AND STAR FORMATION SCALING RELATIONS OF Lyα GALAXIES

Lyα line emission is an increasingly important tool for identifying actively star-forming galaxies in the distant universe. Lyα emission was proposed as a potential signpost for primitive galaxies (Partridge & Peebles 1967) and has now been used to identify thousands of galaxies at redshifts 2 < z < 7, along with smaller samples at z < 2 and several candidates at z > 7.

While no galaxy yet identified by any means is demonstrably primordial, Lyα-selected samples do have several properties suggestive of youth. Their starlight is dominated by young populations with characteristically low stellar masses (Pirzkal et al. 2007; Finkelstein et al. 2007) and small sizes (Bond et al. 2009; Malhotra et al. 2012). Yet, the correlation properties of these objects suggest that they are associated with moderately large halos (mass ∼10¹¹ M_☉; Kovač et al. 2007; Guaita et al. 2010). Combining these results suggests that a Lyα galaxy contains only a small fraction of the baryons that should be associated with its host dark matter halo. It would be interesting to know whether the "missing" baryons are present, either as old stellar populations or in the interstellar medium of the Lyα galaxy.

Dynamical mass estimates for Lyα galaxies could potentially address this question. The dynamical mass is the total gravitating mass of the galaxy, measured using kinematics. Such masses provide a standard for comparison with both the stellar masses and the dark halo masses. However, dynamical mass estimates require an accurate measurement of the galaxy's velocity dispersion. The easiest approach to kinematics would be to use the Lyα line width, which is measured for most spectroscopically confirmed Lyα galaxies. Unfortunately, this does not lead to useful velocity dispersion information as the Lyα line profile can be dramatically affected by the interplay of resonant scattering and gas kinematics in the emitting galaxy.

We therefore turn in this paper to studying Lyα galaxy kinematics using the strong rest-frame optical emission lines of [O iii] λ5007 Å and Hα λ6561 Å. We build on the first detections of such lines in Lyα-selected galaxies at redshifts 2.2 ≲ z ≲ 3.1 (McLinden et al. 2011; Finkelstein et al. 2011; Hashimoto et al. 2012). In Section 2, we describe the sample and the key data. In Section 3, we estimate dynamical masses based on the observed line widths. In Section 4, we analyze the stellar populations and dust reddening in these galaxies, using deep archival photometry. In Section 5, we combine the rest-optical line width measurements with the stellar masses from population synthesis modeling to compare these Lyα galaxies with expectations from the stellar mass Tully–Fisher (SMTF) relation (e.g., Kassin et al. 2007). In Section 6, we examine the relation between gas mass surface density and star formation surface density to show that Lyα galaxies lie on the same sequence as starburst galaxies. Finally, in Section 7, we explore the mass densities of the sample and the implications for the future evolution of Lyα galaxies.

Throughout the paper, we adopt a Λ-CDM "concordance cosmology" with Ω_M = 0.27, Ω_Λ = 0.73, and H₀ = 71 km s⁻¹ Mpc⁻¹.

Our sample consists of Lyα emitting galaxies that were selected from four surveys. All are selected directly by the presence of a strong Lyα emission line in the survey data. For the analysis in this paper, we make use of (1) velocity dispersions σ, derived from spectra of rest-frame optical emission lines, (2) sizes, as measured by the half-light radius r_e in broadband optical Hubble Space Telescope (HST) images, (3) stellar masses and dust extinctions, derived from spectral energy distribution (SED) fits, and (4) star formation rates (SFRs), determined from Hα line flux measurements, where available (SFR_Hα), and from SED fitting otherwise (SFR_sed), and corrected for dust obscuration using the results of the SED fits. In this section, we summarize the sources for various galaxies in the sample, along with the measurements of σ, r_e, and SFR. The stellar mass derivations are discussed later, in Section 4.

The properties of the sample are also tabulated. Basic observational quantities (z, σ_los, r_e) and derived SFRs are in Table 1. Dynamical masses and densities are in Table 2, along with the range of stellar masses from SED fitting. More detailed SED fitting results are summarized in Tables 3 and 4.

