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Showing papers by "Mark Halpern published in 2015"


Journal ArticleDOI
Peter A. R. Ade1, Nabila Aghanim2, Zeeshan Ahmed3, Randol W. Aikin4  +354 moreInstitutions (75)
TL;DR: Strong evidence for dust and no statistically significant evidence for tensor modes is found and various model variations and extensions are probe, including adding a synchrotron component in combination with lower frequency data, and find that these make little difference to the r constraint.
Abstract: We report the results of a joint analysis of data from BICEP2/Keck Array and Planck. BICEP2 and Keck Array have observed the same approximately 400 deg2 patch of sky centered on RA 0h, Dec. −57.5deg. The combined maps reach a depth of 57 nK deg in Stokes Q and U in a band centered at 150 GHz. Planck has observed the full sky in polarization at seven frequencies from 30 to 353 GHz, but much less deeply in any given region (1.2 μK deg in Q and U at 143 GHz). We detect 150×353 cross-correlation in B-modes at high significance. We fit the single- and cross-frequency power spectra at frequencies above 150 GHz to a lensed-ΛCDM model that includes dust and a possible contribution from inflationary gravitational waves (as parameterized by the tensor-to-scalar ratio r). We probe various model variations and extensions, including adding a synchrotron component in combination with lower frequency data, and find that these make little difference to the r constraint. Finally we present an alternative analysis which is similar to a map-based cleaning of the dust contribution, and show that this gives similar constraints. The final result is expressed as a likelihood curve for r, and yields an upper limit r0.05<0.12 at 95% confidence. Marginalizing over dust and r, lensing B-modes are detected at 7.0σ significance.

1,255 citations


Journal ArticleDOI
TL;DR: In this article, the authors examined the internal consistency of the Planck 2015 cosmic microwave background (CMB) temperature anisotropy power spectrum and found that tension exists between cosmological constant cold dark matter (LCDM) model parameters inferred from multipoles l = 1000, particularly the CDM density, Omega_ch^2, which is discrepant at 2.5 sigma for a Planck-motivated prior on the optical depth, tau=0.07+/-0.02.
Abstract: We examine the internal consistency of the Planck 2015 cosmic microwave background (CMB) temperature anisotropy power spectrum. We show that tension exists between cosmological constant cold dark matter (LCDM) model parameters inferred from multipoles l =1000, particularly the CDM density, Omega_ch^2, which is discrepant at 2.5 sigma for a Planck-motivated prior on the optical depth, tau=0.07+/-0.02. We find some parameter tensions to be larger than previously reported because of inaccuracy in the code used by the Planck Collaboration to generate model spectra. The Planck l>=1000 constraints are also in tension with low-redshift data sets, including Planck's own measurement of the CMB lensing power spectrum (2.4 sigma), and the most precise baryon acoustic oscillation (BAO) scale determination (2.5 sigma). The Hubble constant predicted by Planck from l>=1000, H_0=64.1+/-1.7 km/s/Mpc, disagrees with the most precise local distance ladder measurement of 73.0+/-2.4 km/s/Mpc at the 3.0 sigma level, while the Planck value from l<1000, 69.7+/-1.7 km/s/Mpc, is consistent within 1 sigma. A discrepancy between the Planck and South Pole Telescope (SPT) high-multipole CMB spectra disfavors interpreting these tensions as evidence for new physics. We conclude that the parameters from the Planck high-multipole spectrum probably differ from the underlying values due to either an unlikely statistical fluctuation or unaccounted-for systematics persisting in the Planck data.

139 citations


Journal ArticleDOI
TL;DR: In this paper, the authors report results from the 2012 and 2013 observing seasons, during which the Keck Array consisted of five receivers all operating in the same (150 GHz) frequency band and observing field as BICEP2.
Abstract: The Keck Array is a system of cosmic microwave background (CMB) polarimeters, each similar to the BICEP2 experiment. In this paper we report results from the 2012 and 2013 observing seasons, during which the Keck Array consisted of five receivers all operating in the same (150 GHz) frequency band and observing field as BICEP2. We again find an excess of B-mode power over the lensed-$\Lambda$CDM expectation of $> 5 \sigma$ in the range $30 6\sigma$.

