#  A Giant Metrewave Radio Telescope Survey of Radio-loud Broad Absorption
Line Quasars

Takayuki J. Hayashi1,2, Akihiro Doi3,4, Hiroshi Nagai1,5,
1National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo,
181-8588, Japan
2Azabu Junior and Senior High School, 2-3-29 Motoazabu, Minato-ku, Tokyo,
106-0046, Japan
3Institute of Space and Astronautical Science, Japan Aerospace Exploration
Agency, 3-1-1 Yoshinodai, Chuo, Sagamihara, Kanagawa, 252-5210, Japan
4Department of Space and Astronautical Science, The Graduate University for
Advanced Studies, SOKENDAI,
3-1-1 Yoshinodai, Chuo, Sagamihara, Kanagawa, 229-8510, Japan
5Astronomical Science Program, The Graduate University for Advanced Studies,
SOKENDAI, 2-21-1 Osawa, Mitaka, 181-8588, Japan
E-mail<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

A substantial fraction of quasars display broad absorption lines (BALs) in
their rest-frame ultraviolet spectra. While the origin of BALs is thought to
be related to the accretion disc wind, it remains unclear whether the observed
ratio of BAL to non-BAL quasars is due to orientation. We conducted
observations of 48 BAL quasars and the same number of non-BAL quasars at 322
MHz using the Giant Metrewave Radio Telescope. Combined with previous flux
measurements ranging from MHz to GHz frequencies, we compared continuum radio
spectra between the two quasar groups. These data offer insights into low-
frequency radio properties that have been difficult to investigate with
previous observations only at GHz frequencies. Our results present that $73\pm
13$ per cent of the BAL quasars exhibit steep or peaked spectra, a higher
proportion than $44\pm 14$ per cent observed in the non-BAL quasars. In
contrast, there are no discernible differences between the two quasar groups
in the radio luminosity, peak frequency, and spectral index distributions of
sources with steep or peaked spectra and sources with flat or inverted
spectra. Generally, as the jet axis and line of sight become closer to
parallel, quasars exhibit flat or inverted spectra rather than steep or peaked
ones. Therefore, these results suggest that BAL quasars are more frequently
observed farther from the jet axis than non-BAL quasars. However, given that a
certain proportion of BAL quasars exhibit flat or inverted spectra, more than
the simple orientation scenario is required to elucidate the radio properties
of BAL quasars.

###### keywords:

galaxies: active – galaxies: jets – galaxies: evolution – radio continuum:
galaxies – quasars: general – radiation mechanisms: non-thermal

††pagerange:  A Giant Metrewave Radio Telescope Survey of Radio-loud Broad
Absorption Line Quasars – A Giant Metrewave Radio Telescope Survey of Radio-
loud Broad Absorption Line Quasars ††pubyear: 2024††pagerange:  A Giant
Metrewave Radio Telescope Survey of Radio-loud Broad Absorption Line Quasars –
A Giant Metrewave Radio Telescope Survey of Radio-loud Broad Absorption Line
Quasars

##  1 Introduction

Broad absorption line (BAL) quasars exhibit blue-shifted absorption troughs in
their ultraviolet spectra, which result from broad resonance lines (Lynds,
1967; Weymann et al., 1981; Weymann et al., 1991). An active galactic nucleus
(AGN) wind, accelerated by radiation pressure to a velocity of $\sim$ 0.1$c$,
is responsible for the absorption (Laor & Brandt, 2002; Ganguly et al., 2007).
The winds emanating from the accretion disc are the most potent absorber
(e.g., Murray et al., 1995; Elvis, 2000; Proga et al., 2000; Nomura et al.,
2013). AGN winds are of significant importance since they provide substantial
energy to their host galaxies (e.g., Borguet et al., 2013; Hamann et al.,
2019; Choi et al., 2020, 2022), playing a pivotal role in regulating the
coevolution of galaxies and supermassive black holes (Ciotti et al., 2009;
Farrah et al., 2012; Bischetti et al., 2023). Therefore, a thorough
understanding of BAL quasars is imperative in a cosmological context.

BAL quasars fall into two categories based on the ionisation levels of their
absorption troughs. HiBAL quasars display high-ionisation troughs, such as C
IV and Si IV, constituting 10–30 per cent of all quasars (e.g., Trump et al.,
2006; Knigge et al., 2008; Gibson et al., 2009; Allen et al., 2011). LoBAL
quasars, accounting for $\sim$ 10 per cent of all BAL quasars, exhibit low-
ionisation troughs in addition to high-ionisation ones, such as Mg II and Al
III. A small subset of LoBAL quasars, $\sim$ 1 per cent of all BAL quasars,
are referred to as FeLoBAL quasars, showing absorption from excited states of
Fe II or Fe III (Trump et al., 2006). The cause of these observed proportions
is still an enigmatic puzzle, with two prominent models proposed: an
orientation scheme and an evolution scheme. The former suggests that all
quasars have directional winds and that BAL detection depends on the object’s
inclination (Weymann et al., 1991; Goodrich & Miller, 1995). In this scenario,
the ratio of BAL to non-BAL quasars and the proportion of different types of
BAL quasars depend on the number of quasars viewed from various angles (Elvis,
2000). In contrast, the evolution scheme argues that the ratio of BAL to non-
BAL quasars reflects the period during which quasars exhibit AGN winds. LoBAL
quasars, in particular, are believed to be young, recently-fueled quasars
(Voit et al., 1993; Canalizo & Stockton, 2001; Lípari & Terlevich, 2006; Chen
et al., 2022; Lazarova et al., 2023; Peng et al., 2024). Ultimately, the
question concerns whether BAL and non-BAL quasars share the same central
engine.

Previous studies have shown that jet activity is the main factor responsible
for the radio emission observed in radio-loud BAL quasars, which is supported
by high spatial resolution images obtained through very long baseline
interferometry (VLBI; e.g., Jiang & Wang, 2003; Liu et al., 2008; Bruni et
al., 2013; Hayashi et al., 2013; Kunert-Bajraszewska et al., 2015; Cegłowski
et al., 2015). Since thermal disc winds and nonthermal jets arise from the
same central engine, radio observations that detect nonthermal emission can
provide valuable insights into the abovementioned question. Previous
investigations conducted at GHz frequencies have revealed differences between
BAL and non-BAL quasars, with BAL quasars found to be less luminous than non-
BAL quasars (Stocke et al., 1992; Becker et al., 2000; Becker et al., 2001;
Shankar et al., 2008). Additionally, they exhibit steeper spectra (DiPompeo et
al., 2011; Bruni et al., 2012), which supports the orientation scenario where
BAL quasars are viewed from an edge-on perspective (DiPompeo et al., 2012).
However, morphological studies have suggested the presence of a significant
proportion of BAL quasars, including polar BAL quasars, at all inclinations
(Nair & Vivek, 2022). Moreover, BAL quasars exhibiting significant radio
variability, indicative of face-on objects, have been documented (Zhou et al.,
2006; Ghosh & Punsly, 2007; DiPompeo et al., 2011; Cegłowski et al., 2017).
Therefore, the simple orientation scenario cannot fully account for the radio
characteristics of BAL quasars.

Thus far, several observational inquiries have also explored the overall radio
spectral shape of BAL quasars, covering both radio-quiet (Barvainis &
Lonsdale, 1997) and radio-loud samples (Montenegro-Montes et al., 2008; Bruni
et al., 2012; Tuccillo et al., 2017). Initially, there was a prevalent belief
that most radio-loud BAL quasars displayed compact radio morphology (Becker et
al., 2000; Becker et al., 2001). Their spectral characteristics were found to
be typical of compact steep-spectrum (CSS) or GHz peaked-spectrum (GPS)
sources (Montenegro-Montes et al., 2008), which are candidates for lobe-
dominated young radio sources (O’Dea, 1998). These findings were part of the
basis for the evolution scheme of BAL quasars. However, when comparing them
with non-BAL quasars, the fractions of sources suggesting a peaked spectrum
were similar in the two samples (Bruni et al., 2012; Tuccillo et al., 2017).

Despite the efforts mentioned above, observations conducted at GHz frequencies
are suboptimal for comprehending the true nature of objects located at high
redshifts, where the ultraviolet absorption lines fall within the optical
band, owing to their susceptibility to the orientation-dependent relativistic
beaming effects of the jets. Based solely on high-frequency observations, it
is impossible to discern the underlying cause of the radio weakness of BAL
quasars, whether attributed to intrinsically weak jet activity in the central
engine or weak relativistic beaming effects. Moreover, due to the limited low-
frequency observations in the MHz range in the past, comparisons of the
overall spectral shape for high-redshift sources were restricted to the most
extreme cases, where radio spectra peak at high rest frequencies. Therefore,
observations at lower frequencies play a crucial role in addressing these
issues. By capturing the low-frequency extended emission, where relativistic
effects are weak, we can trace the total amount of intrinsic jet activity from
the central engines.

Recently, the all-sky survey conducted at 144 MHz (Shimwell et al., 2022) has
illuminated that the detection of BAL in its optical spectra is uniform across
a range of radio luminosities (Morabito et al., 2019), differing from the
previous findings at GHz frequencies (e.g., Shankar et al., 2008).
Furthermore, Morabito et al. (2019) have reported a potential difference in
spectral indices by comparing the 144-MHz data with conventional 1.4-GHz data
(Becker et al., 1995). Nevertheless, prior estimates of spectral indices based
on the limited number of data points in the MHz regime are inaccurate, and the
underlying causes of these discrepancies have yet to be discussed. Therefore,
multifrequency data obtained at lower frequencies are imperative for capturing
the overall spectral shape and determining the physical parameters at the same
rest frequencies across all sources.

This paper presents the findings of a survey on BAL quasars and a comparison
sample at 322 MHz using the Giant Metrewave Radio Telescope (GMRT). The study
compares the low-frequency radio spectra of BAL quasars with those of non-BAL
quasars. The samples are described in Section 2, while Section 3 explains the
observations and data reduction. The results are presented in Section 4, along
with discussions of the origin of the radio properties in Section 5. The paper
defines spectral index, $\alpha$, as $f_{\nu}\propto\nu^{\alpha}$, where
$f_{\nu}$ represents flux density at frequency, $\nu$. We utilised the
standard cosmological model with cold dark matter and a cosmological constant
having $H_{0}=70$ km s-1 Mpc-1, $\Omega_{\rm M}=0.3$, and
$\Omega_{\Lambda}=0.7$, which is supported by observational studies from the
past decades (e.g., Planck Collaboration et al., 2020).