Table 1. Basic Observational Properties of the Sample

ID	z	σ los	d(σ los)	re(kpc)	SFR	d(SFR)	Refs.a
LAE40845	3.1117	81	${+4\atop -4}$	1.1	113b	${+120\atop -60}$	1
LAE27878	3.11879	43	${+7\atop -7}$	1.3	32b	${+9\atop -7}$	1
HPS194	2.287	65	${+6\atop -6}$	1.5	17	${+1.5 \atop -0.5}$	2
HPS256	2.491	74	${+7\atop -8}$	1.1	25	${+9\atop -5}$	2
COSMOS13636	2.1621	57	${+40\atop -57}$	0.79	7.4	${+2.5\atop -2}$	3
COSMOS30679	2.19855	55	${+40\atop -55}$	1.83	31	${+38\atop -15}$	3
CDFS3865	2.173	105	${+20\atop -20}$	0.96	96	${+21\atop -15}$	3
CDFS6482	2.205	42	${+28\atop -42}$	1.78	29	${+10\atop -7}$	3
LAE-COSMOS-47	2.24654	27	${+7\atop -8}$	1.14	16.3	${+4.6 \atop -1.0}$	4

Notes. ^aReferences: 1. McLinden et al. 2011; Richardson et al. 2013; 2. Finkelstein et al. 2011; Song et al. 2013; 3. Hashimoto et al. 2012; Nakajima et al. 2012; 4. Nilsson et al. 2011. ^bSFR is based on SED fitting results for this object.

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Table 2. Masses and Densities of the Sample

ID	Mdyna		$\log (\bar{\rho }_e)$b		M*, mina	M*, maxa
LAE40844	6.7	$^{+0.6}_{-0.6}$	−22.39	$^{+0.10}_{-0.10}$	2.72	34.0
LAE27878	2.2	$^{+0.8}_{-0.8}$	−23.08	$^{+0.35}_{-0.35}$	3.80	22.5
HPS194	5.8	$^{+1.3}_{-1.3}$	−22.85	$^{+0.27}_{-0.27}$	19.9	21.2
HPS256	5.6	$^{+1.4}_{-1.4}$	−22.47	$^{+0.30}_{-0.30}$	1.75	11.3
COSMOS13636	2.4	$^{+5.1}_{-2.4}$	−22.40	$^{+1.2}_{-\infty }$	4.22	11.0
COSMOS30679	5.1	$^{+11}_{-5.1}$	−23.16	$^{+1.2}_{-\infty }$	1.65	12.0
CDFS3865	9.8	$^{+5.6}_{-4.3}$	−22.04	$^{+0.45}_{-0.58}$	6.52	14.3
CDFS6482	2.9	$^{+3.3}_{-2.9}$	−23.38	$^{+0.76}_{-\infty }$	9.10	32.7
LAE-COSMOS-47	0.95	$^{+0.77}_{-0.55}$	−23.28	$^{+0.75}_{-0.98}$	0.5768	2.13

Notes. The dynamically derived masses, the dynamically derived mean volume mass densities inside the effective radius, and the 1σ range of stellar masses derived from SED fitting. ^aAll masses are given in units of 10⁹ M_☉. ^bDensities are given in units of g cm⁻³.

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2.1. Bok Telescope z = 3.1 Survey Objects

2.2. HETDEX Pilot Survey Objects

2.3. Subaru Narrowband Survey Objects

2.4. ESO z = 2.25 Survey Object

The measured velocity dispersions σ from the rest-frame optical emission lines are a good estimate of the total luminosity-weighted kinematics of the gas. The galaxies we are studying are spatially unresolved even in ∼05 seeing, meaning that the ground-based spectra we use effectively sample the integrated light, with no important dependence on slit width.

The precise conversion from velocity width to mass will depend on the kinematic structure of these galaxies. For a pure rotation-supported disk model with a flat rotation curve, we expect a line-of-sight velocity width

$$\begin{equation} \sigma _{{\rm \scriptsize los}}^2 = \sin ^2{\!i} \; v_c^2 / 2. \end{equation} \tag{ 1 }$$

(Here, we assume that all particles follow circular orbits, with independent orbital phases, but with the same speed v_c and inclination angle i, where i = 90° corresponds to an edge-on system. The factor of 1/2 comes from averaging over an azimuthal angle ϕ: 〈sin ²(ϕ)〉 = 1/2.)

