11institutetext: Aix Marseille Univ, CNRS, CNES, LAM, Marseille 13388, France
22institutetext: National Astronomical Observatories, Chinese Academy of
Sciences, Beijing 100101, China 33institutetext: ARC Centre of Excellence for
All Sky Astrophysics in 3 Dimensions (ASTRO 3D), Australia 44institutetext:
Department of Physics, College of Sciences, Northeastern University, Shenyang
110819, China 55institutetext: School of Astronomy and Space Science,
University of Chinese Academy of Sciences, Beijing 100049, China
66institutetext: Institute of Astronomy and Astrophysics, Academia Sinica,
Astronomy-Mathematics Building, No. 1, Sec. 4, Roosevelt Road, Taipei 10617,
Taiwan 77institutetext: Canadian Institute for Theoretical Astrophysics,
University of Toronto, 60 Saint George Street, Toronto, ON M5S 3H8, Canada
88institutetext: Canadian Institute for Advanced Research, 180 Dundas St West,
Toronto, ON M5G 1Z8, Canada 99institutetext: Dunlap Institute for Astronomy
and Astrophysics, University of Toronto, 50 St George Street, Toronto, ON M5S
3H4, Canada 1010institutetext: Perimeter Institute of Theoretical Physics, 31
Caroline Street North, Waterloo, ON N2L 2Y5, Canada 1111institutetext:
Research Center for Intelligent Computing Platforms, Zhejiang Laboratory,
Hangzhou 311100, China

# Detections of 21-cm absorption with a blind FAST survey at z $\leqslant$
0.09

Wenkai Hu<EMAIL_ADDRESS>Yougang Wang<EMAIL_ADDRESS>Yichao Li 44
Yidong Xu 22 Wenxiu Yang 2255 Guilaine Lagache 11 Ue-Li Pen 667788991010 Zheng
Zheng 221111 Shuanghao Shu 2255 Yinghui Zheng 2255 Di Li 22551111 Tao-Chung
Ching 221111 Xuelei Chen<EMAIL_ADDRESS>
(Received November 24, 2022; accepted January 11, 2023)

We present the early science results from a blind search of the extragalactic
Hi 21-cm absorption lines at $z\leqslant 0.09$ with the drift-scan observation
of the Five-hundred-meter Aperture Spherical radio Telescope (FAST). We
carried out the search using the data collected in 643.8 hours by the ongoing
Commensal Radio Astronomy FasT Survey (CRAFTS), which spans a sky area of 3155
deg2 ($\sim$81 per cent of CRAFTS sky coverage up to January 2022) and covers
44827 radio sources with a flux density greater than 12 mJy. Due to the radio
frequency interference (RFI), only the relatively clean data in the frequency
range of 1.3–1.45 GHz are used in the present work. Under the assumption of
$T_{s}/c_{f}$ = 100 K, the total completeness-corrected comoving absorption
path length spanned by our data and sensitive to Damped Lyman $\alpha$
Absorbers (DLAs; $N_{\textsc{Hi\leavevmode\nobreak\ }}\geqslant 2\times
10^{20}\,{\rm cm}^{-2}$) are $\Delta X^{\mathrm{inv}}$ = 8.33$\times 10^{3}$
($\Delta z^{\mathrm{inv}}=7.81\times 10^{3}$) for intervening absorption. For
associated absorption, the corresponding values are $\Delta X^{\mathrm{asc}}$
= 1.28$\times 10^{1}$ ($\Delta z^{\mathrm{asc}}=1.19\times 10^{1}$). At each
time point of the drift scan, a matched-filtering approach is used to search
Hi absorbers. Three known Hi absorbers (UGC 00613, 3C 293 and 4C +27.14) and
two new Hi absorbers (towards the direction of NVSS J231240-052547 and NVSS
J053118+315412) are detected blindly. We fit the Hi profiles with multi-
components Gaussian functions and calculate the redshift (0.063, 0.066),
width, flux density, optical depth and Hi column densities for each
absorption. Our results demonstrate the power of FAST in blindly searching Hi
absorbers. For absorption towards NVSS J231240-052547, the optical
counterparts are faint and currently lack existing spectra. The most likely
interpretation is that a radio-loud active galactic nucleus (AGN) is faint in
the optical as the background source, with a faint optical absorber in
between. NVSS J053118+315412 exhibits an associated absorption with a complex
profile, which may suggest unsettled gas structures or gas accretion onto the
supermassive black hole (SMBH). The expanding collection of blind radio
detections in the ongoing CRAFTS survey offers a valuable opportunity to study
AGN and associated interstellar medium (ISM) interaction, and intervening
absorbers optically without overwhelming quasi-stellar object (QSO) background
light.

###### Key Words.:

Methods: observational, Methods: data analysis, Radio lines: galaxies, Radio
continuum: galaxies, Line: identification, Line: profiles, (Galaxies:)
quasars: absorption lines

##  1 Introduction

Hydrogen is the most abundant and widely distributed element in the Universe.
The 21-cm hyperfine transition of neutral hydrogen (Hi ) has been used as an
important tool to study a wide range of astrophysical processes, including
galaxy dynamics, galaxy mergers and galaxy interaction, star formation
history, as well as tracing the cosmic large-scale structure (Chang et al.,
2008).

Substantial effort has been dedicated to measuring the Hi  emission line, e.g.
the Hi Parkes All Sky Survey (HIPASS) (Zwaan et al., 2004; Meyer et al.,
2004), and the Arecibo Legacy Fast Arecibo L-Band Feed Array (ALFALFA) survey
(Giovanelli et al., 2005, 2007; Saintonge, 2007), and the Jansky Very Large
Array (JVLA) deep survey (Jarvis et al., 2014). However, due to the limited
sensitivity of the telescopes, wide-field Hi emission survey has been limited
to the local Universe, while individual 21-cm deep field surveys have only
detected Hi galaxies up to $z\approx 0.3$ (Catinella et al., 2008; Zwaan et
al., 2001; Verheijen et al., 2007; Fernández et al., 2016). Combined with the
observations of damped DLAs at high-z, the Hi mass density
($\Omega_{\textsc{Hi\leavevmode\nobreak\ }}$) of the Universe is well-
constrained at z ¡ 0.2 and 2 ¡ z ¡ 5, with the Hi content poorly constrained
at $0.2<z<2$ (c.f. Hu et al. 2019 and references therein).

The Hi 21-cm absorption lines, arising from Hi gas absorbing the flux of the
bright background source, could be a complement to the observation of the Hi
emission at higher redshifts. Unlike Hi flux in emission which is flux-
limited, the detectability of the Hi absorption depends only on the column
density of foreground gas and the strength of the background sources. Hi
absorption may be a good alternative tool to measure the Hi content and
constrain the redshift-evolution of $\Omega_{\textsc{Hi\leavevmode\nobreak\
}}$ at intermediate redshifts $0.2<z<2$ (Morganti & Oosterloo, 2018; Grasha et
al., 2020).

Two types of Hi absorption systems exist, with one being the associated
absorption system where the absorbing gas is situated in the same
extragalactic object that emits the background bright continuum. Studies of
associated absorption systems typically concentrate on the extragalactic
object (usually an AGN) and its interaction with the ISM within the same
object. This includes exploring the kinematics and structure of the ISM in
galaxies that host AGNs and investigating the potential mechanisms by which Hi
gas fuels supermassive black holes.

Significant progress has been made in associated absorption studies in the
past two decades (see Morganti & Oosterloo 2018 for a review). Some physical
pictures have been established and revealed by observations, including the
detection of circumnuclear absorbing structures containing Hi (Taylor, 1996;
Struve & Conway, 2010), the identification of Hi outflows potentially driven
by the jet (Morganti et al., 2003; Schulz et al., 2021) and the indication of
fuelling of SMBH through the accretion of small gas clouds (Araya et al.,
2010; Maccagni et al., 2014). Although many discoveries have been made, the
statistics are still limited by small sample sizes, and there is a lack of
conclusive observational evidence for Hi playing a role in fuelling the
central SMBH. To further the understanding of Hi associated absorption, a
larger and more diverse sample from different physical environments is
necessary.

The other type of Hi absorption system is referred to as the intervening
absorption system that results from gas in a foreground Galactic or
extragalactic object absorbing the flux of a bright background source that is
not related. The intervening absorptions are usually employed to investigate
the ISM characteristics in both our Galaxy and distant galaxies. A major
fraction of the neutral hydrogen of the post-reionization universe has been
found in DLAs, which are found in the optical spectrum of QSO as strong Hi
absorption lines with $N_{\textsc{Hi\leavevmode\nobreak\ }}\geqslant 2\times
10^{20}\,{\rm cm}^{-2}$ (Wolfe et al., 2005). Despite numerous studies, the
physical nature of the DLAs remains an unsolved problem (for recent work, see
e.g. Bordoloi et al. 2022). The QSOs used for such search are usually bright,
making it difficult to observe the optical emission from the DLA system
itself, in analogy to the practical challenge of detecting planets in
reflected light. Besides, the optical surveys have additional biases from dust
extinction, which could be systematically correlated to the self-shielding
required for the existence of DLAs, to the gravitational magnification bias.

Most radio-loud QSOs are optically faint, opening the possibility of
uncovering a sample of absorption systems without blinding the optical
background. To our knowledge, only two 21cm absorbers (towards UGC 6081 and 3C
286) have been discovered in untargeted blind radio searches. Absorber in UGC
6081 is an associated system (Darling et al., 2011) and 3C 286 is a bright
optical QSO (Brown & Roberts, 1973). Only 18 21cm absorbers have been
discovered in bright radio sources targeted blind radio searches (Darling et
al., 2004; Allison et al., 2015, 2020; Grasha et al., 2020; Sadler et al.,
2020; Gupta et al., 2021a, b; Mahony et al., 2022). Of these, 16 still had a
bright optical QSO, one had a radio background with unknown type (Allison et
al., 2020) and one had powerful radio galaxy (PKS 0409-75) with 3000 $\,{\rm
km\,s^{-1}}$and should be considered an associated absorber (Mahony et al.,
2022).

Blind radio searches offer the opportunity to detect DLAs in front of
optically faint QSOs, enabling a detailed study of DLA properties without
interference from a bright background source. A rare opportunity was the
observation of the afterglow of GRB030323, which showed both a DLA and Lyman
$\alpha$ emission (Vreeswijk, P. M. et al., 2004) in the gamma-ray burst (GRB)
host galaxy. However, at present, the number of DLAs detected from GRB
afterglow is still very few.

To achieve sufficient sensitivity, detecting the relatively weak 21-cm
absorption technically requires a long integration time, and the observation
is also affected by technical limitations such as unstable bandpass and RFI.
Known that the compact sources have the higher rate of Hi absorption detection
(Emonts et al., 2010; Chandola et al., 2011) and the majority of DLAs show
strong MgII absorption, most Hi absorption searches have been pointed at
selected targets with these features. However, these pre-selection methods
could introduce biases in studying the intrinsic physics of Hi absorptions,
which have not been well-understood.

An unbiased radio survey would address the DLA question directly, help
overcome these limitations and also produce a more comprehensive depiction of
the interaction between the ISM and host galaxy. Darling et al. (2011) carried
out a pilot search of Hi 21-cm absorption spanning -650 $\,{\rm km\,s^{-1}}$¡
cz ¡ 17,500 $\,{\rm km\,s^{-1}}$and covering 517.0 deg2 with the ALFALFA
Survey. The intrinsic absorption of UGC 6081 was re-detected, but no new
absorption line systems were detected. Allison et al. (2020) reported a
spectroscopically blind search for 21-cm absorption lines in the First Large
Absorption Survey in Hi (FLASH (Allison et al., 2022)) using the Australian
Square Kilometre Array Pathfinder (ASKAP). No absorptions were found in a
purely blind search in the GAMA 23 field. Still, a 21-cm absorption at
$z=0.3562$ towards NVSS J224500-343030 was detected after cross-matching the
radio sources with optical spectroscopic identifications of galaxies. Besides,
Su et al. (2022) presented the results of a search for 21 cm Hi absorption
from three Galaxy And Mass Assembly (GAMA) survey fields. Two associated Hi
absorption systems in SDSS J090331+010847 and SDSS J113622+004852 are detected
from a sample of 326 radio sources with 855.5 MHz peak flux density over 10
mJy. Recently, Gupta et al. (2021b) developed the Automated Radio Telescope
Imaging Pipeline (ARTIP), which is designed to process large volumes of radio
interferometric data from the MeerKAT Absorption Line Survey (MALS). Applying
this pipeline to the observations of a field centred on PKS 1830-211, they re-
detected the known Hi 21-cm absorption at z = 0.19, and OH 1665 and 1667 MHz
absorption at z = 0.89 using MeerKat L-band (Gupta et al., 2021b) and UHF-
bands (Combes et al., 2021).