##  2 Sample

###  2.1 BAL sample

We selected our targets from the quasar catalogue (Schneider et al., 2007)
obtained from the fifth data release (DR5; Adelman-McCarthy et al., 2007) of
the Sloan Digital Sky Survey (SDSS; York et al., 2000). Initially, we
extracted our BAL sample from a subset of quasars, specifically those that
have had their C IV BAL reported by Gibson et al. (2009). The definition of
BAL is a subject of debate, and various studies have addressed this issue
(Hall et al., 2002; Ganguly et al., 2007; Knigge et al., 2008). Here, the
traditional balnicity index (BI; Weymann et al., 1991) is a strict criterion,
and some studies have suggested that it may underestimate the presence of BAL
(Reichard et al., 2003; Knigge et al., 2008). Therefore, in this study, we
adopted the modified balnicity index, BI0, proposed by Gibson et al. (2009),
which is more lenient than BI.

To ensure that the blue-shifted and high-velocity C IV absorption line was
within the SDSS spectral bandpass, we limited our target range to sources with
redshifts of $1.68\leq z\leq 4.93$. Our identification of radio-loud quasars
involved cross-referencing the optical positions from the SDSS with the Faint
Images of the Radio Sky at Twenty centimeters survey (FIRST survey; Becker et
al., 1995), restricting our sample to sources with an integrated flux density
greater than 10 mJy and located within 3 arcsecs of the FIRST radio positions.
We focused on objects within the right ascension range of 10 to 17 h to
accommodate the allocated observing time. Our sample, detailed in Table 1,
comprises 48 sources, 35 of which intersect with the sample in DiPompeo et al.
(2011). The FIRST survey spatially resolved three sources in our sample; Fig.
1 presents their images. It is worth noting that three sources in our sample,
b20 (J123954.15$+$373954.5), b34 (J141437.99$+$045537.4), and b36
(J143340.35$+$512019.3), are also classified as LoBAL quasars by Gibson et al.
(2009), showing BAL in their Al III line. Also, b34 shows BAL in its Mg II
line.

Table 1: BAL sample for GMRT Observation.

ID | Source Name | $z$ | $M_{\mathrm{i}}$ | BI | BI0 | Compo- | R.A. | Dec. | $f_{1.4}^{\textrm{FIRST}}$ | $f_{1.4}^{\textrm{NVSS}}$ | $\log L_{\rm 5}$
---|---|---|---|---|---|---|---|---|---|---|---
| (SDSS J) |  | (mag) | ( km s-1) | ( km s-1) | nent | (J2000) | (J2000) | (mJy) | (mJy) | (W Hz-1)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12)
b01 | 100109.42$+$114608.8 | 2.278 |  $-$27.1 |  0716.1 | 3030.5 | total | … | … |  0023.8 |  0023.6 | 27.5
| … | … | … | … | … | A | 10 01 09.431 |  $+$11 46 08.71 |  0013.7 | … | 27.2
| … | … | … | … | … | B | 10 01 09.392 |  $+$11 45 55.13 |  0010.1 | … | 27.1
b02 | 100424.88$+$122922.2 | 2.640 |  $-$25.8 | 4534.0† | 4534.0† | … | 10 04 24.872 |  $+$12 29 22.39 |  0012.3 |  0011.8 | 27.4
b03 | 104059.79$+$055524.4 | 2.443 |  $-$26.6 | 4120.3 | 4120.3 | … | 10 40 59.802 |  $+$05 55 24.78 |  0042.2 |  0039.1 | 27.8
b04 | 104452.41$+$104005.9 | 1.882 |  $-$27.9 | 2463.3 | 3283.9 | … | 10 44 52.417 |  $+$10 40 05.91 |  0017.2 |  0013.1 | 27.0
b05 | 105416.51$+$512326.0 | 2.341 |  $-$27.2 |  0337.5 | 1056.2 | … | 10 54 16.528 |  $+$51 23 26.21 |  0033.9 |  0035.6 | 27.7
b06 | 110206.66$+$112104.9 | 2.351 |  $-$27.7 |  0000.0 |  0075.3 | … | 11 02 06.657 |  $+$11 21 04.74 |  0083.1 |  0080.8 | 28.1
b07 | 110531.42$+$151215.9 | 2.063 |  $-$27.0 | 4556.4 | 4556.4 | … | 11 05 31.490 |  $+$15 12 17.55 |  0012.3 |  0011.4 | 27.0
b08 | 112241.46$+$303534.9 | 1.810 |  $-$28.6 |  0000.1 |  0000.1 | … | 11 22 41.467 |  $+$30 35 34.88 |  0010.0 |  0009.5 | 26.7
b09 | 112938.47$+$440325.0 | 2.212 |  $-$27.8 |  0000.0 |  0806.5 | … | 11 29 38.475 |  $+$44 03 25.05 |  0042.0 |  0042.3 | 27.7
b10 | 113152.56$+$584510.2 | 2.262 |  $-$26.8 |  0002.5 |  0925.3 | … | 11 31 52.546 |  $+$58 45 10.26 |  0012.8 |  0013.2 | 27.2
b11 | 113445.83$+$431858.0 | 2.184 |  $-$26.9 | 4443.4 | 4443.4 | … | 11 34 45.834 |  $+$43 18 57.87 |  0028.0 |  0025.2 | 27.5
b12 | 115901.75$+$065619.0 | 2.191 |  $-$26.6 | 1675.4 | 1675.4 | … | 11 59 01.713 |  $+$06 56 18.91 |  0160.1 |  0158.3 | 28.2
b13 | 115944.82$+$011206.9 | 2.000 |  $-$28.4 |  0000.0 |  0937.9 | … | 11 59 44.832 |  $+$01 12 06.87 |  0268.5 |  0275.6 | 28.3
b14 | 121323.94$+$010414.7 | 2.829 |  $-$26.0 | 1551.0 | 1551.0 | … | 12 13 23.934 |  $+$01 04 14.82 |  0022.9 |  0027.5 | 27.8
b15 | 121539.66$+$090607.4 | 2.723 |  $-$28.0 |  0116.3 |  0116.3 | … | 12 15 39.670 |  $+$09 06 07.48 |  0049.8 |  0049.1 | 28.1
b16 | 122848.21$-$010414.5 | 2.655 |  $-$28.1 |  0017.1 |  0017.1 | … | 12 28 48.190 |  $-$01 04 14.27 |  0030.8 |  0029.1 | 27.8
b17 | 123411.73$+$615832.6 | 1.946 |  $-$26.9 | 4907.9 | 4907.9 | … | 12 34 11.747 |  $+$61 58 32.40 |  0024.0 |  0022.7 | 27.2
b18 | 123511.59$+$073330.7 | 3.035 |  $-$27.9 |  0000.0 |  0093.5 | … | 12 35 11.609 |  $+$07 33 30.80 |  0011.3 |  0012.9 | 27.6
b19 | 123717.44$+$470807.0 | 2.271 |  $-$27.3 |  0868.7 |  0868.7 | … | 12 37 17.438 |  $+$47 08 07.05 |  0080.2 |  0090.9 | 28.0
b20 | 123954.15$+$373954.5 | 1.841 |  $-$25.5 |  0959.3 |  0959.3 | total | … | … |  0018.5 |  0016.2 | 27.0
| … | … | … | … | … | A | 12 39 54.149 |  $+$37 39 54.45 |  0010.7 | … | 26.8
| … | … | … | … | … | B | 12 39 55.205 |  $+$37 39 42.20 |  0004.3 | … | 26.4
| … | … | … | … | … | C | 12 39 52.533 |  $+$37 40 15.77 |  0003.5 | … | 26.3
b21 | 125243.85$+$005320.1 | 1.693 |  $-$27.1 |  0094.6 |  0094.6 | … | 12 52 43.860 |  $+$00 53 20.17 |  0012.8 |  0015.4 | 26.7
b22 | 130332.05$+$014407.4 | 2.109 |  $-$26.2 |  0000.0 |  0136.0 | … | 13 03 32.061 |  $+$01 44 07.41 |  0038.0 |  0034.7 | 27.5
b23 | 130448.06$+$130416.5 | 2.568 |  $-$27.3 |  0004.8 |  0004.8 | … | 13 04 48.050 |  $+$13 04 16.67 |  0050.0 |  0056.5 | 28.0
b24 | 130756.73$+$042215.5 | 3.022 |  $-$28.7 |  0879.0 |  0879.0 | … | 13 07 56.723 |  $+$04 22 15.50 |  0014.9 |  0015.8 | 27.7
b25 | 133004.34$+$605949.7 | 1.734 |  $-$26.2 |  0072.1 |  0072.1 | total | … | … |  0028.5 |  0038.3 | 27.1
| … | … | … | … | … | A | 13 30 04.335 |  $+$60 59 49.93 |  0018.1 | … | 26.9
| … | … | … | … | … | B | 13 30 03.250 |  $+$60 59 52.71 |  0010.4 | … | 26.7
b26 | 133701.39$-$024630.3 | 3.064 |  $-$27.9 |  0000.0 |  0002.3 | … | 13 37 01.399 |  $-$02 46 29.89 |  0044.8 |  0045.1 | 28.2
b27 | 135550.30$+$361627.6 | 1.855 |  $-$26.3 |  0000.0 |  0604.4 | … | 13 55 50.294 |  $+$36 16 27.55 |  0010.7 |  0015.3 | 26.8
b28 | 135910.45$+$563617.4 | 2.248 |  $-$27.9 |  0056.2 |  0156.9 | … | 13 59 10.410 |  $+$56 36 17.01 |  0017.9 |  0016.8 | 27.3
b29 | 135910.77$+$400218.6 | 2.013 |  $-$26.8 |  0432.9 |  0432.9 | … | 13 59 10.774 |  $+$40 02 18.66 |  0015.0 |  0014.0 | 27.1
b30 | 140126.15$+$520834.6 | 2.972 |  $-$28.0 |  0080.3 |  0080.3 | … | 14 01 26.163 |  $+$52 08 34.63 |  0037.1 |  0030.4 | 28.1
b31 | 140501.12$+$041535.7 | 3.215 |  $-$27.1 |  0012.5 |  0012.5 | … | 14 05 01.114 |  $+$04 15 35.87 | 1055.9 |  0933.0 | 29.7
b32 | 141313.63$+$411637.8 | 2.616 |  $-$28.4 | 1053.3 | 1053.3 | … | 14 13 13.622 |  $+$41 16 37.91 |  0026.7 |  0028.7 | 27.7
b33 | 141334.38$+$421201.7 | 2.817 |  $-$27.9 |  0000.0 | 1446.9 | … | 14 13 34.404 |  $+$42 12 01.76 |  0018.7 |  0016.8 | 27.7
b34 | 141437.99$+$045537.4 | 1.851 |  $-$26.1 | 2015.1 | 2201.2 | … | 14 14 37.977 |  $+$04 55 37.22 |  0011.8 |  0014.4 | 26.8
b35 | 141736.05$+$372825.9 | 2.554 |  $-$26.1 |  0000.0 |  0177.3 | … | 14 17 36.045 |  $+$37 28 26.04 |  0025.8 |  0023.5 | 27.7
b36 | 143340.35$+$512019.3 | 1.863 |  $-$26.9 | 1085.7 | 1085.7 | … | 14 33 40.387 |  $+$51 20 19.70 |  0012.6 |  0013.0 | 26.9
b37 | 144434.80$+$003305.3 | 2.036 |  $-$26.5 |  0000.0 |  0163.0 | … | 14 44 34.816 |  $+$00 33 05.49 |  0013.2 |  0010.5 | 27.0
b38 | 145910.13$+$425213.2 | 2.967 |  $-$28.2 |  0087.1 |  0087.1 | … | 14 59 10.134 |  $+$42 52 13.20 |  0013.7 |  0015.0 | 27.6
b39 | 150332.93$+$440120.6 | 2.050 |  $-$27.0 | 1405.1 | 1405.1 | … | 15 03 32.948 |  $+$44 01 20.63 |  0011.2 |  0010.8 | 27.0
b40 | 150823.71$+$334700.7 | 2.208 |  $-$27.6 |  0663.5 |  0663.5 | … | 15 08 23.730 |  $+$33 47 00.63 |  0132.0 |  0131.3 | 28.2
b41 | 151630.30$-$005625.5 | 1.921 |  $-$27.0 |  0000.0 |  0517.0 | … | 15 16 30.350 |  $-$00 56 24.67 |  0025.5 |  0025.8 | 27.2
b42 | 153729.54$+$583224.6 | 3.059 |  $-$26.8 |  0000.0 | 1432.0 | … | 15 37 29.553 |  $+$58 32 24.79 |  0014.2 |  0014.5 | 27.7
b43 | 155429.40$+$300118.9 | 2.693 |  $-$28.4 |  0574.8 |  0574.8 | … | 15 54 29.403 |  $+$30 01 19.04 |  0041.2 |  0040.5 | 28.0
b44 | 160354.15$+$300208.6 | 2.030 |  $-$27.7 |  0000.0 |  0480.0 | … | 16 03 54.159 |  $+$30 02 08.88 |  0054.2 |  0054.1 | 27.6
b45 | 162453.47$+$375806.6 | 3.381 |  $-$28.4 |  0900.5 |  0900.5 | … | 16 24 53.470 |  $+$37 58 06.65 |  0056.4 |  0055.6 | 28.5
b46 | 162559.90$+$485817.5 | 2.724 |  $-$28.4 | 3447.9 | 3447.9 | … | 16 25 59.905 |  $+$48 58 17.50 |  0025.5 |  0026.0 | 27.8
b47 | 162656.74$+$295328.0 | 2.312 |  $-$26.9 |  0283.4 |  0283.4 | … | 16 26 56.741 |  $+$29 53 28.02 |  0011.3 |  0013.4 | 27.2
b48 | 165543.24$+$394519.9 | 1.753 |  $-$27.2 | 3635.3 | 3635.3 | … | 16 55 43.235 |  $+$39 45 19.91 |  0010.2 |  0009.2 | 26.7

