LBT/LUCIFER OBSERVATIONS OF THE z ∼ 2 LENSED GALAXY J0900+2234^*

LUCIFER1 was built by a collaboration of five German institutes. It is the first of a pair of NIR imagers/spectrographs for the LBT. It is mounted on the bent Gregorian focus of the left primary mirror. The wavelength coverage is from 0.85 to 2.4 μm (zJHK bands) in imaging, long-slit, and multiobject spectroscopy modes. The detector is a Rockwell HAWAII-2 Hd-CdTe 2048 × 2048 pixel² array with a pixel size of 18.5 μm. The quantum efficiency (QE) is about 75% in the H and K bands. In the currently available seeing limited mode, the pixel scales are 025 and 012 for N1.8 and N3.75 cameras, respectively. The commissioning finished in early 2009 December and was immediately followed by 12 nights of scientific demonstration observing. The instrument has been in regular science operation since mid 2009 December.

J0900+2234 was observed with LUCIFER1 on the LBT on 2010 January 6 in imaging mode and on 2010 February 13 in long-slit spectroscopy mode (Table 1). In the imaging mode, the N3.75 camera was used; the 18.5 μm pixels correspond to 012 on the sky, for a 40 × 40 field of view. The seeing was 07 with thin clouds. For each filter (J, H, and Ks), we obtained 10 randomly dithered exposures of 60 s each. For the spectroscopic observations, the seeing was 0.5–06 and the conditions were photometric. The spectra were taken with an N1.8 camera, yielding a plate scale of 025 per pixel. An order separation filter and a 200 l/mm H + K grating were used to cover the wavelength range from 1.40 to 2.20 μm, simultaneously. A 10 by 39 slit was used, resulting in a spectral resolution of 16 Å. The total exposure time was 24 × 300 s with the telescope nodded ∼7'' along the slit between each exposure. The instrument was rotated to P.A. = 8657 in order to place the two brightest lensed components in the slit. Dark exposures and internal quartz lamp flats were obtained in the afternoon, and an Ar lamp was observed for wavelength calibration during the night.

2.3.1. Imaging Reduction

The imaging data were reduced using standard IDL routines. The dark frames were median combined to create a master dark frame. A super-sky flat was constructed from combining the science frames after dark subtraction. The science images were dark subtracted, and then divided by the super-sky flat to correct for the detector response. The science images were registered to the SDSS–DR6 catalog using SCAMP (Bertin 2006) for astrometric calibration; the residuals were less than 01 rms. Finally, the sky background was subtracted from the science frames which were then co-added using SWarp (Bertin et al. 2002). Photometric zero points were determined from Two Micron All Sky Survey stars in the field of view.

The fully reduced J-, H-, and Ks-band images are shown in Figure 1. In addition to the lensed galaxy (components A, B, C, and D in Figure 1) found by Diehl et al. (2009), we discovered another component, A1. The color of A1 suggests that it is also a high-redshift galaxy image lensed by the foreground red galaxy, but not the same galaxy appearing in images as A, B, C, or D (see details in Section 3.1).

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2.3.2. Spectroscopy Reduction

To reduce the LUCIFER spectra, we modified an IDL long-slit reduction package written by G. D. Becker for NIRSPEC (Becker et al. 2009). In this package, the following sky background subtraction procedure was used. First, four types of calibration files were created: a median-combined normalized internal flat field to correct the pixel-to-pixel variations in QE, a median-combined dark image, and two transformation maps created by tracing bright standard stars and bright sky lines. These two transformation maps were used to transform the NIR detector (x, y) coordinates to the slit position and wavelength coordinates. Next, the dark image was subtracted from the science frames which were then divided by the flat field. The background in each science frame was subtracted using a fit to the science frames obtained before and after it in two dimensions, based on the transformation maps. A second-order polynomial function and a b-spline function were used to fit the sky background residual along the slit direction and the dispersion direction, respectively. After the sky background subtraction, the x and y direction distortions of the science frames were corrected based on the transformation maps created in the first step. The one-dimensional spectra were extracted from individual two-dimensional spectrum frames and combined to give the averaged spectrum shown in Figure 2. The wavelength calibration was derived from observations of Ar lamps and applied to the averaged spectrum. The spectrum was corrected for telluric features with the spectrum of an AV star observed at the same average air mass as the science exposures. Finally, we derived the flux calibration by normalizing the spectrum to the H-band magnitude.

