Alma Imaging and Gravitational Lens Models of South Pole Telescope—selected Dusty, Star-Forming Galaxies at High Redshifts

Abstract

The South Pole Telescope has discovered one hundred gravitationally lensed, high-redshift, dusty, star-forming galaxies (DSFGs). We present 0.5 resolution 870 µm Atacama Large Millimeter/submillimeter Array imaging of a sample of 47 DSFGs spanning z = 1.9 − 5.7, and construct gravitational lens models of these sources. Our visibility-based lens modeling incorporates several sources of residual interferometric calibration uncertainty, allowing us to properly account for noise in the observations. At least 70% of the sources are strongly lensed by foreground galaxies (µ 870µm > 2), with a median magnification µ 870µm = 6.3, extending to µ 870µm > 30. We compare the intrinsic size distribution of the strongly lensed sources to a similar number of unlensed DSFGs and find no significant differences in spite of a bias between the magnification and intrinsic source size. This may indicate that the true size distribution of DSFGs is relatively narrow. We use the source sizes to constrain the wavelength at which the dust optical depth is unity and find this wavelength to be correlated with the dust temperature. This correlation leads to discrepancies in dust mass estimates of a factor of 2 compared to estimates using a single value for this wavelength. We investigate the relationship between the [CII] line and the far-infrared luminosity and find that the same correlation between the [CII]/L FIR ratio and Σ FIR found for low-redshift star-forming galaxies applies to high-redshift galaxies and extends at least two orders of magnitude higher in Σ FIR . This lends further credence to the claim that the compactness of the IR-emitting region is the controlling parameter in establishing the "[CII] deficit."

ALMA observations of atomic carbon inz ∼ 4 dusty star-forming galaxies

“…6), there is no difference in gas masses between SPT-DSFGs and the comparison sample. Furthermore, Spilker et al (2016) found that the observed angular sizes of SPT-DSFGs (at <z>∼ 4) are consistent with the angular sizes of lower redshift unlensed DSFGs (at <z>∼ 2). Allowing for the redshift evolution of the angular scale, this implies that DSFGs in the higher-redshift SPT sample are more physically compact (1 at z = 3.5 corresponds to 7.47 kpc, while 1 at z = 2.2 corresponds to 8.42 kpc).…”

“…Members of a flux-selected lensed sample will be biased towards being systematically compact (as a compact source lying close to a lensing caustic will be magnified more than a similarly-positioned extended source). Despite this, however, based on sizes derived from lens model fits to ALMA 870µm data Spilker et al (2016) find that the observed angular 870µm size distribution of SPT-DSFGs is statistically consistent with the distribution of 870µm angular sizes displayed by members of un-lensed comparison samples. With the higher mean redshift of the SPT-DSFG sample, and the redshift evolution of the angular scale, this implies that DSFGs in the higher-redshift SPT sample are slightly more physically compact (i.e., 1 at the mean redshift of SPT-DSFGs, z = 3.5, corresponds to 7.47 kpc, while 1 at the mean redshift of unlicensed DSFG samples, z = 2.2, corresponds to 8.42 kpc).…”

“…The absolute magnification needs to be corrected for if we are to discuss any innate source properties (such as the total molecular gas mass). Lens modelling, carried out based on our ∼ 0.5 870µm ALMA imaging, has been presented by Hezaveh et al (2013) and Spilker et al (2016). All of the sources in this work have their magnification factors measured, spanning a range 3.6 < µ < 27 (with a sample mean and standard deviation of 13.1±9.3).…”

“…The DSFGs discovered by the SPT are typically strongly lensed by an intervening massive galaxy Vieira et al 2013;Spilker et al 2016). In the most simple form, strong gravitational lensing both distorts the lensed source and boosts its apparent luminosity by a magnification factor (µ), which is dependent on both the mass of the intervening lens and the source/lens configuration.…”

“…The remaining unknown is the radius of the gas disk, r. Following the source size analysis of the SPT-DSFGs sample presented by Spilker et al (2016), we take a typical radius of 2kpc. The relation in Eq.…”