We obtain the simplest dynamical mass estimate from these measurements by calculating the gravitating mass needed to hold the outermost particles in a galaxy (at some radius r_max) in circular motion. This gives ${G M}(\!<\!r_{{\rm max}})\, r_{{\rm max}}^{-2} = v_c^2\, r_{{\rm max}}^{-1}$. Solving for mass,

$$\begin{equation} M_{{\rm dyn}}\ge v_c^2 r_{{\rm max}} / G, \end{equation} \tag{ 2 }$$

where M_dyn is a lower bound because it cannot account for mass located beyond r_max. Measuring r_max is problematic. We can estimate r_max as the largest radius where light is observed, but it then becomes sensitive to the depth of the imaging data.

A more practical choice of radius is the effective radius r_e, defined as the radius that encloses half of the galaxy's light in projection. If we presume that the half-light radius is also the half-mass radius, our revised estimate of the dynamical mass becomes

$$\begin{equation} M_{{\rm dyn}}\approx \, 2\, v_c(r_e)^2 \, r_e / G \; \approx \; 4 \sigma _{{\rm \scriptsize los}}^2 r_e / (G \sin ^2{i}) \; \gtrsim \; 4 \sigma _{{\rm \scriptsize los}}^2 r_e / G. \end{equation} \tag{ 3 }$$

The resulting mass estimates range from 10⁹ to 10¹⁰ M_☉ and are summarized in Table 2. We also tabulate their associated statistical uncertainties, which we estimate using the random errors both in σ_los and r_e. The σ_los uncertainties are estimated by adding simulated noise to spectra and re-measuring the line widths. The r_e uncertainties are in the 5%–15% range for our sample, following the treatment of Venemans et al. (2005), who use δr_e ≈ r_e/(s/n). The σ_los uncertainties dominate the random errors in M_dyn.

Several circumstances could affect our estimated masses. A rotating disk with i < 90° would reduce the measured σ_los (relative to the edge-on case). Also, in our spatially unresolved spectroscopy, the observed $\sigma _{{\rm \scriptsize los}}^2$ reflects the luminosity-weighted average kinematics. If a significant fraction of the galaxy's light is emitted from regions where the local circular speed v_c(r) is below the maximum circular speed (v_max), we should expect the weighted average $\sigma _{{\rm \scriptsize los}}^2$ to underestimate v_max and hence the mass. The precise magnitude of this effect depends on the galaxy's light profile and rotation curve. Also, like any dynamical mass based on luminous tracers, our estimate is insensitive to mass located outside the luminous matter distribution of the galaxies. If the galaxies are embedded in extended dark matter halos, the total mass of the halo could be many times the mass estimates derived from the observed r_e and $\sigma _{{\rm \scriptsize los}}^2$.

Turbulence in the galaxy's gas would contribute to the measured σ_los, although in virial equilibrium that turbulence would constitute a source of pressure support and the ordered rotation of the galaxy would be correspondingly reduced. Most interestingly, if the galaxy is not in equilibrium at all, our assumed relations between kinematics and mass could be substantially wrong. Our mass estimate implicitly assumes that the virial theorem is fulfilled, that is, that the kinetic energy K and potential energy U of the galaxy are related by K = −U/2. On the other hand, in a cold accretion scenario, new material falling into a galaxy for the first time should have K = −U, i.e., the motions are faster for the same gravitating mass under these conditions and the mass inferred from gas motions would be correspondingly overestimated by a factor up to ∼2.

Given these uncertainties, it is best to regard our direct dynamical mass estimates as approximate numbers, good to a factor of perhaps two when regarded as lower bounds on the true dynamical mass. Other dynamical mass estimates in the literature consider a more general scaling coefficient so that $M_{{\rm dyn}}= \beta \sigma _{{\rm \scriptsize los}}^2 r_e / G$ (see Toft et al. 2012 and references therein, especially Jorgensen et al. 1996 and Cappellari et al. 2006). These works favor β ≈ 5 for early-type galaxies with Sersic indices n ≈ 4 and find that despite theoretical expectations for some increase of β with decreasing Sersic n, the observational evidence favors β ≈ 5 for a wide range of n. Thus, the simple arguments that led us to use β = 4 come fairly close to the correct dynamical masses.

A complementary approach to interpreting the kinematic data of these galaxies is to use their linewidths to place them on some form of the Tully–Fisher relation and so to compare them on an equal footing with other galaxy populations. Such an approach avoids the difficulties associated with identifying the right radius to use in estimators of the form M ∼ v²R/G. For high-redshift galaxy populations, a small scatter with weak redshift evolution has been demonstrated for the SMTF relation, and we place our galaxies on such a relation in Section 5 below. To do so, we first need their stellar masses.