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The GALFIT program (Peng et al. 2002, 2010) was used to model the central lensing galaxies and lensed components. We fitted each of the two central massive galaxies with de Vaucouleurs models, and fitted the three lensed knots and two arcs with exponential disk models. The initial input parameters—namely, position, total magnitude, axis ratio, and position angle for each component—were determined using SExtractor (Bertin & Arnouts 1996). We used the Ks-band co-added image to fit the profile parameters (Figure 3 and Table 2), and fixed these parameters when fitting the J- and H-band images to obtain the magnitude of each component (Table 3). The values of best-fit reduced χ² for J, H, and Ks bands were 1.064, 1.094, and 1.088, respectively.

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Table 3. Photometry of the LUCIFER Images from GALFIT

Component	$J_{\rm {AB}}$	$H_{\rm {AB}}$	$K\!s_{\rm {AB}}$
G1	17.34 ± 0.01	16.98 ± 0.01	16.68 ± 0.03
G2	18.43 ± 0.01	18.06 ± 0.01	17.69 ± 0.02
A	20.99 ± 0.03	20.87 ± 0.04	20.87 ± 0.06
B	20.63 ± 0.02	20.33 ± 0.04	20.30 ± 0.04
C	20.45 ± 0.03	20.44 ± 0.04	19.97 ± 0.03
D	20.79 ± 0.07	21.08 ± 0.18	20.23 ± 0.09
A1	21.81 ± 0.09	21.26 ± 0.11	20.47 ± 0.04

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The NIR colors of the A and B components are similar, with J − H ∼ 0.1 and H − Ks ∼ 0.0, while the colors of the C and D components appear to be different from those of the A and B components. For the D component, the reason for this discrepancy may be that the exponential disk profile is not a good fit to the observed arc structure. For the C component, the follow-up spectroscopy was performed with an MMT/Blue Channel spectrograph, which shows that the C component is not part of this lens system.

Current data are not yet extensive enough to uncover other components of the weak A1 component. If confirmed by spectroscopy and deeper imaging, this newly discovered arc would make J0900+2234 a rare example of a double Einstein ring system.

We used the IDL MPFIT⁹ package to fit the emission lines. The results are listed in Table 4. The Hβ, [O iii]λ4959 and [O iii]λ5007 were fit as Gaussian functions individually. The positions of Hα and [N ii]λ6583 as well as [S ii]λλ6717, 6732 are close to each other, so they were fit by two Gaussian functions together to deblend these two lines. The observed line wavelength, line flux, and full width at half maximum (FWHM) were derived from the Gaussian fitting (Table 4). Monte Carlo (MC) simulation was used to estimate the uncertainties of line flux and FWHM. One thousand artificial spectra were generated by perturbing the flux of each data point from the true spectrum by a random amount proportional to the 1σ flux error. We then measured the line flux of each fake spectrum, leaving all the parameters free for both the single lines and deblended line pairs. The standard deviations of the distributions of the line flux and the FWHM were adopted as the uncertainty of measurements of the line flux and the FWHM (Table 4). The emission-line redshifts of A and B knots are 2.0321 ± 0.0009 and 2.0318 ± 0.0005, respectively, and are consistent with each other within Δz/(1 + z) = 0.0001. These results also agree with the mean redshift from the optical spectra, z = 2.0325 ± 0.0003 (Diehl et al. 2009).

First, it is important to examine the observed values of well-known empirical line ratio diagnostics to determine whether the emission is from an H ii region, active galaxy, or shocked gas. The line ratios of the A and B components on the diagram of Baldwin et al. (1981) (BPT diagram) are shown in Figure 5. The weak N ii emission rules out the possibility that the emission is from the activity of a central active galactic nucleus (AGN). The location of the A and B components on the BPT diagram are similar to other high-z star-forming galaxies (e.g., Liu et al. 2008; Hainline et al. 2009). They have relatively higher [O iii]λ5007/Hβ values and lower [N ii]λ6584/Hα values compared to the local star-forming galaxies from the SDSS (Figure 5). This offset could be the result of relatively intensive star formation activity and high electron density in these high-redshift galaxies, compared to the local sample. Overall, we conclude that the line emission is from gas that is photoionized by a hot stellar continuum, that is, the emission is from star formation regions.