135 citations


Journal ArticleDOI
TL;DR: In this article, the authors report results from the 2012 to 2013 observing seasons, during which the Keck Array consisted of five receivers all operating in the same (150 GHz) frequency band and observing field as Bicep2, and again find an excess of Bmode power over the lensed-ΛCDM expectation of >5σ in the range 30 6σ.
Abstract: The Keck Array is a system of cosmic microwave background polarimeters, each similar to the Bicep2 experiment In this paper we report results from the 2012 to 2013 observing seasons, during which the Keck Array consisted of five receivers all operating in the same (150 GHz) frequency band and observing field as Bicep2 We again find an excess of B-mode power over the lensed-ΛCDM expectation of >5σ in the range 30 6σ

107 citations


Journal ArticleDOI
TL;DR: In this article, the cross-correlation of cosmic microwave background (CMB) convergence maps derived from Atacama Cosmology Telescope data with galaxy lensing convergence maps as measured by the Canada-France-Hawaii Telescope Stripe 82 Survey was measured for the first time with a significance of 4.2 sigma.
Abstract: We measure the cross-correlation of cosmic microwave background (CMB) lensing convergence maps derived from Atacama Cosmology Telescope data with galaxy lensing convergence maps as measured by the Canada-France-Hawaii Telescope Stripe 82 Survey. The CMB-galaxy lensing cross power spectrum is measured for the first time with a significance of 4.2 sigma, which corresponds to a 12% constraint on the amplitude of density fluctuations at redshifts similar to 0.9. With upcoming improved lensing data, this novel type of measurement will become a powerful cosmological probe, providing a precise measurement of the mass distribution at intermediate redshifts and serving as a calibrator for systematic biases in weak lensing measurements.

81 citations


Journal ArticleDOI
TL;DR: In this paper, the authors developed antenna-coupled transition-edge sensor bolometers for a wide range of cosmic microwave background (CMB) polarimetry experiments, including Bicep2, Keck Array, and the balloon borne Spider.
Abstract: We have developed antenna-coupled transition-edge sensor bolometers for a wide range of cosmic microwave background (CMB) polarimetry experiments, including Bicep2, Keck Array, and the balloon borne Spider. These detectors have reached maturity and this paper reports on their design principles, overall performance, and key challenges associated with design and production. Our detector arrays repeatedly produce spectral bands with 20%–30% bandwidth at 95, 150, or 230 GHz. The integrated antenna arrays synthesize symmetric co-aligned beams with controlled side-lobe levels. Cross-polarized response on boresight is typically $\sim 0.5\%$, consistent with cross-talk in our multiplexed readout system. End-to-end optical efficiencies in our cameras are routinely 35% or higher, with per detector sensitivities of NET ~ 300 $\mu {{\rm{K}}}_{\mathrm{CMB}}\sqrt{{\rm{s}}}$. Thanks to the scalability of this design, we have deployed 2560 detectors as 1280 matched pairs in Keck Array with a combined instantaneous sensitivity of $\sim 9\;\mu {{\rm{K}}}_{\mathrm{CMB}}\sqrt{{\rm{s}}}$, as measured directly from CMB maps in the 2013 season. Similar arrays have recently flown in the Spider instrument, and development of this technology is ongoing.

72 citations


Journal ArticleDOI
TL;DR: In this paper, the authors provide a detailed study of potential instrumental systematic contamination to B-mode polarization at 150 GHz by the Bicep2 experiment and present a heuristic classification of beam imperfections according to their symmetries and uniformities.
Abstract: In a companion paper, we have reported a >5σ detection of degree scale B-mode polarization at 150 GHz by the Bicep2 experiment. Here we provide a detailed study of potential instrumental systematic contamination to that measurement. We focus extensively on spurious polarization that can potentially arise from beam imperfections. We present a heuristic classification of beam imperfections according to their symmetries and uniformities, and discuss how resulting contamination adds or cancels in maps that combine observations made at multiple orientations of the telescope about its boresight axis. We introduce a technique, which we call "deprojection," for filtering the leading order beam-induced contamination from time-ordered data, and show that it reduces power in Bicep2's actual and null-test BB spectra consistent with predictions using high signal-to-noise beam shape measurements. We detail the simulation pipeline that we use to directly simulate instrumental systematics and the calibration data used as input to that pipeline. Finally, we present the constraints on BB contamination from individual sources of potential systematics. We find that systematics contribute BB power that is a factor of ~10× below Bicep2's three-year statistical uncertainty, and negligible compared to the observed BB signal. The contribution to the best-fit tensor/scalar ratio is at a level equivalent to r = (3–6) × 10^(−3).