All of the galaxies we study have extensive multiband photometry in the literature, generally including multiband optical data, some deep ground-based, near-infrared photometry, and Spitzer IRAC (Fazio et al. 2004) observations that are deep enough to be constraining in at least the 3.6 μm channel.

We have used these data to derive stellar mass estimates for the full sample. Stellar mass estimates are also available in the published literature for many of these galaxies (Finkelstein et al. 2011; Hashimoto et al. 2012; Nakajima et al. 2012; McLinden et al. 2013). While these values are mostly consistent with our estimates where samples overlap, we opted to fit the entire sample using a single procedure to avoid potential difficulties comparing masses derived using different methodologies.

4.1. General Comments on SED Fitting

4.2. Starburst99 Modeling

The SMTF relation is a correlation between the kinematic line widths of galaxies and their stellar masses. The SMTF relation is more robust to differences in the stellar population mass-to-light ratio than the original Tully–Fisher relation (which correlates luminosity with line width; Tully & Fisher 1977). The relation is further generalized by Kassin et al. (2007), who demonstrated that replacing the circular speed V_c with the kinematic estimator $S_{0.5} = (0.5 V_{{\rm rot}}^2 + \sigma ^2)^{1/2}$ results in an SMTF that is both tighter and more applicable to the wide range of galaxy properties seen at high redshift. Here, V_rot characterizes the ordered rotation of a galaxy and σ is its disordered, random motions. Besides reduced scatter, S_0.5 has an additional advantage: for spatially unresolved galaxies (like those we study here), S_0.5 can be measured reasonably accurately regardless of whether the width is dominated by ordered rotation or random motions.

Our actual measurement is a single number, the line width, characterized by the observed line-of-sight velocity dispersion σ_los. We then use S_0.5 = σ_los for our galaxies. Consider pure circular motion with a flat rotation curve of velocity V_c, viewed edge-on: we find $\sigma _{{\rm \scriptsize los}}^2 = \langle (\sin (\phi) V_c)^2 \rangle = 0.5 V_{c}^2$, so that S_0.5 = σ_los. If instead the motion is entirely random, with V_rot = 0, we again obtain S_0.5 = σ_los. Only for ordered rotation in a face-on configuration do we expect σ_los to be a significant underestimate of S_0.5. While we cannot rule out this possibility with our data, it is likely that these galaxies are dynamically hot ($\sigma / V_{{\rm rot}} \not\ll 1$), since the stellar populations dominating the observed light are at most ∼1 dynamical time old.

Our results are shown in Figure 1, both for stellar masses from SED fitting and for dynamical masses from line width and spatial extent. The error bars for the stellar masses show the ranges of stellar mass permitted by models with $\Delta \chi ^2 \equiv \chi ^2 - \chi ^2_{{\rm min}} < 4$ and with Δχ² ⩽ 1. The error bars for dynamical mass are determined by the uncertainties in σ_los and are diagonal since the x-axis of the plot is σ_los. For three objects from the Hashimoto et al. (2012) sample, σ_los and M_dyn are plotted as upper bounds.

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Comparing our Lyα sample with the SMTF relation that Kassin et al. (2007) reported for 0.1 < z < 1.2 star-forming galaxies, we find that both the stellar masses and dynamical masses of Lyα emitters generally follow the established relation. Dynamical mass estimates show less scatter than stellar masses, as might be expected given the vagaries of star formation histories.

About half the galaxies are consistent with stellar masses falling a factor of two or more below their dynamical masses, when we account for the range of acceptable estimates for both. For these galaxies, it is possible that the dynamical mass within the central 1–2 kpc is dominated not by the young stars that power the observed Lyα emission, but by some other unseen component. Collisionless dark matter should not be so strongly concentrated in the central kpc of a dark matter halo. Old stars (formed from centrally concentrated gas ≫10⁸ yr ago) are a possible alternative. The dynamical mass estimates we present are in fact a tighter limit on the total mass in old stars within the inner ∼kpc than the photometric limits are. Given the actively star-forming nature of these Lyα emitting galaxies, a reservoir of gas is the most intriguing possibility for the "excess" dynamical mass. Overall, though, such excess mass is merely permitted and not required by the data—so the Lyα galaxy sample shows consistency with the SMTF relation for other samples. Whatever physical properties allow Lyα to escape from these particular star-forming galaxies, they do not strongly affect the mass–linewidth relation.