In the not-too-distant future, an unbiased census of intrinsic Hi absorption
could be established by large blind Hi absorption line surveys planned with
the next-generation telescopes, i.e. the Square Kilometre Array or its
pathfinders, including the MeerKAT Absorption Line Survey (MALS; Gupta et al.
2018), the Widefield ASKAP L-band Legacy All-sky Blind surveY (WALLABY;
Koribalski et al. 2020), the First Large Absorption Survey in Hi (FLASH;
Allison et al. 2020), and the Search for Hi Absorption with AperTIF (SHARP;
Maccagni et al. 2017).

As a complement in the northern hemisphere, the FAST (Nan et al., 2011; Jiang
et al., 2020) can play an important role in blind survey of Hi absorption.
FAST is the largest filled-aperture single-dish radio antenna in the world,
with high sensitivity and large sky coverage. Equipped with 19-beams L-band
receiver, covering a wide band from 1050 MHz to 1450 MHz (Smith et al., 2017;
Jiang et al., 2020), corresponding to redshift $0<z<0.35$ for Hi observations,
FAST can effectively search for Hi absorption lines in the above redshift
range. According to the forecast provided by Yu et al. (2017), FAST should be
able to detect $\sim$ 200 Hi absorption systems, including associated and
intervening systems, in a one-month survey around the celestial equator. Zhang
et al. (2021) presented a study of extragalactic Hi 21-cm absorption lines
using FAST. They observed 5 Hi absorption systems which were previously
identified in the 40$\%$ data release of the ALFALFA survey. The Hi absorption
profiles given by FAST have much higher spectral resolution and higher
$\mathrm{S/N}$ ratio than obtained in the previous searches, demonstrating the
power of FAST in revealing detailed structures of Hi absorption lines. Also,
Zheng et al. (2020) carried out an OH absorption survey towards 8 associated
and 1 intervening Hi absorbers at redshifts z $\in$ [0.1919, 0.2241] using
FAST and constrained the OH to Hi relative abundance ([OH]/[HI]) to be
$\leqslant$ 5.45 $\times 10^{-8}$.

In this paper, we report the early science results from a purely blind search
for Hi absorption lines at $z\leqslant$0.09 in $\sim 81$ per cent (643.8 hours
and 3155 deg2) of the sky covered by the CRAFTS survey up to January 2022.
Three known Hi absorbers (UGC 00613, 3C 293 and 4C +27.14) and two new Hi
absorbers (NVSS J231240-052547 and NVSS J053118+315412) are found using our
search pipeline. The signal of 4C +27.14 has also been re-detected in follow-
up observations with FAST.

This paper is organized as follows: Section 2 describes the CRAFTS data and
the follow-up observation used in this work. We then summarize the data
processing procedure, including candidate searching by the matched-filtering
approach, candidates selection methods and Hi absorption measuring method in
Section 3. The 10 candidates selected from the CRAFTS data and the confirmed
Hi absorbers are presented in Section 4. We discuss the implications of our
methods for the blind Hi absorption survey in the future in Section 5. In
Section 6, a summary of this work is presented. Throughout this paper we
assume H${}_{0}=70$ km s-1 Mpc-1, $\Omega_{\rm m}=0.3$ and
$\Omega_{\Lambda}=0.7$, but the results are not sensitive to these parameters.

##  2 Data

###  2.1 CRAFTS

Figure 1: The CRAFTS sky coverage in Equatorial coordinates, as up to January
7th, 2022. We have carried out our search in the orange regions, and the
orange and blue regions have been surveyed with CRAFTS. The zenith angle of
40° (maximum zenith angle for FAST) and 26.4° (zenith angle within which FAST
has full gain) are shown as black circles and red circles, respectively.

The Commensal Radio Astronomy FasT Survey (CRAFTS; Li et al. 2018) is a multi-
purpose drift-scan survey using the FAST L-band Array of 19 feed-horns (FLAN,
Dunning et al. 2017), which aims to observe the galactic and extragalactic Hi
emission and to search for pulsars and radio transients. According to the
CRAFTS plan, the survey region will be observed by two passes of drift scans,
with the 19-beam feed rotated by 23.4° to achieve a super-Nyquist sampling of
the surveyed area. The full survey will cover over 20000 deg2 within a
declination (DEC) range between $-14^{\circ}$ and $66^{\circ}$, and reach a
redshift of 0.35. Limited by the allocated time, there is only one survey pass
at present.

In Figure 1, we show the CRAFTS sky coverage up to 2022-01-07. Data have been
taken for both the orange and blue regions, while the orange regions have been
used for Hi absorption search in the present work, which is $\sim$81% of the
total surveyed region.

The raw CRAFTS data set has a time resolution of 0.2 s, and a frequency
resolution of 7.63 kHz ($\sim 1.61$ km s-1 at $z=0$), covering a frequency
range from 1000 MHz to 1500 MHz. The receiver response drops at the two ends
of the frequency band, so only the data in the frequency range of 1.05–1.45
GHz is utilized. Additionally, in consideration of our scientific objectives
and computing capacity, we further re-bin the data into a frequency resolution
of 15.26 kHz and a time resolution of 12$/\cos\delta_{\rm{dec}}$ s ($\sim$ the
transit time in drift scan), where $\delta_{\rm{dec}}$ is the declination of
the pointing. The instantaneous sensitivity of each beam of the FAST system
will be 2.15 mJy beam-1, assuming a bandwidth of $\Delta\nu$ = 15.26 kHz, and
12 s integration time per beam (Hu et al., 2020). According to the calculation
presented in Section 3.2, a velocity-integrated signal-to-noise ratio
($(\mathrm{S/N})_{\rm{int}}$) of $\sim$ 12 corresponds to the 90% completeness
limit. Considering the expected final RMS noise of 2.15 mJy beam-1 and
assuming source coverage of 100 per cent, a source with a flux density greater
than 12 mJy is sufficient to detect Hi absorption with a peak signal-to-noise
ratio ($(\mathrm{S/N})_{\rm{peak}}$) better than 5.5 (corresponding to a
velocity-integrated signal-to-noise ratio ($(\mathrm{S/N})_{\rm{int}}$) of
$\sim$ 12, for the Gaussian narrow line template with a full width at half
maximum (FWHM) of 30 $\,{\rm km\,s^{-1}}$and the frequency resolution of 15.26
kHz). According to the NRAO VLA Sky Survey (NVSS) (Condon et al., 1998)
Catalogue, whose completeness limit is about 2.5 mJy, 44827 radio sources with
a flux density greater than 12 mJy are covered in our search region.

Figure 2 shows a sample of the raw time-averaged frequency spectra of the
CRAFTS data for the 19 beams, each with one curve. RFI dominates the frequency
range from 1.15 GHz to 1.3 GHz (green shaded region in Figure 2). In the range
of 1.05 GHz to 1.15 GHz (yellow shaded region in Figure 2), there are also
many smaller peaks due to chronically present RFI (Hu et al., 2021).
Considering the data quality, the data in the frequency range of 1.3 GHz to
1.45 GHz (blue shaded region in Figure 2) which is relatively clean, is used
in the present study. We are also searching the Hi absorption in the range of
1.05 GHz to 1.15 GHz, this will be presented in the future. The peaks at 1420
MHz are from the Galactic neutral hydrogen.

As an example, in Figure 3, we show the waterfall plot of the raw data of feed
1 from the observation on February 13th 2020, which scanned a stripe at the
Declination of +27d15m0.0s. The horizontal linear features at some frequency
points are chronically RFI.

Figure 2: The raw frequency spectra for the 19 feeds of the FAST L-band multi-
beam receiver feeds. These spectra are obtained by taking the time average of
the raw data throughout the whole time of observation. The XX and YY
polarizations are shown in the top and bottom panels, respectively.

Figure 3: The waterfall plot of the raw data for feed 1 of the FAST L-band
multi-beam receiver feeds. The two polarizations are shown in the top and
bottom subpanels, respectively.

###  2.2 Follow-up Observation

In the blind searching in CRAFTS data (described in the next section), 10
candidates, including 3 previously known Hi absorption systems (UGC 00613, 3C
293 and 4C +27.14) are detected. Two known absorbers (UGC 00613 and 3C 293)
and all new absorption systems are further confirmed by the CRAFTS data of
several neighbouring beams with a high signal-to-noise ratio (see Section 3.4
and Section 4). In order to confirm the signal of the candidates and obtain a
more significant Hi absorption feature for 4C +27.14, we also made a follow-up
observation with FAST. It was carried out at night from 18:55:00 UTC to
23:17:00 UTC on 2021-08-21.

To suppress the fluctuations in the bandpass and remove the sky signal, the
follow-up observation used the ON-OFF tracking mode. The integration time for
both source-on and source-off observations is 990 s. The cycle of 330s source-
on followed by 330 s source-off observation is repeated 3 times for a target.
The follow-up data set has a time resolution of 1 s, and a frequency
resolution of 7.63 kHz, covering the frequency from 1000 MHz to 1500 MHz.
Under the condition that the frequency resolution is 7.63 kHz and the
integration time is 990 s, the spectral RMS of 0.33 mJy can be obtained. The
source 3C 48 was also observed for flux calibration.

##  3 Analysis

To begin, we extract spectra at each time point from the data cubes. We
process the XX and YY spectra separately to search for Hi absorption and
combine them to create the final spectra if selected as candidates. For each
XX and YY polarization, we mask the RFI and obtain the band baseline by
smoothing with a low-pass filter using the medfilt function (Van Rossum &
Drake Jr, 1995; Virtanen et al., 2020). The median filter window size is set
to 0.65 MHz, carefully selected to be smaller than the chronically present RFI
and bandpass fluctuations yet larger than the typical size of Hi absorption
profiles.

Note that we flag only strong RFI ($\geqslant 5\sigma$) in our data. This is
because some true Hi absorbers may reside in the location of chronically
present RFI. Furthermore, the spurious candidates produced by RFI will be
excluded later in our blind search pipeline.

We then search for the Hi absorbers blindly by cross-correlating the flux
spectrum with templates. This matched-filtering approach was developed for
identifying emission signals in the Arecibo Legacy Fast ALFA survey
(Saintonge, 2007) and is more sensitive and faster than the usual peak-finding
algorithms. Here, we provide a brief summary of the key steps. Spectra at each
time point were extracted from the data cubes. After the removal of the
baseline of the bandpass, the matched-filtering approach was applied to find
the absorption profiles. The final candidates are selected by use of the
transit information recorded by the 19-beams of FAST.

###  3.1 Searching Algorithms

The matched filter is applied to the bandpass baseline-removed data. The
signal $g(x)$ is assumed to be represented as:

$\displaystyle g(x)\simeq\alpha t(x-\mu;\sigma),$ (1)

where $t$ is a template function over frequency channel $x$, $\alpha$, $\mu$
and $\sigma$ are the amplitude, the central position and the width,
respectively. The Gaussian function with negative amplitude is used as the
template,

$\displaystyle t(x)$ $\displaystyle=$
$\displaystyle-\exp(-\frac{(x-\mu)^{2}}{2\sigma^{2}}).$ (2)

The best-fit template is found by minimising the $\chi^{2}$:

$\displaystyle\chi^{2}=\sum_{x=1}^{N_{\rm f}}[\alpha
t(x-\mu;\sigma)-g(x)]^{2},$ (3)

where $N_{\rm f}$ is the number of the spectral channel. Expanding the
$\chi^{2}$ gives:

$\displaystyle\chi^{2}=\alpha^{2}N_{\rm f}\sigma_{\rm t}^{2}+N_{\rm
f}\sigma_{\rm g}^{2}-2\alpha N_{\rm f}\sigma_{\rm g}\sigma_{\rm t}c(\mu),$ (4)

where $\sigma_{\rm g}^{2}$ and $\sigma_{\rm t}^{2}$ are the variance of the
signal and the template, $c(x)$ is the normalized cross-correlation function:

$\displaystyle c(x)=g(x)*t(x-\mu;\sigma)=\frac{1}{N_{\rm f}\sigma_{\rm
g}\sigma_{\rm t}}\sum_{n}[g(n)t(n-x)].$ (5)

Minimizing the $\chi^{2}$ with respect to $\alpha$ gives:

$\displaystyle\alpha=\frac{\sigma_{\rm g}}{\sigma_{\rm t}}c(\mu).$ (6)

Replacing the $\alpha$ in $\chi^{2}$ using Eq. (6), we have:

$\displaystyle\chi^{2}=N_{\rm f}\sigma_{\rm g}^{2}[1-c(\mu)^{2}],$ (7)

$\chi^{2}$ is minimized by maximizing the value of the cross-correlation
between the observational data and the template.

