EXTREMELY BRIGHT SUBMILLIMETER GALAXIES BEYOND THE LUPUS-I STAR-FORMING REGION

MM-J1545 was observed with the SMA at 890 μm in 2010 January and at 1.3 mm in 2011 April. The 890 μm observations were performed in the extended configuration with eight antennas, which provided projected baselines ranging from 15 to 171 m. The observing conditions were good (225 GHz zenith opacity of 0.05). The double side-band (DSB) receivers were tuned to a local oscillator (LO) frequency of 335.15 GHz, and the correlator provided a 4 GHz bandwidth in each sideband. The 1.3 mm observations were carried out in the compact configuration. The receivers were tuned so that ¹²CO, ¹³CO, and C¹⁸O J = 2–1 emission lines from the Lupus-I cloud (i.e., z = 0), as well as 1.3 mm continuum emission of MM-J1545, can be imaged. The LO frequency was set to 224.86 GHz. The atmospheric transparency was again good. In both observing runs, two quasars J1626−298 (${S}_{890\mu {\rm{m}}}=1.6$ Jy) and J1454−377 (0.33 Jy) were used for complex gain calibration, while the passband response was calibrated using 3C273 and 3C279. The absolute flux density was scaled from the primary calibrator, Titan. The accuracy of the flux calibration is estimated to be 15%.

All of the data editing and calibration were performed using idl-based standard routines in the mir software package. The calibrated visibility data were imaged (Fourier-transformed) and deconvolved using miriad (Sault et al. 1995) tasks, invert and clean, respectively. In continuum imaging, the upper (USB) and lower sideband (LSB) data, eliminating channels where the local molecular lines are expected, were combined before imaging. The natural-weighted synthesized beam sizes at 335 and 225 GHz are $1\buildrel{\prime\prime}\over{.} 49\times 1\buildrel{\prime\prime}\over{.} 17$ (the position angle, PA = $-53\buildrel{\circ}\over{.} 8$) and $4\buildrel{\prime\prime}\over{.} 94\times 3\buildrel{\prime\prime}\over{.} 21$ (PA = $-5\buildrel{\circ}\over{.} 7$), respectively. The resulting rms noise levels at 335 and 225 GHz are 3.0 and 0.76 mJy beam⁻¹, respectively.

The Karl G. Jansky VLA 6 cm data were taken in C-configuration in 2010 November (project ID: 10C-226). The correlator was configured to provide 16 × 128 MHz subbands covering from 4.2 to 6.1 GHz. The data were calibrated using the VLA Calibration Pipeline,²³ which is based on the casa data reduction package (McMullin et al. 2007). Imaging was also carried out using casa employing the multi-frequency synthesis algorithm (spectral Taylor expansion) with nterms = 2 during the deconvolution, to take into account the spectral index of the sources within the field (Rau & Cornwell 2011), along with Briggs weighting (robust = 0.5). The resulting synthesized beam is $10\buildrel{\prime\prime}\over{.} 36\times 3\buildrel{\prime\prime}\over{.} 22$ at position angle $3\buildrel{\circ}\over{.} 7$, and the rms noise is 5.8 μJy beam⁻¹.

The ATCA was used to take 7 mm continuum data in the H214 array configuration in 2013 October and in the H168 configuration in 2014 April (project ID: C2910). We used five tunings to fully cover the 33.4–50.4 GHz band to search for a redshifted ¹²CO (2–1) line (A. Taniguchi et al. 2015, in preparation). The center frequencies were set to 35.25, 38.75, 42.20, 45.40, and 48.60 GHz, and two 2 GHz spectral windows of the CABB correlator were configured adjacently, resulting in an instantaneous frequency coverage of 3.9 GHz for each tuning. The complex gain was monitored using a radio source B1541−375 (${S}_{7\mathrm{mm}}=1.1$ Jy, $10\buildrel{\circ}\over{.} 7$ away from MM-J1545). Bandpass and delay calibrations were performed using 3C 279 once per night before the observations started. Mars was used for absolute flux density calibration. The absolute flux density uncertainty is estimated to be $\lt 15\%$. The data were calibrated using miriad and imaged using casa with Briggs weighting (robust parameter of 0.5). We did not use the five longest baselines including the antenna at the W392 station because of poor phase stability. The resulting synthesized beam size and rms noise level were $6\buildrel{\prime\prime}\over{.} 02\times 4\buildrel{\prime\prime}\over{.} 43$ (PA = $82\buildrel{\circ}\over{.} 4$) and 35 μJy beam⁻¹, respectively.