Note. Columns are as follows: (1) Object ID; (2) SDSS source name; (3), (4)
Redshift and $i$-band absolute magnitude from the SDSS quasars catalog DR5
(Schneider et al., 2007); (5), (6) balnicity index, BI, and modified balnicity
index, BI0, of C IV absorption line, respectively (Gibson et al., 2009). BI
and BI0 of b02 indicated by † were measured based on the estimated redshift of
$z=4.66$. See text for details; (7) Name of each component if multiple radio
source is associated; (8), (9) Radio positions; (10) Flux density at 1.4 GHz
from the FIRST survey. Reference for the columns (7)–(9) is Becker et al.
(1995); (11) Flux density at 1.4 GHz from the NVSS (Condon et al., 1998); (12)
Log specific luminosity at rest 5 GHz calculated by flux density at 1.4 GHz
assuming spectral index of $\alpha=-0.7$. For quasars associated with multiple
radio sources, we provide information on each source.

Subsequently, we identified a discrepancy in the redshift of b02
(100424.88$+$122922.2; $z=2.64$) reported by Schneider et al. (2007) and
Gibson et al. (2009), with the latter presenting a value of $z=4.66$. Further
analysis, based on a broader SDSS spectrum obtained during a different epoch
(Lyke et al., 2020), suggested a redshift closer to that of Schneider et al.,
which we ultimately adopted. Assuming the redshift of $z=2.64$, we detected no
C IV absorption from this source; hence, the BI and BI0 presented in Table 1
should be 0. However, the source displayed potential BAL in Al III and Mg II,
indicating characteristics of a LoBAL quasar. Despite this issue, we could not
acquire GMRT observational data for this source due to radio frequency
interference (RFI). Even in statistical analyses that do not require the GMRT
data, we provide both examinations, considering and excluding this specific
object.

Figure 1:  Radio images at 1.4 GHz for b01 (J100109$+$114608), b20
(J123954$+$373954), b25 (J133004$+$605949), n24 (J141031$+$614136), and n27
(J142033$-$003233) from top left to bottom right, all of which are resolved
BAL quasars, provided by the FIRST survey. The optical position of the quasar
corresponds to the component A in each image. From top left to bottom right,
the contour levels commence at 520, 546, 479, 494, and 394 $\mu$Jy beam-1
(equivalent to the 3$\sigma$ noise level of the image) and are then multiplied
by a factor of 2.

###  2.2 Non-BAL sample

To establish a comparison group, we created a non-BAL sample where each object
was paired with objects in the BAL sample based on each physical quantity. The
criteria for selection comprises a redshift of 10 per cent of the
corresponding BAL quasar within the range of $1.68\leq z\leq 4.93$, a flux
density at 1.4 GHz of 20 per cent of the BAL quasar, and an $i$-band magnitude
within $\pm$1.0 of the BAL quasar. In addition, we tried to select objects
that could be observed using the same phase calibrators as the BAL sample to
minimise the total observation time. Table 2 lists the resulting non-BAL
sample, which contains two sources that the FIRST survey resolved; Fig. 1 also
shows their images. Additionally, we visually inspected the SDSS spectra of
the non-BAL sample in the rest-frame wavelength range of 1400–1600 Å. We
confirmed they were free from significant broad absorption of Si IV or C IV.
We note, however, that we inadvertently incorporated a source, n24
(J141031.00$+$614136.9), that displays a BAL in Al III at 1857.4 Å in our
sample. We will present both analyses, incorporating and excluding this
object.

Fig. 2 depicts the distributions of redshift, specific luminosity at 5 GHz
with a spectral index of $\alpha=-0.7$, and $i$-band absolute magnitude for
both the BAL and non-BAL samples. The Kolmogorov-Smirnov (KS) and Wilcoxon
rank sum (RS) tests indicate no notable distinctions between the distributions
of the two samples. Consequently, we can deduce that the two samples exhibit
homogeneity, except for BALs.

Figure 2:  Comparison of the characteristics of the BAL and non-BAL samples:
redshift $z$, specific radio luminosity at rest 5.0 GHz, $L_{5.0}$, and
$i$-band absolute magnitude, $M_{i}$, from left to right. Each panel shows the
distribution of the two samples, represented respectively in blue and orange,
both in terms of number and cumulative frequency. We have applied two
statistical tests, the KS and RS tests, to evaluate the likelihood that the
two distributions do not originate from different parent populations. The KS
test yields a test statistic of $D_{\rm KS}$ = 0.0833, 0.0833, and 0.1875 for
$z$, $L_{5.0}$, and $M_{i}$, respectively, with corresponding probabilities of
$p=0.996$, 0.996 and 0.368. The RS test give a test statistic of $Z_{\rm RS}$
= 1194, 1162, and 1018 for $z$, $L_{5.0}$, and $M_{i}$, respectively, with
corresponding probabilities of $p=0.764$, 0.945 and 0.326. These $p$-values
indicate the probability of obtaining a result equal to or more extreme than
the observed result, assuming the null hypothesis that the two samples are
drawn from the same parent population.  Table 2: Non-BAL sample for GMRT
Observation.