The template is parameterized by the peak amplitude $\alpha_{\rm max}$, the
central channel position $\mu_{\rm max}$ and the width $\sigma_{\rm max}$. In
realistic data processing, the best fit parameters ($\alpha$, $\mu$ and
$\sigma$) which minimize the $\chi^{2}$ are obtained as follows:

  1. 1.

Generating a set of templates covering a physical range (from 3.22 $\,{\rm
km\,s^{-1}}$to 325.22 $\,{\rm km\,s^{-1}}$with an increment of 0.322$\,{\rm
km\,s^{-1}}$, the range is selected to ensure comprehensive coverage of all
detected absorptions in terms of their width (Geréb et al., 2015)) of width
$\sigma$;

  2. 2.

Calculating the convolution function $c(x)$ for each template;

  3. 3.

For each convolution function, obtain $\mu_{\rm max}$ by finding the spectral
channel at which $c(x)$ is maximized;

  4. 4.

For these values of $c(\mu_{\rm max})$ from templates with different $\sigma$,
obtaining the $\sigma_{\rm max}$ by finding the largest value of $c(\mu_{\rm
max})$;

  5. 5.

Obtaining the peak amplitude $\alpha_{\rm max}$ using Eq. (6).

The velocity-integrated signal-to-noise ratio of the absorption profile can be
calculated following Saintonge (2007) :

$\displaystyle\mathrm{S/N}=\begin{cases}\frac{F_{\rm{int}}/W}{\sigma_{\mathrm{rms}}}\times\left(\frac{W/2}{dv}\right)^{1/2}&\text{W
< 400 $\,{\rm km\,s^{-1}}$}\\\
\frac{F_{\rm{int}}/W}{\sigma_{\mathrm{rms}}}\times\left(\frac{400/2}{dv}\right)^{1/2}&\text{W
$\geqslant$ 400 $\,{\rm km\,s^{-1}}$,}\\\ \end{cases}$ (8)

where $F_{\rm{int}}$ is the velocity-integrated flux, $\sigma_{\mathrm{rms}}$
is the RMS noise, $W$ is the width of the signal in $\,{\rm km\,s^{-1}}$and
$dv$ is the velocity resolution. For the rest of the content, all signal-to-
noise ratios are velocity-integrated unless stated otherwise.

The Hi absorption signal is searched in both the XX and YY polarizations of
each beam. Only those candidates with a total $\mathrm{S/N}$ $>5.5$ and can be
found at nearly the same frequency ($\Delta\nu<0.05$MHz) with
$\mathrm{S/N}>3.5$ in both XX and YY polarizations are selected.

###  3.2 Completeness

The absorption signal may be diluted either due to the presence of emission
(Maina et al., 2022) at low redshift or poor baseline subtraction as a result
of fluctuations of the bandpass. In order to quantify how this affects our Hi
absorption search, we estimate completeness by adding 1.67$\times 10^{8}$ mock
absorption lines to real spectra and calculating the fraction detected using
our search method and selection threshold. The mock absorption signals are
simulated using a Gaussian function template. The peak flux of mock absorption
($F_{\rm{peak}}$) is calculated using Eq. (8) and
$F_{\rm{int}}=\sigma_{\rm{abs}}\sqrt{2\pi}F_{\rm{peak}}$, where
$\sigma_{\rm{abs}}$ refers to the standard deviation of the Gaussian template
for absorption signals.

In Figure 4, we show the estimated completeness of mock absorption profiles
under different conditions, including velocity widths FWHM of 15 $\,{\rm
km\,s^{-1}}$, 30 $\,{\rm km\,s^{-1}}$, and 60 $\,{\rm km\,s^{-1}}$, as well as
velocity-integrated $\mathrm{S/N}$ of 5.5 (the threshold we used for search in
real data) and 12. For a fixed velocity-integrated sensitivity, narrower lines
are more complete compared to broader lines, as the latter is more susceptible
to being diluted by bandpass fluctuations. Recognizing that the sensitivity is
affected by the selection of velocity width, we have chosen a value of FWHM =
30 $\,{\rm km\,s^{-1}}$, which corresponds to the mean velocity width for all
intervening 21-cm detected absorbers (Curran et al., 2016; Allison et al.,
2016). Figure 5 shows the average completeness for mock absorption with
velocity width of FWHM = 30 $\,{\rm km\,s^{-1}}$ and velocity-integrated
$\mathrm{S/N}$ ranging from 5.5 to 33.0 at frequency 1.30 - 1.42 GHz.
Frequency-dependent structures exhibited in the completeness result from the
chronically present RFI at specific frequencies (as shown in Figure 3). As
expected, our search is less complete for absorption with lower
$\mathrm{S/N}$. As shown in Figure 5, the velocity-integrated $\mathrm{S/N}$
cut of $\sim$ 12 corresponds to the estimate of the 90$\%$ completeness limit.
As a consequence, the signal-to-noise ratio of 12 is adopted in the comoving
absorption path calculation in Section 5.4.

Figure 4: The estimated completeness of mock absorption for various
combinations of parameters, including velocity widths of 15 $\,{\rm
km\,s^{-1}}$ (blue), 30 $\,{\rm km\,s^{-1}}$ (green), and 60 $\,{\rm
km\,s^{-1}}$ (red), as well as velocity-integrated $\mathrm{S/N}$ of 5.5
(dashed lines) and 12 (solid lines). Figure 5: The estimated completeness for
mock absorption with velocity-integrated $\mathrm{S/N}$ ranges from 5.5 to
33.0 at frequencies 1.30 - 1.42 GHz.

###  3.3 Standing Waves

However, even with the threshold shown in Section 3.1, tens of thousands of
candidates have passed this screening. Nearly all of the spurious candidates
originate from the fluctuations of the bandpass and chronically present RFI.
The instability of the bandpass, which is mainly the result of standing waves,
makes it difficult to remove the bandpass baseline accurately and find the
true absorption signals. Most of these are excluded by using the multi-beam
information in the drift scans, but the variation of the bandpass can be a
severe source of error in such searches.

In the Hi absorption feature search above, we ran our pipeline with the raw
data before bandpass calibration. We have also tried to carry out the analysis
of the bandpass-calibrated data. The built-in noise diode of the FAST receiver
is used as a real-time calibrator to estimate the bandpass variations. For
CRAFTS high-cadence calibration mode, the noise diode is injected for
$81.92\,{\rm\mu s}$ in every $196.608\,{\rm\mu s}$, with an amplitude of $\sim
1\,$K, which is a small fraction of the system temperature ( $\sim 20\,$K).
Data with or without noise collected by the pulsar backend are averaged for
every $0.2\,$s (equals to the sampling time of the spectral line backend)
respectively, and their difference can be converted to spectrum backend units,
relying on the fact that the bandpass shape and system temperature are
determined mostly by the front end, and the two backends produce similar
bandpasses. The 30-minutes averaged noise spectra are used to calibrate the
variations of the bandpass. We then carry out the same analysis using the
calibrated data. However, the final result is not affected much. To ensure no
absorption is left out because of the imperfect baseline fitting (due to the
presence of standing waves), we also tried a smaller median filter window size
(0.45 MHz) and lower $\mathrm{S/N}$ threshold (4 $\sigma$). We find that it
has little effect on the final candidate samples after multi-beam cross-
correlation selection.

The results show that our calibration can only correct the variations over
large frequency scales ($\Delta\nu>10\,{\rm MHz}$), the fluctuations at small
frequency scales ($\Delta\nu\sim 1$ MHz) remain unimproved, and it is the
small-scale fluctuations which generate the spurious signals. The precision of
the calibration procedure is therefore limited, due to noise or fluctuations
in the noise-diode signal. So further selection methods are needed to screen
for spurious candidates.

###  3.4 Candidates Selection

Figure 2 and Figure 3 demonstrate the chronically present RFI and features
produced by standing waves, which presents a challenge in accurately modelling
the bandpass baseline and results in numerous false candidates. It is not
feasible to determine the authenticity of a candidate using only one scan.
However, with the drift-scan strategy and multi-beam system data, it becomes
possible to differentiate the genuine Hi absorption signal from the spurious
signal.

In CRAFTS, the feed array is rotated by 23.4 degrees to achieve super-Nyquist
sampling. Perpendicular to the scanning direction, the spacing between the
inner 17 beams is less than half FWHM. During the drift scan, the true Hi
absorber will be scanned by multiple beams distributed along the scanning
path, resulting in detection in different beams but the same sky location. In
contrast, the spurious signals caused by RFI may appear in data from multiple
beams, but do not necessarily originate from the same location in the sky. On
the other hand, the transit time for each beam in drift scan is $\sim$
12$/\cos\theta_{\rm{za}}$ seconds. In the drift-scan data with a time
resolution of 12$/\cos\theta_{\rm{za}}$ seconds, the true signal can be
detected in $<3$ continuous time points (corresponding to 9 $\,{\rm arcmin}$
in size, a conservative estimate of the angular size of extragalactic radio
source), while the spurious signals can be detected in $\geqslant 5$
continuous or discontinuous time points.

We apply our selection pipeline to the preliminary Hi absorption candidates
that passed the matched-filtering search:

  1. 1.

Excluding the candidates if they can be detected at the same time point in
more than 5 beams that are far apart,

  2. 2.

Excluding the candidates if they can be detected in more than 6 continuous or
discontinuous time points in the data from every single beam,

  3. 3.

Giving priority to the candidates in the remaining catalogue if they can be
detected in more than one beams which distribute along the direction of the
scanning.

  4. 4.

Checking the candidates survived after step 1 and step 2 by eye and comparing
automated candidates from step 3 with the visual candidates.

We take the known Hi absorption system UGC 00613 as an example of how our
candidate selection pipeline works. Using the Matched-Filtering Approach, the
absorption profile of UGC 00613 can be detected in the data from Beam 10, Beam
4 and Beam 13, respectively. In Figure 6, we show the raw spectra (left
column) and baseline-removed spectra (right column) from Beam 10, Beam 4 and
Beam 13. A high emission peak is beside the absorption profile, which arises
from the chronically present RFI. Even though contaminated by the RFI, all
detections have significant $\mathrm{S/N}$ (larger than 12). These 3 beams are
horizontal along the scanning direction, as shown in Figure 7. Besides, no
other distant beam has detection of this feature. These show that the
absorption profile we detected is a true signal, not one from RFI or bandpass
variation.

Figure 6: The spectra extracted from different beams at the pointing position
closest to UGC 00613. Left: The spectra of the (previously known) Hi
absorption system UGC 00613. The top, middle and bottom sub-panels show the
detection from Beam 10, Beam 4 and Beam 13, respectively. The left column
shows the raw data, and the right column shows the baseline removed data. The
red-solid lines in the left column indicate the baselines estimated using
medfilt. The red-solid lines in the right column depict the best template
modelling the Hi absorption profile. The vertical orange-dashed lines show the
central channel position of the template. The $\mathrm{S/N}$ of the absorption
profiles are given as the title of the sub-figures in the right column. Right:
Same as the left sub-panels, but for neighbouring Beam 3, Beam 11 and Beam 14,
there is no precise detection. The vertical orange-dashed lines refer to the
frequency position of UGC 00613.  Figure 7: The distribution of the beams from
which the Hi absorption system UGC 00613 was detected. The known Hi absorption
system UGC 00613 can be detected in the data of Beam 10, Beam 4 and Beam 13,
which are labelled with orange. These 3 beams distribute in a horizontal line
along the scanning direction. The 19 beams have been rotated by 23.4°.