We also use the Nobeyama Millimeter Array (NMA) at the Nobeyama Radio Observatory (NRO) to constrain the 3 mm photometry. The observations were done during 2010 April and May in the D configuration, where only five antennas were operational. The DSB receivers were tuned at 98.20 GHz (LSB, $\lambda =3.05$ mm) and 110.20 GHz (USB), and the UWBC correlator (Okumura et al. 2000) with a 1 GHz bandwidth was used. We did not use the USB data because of poor quality. The visibility data were calibrated with uvproc-ii (Tsutsumi et al. 1997), and then imaged using the aips (Greisen 2003) task, imagr. The resulting beam size and rms noise level are $16\buildrel{\prime\prime}\over{.} 2\times 9\buildrel{\prime\prime}\over{.} 4$ (PA = $-16\buildrel{\circ}\over{.} 3$) and 2.0 mJy beam⁻¹, respectively.

Since MM-J1545 is toward the edge region of a Galactic molecular cloud, it is necessary to carefully investigate whether the source is indeed extragalactic. We used the NRO 45 m telescope to observe Galactic ¹²CO (1–0), ¹³CO (1–0), and C¹⁸O (1–0) emission lines. The 45 m observations were performed during 2010 January to April. The ¹²CO and ¹³CO observations were carried out with the on-the-fly (OTF) mode of the multi-beam BEARS receiver (Sunada et al. 2000) and with the position switching mode of the T100 single-beam receiver (Nakajima et al. 2008), respectively. The ¹²CO map covered a $17\prime \times 17\prime$ region including MM-J1545 and a part of the Lupus-I cloud located northeast of MM-J1545. The ¹³CO OTF observations covered a $4\prime \times 4\prime$ region centered on MM-J1545. In both of the observations, the AC45 digital spectrometer was used. For the C¹⁸O observations, we used the T100 single-beam receiver and the acousto-optical spectrometers with a high-dispersion mode (AOS-H) in the standard position-switching mode, providing a spectral resolution of 0.10 km s⁻¹ at 110 GHz. Intensity calibration was done using the single-temperature chopper-wheel method, and the accuracy of intensity calibration is estimated to be 20%.

We carried out near-infrared (NIR) imaging observations of MM-J1545 with the Subaru telescope equipped with the MOIRCS instrument (Ichikawa et al. 2006; Suzuki et al. 2008) on 2010 April 23. The observations were made with the K_s-band filter at λ = 2.15 μm, with a pixel scale of $0\buildrel{\prime\prime}\over{.} 12$ pix⁻¹. The total integration time was 2.9 ks. The position and magnitude were calibrated with several 2MASS point sources with ${K}_{{\rm{s}}}\sim 15$ within $\sim 1\prime$. The systematic uncertainties of the astrometry and magnitude are estimated to be $0\buildrel{\prime\prime}\over{.} 1$ and 0.07 mag, respectively.

JH-band imaging observations were performed with the Wide Field Camera (WFCAM; Casali et al. 2007) attached to the United Kingdom Infrared Telescope (UKIRT) on Mauna Kea, during 2010 March 15–19. These observations were complemented with the MOIRCS K_s and Spitzer data. The sky was photometric throughout these nights and seeing sizes were mostly $0\buildrel{\prime\prime}\over{.} 7$–$1\buildrel{\prime\prime}\over{.} 1$. A five-point dithering and a four-point micro-stepping were used in all observations to compensate for bad pixels and to recover full point-spread function sampling. This results in proper sampling of the seeing size with the $0\buildrel{\prime\prime}\over{.} 4$ WFCAM pixels. Each exposure time was 10 s, yielding total integration times of 2.8 and 2.4 ks at J and H, respectively. All of the data were reduced in a standard manner. The astrometric uncertainties are less than $0\buildrel{\prime\prime}\over{.} 1$, and the photometric errors at J and H are 0.18 and 0.32 mag, respectively.