ID | Source Name | $z$ | $M_{\mathrm{i}}$ | Compo- | R.A. | Dec. | $f_{1.4}^{\textrm{FIRST}}$ | $f_{1.4}^{\textrm{NVSS}}$ | $\log L_{\rm 5}$
---|---|---|---|---|---|---|---|---|---
| (SDSS J) |  | (mag) | nent | (J2000) | (J2000) | (mJy) | (mJy) | (W Hz-1)
(1) | (2) | (3) | (4) | (7) | (5) | (6) | (7) | (8) | (9)
n01 | 103808.94$+$464249.1 | 1.924 |  $-$26.9 | … | 10 38 08.950 |  $+$46 42 49.46 |  0012.2 |  0012.4 | 26.9
n02 | 111048.93$+$045608.0 | 2.208 |  $-$26.8 | … | 11 10 48.963 |  $+$04 56 07.13 |  0065.2 |  0074.2 | 27.9
n03 | 111336.10$+$494034.7 | 2.466 |  $-$27.6 | … | 11 13 36.087 |  $+$49 40 34.63 |  0028.7 |  0027.4 | 27.7
n04 | 111434.01$+$041434.0 | 1.719 |  $-$26.0 | … | 11 14 34.018 |  $+$04 14 33.97 |  0017.1 |  0018.7 | 26.9
n05 | 112854.24$+$035341.4 | 1.829 |  $-$26.9 | … | 11 28 54.258 |  $+$03 53 41.05 |  0019.8 |  0020.3 | 27.0
n06 | 113017.37$+$073212.9 | 2.647 |  $-$28.9 | … | 11 30 17.371 |  $+$07 32 13.09 |  0031.6 |  0027.6 | 27.8
n07 | 113716.36$+$371046.4 | 2.027 |  $-$27.3 | … | 11 37 16.365 |  $+$37 10 46.67 |  0010.3 |  0009.5 | 26.9
n08 | 113854.52$+$394553.6 | 2.159 |  $-$27.2 | … | 11 38 54.533 |  $+$39 45 53.62 |  0021.2 |  0019.7 | 27.3
n09 | 115534.50$+$575156.4 | 1.967 |  $-$26.4 | … | 11 55 34.509 |  $+$57 51 56.49 |  0023.9 |  0024.2 | 27.2
n10 | 121911.23$-$004345.5 | 2.293 |  $-$27.7 | … | 12 19 11.247 |  $-$00 43 45.42 |  0094.5 |  0104.5 | 28.1
n11 | 123215.09$+$554049.4 | 2.307 |  $-$26.3 | … | 12 32 15.115 |  $+$55 40 49.53 |  0011.1 |  0032.2 | 27.2
n12 | 123545.38$-$033610.9 | 2.375 |  $-$26.6 | … | 12 35 45.391 |  $-$03 36 10.79 |  0010.2 |  0011.3 | 27.2
n13 | 123856.09$-$005930.8 | 1.844 |  $-$27.3 | … | 12 38 56.101 |  $-$00 59 30.89 |  0014.0 |  0015.5 | 26.9
n14 | 124409.64$+$554823.4 | 1.768 |  $-$25.9 | … | 12 44 09.639 |  $+$55 48 23.49 |  0010.2 |  0010.5 | 26.7
n15 | 125321.59$-$032315.7 | 1.771 |  $-$26.6 | … | 12 53 21.602 |  $-$03 23 15.96 |  0026.7 |  0030.0 | 27.1
n16 | 131003.35$+$535348.2 | 3.278 |  $-$27.2 | … | 13 10 03.352 |  $+$53 53 48.16 |  0014.5 |  0013.1 | 27.8
n17 | 131926.27$+$143439.9 | 2.541 |  $-$27.6 | … | 13 19 26.285 |  $+$14 34 39.88 |  0059.3 |  0060.0 | 28.0
n18 | 133754.41$+$451239.1 | 2.758 |  $-$28.3 | … | 13 37 54.428 |  $+$45 12 39.32 |  0025.8 |  0029.7 | 27.8
n19 | 134253.64$+$390223.6 | 1.723 |  $-$26.2 | … | 13 42 53.653 |  $+$39 02 23.68 |  0013.4 |  0013.4 | 26.8
n20 | 134303.25$+$502832.0 | 1.962 |  $-$26.6 | … | 13 43 03.252 |  $+$50 28 32.16 |  0039.9 |  0040.9 | 27.5
n21 | 134520.40$+$324112.5 | 2.255 |  $-$27.7 | … | 13 45 20.421 |  $+$32 41 12.59 |  0014.6 |  0014.9 | 27.2
n22 | 140637.60$+$141530.0 | 2.926 |  $-$27.3 | … | 14 06 37.619 |  $+$14 15 30.19 |  0040.9 |  0041.8 | 28.1
n23 | 140909.74$+$071226.1 | 2.734 |  $-$27.1 | … | 14 09 09.748 |  $+$07 12 26.26 |  0011.7 |  0010.5 | 27.4
n24 | 141031.00$+$614136.9 | 2.246 |  $-$27.0 | total | … | … |  0125.0 |  0098.2 | 28.2
| … | … | … | A | 14 10 30.992 |  $+$61 41 36.89 |  0118.4 | … | 28.1
| … | … | … | B | 14 10 30.113 |  $+$61 41 25.51 |  0004.9 | … | 26.8
| … | … | … | C | 14 10 32.179 |  $+$61 41 48.03 |  0001.8 | … | 26.3
n25 | 141846.20$+$482308.2 | 2.193 |  $-$26.2 | … | 14 18 46.211 |  $+$48 23 08.23 |  0012.8 |  0011.1 | 27.1
n26 | 142009.33$+$392738.5 | 2.295 |  $-$26.9 | … | 14 20 09.377 |  $+$39 27 38.77 |  0038.4 |  0038.1 | 27.7
n27 | 142033.25$-$003233.3 | 2.682 |  $-$27.3 | total | … | … |  0077.6 |  0077.0 | 28.2
| … | … | … | A | 14 20 33.238 |  $-$00 32 33.54 |  0016.4 | … | 27.6
| … | … | … | B | 14 20 33.569 |  $-$00 32 40.42 |  0038.5 | … | 27.9
| … | … | … | C | 14 20 32.982 |  $-$00 32 27.06 |  0022.7 | … | 27.7
n28 | 142326.05$+$325220.3 | 1.905 |  $-$29.3 | … | 14 23 26.073 |  $+$32 52 20.34 |  0008.2 |  0008.1 | 26.7
n29 | 142352.38$+$031125.8 | 1.884 |  $-$26.9 | … | 14 23 52.396 |  $+$03 11 26.08 |  0055.8 |  0052.8 | 27.5
n30 | 142921.87$+$540611.2 | 3.013 |  $-$26.5 | … | 14 29 21.891 |  $+$54 06 10.95 | 1165.4 | 1028.3 | 29.6
n31 | 143243.29$+$410327.9 | 1.970 |  $-$27.8 | … | 14 32 43.322 |  $+$41 03 28.04 |  0261.7 |  0261.9 | 28.3
n32 | 143708.18$+$040534.3 | 2.025 |  $-$27.5 | … | 14 37 08.201 |  $+$04 05 34.65 |  0016.5 |  0015.3 | 27.1
n33 | 143737.06$+$094847.7 | 2.162 |  $-$26.8 | … | 14 37 37.042 |  $+$09 48 47.81 |  0181.2 |  0191.5 | 28.3
n34 | 144752.46$+$582420.3 | 2.983 |  $-$28.1 | … | 14 47 52.441 |  $+$58 24 20.39 |  0033.2 |  0032.8 | 28.0
n35 | 145627.72$+$414944.2 | 2.668 |  $-$26.5 | … | 14 56 27.731 |  $+$41 49 44.43 |  0013.2 |  0012.1 | 27.5
n36 | 145924.24$+$340113.1 | 2.790 |  $-$28.3 | … | 14 59 24.251 |  $+$34 01 13.11 |  0021.7 |  0022.2 | 27.7
n37 | 151258.36$+$352533.2 | 2.236 |  $-$26.7 | … | 15 12 58.373 |  $+$35 25 33.32 |  0047.5 |  0053.6 | 27.7
n38 | 152314.87$+$381402.0 | 3.159 |  $-$27.9 | … | 15 23 14.870 |  $+$38 14 02.13 |  0047.7 |  0051.9 | 28.3
n39 | 154644.24$+$311711.3 | 2.122 |  $-$26.3 | … | 15 46 44.250 |  $+$31 17 11.47 |  0012.7 |  0014.0 | 27.1
n40 | 154935.74$+$314338.2 | 1.815 |  $-$25.8 | … | 15 49 35.725 |  $+$31 43 38.38 |  0011.0 |  0009.9 | 26.8
n41 | 155816.63$+$502953.7 | 1.900 |  $-$26.5 | … | 15 58 16.632 |  $+$50 29 53.77 |  0016.7 |  0016.9 | 27.0
n42 | 160911.26$+$374635.7 | 2.412 |  $-$26.4 | … | 16 09 11.287 |  $+$37 46 36.42 |  0022.7 |  0025.9 | 27.5
n43 | 161920.20$+$375502.7 | 2.966 |  $-$26.7 | … | 16 19 19.962 |  $+$37 55 02.77 |  0018.9 |  0019.9 | 27.8
n44 | 162004.73$+$351554.6 | 2.960 |  $-$27.6 | … | 16 20 04.690 |  $+$35 15 54.93 |  0050.0 |  0057.3 | 28.2
n45 | 165137.53$+$400219.0 | 2.343 |  $-$28.5 | … | 16 51 37.565 |  $+$40 02 18.71 |  0043.9 |  0043.1 | 27.8
n46 | 165508.72$+$373244.6 | 2.092 |  $-$26.6 | … | 16 55 08.724 |  $+$37 32 44.77 |  0009.5 |  0008.8 | 26.9
n47 | 074927.90$+$415242.3 | 3.111 |  $-$28.9 | … | 07 49 27.911 |  $+$41 52 42.20 |  0015.2 |  0015.5 | 27.8
n48 | 095537.94$+$333503.9 | 2.477 |  $-$28.6 | … | 09 55 37.936 |  $+$33 35 03.97 |  0036.6 |  0033.0 | 27.8

Note. Columns are as follows: (1) Object ID; (2) SDSS source name; (3), (4)
Redshift and $i$-band absolute magnitude from SDSS DR5 (Adelman-McCarthy et
al., 2007); (5) Name of each component if multiple radio source is associated;
(6), (7) Radio positions; (8) Flux density at 1.4 GHz from the FIRST survey.
Reference for the columns (5)–(7) is Becker et al. (1995); (9) Flux density at
1.4 GHz from the NVSS (Condon et al., 1998). (10) Log specific luminosity at
rest 5 GHz calculated by flux density at 1.4 GHz assuming spectral index of
$\alpha=-0.7$. For quasars associated with multiple radio sources, we provide
information on each source.

###  2.3 Flux variability

The primary objective of this investigation is to examine the radio spectra of
quasars using new GMRT observations and previous flux measurements. Generally,
quasars display variations in flux density at radio wavelengths (Hufnagel &
Bregman, 1992; Barvainis et al., 2005; Hovatta et al., 2007), which may impact
the data collected at different epochs. To assess this impact on the samples,
we compared the 1.4-GHz flux density measurements acquired from the FIRST
survey with those obtained from the NRAO VLA Sky Survey (NVSS; Condon et al.,
1998). Figure 3 depicts the comparison of the integrated flux densities. To
evaluate the extent of flux-density variability, we utilised the index
introduced by Zhou et al. (2006), given by

$\displaystyle V=\frac{|f_{1}-f_{2}|}{\sqrt{\sigma_{1}^{2}+\sigma_{2}^{2}}},$
(1)

where $f_{i}$ and $\sigma_{i}$ denote the flux density and measurement error
for the $i$-th epoch data, respectively. The errors in flux density are the
root mean square of the thermal noise and calibration uncertainty, which were
assumed to be 5 per cent. When comparing data acquired from different array
configurations, objects with a high-resolution peak flux density greater than
the integrated flux density at a lower resolution are considered potential
variable objects.

