THE SINS SURVEY: SINFONI INTEGRAL FIELD SPECTROSCOPY OF z ∼ 2 STAR-FORMING GALAXIES^*

The BX/BM criteria (Adelberger et al. 2004; Steidel et al. 2004) are based on observed optical $U_{n}G\mathcal {R}$ colors and represent an extension to z ∼ 1.5–2.5 of the classical Lyman-break technique targeting z ∼ 3 galaxies (Steidel & Hamilton 1993; Giavalisco et al. 1998; Steidel et al. 1999). The efficient BX/BM and Lyman-break techniques have yielded the first substantial (>1000) samples of spectroscopically confirmed z ∼ 1–3 galaxies, at $\mathcal {R}_{\rm AB} < 25.5\, {\rm mag}$. By construction, the BX/BM criteria identify primarily actively star-forming galaxies with moderate amounts of extinction in the ranges z ∼ 2–2.5 (BX objects) and z ∼ 1.5–2 (BM objects). The properties of the BX/BM population have been extensively discussed in many papers (e.g., Erb et al. 2003; Steidel et al. 2004; Shapley et al. 2004, 2005; Adelberger et al. 2005a, 2005b; Reddy et al. 2005, 2006; Erb et al. 2006a, 2006b, 2006c; Law et al. 2007b). In brief, they have typical stellar ages of ∼500 Myr, stellar masses M_⋆ ∼ 2 × 10¹⁰ M_☉, SFRs ∼ 50 M_☉ yr⁻¹, and extinction A_V ∼ 0.8 mag, with a tail extending to more massive, evolved, and/or dustier galaxies.

We drew our BM/BX targets from the near-IR spectroscopic sample of Erb et al. (2006a, 2006b, 2006c; see also Erb et al. 2003; Shapley et al. 2004; Steidel et al. 2004). This spectroscopic survey was carried out with NIRSPEC at the Keck II telescope. In the initial phases of the SINS survey—for observational reasons—we emphasized brighter sources with spatially resolved velocity gradients, large velocity dispersions, or spatially extended emission based on the existing spectroscopy. At later phases, we also observed compact sources without indications for velocity gradients and with average or unresolved Hα line widths to expand the range of kinematic properties probed. We observed a total of 17 galaxies, including 16 BX objects with median z = 2.2 and one BM object at z = 1.41. Emission lines were detected in all of the objects (with the main line of interest being Hα). Two galaxies form a pair at nearly the same redshift (Q2346-BX404/405), with relative velocity of 140 km s⁻¹ and projected separation of 363 (30.3 kpc). The results on the first 14 galaxies were presented by Förster Schreiber et al. (2006a). Since then, we have collected data of three new targets, re-observed a number of sources leading to longer integration times and higher S/N, and complemented the K-band data targeting Hα+[N ii] emission with H-band data for Hβ+[O iii] for several of the z > 2 BX objects.

Near-IR surveys yield important complementary, and to some extent overlapping samples of z ≳ 1 galaxies. Efficient color criteria have been devised to isolate high-redshift photometric candidates from K-band-limited source catalogs, intended to include more specifically evolved and/or dust-obscured populations that may be underrepresented in optically selected samples. One of the most efficient and widely used is the "BzK" selection, introduced by Daddi et al. (2004a). It combines near-IR and optical colors, defining regions in the B − z versus z − K color diagram to identify star-forming ("sBzK") or passively evolving ("pBzK") galaxies at 1.4 < z < 2.5. For our SINS survey, pBzK objects are not relevant because, by selection, they are expected to lack the nebular line emission we are interested in. The sBzK criterion has the feature of being insensitive to reddening by dust, and so it selects star-forming galaxies with a wide range of extinction as well as ages. There is a significant overlap between near-IR-selected sBzK and optically selected BX/BM populations to a given K-band limit (and increasing toward fainter limits), although sBzK objects tend to include a larger proportion of more evolved and massive systems, and with higher SFRs and amounts of extinction (e.g., Reddy et al. 2005; Kong et al. 2006; Grazian et al. 2007; Daddi et al. 2007).

More recently, sensitive 3–8 μm imaging with the IRAC camera onboard the Spitzer Space Telescope has extended the coverage of optical/near-IR surveys to longer wavelengths. This allows in principle the construction of more genuinely mass-selected samples at high redshift based on rest-frame near-IR emission, better tracing the light from stars dominating the stellar mass and less affected by dust extinction and star formation than the emission at shorter wavelengths. In the context of this paper, "near-/mid-IR selection" refers to galaxies drawn from 2.2 μm (K band) or 4.5 μm magnitude-limited surveys.²⁰

In total, the SINS near-/mid-IR-selected subsamples count 45 sources; 43 were drawn from various surveys and two were serendipitously discovered in line emission in our SINFONI data. The sources span the redshift range 1.3 < z < 2.6, with median z = 2.1. Depending on the field/survey, different indicators of star formation activity were available to estimate the expected observed integrated line fluxes, and, for some subsets, we also considered colors and/or morphologies in addition to the criteria applied for all SINS targets described above. Eleven sources (from the Deep3a and zCOSMOS surveys) were specifically chosen to satisfy the sBzK criterion. However, the common key features of estimated SFR of ≳10 M_☉ yr⁻¹ (to ensure Hα detectability), brightness in observed K band (from the magnitude limits of the parent surveys), and redshift range ∼1–3 naturally result in a majority of our near-/mid-IR-selected targets with B − z and z − K measurements having the colors of sBzK objects (90%), even if most were not explicitly selected so (see Section 3). Morphologies (from high-resolution Hubble Space Telescope (HST) imaging) were considered for 23 sources (from the GMASS and zCOSMOS surveys), to probe a range of types. This was a secondary factor in that we first selected based on redshift, expected line flux, and source visibility, and after looked at the morphologies.

The fraction of the SINS near-/mid-IR-selected galaxies detected in at least one emission line is 77% (33 out of 43, excluding our serendipitous detections described below). This is driven in part by the fact that the large majority of these sources had no previous near-IR spectroscopy to verify a priori the exact line fluxes and wavelengths. In addition, some of those sources were observed in poorer conditions for comparatively short integration times, leading effectively to brighter limiting fluxes (see Section 6). The properties of these undetected targets are further discussed in Section 3.

2.2.1. K20 Targets

2.2.2. Deep3a Targets

2.2.3. GMASS Targets

2.2.4. zCOSMOS Targets

2.2.5. GDDS Targets

We observed a small collection of LBGs at z ∼ 3. Seven of them were taken from the large survey of photometrically selected (by the classical Lyman-break technique based on observed $U_{n}G\mathcal {R}$ colors; see Steidel & Hamilton 1993; Steidel et al. 1999) and spectroscopically confirmed LBGs carried out by Steidel and coworkers, and described in detail by Steidel et al. (2003). The objects were detected in the optical $\mathcal {R}$ band, and candidate LBGs at $\mathcal {R}_{\rm AB} \le 25.5\, {\rm mag}$ were followed up with optical spectroscopy for accurate redshift determination. Three of them (Q0201 + 113C6, Q0347-383C5, and Q1422 + 231D81) had previous near-IR long-slit spectroscopy with Keck/NIRSPEC and VLT/ISAAC, presented by Pettini et al. (2001). Q0347-383C5 was well detected and spatially resolved in the SINFONI data, and is a clear merger (Nesvadba et al. 2008). Q0201 + 113C6 and Q1422 + 231D81 were also detected but are marginally resolved spatially and the data were taken under unfavorable conditions, so that reliable analysis could only be carried out for the source-integrated properties (Nesvadba 2005). The other four LBGs from the Steidel et al. (2003) survey were undetected in our SINFONI data, which is likely due to the poor observing conditions; in addition, three of them were observed only once with integration times of 1 or 2 hr, which may have been insufficient to detect line emission.

We targeted two other LBGs from different surveys and fields. One is the so-called "Arc + core," a z = 3.24 galaxy behind the z = 0.3 X-ray cluster 1E 06576-56 (e.g., Mehlert et al. 2001). The strong lensing (by a factor of >20) together with the spatial resolution of the SINFONI data resolved the kinematics in the inner few kpc on physical scales of ≈200 pc (Nesvadba et al. 2006b). The other one was drawn from the ESO EIS survey of the CDFS field with spectroscopic z = 3.083 obtained from VLT/FORS1 optical follow-up (Cristiani et al. 2000). We did not detect line emission in our 9600 s integration in the K band.