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The SMA interferometric observations at 890 μm and 1.3 mm confirms the exact position at the J2000 equatorial coordinate of ($\alpha ,\delta$) = (${15}^{{\rm{h}}}\ {45}^{{\rm{m}}}\ 6\buildrel{\rm{s}}\over{.} 347,\ -34^\circ \ 43\prime \ 18\buildrel{\prime\prime}\over{.} 18$) with the uncertainties of $\simeq 0\buildrel{\prime\prime}\over{.} 09$ and $\simeq 0\buildrel{\prime\prime}\over{.} 10$ at 890 μm and 1.3 mm, respectively, (see below for estimation of positional uncertainties). The flux densities at 890 μm and 1.3 mm are 69.7 ± 12.1 mJy and 20.8 ± 1.9 mJy, respectively. The 890 μm image is resolved with its 1'' beam, and the beam-deconvolved source size fitted with a single two-dimensional Gaussian using a miriad task uvfit is $1\buildrel{\prime\prime}\over{.} 2\times 0\buildrel{\prime\prime}\over{.} 64$ (PA = $37^\circ$). Figure 3 shows the visibility amplitudes versus projected baseline length (i.e., the Fourier transform of a radial profile as a function of spatial frequency) for MM-J1545. The Fourier components are well expressed by a single Gaussian ($2\buildrel{\prime\prime}\over{.} 1\pm 0\buildrel{\prime\prime}\over{.} 6$ in FWHM) with a constant offset (25 ± 6 mJy), implying a cusp-like compact structure embedded in a extended ($\approx 2\prime\prime$) component.

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At the SMA position, VLA 6 cm and ATCA 7 mm emission is also detected at $66\pm 5\;\mu \mathrm{Jy}$ and $210\pm 35\;\mu \mathrm{Jy}$, respectively, but it is not resolved with the VLA and ATCA beams. We do not detect 2.7 mm emission in the NMA image, which provides a $3\sigma$ upper limit of 5.9 mJy. The counterpart was not detected in the MIPS 24 μm down to the $3\sigma$ limiting flux density of 0.3 mJy.

In Figure 4, we fit the SED from the infrared to the radio with a single-component modified black body (or gray body), ${\kappa }_{{\rm{d}}}{B}_{\nu }(\nu ,T)$, where ${B}_{\nu }$ is the Planck function and ${\kappa }_{{\rm{d}}}={\kappa }_{0}{\nu }^{\beta }$ is the dust absorption coefficient which follows a power-law function of frequency ν. The FIR-to-mm part of the SED is well described with a single modified black body with an effective temperature of ${T}_{\mathrm{dust}}/(1+z)=7.1\pm 0.3$ K and the emissivity index of $\beta =1.4\pm 0.1$. However, the 6 cm flux clearly exceeds the gray body function. The spectral index over the 6 cm band is $\alpha =0\pm 1$ (the error is the 1σ confidence interval), where ${S}_{\nu }\propto {\nu }^{\alpha }$. This is rather flat compared with the Rayleigh–Jeans slope of $\alpha =2+\beta =3.4\pm 0.1$, suggesting that the 6 cm flux arises from synchrotron and/or free–free emission.