We have identified two candidates, b04 (J104452.41$+$104005.9) and n24
(J141031.00$+$614136.9), representing significant variability of $V>3$, with
$V=3.57$ and 3.52, respectively. While we acknowledge that only two epochs of
observations may not be sufficient to provide conclusive evidence regarding
the stability or variability of the targets, we will present both analyses,
encompassing and omitting these candidates for variable sources.

Figure 3:  Flux density distribution at 1.4 GHz obtained from the FIRST survey
and the NVSS. Blue-filled circles and orange crosses indicate BAL and non-BAL
quasars, respectively. The dashed line indicates where the two survey fluxes
are equal, and the dotted lines show the 3$\sigma$ variation of the sources
around the line of equal flux. Two BAL quasars that appear to lie well above
the line may have a second object contaminating the NVSS flux density and are
likely not variable.

##  3 Observations and Data Reduction

###  3.1 New 322-MHz observation

We conducted the new GMRT observations between 16–19 May 2013 under project
code 24_006. To reduce the impact of ionospheric variations, we initiated the
observations in the early evening and continued throughout the night as a
contiguous block lasting ten hours. During the observations, we utilised the
default parameters of the 306-MHz band of the legacy GMRT system, with a
32-MHz wide intermediate frequency centred at 322 MHz for both LL and RR
polarisations. We collected the data using 256 spectral channels, each with a
width of 12.5 kHz. We monitored the flux and bandpass calibrator, 3C 286,
every 3–4 hours, and we observed each target for 6–8 minute scans at two
different hour angles. Additionally, we observed phase calibrators
approximately every 30 minutes, with a typical angular separation of 6 degrees
and a maximum separation of 13.5 degrees between targets and each calibrator.
Please refer to Table 3 for an overview of the observations.

Table 3: Observation summary.

Date | Phase calibrator | Observed targets
---|---|---
2013 May 16 | 1131$+$4514 | b05, b09, b11, n01, n03, n08
| 1338$+$3851 | b20, b29, b32, b33, b35, n18, n19, n26, n28, n31
| 1531$+$3533 | b40, n35, n36, n37, n38
| 1653$+$3945 | b45, b48, n45, n46
2013 May 17 | 0753$+$4231 | n47
| 1123$+$0530 | b03, b04, b06, b07, b12, b13, b14, b15, n02, n04, n05, n06
| 1308$-$0950 | b26
| 1419$+$0628 | b31, b34, b37, n23, n27, n29, n32, n33
| 1510$-$0543 | b41
2013 May 18 | 1252$+$5634 | b19, n09, n11, n14, n16
| 1313$+$6735 | b10, b17, b25, b28
| 3C 286 | b27, n21
| 1411$+$5212 | b30, b36, n20, n25, n30
| 1449$+$6316 | b42, n24, n34
| 1545$+$4751 | b38, b39, b46, n41
2013 May 19 | 0958$+$3224 | n48
| 1021$+$2159 |  b01, b02
| 1156$+$3128 | b08, n07
| 1242$-$0446 | b16, b18, b21, b22, n10, n12, n13, n15
| 1347$+$1217 | b23, b24, n17, n22
| 1602$+$3326 | b43, b44, b47, n39, n40, n42, n43, n44

Note. IDs in observed targets column are object IDs in Table 1 and 2. Targets
whose flux measurements were not made due to severe RFI are indicated in bold.

We processed the data using the Common Astronomy Software Applications (CASA;
McMullin et al., 2007) package, with reference to the calibration and imaging
pipeline developed by Ishwara-Chandra et al. (2020). We started with an
initial delay correction using the CASA task gaincal with a bright calibrator,
3C 286. We then performed amplitude and phase bandpass calibration using the
same calibrator. Next, the flux density scale was determined using the formula
from Perley & Butler (2017), with 3C 286 as the calibrator. Finally, we
calibrated the antenna-based amplitude and phase time variations using phase
calibrators. We identified and flagged radio frequency interference in the
time and frequency domains at each stage using the rflag and tfcrop modes of
the CASA task flagdata. Unfortunately, due to significant scintillation of the
ionosphere, we could not achieve proper phase calibration for three BAL
quasars (b01, b02, and b18) and one non-BAL quasar (n10). Due to the absence
of low-frequency flux measurements potentially impacting the statistical
outcomes, we present both analyses, inclusive and exclusive of these objects.
These sources requiring careful consideration in subsequent statistical
analyses are listed in Table 4.

Table 4: Annotation of objects requiring consideration in statistical analyses ID | comments
---|---
b01 | RFI in the 322-MHz data, source with multi components
b02 | RFI in the 322-MHz data, no C IV BAL but potential presence of Al III BAL
b04 | candidate exhibiting variability
b11 | no detection at both 150 and 322 MHz
b18 | RFI in the 322-MHz data
b20 | source with multi components
b25 | source with multi components
n10 | RFI in the 322-MHz data
n24 | candidate exhibiting variability, source with multi components, no C IV BAL but potential presence of Al III BAL
n27 | source with multi components
n32 | no detection at both 150 and 322 MHz

We utilised the CASA task tclean equipped with widefield imaging mode and
multiterm multifrequency synthesis capabilities to carry out imaging
processes. First, we reduced the size of the data set by averaging the data to
32 channels, each 2 MHz wide. In order to resolve the antenna-based amplitude
and phase corrections for Stokes $I$, self-calibration was executed.
Initially, we performed phase-only calibration to the data with $u$-$v$ length
greater than $2\,\textrm{k}\lambda$ against a basic point source model of
$\sim$ $1\times 1$ square degrees, obtained from the FIRST survey (Becker et
al., 1995) utilising the Montage Image Mosaic Engine (Jacob et al., 2010).
Subsequently, we gradually integrated short baselines and resolved radio
sources, followed by several rounds of widefield imaging and phase and
amplitude calibration. Ultimately, we generated final images using a Briggs
weighting of $\texttt{robust}=0.5$ (Briggs, 1995), encompassing a field of
view as large as $2.5\times 2.5$ square degrees to include probable strong
sources positioned beyond the primary lobe. The typical synthesised beam size
for the resulting images was $\sim$ 11 and $\sim$ 8 arcsecs for the major and
minor axes, respectively.

To determine the flux densities of our targets, we used the CASA task IMFIT,
which fits an elliptical Gaussian component within a small box enclosing the
radio source. We estimated the flux-density errors by taking the root mean
square of a calibration uncertainty and the error provided by IMFIT, which
contains thermal noise and fitting errors. To be conservative, we assumed a
calibration uncertainty of 10 per cent (e.g., Chandra et al., 2004). The
typical rms noise level obtained from IMFIT was approximately 0.5 mJy beam-1,
consistent with the previous snapshot survey observations made using the
legacy GMRT system (e.g., Prescott et al., 2016).

###  3.2 Archival data

We additionally used data points from previous publications to determine the
overall spectral shape.

For 144-MHz data, we initially endeavoured to utilise data obtained from the
second data release of the LOFAR Two-metre Sky Survey (LoTSS-DR2; Shimwell et
al., 2022). This survey observes at a frequency centred on 144 MHz and has a
spatial resolution of 6 arcsecs. Although the survey’s catalogue tables
provide error estimates, these estimations only reflect thermal noise and do
not account for the uncertainty associated with amplitude calibration.
Therefore, we calculated the flux density error by taking the root mean square
of thermal noise and amplitude calibration error. The latter was assumed to be
10 per cent of the flux density measurement (Shimwell et al., 2022). Since the
survey observations are still ongoing, flux density measurements are not
accessible for some sources. For such sources, we relied on the flux density
at 147.5 MHz provided by the TIFR GMRT Sky Survey (TGSS; Intema et al., 2017),
whose spatial resolution is 25 arcsecs. We directly utilised the flux
measurement errors listed in the survey’s catalogue, which account for thermal
noise and amplitude calibration errors. The TGSS did not detect some sources
that LoTSS has yet to observe. For these sources, we estimated the thermal
noise from the image cutouts provided by the TGSS and adopted 5$\sigma$ as an
upper limit.

For GHz-frequency data, we acquired flux density measurements at 1.4 and 3.0
GHz from the FIRST survey and the VLA Sky Survey (VLASS; Lacy et al., 2020),
respectively. These surveys have an angular resolution of 5.0 and 2.5 arcsecs,
respectively. We calculated the flux density error by taking the square root
of the sum of the squares of thermal noise from the catalogues and a 5 per
cent amplitude calibration error (Lacy et al., 2019). As Gordon et al. (2021)
recommend, we corrected the catalogue values by multiplying them by 1/0.87 in
our analysis due to a systematic underestimation of the flux density
measurements.

In addition to the data mentioned above, where flux measurements at the same
frequency are provided for all objects in the samples, the following archive
data were also utilised to evaluate the overall spectral shape of targets: the
LOFAR LBA Sky Survey (LoLSS) at 54 MHz with a resolution of 15 arcsecs (de
Gasperin et al., 2023), the VLA Low-Frequency Sky Survey (VLSS) at 74 MHz with
a resolution of 80 arcsecs (Cohen et al., 2007), the GaLactic and
Extragalactic All-sky Murchison Widefield Array (GLEAM) survey at 200 MHz with
a resolution of 120 arcsecs (Hurley-Walker et al., 2017), the Texas Survey at
365 MHz with a resolution of 20 arcsecs (Douglas et al., 1996), the Rapid
ASKAP Continuum Survey (RACS) at 887.5 MHz with a resolution of 25 arcsecs
(Hale et al., 2021), and the Cosmic Lens All-Sky Survey (CLASS) at 8.4 GHz,
with a resolution of 0.2 arcsecs (Myers et al., 2003). As these data are not
available for all objects in the samples, a statistical comparison of spectral
indices including them was not performed. If the flux error in the catalogue
does not consider calibration uncertainty, we estimated the error by
calculating the root mean square of the thermal noise and amplitude
calibration error as described in the source paper. Furthermore, we also
utilised prior flux measurements carried out by VLA specifically for BAL
quasars, as documented in studies by DiPompeo et al. (2011), Montenegro-Montes
et al. (2008), and Bruni et al. (2012).