56 citations


Journal ArticleDOI
TL;DR: The BICEP2 and the Keck Array as mentioned in this paper have been used to observe the cosmic microwave background (CMB) from the South Pole at degree angular scales in search of a signature of inflation imprinted as Bmode polarization in the CMB.
Abstract: BICEP2 and the Keck Array are polarization-sensitive microwave telescopes that observe the cosmic microwave background (CMB) from the South Pole at degree angular scales in search of a signature of inflation imprinted as B-mode polarization in the CMB. BICEP2 was deployed in late 2009, observed for three years until the end of 2012 at 150 GHz with 512 antenna-coupled transition edge sensor bolometers, and has reported a detection of B-mode polarization on degree angular scales. The Keck Array was first deployed in late 2010 and will observe through 2016 with five receivers at several frequencies (95, 150, and 220 GHz). BICEP2 and the Keck Array share a common optical design and employ the field-proven BICEP1 strategy of using small-aperture, cold, on-axis refractive optics, providing excellent control of systematics while maintaining a large field of view. This design allows for full characterization of far-field optical performance using microwave sources on the ground. Here we describe the optical design of both instruments and report a full characterization of the optical performance and beams of BICEP2 and the Keck Array at 150 GHz.

42 citations


Journal ArticleDOI
TL;DR: In this paper, weak lensing mass measurements from the Canada-France-Hawaii Telescope Stripe 82 Survey for galaxy clusters selected through their high signal-to-noise thermal Sunyaev-Zeldovich (tSZ) signal measured with the Atacama Cosmology Telescope (ACT).
Abstract: Mass calibration uncertainty is the largest systematic effect for using clusters of galaxies to constrain cosmological parameters. We present weak lensing mass measurements from the Canada-France-Hawaii Telescope Stripe 82 Survey for galaxy clusters selected through their high signal-to-noise thermal Sunyaev-Zeldovich (tSZ) signal measured with the Atacama Cosmology Telescope (ACT). For a sample of 9 ACT clusters with a tSZ signal-to-noise greater than five the average weak lensing mass is $\left(4.8\pm0.8\right)\,\times10^{14}\,\mathrm{M}_\odot$, consistent with the tSZ mass estimate of $\left(4.70\pm1.0\right)\,\times10^{14}\,\mathrm{M}_\odot$ which assumes a universal pressure profile for the cluster gas. Our results are consistent with previous weak-lensing measurements of tSZ-detected clusters from the Planck satellite. When comparing our results, we estimate the Eddington bias correction for the sample intersection of Planck and weak-lensing clusters which was previously excluded.

41 citations


Journal ArticleDOI
TL;DR: The bicep2 and the Keck Array as mentioned in this paper have been used to observe the cosmic microwave background (CMB) from the South Pole at degree angular scales in search of a signature of inflation imprinted as Bmode polarization in the CMB.
Abstract: bicep2 and the Keck Array are polarization-sensitive microwave telescopes that observe the cosmic microwave background (CMB) from the South Pole at degree angular scales in search of a signature of inflation imprinted as B-mode polarization in the CMB. bicep2 was deployed in late 2009, observed for three years until the end of 2012 at 150 GHz with 512 antenna-coupled transition edge sensor bolometers, and has reported a detection of B-mode polarization on degree angular scales. The Keck Array was first deployed in late 2010 and will observe through 2016 with five receivers at several frequencies (95, 150, and 220 GHz). bicep2 and the Keck Array share a common optical design and employ the field-proven bicep1 strategy of using small-aperture, cold, on-axis refractive optics, providing excellent control of systematics while maintaining a large field of view. This design allows for full characterization of far-field optical performance using microwave sources on the ground. Here we describe the optical design of both instruments and report a full characterization of the optical performance and beams of bicep2 and the Keck Array at 150 GHz.

40 citations


Journal ArticleDOI
TL;DR: Integrated, post-correlation data are first passed through a nearly lossless rounding step which compares the precision of the data to a generalized and calibration-independent form of the radiometer equation, and the newly developed Bitshuffle lossless compression algorithm is subsequently applied.

Journal ArticleDOI
TL;DR: The S pider flight cryostat as mentioned in this paper was designed to cool six millimeter-wavelength telescopes during an Antarctic long-duration balloon flight, which performed successfully during a 17-day flight in the 2014-2015 Antarctic summer.