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In the MOIRCS, WFCAM, and IRAC images, a faint (${K}_{{\rm{s}}}=18.55$ in the Vega magnitude system, ${S}_{3.6\mu {\rm{m}}}=49.8\pm 5.2\;\mu$ Jy) source is detected at $0\buildrel{\prime\prime}\over{.} 9$ east of the SMA 890 μm peak. Hereafter, we refer to this NIR object as J1545B. Table 2 lists the optical to NIR photometry of J1545B. Figure 5 shows the centroids and uncertainties of multi-wavelength counterparts detected in the NIR (2.15, 3.6 μm) and the submm to centimeter (890 μm, 1.3 mm, 7 mm, 6 cm). The positional uncertainty of each counterpart is estimated by adding statistical and systematic errors in quadrature. The statistical error is obtained from ${\rm{\Delta }}{\theta }_{\mathrm{stat}}\approx 0.6\;{\theta }_{\mathrm{beam}}/{\rm{S}}/{\rm{N}}$, where ${\theta }_{\mathrm{beam}}$ and S/N are the beam FWHM and S/N. Given the small positional uncertainty of the SMA and MOIRCS ($\lt 0\buildrel{\prime\prime}\over{.} 1$), this offset is significant and it is unlikely that J1545B is a counterpart to MM-J1545. The FWHM of the MOIRCS image of J1545B is the $0\buildrel{\prime\prime}\over{.} 97$, whereas that of a nearby star (point-spread function, PSF) is $0\buildrel{\prime\prime}\over{.} 69$, suggesting that J1545B is intrinsically extended (a PSF-deconvolved size of $\approx 0\buildrel{\prime\prime}\over{.} 68$) and likely a low-z galaxy along the line of sight toward MM-J1545. This close association of a foreground galaxy may gravitationally magnify the background object, which can naturally explain the extreme flux density of MM-J1545. The possible gravitational lensing will be discussed in Section 4.1.

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Table 2.  Photometry of Optical/Near-infrared Objects J1545B and J1541B

Instrument	Band	Flux Density		Unit
		J1545B	J1541B
IRAC	5.8 μm	59.0 ± 39.2a	...	μJy
	3.6 μm	49.8 ± 5.2a	...	μJy
WISE	4.6 μm	$\lt 100$ e	253 ± 19b	μJy
	3.2 μm	$\lt 90$ e	260 ± 12b	μJy
MOIRCS	2.15 μm	25.0 ± 2.1	...	μJy
WFCAM	1.64 μm	27.5 ± 10.1	...	μJy
	1.26 μm	17.2 ± 5.9	...	μJy
2MASS	Ks	...	231 ± 28c	μJy
	H	...	237 ± 28c	μJy
	J	...	286 ± 34c	μJy
DSS	I	$\lt 93$	261 ± 44d	μJy
	R	$\lt 14$	275 ± 33d	μJy
	B	$\lt 2.5$	182 ± 22d	μJy

Notes.

^aFrom the catalog of the C2D survey (Evans et al. 2003, 2009) Data Release 4, in which the object is identified as SSTc2d J154506.4−344318. ^bFrom the WISE All-sky Source Catalog. ^cFrom the 2MASS All-sky Point Source Catalog, in which the object is identified as 2MASS J15413256−3503233. ^dFrom the USNO-B1.0 Catalog (Monet et al. 2003). The uncertainty includes the statistical and systematic photometric errors. ^eThe limit is uncertain due to source confusion from an adjacent bright source.

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Furthermore, we do not detect the J = 2–1 and 1–0 transitions of C¹⁸O toward MM-J1545, as shown in Figure 6. From this, we put a meaningful constraint on a molecular mass of a possible Galactic dense gas core, suggesting that MM-J1545 is not of Galactic origin. The J = 2–1 and 1–0 transitions of C¹⁸O trace molecular gas with $n({{\rm{H}}}_{2})\gtrsim {10}^{4.3}$ and $\gtrsim {10}^{3.3}$ cm⁻³, respectively, and are universally seen in association with Galactic starless cores. The $3\sigma$ upper limits on the main-beam temperature with a velocity resolution of 0.5 km s⁻¹ are ${T}_{\mathrm{mb}}\lt 0.3$ K (C¹⁸O J = 2–1) and ${T}_{\mathrm{mb}}\lt 0.07$ K (C¹⁸O J = 1–0), yielding an upper limit to the dense gas mass under the local thermodynamical equilibrium (LTE) of $\lt 0.005{M}_{\odot }$ from the C¹⁸O (1–0) constraint. This LTE mass is much smaller than those found in Galactic starless cores. Neither compact ¹²CO nor ¹³CO emission is significantly detected at the SMA continuum position, though ambient molecular gases are contaminated across the field of view of the 45 m and SMA maps. The absence of high-velocity components in ¹²CO spectra, which trace molecular outflows from an accreting protostellar system, rules out any protostellar phases.