Six bright submillimeter-selected galaxies (SMGs) were observed, at redshifts between 1 and 3. All of these were part of the target list for a long-term program of CO molecular line mapping carried out with the IRAM Plateau de Bure mm interferometer (e.g., Genzel et al. 2003; Neri et al. 2003; Greve et al. 2005; Tacconi et al. 2006, 2008; I. Smail et al. 2009, in preparation). The SMGs chosen for our SINFONI observations all had accurate radio positions and optical spectroscopic redshifts.²² Three of the SMGs were originally drawn from the SCUBA Lens Survey (Smail et al. 2002), and are magnified by foreground lensing clusters and, for SMM J04431 + 0210, also by a foreground spiral galaxy.

We detected two of the lensed SMGs in our SINFONI data sets: SMM J14011 + 0252 and SMM J04431 + 0210, both well-studied in the literature (e.g., Frayer et al. 1999, 2003; Neri et al. 2003; Swinbank et al. 2004). We used SINFONI in J, H, and K bands for a detailed study of the kinematics and physical conditions from the rest-frame optical line ratios of the merging system SMM J14011 + 0252 (Tecza et al. 2004; Nesvadba et al. 2007). Our high-quality, high-S/N K-band data of SMM J04431 + 0210 revealed a compact source with kinematics and [N ii]/Hα ratio indicative of a dominant AGN component (Nesvadba 2005). None of the three SMGs in the SSA22 field were detected in our SINFONI data; the observations of these sources suffered from poor observing conditions and, moreover, the integration times of ∼1–2.5 hr may have been too short to detect the emission lines targeted in the K band.

We targeted the field around the z = 2.16 radio galaxy MRC 1138 − 262, which was found to have an overdensity of Hα emitters (Kurk et al. 2004). Detailed analysis of the SINFONI data, and in particular focusing on the feedback energetics from the AGN powering the radio galaxy, are presented by Nesvadba et al. (2006b; see also Nesvadba 2005).

We also observed a pair of line emitters from the NICMOS/HST parallel GRISM survey of McCarthy et al. (1999). The slitless G141 grism used spans the wavelength range λ ≈ 1.1–1.9 μm with spectral resolution R ≡ λ/Δλ ∼ 200. In this survey of random fields covering 64 arcmin², 33 sources were discovered serendipitously on the basis of detection of an emission line in the grism data, without biases from color selection schemes. McCarthy et al. (1999) argued that the most likely identification is Hα, which was subsequently confirmed with detection of [O ii] λ 3727 emission in nine of the 14 galaxies by Hicks et al. (2002). The pair we targeted, NIC J1143-8036a/b (with projected angular separation of 08, not observed by Hicks et al. 2002) would lie at z = 1.35 and 1.36 if the lines seen around 1.54 μm are Hα. Detection of Hα and [N ii] λ6584 Å, with a ratio of [N ii]/Hα = 0.17, in our >10 times higher spectral resolution SINFONI data confirms the line identification of NIC J1143-8036a and implies z = 1.334. An emission line is detected at the position of NIC J1143-8036b and with velocity offset of ≈130 km s⁻¹ (about 10 times smaller than inferred from the NICMOS G141 observations, perhaps due to lower spectral resolution and more uncertain wavelength calibration of these data). While [N ii] emission is not seen in our data for NIC J1143-8036b, implying [N ii]/Hα <0.09, the proximity in wavelength and in angular separation of the components makes it very likely that the two sources are indeed a merging pair (see Nesvadba 2005).

The observations of the SINS Hα sample were carried out with SINFONI (Eisenhauer et al. 2003a; Bonnet et al. 2004) mounted at the Cassegrain focus of the VLT UT4 telescope. SINFONI consists of the near-IR cryogenic integral field spectrometer SPIFFI (Eisenhauer et al. 2003b) and of a curvature-sensor adaptive optics (AO) module called MACAO (Bonnet et al. 2003). A set of mirror slicers in SPIFFI splits the focal plane in 32 parallel slitlets and rearranges them in a pseudo long-slit fed into the spectrometer part of the instrument. The light is then dispersed onto the 2K² HAWAII detector. The width of each slitlet corresponds to the projected angular size of two pixels, resulting in effective spatial pixels ("spaxels") with rectangular shape. Spatial dithering of on-source exposures by an odd or fractional number of pixels during the observations allows full sampling of the spatial axis perpendicular to the slitlets. Pre-optics enable selection between pixel scales of 125, 50, and 12.5 mas pixel⁻¹. Three gratings cover the full J, H, and K atmospheric windows and a lower resolution grating covers the H + K bands simultaneously. The nominal FWHM spectral resolution for the pixel scales relevant to our SINS observations are as follows: R ≈ 1900, 2900, and 4500 for J, H, and K at 125 mas pixel⁻¹, and R ≈ 2700 and 5000 at 50 mas pixel⁻¹. SINFONI can be operated in pure seeing-limited mode, in which case the AO module acts as relay optics. For AO-assisted observations, the correction can be performed using a natural guide star (NGS-AO mode) or an artificial star created by the Laser Guide Star Facility (LGS-AO mode), including the sodium laser system PARSEC (Rabien et al. 2004; Bonaccini et al. 2006).

The data were collected during 24 observing campaigns between 2003 March and 2008 July, as part of Guest Instrument and MPE guaranteed time observations. In addition, data of several GMASS targets were obtained under normal program allocations as part of a collaboration between the SINS and GMASS teams. The observing conditions were generally good to excellent, with clear to photometric sky transparency and typical seeing at near-IR wavelengths with FWHM = 05–06. Table 4 lists all the observing runs. Table 5 summarizes the observations for each target, with the band/grating, pixel scale, and observing mode used, the total on-source integration time, the spatial resolution of the data (see below), and the runs during which the data were taken. For completeness, we list observations for the entire SINS survey, although specific details given hereafter refer to the Hα sample only.