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We estimated the extinction of the lensed galaxy by two methods: (1) a fit to the stellar continuum as measured by broadband photometry and (2) Balmer decrement. These two methods represent the dust extinction to the stellar continuum E_s(B − V) and the dust extinction to the nebular gas in the H ii region (E_g(B − V)), respectively. One expects these two estimates to differ, and indeed some previous studies have observed that there is more extinction toward the ionized gas than the stellar continuum in local star-forming galaxies (Calzetti et al. 2000) and high-redshift galaxies (e.g., Förster Schreiber et al. 2009). In contrast, Erb et al. (2006b) did not find any extinction difference between ionized gas and the stellar continuum in star-forming galaxies at a redshift of ∼2. For lensed galaxies, the reddening derived from individual images often differs because of reddening by different amounts of foreground dust, since the images traverse different sight lines through the lensing galaxies.

With optical photometry alone, one can measure only the UV continuum shape in high-redshift galaxies, making it difficult to distinguish between reddening by dust and age of the stellar population. By adding the NIR photometry, we can measure the Balmer break (3600–3700 Å) which is sensitive to the age of the stellar population, and the 4000 Å break strength only weakly depends on metallicity. By combining our NIR photometry with the optical, we can fit stellar population models and simultaneously determine the age of the galaxy and average extinction.

Here, we used the J-, H-, and Ks-band (rest-frame optical bands) magnitudes combined with the g-, r-, and i-band (rest-frame UV bands) magnitudes (3'' from Diehl et al. (2009) to estimate the E_s(B − V) and the age of the galaxy. The Bruzual & Charlot (2003, BC03) standard simple stellar population model was used to build the spectral templates of star-forming galaxies. We adopted a constant star formation rate (SFR) with the Chabrier initial mass function (IMF; Chabrier 2003), and solar metallicity, to generate a series of spectra with different ages and reddening. Figure 4 shows the best-fit spectra with the photometry data of the A and B components. From the fitting, we found that the ages of the components A and B were consistent with each other, and equal to 180 Myr, with the values of E_s(B − V) equal to 0.07 and 0.20 for the components A and B, respectively. Based on the metallicity found in Section 5.4, we also generated the spectra with 0.25 solar metallicity to fit the broadband photometry data, and found similar results.

With this fit to the stellar population, we derived the intrinsic stellar mass of the source galaxy to be 1.9 × 10¹⁰ M_☉ after correcting for lensing magnification, which is smaller than the mean stellar mass of 3.6 × 10¹⁰ M_☉ found in a z ∼ 2 UV-selected galaxy sample (Erb et al. 2006c). Using Ks-band magnitude to approach the rest-frame R-band magnitude, we found that the M/L_R in J0900+2234 is 0.13. Shapley et al. (2005) found that the mean of M/L_R is 0.29 with a large scatter from 0.02 to 1.4 (where the values were divided by 1.8 to convert the Salpeter IMF to Chabrier IMF) in z ∼ 2 UV-selected star-forming galaxies. Considering the high scatter, M/L_R in J0900+2234 agrees with that in other z ∼ 2 star-forming galaxies. The intrinsic UV (∼1700 Å) brightness of the J0900 + 2234 is 22.1 magnitude, so that the absolute magnitude is M(1700)_AB = −22.7, compared to L* = −20.20 to −20.97 at z ∼ 2 (e.g., Oesch et al. 2010; Reddy et al. 2008; Reddy & Steidel 2009). Thus, J0900+2234 has L/L* ≈ 5–10, and is an intrinsically luminous galaxy. Galaxies with these high luminosities are very rare, and their number density is about a few 10⁻⁶ Mpc⁻³ mag⁻¹ based on the luminosity function from Reddy et al. (2008) and Reddy & Steidel (2009). The high-intrinsic UV luminosity indicates a high SFR (see details in Section 5.3) in this galaxy.

We estimated E_g(B − V) of J0900+2234 using the flux ratio of the Hα and Hβ lines. Under Case B, H i recombination at a temperature T = 10,000 K and electron density n ⩽100 cm⁻³ (Zaritsky et al. 1994), the intrinsic value of Hα/Hβ is 2.86 (Osterbrock & Ferland 2006, p. 73). Using the extinction law proposed by Calzetti et al. (2000), we found that the values of E_g(B − V) were 0.84 ±  0.31 and 0.59 ±  0.08 for the A and B components. For both A and B components, the values of E_g(B − V) are significantly larger than those of E_s(B − V), in agreement with the results of Calzetti et al. (2000) and Förster Schreiber et al. (2009). The stars and line-emitting gas are not co-spatial, and the line-emitting regions are dustier than the galaxy as a whole. Note that the low S/N of the Hβ line in knot a makes the uncertainty of the E_g(B − V) for component A large. Therefore, we use the value of E_g(B − V) = 0.59 ± 0.08 of knot B for further analysis.