Journal ArticleDOI
TL;DR: In this paper, the authors provide a detailed study of potential instrumental systematic contamination to the BICEP2 measurement, focusing extensively on spurious polarization that can potentially arise from beam imperfections, and discuss how resulting contamination adds or cancels in maps that combine observations made at multiple orientations of the telescope about its boresight axis.
Abstract: In a companion paper we have reported a $>5\sigma$ detection of degree scale $B $-mode polarization at 150 GHz by the BICEP2 experiment. Here we provide a detailed study of potential instrumental systematic contamination to that measurement. We focus extensively on spurious polarization that can potentially arise from beam imperfections. We present a heuristic classification of beam imperfections according to their symmetries and uniformities, and discuss how resulting contamination adds or cancels in maps that combine observations made at multiple orientations of the telescope about its boresight axis. We introduce a technique, which we call "deprojection", for filtering the leading order beam-induced contamination from time ordered data, and show that it removes power from BICEP2's $BB$ spectrum consistent with predictions using high signal-to-noise beam shape measurements. We detail the simulation pipeline that we use to directly simulate instrumental systematics and the calibration data used as input to that pipeline. Finally, we present the constraints on $BB$ contamination from individual sources of potential systematics. We find that systematics contribute $BB$ power that is a factor $\sim10\times$ below BICEP2's 3-year statistical uncertainty, and negligible compared to the observed $BB$ signal. The contribution to the best-fit tensor/scalar ratio is at a level equivalent to $r=(3-6)\times10^{-3}$.

Journal ArticleDOI
TL;DR: In this article, post-correlation data are first passed through a nearly lossless rounding step which compares the precision of the data to a generalized and calibration-independent form of the radiometer equation.
Abstract: We present a procedure for efficiently compressing astronomical radio data for high performance applications. Integrated, post-correlation data are first passed through a nearly lossless rounding step which compares the precision of the data to a generalized and calibration-independent form of the radiometer equation. This allows the precision of the data to be reduced in a way that has an insignificant impact on the data. The newly developed Bitshuffle lossless compression algorithm is subsequently applied. When the algorithm is used in conjunction with the HDF5 library and data format, data produced by the CHIME Pathfinder telescope is compressed to 28% of its original size and decompression throughputs in excess of 1 GB/s are obtained on a single core.

Journal ArticleDOI
TL;DR: In this paper, the authors have developed antenna-coupled transition-edge sensor (TES) bolometers for a wide range of cosmic microwave background (CMB) polarimetry experiments, including BICEP2, Keck Array, and balloon borne SPIDER.
Abstract: We have developed antenna-coupled transition-edge sensor (TES) bolometers for a wide range of cosmic microwave background (CMB) polarimetry experiments, including BICEP2, Keck Array, and the balloon borne SPIDER. These detectors have reached maturity and this paper reports on their design principles, overall performance, and key challenges associated with design and production. Our detector arrays repeatedly produce spectral bands with 20%-30% bandwidth at 95, 150, or 220~GHz. The integrated antenna arrays synthesize symmetric co-aligned beams with controlled side-lobe levels. Cross-polarized response on boresight is typically ~0.5%, consistent with cross-talk in our multiplexed readout system. End-to-end optical efficiencies in our cameras are routinely 35% or higher, with per detector sensitivities of NET~300 uKrts. Thanks to the scalability of this design, we have deployed 2560 detectors as 1280 matched pairs in Keck Array with a combined instantaneous sensitivity of ~9 uKrts, as measured directly from CMB maps in the 2013 season. Similar arrays have recently flown in the SPIDER instrument, and development of this technology is ongoing.

Proceedings ArticleDOI
27 Jul 2015
TL;DR: A custom GPU-based compute cluster that provides the correlation X-engine of the CHIME Pathfinder radio telescope is presented, taking advantage of low-cost hardware and leveraging packed integer operations to double algorithmic efficiency.
Abstract: We present the design and implementation of a custom GPU-based compute cluster that provides the correlation X-engine of the CHIME Pathfinder radio telescope. It is among the largest such systems in operation, correlating 32,896 baselines (256 inputs) over 400MHz of radio bandwidth. Making heavy use of consumer-grade parts and a custom software stack, the system was developed at a small fraction of the cost of comparable installations. Unlike existing GPU backends, this system is built around OpenCL kernels running on consumer-level AMD GPUs, taking advantage of low-cost hardware and leveraging packed integer operations to double algorithmic efficiency. The system achieves the required 105 TOPS in a 10kW power envelope, making it one of the most power-efficient X-engines in use today.