Table 5. Summary of the SINFONI Observations

Source	zspa	Band	Scaleb (mas)	Mode	tintc (s)	PSF FWHMd	Run IDe
Q1307-BM1163	1.4105	H	125	Seeing-limited	14400	061	Mar 05
		J	125	Seeing-limited	7200	077	Mar 05
Q1623-BX376	2.4085	K	125	Seeing-limited	15600	049	Mar 05, Apr 05
Q1623-BX447	2.1481	K	125	Seeing-limited	14400	056	Mar 06, Aug 06
		H	125	Seeing-limited	1800	083	Apr 07
Q1623-BX455	2.4074	K	125	Seeing-limited	12000	057	Mar 05
Q1623-BX502	2.1550	K	50	NGS/LGS-AO	22800	024	Apr 05, Mar 08, Apr 08
Q1623-BX528	2.2682	K	125	Seeing-limited	24300	063	Jul 04, (Aug 05), Mar 07
Q1623-BX543	2.5211	K	125	Seeing-limited	8400	⋅⋅⋅	Mar 06
Q1623-BX599	2.3304	K	125	Seeing-limited	5400	⋅⋅⋅	Jul 04
Q1623-BX663	2.4333	K	125	NGS-AO	26400	039	Jul 04, (Mar 07), Apr 07
		H	125	Seeing-limited	3600	063	Apr 07
SSA22a-MD41	2.1713	K	125	Seeing-limited	25200	044	Nov 04, Jun05
		H	125	Seeing-limited	9000	043	Aug 06
Q2343-BX389	2.1716	K	125	Seeing-limited	14400	054	Oct 05
		H	125	Seeing-limited	15900	050	Jun06, Aug 06
Q2343-BX513	2.1079	K	125	Seeing-limited	3600	⋅⋅⋅	Aug 04
Q2343-BX610	2.2094	K	125	Seeing-limited	10800	039	Jun05, (Aug 05)
		H	125	Seeing-limited	30000	057	Oct 05, Nov 07
		J	125	Seeing-limited	14400	060	Oct 05
Q2346-BX404f	2.0282	K	125	Seeing-limited	6300	⋅⋅⋅	Jul 04
		H	125	Seeing-limited	9000	⋅⋅⋅	Jul 04
Q2346-BX405f	2.0300	K	125	Seeing-limited	6300	⋅⋅⋅	Jul 04
		H	125	Seeing-limited	9000	⋅⋅⋅	Jul 04
Q2346-BX416	2.2404	K	125	Seeing-limited	7200	066	Dec 04
Q2346-BX482	2.2569	K	125	Seeing-limited	14400	050	Nov 04, (Aug 05, Oct 05), Aug 07
		K	50	LGS-AO	24600	017	Oct 07, Nov 07, Jul 08
		H	125	Seeing-limited	15000	061	Aug 06, Nov 06
K20-ID5	2.225	K	125	Seeing-limited	9600	051	Mar 05
		H	125	Seeing-limited	7200	071	Mar 05
K20-ID6	2.226	K	125	Seeing-limited	16200	056	(Aug 05), Oct 05
K20-ID7	2.227	K	125	Seeing-limited	31200	050	(Aug 05), Oct 05, Nov 06
K20-ID8	2.228	K	125	Seeing-limited	18600	044	(Aug 05), Oct 05, Nov 06
K20-ID9	2.0343g	K	125	Seeing-limited	22800	047	Oct 05, (Mar 06), Nov 06, Mar 07
D3a-4751	2.266	K	125	LGS-AO+Seeing-limited	10800	026	Mar 07, Mar 08
D3a-6004	2.387	K	125	LGS-AO+Seeing-limited	36000	053	Mar 06, Mar 07
D3a-6397	1.513	H	125	Seeing-limited	24000	077	Apr 07, Mar 08
		J	125	Seeing-limited	10800	077	Apr 07
D3a-7144	1.648	H	125	Seeing-limited	7200	054	Mar 06
D3a-7429	1.694	H	125	Seeing-limited	1200	110	Apr 07
D3a-12556	1.584	H	125	Seeing-limited	9900	057	Mar 06, Jun06
D3a-15504	2.3834	K	125	NGS-AO	14400	034	Mar 06
		K	50	NGS-AO	20400	017	Mar 06
		H	125	NGS-AO	18000	068	Apr 06
		H	50	NGS-AO	3600	019	Apr 06
GMASS-167	2.573	K	125	Seeing-limited	23400	⋅⋅⋅	Dec 06
GMASS-1084	1.552	H	125	Seeing-limited	22800	050	Nov 06, Dec 06, Oct 07, Nov 07
GMASS-1146	1.537	H	125	Seeing-limited	4800	114	Dec 06, (Nov 07)
GMASS-1274	1.670	H	125	Seeing-limited	2400	111	Dec 06
GMASS-2090	2.416	K	125	Seeing-limited	3600	⋅⋅⋅	Nov 06
GMASS-2113Wf	1.613	H	125	Seeing-limited	13200	058	Nov 06, (Aug 07), Oct 07
GMASS-2113Ef	1.6115g	H	125	Seeing-limited	13200	058	Nov 06, (Aug 07), Oct 07
GMASS-2207	2.449	K	125	Seeing-limited	3600	047	Nov 06
GMASS-2252	2.407	K	125	Seeing-limited	18000	074	Dec 06
GMASS-2303	2.449	K	125	Seeing-limited	7200	073	Oct 07
		K	50	LGS-AO	15600	017	Nov 07
GMASS-2363	2.448	K	125	Seeing-limited	20400	063	Nov 06, Dec 06
GMASS-2438	1.615	H	125	Seeing-limited	13200	076	Nov 07
GMASS-2443	2.298	K	125	Seeing-limited	3600	073	Dec 06
GMASS-2454	1.602	H	125	Seeing-limited	3600	054	Dec 06
GMASS-2471	2.430	K	125	Seeing-limited	23400	056	Nov 06, Dec 06
GMASS-2540	1.613	H	125	Seeing-limited	6000	072	Nov 07
GMASS-2550	1.601	H	125	Seeing-limited	3000	031	Nov 07
GMASS-2562	2.450	K	125	Seeing-limited	3600	080	Dec 06
GMASS-2573	1.550	H	125	Seeing-limited	3600	110	Dec 06
GMASS-2578	2.448	K	125	Seeing-limited	3600	144	Oct 07
ZC-772759	2.1792	K	125	Seeing-limited	7200	060	Mar 07, Apr 07
ZC-782941	2.183	K	125	Seeing-limited	7200	056	Mar 07
		K	50	LGS-AO	12600	018	Apr 07
ZC-946803	2.090	K	125	Seeing-limited	3600	071	Apr 07
ZC-1101592	1.404	H	125	Seeing-limited	3600	082	Apr 07
SA12-5241	1.356	H	125	Seeing-limited	7200	058	Mar 05
SA12-5836	1.348	H	125	Seeing-limited	15600	062	Mar 05
SA12-6192	1.505	H	125	Seeing-limited	10800	046	Mar 05
SA12-6339	2.293	K	125	Seeing-limited	19200	037	Mar 05
SA12-7672	2.147	K	125	Seeing-limited	6000	053	Jun05
SA12-8768f	2.185	K	125	Seeing-limited	10800	061	Jun05
SA12-8768NWf	2.1876g	K	125	Seeing-limited	10800	061	Jun05
SA15-5365	1.538	H	125	Seeing-limited	10800	057	Mar 05, Apr 05
SA15-7353	2.091	K	125	Seeing-limited	7200	058	Jun05
SMM J02399-0134	1.0635	J	125	Seeing-limited	1800	00	Jul 04
SMM J04431 + 0210	2.5092	K	125	Seeing-limited	39600	⋅⋅⋅	Mar 03, Nov 04, Mar 05
SMM J14011 + 0252	2.5652	K	125	Seeing-limited	27600	05	Mar 03
		H	125	Seeing-limited	7200	05	Mar 03
		J	125	Seeing-limited	4800	05	Mar 03
SMM J221733.91 + 001352.1	2.5510	K	125	Seeing-limited	9000	⋅⋅⋅	Oct 05
SMM J221735.15 + 001537.2	3.098	K	125	Seeing-limited	4200	⋅⋅⋅	Aug 05
SMM J221735.84 + 001558.9	3.089	K	125	Seeing-limited	7200	⋅⋅⋅	Aug 05
Q0201 + 113C6	3.053	K	125	Seeing-limited	4200	077	Dec 04
Q0347-383C5	3.236	K	125	Seeing-limited	14400	052	Dec 04
Q0933 + 289C27	3.549	HK	50	NGS-AO	3600	⋅⋅⋅	Mar 06
Q1422 + 231C43	3.281	HK	125	NGS-AO	3600	⋅⋅⋅	Mar 06
Q1422 + 231D81	3.098	K	125	Seeing-limited	7800	055	Mar 03, (Mar 05)
SSA22aC36	3.060	HK	125	NGS-AO	7200	⋅⋅⋅	Aug 05
DSF2237aC15	3.138	HK	50	NGS-AO	7200	⋅⋅⋅	Aug 05
EISU12	3.083	K	125	Seeing-limited	9600	⋅⋅⋅	Dec 04
1E06576-56 Arc+core	3.24	K	125	Seeing-limited	11400	05	Mar 03
MRC 1138-262	2.1558	K	125	Seeing-limited	8400	05	Mar 03
		H	125	Seeing-limited	6600	05	Mar 03
NIC J1143-8036af	1.35	H	125	Seeing-limited	9300	05	Mar 03
NIC J1143-8036bf	1.36	H	125	Seeing-limited	9300	05	Mar 03

Notes. ^aSpectroscopic redshift based on rest-frame UV emission or absorption lines (e.g., Lyα, interstellar absorption lines) obtained with optical spectroscopy, or based on Hα from near-IR long-slit spectroscopy. ^bPixel scale used for the observations, where 125 mas refers to the largest scale with nominal pixels of 0125 × 025 and FOV of 8'' × 8'', and 50 mas refers to the intermediate scale with nominal pixels of 05 × 01 and FOV of 32 × 32. ^cTotal on-source integration time of the combined data sets used for analysis; this excludes for some sources low-quality frames or OBs, e.g., taken under poorer observing conditions. ^dThe PSF FWHM corresponds to the effective spatial resolution of all observations for a given object and instrument setup. It is estimated from the combined images of the acquisition star taken regularly during the observations of a science target (see Section 4.2). ^eObserving runs during which the SINFONI data were taken (see Table 4). The runs listed in parenthesis for some sources yielded lower quality data that were then excluded in the final combined data used for analysis. ^fThe four galaxy pairs Q2346-BX404/405, GMASS-2113E/W, SA12-8768/8768NW, and NIC J1143-8036a/b have projected angular separations smaller than 4'', and were thus observed simultaneously at the 125 mas scale with FOV of 8'' × 8''. ^gHα redshift from our SINFONI data. For K20-ID9, the (uncertain) optical redshift reported by Daddi et al. (2004b) was 2.25. No spectroscopic redshift was available for GMASS-2113E and SA12-8768NW identified through their Hα line emission in our observations of the targets GMASS-2113W and SA12-8768.

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To map the Hα and [N ii] λλ 6548, 6584 line emission of the SINS Hα sample galaxies, we used the higher resolution H or K gratings, depending on the redshift of the sources. For a subset of twelve, we also obtained observations of [O iii] λλ 4959, 5007 and Hβ, and of [O ii] λ 3727 for one them, accessible through different bands. The majority of the observations were carried out in seeing-limited mode with the largest pixel scale of 125 mas pixel⁻¹ giving an FOV of 8'' × 8''. We observed a total of eight targets with AO (twelve when including the z ∼ 3 LBGs), which have suitable reference stars for NGS-AO and, at later times, also for LGS-AO. For five of them (seven when counting the LBGs), we selected the intermediate 50 mas pixel⁻¹ scale with FOV of 32 ×  32 to take full advantage of the gain in angular resolution provided by the AO, achieving FWHM resolution of 015–025 (see Figure 5).²⁶ Except for one (Q1623-BX502), all those targets were first observed at the 125 mas pixel⁻¹ scale to verify the accuracy of the blind offsets and the appropriate observing strategy for the AO-follow up with the smaller pixel scale and FOV. For the other targets with AO data, we used the larger pixel scale as trade-off between enhanced angular resolution and sensitivity.