We estimated the SFR in J0900 + 2234 using the luminosity of Hα (L_Hα; Kennicutt et al. 1998). The relation between the SFR and L_Hα is

$$\begin{equation} {\rm SFR}(M_\odot \, \rm yr^{-1})=7.9\times 10^{-42}\frac{L_{\rm H\alpha }}{\rm erg\, s^{-1}} \end{equation} \tag{ 1 }$$

The Hα fluxes of the A and B components are 37.01 ± 0.79 × 10⁻¹⁷ erg s⁻¹ cm⁻² and 84.64 ± 3.21 × 10⁻¹⁷ erg s⁻¹ cm⁻². We used E_g(B − V) = 0.59 ± 0.08 to correct the fluxes for extinction and found the extinction-corrected fluxes to be (225.5 ± 55.5) × 10⁻¹⁷ erg s⁻¹ cm⁻² and (516.0 ± 128.0) × 10⁻¹⁷ erg s⁻¹ cm⁻². The extinction-corrected luminosities are, therefore, (15.4 ± 3.8) × 10⁴³ erg s⁻¹ and (6.75 ± 1.66) × 10⁴³ erg s⁻¹. The lensed SFRs of components A and B are $533\pm 131 \,M_\odot \, \rm yr^{-1}$ and $1220\pm 303 \,M_\odot \, \rm yr^{-1}$. We added the SFRs of the components A and B together, corrected for the magnification, and found that the intrinsic SFR of the lensed galaxy was $365\pm 69 \,M_\odot \, \rm yr^{-1}$. Note that if we use the Chabrier IMF, the SFR derived from the $L_{\rm H_\alpha }$ will be $203\pm 38 \,M_\odot \, \rm yr^{-1}$. We also estimated the SFR from the UV luminosity (Kennicutt et al. 1998) which is derived from the average of g and r-band flux. We found that the SFR is $276 \,M_\odot \,\rm yr$ for Shalpeter IMF and $153 \,M_\odot \,\rm yr$ for Chabrier IMF by correcting for the dust extinction, E_s(B − V) = 0.07(0.20) for the A (B) components. The SFR based on the dust-corrected Hα emission is consistent with that from the dust-corrected UV emission. If we use E_s(B − V) = 0.20 to correct for the extinction of the Hα flux, the Hα-derived SFR of $110 \,M_\odot \, \rm yr^{-1}$ will be significantly lower than UV-derived SFR. This supports the result that the E_g(B − V) is larger than E_s(B − V). The average of the SFR for z ∼ 2 star-forming galaxies is 〈$\rm SFR_{\rm H\alpha }$〉$=31 \,M_\odot \, \rm yr^{-1}$ and 〈$\rm SFR_{\rm UV}$〉$=29 \,M_\odot \, \rm yr^{-1}$(Erb et al. 2006c). Despite the uncertainties in interpreting the SFR measurements, we conclude that the SFR of J0900 + 2234 is an order of magnitude higher than typical star-forming galaxies at z ∼ 2.

Emission lines from H ii regions can be used to measure metallicity. The oxygen abundance was calculated using the following indicators: the N2 index (N2 $\equiv \log (F_{\rm {[N\,\mathsc{ii}]}\lambda 6584}/ F_{\rm H\alpha })$) and the O3N2 index (O3N2 $\equiv \break \log \lbrace (F_{\rm [O\,\mathsc{iii}] \lambda 5007}/F_{\rm H\beta })/(F_{\rm [N\,\mathsc{ii}]\lambda 6584}/F_{\rm H\alpha)}\rbrace$), which have been well calibrated using nearby extragalactic H ii regions to measure O/H (Pettini & Pagel 2004). The advantage of using the N2 and O3N2 indices as metal abundance estimators is that Hα and the [N ii]λ6584 pair, as well as the Hβ and [O iii]λ5007 pair, are close in wavelength, making these two estimators relatively insensitive to extinction.