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The 6 cm emission is also critical to judge if the object is extragalactic; starless cores have neither synchrotron nor free–free emission, unlike galaxies. The clear excess to the gray body defined at 250 μm to 7 mm and the rather flat spectral index in the 6 cm band excludes the possibility that the 6 cm signal is dominated by dust emission from a Galactic starless core. Thus, it is natural to suppose the object to be extragalactic. We will further discuss the Galactic possibility in Section 4.4.

It is unlikely that MM-J1541 is a Galactic source because it is well isolated from the main clouds (${A}_{V}\gt 2$) of Lupus-I and meets the "off-cloud" criterion defined by Rygl et al. (2013). It is significantly detected at 24 μm with Spitzer (S/N ≈6) at $(\alpha ,\delta )$ = (${15}^{{\rm{h}}}\ {41}^{{\rm{m}}}\ 32\buildrel{\rm{s}}\over{.} 706,\ -35^\circ \ 03\prime \ 19\buildrel{\prime\prime}\over{.} 03$), all consistent with a $z\approx 3$ SMG, though no IRAC data are available. A small enhancement ($2.5\sigma$, 1.3 mJy) at 20 cm is seen in the NVSS 20 cm image. As shown in Figure 4, the FIR-to-mm part of the SED is well described by a single component gray body with an effective dust temperature of ${T}_{\mathrm{dust}}/(1+z)=8.5$ K, where we assume a dust emissivity index of $\beta =1.8$ because of the limited number of photometric data points.

A bright NIR/optical source is detected in 2MASS JHK_s and DSS BRI images at $(\alpha ,\delta )$ = (${15}^{{\rm{h}}}\ {41}^{{\rm{m}}}\ 32\buildrel{\rm{s}}\over{.} 56$, $-35^\circ 03\prime 23\buildrel{\prime\prime}\over{.} 3$), which is 3'' southwest of the 24 μm centroid. Hereafter, we refer to this 2MASS/DSS object as J1541B. We also find a 3.2 and 4.6 μm object in WISE data at this position. Unfortunately, we have no higher resolution images at 24 μm or longer wavelengths, at which the emission likely comes from MM-J1541. However, given that the 24 μm source is detected at a high S/N and is likely a counterpart to MM-J1541, we can place a constraint on its position; the statistical uncertainty is estimated to be $0\buildrel{\prime\prime}\over{.} 6$ while the systematic error is $1\buildrel{\prime\prime}\over{.} 4$, yielding a total positional uncertainty of 24 μm image of approximately $1\buildrel{\prime\prime}\over{.} 5$. The positions of J1541B measured in six 2MASS/DSS bands coincide with each other, and the astrometric accuracy is estimated to be better than $0\buildrel{\prime\prime}\over{.} 3$ for J1541B.²⁴ Therefore, the offset between the 24 μm peak and the 2MASS/DSS position is significant at a $\sim 2\sigma$ level. Furthermore, the shape of the SED is consistent with that of a low-z passive elliptical, as discussed later in Section 4.1, suggesting that J1541B may be a galaxy that lenses the background SMG MM-J1541 at $z\sim 3$. We list flux densities of J1541B in Table 2 and will further discuss the possible lensing in Section 4.1.