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Depending on the source, we adopted one of two observing strategies: an efficient "on-source dithering" where the object was kept within the FOV in all exposures but at different positions, and an "offsets-to-sky" strategy where the exposures for background subtraction were taken at positions away from the target. The "on-source dithering" was used for the majority of the sources. In this scheme, the data were taken in series of "AB" cycles, with typical nod throws of about half the SINFONI FOV so as to image the source in all frames, and jitter box widths of about one-tenth the FOV to minimize the number of redundant positions on the detector array. A typical "observing block" (OB) consisted of six such dithered on-source exposures. For the "offsets-to-sky" scheme, the telescope pointing was alternated between the object ("O") and adjacent sky regions ("S") empty of sources usually in an "O-S-O-O-S-O" pattern for each OB. The pointing on the object and sky positions was varied by about one-tenth of the FOV, thus ensuring adequate independent sampling of the sky signal subtracted from each of two object frames sharing the same sky frame.

The individual exposure times varied between 300 s, 600 s, and 900 s depending mainly on the variability and intensity of the background and night sky line emission, in order to optimize the background subtraction and remain in the background-limited regime in the wavelength regions around the lines of interest. The total on-source integration times range from 20 minutes to 10 hr, with an average of 3.4 hr spent per band and pixel scale for each target. The total integration times were driven by the surface brightness of the sources and by our aim of mapping the line emission and kinematics out to large radii. In general, if a new target was not detected after 1–2 hr, we did not observe it further. Therefore, the non-detections among our SINS sample may have line emission but fainter than the relatively shallow sensitivity limits of these data sets. Also, for a few targets with the shortest integration times, more observations were not obtained because of various factors including weather conditions, observing run duration, and target priorities. The consequences on the distributions of Hα properties of these observational strategies and constraints are investigated in Section 6.

Exposures of the acquisition stars used for blind offsetting to the galaxies were taken to monitor the seeing and the positional accuracy (generally one "O-S-O" set per science OB). For flux calibration and atmospheric transmission correction, we observed late-B, early-A, and G1V to G3V stars with near-IR magnitudes in the range ∼7–10 mag. These telluric standards data were taken every night, as close in time and airmass as possible to each target observed during the night. Acquisition stars and telluric standards were always observed with the same instrument setup as for science objects (band and pixel scale).

We reduced the data using the software package SPRED developed specifically for SPIFFI (Schreiber et al. 2004; Abuter et al. 2006), complemented with additional custom routines to optimize the reduction for faint high-redshift targets. The data reduction is analogous to standard procedures applied for near-IR long-slit spectroscopy but with additional processing to reconstruct the three-dimensional (3D) data cube. The main reduction steps applied to each science target for a given instrument band and pixel scale setup were as follows.

The night sky line and background emission as well as the dark current were first removed from the science data. This was done by subtracting (without shifting) the raw science frames pairwise for data sets taken with the "on-source dithering" pattern, or subtracting the sky frame from its adjacent object frames for those obtained with the "offsets-to-sky" sequence. The data were then flatfielded with exposures of a halogen calibration lamp. Bad pixels identified from the dark and flat-field frames were corrected for in the science data by interpolation, completing the pre-processing stage. Arc lamp frames were used to generate the "wavemap," and to trace the edges and curvature of the slitlets. The arc lamp frames were reconstructed to data cubes to verify the 3D reconstruction parameters.

The pre-processed science data frames were then reconstructed into cubes, corrected for distortion, and flux-calibrated and transmission-corrected as described below. All science cubes within a given OB were spatially aligned according to the dither offsets sequence used for the observations. Our high-redshift targets were always too faint to allow the determination of spatial shifts from centroiding or cross-correlating of single exposures. However, the small offsets applied within an OB for dithering or offsets-to-sky are very accurate at the VLT, as they are performed relative to the telescope active optics guide star. We verified this whenever possible by comparing the morphology of the targets between individual combined OBs (i.e., averaging the aligned exposures within an OB). The relative offsets between different OBs (often taken on different nights) were determined based on the measured position of the acquisition star observed for each OB and the known offsets applied to go on target, from the centroid position of the sources in the individual combined OBs when sufficiently bright, or from the relative offsets between OBs for those that were taken successively without re-acquisition in between. All aligned, flux- and transmission-calibrated science cubes of a given target were finally combined together by averaging with sigma-clipping (i.e., iteratively removing data points deviating from the mean, typically clipping at the 2.5σ level). This step also generated a "sigma-cube," recording the standard deviation of the values for a given pixel in the 3D data cube across all cubes combined.

The reduced data often showed very large residuals from the strong night sky lines because our individual exposure times of 5–15 minutes are comparable or longer than the variability timescales of the sky lines. Moreover, due to effects of instrumental flexure while tracking the targets, the exact wavelength calibration for individual science exposures can deviate from the master wavemap based on the arc lamp data by up to ∼1/2 of a pixel or more along the dispersion axis, leading to asymmetric residual profiles. To reduce these residuals, the wavelength calibration and sky subtraction steps were repeated with optimization following the method described by Davies (2007). In brief, the wavelength calibration of the individual exposures was refined using the positions of the night sky lines in the raw frames (before sky subtraction). This ensured that all science frames were interpolated to a common wavelength grid, with an accuracy better than 1/30 of a pixel. A more sophisticated sky subtraction procedure was applied next, which involves scaling each transition group of telluric OH lines separately in order to further reduce the residuals around the emission lines of interest for a given source.

The data of the telluric standard stars and the acquisition stars were reduced in a similar way as the science data. Flux calibration was performed on a night-by-night basis using the broadband magnitudes of the telluric standards. Correction for atmospheric transmission was done by dividing the science cubes by the integrated spectrum of the telluric standard.

Broadband images of the acquisition stars were created by averaging together all wavelength channels of the reduced cubes, with σ-clipping to exclude the strongest residuals from night sky lines. The resulting angular resolution for a given target in a given instrument setup was determined on the combined image obtained from the acquisition star's data associated with all of the target's OBs, providing the effective spatial PSF of the data sets. For both no-AO and AO-assisted data, and for the purpose of characterizing the angular resolution of the data, the effective PSF shape is well approximated by a Gaussian. In Appendix B, we investigate in more detail the PSF characteristics and quantify the (small) impact of uncertainties on the extraction and modeling of kinematics maps. Table 5 lists the FWHMs of the best-fit two-dimensional Gaussian profiles to the effective PSFs. Figure 5 shows the distribution of the Hα data sets as a function of their PSF FWHM for all objects observed and for the detected ones. Since the PSF calibrations were not obtained simultaneously with the science data (and, for AO-assisted observations, were taken on-axis), these values represent approximately the effective angular resolution of the data sets. Inspection of the individual images of the stars interleaved between the science OBs indicate typical variations in PSF FWHM of ≈20% for OBs of a given galaxy, but these variations do not significantly affect the results (as we show in Appendix B).

The data reduction affects the resulting spectral resolution. To determine the effective resolution at the reconstructed data cube level, we applied a similar reduction procedure but without sky subtraction and spatial registration, thus creating "sky" data cubes. We extracted the night sky spectrum by integrating over a square aperture of ≈30 pixels on a side (the results are little sensitive to the size of the region). The line shape of unblended sky lines is well approximated by a Gaussian profile, and the FWHM in wavelength units is constant across each band. For the instrument setups relevant to the Hα line measurements discussed in this paper, the effective FWHM spectral resolution corresponds to ≈85 and 120 km s⁻¹ in K and H at the 125 mas pixel⁻¹ scale, and ≈80 km s⁻¹ in K at the 50 mas pixel⁻¹ scale.

We extracted maps of the velocity-integrated line fluxes, relative velocities, and velocity dispersion from the reduced data cubes using line profile fitting. We employed the code LINEFIT developed by our group specifically for SINFONI applications (R. I. Davies et al. 2009, in preparation). It is an evolved version of the procedure applied in our previously published work (e.g., Förster Schreiber et al. 2006a). The key (and new) features of LINEFIT include the following: (1) the spectral resolution is implicitly taken into account by convolving the assumed intrinsic emission line profile and a template line shape for the effective instrumental resolution before performing the fits; (2) weighted fits are performed according to three possible schemes based on an input noise cube: uniform (effectively no weighting), Gaussian, or Poisson weighting; and (3) formal fitting uncertainties are computed from 100 Monte Carlo simulations, where the points of the input spectrum at each spatial pixel are perturbed assuming Gaussian noise properties characterized by the rms from the input noise cube.