##  4 Results

###  4.1 Flux measurement and spectral indices

We found that the images of all targets at all bands are consistent with those
from the FIRST survey (Fig. 1), and we did not detect any new components. Our
GMRT observations have revealed that all targets, except those shown in Fig.
4, are point sources. Tables 5 and 6 show the results of the GMRT observations
and prior all-sky surveys, including the corresponding spectral indices and
radio luminosities. Please see Figs. 5 and 6 for the radio spectra of the BAL
and non-BAL samples, respectively. As described in Section 3.1, RFI prevented
us from measuring the flux density at 322 MHz for three BAL quasars (b01, b02,
and b18) and one non-BAL quasar (n10). In addition, we did not detect one
source from each group at this frequency (b11 and n32), which was also
undetected at 144 MHz; thus, we could not establish constraints on their low-
frequency spectral index between 144 and 322 MHz. Table 4 summarises the
objects requiring careful consideration in subsequent statistical analyses.

Figure 4:  Radio images at 322 MHz for b20 (J123954$+$373954), b25
(J133004$+$605949), n24 (J141031$+$614136), and n27 (J142033$-$003233) from
top left to bottom right, whose contour levels commence at 1.7, 1.0, 1.4, and
2.2 mJy beam-1 (equivalent to the 3$\sigma$ noise level of the image),
respectively, and are then multiplied by a factor of 2.  Table 5: Flux
densities, spectral indices, and radio luminosities of the BAL sample.