The tight correlation observed between M_dyn and line width is related to the small and nearly constant physical sizes of the Lyα galaxy sample (Malhotra et al. 2012). A fixed physical size, combined with variable (and sometimes uncertain) line widths, can generate the observed slope of the M_dyn–S_0.5 relation. The M_⋆–S_0.5 relation from Kassin et al. (2007) has a somewhat steeper slope. Presuming that stars form a fairly large and constant fraction of the dynamical mass, this slope could be interpreted as evidence for a size–linewidth relation in the Kassin et al. (2007) sample, with $r_e \propto S_{0.5}^\gamma$ for γ ∼ 1.

We now take the dynamical mass as an upper bound on the gas mass in these galaxies and compare their properties with the scaling relations that describe star formation in other galaxy classes.

We use the gas surface mass density limit $\Sigma _{g,{\rm max}} = M_{{\rm dyn}}/ (2 \pi r_e^2)$. (Here, the factor of two enters because r_e is the half-mass radius and so encloses mass M_dyn/2.) We can improve this bound by subtracting our stellar mass estimates. In practice, our maximum stellar mass always exceeds the dynamical mass, allowing for the possibility that there is no gas mass. In most cases, though, our minimum stellar masses are below the dynamical masses and we can subtract them to yield refined estimates of the gas mass surface density ($\Sigma _g \lesssim (M_{{\rm dyn}}- M_{\star,{\rm min}})/(2 \pi r_e^2)$).

The SFR and gas surface density can be related according to scaling laws of the form log Σ_SFR ≈ α_SF log Σ_g + β_SF (where Σ_SFR is in M_☉ yr⁻¹ kpc⁻² and Σ_g is in M_☉ kpc⁻²). For nearby spirals and for distant star-forming BzK galaxies, Daddi et al. (2010) find α_SF = 1.42 and β_SF = −9.83 for our choice of units. For submillimeter galaxies and (U)LIRGS, Daddi et al. find a parallel but offset "starburst" sequence, with β_SF ≈ −8.93 (corresponding to 8 × more star formation for the same gas surface density).

We determined Σ_SFR for our sample using the SFR estimates and half-light radius measurements discussed in Section 2. (In particular, we use SFR_Hα for all objects except 40844 and 27878, where SFR_Hα is unavailable, and we instead use SFR_sed.) We have selected a Chabrier IMF for consistency with Daddi et al. (2010). These values of Σ_SFR exceed the expectations for "normal" star-forming galaxies by a median factor of four, based on Σ_{g, max} alone (i.e., assuming that all the gravitating mass is gas). The disagreement is significant at the >3σ level, relative to the 0.33 dex scatter in the scaling relation reported by Daddi et al. (2010). A factor of four would place the Lyα galaxies in between the normal and starburst sequences, although closer to the starburst sequence. If we use $\Sigma _g = (M_{{\rm dyn}}- M_{\star,{\rm min}})/(2 \pi r_e^2)$ in the scaling relations, we find that the median galaxy in our sample is forming stars at twice the rate expected even under the starburst scaling. The bottom line from this comparison is that Lyα galaxies likely belong to a family of starbursting objects that includes ULIRGS and submillimeter galaxies, despite order-of-magnitude differences in mass and SFRs.

While the "normal" and starburst galaxies follow distinct Σ_SFR–σ_g relations, they obey a single relation when Σ_g is replaced with the quantity Σ_g/τ_dyn, where τ_dyn is the dynamical time. We use τ_dyn ≈ 2πr_e/σ to also place our Lyα galaxy sample on this relation. While the Lyα galaxies appear less unusual when measured against this relation, they remain systematically above the trend line found by Daddi et al. (2010). The difference is suggestive, rather than significant, being a 2σ effect. The median offset is a factor of ∼3 in Σ_SFR at fixed Σ_g/τ_dyn. This is comparable to the 0.44 dex scatter in the relation, as reported by Daddi et al. (2010). This possible deviation should be explored using a larger sample.