The weighted fits lead to more robust measurements of the line fluxes, central wavelengths, and widths for our near-IR spectroscopic data where the noise level varies strongly as a function of wavelength (due to the increased noise level at wavelengths of strong night sky lines). The complex noise properties complicate analytic error propagation to compute measurements uncertainties. After experimentation, we found than an empirical approach based on Monte Carlo simulations leads to realistic estimates of the formal uncertainties on all fitted parameters. The underlying assumption is that while the noise behavior is not Gaussian across wavelengths and as a function of aperture size, it is for a given wavelength channel and a given aperture size. We verified this in our data sets from an analysis of the pixel-to-pixel rms and of the distribution of counts measured in non-overlapping apertures randomly placed in regions empty of source emission in the reduced data cubes. These distributions are indeed well described by Gaussian functions for a given aperture size and spectral channel. This analysis provides the average pixel-to-pixel rms noise at each wavelength over the effective FOV (the region of overlap of all science exposures for a target) and the appropriate scaling as a function of aperture size (most relevant for the integrated spectra and axis profiles extracted in Sections 5.2 and 5.3), which we used as input noise spectrum in the line fitting. The details of the noise analysis are given in Appendix C.

Before fitting, we median-filtered the data cubes to slightly increase the S/N with a 2 pixel-wide filter along each of the three axes or, for some of the most diffuse and extended sources, with a 3 pixel-wide filter spatially (e.g., K20-ID9). In the fitting procedure, we always assumed a single Gaussian line profile, which we found to be appropriate on a pixel-to-pixel basis for our galaxies. With this assumption, our fits are sensitive to the dominant emission line component and, in particular, are negligibly influenced by a possible faint broad underlying component (either intrinsic to the galaxies or due, for instance, to beam-smearing at larger radii of a central high-velocity dispersion source). To account for instrumental spectral resolution, we used the average of unblended night sky line profiles for the corresponding band and pixel scale that was determined empirically from the "sky" data cubes (see Section 4.2). After initial sigma-clipping rejection of the strongest outliers, we applied Gaussian weighting ∝1/rms² in the line fitting procedure using the associated noise cube. Pixels with formal S/N < 5 on their velocity-integrated line flux or with obvious bad fits were masked out in the output velocity and velocity dispersion maps.

In performing the line fits, a continuum component was subtracted. This component was determined as the best-fit first-order polynomial through adjacent spectral intervals free from possible line emission from the galaxies and from residuals (>2σ–3σ) from night sky lines. This generally leads to rather noisy continuum maps for the fainter continuum sources, because of the limited wavelength range used for the linear fit to the continuum, although the line fluxes are not significantly affected in those cases. In order to obtain more robust continuum maps, or at least detect the region(s) of peak continuum emission, we took advantage of the full band coverage of SINFONI and computed the continuum from an iterative procedure, where we averaged the data spectrally excluding channels corresponding to strong night sky lines and those including line emission from the galaxies. The iterations consisted of varying the threshold applied to exclude spectral channels based on the noise cube, so as to optimize for S/N of the resulting continuum map.

For the detected galaxies of our SINS Hα sample, the effective angular resolution of the Hα maps obtained from seeing-limited observations is typically ≈06 (median value) and ranges from 040 to 115 (from the near-IR seeing FWHM and accounting for the spatial median filtering applied when extracting the maps). This corresponds to typically ≈5 kpc and a range of 3.5–10 kpc at the respective redshift of the sources. For the objects observed with AO at the 125 mas pixel⁻¹ scale, the resulting resolution is ≈033 and, after median filtering, ≈041 or ≈3.4 kpc. For the AO-assisted data sets at the 50 mas pixel⁻¹ scale, the resolution is about three times better than for the seeing-limited data: 017 and, after smoothing, 020 or ≈1.6 kpc.

We measured for each galaxy the global emission line properties from spatially integrated spectra from the unsmoothed reduced data cubes. The spectra were integrated in circular apertures centered on the centroid of the line emission as determined from the line maps. Significant noise levels, especially toward the noisier edges of the effective FOV and for the fainter sources, complicated the definition of more optimum integration regions such as isophotal apertures. The radius of the circular apertures was taken to enclose ⩾90% of the total Hα flux based on curve-of-growth analysis, carried out from the spectra integrated in apertures of increasing radius for each galaxy. This radius is typically 10–125 for the (mostly seeing-limited) data sets at the 125 mas pixel⁻¹ scale, and 05–075 for most of the AO-assisted data sets at the 50 mas pixel⁻¹ scale.

The fits to the primary line of interest, Hα, were performed in the exact same manner as described in Section 5.1.²⁷ In some of the sources, the integrated line profiles exhibit significant asymmetries, double-peaked profiles or faint blue-/redshifted tails (e.g., Q2343-BX389 in Figure 24, K20-ID9 in Figure 26, D3a-15504 in Figure 28, ZC-1101592 in Figure 32) or a superposition of narrow and broad components (e.g., Q1623-BX663 in Figure 23, K20-ID5 in Figure 26). In those cases, multi-component fits or moments calculation would be more appropriate (see, e.g., Shapiro et al. 2009). For the purpose of this paper, we kept with the simple approach of fitting a single Gaussian profiles and verified that the results did not differ substantially from those obtained with more sophisticated methods.

Weighting and derivation of the formal uncertainties of the best-fit fluxes, relative velocities and redshift, and velocity widths were based on an input noise spectrum calculated for the aperture size over which the spectra were spatially integrated. This was done according to the empirically derived noise model described in Appendix C, which accounts for the fact that the effective noise properties in our reduced SINFONI data cubes are not purely Gaussian. For undetected lines, we determined 3σ upper limits on the line fluxes based on the noise spectrum calculated for a circular aperture of 10 radius, assuming an intrinsic line width equal to the mean of the detected sources (i.e., for σ = 130 km s⁻¹) and a central wavelength as expected from the optical redshift of the galaxy.

The resulting uncertainties of the line flux, velocity, and velocity width from the Monte Carlo simulations using the noise from the empirical model represent formal measurements errors. The uncertainties from the absolute flux calibration are estimated to be ∼10% and those from the wavelength calibration, ≲5%. Other sources of uncertainties include continuum placement and the wavelength intervals used for line and continuum fits. To gauge the effects of such possible systematics, we compared measurements in a subset of the sources obtained by varying slightly the continuum and line intervals, and also computed total line fluxes by summing over all pixels in the line maps within the aperture adopted to integrate the spectrum. Together with results from curve-of-growth analysis described above, this suggests that systematics amount to 20%–30% typically, and in some data sets with lowest S/N up to ∼50%.

Table 6 lists the Hα flux, vacuum redshift, and velocity dispersion derived from the integrated spectrum of each source, along with the formal fitting uncertainties and the radius of the circular aperture used for the measurements. The table also lists the fractional contribution f_BB(Hα) from the integrated Hα line flux to the total broadband flux density (from the H- or K-band magnitudes for sources at z < 2 and z > 2, respectively; Table 2). The integrated velocity dispersion (and all measurements of velocity dispersions throughout the paper) is corrected for instrumental spectral resolution (implicitly done within LINEFIT). We emphasize that the measurements of integrated velocity dispersion used in this paper, which we denote as σ_int(Hα), refer to the width of the emission line in the spatially integrated spectrum without any shifting of the spectra of individual spatial pixels to a common or systemic velocity. It thus includes possible contributions from velocity gradients or non-circular gas motions that may be present in the galaxies. Determination of the "intrinsic" velocity dispersion free from large-scale velocity gradients due, e.g., to rotation in a disk, requires detailed kinematic modeling, a velocity correction for individual co-added pixel spectra, or, at least for disks, to map out the velocity dispersion profile well outside of the central regions affected by beam-smearing of the steep inner rotation curve (e.g., Förster Schreiber et al. 2006a; Genzel et al. 2006, 2008; Wright et al. 2009; Cresci et al. 2009; Law et al. 2009)

We determined the position angle (P.A.) of the morphological major axis by fitting a two-dimensional elliptical Gaussian to the Hα line maps while we took the kinematic major axis as the direction of steepest gradient in the Hα velocity fields. On average, the respective P.A.'s agree within ≈20°. With one exception, the largest differences are for marginally resolved sources (i.e., with morphological major axis FWHM ≈ PSF FWHM, where the major axis FWHM is measured as explained in Section 5.4), including Q1623-BX455, Q1623-BX599, Q2346-BX416, and SA12-8768NW with P.A. differences larger than ≈45°. Deep3a-6004 is well resolved (morphological major axis FWHM ≈3× PSF FWHM; Figure 27) but its morphological P.A. is nearly orthogonal to the kinematic P.A. (≈80°). This may be due to a variety of reasons—one of them being an asymmetric distribution of the most intense star-forming regions traced by Hα and/or of the obscuring dust within the galaxy. In general, we adopted as major axis of the galaxies the kinematic P.A. except for the cases with too poor quality velocity fields from low S/N, or simply no clearly apparent velocity gradient, where we took the morphological P.A. instead.