In our data analysis, using criteria (i) and (ii) alone can exclude 73$\%$ and
89$\%$ of the spurious detections, respectively, and combining the spatial and
time information together makes our method more effective. From the results,
all the excluded candidates are produced by the RFI and standing waves. No
true signals are diagnosed as spurious in either criterion (i) or (ii). Using
the selection method described above, we excluded most spurious detections
($\sim$ 140,000 cases), and 3 known, 2 new Hi absorption systems and 5
unverified candidates survived.

###  3.5 Hi Absorption Measurement

According to the radiative transfer theory, the observed signal ($T_{\rm
b}(\nu)$) of an Hi source which is partially covering a background continuum
source can be described as (Morganti & Oosterloo, 2018):

$\displaystyle T_{\rm b}(\nu)=c_{\rm f}T_{\rm c}e^{-\tau(\nu)}+(1-c_{\rm
f})T_{\rm c}+T_{\rm s}(1-e^{-\tau(\nu)}),$ (9)

where $c_{\rm f}$ is the covering factor which is the fraction of the
background source covered by foreground gas clouds, as seen from the centre.
$\tau(\nu)$ and $T_{\rm s}$ are the optical depth and spin temperature of the
Hi source respectively, and $T_{\rm c}$ is the brightness temperature of the
background continuum source. In Eq. (9), the first term denotes the absorbed
emission from the continuum source, the second term is the emission from the
part of the continuum source not covered by the cloud, and the last term
describes self-absorbed 21-cm line emission from the Hi source.

The difference between the $T_{\rm b}(\nu)$ and $T_{\rm c}$ is then:

$\displaystyle\Delta T(\nu)=T_{\rm b}(\nu)-T_{\rm c}=(T_{\rm s}-c_{\rm
f}T_{\rm c})(1-e^{-\tau(\nu)}).$ (10)

If $T_{\rm s}$ ¿ $c_{\rm f}T_{\rm c}$, the spectral line will be seen in
emission, while if $T_{\rm s}$ ¡ $c_{\rm f}T_{\rm c}$, the absorption
dominates. For most Hi absorption observations, $T_{\rm s}\ll c_{\rm f}T_{\rm
c}$, then $\Delta T(\nu)=-c_{\rm f}T_{\rm c}(1-e^{-\tau(\nu)})$. After
converting the frequency ($\nu$) to velocity (V), the optical depth can be
expressed as :

$\displaystyle\tau(V)\approx-\mathrm{ln}(1+\Delta T(V)/(c_{\rm f}T_{\rm c})),$
(11)

in the limit $T_{\rm s}\ll c_{\rm f}T_{\rm c}$, where $T_{\rm c}$ can be
deduced from the line-free parts of the spectrum or the other database. In
this work, we use the $T_{\rm c}$ from the NASA/IPAC Extragalactic
Database111https://ned.ipac.caltech.edu (NED).

The optical depth $\tau$ is proportional to $N_{\textsc{Hi\leavevmode\nobreak\
}}/T_{\rm s}$, the Hi column density is given by

$\displaystyle N_{\textsc{Hi\leavevmode\nobreak\
}}[\mathrm{cm^{-2}}]=1.82\times 10^{18}T_{\rm
s}[\mathrm{K}]\int\tau(V)dV[\mathrm{km\,s^{-1}}].$ (12)

Throughout this paper we take the assumption that $c_{\rm f}=1$ (Maccagni et
al., 2017) for the calculation of $\tau$ and
$N_{\textsc{Hi\leavevmode\nobreak\ }}$.

##  4 Results

By utilizing the matched filter and multi-beam candidate selection pipeline on
the collected data, we have identified a total of 10 candidates, among which
are three that have been previously detected: UGC 00613 (Zhang et al., 2021),
3C 293(Baan & Haschick, 1981; Beswick et al., 2004b) and 4C
+27.14(Stanimirović et al., 2014). The spectra of these 10 candidates are
shown in Figure 8. All spectra have been corrected for the Doppler shift
induced by the Earth’s revolution. The high peaks besides the absorption
profile (Candidate 5, UGC 00613 and NVSS J231240-052547, for example) are the
chronically present RFI. As shown in Figure 8, the baseline fit in some cases
is not good enough. Although the median filter window size is carefully
determined, it cannot always provide a perfect estimation of the baseline,
especially when factors such as RFI, standing waves (Candidate 4 in Figure 8
for example), or broad absorption lines (3C 293 in Figure 8 for example)
exist. To improve the results, we also tested a smaller median filter window
size of 0.45 MHz. However, this did not yield any new Hi absorption detections
beyond the five already identified. While spurious detections decreased, the
$\mathrm{S/N}$ ratio of the previously identified candidates was reduced. To
eliminate the effects of fluctuations and RFI around Hi absorption signals, we
will employ a finely-tuned fitting technique using high-order polynomials +
multi-component Gaussian functions on the spectra from follow-up observations.

We have made follow-up observations for these candidates in the ON-OFF
tracking observation mode, with 990 s integration on each. Besides the three
previously known ones, two are confirmed to be bona fide absorbers (along the
l.o.s. towards NVSS J231240-052547 and NVSS J053118+315412), while the other 5
candidates are either produced by features in the bandpass or the combined
features from the Hi emission and bandpass ripples (this will be discussed
later). We fit the profiles of the true Hi absorptions with multi-components
Gaussian functions and presented the basic physical information for each
source. The absolute photometric flux is calibrated with 3C 48 and the FAST
built-in noise diode.

Figure 8: The CRAFTS spectra of the 5 Hi absorber candidates, 4C +27.14 3C
293, NVSS J231240-052547 and NVSS J053118+315412. In each row, the odd and
even-numbered columns show the raw spectra and the baseline removed spectra,
respectively. The vertical lines indicate the frequencies of the absorbers.
The red-solid lines in the raw spectra show the baseline. The red-solid lines
in the baseline removed spectra show the Gaussian fit absorption profile.
Spectra of UGC 00613 are shown in Figure 6.

###  4.1 Previously Known Absorbers

####  4.1.1 UGC 00613

The Hi absorption feature of UGC 00613 was firstly reported in Zhang et al.
(2021) with a flux density depth of $S_{\textsc{Hi\leavevmode\nobreak\ },\rm
peak}=-64.28\pm 6.61$ mJy, FWHM of 26.36 $\pm$ 1.74 $\,{\rm km\,s^{-1}}$, and
$\int\tau dv=$ 21.24 $\pm$ 4.10 $\,{\rm km\,s^{-1}}$, from a one-component
Gaussian fitting. UGC 00613 is a flat-spectrum extended radio source (Healey
et al., 2007) which probably locates in an unrelaxed, merging system
(Hardcastle et al., 2019). We blindly re-detected its Hi absorption in beam
10, beam 4 and beam 13 in the CRAFTS drift-scan data. As Figure 6 shows, the
absorption feature overlaps in the frequency band with an emission feature,
which is a chronically present RFI. To remove the baseline and RFI, a Gaussian
+ 2nd-order polynomial function was fitted to the absorption line-free parts
of the spectrum. We use the FAST built-in noise diode for flux calibration.
The system temperature $T_{\rm sys}$ is estimated as

$\displaystyle T_{\rm sys}=\frac{P_{\rm obs}}{P_{\rm noise}}\times T_{\rm
noise},$ (13)

where $P_{\rm noise}$ is the recorded noise power from the noise diode,
$P_{\rm obs}$ is the CRAFTS recorded observational data, $T_{\rm noise}$ is
the noise temperature. $T_{\rm sys}$ was converted to flux density using pre-
measured antenna gain (Jiang et al., 2020): Flux = $T_{\rm sys}$/Gain.

The absorption spectra of UGC 00613 and its Gaussian fitting are presented in
Figure 9. Two components are found in the absorption feature, and some basic
physical information is given in Table 2 and Table 3. Our measurements of the
Hi absorption of UGC 00613 with a flux density depth of
$S_{\textsc{Hi\leavevmode\nobreak\ },\rm peak}=$ -69.46 $\pm$ 5.56 mJy, FWHM
of 31.74 $\pm$ 1.85 $\,{\rm km\,s^{-1}}$, and $\int\tau dv=$ 32.75 $\pm$
4.39$\,{\rm km\,s^{-1}}$. The measurements of Gaussian component 2 (Table 3)
are consistent with the previous results reported in Zhang et al. (2021).

####  4.1.2 3C 293

3C 293 is a Fanaroff and Riley type II (FR II) (Fanaroff & Riley, 1974) radio
galaxy, with a compact core of steep spectrum and multiple knots in the radio
lobe (Evans et al., 1999; Beswick et al., 2004b). Both emission and absorption
in CO have been detected (Evans et al., 1999), showing that 3C 293 is a disk
galaxy with an optical jet or tidal tail toward its companion galaxy. The
outflow of Hi had also been detected, which is probably driven by the radio
jet (Mahony et al., 2013). The radio jets twist by 30°, probably as a result
of strong interaction or a recent merger event. Besides, an extremely broad
and multi-components Hi absorption feature has been detected (Baan & Haschick,
1981; Beswick et al., 2004a, b), indicating a rotating Hi disk.

We detected again the Hi absorption in 3C 293 in our blind search. Its signal
can be detected in beam 10, beam 11, beam 4 and beam 13 with a high signal-to-
noise ratio ($\mathrm{S/N}>10$). We use the built-in noise diode to calibrate
the data and measure the basic physical parameters using the method described
in Section 3.5. The absorption feature is fitted by a triple-component
Gaussian function and is presented in Figure 10, and the physical parameters
are given in Table 2 and Table 3.

As shown in Figure 10, a broad Hi absorption feature with multiple components
is obtained. For the total signal, the Hi absorption of 3C 293 is detected
with a flux density depth of $S_{\textsc{Hi\leavevmode\nobreak\ },\rm
peak}=$-283.33 $\pm$ 17.24 mJy, FWHM $=61.54\pm 4.32\,{\rm km\,s^{-1}}$,
$\tau_{\rm peak}=0.062\pm 0.004$, $\int\tau dv=6.47\pm 0.41\,{\rm km\,s^{-1}}$
and $N_{\textsc{Hi\leavevmode\nobreak\ }}=0.12T_{s}\times 10^{20}\,{\rm
cm}^{-2}\,{\rm K}^{-1}$, which are consistent with the previous measurement
reported in Baan & Haschick (1981) which detected the Hi absorption signal for
the first time and gave $\tau_{\rm peak}=0.085$ and a column density of
$0.18T_{s}\times 10^{20}\,{\rm cm}^{-2}\,{\rm K}^{-1}$. The difference is a
result of different adoption of flux density of 3C 293 at 1.4 GHz ($S_{\rm
1.4GHz}$), Baan & Haschick (1981) used $S_{\rm 1.4GHz}=3.76$ Jy while we adopt
recent measurement $S_{\rm 1.4GHz}=4.69$ Jy (Lin et al., 2018).

Figure 9: Hi absorption feature of UGC 00613. The blue solid line depicts the
absorption spectrum, and the red solid line shows the fit with a double-
component Gaussian model ( components shown as orange and green dashed lines).
The magenta dot-dashed vertical line marks the redshift of UGC 00613 as given
in the NASA/IPAC Extragalactic Database. The fitting residual is shown as the
black solid line at the bottom. Optical depth value for the Hi absorption is
shown on the right scale. Figure 10: Same as Figure 9, but for the Hi
absorption feature of 3C 293.  Figure 11: Same as Figure 9, but for the Hi
absorption feature of 4C +27.14 obtained by processing the follow-up ON-OFF
tracking data.

####  4.1.3 4C +27.14

4C +27.14 is a Type II Seyfert galaxy and displays the properties of a radio-
loud AGN (Parisi et al., 2014). Broad Hi absorption profile has been observed
in the direction of radio continuum source 4C +27.14 (Stanimirović et al.,
2014) for the first time. The Hi absorption lines are detected in the CRAFTS
drift-scan data with blind search and the follow-up observation using ON-OFF
tracking mode. The absorption signal of 4C +27.14 is faint, only detected in
beam 11 in the CRAFTS data. The fluctuations in the bandpass are suppressed by
subtracting the source-off data from the source-on data. The calibrator 3C 48
was also observed to calibrate the data. A 2nd order polynomial function was
fitted to the absorption line-free parts of the spectrum to remove the
baseline of the bandpass.