ID | Compo- | $f_{0.144}$ | $f_{0.322}$ | $f_{1.4}$ | $f_{3.0}$ | $\alpha_{\rm low}$ | $\alpha_{\rm mid}$ | $\alpha_{\rm high}$ | $\log L_{0.7}$ | $\log L_{3}$ | $\log L_{7}$
---|---|---|---|---|---|---|---|---|---|---|---
| nent | (mJy) | (mJy) | (mJy) | (mJy) |  |  |  | (W Hz-1) | (W Hz-1) | (W Hz-1)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12)
b01 | total |  0112.1 $\pm$ 012.6† | … |  0023.8 $\pm$ 01.2 |  0023.0 $\pm$ 01.1 | … | … |  $-$0.04 $\pm$ 0.09 | … | … | 27.5
| A | … | … |  0013.7 $\pm$ 00.7 |  0017.9 $\pm$ 00.6 | … | … |  $-$0.35 $\pm$ 0.08 | … | … | 27.3
| B | … | … |  0010.1 $\pm$ 00.5 |  0005.1 $\pm$ 00.4 | … | … |  $-$0.90 $\pm$ 0.12 | … | … | 27.0
b02 | … | … | … |  0012.3 $\pm$ 00.6 |  0009.9 $\pm$ 00.4 | … | … |  $-$0.29 $\pm$ 0.09 | … | … | 27.4
b03 | … |  0174.2 $\pm$ 017.9† |  0174.1 $\pm$ 017.5 |  0042.2 $\pm$ 02.1 |  0018.7 $\pm$ 00.7 |  $-$0.00 $\pm$ 0.18 |  $-$0.96 $\pm$ 0.15 |  $-$1.07 $\pm$ 0.08 | 28.4 | 28.0 | 27.7
b04 | … |  $<$ 50.3† |  0012.7 $\pm$ 001.8 |  0017.2 $\pm$ 00.9 |  0006.4 $\pm$ 00.3 |  $>$ $-$1.76 |  $-$0.21 $\pm$ 0.20 |  $-$1.29 $\pm$ 0.09 |  $<$ 27.2 | 27.1 | 26.8
b05 | … |  0081.9 $\pm$ 008.4 |  0066.9 $\pm$ 006.7 |  0033.9 $\pm$ 01.7 |  0020.1 $\pm$ 00.7 |  $-$0.25 $\pm$ 0.18 |  $-$0.46 $\pm$ 0.15 |  $-$0.68 $\pm$ 0.08 | 28.0 | 27.8 | 27.6
b06 | … |  $<$ 20.9† |  0006.9 $\pm$ 001.2 |  0083.1 $\pm$ 04.2 |  0059.6 $\pm$ 01.8 |  $>$ $-$1.43 |  $-$1.70 $\pm$ 0.24 |  $-$0.44 $\pm$ 0.08 |  $<$ 27.3 | 27.7 | 28.0
b07 | … |  0058.4 $\pm$ 007.1† |  0047.4 $\pm$ 004.8 |  0012.3 $\pm$ 00.6 |  0007.2 $\pm$ 00.3 |  $-$0.27 $\pm$ 0.20 |  $-$0.92 $\pm$ 0.15 |  $-$0.70 $\pm$ 0.09 | 27.7 | 27.2 | 26.9
b08 | … |  0003.5 $\pm$ 000.4 |  0005.6 $\pm$ 000.6 |  0010.0 $\pm$ 00.5 |  0013.2 $\pm$ 00.5 |  $-$0.61 $\pm$ 0.19 |  $-$0.39 $\pm$ 0.16 |  $-$0.36 $\pm$ 0.08 | 26.5 | 26.8 | 26.9
b09 | … |  0009.9 $\pm$ 001.0 |  0017.1 $\pm$ 002.2 |  0042.0 $\pm$ 02.1 |  0045.6 $\pm$ 01.4 |  $-$0.68 $\pm$ 0.20 |  $-$0.61 $\pm$ 0.18 |  $-$0.11 $\pm$ 0.08 | 27.2 | 27.6 | 27.7
b10 | … |  0056.9 $\pm$ 005.9 |  0039.7 $\pm$ 004.1 |  0012.8 $\pm$ 00.7 |  0007.4 $\pm$ 00.3 |  $-$0.45 $\pm$ 0.18 |  $-$0.77 $\pm$ 0.15 |  $-$0.72 $\pm$ 0.09 | 27.8 | 27.4 | 27.1
b11 | … |  $<$ 21.0† |  $<$ 15.1 |  0028.0 $\pm$ 01.4 |  0020.0 $\pm$ 00.7 |  $-$… |  $>$ 0.42 |  $-$0.44 $\pm$ 0.08 |  $<$ 27.4 |  $<$ 27.4 | 27.4
b12 | … |  0797.3 $\pm$ 079.9† |  0546.1 $\pm$ 054.7 |  0160.1 $\pm$ 08.0 |  0086.4 $\pm$ 02.7 |  $-$0.48 $\pm$ 0.18 |  $-$0.83 $\pm$ 0.15 |  $-$0.81 $\pm$ 0.08 | 28.9 | 28.4 | 28.1
b13 | … |  0340.2 $\pm$ 034.3† | 1144.9 $\pm$ 114.7 |  0268.5 $\pm$ 13.4 |  0164.6 $\pm$ 05.0 |  $-$1.55 $\pm$ 0.18 |  $-$0.99 $\pm$ 0.15 |  $-$0.64 $\pm$ 0.08 | 28.8 | 28.5 | 28.2
b14 | … |  $<$ 16.4† |  0014.3 $\pm$ 001.6 |  0022.9 $\pm$ 01.2 |  0023.7 $\pm$ 00.8 |  $>$ $-$0.17 |  $-$0.32 $\pm$ 0.16 |  $-$0.05 $\pm$ 0.08 |  $<$ 27.6 | 27.7 | 27.8
b15 | … |  $<$ 27.0† |  0015.2 $\pm$ 001.7 |  0049.8 $\pm$ 02.5 |  0053.0 $\pm$ 01.6 |  $>$ $-$0.74 |  $-$0.81 $\pm$ 0.16 |  $-$0.08 $\pm$ 0.08 |  $<$ 27.7 | 27.9 | 28.1
b16 | … |  $<$ 19.5† |  0026.5 $\pm$ 004.6 |  0030.8 $\pm$ 01.5 |  0019.1 $\pm$ 00.6 |  $>$ $-$0.39 |  $-$0.10 $\pm$ 0.24 |  $-$0.63 $\pm$ 0.08 |  $<$ 27.7 | 27.8 | 27.7
b17 | … |  0007.2 $\pm$ 000.7 |  0018.4 $\pm$ 001.9 |  0024.0 $\pm$ 01.2 |  0019.3 $\pm$ 00.6 |  $-$1.17 $\pm$ 0.18 |  $-$0.18 $\pm$ 0.15 |  $-$0.28 $\pm$ 0.08 | 27.0 | 27.3 | 27.2
b18 | … |  $<$ 26.1† | … |  0011.3 $\pm$ 00.6 |  0005.4 $\pm$ 00.3 |  $-$… | … |  $-$0.97 $\pm$ 0.11 | … | … | 27.5
b19 | … |  0056.5 $\pm$ 005.7 |  0065.2 $\pm$ 006.5 |  0080.2 $\pm$ 04.0 |  0086.7 $\pm$ 02.6 |  $-$0.18 $\pm$ 0.18 |  $-$0.14 $\pm$ 0.15 |  $-$0.10 $\pm$ 0.08 | 27.9 | 28.0 | 28.0
b20 | total |  0093.4 $\pm$ 009.4 |  0064.0 $\pm$ 006.6 |  0018.5 $\pm$ 01.0 |  0008.2 $\pm$ 00.8 |  $-$0.47 $\pm$ 0.18 |  $-$0.85 $\pm$ 0.15 |  $-$1.06 $\pm$ 0.15 | 27.7 | 27.2 | 26.8
| A |  0027.0 $\pm$ 002.7 |  0027.6 $\pm$ 003.0 |  0010.7 $\pm$ 00.6 |  0004.2 $\pm$ 00.3 |  $-$0.03 $\pm$ 0.18 |  $-$0.65 $\pm$ 0.16 |  $-$1.21 $\pm$ 0.10 | 27.3 | 26.9 | 26.6
| B |  0033.8 $\pm$ 003.4 |  0022.4 $\pm$ 002.5 |  0004.3 $\pm$ 00.3 |  0001.8 $\pm$ 00.3 |  $-$0.51 $\pm$ 0.19 |  $-$1.12 $\pm$ 0.17 |  $-$1.12 $\pm$ 0.23 | 27.2 | 26.6 | 26.2
| C |  0032.6 $\pm$ 003.3 |  0014.0 $\pm$ 001.7 |  0003.5 $\pm$ 00.2 |  0002.1 $\pm$ 00.3 |  $-$1.05 $\pm$ 0.20 |  $-$0.95 $\pm$ 0.18 |  $-$0.66 $\pm$ 0.22 | 27.1 | 26.5 | 26.2
b21 | … |  $<$ 19.2† |  0006.7 $\pm$ 001.4 |  0012.8 $\pm$ 00.7 |  0013.8 $\pm$ 00.5 |  $>$ $-$1.35 |  $-$0.44 $\pm$ 0.28 |  $-$0.10 $\pm$ 0.08 |  $<$ 26.7 | 26.8 | 26.8
b22 | … |  $<$ 27.9† |  0033.8 $\pm$ 003.6 |  0038.0 $\pm$ 01.9 |  0017.9 $\pm$ 00.6 |  $>$ $-$0.24 |  $-$0.08 $\pm$ 0.15 |  $-$0.98 $\pm$ 0.08 |  $<$ 27.5 | 27.6 | 27.4
b23 | … |  $<$ 22.9† |  0014.2 $\pm$ 001.6 |  0050.0 $\pm$ 02.5 |  0038.0 $\pm$ 01.2 |  $>$ $-$0.61 |  $-$0.86 $\pm$ 0.16 |  $-$0.36 $\pm$ 0.08 |  $<$ 27.6 | 27.8 | 27.9
b24 | … |  0030.0 $\pm$ 005.0† |  0026.7 $\pm$ 002.7 |  0014.9 $\pm$ 00.8 |  0012.2 $\pm$ 00.4 |  $-$0.15 $\pm$ 0.25 |  $-$0.40 $\pm$ 0.15 |  $-$0.26 $\pm$ 0.08 | 28.0 | 27.8 | 27.6
b25 | total |  0158.4 $\pm$ 015.9 |  0099.7 $\pm$ 010.0 |  0028.5 $\pm$ 01.4 |  0026.5 $\pm$ 02.6 |  $-$0.58 $\pm$ 0.18 |  $-$0.85 $\pm$ 0.15 |  $-$0.10 $\pm$ 0.15 | 27.8 | 27.3 | 27.2
| A |  0101.4 $\pm$ 010.2 |  0048.4 $\pm$ 004.9 |  0018.1 $\pm$ 00.9 |  0020.3 $\pm$ 00.7 |  $-$0.92 $\pm$ 0.18 |  $-$0.67 $\pm$ 0.15 |  $-$0.15 $\pm$ 0.08 | 27.5 | 27.1 | 27.0
| B |  0057.0 $\pm$ 005.7 |  0051.3 $\pm$ 005.2 |  0010.4 $\pm$ 00.5 |  0006.2 $\pm$ 00.3 |  $-$0.13 $\pm$ 0.18 |  $-$1.09 $\pm$ 0.15 |  $-$0.68 $\pm$ 0.10 | 27.5 | 26.9 | 26.6
b26 | … |  $<$ 21.4† |  0005.8 $\pm$ 001.1 |  0044.8 $\pm$ 02.2 |  0071.5 $\pm$ 02.2 |  $>$ $-$1.67 |  $-$1.39 $\pm$ 0.26 |  $-$0.61 $\pm$ 0.08 |  $<$ 27.7 | 27.8 | 28.2
b27 | … |  $<$ 28.3† |  0010.4 $\pm$ 001.3 |  0010.7 $\pm$ 00.6 |  0013.2 $\pm$ 00.5 |  $>$ $-$1.28 |  $-$0.02 $\pm$ 0.18 |  $-$0.27 $\pm$ 0.09 |  $<$ 27.0 | 26.9 | 26.9
b28 | … |  0068.5 $\pm$ 006.9 |  0051.7 $\pm$ 005.2 |  0017.9 $\pm$ 00.9 |  0011.8 $\pm$ 00.4 |  $-$0.35 $\pm$ 0.18 |  $-$0.72 $\pm$ 0.15 |  $-$0.54 $\pm$ 0.08 | 27.9 | 27.5 | 27.2
b29 | … |  0035.3 $\pm$ 003.5 |  0026.2 $\pm$ 002.8 |  0015.0 $\pm$ 00.8 |  0014.7 $\pm$ 00.6 |  $-$0.37 $\pm$ 0.18 |  $-$0.38 $\pm$ 0.15 |  $-$0.03 $\pm$ 0.08 | 27.4 | 27.2 | 27.1
b30 | … |  0008.0 $\pm$ 000.8 |  0021.1 $\pm$ 002.3 |  0037.1 $\pm$ 01.9 |  0041.6 $\pm$ 01.3 |  $-$1.21 $\pm$ 0.19 |  $-$0.38 $\pm$ 0.16 |  $-$0.15 $\pm$ 0.08 | 27.5 | 27.9 | 28.1
b31 | … | 1674.6 $\pm$ 167.7† | 1356.7 $\pm$ 135.7 | 1055.9 $\pm$ 52.8 | 1056.6 $\pm$ 32.1 |  $-$0.27 $\pm$ 0.18 |  $-$0.17 $\pm$ 0.15 |  $-$0.00 $\pm$ 0.08 | 29.8 | 29.7 | 29.6
b32 | … |  0027.9 $\pm$ 002.8 |  0028.7 $\pm$ 009.5 |  0026.7 $\pm$ 01.3 |  0044.4 $\pm$ 01.4 |  $-$0.03 $\pm$ 0.43 |  $-$0.05 $\pm$ 0.44 |  $-$0.67 $\pm$ 0.08 | 27.8 | 27.7 | 27.8
b33 | … |  0008.8 $\pm$ 000.9 |  0017.5 $\pm$ 002.0 |  0018.7 $\pm$ 00.9 |  0013.5 $\pm$ 00.5 |  $-$0.85 $\pm$ 0.19 |  $-$0.05 $\pm$ 0.16 |  $-$0.43 $\pm$ 0.08 | 27.4 | 27.7 | 27.6
b34 | … |  $<$ 46.5† |  0019.8 $\pm$ 002.2 |  0011.8 $\pm$ 00.6 |  0006.2 $\pm$ 00.4 |  $>$ $-$1.09 |  $-$0.35 $\pm$ 0.16 |  $-$0.84 $\pm$ 0.11 |  $<$ 27.3 | 26.9 | 26.7
b35 | … |  0002.0 $\pm$ 000.3 |  0004.5 $\pm$ 001.3 |  0025.8 $\pm$ 01.3 |  0011.2 $\pm$ 00.4 |  $-$0.99 $\pm$ 0.40 |  $-$1.19 $\pm$ 0.39 |  $-$1.09 $\pm$ 0.08 | 26.7 | 27.4 | 27.5
b36 | … |  0043.1 $\pm$ 004.5 |  0050.1 $\pm$ 005.0 |  0012.6 $\pm$ 00.6 |  0004.9 $\pm$ 00.4 |  $-$0.19 $\pm$ 0.18 |  $-$0.94 $\pm$ 0.15 |  $-$1.23 $\pm$ 0.12 | 27.5 | 27.1 | 26.6
b37 | … |  0059.0 $\pm$ 009.8† |  0036.1 $\pm$ 003.7 |  0013.2 $\pm$ 00.7 |  0012.0 $\pm$ 00.5 |  $-$0.63 $\pm$ 0.25 |  $-$0.68 $\pm$ 0.15 |  $-$0.12 $\pm$ 0.08 | 27.6 | 27.2 | 27.1
b38 | … |  0004.5 $\pm$ 000.5 |  0008.4 $\pm$ 001.5 |  0013.7 $\pm$ 00.7 |  0019.0 $\pm$ 00.7 |  $-$0.77 $\pm$ 0.26 |  $-$0.33 $\pm$ 0.24 |  $-$0.43 $\pm$ 0.08 | 27.2 | 27.5 | 27.7
b39 | … |  0028.8 $\pm$ 002.9 |  0024.0 $\pm$ 002.4 |  0011.2 $\pm$ 00.6 |  0008.9 $\pm$ 00.4 |  $-$0.23 $\pm$ 0.18 |  $-$0.52 $\pm$ 0.15 |  $-$0.30 $\pm$ 0.09 | 27.4 | 27.1 | 27.0
b40 | … |  0135.6 $\pm$ 013.6 |  0185.4 $\pm$ 018.5 |  0132.0 $\pm$ 06.6 |  0088.5 $\pm$ 02.7 |  $-$0.39 $\pm$ 0.18 |  $-$0.23 $\pm$ 0.15 |  $-$0.52 $\pm$ 0.08 | 28.3 | 28.2 | 28.1
b41 | … |  0048.7 $\pm$ 008.9† |  0055.8 $\pm$ 006.5 |  0025.5 $\pm$ 01.3 |  0021.2 $\pm$ 00.7 |  $-$0.17 $\pm$ 0.28 |  $-$0.53 $\pm$ 0.17 |  $-$0.24 $\pm$ 0.08 | 27.6 | 27.4 | 27.2
b42 | … |  0012.3 $\pm$ 001.2 |  0010.0 $\pm$ 001.5 |  0014.2 $\pm$ 00.7 |  0040.9 $\pm$ 01.3 |  $-$0.26 $\pm$ 0.22 |  $-$0.24 $\pm$ 0.20 |  $-$1.39 $\pm$ 0.08 | 27.6 | 27.6 | 27.8
b43 | … |  0040.9 $\pm$ 004.1 |  0044.7 $\pm$ 004.5 |  0041.2 $\pm$ 02.1 |  0044.9 $\pm$ 01.4 |  $-$0.11 $\pm$ 0.18 |  $-$0.06 $\pm$ 0.15 |  $-$0.11 $\pm$ 0.08 | 28.0 | 28.0 | 28.0
b44 | … |  0013.8 $\pm$ 001.4 |  0056.5 $\pm$ 005.9 |  0054.2 $\pm$ 02.7 |  0042.4 $\pm$ 01.3 |  $-$1.75 $\pm$ 0.18 |  $-$0.03 $\pm$ 0.15 |  $-$0.32 $\pm$ 0.08 | 27.5 | 27.7 | 27.6
b45 | … |  0036.7 $\pm$ 003.7 |  0050.8 $\pm$ 005.1 |  0056.4 $\pm$ 02.8 |  0034.9 $\pm$ 01.1 |  $-$0.40 $\pm$ 0.18 |  $-$0.07 $\pm$ 0.15 |  $-$0.63 $\pm$ 0.08 | 28.2 | 28.4 | 28.4
b46 | … |  0041.9 $\pm$ 004.4 |  0044.6 $\pm$ 004.5 |  0025.5 $\pm$ 01.3 |  0014.4 $\pm$ 00.5 |  $-$0.08 $\pm$ 0.18 |  $-$0.38 $\pm$ 0.15 |  $-$0.74 $\pm$ 0.08 | 28.0 | 27.9 | 27.7
b47 | … |  0002.0 $\pm$ 000.3 |  0002.4 $\pm$ 000.6 |  0011.3 $\pm$ 00.6 |  0006.1 $\pm$ 00.3 |  $-$0.21 $\pm$ 0.34 |  $-$1.06 $\pm$ 0.31 |  $-$0.80 $\pm$ 0.09 | 26.5 | 27.0 | 27.0
b48 | … |  0015.0 $\pm$ 001.5 |  0025.7 $\pm$ 002.6 |  0010.2 $\pm$ 00.5 |  0004.7 $\pm$ 00.3 |  $-$0.67 $\pm$ 0.18 |  $-$0.63 $\pm$ 0.15 |  $-$1.02 $\pm$ 0.11 | 27.1 | 26.8 | 26.5