To extract profiles of the flux, velocity, and velocity dispersion along the major and minor axis of each galaxy, we applied the same procedure as described in Section 5.2. We computed spectra integrated from the unsmoothed reduced data cubes in circular apertures spaced equally along the major and minor axes (with typical diameters of 6 pixels and separations of 3 pixels, roughly ≈1.5 and 0.75 times the PSF FWHM of the data sets). Weighting and formal uncertainties in the line fitting procedure were based on the noise spectrum for the corresponding aperture size inferred from the empirical noise model (Appendix C). We extracted position–velocity diagrams in 6 pixel-wide synthetic slits along the major axis of the galaxies, integrating the light along the spatial direction perpendicular to the slit orientation.

We determined the intrinsic half-light radii r_1/2(Hα) of the galaxies from the Hα curves-of-growth extracted as described in Section 5.2, and corrected for the respective PSF FWHMs. We also measured the intrinsic FWHMs of one-dimensional Gaussians fitted to the major axis Hα light profiles and corrected for spatial resolution, which is appropriate for getting an estimate of the linear size of inclined disk systems (see also Förster Schreiber et al. 2006a; Bouché et al. 2007). For the detected sources that are spatially resolved (i.e., with morphological major axis FWHM(Hα)> PSF FWHM), we find an average 0.5 × FWHM(Hα)/r_1/2(Hα) ≈ 1.45, and a median ratio of ≈1.3. Clearly, the assumption of Gaussians is simplistic since the spatial distribution of the line emission is generally irregular and often asymmetric and clumpy for our SINS galaxies. Nevertheless, inspection of the fits and of the radial distributions of pixel values about the center indicates that Gaussian profiles are reasonable representations of the overall observed light profiles (modulo clumps or other prominent features that produce obvious substructure in the radial distributions).

While both methods are affected by the spatial resolution, the FWHMs of Gaussian fits to the major axis light profiles are more sensitive to differences between different data sets due to the fixed synthetic slit width. This is less of a concern for data taken with similar effective PSFs or for sources that are well resolved (e.g., with AO), as was the case for our previous studies (e.g., Förster Schreiber et al. 2006a; Bouché et al. 2007; Genzel et al. 2008; Cresci et al. 2009). For this paper, however, we consider all Hα data sets with a range of spatial resolution (see Figure 5). For consistent analysis of the full SINS Hα sample, we thus adopted the r_1/2(Hα) estimates throughout most of this paper.

Table 6 lists the r_1/2(Hα) and FWHM(Hα) values. For some objects, the size measurements (major axis FWHM or twice the half-light radius) are smaller than the resolution element from the estimated PSF. This is most likely due to variations in time of the actual seeing conditions, and which may not be reflected in the PSF calibration since the acquisition stars used for that purpose were not observed simultaneously with the science data. In those cases, we consider the observed sizes as upper limits to the intrinsic sizes.

Uncertainties on the size estimates were determined as follows. Inspection of the PSFs associated with individual OBs of a given object suggests that typical seeing (or effective resolution for AO data sets) variations are of order 20%. In addition, in correcting for beam smearing, we assumed the PSF is axisymmetric, which is not always the case (although the average ellipticity of ≈0.1 and 0.06 for the seeing-limited and AO effective PSFs indicates this is a reasonable assumption; see Appendix B). We computed the uncertainties taking 20% as a representative uncertainty on the measurements of observed galaxy sizes themselves from possible PSF variations during the observations, and using the ellipticity of the effective PSF for each galaxy as a measure of the error from the PSF shape. These were propagated analytically in calculating the resulting uncertainties on the intrinsic (physical) sizes of galaxies. The errors derived from the PSF ellipticities are typically 20% (with rms scatter 10%) for the seeing-limited data sets, 30% for the AO-assisted data sets at 125 mas pixel⁻¹, and 13% for the AO-assisted data sets at 50 mas pixel⁻¹. Overall, the size uncertainties are ≈30%–35% (with rms scatter 20%). These do not account for other sources of errors that are essentially impossible to quantify, such as the dependence on the sensitivity of the data and the actual surface brightness distribution of each individual source (but see Section 6.2).

More detailed derivations of morphological parameters possible for the sources with higher S/N data were presented elsewhere (Genzel et al. 2008; Shapiro et al. 2008; Cresci et al. 2009). There, whenever possible, we verified the morphological parameters from the Hα line maps against the continuum maps from our SINFONI data or available sensitive ground-based imaging of comparable resolution (e.g., the ISAAC imaging of CDFS). While the line and continuum morphologies can differ in detail, the centroid, major axis, and sizes typically agree reasonably well. This is further confirmed from the higher resolution NICMOS/NIC2 F160W (H band) data obtained for six of the BX galaxies and AO-assisted K-band imaging for a few more sources obtained with NACO at the VLT (N. M. Förster Schreiber et al. 2009a, in preparation).

Of the 62 galaxies from the SINS Hα sample, 60 were targets drawn from photometric surveys, 50 of them were detected in Hα and two "serendipitous" companions were identified from their line emission. All of the non-detections are for galaxies without prior near-IR spectroscopy that would have provided line fluxes and guided us in the choice of sufficiently bright targets (see Figure 1). Some of the non-detections can probably be attributed to the moderate to poor seeing conditions under which the data were taken, with estimated PSF FWHM ≈08–145 at near-IR wavelengths (Figure 5). Because we did not repeat observations of targets undetected after the first 1–2 hr, these data sets have relatively bright limiting fluxes compared to the depth achieved in our typical SINS Hα data sets. In some cases, this short integration may have been insufficient for even moderately bright but very extended sources, with lower average surface brightness.

A "typical detection limit" for our data is not straightforward to quantify as the sensitivity varies strongly with wavelength and our data sets have a wide range of integration times. The faintest sources have observed integrated Hα fluxes of ≈2 × 10⁻¹⁷ erg s⁻¹ cm⁻² and averaged surface brightness of ∼1 × 10⁻¹⁷ erg s⁻¹ cm⁻² arcsec⁻²; their integrated line emission is detected at S/N ≈ 5. The 3σ upper limits for the undetected sources, calculated from the noise spectrum within a circular aperture of radius 1'' and assuming an intrinsic integrated velocity dispersion of 130 km s⁻¹, range from 8 × 10⁻¹⁸ to 8 × 10⁻¹⁷ erg s⁻¹ cm⁻², with mean and median of ≈4 × 10⁻¹⁷ erg s⁻¹ cm⁻². Some of those limits are higher than the flux of the faintest sources detected, again because of the important variations of noise levels with wavelength (the optical redshift of several of the undetected sources place their Hα line close to regions of bright night sky lines, poorer atmospheric transmission, or higher thermal background emission) together with the short integration times of 40 minutes  to  2 hr.

In terms of Hα luminosities (uncorrected for extinction), the faintest SINS galaxies have integrated L(Hα) ≈ 3 × 10⁴¹ erg s^-1. With half the total light within an area of radius r_1/2(Hα) and accounting for beam smearing in computing the intrinsic physical area, the sources with faintest Hα surface brightness have central averaged luminosity surface densities of ∼5 × 10³⁹ erg s^-1 kpc⁻². Using the conversion of Kennicutt (1998), corrected to a Chabrier (2003) IMF (see Section 8.1), these imply lowest observed star formation rates and star formation rate surface densities of ≈1 M_☉ yr⁻¹ and ∼0.03 M_☉ yr⁻¹ kpc⁻². The median integrated Hα flux and surface brightness are about five times higher, or ≈1 × 10⁻¹⁶ erg s⁻¹ cm⁻² and ∼5 × 10⁻¹⁷ erg s⁻¹ cm⁻² arcsec⁻² (median values for luminosities and star formation rates are about 15 times higher than the faintest/lowest ones).