The calibrated ON-OFF spectrum and its Gaussian fitting are presented in
Figure 11 (and Figure 16 for the follow-up observation). Some physical
parameters of the system are given in Table 3. Our measurement of the Hi
absorption profile of 4C +27.14 is consistent with Stanimirović et al. (2014).

However, Eq. (11) is no more a good assumption because $T_{\rm s}\ll c_{\rm
f}T_{\rm c}$ is not satisfied for 4C +27.14. Heiles & Troland (2003) developed
a 17-point observing pattern with the Arecibo telescope and used the least-
squares procedure to measure the optical depth and the expected emission
profile, which is the profile of Hi source that would be observed at the
source position if the background continuum sources were absent. Sixteen off-
source measurements and one on-source measurement were applied to each source.
The off-source spectra were expressed in a Taylor series expansion of the
expected profile and a small contribution from the source intensity attenuated
by the optical depth. A least-squares fitting technique is then used to
estimate the expected Hi emission and the optical depth. Using this method,
Stanimirović et al. (2014) derived the expected Hi emission profile. The
opacity spectrum was then obtained by subtracting the expected Hi emission
spectrum from the on-source spectrum.

We re-scale our optical depth profile in Figure 11 and Table 3 using the data
presented in Stanimirović et al. (2014). our measurements of the Hi absorption
associated with 4C +27.14 give a flux density depth of
$S_{\textsc{Hi\leavevmode\nobreak\ },\rm peak}=-11.11\pm 0.34\,{\rm mJy}$, an
FWHM of $54.58\pm 1.99\,{\rm km\,s^{-1}}$, and $\int\tau dv=3.01\pm 0.09\,{\rm
km\,s^{-1}}$.

###  4.2 New Absorbers

Here we report two newly discovered absorbers. We name them by the bright
radio sources located very close to the peak position of the absorption seen
in our observation, NVSS J231240-052547 and NVSS J053118+315412. According to
the NED and VLASS, these are the only radio sources found within 3 arc mins
around these positions where Hi absorptions are detected.

Is the absorption really produced along the line of sight towards the bright
background radio source, or is produced against the blank sky or some fainter,
fused sources within the beam? We note that the flux decrements for the two
absorbers are quite large. Given that there are bright sources at the position
where absorbers are detected, it is much more likely to obtain such a large
decrement against a single, bright radio background source since only an
absorber of a small area on that line of sight is required, while it is far
more difficult to achieve such absorption against fainter, possibly multiple
background sources within the same beam, which would require a much larger
area for the absorber. Combined with the fact that in CRAFTS drift scan data,
there is a tight negative relation between the intensity of the absorption
signal and the angular distance between the beam centre and the radio sources
mentioned above, these two radio sources are very likely related to the newly
discovered Hi absorbers. Therefore, we shall proceed under the assumption that
these two absorbers are indeed related to that strong radio sources, and this
justifies our naming of the absorbers with the radio sources.

####  4.2.1 NVSS J231240-052547

Figure 12: Absorption spectrum and images towards NVSS J231240-052547. Left
panel: same as Figure 9, but for the Hi absorption feature towards NVSS
J231240-052547. Middle panel: image centred at NVSS J231240-052547 (or WISEA
J231240.69-052548.8), using WISE data at 4.618 microns. Right panel: radio
image centred at NVSS J231240-052547, using VLASS data. The straight cross
shows the position of the radio source.

Figure 13: Absorption spectrum and images towards NVSS J053118+315412. Left
panel: same as Figure 9, but for the Hi absorption feature of NVSS
J053118+315412. Middle panel: image centred at NVSS J053118+315412 (or WISEA
J053118.83+315412.0), using WISE data at 4.618 microns. Right panel: radio
image centred at NVSS J231240-052547, using VLASS data. The straight cross
shows the position of the radio source.

The Hi absorption towards NVSS J231240-052547 is here reported for the first
time. NVSS J231240-052547 is a radio source detected in the NRAO VLA Sky
Survey with flux $S_{\rm 1.4GHz}=$ 181.9 mJy. We blindly detected Hi
absorption in beam 10, beam 4 and beam 14 in the CRAFTS drift-scan data.

The absorption spectra towards NVSS J231240-052547 and its Gaussian fitting
are shown in the upper panel of Figure 12. Two components are found in the
absorption feature, and some basic physical parameters are given in Table 2
and Table 3. Under the assumption $T_{\rm s}\ll c_{\rm f}T_{\rm c}$, the Hi
absorption towards NVSS J231240-052547 has a flux density depth of
$S_{\textsc{Hi\leavevmode\nobreak\ },\rm peak}=-54.04\pm 6.02\,{\rm mJy}$, an
FWHM of $9.12\pm 1.01\,{\rm km\,s^{-1}}$, $\int\tau dv=3.01\pm 0.36\,{\rm
km\,s^{-1}}$ and $N_{\textsc{Hi\leavevmode\nobreak\ }}=0.05T_{s}\times
10^{20}\,{\rm cm}^{-2}\,{\rm K}^{-1}$.

At this same position, a mid-infrared source WISEA J231240.69-052548.8 has
been detected by the Wide-field Infrared Survey Explorer (WISE, Cutri et al.
2013), and cross-identified as the radio source NVSS J231240-052547 in the
NASA/IPAC Extragalactic Database. The left and right panels of Figure 12 show
the image centred at NVSS J231240-052547 (or WISEA J231240.69-052548.8),
constructed using data at 4.618 microns (W2) from WISE and radio data at
S-band from the Karl G. Jansky Very Large Array Sky Survey (VLASS) (Lacy et
al., 2020), respectively. The straight cross marks the position of NVSS
J231240-052547. The WISE magnitudes for WISEA J231240.69-052548.8 are
presented in Table 1. The W1-W2 colour of value 0.8 is often used as a simple
mid-infrared colour criterion for AGN candidates (Stern et al., 2012). The
W1-W2 colour of 0.827 indicates that is an AGN candidate. Combining with the
W2-W3 value of 3.752 mag, this source lies in the intersecting region of
Seyferts and the Ultra-luminous Infrared Galaxies (ULIRGs) in the WISE
colour–colour diagram (Wright et al., 2010). It is probably associated with
the background radio source, though there is also the chance that it is
located at a lower redshift, and in that case, the absorber could be
associated with it.

There is also an optical counterpart located at the same position. According
to the information shown in SDSS DR17 SkyServer
website222https://skyserver.sdss.org/dr17/en/home.aspx, WISEA
J231240.69-052548.8 is cross-identified as SDSS J231240.73-052541.1 in the
optical band. SDSS J231240.73-052541.1 is a galaxy with a Petrosian radius of
7.36 arcsec, with a photometric redshift of $photoZ=0.091\pm 0.0364$. The
magnitudes of SDSS J231240.73-052541.1 are $u=20.66\pm 0.20,g=19.68\pm
0.03,r=19.37\pm 0.03,i=19.16\pm 0.05$ and $z=19.09\pm 0.16$. The absorption
line towards NVSS J231240-052547 is located at $z\sim 0.063$, which is within
the error box of the photometric redshift of SDSS J231240.73-052541.1. It
could be associated with the absorber, though spectroscopic observations are
needed to give a definite answer. The optical image for SDSS
J231240.73-052541.1 is extracted from the SDSS SkyServer website and is shown
as the central galaxy in Figure 14.

Figure 14: The optical image for SDSS J231240.73-052541.1 (central galaxy).
Blue circles mark the photometric objects, and the green squares depict the
SDSS outlines.

####  4.2.2 NVSS J053118+315412

The other new absorber is found in the line of sight towards NVSS
J053118+315412. NVSS J053118+315412 has been detected at 1.4 GHz in NVSS with
flux $S_{\rm 1.4GHz}=$ 40.2 mJy. Its Hi absorption is only detected in beam 12
of the drift scan covering Declination of +31d57m00s. In order to verify this
detection, it was observed in follow-up observation using ON-OFF tracking
mode. The absorption spectra towards NVSS J053118+315412 and its Gaussian
fitting are shown in the upper panel of Figure 13. Six components are found in
the absorption feature, and some basic parameters are given in Table 2 and
Table 3. Under the assumption $T_{\rm s}\ll c_{\rm f}T_{\rm c}$, the
measurements of the Hi absorption towards NVSS J053118+315412 give a flux
density depth of $S_{\textsc{Hi\leavevmode\nobreak\ },\rm peak}=-21.85\pm
0.77\,{\rm mJy}$, an FWHM of $89.53\pm 2.85\,{\rm km\,s^{-1}}$, $\int\tau
dv=55.81\pm 2.23\,{\rm km\,s^{-1}}$ and $N_{\textsc{Hi\leavevmode\nobreak\
}}=1.016T_{s}\times 10^{20}\,{\rm cm}^{-2}\,{\rm K}^{-1}$.

The radio source has also been cross-identified to a source in the 2MASS Two
Micron All Sky Survey (2MASS, Skrutskie et al. 2006) and one in the mid-
infrared band by WISE by the NASA/IPAC Extragalactic Database. We show the
image centred at NVSS J053118+315412 (or WISEA J053118.83+315412.0),
constructed using infrared data at 4.618 microns (W2) from WISE and radio data
at S-band from VLASS, in the middle and right panel of Figure 13. The straight
cross marks the position of NVSS J053118+315412. The WISE magnitudes for WISEA
J053118.83+315412.0 are presented in Table 1. The W1-W2 colour is 1.630, which
is higher than the value of 0.8 often used to select AGN candidates and
implies that the mid-IR emission comes mainly from the AGN. Combined with the
W2-W3 value of 3.598 mag, NVSS J053118+315412 lies in the region of QSOs in
the WISE colour–colour diagram. The 2MASS counterpart has
J-band[$1.235\text{\,}\mathrm{\SIUnitSymbolMicro m}$],
H-band[$1.662\text{\,}\mathrm{\SIUnitSymbolMicro m}$] and Ks-
band[$2.159\text{\,}\mathrm{\SIUnitSymbolMicro m}$] magnitudes 15.180 $\pm$
0.043, 13.943 $\pm$ 0.044 and 13.219 $\pm$ 0.028.

We should note that although the velocity of the absorption is $\sim
1500\,{\rm km\,s^{-1}}$ higher than the velocity of WISEA J053118.83+315412.0
(or NVSS J053118+315412) as shown in the NED database (given by 2MASS Redshift
Catalog, Bilicki et al. 2014), this velocity difference is smaller than the
typical precision of 2MASS redshift estimates ($\sim$ 12$\%$), indicating the
velocity of absorption is similar to that of NVSS J053118+315412.

The complicated structures of the absorption profile indicate the interaction
between ISM and host AGN. NVSS J053118+315412 exhibits a symmetric absorption
spectrum (Gaussian components 2 and 3) relative to the systemic velocity of
its host galaxy, suggesting that the Hi gas traces a regular rotating
structure. On the other hand, asymmetric absorption wings (Gaussian components
1 and 6) in the absorption profile are generally indicative of unsettled gas
structures (Morganti & Oosterloo, 2018), such as gas outflows that are
propelled by the radio jet or tidal gas streams. Additionally, the redshifted
absorption components (Gaussian components 4 and 5) could be evidence of
accretion onto the SMBH (Araya et al., 2010; Maccagni et al., 2014). However,
precise identification of infalling Hi can only be achieved via high-
resolution observations.

The position of NVSS J053118+315412 is outside the footprint of SDSS and other
optical surveys. We are applying the telescope time to obtain the optical
spectrum of the potential foreground and background sources, which will be
investigated in future work.

###  4.3 Mid-infrared Colour

The mid-infrared wavelength colour information from the WISE survey for the
WISE counterparts of UGC 00613, 3C 293, 4C +27.14, NVSS J231240-052547 and
NVSS J053118+315412 is shown in Table 1. Figure 15 presents the WISE colour-
colour diagram from Wright et al. (2010), overlaid with the WISE counterparts
of UGC 00613, 3C 293, 4C +27.14, NVSS J231240-052547, NVSS J053118+315412 as
well as 3 associated absorption (PKS B1740-517, 3C 216 and M1540-1453)
detected in previous blind surveys. In the WISE colour-colour diagram,
extragalactic objects are grouped into different classes based on their mid-
infrared colour signatures.

