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ALMA Deep Field in SSA22: Reconstructed [CII] Luminosity Function at z = 6

Natsuki H. Hayatsu, Rob J. Ivison, Paola Andreani, Fabrizia Guglielmetti, Zhi-Yu Zhang, Andy Biggs, Hideki Umehata, Yuichi Matsuda, Naoki Yoshida, Mark A. Swinbank, Kotaro Kohno, Yoichi Tamura, Bunyo Hatsukade, Kouichiro Nakanishi, Yiping Ao, Tohru Nagao, Mariko Kubo, Tsutomu T. Takeuchi, Minju Lee, Takuma Izumi, Soh Ikarashi, Tohru Yamada

TL;DR

This study reexamines the ALMA ADF22 Cycle 2 detections that suggested high-z [CII] emitters by quantifying contamination and completeness with large-scale mock observations and source-injection experiments. By separating non-Gaussian noise, spectral smoothing effects, and technical factors, the authors show that the original >6σ candidates are likely spurious due to statistical fluctuations in a highly correlated data set. They develop a formal LF reconstruction method that corrects counts using parameterized contamination and completeness (Q and C), and apply it to estimate the z ~ 6 [CII] LF with a double power-law form whose amplitude evolves with redshift. The results imply that substantial corrections (up to an order of magnitude for certain luminosities) are needed to infer the intrinsic LF from blind ALMA surveys, with implications for the cosmic star-formation history and the design of future blind line surveys.

Abstract

The ADF22 line survey reported detections of two high-$z$ line-emitting source candidates above 6-$σ$, both of which were shown to be spurious after follow-up observations. We investigate the detectability of far-infrared emitters in ALMA deep fields using mock observations by injecting artificial line-emitting sources into the visibility planes. We also discuss our investigation, conducted together with the ALMA operations team, of a possible technical problem in the original observations. Finally, we devise a method to estimate the [CII] luminosity function (LF) at $z \sim 6$, including a full analysis of signal contamination and sample completeness. The comparison of pixel distributions between the real and mock datacubes does not show significant differences, confirming that the effect of non-Gaussian noise is negligible for the ADF22 datacube. Using 100 blank mock-mosaic datasets, we show 0.43 $\pm$ 0.67 false detections per datacube with the previous source-finding method. We argue that the underestimation of the contamination rate in the previous work is caused by the smaller number of datacubes, using only 4 real ADF22 datacubes. We compare the results of clump-finding between the time division mode and frequency division mode correlator datacubes and confirm that the velocity widths of the clumps in the TDM case are up to 3 times wider than in the FDM case. The LF estimation using our model shows that a correction for the number count is required, up to one order of magnitude, in the luminosity range of $\geq 5 \times 10^8 L_\odot$. Our reconstruction method for the line LF can be applied to future blind line surveys.

ALMA Deep Field in SSA22: Reconstructed [CII] Luminosity Function at z = 6

TL;DR

This study reexamines the ALMA ADF22 Cycle 2 detections that suggested high-z [CII] emitters by quantifying contamination and completeness with large-scale mock observations and source-injection experiments. By separating non-Gaussian noise, spectral smoothing effects, and technical factors, the authors show that the original >6σ candidates are likely spurious due to statistical fluctuations in a highly correlated data set. They develop a formal LF reconstruction method that corrects counts using parameterized contamination and completeness (Q and C), and apply it to estimate the z ~ 6 [CII] LF with a double power-law form whose amplitude evolves with redshift. The results imply that substantial corrections (up to an order of magnitude for certain luminosities) are needed to infer the intrinsic LF from blind ALMA surveys, with implications for the cosmic star-formation history and the design of future blind line surveys.