To characterize the properties of J1541B, we perform SED fits to the optical-to-NIR photometric data of J1541B using the Hyperz code²⁵ developed by Bolzonella et al. (2000). In SED fits, we used SED templates of Bruzual & Charlot (2003). From the SPIRE A_V map, the visual extinction toward MM-J1541 is approximately 1.5, but the stray light from the Moon in the SPIRE observations (Rygl et al. 2013) can bias against low visual extinction. We assume a conservative value of A_V = 1. Note that this assumption does not dramatically affect the result because the total extinction is considered by combining the Galactic reddening and the intrinsic extinction, which eventually compensates the uncertainty in the Galactic extinction. Figure 7 shows the result of SED fits. The photometric redshift (photo-z) of J1541B is ${z}_{{\rm{L}}}={0.26}_{-0.13}^{+0.29}$ (${\chi }_{\nu }^{2}=0.10$, the error bar is from the 68% confidence interval). The optical to NIR SED is well described by a 33 Myr elliptical model with a stellar mass of $1\times {10}^{11}\;{M}_{\odot }$ and an intrinsic extinction of A_V = 0.10. The B-band decrement can be accounted for by the 4000 Å break at $z\sim 0.3$, which is well within the photo-z range. The best-fit stellar age is young (33 Myr) but maturer stellar SEDs can reasonably match the actual SED as well.

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Then we make use of the Faber–Jackson relation (FJR; Faber & Jackson 1976) to constrain the velocity dispersion of the lensing galaxy, which allows us to model a singular isothermal sphere (SIS) as a lensing dark halo. FJR  was originally proposed as an empirical relation between theB-band absolute magnitude and velocity dispersion of galaxies. Similar relations are now confirmed in many filter bands out to the NIR (Pahre et al. 1998; La Barbera et al. 2010). In our case, the reddening can be significant because of the foreground Galactic molecular cloud; thus, we use the NIR version of FJR presented in Equation (5) of La Barbera et al. (2010). The Einstein radius of a SIS mass distribution is expressed as

$$\begin{eqnarray*}&&{\theta }_{{\rm{E}}}=1\buildrel{\prime\prime}\over{.} 154\times {\left(\displaystyle \frac{{\sigma }_{v}}{200\;\mathrm{km}\;{{\rm{s}}}^{-1}}\right)}^{2}\left(\displaystyle \frac{{D}_{{\rm{A}}}^{{\rm{S}}}}{1\;\mathrm{Gpc}}\right){\left(\displaystyle \frac{{D}_{{\rm{A}}}^{\mathrm{LS}}}{1\;\mathrm{Gpc}}\right)}^{-1},\end{eqnarray*}$$

where ${\sigma }_{v}$ is the velocity dispersion, ${D}_{{\rm{A}}}^{{\rm{S}}}$ and ${D}_{{\rm{A}}}^{\mathrm{LS}}$ are the angular diameter distances from the observer to the background source and from the foreground lens to the background source, respectively. In the redshift range of $0.1\lt {z}_{{\rm{L}}}\lt 0.7$, which covers the 68% redshift confidence interval of J1541B, we find the velocity dispersion ranging $100\lt {\sigma }_{v}\lt 250$ km s⁻¹ from the K_s magnitude and FJR. When we consider the background SMG at z = 3.0 (Section 3.2), then we find ${\theta }_{{\rm{E}}}\sim 0\buildrel{\prime\prime}\over{.} 3$–2'', which is smaller than the actual separation between J1541B and the 24 μm peak. We estimate the magnification factor ${\mu }_{\;{\rm{g}}}$ at the 24 μm position (3'' apart from the lens centroid) using a gravitational lensing model glafic (Oguri 2010), in which we employ a circular-symmetric SIS with the velocity dispersion ${\sigma }_{v}$ derived above. For ${z}_{{\rm{L}}}=0.26$ and ${z}_{{\rm{S}}}=3.0$, we find ${\theta }_{{\rm{E}}}=0\buildrel{\prime\prime}\over{.} 7$ and the magnification factor at the position of MM-J1541, ${\mu }_{{\rm{g}}}=1.2$. If we go to ${z}_{{\rm{L}}}=0.55$, which is the edge of the 68% confidence interval, then we have ${\theta }_{{\rm{E}}}=1\buildrel{\prime\prime}\over{.} 2$ and ${\mu }_{{\rm{g}}}=1.4$. To get the Einstein radius closer to the $3\prime\prime$ separation angle, it would be necessary to double the angular diameter distance to the lens and/or increase the luminosity of the lens galaxy by a factor of $\approx 4$, which is very difficult to achieve within the uncertainties in the measured quantities. We have another likelihood peak at ${z}_{{\rm{L}}}={1.73}_{-0.52}^{+0.77}$ (${\chi }_{\nu }^{2}=0.20$; see Figure 7), but this is unlikely because the inferred stellar mass is too high ($1\times {10}^{13}\;{M}_{\odot }$). Even if this would be the case, the magnification still remains a moderate value of ${\mu }_{{\rm{g}}}=2.0$. Consequently, the magnification factor of MM-J1541 is not likely as high as $\approx 10$ but rather moderate (${\mu }_{{\rm{g}}}\approx 1.2$), suggesting that MM-J1541 might be an intrinsically hyper-luminous star-forming galaxy with a demagnified 1.1 mm flux density of ∼20 mJy or the intrinsic FIR luminosity of $\mathrm{log}({L}_{\mathrm{FIR}}/{L}_{\odot })\sim 13.7$–13.9.