Proceedings ArticleDOI
TL;DR: In this paper, the authors present the design and implementation of a custom GPU-based compute cluster that provides the correlation X-engine of the CHIME Pathfinder radio telescope, which is among the largest such systems in operation, correlating 32,896 baselines (256 inputs) over 400MHz of radio bandwidth.
Abstract: We present the design and implementation of a custom GPU-based compute cluster that provides the correlation X-engine of the CHIME Pathfinder radio telescope. It is among the largest such systems in operation, correlating 32,896 baselines (256 inputs) over 400MHz of radio bandwidth. Making heavy use of consumer-grade parts and a custom software stack, the system was developed at a small fraction of the cost of comparable installations. Unlike existing GPU backends, this system is built around OpenCL kernels running on consumer-level AMD GPUs, taking advantage of low-cost hardware and leveraging packed integer operations to double algorithmic efficiency. The system achieves the required 105TOPS in a 10kW power envelope, making it among the most power-efficient X-engines in use today.

Journal ArticleDOI
TL;DR: In this paper, the authors report contributions to cosmic infrared background (CIB) intensities originating from known galaxies and their faint companions at sub-millimeter wavelengths using the publicly available UltraVISTA catalog and maps at 250, 350, and 500 μm from the Herschel Multi-tiered Extragalactic Survey.
Abstract: We report contributions to cosmic infrared background (CIB) intensities originating from known galaxies and their faint companions at submillimeter wavelengths. Using the publicly available UltraVISTA catalog and maps at 250, 350, and 500 μm from the Herschel Multi-tiered Extragalactic Survey, we perform a novel measurement that exploits the fact that uncataloged sources may bias stacked flux densities—particularly if the resolution of the image is poor—and intentionally smooth the images before stacking and summing intensities. By smoothing the maps we are capturing the contribution of faint (undetected in K_S ~ 23.4) sources that are physically associated, or correlated, with the detected sources. We find that the cumulative CIB increases with increased smoothing, reaching 9.82 ± 0.78, 5.77 ± 0.43 and 2.32 ± 0.19 nWm^(-2) sr^(-1) at 250, 350, and 500 μm at 300 arscec FWHM. This corresponds to a fraction of the fiducial CIB of 0.94 ± 0.23, 1.07 ± 0.31, and 0.97 ± 0.26 at 250, 350, and 500 μm, where the uncertainties are dominated by those of the absolute CIB. We then propose, with a simple model combining parametric descriptions for stacked flux densities and stellar mass functions, that emission from galaxies with log(M/M⊙) > 8.5 can account for most of the measured total intensities and argue against contributions from extended, diffuse emission. Finally, we discuss prospects for future survey instruments to improve the estimates of the absolute CIB levels, and observe any potentially remaining emission at z > 4.

Journal ArticleDOI
TL;DR: In this article, the authors report contributions to cosmic infrared background (CIB) intensities originating from known galaxies and their faint companions at submillimeter wavelengths using the publicly-available UltraVISTA catalog, and maps at 250, 350, and 500 µm from the HerMES.
Abstract: We report contributions to cosmic infrared background (CIB) intensities originating from known galaxies and their faint companions at submillimeter wavelengths. Using the publicly-available UltraVISTA catalog, and maps at 250, 350, and 500 {\mu}m from the \emph{Herschel} Multi-tiered Extragalactic Survey (HerMES), we perform a novel measurement that exploits the fact that uncatalogued sources may bias stacked flux densities --- particularly if the resolution of the image is poor --- and intentionally smooth the images before stacking and summing intensities. By smoothing the maps we are capturing the contribution of faint (undetected in K_S ~ 23.4) sources that are physically associated, or correlated, with the detected sources. We find that the cumulative CIB increases with increased smoothing, reaching 9.82 +- 0.78, 5.77 +- 0.43, and 2.32 +- 0.19$\, \rm nW m^{-2} sr^{-1}$ at 250, 350, and 500 {\mu}m at 300 arcsec FWHM. This corresponds to a fraction of the fiducial CIB of 0.94 +- 0.23, 1.07 +- 0.31, and 0.97 +- 0.26 at 250, 350, and 500 {\mu}m, where the uncertainties are dominated by those of the absolute CIB. We then propose, with a simple model combining parametric descriptions for stacked flux densities and stellar mass functions, that emission from galaxies with log(M/Msun) > 8.5 can account for the most of the measured total intensities, and argue against contributions from extended, diffuse emission. Finally, we discuss prospects for future survey instruments to improve the estimates of the absolute CIB levels, and observe any potentially remaining emission at z > 4.