Abstract

The ADF22 line survey reported detections of two high- line-emitting source candidates above 6-, both of which were shown to be spurious after follow-up observations. We investigate the detectability of far-infrared emitters in ALMA deep fields using mock observations by injecting artificial line-emitting sources into the visibility planes. We also discuss our investigation, conducted together with the ALMA operations team, of a possible technical problem in the original observations. Finally, we devise a method to estimate the [CII] luminosity function (LF) at , including a full analysis of signal contamination and sample completeness. The comparison of pixel distributions between the real and mock datacubes does not show significant differences, confirming that the effect of non-Gaussian noise is negligible for the ADF22 datacube. Using 100 blank mock-mosaic datasets, we show 0.43 0.67 false detections per datacube with the previous source-finding method. We argue that the underestimation of the contamination rate in the previous work is caused by the smaller number of datacubes, using only 4 real ADF22 datacubes. We compare the results of clump-finding between the time division mode and frequency division mode correlator datacubes and confirm that the velocity widths of the clumps in the TDM case are up to 3 times wider than in the FDM case. The LF estimation using our model shows that a correction for the number count is required, up to one order of magnitude, in the luminosity range of . Our reconstruction method for the line LF can be applied to future blind line surveys.

Paper Structure

This paper contains 30 sections, 16 equations, 20 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Investigations of the Cycle 2 Data and Possible Explanations of the False Detections
  3. Statistical Fluctuation After Convolution
  4. Spectral Smoothing Process
  5. Non-Gaussian Noise
  6. Technical Problems
  7. The Mock Observations
  8. Replaced Data
  9. Simulated Data
  10. Artificial Sources
  11. Source Injection
  12. The Detection Methods
  13. Detection Classes
  14. The LF Reconstruction
  15. Results
  16. ...and 15 more sections

Figures (20)

  • Figure 1: The comparison of auto-correlation between TDM and FDM mode. The FDM observation shown in the right panel is binned from the frequency resolution of 1.129 MHz to 16.935 MHz so that the data have a comparable frequency, i.e., velocity resolution, to the TDM data. ALMA data exhibit auto-correlation on a scale of several frequency channels and angular resolutions, whereas the binned FDM data do not show correlation in the frequency/velocity domain (blue lines). Thus, ALMA data tend to have clumps on the scale of angular resolution and several channels, corresponding to a velocity width of $\sim$ 100 km s$^{-1}$. This implies that the datacube obtained with TDM has more clumps than the binned FDM datacube.
  • Figure 2: Appearance of an injected source. We inject a continuum emission as a point source with a peak flux of 1 Jy. The top panels show the result using 2dconvolve, which performs a 2-dimensional convolution process at the source location. The bottom panels show the result using cl.addcomponent or simobserve, which process the visibility domain. These two methods exhibit different tendencies in the pixel distribution.
  • Figure 3: Comparison of the RMS noise for simulated and original data as a function of frequency channel. The blue and red lines show different generation processes; original and replaced. All mock data sets successfully reproduce the RMS noise level.
  • Figure 4: An example of input positions of the artificial sources. The color indicates different primary beam (pb) values. The pb value increases from blue to red. We select the input so that there is no overlap for each of the sources.
  • Figure 5: (Top) An example of the contamination rate (solid line) and completeness (dashed line) as a function of peak SN ratio. The contamination rate is normalized and cumulative. The orange and purple lines represent small and large velocity widths (90 km s$^{-1}$ and 252 km s$^{-1}$ respectively) with corresponding smoothing values (5 channels smoothing and 14 channels smoothing). The numbers in parentheses show the parameters $a$ and $b$ used in Eqs. \ref{['eq:Qfit']} and \ref{['eq:Cfit']}. For the 90 km s$^{-1}$ case, $a_1 < a_2$, while for the 252 km s$^{-1}$ case, it's vice versa, meaning the larger velocity width achieves higher completeness. (Bottom) When the functions are combined using the SN ratio as a parameter, we see the detectability of the source is classified into three categories based on the inflection points. The threshold peak SN values are 3.9$\sigma$ and 4.5$\sigma$ for the 90 km s$^{-1}$ case and 3.5$\sigma$ and 4.2$\sigma$ for the 252 km s$^{-1}$ case, respectively.
  • ...and 15 more figures