The range of gas surface densities plotted in Figure 2 is from ∼30 to ∼1000 M_☉ pc⁻². Based on a standard ratio of dust to gas column density, A_B ≈ Σ_g/(11 M_☉ pc⁻²) (Bohlin et al. 1978), this corresponds to A_B ∼ 3–90 mag of extinction. Yet, our SED fits suggest modest extinctions, A_v ≲ 1, in all cases. There are a few possible explanations. First, the gas surface density could be much lower than one would expect for the observed level of star formation activity. In this case, the star formation versus gas surface density scaling must be more extreme than even the starburst relation. Second, the dust-to-gas ratio could be about 1–2 orders of magnitude lower than in the Milky Way. This would be most easily accommodated if the dust-to-gas ratio scales as the square of the metal abundance. Third, the extinctions inferred from SED fitting could be dramatic underestimates. If so, these objects' bolometric luminosities would mostly emerge in the rest-frame far infrared, making them readily detectible with submillimeter imaging (cf. Finkelstein et al. 2009; J. L. Wardlow et al. 2013, in preparation).

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Given our estimates of the dynamical mass, it is straightforward to determine the mean density within the effective radius for our sample. We find

$$\begin{equation} \bar{\rho _e}= {3\over 2 \pi G } {\sigma _{{\rm \scriptsize los}}^2 \over r_e^2} = {3\pi \over G t_{{\rm orb}}^2}, \end{equation} \tag{ 4 }$$

where we have used $v_c = \sqrt{2} \sigma$ (from Equation (1), assuming sin i ≈ 1) and t_orb = 2πr_e/v_c.

The likely descendents of high-redshift Lyα galaxies can be inferred by combining their observed spatial clustering (e.g., Ouchi et al. 2003; Kovač et al. 2007; Gawiser et al. 2007) with merger tree analyses. Gawiser et al. (2007) found that the typical descendents of high-z Lyα galaxies should be ∼L* galaxies based on their own correlation length measurement at z ≈ 3.1, but could be considerably more massive (∼3–5L* objects) based on the stronger correlations measured by Ouchi et al. (2003) and Kovač et al. (2007). Especially in the latter case, Lyα galaxy descendents should be primarily early-type systems (galaxy bulges and/or elliptical galaxies), which are the densest stellar systems in the nearby universe.

We therefore compare the density measurements for Lyα galaxies with the corresponding densities for early-type galaxies and bulges in Figure 3. The Lyα galaxy densities are the mean density within the effective radius, derived dynamically and therefore inclusive of all gravitating mass. For disk galaxy bulges, we take an intermediate-redshift sample from MacArthur et al. (2008). Here, we use the published effective radii and velocity dispersions to obtain dynamical estimates of density. We use two nearby elliptical galaxy samples (one from Kelson et al. 2000 and one compiled by Bezanson et al. 2009 from earlier work by Franx et al. 1989, Peletier et al. 1990, and Jedrzejewski 1987). For the Kelson et al. (2000) sample, we determine densities from published σ_los and r_e measurements; for the Bezanson et al. (2009) sample, we use plotted values of r_e and $\bar{\rho }(r_e)$. The Lyα galaxies are smaller at fixed density and less dense at fixed radius than the nearby ellipticals and spiral bulges. On the other hand, they tend to be smaller and denser than the handful of local ellipticals that have similar dynamical masses. We also compare with a sample of early-type galaxies at z ∼ 2.3 (Bezanson et al. 2009), which overlaps our Lyα sample in redshift. Here, the Lyα galaxies are of considerably lower density. In the samples from Bezanson et al. (2009), we are using stellar mass rather than dynamical mass, since σ_los is generally unavailable for the high-redshift early-type galaxies. Were dynamical masses available, we might expect these two samples to shift upward in Figure 3, but the effect would be modest, since the central regions of early-type galaxies are likely dominated by stellar mass.

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The relation between initial overdensity and epoch of collapse ensures that bound galaxies at 2 < z ≲ 3 will, by the present epoch, be parts of more massive structures. We expect that the Lyα galaxies we observe will grow through some combination of merging and smooth accretion. Merging can proceed either without dissipation, as expected for pure mergers of stellar systems ("dry mergers"), or with dissipation, as generally expected for gas-rich objects. Conservation of energy and the virial theorem can be combined to infer the expected evolution of radius with mass for dry mergers, both in the limit of equal-mass ("major") mergers and in the limit of large mass ratio ("minor") mergers. For major mergers, we expect R_e∝M, while for minor mergers, we expect R_e∝M² (e.g., Bezanson et al. 2009). In Figure 3, these correspond to $\rho \propto R_e^{-2}$ for major mergers and $\rho \propto R_e^{-2.5}$ for minor mergers. We plot vectors for both scalings. These show that the Lyα galaxies we observe cannot grow to reproduce the observed masses, sizes, and densities of modern elliptical galaxies through simple dry merging. Instead, dissipational ("wet") merging is required in order to grow the galaxies at an approximately constant mass density.