Figure 6 shows the distribution of integrated velocity dispersions and half-light radii as a function of total Hα line fluxes for our SINS Hα sample. The velocity dispersions are corrected for instrumental spectral resolution, and the radii are corrected for beam-smearing accounting for the effective PSF. The Hα fluxes are not corrected for extinction. While one could use, e.g., the best-fit extinction A_V derived from the SED modeling, it is here more appropriate to stick to uncorrected quantities as the velocity dispersions and sizes were measured from the emergent line emission. Correcting for extinction would rely on the assumption that the obscured regions have the same kinematics and spatial distribution as those suffering less extinction and dominating the observed properties, a hypothesis that we cannot verify with current available data. For the 52 detected sources, the total observed Hα fluxes F(Hα) cover a range by a factor of ≈40 with median 1 × 10⁻¹⁶ erg s⁻¹ cm⁻². The integrated intrinsic velocity dispersions span σ_int(Hα) ≈ 35–280 km s^-1 with mean and median of 130 km s⁻¹. The intrinsic half-light radii inferred from the curve-of-growth analysis range from ≲1.5 to 7.5 kpc with mean and median of 3.4 kpc and 3.1 kpc, respectively.

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Despite differential cosmological dimming given the redshift range spanned by the sources, with clear bimodality (Figure 1), Figure 7 shows qualitatively similar distributions in terms of total absolute Hα luminosities (uncorrected for extinction) as obtained as a function of total apparent fluxes. The observed Hα luminosities of the detected sources range from L(Hα) = 2.5 × 10⁴¹ to 1.3 × 10⁴³ erg s⁻¹, with mean and median of 4.2 and 3.5 × 10⁴² erg s⁻¹. Figure 8 shows again the integrated intrinsic velocity dispersions and half-light radii now as a function of stellar masses from the SED modeling (the three galaxies for which broadband photometry is unavailable are excluded). Overall, similar trends of increasing σ_int(Hα) and r_1/2(Hα) with increasing M_⋆ are seen as when plotting against F(Hα) and L(Hα).²⁸ This is not surprising given that more massive star-forming galaxies also tend to have higher Hα luminosities, reflecting the empirical M_⋆–SFR relationship among star-forming galaxies (see Section 8; also, e.g., Daddi et al. 2007). The various trends discussed above, however, can be affected by the sensitivity limits resulting from observational strategies, which we quantify in Section 6.3.

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In Figures 6–8, the disks and mergers classified by kinemetry (Shapiro et al. 2008) tend to lie at brighter Hα fluxes/luminosities (and stellar masses) and at larger sizes, driven by the necessity of sufficient S/N and number of resolution elements for reliable kinemetry. However, as was the case for the photometric and stellar properties (Section 3, and Figures 3 and 4), our data do not show any evidence that these fairly massive, large, bright disks and mergers at z ∼ 2 are different in terms of their integrated Hα fluxes/luminosities, velocity dispersions, or sizes. The mean and median values for these disks and mergers are the same within 20% or less, and the Mann–Whitney U-test indicates that they do not differ significantly in global Hα properties. Obviously, it will be important to investigate this issue further with larger numbers of sources. Likewise, the four AGNs do not appear to be strong outliers in their Hα properties, although the sample is very limited and this should not be overinterpreted. Consequently, median values and ranges in the integrated Hα properties of our SINS sample change very little when excluding the four known AGNs.

With the full 2D mapping of the line emission and kinematics of our SINFONI data, we can examine in more detail the possible AGN contribution to the global Hα properties, as measured from the dominant narrow component to which our line extraction procedure is sensitive (Section 5.2; see also Shapiro et al. 2009 for a discussion of the presence of broad underlying Hα emission). For D3a-15504, a fairly large system observed with AO at the 50 mas pixel⁻¹ scale, the AGN affects only the central few kpc while star formation in giant kpc-size sites all across the rotating disk clearly dominate the global Hα properties (the σ_int = 148 km s^-1 is close to the average of the SINS sample, and the integrated [N ii]/Hα line ratio is 0.35; Genzel et al. 2006, 2008). For K20-ID5, the AGN (or shock excitation) appears to dominate the Hα line emission and kinematics, given its very bright central peak showing one of the broadest line width among our sample (σ_int = 281 km s^-1) and a fairly high global [N ii]/Hα ratio of ≈0.6. The other two are probably intermediate cases; both show indications of a small monotonic velocity gradient, with Q1623-BX663 having higher Hα line width but lower integrated [N ii]/Hα ratio (172 km s⁻¹ and 0.3) and vice-versa for D3a-7144 (140 km s⁻¹ and 0.8).

Our SINS data in Figures 6–8 suggest possible trends of increasing velocity dispersion and size with Hα flux or luminosity and with stellar mass, although with significant scatter increasing in σ_int at low fluxes, and toward small sizes. Taken at face value, this would imply that the most intense (unobscured) star formation activity takes place in the larger and more massive systems, and that the integrated Hα velocity dispersion is related to galaxy stellar mass despite varying contributions by large-scale velocity gradients, non-circular motions, and intrinsic gas turbulence (see also, e.g., Erb et al. 2006b; Förster Schreiber et al. 2006a). However, it is important to assess carefully the impact of our detection limits and observational strategy on the apparent trends.

To evaluate our sensitivity limits in terms of size, we did the following simulations based on the real SINFONI data. We first determined the average S/N per spatial resolution element for each galaxy and calculated the necessary increase in half-light radius for the S/N to drop below S/N = 3, keeping the other properties constant (total Hα flux and integrated line width). The sizes thus derived, r^det.lim.data_1/2, correspond to the actual surface brightness sensitivity limits of the data sets, with their respective integration times. The running median through r^det.lim.data_1/2 as a function of F(Hα) in logarithmic units follows closely a straight line with slope β ≈ 0.5, implying approximately r^det.lim.data_1/2 ∝ F(Hα)^0.5 (dashed line in Figure 6(b)). The standard deviation of the individual r^det.lim.data_1/2 about this line is ≈0.25 dex, comparable to that of the measured r_1/2(Hα) themselves about their running median. The line of sensitivity limit of the data lies about 0.6 dex above the locus of data points, or a factor of 4; this is also the average ratio of r^det.lim.data_1/2/r_1/2 of the individual galaxies. The immediate implication is that the Hα sizes we measured are little affected by the sensitivity of our data sets.

However, as already mentioned, when observing we followed the strategy that if a source was not detected within 1–2 hr irrespective of actual morphology, we did not reobserve it. This is a potential concern for interpreting possible trends, as it means that we may have missed the more extended and/or diffuse sources for a given flux. To mimic this effect in our simulations, we re-did the same calculations but this time normalizing the S/N per resolution element for each source to a common integration time of 1 hr (this is a rather conservative estimate as in some cases we observed up to 2.5 hr before abandoning sources that were not detected). The running median of the resulting r^det.lim.1hr_1/2 versus F(Hα) follows a line nearly parallel to that for r^det.lim.data_1/2 but is offset by ≈0.3 dex toward smaller sizes and corresponds roughly to the upper envelope of the data points (solid line in Figure 6(b)). This suggests that the apparent trend possibly results partly from our observational strategy. The standard deviation of the individual r^det.lim.1hr_1/2 about the running median line is ≈0.25 dex, similar to that for r^det.lim.data_1/2. This indicates that the scatter in limiting size estimates reflects the different sensitivities in different wavelength regions more than the different integration times among the sources.

We evaluated our sensitivity limits in terms of velocity dispersion in a similar manner, increasing the intrinsic velocity dispersion while keeping the total Hα line flux and half-light radius constant. The criterion for detection limits was here S/N = 3 per spectral resolution element. The lines through the running median of σ^det.lim.data_int and σ^det.lim.1hr_int as a function of F(Hα) are plotted as dashed and solid lines in Figure 6(a). The logarithmic slopes are β ≈ 0.8, significantly steeper than that for the measured σ_int(Hα) (about 0.2), and the lines lie well above that of the measurements by ∼0.9 and 0.3 dex, respectively (taking the average over the range of fluxes of our SINS galaxies). This analysis indicates that our observing strategy may have prevented the detection of faint sources with broad lines at the lowest flux levels but that it is most likely not a limiting factor in the ensemble, as the σ^det.lim.1hr_int typically are up to a factor of ∼5–10 higher than the measured σ_int(Hα) for the brighter half of the F(Hα) range.

Similar lines indicating the inferred limits in velocity dispersion and size of the data sets and resulting from the observing strategy are plotted in Figures 7 and 8. Inspection of these figures leads to the same conclusions about the apparent trends with observed Hα luminosity and stellar mass as with observed Hα flux. The lines of r^det.lim.data_1/2 versus F(Hα) correspond to limiting Hα luminosities and star formation rates per unit intrinsic area at z = 2 (uncorrected for extinction) of 6 × 10³⁹ erg s⁻¹ kpc⁻² and 0.03 M_☉ yr⁻¹ kpc⁻² for our data sets with average integration times of 3.4 hr. Normalized to a total integration time of 1 hr, the corresponding limits are 2 × 10⁴⁰ erg s⁻¹ kpc⁻² and 0.1 M_☉ yr⁻¹ kpc⁻².