From the Hi absorption experiment towards radio AGNs classified as either low-
excitation radio galaxies (LERGs) or high-excitation radio galaxies (HERGs),
Chandola et al. (2020) confirmed that compact radio AGNs with WISE colour
W2-W3 ¿ 2 have higher detection rates compared to those with W2-W3 ¡ 2
(Chandola & Saikia, 2017). This is because the sources with W2-W3 ¿ 2 are
typical of gas-rich systems.

All the 4 associated Hi absorption in our work and 3 associated absorption
(PKS B1740-517 (Allison et al., 2015), 3C 216 (Grasha et al., 2020) and
M1540-1453 (Gupta et al., 2021a)) from previous blind surveys reside in the
W2-W3 ¿ 2 region, which supports the conclusion given by Chandola et al.
(2020). More importantly, this associated absorption sample is obtained from a
blind survey without any prior selection, indicating a universal relation
between mid-infrared wavelength colour and detection rate for all radio
sources. However, limited by the small number of unbiased Hi absorption
samples, it is necessary to use more Hi absorbers from blind surveys to verify
the relationship between mid-infrared colour and detectability for associated
and intervening absorption.

Figure 15: The WISE colour-colour diagram. The WISE colour for the WISE counterparts of UGC 00613, 3C 293, 4C +27.14, NVSS J231240-052547 , NVSS J053118+315412 and 3 associated absorption (PKS B1740-517, 3C 216 and M1540-1453) from blind surveys. Table 1: WISE magnitudes for the WISE counterparts of two new absorbers NVSS J231240-052547 and NVSS J053118+315412. Uncertainty is not available if magnitude is a 95% confidence upper limit (flux measurement has $\mathrm{S/N}$ ¡ 2). Radio Source | WISE Counterpart | W1[$3.4\text{\,}\mathrm{\SIUnitSymbolMicro m}$] | W2[$4.6\text{\,}\mathrm{\SIUnitSymbolMicro m}$] | W3[$12.1\text{\,}\mathrm{\SIUnitSymbolMicro m}$] | W4[$22.2\text{\,}\mathrm{\SIUnitSymbolMicro m}$]
---|---|---|---|---|---
UGC 00613 | WISEA J005924.42+270332.6 | 11.226 $\pm$ 0.024 | 11.120 $\pm$ 0.020 | 7.812 $\pm$ 0.017 | 5.695 $\pm$ 0.039
3C 293 | WISEA J135217.81+312646.6 | 11.328 $\pm$ 0.023 | 10.787 $\pm$ 0.021 | 8.124 $\pm$ 0.018 | 5.962 $\pm$ 0.038
4C +27.14 | WISEA J045956.08+270602.1 | 10.344 $\pm$ 0.022 | 9.050 $\pm$ 0.019 | 5.836 $\pm$ 0.015 | 3.191 $\pm$ 0.019
NVSS J231240-052547 | WISEA J231240.69-052548.8 | 16.937 $\pm$ 0.162 | 16.110 | 12.358 | 9.016
NVSS J053118+315412 | WISEA J053118.83+315412.0 | 11.607 $\pm$ 0.024 | 9.977 $\pm$ 0.021 | 6.379 $\pm$ 0.014 | 3.613 $\pm$ 0.020
Table 2: Some basic physical parameters of radio source UGC 00613, 3C 293, 4C +27.14, NVSS J231240-052547 and NVSS J053118+315412. The values are retrieved from NASA/IPAC Extragalactic Database (Helou et al., 1991). The redshifts of NVSS J231240-052547 and NVSS J053118+315412 are SDSS and 2MASS photometric estimates for the nearest optical galaxies cross-matched to the radio sources. Radio Source | Source Type | RA(J2000) | DEC(J2000) | cz ($\,{\rm km\,s^{-1}}$) |  $S_{\rm 1.4GHz}$ (mJy)
---|---|---|---|---|---
UGC 00613 | Diffuse Radio Source | 00h 59m 24.42s | +27d 03m 32.6s | 13770.07 $\pm$ 23.08 | 112.6 $\pm$ 4.0
3C 293 | Extended Radio Source | 13h 52m 17.842s | +31d 26m 46.50s | 13547.51 $\pm$ 3.00 | 4690
4C +27.14 | Compact Radio Source | 04h 59m 56.08s | +27d 06m 02.10s | 18347.30 $\pm$ 0 | 857
NVSS J231240-052547 | Radio Source | 23h 12m 40.73s | -05d 25m 47.50s | 27281.11 $\pm$ 10912.44 | 181.9 $\pm$ 5.5
NVSS J053118+315412 | Radio Source | 05h 31m 18.83s | +31d 54m 11.7s | 18359.29 $\pm$ 0 | 40.2 $\pm$ 1.3
Table 3: Some basic physical parameters of FAST observations of the Hi absorption profiles for UGC 00613, 3C 293 and 4C +27.14. The estimations of $\tau$ for 4C +27.14 are re-scaled use the data in Stanimirović et al. (2014). Radio Source | absorption type | Component | czpeak | FWHM | $S_{\textsc{Hi\leavevmode\nobreak\ },\rm peak}$ | $\int S_{\textsc{Hi\leavevmode\nobreak\ }}dv$ | $\tau_{\rm peak}$ | $\int\tau dv$ | $N_{\textsc{Hi\leavevmode\nobreak\ }}$
---|---|---|---|---|---|---|---|---|---
|  |  | ($\,{\rm km\,s^{-1}}$) | ($\,{\rm km\,s^{-1}}$) | (mJy) | (mJy$\,{\rm km\,s^{-1}}$) |  | ($\,{\rm km\,s^{-1}}$) | (1020cm-2K-1)
|  | 1 | 13987.58 | 40.34 | -23.50 | -1016.51 | 0.23 | 9.78 | 0.18$T_{s}$
UGC 00613 | associated | 2 | 13957.59 | 27.03 | -64.31 | -1826.04 | 0.84 | 21.17 | 0.39$T_{s}$
|  | Total | 13957.59 | 31.74 | -69.46 | -2842.55 | 0.96 | 32.75 | 0.60$T_{s}$
|  | 1 | 13483.28 | 29.93 | -168.09 | -5354.07 | 0.036 | 1.16 | 0.02$T_{s}$
3C 293 | associated | 2 | 13458.66 | 80.60 | -141.90 | -12164.45 | 0.031 | 2.62 | 0.05$T_{s}$
|  | 3 | 13354.95 | 110.95 | -104.45 | -12331.98 | 0.023 | 2.65 | 0.05$T_{s}$
|  | Total | 13481.49 | 61.54 | -283.33 | -29850.50 | 0.062 | 6.47 | 0.12$T_{s}$
|  | 1 | 18776.96 | 42.09 | -7.98 | -357.40 | 0.87 | 38.72 | 0.7$T_{s}$
4C +27.14 | associated | 2 | 18755.13 | 155.74 | -3.32 | -550.31 | 0.36 | 59.51 | 1.08$T_{s}$
|  | Total | 18776.96 | 54.58 | -11.11 | -907.70 | 1.21 | 98.37 | 1.79$T_{s}$
|  | 1 | 18790.52 | 5.20 | -53.17 | -294.82 | 0.33 | 1.82 | 0.03$T_{s}$
NVSS J231240-052547 | unknown | 2 | 18797.77 | 7.15 | -26.10 | -198.50 | 0.15 | 1.15 | 0.02$T_{s}$
|  | Total | 18797.77 | 9.12 | -54.04 | -493.32 | 0.34 | 3.01 | 0.05$T_{s}$
|  | 1 | 19899.88 | 60.81 | -3.70 | -239.20 | 0.097 | 6.19 | 0.113$T_{s}$
|  | 2 | 19933.06 | 26.08 | -20.17 | -559.72 | 0.702 | 17.53 | 0.319$T_{s}$
|  | 3 | 19960.99 | 18.78 | -17.84 | -356.73 | 0.591 | 10.81 | 0.197$T_{s}$
NVSS J053118+315412 | associated | 4 | 19994.99 | 38.18 | -11.08 | -450.01 | 0.324 | 12.55 | 0.229$T_{s}$
|  | 5 | 20004.30 | 5.94 | -4.47 | -28.25 | 0.118 | 0.74 | 0.013$T_{s}$
|  | 6 | 20055.36 | 75.00 | -2.46 | -196.30 | 0.063 | 5.02 | 0.091$T_{s}$
|  | Total | 19944.95 | 89.53 | -21.85 | -1830.21 | 0.790 | 55.81 | 1.016$T_{s}$

###  4.4 Spurious Detections

The other 5 candidates in the follow-up observations are also checked and
found to be not true Hi absorptions. The spectra of these sources, together
with 4C +27.14, are shown in Figure 16. The spectra are obtained by
subtracting the source off spectra from the source on spectra and are
calibrated with 3C 48. The orange-dashed lines show the central frequency
position of the absorber candidates (see Figure 8 for comparison). Compared
with the spectra in CRAFTS (Figure 8), we found that Candidate 1, 3, 4 and 5
arise from the combination of the fluctuations of the bandpass and the Hi
emission, while Candidate 2 comes from the fluctuations of the bandpass.

Although there are significant Hi emission profiles in the source ON - source
OFF spectra from follow-up observation, in the CRAFTS data, they are mixed
with the bandpass fluctuations induced by standing wave and chronically
present RFI, making it difficult to distinguish the Hi emission from the
bandpass ripples. The standing wave ripples of the FAST have $c/2f\sim
1.1\,{\rm MHz}$ (where c denotes the speed of light and $f\sim 138$ m is the
FAST focal length), which is not far from the width of Hi emission.

The spurious absorbers such as Candidate 1, 3, 4 and 5 are the results of the
interplay between Hi mission, RFI and bandpass ripples, such spurious
absorption features can survive the multi-beam cross-correlation selection and
can not be easily excluded without further observation (Section 3.4).

Figure 16: The spectra for the candidates 1, 2, 3, 4, 5 and 4C +27.14 from the
follow-up observation. The orange-dashed lines show the central frequency
position of the Hi candidates found in CRAFTS searching (see Figure 8).

##  5 Discussions

###  5.1 Correction for Standing Waves

There have been attempts to suppress the standing waves in radio data. Kern et
al. (2019) described techniques for modelling and removing the reflections and
standing waves in the HERA (the Hydrogen Epoch of Reionization Array)
data(Kern et al., 2020). They showed that by combining reflection calibration
and cross-coupling subtraction, standing waves could be suppressed down to the
integrated noise floor. Li et al. (2021) recognized the standing waves in the
Tianlai cylinder array and found the oscillating modulations in the frequency
spectrum could be mitigated by removing the corresponding components in the
Fourier space. Tests are also being made on correcting the FAST standing
waves. By fitting or extracting peaks in Fourier space caused by standing
waves components with the period of $\sim 1.1\,$MHz, we can remove them and
bring the level of fluctuation down to below 1 mJy or even lower (W. Yang et
al, in preparation). A careful study of the small-scale fluctuations may help
improve the calibration. However, the standing waves do vary with time, making
it difficult to remove their effect completely.

On the other hand, only a one-pass drift scan has been carried out to date. In
the near future, after the 2-pass drift scan is finished, more time-varied RFI
and other fluctuations can be excluded by comparing the data covering the same
sky at different times.

###  5.2 Information from Neighboring Beams

With so many spurious signals originating from the bandpass fluctuations and
RFI being selected as preliminary candidates, it is of vital importance to
find a valid and easy-to-use method to distinguish the intrinsic Hi absorption
from man-made signals. Fortunately, the 19 beams of the L-band receiver and
the drift-scan survey strategy provide an effective solution (described in
Section 3.4). The unique design of FAST makes it a powerful instrument for Hi
absorption searching. Considering that only $\sim$ a half of the frequency
band from a small part of CRAFTS observable sky has been searched, we expect a
larger number of Hi absorbers could be detected with the 2-pass full survey.

In the blind search presented in this work, we run our pipeline in the data
from every single beam separately. For drift scan at the meridian circle,
$12/\cos\delta$ seconds integration time is obtained in each beam-size pixel.
Considering the drift-scan strategy and the positions of the 19 beams, there
are overlaps among nearby beams. About $24/\cos\delta$ seconds integration
time can be obtained on each beam-size pixel (Hu et al., 2020) if we combine
the data from the 19 beams together. All of the data from the scans of the 19
beams can be utilized fully without losing information by using the linear
map-making method (Tegmark, 1997). It is a well-known technique for turning
time-ordered raw data into estimators of the true sky. We have developed an
effective map-making pipeline for FAST to combine the data from the 19 beams
and make the high signal-to-noise ratio map (Y. Li et al, in preparation). It
will be used to process the CRAFTS data in the near future. Predictably more
and fainter Hi absorption systems could be detected in the data processed from
the full map.