The N2 index is sensitive to the oxygen abundance (Storchi-Bergmann et al. 1994), and was further calibrated by Raimann et al. (2000) and Denicoló et al. (2002). Here, we use the best linear fit between the N2 and ($12+\log (\rm {O/H})$) from Pettini & Pagel (2004)

$$\begin{equation} 12 + \log (\rm {O/H}) = 8.90 + 0.57 \times \rm {N2}, \end{equation} \tag{ 2 }$$

where N2 is in the range from −2.5 to −0.3, and the 1σ error of the measurements of $\log (\rm {O/H})$ is 0.18. We find the values of $12+\log (\rm {O/H})$ equal to 8.12 ± 0.21 and 8.23 ± 0.19 for components A and B, respectively, which are about 0.27 ± 0.13 to 0.35 ± 0.15 solar abundance (for the Sun: $12+\log (\rm {O/H_{\odot }})$ = 8.69; Asplund et al. 2009).

The O3N2 index was first introduced by Alloin et al. (1979), and was well calibrated by Pettini & Pagel (2004) using 137 extragalactic H ii regions. The relation between the metallicity ($12+\log (\rm {O/H})$) and the O3N2 index is

$$\begin{equation} 12 + \log (\rm {O/H}) = 8.73 - 0.32 \times \rm {O3N2}, \end{equation} \tag{ 3 }$$

where O3N2 is in the range from −1 to 1.9, and the 1σ error of the measurements of $\log (\rm {O/H})$ is 0.14, which indicates less scattering than the N2 index. We found the values of $12+\log \rm {(O/H)}$ of components A and B were 8.00 ± 0.16 and 8.09 ± 0.15, which are 0.21 ± 0.08 and 0.25 ± 0.08 solar abundance.

Both the N2 and O3N2 indices indicate that J0900+2234 has a low oxygen abundance compared with other z ∼ 2 star-forming galaxies. Figure 6 shows the stellar mass and metallicity relation in the local SDSS starburst galaxies and z ∼ 2 star-forming galaxies (Erb et al. 2006a). The metallicity is derived from the N2 index. We averaged the value $12 + \log (\rm {O/H})$ of the A and B components and the stellar mass is from the broadband fitting result. Our data point is significantly lower than the mass and metallicity relation in star-forming galaxies at z ∼ 2 (Erb et al. 2006a). Mannucci et al. (2010) proposed a more general fundamental relation between stellar mass, SFR, and metallicity derived with SDSS galaxies, in which the metallicity decreases with the increase of SFR. We used the relation derived in Mannucci et al. (2010) (Equation (2)) to obtain the predicted metallicity from SFR and stellar mass and found the value to be 8.45. Although our measured metallicity is ∼0.27 dex lower than the predicted value, this dispersion is consistent with the results of Mannucci et al. (2010) that the distant galaxies show 0.2–0.3 dex dispersions for the fundamental metallicity relation.

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The flux ratio of [S ii]λ6717 and [S ii]λ6732 was used to estimate the electron density in the H ii region of J0900 + 2234. The IRAF task stdas.analysis.nebular.temden was used to compute the density. We assumed that the temperature in these regions was 10,000 K. We found that the values of $F_{\rm [S\, \mathsc{ii}]\lambda 6717}$/$F_{\rm [S\, \mathsc{ii}]\lambda 6732}$ were 0.88 ± 0.24 and 0.84 ± 0.31 for the components A and B. The large error bar is due to the low S/N (<5) of these [S ii] lines in both apertures. The values of the ratio yielded a range of electron number density 1029⁺³³³³₋₆₆₉ cm⁻³ and 1166⁺⁷⁰²⁰₋₈₅₅ cm⁻³, respectively, for these two components. Nonetheless, these densities are much higher than those typical of local H ii regions n_e∼ 100 cm⁻³ (e.g., Zaritsky et al. 1994). The electron density of J0900+2234 is similar to that in the lensed galaxies, the Cosmic Horseshoe and the Clone, which is also derived from the ratio of [S ii] double lines (Hainline et al. 2009). The high electron density was also found in the Cosmic Horseshoe with 5000–25,000 cm⁻³ derived from the ratio of C iii]λλ1906, 1908 doublet (Quider et al. 2009). The high electron density implies the compact size of the H ii regions in the high-z galaxies. If these high-z H ii regions follow a similar electron density–size relation to that found in the local galaxies (Kim & Koo 2001), their sizes should be less than 1 pc.