In summary, the above analysis (albeit simplistic) indicates that the Hα sizes and integrated velocity dispersions of our SINS Hα sample galaxies are well determined and not affected by the depth of the respective data sets. However, we cannot exclude that an observational bias shapes the upper envelope of our distributions of r_1/2(Hα) with Hα flux/luminosity and stellar mass. This limits our ability to assess relationships between these properties based on our data. On the other hand, this does not seem to be a limiting factor for σ_int toward the brighter and more massive end and the apparent trend could reflect a real physical relationship.

Near-IR spectroscopic samples at z ∼ 2 are still rare, especially for spatially resolved 2D mapping. Our SINS Hα sample is the largest to date based on integral field spectroscopy. With 62 objects, it fares well compared to the NIRSPEC sample of 114 BM/BX-selected sample of Erb et al. (2006b), the largest long-slit spectroscopic survey. It is thus interesting to compare the integrated Hα properties between both surveys, also given that our SINS sample includes ∼2/3 of near-/mid-IR-selected galaxies. Moreover, our 17 optically selected BX/BM were drawn from the NIRSPEC sample and are also the only ones with previously existing near-IR spectroscopy, allowing direct comparisons of the properties measured with different types of instrument.

Figure 9 plots the integrated Hα fluxes, intrinsic velocity dispersions, and intrinsic sizes measured with SINFONI against those measured with NIRSPEC. Here, we use the fluxes as reported in Table 4 of Erb et al. (2006b), without any aperture correction. There is a tight relation between the fluxes, with scatter of 0.21 dex but a systematic offset corresponding to higher fluxes with SINFONI by a factor of 1.6. Based on narrow-band imaging for Hα of sources in the Q1700 field, Erb et al. (2006b) had estimated an average factor of ∼2 "aperture correction" accounting for slit losses and slit misalignment possibly missing part of the sources' emission. Absolute flux calibration is challenging for both narrow-band imaging and long-slit spectroscopy. For SINFONI, the full coverage of the atmospheric bands with each of the gratings allows us to synthesize the broadband fluxes of our telluric standards, which should help reduce uncertainties of the absolute flux calibration. In addition, with the full 2D mapping, we recover the total fluxes of the sources irrespective of their sizes, P.A., or morphologies. If the comparison with our SINS BM/BX galaxies applies to the NIRSPEC sample as a whole, the average aperture correction used by Erb et al. (2006b) might have been overestimated by ≈25%.

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In terms of integrated velocity dispersion and half-light radii, the SINFONI measurements are on average 10% larger (scatter 0.18 dex) and 5% smaller (scatter 0.13 dex). The agreement is remarkable considering that the NIRSPEC slit apertures may have missed part of the galaxies, and the sizes were estimated also from the long-slit data. When significant, the differences between fluxes, velocity dispersions, and sizes of individual objects can be attributed to possible slit misalignment with respect to the major axis of the galaxies, or to the proximity of bright night sky lines which may have affected more the lower spectral resolution NIRSPEC data.

Figure 10 now compares the distributions of Hα properties of the full SINS and NIRSPEC samples, as a function of stellar masses. The fluxes for the NIRSPEC sample in these plots have been scaled by the factor of 2 aperture correction estimated by Erb et al. (2006c); for the purpose of this comparison, the 25% difference with the factor of 1.6 we inferred above has little impact. Overall, the SINS sample covers the same range of Hα fluxes, luminosities, intrinsic integrated velocity dispersions, and half-light radii as the NIRSPEC sample. The median values in all these properties are nearly the same to within ⩽15% (ignoring the possible 25% adjustment for aperture correction). In terms of stellar masses, both samples cover a very comparable range, with the median for the NIRSPEC sample being only ≈30% lower than the median for the SINS sample (reflecting the somewhat more important tail at M_⋆ ≲ 4 × 10⁹ M_☉). In all of these properties, the differences in median values between the SINS and NIRSPEC samples are much smaller than the ranges covered.

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In view of the significant overlap (to a given K magnitude) between the BM/BX and sBzK populations (to which almost all our SINS near-/mid-IR-selected galaxies belong even if not explicitly selected so), it may not be surprising to find large overlap in integrated Hα properties between the SINS and NIRSPEC samples. In addition, for both studies, the same requirement of an optical spectroscopic redshift was applied in the target selection, leading to similar biases toward the bluer and brighter part of the high-redshift population compared to a pure K-selected sample (Section 3; Erb et al. 2006b). Perhaps the most interesting outcome of the comparisons above, based on real data sets, is that even if the total fluxes are subject to significant uncertainties from aperture corrections, slit spectroscopy seems to be reliable in recovering the integrated emission line widths and even the sizes of faint high-redshift galaxies under typical observing conditions. This seems to be encouraging for studies of spatially integrated kinematics using near-IR multi-object spectrographs such as MOIRCS on Subaru, or in the near future LUCIFER at the Large Binocular Telescope and MOSFIRE at Keck.

Figure 11 makes a similar comparison as above with the NIRSPEC sample of Erb et al. (2006b) but with data from other studies using near-IR integral field spectrometers and for galaxies in the redshift interval 1.3 ≲ z ≲ 2.6. This is not an exhaustive comparison as we restricted ourselves to samples with published integrated Hα fluxes, and intrinsic velocity dispersions and/or half-light radii measurements. We included the Keck/OSIRIS observations of Law et al. (2007a; 2009; 12 objects in the relevant redshift range) and of Wright et al. (2007, 2009, nine objects, counting merger components separately). These were all optically selected BX/BM sources. We also included the SINFONI data of van Starkenburg et al. (2008; six sources, consisting of MIPS 24 μm selected and/or morphologically large disks at z ∼ 2) and of Épinat et al. (2009; nine I-band-selected objects with strong [O ii] λ 3727 line emission from the VIMOS VLT Deep Survey). Other samples exist (the bright SMGs of Swinbank et al. 2006, or the massive K < 20 spectroscopic sample of Kriek et al. 2007) but the relevant set of measurements were unfortunately not available in the literature.

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As can be seen from Figure 11, these samples together cover the ranges of stellar masses, Hα fluxes and luminosities, and integrated velocity dispersions spanned by our SINS galaxies. There are little differences in terms of Hα fluxes and luminosities, with large overlap among all samples. The main difference is in the mass ranges, with the 24 μm-detected large disks of van Starkenburg et al. (2008) lying at the high mass end and the BM/BX objects of Law et al. (2007a, 2009) and Wright et al. (2007, 2009) toward lower masses, which then translates into different ranges of velocity dispersions given the trend in σ_int versus M_⋆. Each sample covers roughly 1/2–2/3 of the total mass range of our SINS sample, with the Épinat et al. (2009) galaxies spanning a more intermediate interval. No Hα sizes are available for the van Starkenburg et al. (2008) galaxies. As these were mostly selected to be morphologically large disks based on deep near-IR imaging, these would probably sit at the top right of the distribution in r_1/2(Hα) versus M_⋆.

There is a striking difference between the Law et al. (2007a, 2009) sample with respect to that of Wright et al. (2007, 2009), Épinat et al. (2009), and the SINS galaxies: they all appear to be significantly smaller. This may be a natural consequence of the higher resolution of the OSIRIS+AO data, at least concerning the difference with the mostly seeing-limited SINS and Épinat et al. (2009) samples. On the other hand, this could reflect an observational bias or surface brightness sensitivity effects, as discussed by Law et al. (2009) and for our SINS sample in Section 6.3. Their 11 non-detections were observed for comparatively short integration times, and include two of our brightest SINS sources (Q1623-BX663 and Q2343-BX389, with the latter particularly extended) although poor observing conditions may have conspired. Law et al. (2009) discussed that this may explain in part the discrepancy by a factor of ∼2 between their Hα fluxes and those of Erb et al. (2006b, from whose sample their targets were drawn) after aperture correction, but also note that for the most compact objects the aperture correction may simply be too large. Our SINFONI flux measurements show excellent agreement for Q1623-BX502 (23% difference between OSIRIS and SINFONI). For Q2343-BX513, we measured a total flux twice higher than Law et al. (2009). In both cases, in fact, the NIRSPEC fluxes without aperture correction agree very well with our SINFONI fluxes, suggesting that for those compact sources, the aperture correction may indeed have been overestimated. For SINS, while we did emphasize somewhat larger brighter objects at early stages, we took care subsequently (for about 2/3 of the final sample) of minimizing such a selection bias. It seems unclear what factors played what role in the overall size differences, and it could reflect a genuine difference of the galaxies properties (we discuss this point further in Section 9).

In this subsection, we detail our derivation of the various intrinsic quantities used in the following discussion. The results are reported in Tables 7 and 8.