We have performed the first study of dynamical masses for high-redshift Lyα galaxies, using a sample of nine objects assembled from four samples (McLinden et al. 2011; Richardson et al. 2013; Finkelstein et al. 2011; Hashimoto et al. 2012; Nakajima et al. 2012; Nilsson et al. 2011). Such studies have been previously impractical, given the small galaxy sizes that require HST imaging for size measurements (Malhotra et al. 2012), a faint continuum that precludes absorption line measurements, and redshifts that require near-infrared spectroscopy to access those emission lines most useful for kinematic line width measurements. We measure dynamical masses ranging from 10⁹ M_☉ to 10¹⁰ M_☉.

We combine these dynamical masses with stellar masses, to study the position of Lyα galaxies on a version of the SMTF relation between mass and line width. To derive stellar masses consistently for the full sample, we fit population models to extensive multiband photometry covering rest wavelengths from Lyα to beyond the 4000 Å break. This affords constraints on young stars, older stars, and dust.

We find that the Lyα galaxies are broadly consistent with the SMTF relation established at lower redshift. Thus, whatever physical conditions allow the production and escape of significant Lyα do not result in strong departures from the linewidth–mass relation. On the other hand, about half of the sample galaxies are consistent with stellar masses significantly below their dynamical masses. In these cases, there is a possibility of a dynamically significant reservoir of gas that is present in the inner kpc region and provides fuel for ongoing star formation. The dynamical mass measurements are in fact the most powerful constraint we have on the presence of old stars in the sample galaxies. In most cases, the stellar population fits allow up to ∼3 × 10¹⁰ M_☉ of old stars before the resulting light appreciably degrades the quality of the SED fit. However, dynamical constraints place a tighter limit of ⩽1 × 10¹⁰ M_☉ on the total mass for the galaxies in our sample.

By using the dynamical masses as an upper bound on the gas mass and using the Hα line measurements and/or stellar population fits to infer SFRs, we have examined the way the Lyα galaxies fall on the scaling relations for star formation. We conclude that they form stars more actively than the "normal" star-forming galaxy population at a comparable gas mass surface density. Their behavior is consistent with that observed in starburst galaxies, despite the typically smaller masses and sizes of the Lyα galaxy population.

The dynamical masses we infer remain 1–2 orders of magnitude below the characteristic dark halo masses inferred from the clustering of Lyα galaxies. Since the ratio of baryonic to dark mass should be globally uniform at around 14%, we infer that a significant part of the baryonic matter associated with these halos has not yet accreted to the central kpc, where the active star formation is observed.

Finally, we examined densities of these objects. While hierarchical structure formation models suggest that small galaxies at z ∼ 2–3 should become parts of early-type galaxies or spiral bulges by z = 0, the Lyα galaxies are of smaller size and comparable density with present-day elliptical galaxies and of comparable size but smaller density than present-day spiral galaxy bulges. If the Lyα galaxies are to evolve into either, they must do so through dissipational merging. This is consistent with the picture of Lyα galaxies as young, starbursting galaxies, whose present properties and future evolution include a large role for gas physics.

We thank the DARK Cosmology Centre and Nordea Fonden in Copenhagen, Denmark, for hospitality during the completion of this work. We thank Ignacio Ferreras and Sune Toft for helpful discussions and an anonymous referee for constructive comments. This work has been supported by the US National Science Foundation through NSF grant AST-0808165. Based in part on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Science and Technology Facilities Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministério da Ciência, Tecnologia e Inovação (Brazil) and Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina). This work was supported in part by a NASA Keck PI Data Award, administered by the NASA Exoplanet Science Institute. Some data presented herein were obtained at the W. M. Keck Observatory from telescope time allocated to the National Aeronautics and Space Administration through the agency's scientific partnership with the California Institute of Technology and the University of California. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.