On the other hand, amplification for MM-J1545 at $z\simeq 4$–5 may be larger, though the measurement of its magnification using existing data is difficult. The Fourier analysis of the SMA visibility data of MM-J1545 clearly shows its extended morphology (FWHM $\sim 1\prime\prime$–2''; see Figure 3), suggesting that the source could be magnified by a foreground galaxy seen as J1545B. Unfortunately, we only have a limited number of photometric data points for J1545B, which likely suffer from the relatively large Galactic reddening of ${A}_{V}\simeq 2.4$. We find no apparent spectral break at ${\lambda }_{\mathrm{obs}}\geqslant 1.2\;\mu {\rm{m}}$, suggesting a lens redshift of ${z}_{{\rm{L}}}\lt 2$. Thus we assume several lens redshifts and a source redshift (${z}_{{\rm{S}}}=4.8$, from Section 3.2) to estimate the Einstein radius in the same manner as MM-J1541. Note that a rest-frame K_s-band extinction of 0.2 mag is used to correct the Galactic reddening. We find ${\theta }_{{\rm{E}}}\gt 1\buildrel{\prime\prime}\over{.} 5$ at ${z}_{{\rm{L}}}\gt 0.7$, which is inconsistent with our SMA image showing the smaller separation ($0\buildrel{\prime\prime}\over{.} 9$) and no counter-images split by a gravitational lens. This suggests a lens redshift of $z\lesssim 0.6$. Actually, if the lensing galaxy is at ${z}_{{\rm{L}}}=0.5$, we have the absolute magnitude in rest-frame K_s-band of ${M}_{{K}_{{\rm{s}}}}\sim -25$ and ${\sigma }_{v}\sim 160$−170 km s⁻¹ from the FJR. This yields the Einstein radius of $\approx 0\buildrel{\prime\prime}\over{.} 9$, consistent with the observed situation.

Unfortunately, we cannot exactly predict the magnification factor of MM-J1545; the SMA 890 μm image exhibits neither multiple counter-images nor a large arc/ring, and the spatial extent of the source is unknown. Furthermore, the accurate redshifts of the lens and source are not available. All of the facts prevent us from precisely constructing a lens model. However, given that no lensed source with a magnification of ${\mu }_{{\rm{g}}}\gt 10$, showing a single image with a 1''-beam has been reported thus far (e.g., Bussmann et al. 2013), it should be reasonable to assume ${\mu }_{{\rm{g}}}\sim 10$ as an upper limit for the magnification factor of MM-J1545. In this case, the intrinsic FIR luminosity is still very high (${L}_{\mathrm{FIR}}^{\mathrm{int}}\gtrsim 1\times {10}^{13}\;{L}_{\odot }$), even after correcting for magnification. Such a starburst galaxy in the hyperluminous regime at $z\simeq 4$–5 is still rare compared to existing studies (e.g., Riechers et al. 2010; Combes et al. 2012; Walter et al. 2012; Vieira et al. 2013; Weiß et al. 2013) and is a unique laboratory to investigate properties of star-formation in the early universe.