Journal ArticleDOI
TL;DR: The Cosmology Large Angular Scale Surveyor (CLASS) as discussed by the authors uses a variable-delay polarization modulator (VPM) to suppress the 1/f noise of the atmosphere and enable the measurement of the large angular scale polarization modes.
Abstract: The Cosmology Large Angular Scale Surveyor (CLASS) will measure the polarization of the Cosmic Microwave Background to search for and characterize the polarized signature of inflation. CLASS will operate from the Atacama Desert and observe $\sim$70% of the sky. A variable-delay polarization modulator (VPM) modulates the polarization at $\sim$10 Hz to suppress the 1/f noise of the atmosphere and enable the measurement of the large angular scale polarization modes. The measurement of the inflationary signal across angular scales that span both the recombination and reionization features allows a test of the predicted shape of the polarized angular power spectra in addition to a measurement of the energy scale of inflation. CLASS is an array of telescopes covering frequencies of 38, 93, 148, and 217 GHz. These frequencies straddle the foreground minimum and thus allow the extraction of foregrounds from the primordial signal. Each focal plane contains feedhorn-coupled transition-edge sensors that simultaneously detect two orthogonal linear polarizations. The use of single-crystal silicon as the dielectric for the on-chip transmission lines enables both high efficiency and uniformity in fabrication. Integrated band definition has been implemented that both controls the bandpass of the single mode transmission on the chip and prevents stray light from coupling to the detectors.

Journal ArticleDOI
TL;DR: The cryogenic half-wave plate rotation mechanisms built for and used in Spider, a polarization-sensitive balloon-borne telescope array that observed the cosmic microwave background at 95 GHz and 150 GHz during a stratospheric balloon flight from Antarctica in January 2015 are described.
Abstract: We describe the cryogenic half-wave plate rotation mechanisms built for and used in Spider, a polarization-sensitive balloon-borne telescope array that observed the Cosmic Microwave Background at 95 GHz and 150 GHz during a stratospheric balloon flight from Antarctica in January 2015. The mechanisms operate at liquid helium temperature in flight. A three-point contact design keeps the mechanical bearings relatively small but allows for a large (305 mm) diameter clear aperture. A worm gear driven by a cryogenic stepper motor allows for precise positioning and prevents undesired rotation when the motors are depowered. A custom-built optical encoder system monitors the bearing angle to an absolute accuracy of +/- 0.1 degrees. The system performed well in Spider during its successful 16 day flight.

Posted Content
TL;DR: In this article, the spectral energy distributions (SEDs) of nine candidate gravitationally-lensed dusty star-forming galaxies (DSFGs) selected at 218 GHz from the ACT equatorial survey were analyzed.
Abstract: We present multi-wavelength detections of nine candidate gravitationally-lensed dusty star-forming galaxies (DSFGs) selected at 218 GHz ($\sim$1.4 mm) from the ACT equatorial survey. These represent the subset of the total ACT sample lying in Herschel SPIRE fields, and all nine of the 218 GHz detections were found to have bright Herschel counterparts. By fitting their spectral energy distributions (SEDs) with a modified blackbody model with power-law temperature distribution, we find the sample has a median redshift of $z=4.1^{+1.1}_{-1.0}$ (68 percent confidence interval), as expected for 218 GHz selection, and an apparent total infrared luminosity of $\log_{10}({\mu L_{\rm IR}}/L_\odot) = 13.32^{+0.25}_{-0.19}$, which suggests that they are either strongly lensed sources with magnification $\mu=5-10$ or unresolved collections of unlensed DSFGs. The effective apparent diameter of the sample is $ {\sqrt{\mu}\,d} \sim 4.2^{+1.7}_{-1.0}$ kpc, further evidence of strong lensing or multiplicity as the typical diameter of dusty star-forming galaxies is $1-3$ kpc. Additionally, we find that the sources have substantial optical depth ($\tau = 4.2^{+3.7}_{-1.9}$) around the peak in the modified blackbody spectrum ($\lambda_{\rm obs} \le 500$ $\mu$m).