###  5.3 Counterparts to the Radio Sources

Finding the counterpart of the radio source has long been an important yet
challenging problem (Laing et al., 1983). In the above, we have argued that
the absorption is very likely against the background radio source seen at the
position of the beam if such a radio source is present within the beam. The
absorber is then located precisely in the same line of sight. However, there
is also the question of the nature of the optical/infrared counterpart, which
is found by matching the radio source and the sources in the SDSS/WISE
catalogue within a fiducial radius of several arcsecs. These optical/IR
sources could be associated with the background radio source or the absorber,
or they could be simply coincidentally located near the line of sight.

We quantify the probability of finding coincident optical/infrared sources in
the SDSS photometric catalogue, whose surface density is $\sim$ 4.2 per square
arcmin, near the line of sight by simulation. We generate 10000 random
positions (Ra, Dec) in the surveyed sky region and compute the probability of
having galaxies within a fiducial radius to these positions. Figure 17 shows
the probability of matching as a function of radius. The probability of
finding a galaxy is only 0.0036 at a matching radius of 1 arcsec but increases
rapidly with the matching radius. The average separation between the radio
sources of our 5 Hi absorption systems and their SDSS counterparts is 0.734
arcsec, within which the probability of having an SDSS galaxy by chance is
only 0.0021. For the two newly discovered absorbers towards NVSS
J231240-052547 and NVSS J053118+315412, the separation are 2.351 and 0.387
arcsec, indicating a coincidence probability of 0.018 and 0.0002,
respectively. This indicates that the detected SDSS matches are unlikely to be
pure coincidence.

As we argued earlier, the radio background source and the absorber are most
likely in the same line of sight. If the background sources are all located at
high redshift ($z\sim 1$), for which the optical counterpart would be too
faint to be listed in the present SDSS catalogue, then these optical
counterparts should be associated with the absorber. However, although most
NVSS sources are located at high redshift (Nolta et al., 2004; Ho et al.,
2008; Rahman et al., 2015), there is also a fraction of NVSS sources located
at low redshift ($z<0.1$) (Condon et al., 1998). A spectroscopic measurement
of its redshift is needed to find the final answer.

Figure 17: The probability of finding SDSS galaxies within a certain matching
radius centred at arbitrary directions.

###  5.4 Expected Detection

####  5.4.1 Comoving Absorption Path

We estimate the total absorption path length ($\Delta X$) and the
$N_{\textsc{Hi\leavevmode\nobreak\ }}$ frequency distribution function,
f($N_{\textsc{Hi\leavevmode\nobreak\ }}$, $X$) for the CRAFTS data survey used
here (1300-1450 MHz), following the method described in Allison et al. (2015,
2020); Allison (2021). The absorption path length is defined as the comoving
interval of the survey that is sensitive to intervening absorbers. It can be
obtained by summing over all data elements that are sensitive to a given
minimum column density threshold:

$\displaystyle\Delta
X=\sum^{n_{t}}_{i}\sum^{n_{f}}_{j}C(z_{i,j})w_{i,j}(z_{i,j})\Delta
X_{i,j}\delta_{i,j},$ (14)

where $n_{t}$ and $n_{f}$ are the total number of time points and frequency
channels, $\delta_{i,j}$ = 1 when the data element (i,j) is sensitive to a
given minimum column density, otherwise $\delta_{i,j}$ = 0. $X_{i,j}$ is the
comoving absorption path length for a certain element, $C(z_{i,j})$ denotes
the completeness at a certain redshift (frequency), $w_{i,j}$ refers to the
redshift weighting function, which gives the probability of the radio source
being located beyond $z_{i,j}$,

$\displaystyle
w(z)=\frac{\int^{\infty}_{z}N_{\mathrm{src}}(z^{\prime})dz^{\prime}}{\int^{\infty}_{0}N_{\mathrm{src}}(z^{\prime})dz^{\prime}},$
(15)

where the redshift distribution of source is (de Zotti et al., 2010),

$\displaystyle
N_{\mathrm{src}}(z)=1.29+32.37z-32.89z^{2}+11.13z^{3}-1.25z^{4},$ (16)

which is obtained by fitting the bright ($S_{1.4\rm GHz}\geqslant$ 10 mJy)
sources in the Combined EIS-NVSS Survey Of Radio Sources (CENSORS; Brookes et
al. 2008). For intervening Hi absorption, we adopt $w_{i,j}=w(z_{i,j}+\Delta
z^{\mathrm{asc}}_{i,j})$, where $\Delta
z^{\mathrm{asc}}_{i,j}=(1+z_{i,j})\Delta v^{\mathrm{asc}}/c$ and $\Delta
v^{\mathrm{asc}}=3000\,{\rm km\,s^{-1}}$. For associated Hi absorption, we
exclude Hi absorption not associated with Hi gas in the host galaxy of the
radio source by setting the upper limit of the integral of the denominator to
$z_{i,j}+\Delta z^{\mathrm{asc}}_{i,j}$.

The comoving absorption path element for the element i,j in the $\Lambda$CDM
model is:

$\displaystyle\Delta X_{i,j}=\Delta z_{i,j}(1+z_{i,j})^{2}E(z_{i,j})^{-1},$
(17)

where

$\displaystyle E(z)=\sqrt{(1+z)^{3}\Omega_{\rm m}+(1+z)^{2}(1-\Omega_{\rm
m}-\Omega_{\Lambda})+\Omega_{\Lambda}}.$ (18)

The elements sensitive to a given column density are selected by calculating
the column density sensitivity for each element. Assuming the spin temperature
of $T_{\rm s}=100$K, covering factor $c_{\rm f}=1$, velocity FWHM $\Delta
v_{\rm{FWHM}}=30$ $\,{\rm km\,s^{-1}}$, the column density sensitivity can be
expressed as:

$\displaystyle N_{\textsc{Hi\leavevmode\nobreak\ },s}=5.82\times
10^{21}\left[\frac{T_{\mathrm{s}}}{100\mathrm{K}}\right]\left[\frac{\Delta
v_{\rm{FWHM}}}{30\mathrm{km\,s^{-1}}}\right]\tau_{\rm{peak}}\mathrm{cm}^{-2},$
(19)

where $\tau_{\rm{peak}}$ is the peak optical depth sensitivity estimated from
the spectral noise. Adjusting Eq. (11), $\tau_{\rm{peak}}$ can be expressed
as:

$\displaystyle\tau_{\rm{peak}}=-\mathrm{ln}\left(1-(\mathrm{S/N})_{\rm{peak}}\left[\frac{\sigma_{\mathrm{rms}}}{S_{c}c_{\mathrm{f}}}\right]\right),$
(20)

where $(\mathrm{S/N})_{\rm{peak}}$ is the minimum peak signal-to-noise ratio
required to reach high completeness. $(\mathrm{S/N})_{\rm{peak}}$ is adopted
as 5.5 in the comoving path calculation, corresponding to a
$(\mathrm{S/N})_{\rm{int}}$ of $\sim$ 12, for the Gaussian narrow line
absorption template with an FWHM of 30 $\,{\rm km\,s^{-1}}$and the frequency
resolution of 15.26 kHz. From Figure 5, the detection of mock absorption lines
with a $(\mathrm{S/N})_{\rm{int}}$ of 12 can hit the completeness of 0.9. In
Eq. (20), $\sigma_{\mathrm{rms}}$ is the RMS noise, $S_{c}$ is the background
continuum flux density, which is estimated by calibrating the CRAFTS data
using the FAST built-in noise diode and then removing the system temperature
and Galactic foreground signal. The system temperature for each beam and
observations pointing at different Declination is estimated using the models
and parameters given by Jiang et al. (2020). The Galactic foreground signal is
estimated from the global sky model (GSM) (de Oliveira-Costa et al., 2008;
Zheng et al., 2017; Huang et al., 2019). In order to make sure all RFI are
masked, the calibrated spectra are then flagged with a 3 sigma criterion.

The completeness correction employed in comoving absorption path estimation is
determined using mock absorption with $\mathrm{S/N}$ = 12 and FWHM = 30
$\,{\rm km\,s^{-1}}$. Nonetheless, at a fixed velocity-integrated sensitivity,
absorptions with broader lines exhibit lower completeness when considering.
Figure 4 demonstrates that when the velocity-integrated sensitivity is low
(e.g., $\mathrm{S/N}$ = 5.5), the completeness decreases rapidly with
increasing velocity widths. On the other hand, for a fixed high velocity-
integrated sensitivity (e.g., $\mathrm{S/N}$ = 12), there is little disparity
in completeness among absorptions with velocity widths of 15 $\,{\rm
km\,s^{-1}}$, 30 $\,{\rm km\,s^{-1}}$, and 60 $\,{\rm km\,s^{-1}}$.
Consequently, the selection of velocity width has a minor impact on our
estimation of the comoving absorption path length.

We show the comoving absorption path length for our current data as a function
of Hi column density in Figure 18. We present the results for $T_{s}/c_{f}$ =
100 and 1000 K, which are the typical spin temperature of the cold neutral
medium (CNM) and warm neutral medium (WNM) (Murray et al., 2018). The comoving
absorption paths for $T_{s}/c_{f}$ = 100 K and 1000 K are labelled as solid
and dashed lines in Figure 18. Under the assumption of $T_{s}/c_{f}$ = 100 K,
the total comoving absorption path length spanned by our data is $\Delta
X^{\mathrm{inv}}$ = 1.05$\times 10^{4}$ ($\Delta z^{\mathrm{inv}}=9.80\times
10^{3}$) and $\Delta X^{\mathrm{asc}}$ = 1.63$\times 10^{1}$ ($\Delta
z^{\mathrm{asc}}=1.51\times 10^{1}$). The absorption path sensitive to all
DLAs ($N_{\textsc{Hi\leavevmode\nobreak\ }}\geqslant 2\times 10^{20}\,{\rm
cm}^{-2}$) and super-DLAs ($N_{\textsc{Hi\leavevmode\nobreak\ }}\geqslant
2\times 10^{21}\,{\rm cm}^{-2}$) are $\Delta X^{\mathrm{inv}}_{\mathrm{all}}$
= 8.33$\times 10^{3}$ ($\Delta z^{\mathrm{inv}}_{\mathrm{all}}=7.81\times
10^{3}$) and $\Delta X^{\mathrm{inv}}_{\mathrm{super}}$ = 1.05$\times 10^{4}$
($\Delta z^{\mathrm{inv}}_{\mathrm{super}}=9.80\times 10^{3}$) for intervening
absorption and $\Delta X^{\mathrm{asc}}_{\mathrm{all}}$ = 1.28$\times 10^{1}$
($\Delta z^{\mathrm{asc}}_{\mathrm{all}}=1.19\times 10^{1}$) and $\Delta
X^{\mathrm{asc}}_{\mathrm{super}}$ = 1.63$\times 10^{1}$ ($\Delta
z^{\mathrm{asc}}_{\mathrm{super}}=1.51\times 10^{1}$) for associated
absorption, respectively.

The maximum zenith angle for FAST is $\sim 40^{\circ}$, allowing the full
cover of the FAST observable sky $\sim$ 23800 deg2. The predicted results for
Hi absorption searching at $z\leqslant 0.09$ in map-making data from the full
coverage of the FAST observable sky are also presented in Figure 18. Under the
assumption of $T_{s}/c_{f}$ = 100 K, for full cover searching in map-making
data, the total path sensitive to all DLAs and super-DLAs increases to $\Delta
X^{\mathrm{inv}}_{\mathrm{all}}$ = 7.37$\times 10^{4}$ and $\Delta
X^{\mathrm{inv}}_{\mathrm{super}}$ = 7.90$\times 10^{4}$ for intervening
absorption and to $\Delta X^{\mathrm{asc}}_{\mathrm{all}}$ = 1.14$\times
10^{2}$ and $\Delta X^{\mathrm{asc}}_{\mathrm{super}}$ = 1.23$\times 10^{2}$
for associated absorption, respectively.