The width of the emission lines can be used to probe the dynamics and the total mass of the parent galaxy. By fitting the emission lines (e.g., Hα, [O iii]) as Gaussian profiles, we found that the FWHMs of Hα of A and B knots were 19.0 Å and 21.8 Å. These observed FWHMs were corrected by subtracting the instrument resolution (∼16 Å) in quadrature. The corrected FWHMs were converted to the 1D velocity dispersion with σ = FWHM/2.355 × c/λ. The values of σ for the A and B knots were 66 ± 5 km s⁻¹ and 95 ± 6 km s⁻¹, respectively. We averaged the σ components of A and B to estimate the velocity dispersion of J0900+2234, which is 81 ± 4 km s⁻¹. Our velocity dispersion is about 30% lower than that in a sample of z ∼ 2 star-forming galaxies (Erb et al. 2003), where a mean velocity dispersion of ∼110 km s⁻¹ was found.

The mass of the galaxies can be estimated by assuming a simplified case of a uniform sphere (Pettini et al. 2001)

$$\begin{equation} M_{\rm vir} = \frac{5\sigma ^2r_{1/2}}{G}, \end{equation} \tag{ 4 }$$

$$\begin{equation} M_{\rm vir} = 1.2\times 10^{10} M_{\odot }\left(\frac{\sigma }{100\; \rm {km}\; \rm {s}^{-1}}\right)^2\frac{r_{1/2}}{\rm {kpc}}, \end{equation} \tag{ 5 }$$

where G is the gravitational constant and r_1/2 is the half-light radius, which is 7.4 ± 0.8 kpc from the lens model. We find that the dynamical mass of J0900 + 2234 is (5.8 ± 0.9) × 10¹⁰M_☉, an upper limit since the line-emitting gas may not be in virial equilibrium with the gravitational potential of the galaxy.

Using the global Kennicutt–Schmidt law (Kennicutt et al. 1998), we convert the surface gas density (Σ_gas) with the SFR derived from Hα:

$$\begin{equation} \Sigma _{\rm gas} = 1.6\times 10^{-27}\left(\frac{\Sigma _{\rm H\alpha }}{\rm erg^{-1}\,\rm kpc^{-2}}\right)^{0.71} M_{\odot } \,\rm pc^{-2}, \end{equation} \tag{ 6 }$$

where Σ_Hα ≃ L_Hα/r²_e is the surface density of Hα luminosity (Erb et al. 2006b; Finkelstein et al. 2009). Then the gas mass, M_gas, can be derived from Σ_Hα × r²_e, which is (5.1 ± 1.1) × 10¹⁰M_☉. The gas fraction, f_gas = M_gas/(M_gas + M_stellar), is 0.74 ± 0.19. Erb et al. (2006a) found the gas fraction increases when the stellar mass decreases in the UV-selected star-forming galaxies at z ∼ 2. The gas fraction in J0900+2234 is higher than the mean gas fraction (0.48 ± 0.19) of Erb et al.'s (2006a) galaxies in a similar stellar mass bin ((1.5 ± 0.3) × 10¹⁰M_☉), but still 1σ consistent. The total baryonic mass M_gas + M_stelar is (6.9 ± 1.1) × 10¹⁰M_☉, which is in the agreement with the dynamic mass.

The main uncertainty in the measurement of the extinction and abundance is from the uncertainties in the measurements of the weak emission lines (e.g., Hβ and S ii) in the observed NIR. There are many prominent sky emission lines in the NIR, especially in the H-band, which can contaminate our line measurements, especially for the weak emission lines. In the LUCIFER spectra of J0900+2234, the Hβ sits near the blue cut of the H-band, where there are several moderate strong sky emission lines and the instrument efficiency is low, which contributes large flux errors (S/N < 5) and underestimates/overestimates the fluxes. The higher E_g(B − V) value of the A (fainter) component and systematically lower metallicities estimated from O3N2 index compared to those from the N2 index may imply that the flux of Hβ is underestimated.

The systematic uncertainty of SFR, associated with the absolute flux of the Hα, is mainly due to the uncertainties in the absolute calibration of the NIR spectra. We calibrated the spectra with an AV star, and scaled the spectral flux to the H-band magnitude to correct the light loss in the spectrograph slit. The scale factors are ∼1.6 (∼1.8) for the A (B) knots, which are reasonable values for light loss. Converting the lensed Hα luminosity to the intrinsic Hα luminosity is another uncertainty in the SFR estimation. The uncertainty of the lens model fitting is 20%–30%. The uncertainty also affects the estimation of the stellar mass and dynamical mass, which depend on the results of the lens model. The Hα and SFR relation (Kennicutt et al. 1998) is derived from stellar synthesis models with solar metallicity. The SFR in J0900+2234 could be overestimated, given the low metallicity (∼0.25 Z_☉) in this galaxy.