Figure 18: The comoving absorption path length ($\Delta X$) as a function of
Hi column density sensitivity. The results for the spin temperature to source
covering fraction ratios of 100 and 1000 K are depicted as solid and dashed
lines, respectively. The comoving absorption paths spanned by our data are
labelled as blue (intervening absorption) and red (associated absorption)
colour. The predicted results from Hi absorption searching in map-making data
from the full coverage of the FAST observable sky are presented as green
(intervening absorption) and orange (associated absorption) colour.

####  5.4.2 $N_{\textsc{Hi\leavevmode\nobreak\ }}$ Frequency Distribution
Function

With the comoving absorption path estimated above, we compute the
$N_{\textsc{Hi\leavevmode\nobreak\ }}$ frequency distribution function
(Prochaska et al., 2005; Cooksey et al., 2010; Darling et al., 2011; Allison
et al., 2020; Grasha et al., 2020), $f(N_{\textsc{Hi\leavevmode\nobreak\
}},X)$, which is the number of absorbers per column density
$N_{\textsc{Hi\leavevmode\nobreak\ }}$ bin per absorption path length
sensitive to $N_{\textsc{Hi\leavevmode\nobreak\ }}$, it is given by:

$\displaystyle f(N_{\textsc{Hi\leavevmode\nobreak\
}},X)=\frac{\lambda_{\mathrm{absorption}}}{\Delta
N_{\textsc{Hi\leavevmode\nobreak\ }}\Delta X},$ (21)

where $\lambda_{\mathrm{absorption}}$ is the number of Hi absorption systems
within each column density interval, $\Delta N_{\textsc{Hi\leavevmode\nobreak\
}}$ = 0.5 dex here and $\Delta X$ is the comoving absorption path length
searched with $N_{\textsc{Hi\leavevmode\nobreak\ }}$. Making use of the five
detected Hi absorption systems, we calculate the measured
$f(N_{\textsc{Hi\leavevmode\nobreak\ }},X)$ for the analysed data in this work
and present it in Figure 19 as oblique crosses.

We also compare our results with the upper limits on the
$f(N_{\textsc{Hi\leavevmode\nobreak\ }},X)$ for the other surveys. For the
case of upper limits, $N_{\textsc{Hi\leavevmode\nobreak\ }}$ frequency
distribution function is expressed as $f(N_{\textsc{Hi\leavevmode\nobreak\
}},X)<\frac{\lambda_{\mathrm{max}}}{\Delta N_{\textsc{Hi\leavevmode\nobreak\
}}\Delta X},$ where $\lambda_{\mathrm{max}}$ is the Poisson upper limit on the
detection rate of absorbers with column density
$N_{\textsc{Hi\leavevmode\nobreak\ }}$ in the interval $\Delta
N_{\textsc{Hi\leavevmode\nobreak\ }}$. The 95% confidence upper limit on the
Poisson rate is $\lambda_{\mathrm{max}}$ = 3.0 when non-detection is assumed
(Gehrels, 1986).

Considering 4 associated and only 1 tentative intervening Hi absorption are
detected in this work, we present measured
$f(N_{\textsc{Hi\leavevmode\nobreak\ }},X)$ for associated absorption and the
95 % upper limits of $f(N_{\textsc{Hi\leavevmode\nobreak\ }},X)$ for
intervening absorption for $T_{s}/c_{f}$ = 100 and 1000 K in Figure 19,
together with the distribution from planned FLASH survey (Allison et al.,
2020) (integration time 2 hours, 36 antennas, sky area of $\delta$ = +10 deg
and redshift coverage from 0.4 to 1.0), the ALFALFA absorption pilot survey
(Darling et al., 2011) and model fits to Hi emission-line observations with
WSRT (Westerbork Synthesis Radio Telescope) at z=0 (Zwaan et al., 2005) and
DLA systems in SDSS-DR7 at z $\sim$ 3 (Noterdaeme et al., 2009). The predicted
$f(N_{\textsc{Hi\leavevmode\nobreak\ }},X)$ for the Hi absorption searching in
map-making data from the full coverage of the FAST observable sky is
comparable with FLASH $f(N_{\textsc{Hi\leavevmode\nobreak\ }},X)$ upper limits
prediction at super-DLAs ($N_{\textsc{Hi\leavevmode\nobreak\ }}\geqslant
2\times 10^{20}\,{\rm cm}^{-2}$) regions.

We should note that limited by the RFIs, computing resources and authorized
follow-up observation time, only the 1300-1450 MHz band are used for
absorption lines search and sensitivity calculation. With more comprehensive
data processing methods and more frequency bands (1000-1300 MHz) and larger
sky searched in the near future, a much larger comoving absorption path and
higher sensitivity to N${}_{\textsc{Hi\leavevmode\nobreak\ }}$ frequency
distribution function could be obtained with CRAFTS.

####  5.4.3 Comparing Forecast with real Blind Searching

Utilising the number density distribution of Hi clouds and radio sources over
the sky, Yu et al. (2017) predicted that a one-month drift scan around the
celestial equator by FAST could detect $\sim$ 200 absorption systems with
$\mathrm{S/N}$ of 10 $\sigma$ in redshift range 0 ¡ z ¡ 0.39. Zhang et al.
(2021) considered the NVSS bright source within the FAST observable sky and
forecasted that $\sim$ 6000 extragalactic Hi absorbers can be found with a
detection rate of $\sim$ 5.5 per cent (detection rate of 40$\%$ of the ALFALFA
data). However, we only blindly find 5 absorption systems in the 643.8-hour
drift scan survey. This difference between forecast and real data processing
is attributed to the RFI and unstable bandpass (standing waves), which can
contaminate the spectrum profile of true absorption systems and produce a
spurious absorption line shape. It is expected that with standing waves
corrected and the map-making method applied in the near future, more Hi
absorbers could be unveiled with the FAST extra-galactic sky survey data.

Figure 19: The measured Hi column density frequency distribution
($f(N_{\textsc{Hi\leavevmode\nobreak\ }},X)$) or the 95 per cent upper limits
on $f(N_{\textsc{Hi\leavevmode\nobreak\ }},X)$ for CRAFTS data and previous
works. For data used in this work, $f(N_{\textsc{Hi\leavevmode\nobreak\ }},X)$
for associated Hi absorption (measured using the 4 associated absorption) and
intervening Hi absorption (the 95 per cent upper limits) are presented as
oblique and straight crosses, the distributions for the spin temperature to
source covering fraction ratio of 100 K and 1000 K are shown as blue and red
crosses. The predicted $f(N_{\textsc{Hi\leavevmode\nobreak\ }},X)$ for the Hi
absorption searching in map-making data from the full coverage of the FAST
observable sky are presented as green oblique (associated) and straight
(intervening) crosses. The predicted distribution from planned FLASH survey
(Allison et al., 2020) (integration time 2 hours, 36 antennas, sky area of
$\delta$ = +10 deg and redshift coverage of z = 0.4 to 1.0), the ALFALFA
absorption pilot survey (Darling et al., 2011) and model fits to Hi emission-
line observations with WSRT (Westerbork Synthesis Radio Telescope) at z=0
(Zwaan et al., 2005) and DLA systems in SDSS-DR7 at z$\sim$3 (Noterdaeme et
al., 2009) are also presented.

##  6 Summary

In this paper, we present the early science results of a purely blind search
for extragalactic Hi 21-cm absorption lines in the CRAFTS drift-scan data from
FAST. Nearly 643.8 hours and 3155 deg2 survey (covers 44827 radio sources with
a flux density greater than 12 mJy) from the Commensal Radio Astronomy FAST
Survey (CRAFTS) are searched for Hi absorber. The total comoving absorption
path length spanned by our data for intervening and associated absorption is
$\Delta X^{\mathrm{inv}}$ = 1.05$\times 10^{4}$ ($\Delta
z^{\mathrm{inv}}=9.80\times 10^{3}$) and $\Delta X^{\mathrm{asc}}$ =
1.63$\times 10^{1}$ ($\Delta z^{\mathrm{asc}}=1.51\times 10^{1}$, assuming
$T_{s}/c_{f}$ = 100 K). The completeness correction, determined using mock
absorption signals with FWHM = 30 $\,{\rm km\,s^{-1}}$, has been applied to
the estimates of comoving absorption path. Both polarizations data of all 19
beams are processed. Due to the RFI, only the relatively clean data in the
frequency range of 1.3 GHz to 1.45 GHz are searched.

We use a matched-filtering approach to detect the Hi absorption profiles at
each time point of the drift scan. By cross-correlating information from
different beams, we effectively eliminate spurious signals and identify three
previously known Hi absorbers (UGC 00613, 3C 293 and 4C +27.14) as well as two
newly discovered ones (NVSS J231240-052547 and NVSS J053118+315412). We fit
the Hi profiles with multi-components Gaussian functions and calculate the
redshift, FWHM, flux density, optical depth and Hi column densities for each
source. The newly discovered Hi absorption feature in NVSS J053118+315412
displays associated absorption with both blueshifted and redshifted wings, as
well as redshifted components. These characteristics suggest the presence of
unsettled gas structures and possible accretion of gas onto the SMBH. Our
results demonstrate the power of FAST in Hi absorption blind searching. The
forecast for the FAST Hi absorption searching indicates a long comoving
absorption path and high sensitivity to N${}_{\textsc{Hi\leavevmode\nobreak\
}}$ frequency distribution function could be obtained with CRAFTS.

Discovery of intervening Hi absorbers in blind radio search may enable us to
unravel the nature of the DLAs. As most DLAs were discovered in the
observation of optically bright background quasars, it is often difficult to
observe the absorber itself. In the present case, Hi absorbers with column
density comparable to the DLAs are detected in the radio, it is hopeful that
the absorber could also be observed optically. We have found optical/IR
counterparts in data archives along the line of sight where the two
absorptions are detected, and follow-up observation with redshift measurement
will determine whether NVSS J231240-052547 is associated with the Hi absorbers
and the nature of the counterparts.

## Acknowledgements

We acknowledge the support of the National SKA Program of China,
No.2022SKA0110100. This work is supported by the National Key R&D Program
2017YFA0402603, the Ministry of Science and Technology (MoST) inter-government
cooperation program China-South Africa Cooperation Flagship project
2018YFE0120800, the MoST grant 2016YFE0100300, the National Natural Science
Foundation of China (NSFC) key project grant 11633004, the Chinese Academy of
Sciences (CAS) Frontier Science Key Project QYZDJ-SSW-SLH017 and the CAS
Interdisciplinary Innovation Team grant (JCTD-2019-05), the NSFC-ISF joint
research program No. 11761141012, the CAS Strategic Priority Research Program
XDA15020200, and the NSFC grant 11773034.

Wenkai Hu and Guilaine Lagache are supported by the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation
programme (project CONCERTO, grant agreement No 788212) and from the
Excellence Initiative of Aix-Marseille University-A*Midex, a French
”Investissements d’Avenir” programme. Zheng Zheng is supported by NSFC grant
No. 11988101, U1931110 and 12041302. Zheng Zheng is also supported by CAS
Interdisciplinary Innovation Team (JCTD-2019-05). The authors thank
Sne$\rm\check{z}$ana Stanimirovi$\rm\acute{c}$, Elizabeth K. Mahony, Stephen
J. Curran and James R. Allison for helpful discussion. Ue-Li Pen receives
support from Ontario Research Fund—Research Excellence Program (ORF-RE),
Natural Sciences and Engineering Research Council of Canada (NSERC) [funding
reference number RGPIN-2019-067, CRD 523638-18, 555585-20], Canadian Institute
for Advanced Research (CIFAR), the National Science Foundation of China
(Grants No. 11929301), Thoth Technology Inc, Alexander von Humboldt
Foundation, and the National Science and Technology Council (NSTC)
(111-2123-M-001 -008 -, and 111-2811-M-001 -040 -). Computations were
performed on the SOSCIP Consortium’s [Blue Gene/Q, Cloud Data Analytics, Agile
and/or Large Memory System] computing platform(s). SOSCIP is funded by the
Federal Economic Development Agency of Southern Ontario, the Province of
Ontario, IBM Canada Ltd., Ontario Centres of Excellence, Mitacs and 15 Ontario
academic member institutions.

The radio data analyzed in this work can be accessed by sending a request to
the FAST Data Centre or the corresponding authors of this paper.

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