Note. Columns are as follows: (1) Object ID; (2) subcomponent name of the
sources; (3)–(6) flux densities at 144 MHz, 322 MHz, 1.4 GHz, and 3.0 GHz,
respectively. Reference for columns (3), (5), and (6) are Shimwell et al.
(2022), Becker et al. (1995), and Gordon et al. (2021), respectively. Data in
column (3) indicated by † was obtained from the TGSS at 147.5 MHz (Intema et
al., 2017); (7)–(9) spectral indices between neighbouring bands; (10)–(12) Log
specific luminosity at rest 700 MHz, 3 GHz, and 7.0 GHz calculated by
interpolating the obtained flux densities.

Table 6: Flux densities, spectral indices, and radio luminosities of the non-
BAL sample.

ID | Compo- | $f_{0.144}$ | $f_{0.322}$ | $f_{1.4}$ | $f_{3.0}$ | $\alpha_{\rm low}$ | $\alpha_{\rm mid}$ | $\alpha_{\rm high}$ | $\log L_{0.7}$ | $\log L_{3}$ | $\log L_{7}$
---|---|---|---|---|---|---|---|---|---|---|---
| nent | (mJy) | (mJy) | (mJy) | (mJy) |  |  |  | (W Hz-1) | (W Hz-1) | (W Hz-1)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12)
n01 | … |  0037.8 $\pm$ 003.8 |  0028.9 $\pm$ 003.1 |  0012.2 $\pm$ 00.6 |  010.0 $\pm$ 01.0 |  $-$0.33 $\pm$ 0.18 |  $-$0.59 $\pm$ 0.08 |  $-$0.26 $\pm$ 0.15 | 27.4 | 27.0 | 26.9
n02 | … |  0095.0 $\pm$ 010.6† |  0089.7 $\pm$ 009.1 |  0065.2 $\pm$ 03.3 |  073.3 $\pm$ 07.3 |  $-$0.07 $\pm$ 0.19 |  $-$0.22 $\pm$ 0.08 |  $-$0.15 $\pm$ 0.15 | 28.0 | 27.9 | 27.9
n03 | … |  0066.2 $\pm$ 006.7 |  0059.9 $\pm$ 006.0 |  0028.7 $\pm$ 01.4 |  033.3 $\pm$ 03.3 |  $-$0.12 $\pm$ 0.18 |  $-$0.50 $\pm$ 0.08 |  $-$0.19 $\pm$ 0.15 | 28.0 | 27.8 | 27.7
n04 | … |  $<$ 24.4† |  0011.9 $\pm$ 001.7 |  0017.1 $\pm$ 00.9 |  013.0 $\pm$ 01.3 |  $>$ $-$0.92 |  $-$0.25 $\pm$ 0.10 |  $-$0.35 $\pm$ 0.15 |  $<$ 26.9 | 26.9 | 26.9
n05 | … |  $<$ 16.1† |  0015.8 $\pm$ 001.8 |  0019.8 $\pm$ 01.0 |  010.2 $\pm$ 01.1 |  $>$ $-$0.02 |  $-$0.15 $\pm$ 0.09 |  $-$0.87 $\pm$ 0.15 |  $<$ 27.0 | 27.1 | 26.9
n06 | … |  $<$ 16.2† |  0012.7 $\pm$ 001.4 |  0031.6 $\pm$ 01.6 |  068.6 $\pm$ 06.9 |  $>$ $-$0.31 |  $-$0.62 $\pm$ 0.08 |  $-$1.02 $\pm$ 0.15 |  $<$ 27.5 | 27.7 | 28.0
n07 | … |  0006.8 $\pm$ 000.8 |  0007.0 $\pm$ 000.8 |  0010.3 $\pm$ 00.5 |  006.8 $\pm$ 00.7 |  $-$0.03 $\pm$ 0.21 |  $-$0.26 $\pm$ 0.09 |  $-$0.56 $\pm$ 0.16 | 26.8 | 26.9 | 26.9
n08 | … |  0015.1 $\pm$ 001.5 |  0026.3 $\pm$ 002.7 |  0021.2 $\pm$ 01.1 |  023.9 $\pm$ 02.4 |  $-$0.69 $\pm$ 0.18 |  $-$0.15 $\pm$ 0.08 |  $-$0.16 $\pm$ 0.15 | 27.4 | 27.4 | 27.4
n09 | … |  0018.5 $\pm$ 001.9 |  0020.5 $\pm$ 002.2 |  0023.9 $\pm$ 01.2 |  031.8 $\pm$ 03.2 |  $-$0.13 $\pm$ 0.18 |  $-$0.11 $\pm$ 0.08 |  $-$0.37 $\pm$ 0.15 | 27.2 | 27.3 | 27.4
n10 | … |  0077.7 $\pm$ 009.4† | … |  0094.5 $\pm$ 04.7 |  065.1 $\pm$ 06.5 |  $-$… | … |  $-$0.49 $\pm$ 0.15 | … | … | 28.0
n11 | … |  0013.4 $\pm$ 001.3 |  0016.9 $\pm$ 001.7 |  0011.1 $\pm$ 00.6 |  013.2 $\pm$ 01.3 |  $-$0.29 $\pm$ 0.18 |  $-$0.29 $\pm$ 0.08 |  $-$0.23 $\pm$ 0.15 | 27.3 | 27.2 | 27.2
n12 | … |  $<$ 15.8† |  0005.3 $\pm$ 001.1 |  0010.2 $\pm$ 00.5 |  007.8 $\pm$ 00.8 |  $>$ $-$1.39 |  $-$0.44 $\pm$ 0.14 |  $-$0.34 $\pm$ 0.15 |  $<$ 27.2 | 27.1 | 27.1
n13 | … |  $<$ 17.1† |  0005.2 $\pm$ 000.9 |  0014.0 $\pm$ 00.7 |  023.6 $\pm$ 02.4 |  $>$ $-$1.53 |  $-$0.68 $\pm$ 0.13 |  $-$0.68 $\pm$ 0.15 |  $<$ 26.7 | 26.9 | 27.1
n14 | … |  0020.6 $\pm$ 002.1 |  0016.2 $\pm$ 001.7 |  0010.2 $\pm$ 00.5 |  009.0 $\pm$ 00.9 |  $-$0.30 $\pm$ 0.18 |  $-$0.31 $\pm$ 0.08 |  $-$0.17 $\pm$ 0.15 | 27.0 | 26.8 | 26.7
n15 | … |  0078.2 $\pm$ 009.4† |  0074.1 $\pm$ 008.3 |  0026.7 $\pm$ 01.3 |  017.8 $\pm$ 00.3 |  $-$0.07 $\pm$ 0.21 |  $-$0.69 $\pm$ 0.08 |  $-$0.53 $\pm$ 0.07 | 27.7 | 27.3 | 27.1
n16 | … |  0063.3 $\pm$ 006.4 |  0045.9 $\pm$ 005.1 |  0014.5 $\pm$ 00.7 |  008.5 $\pm$ 00.9 |  $-$0.40 $\pm$ 0.19 |  $-$0.79 $\pm$ 0.08 |  $-$0.69 $\pm$ 0.15 | 28.4 | 28.0 | 27.7
n17 | … |  0027.9 $\pm$ 005.5† |  0062.6 $\pm$ 006.3 |  0059.3 $\pm$ 03.0 |  037.2 $\pm$ 03.7 |  $-$1.03 $\pm$ 0.28 |  $-$0.04 $\pm$ 0.08 |  $-$0.61 $\pm$ 0.15 | 27.8 | 28.0 | 27.9
n18 | … |  0013.6 $\pm$ 001.5 |  0027.5 $\pm$ 002.8 |  0025.8 $\pm$ 01.3 |  022.4 $\pm$ 02.3 |  $-$0.88 $\pm$ 0.18 |  $-$0.04 $\pm$ 0.08 |  $-$0.19 $\pm$ 0.15 | 27.6 | 27.8 | 27.8
n19 | … |  0018.6 $\pm$ 001.9 |  0026.5 $\pm$ 004.0 |  0013.4 $\pm$ 00.7 |  008.2 $\pm$ 00.9 |  $-$0.44 $\pm$ 0.23 |  $-$0.46 $\pm$ 0.11 |  $-$0.65 $\pm$ 0.15 | 27.1 | 26.9 | 26.7
n20 | … |  0060.3 $\pm$ 006.1 |  0067.1 $\pm$ 006.9 |  0039.9 $\pm$ 02.0 |  025.0 $\pm$ 02.5 |  $-$0.13 $\pm$ 0.18 |  $-$0.35 $\pm$ 0.08 |  $-$0.61 $\pm$ 0.15 | 27.7 | 27.6 | 27.4
n21 | … |  0006.5 $\pm$ 000.8 |  0005.3 $\pm$ 000.9 |  0014.6 $\pm$ 00.7 |  007.4 $\pm$ 00.8 |  $-$0.26 $\pm$ 0.26 |  $-$0.70 $\pm$ 0.12 |  $-$0.89 $\pm$ 0.15 | 26.9 | 27.1 | 27.1
n22 | … |  0218.0 $\pm$ 022.9† |  0147.3 $\pm$ 014.8 |  0040.9 $\pm$ 02.0 |  020.5 $\pm$ 02.1 |  $-$0.50 $\pm$ 0.19 |  $-$0.87 $\pm$ 0.08 |  $-$0.91 $\pm$ 0.15 | 28.8 | 28.3 | 28.0
n23 | … |  $<$ 40.1† |  0010.1 $\pm$ 001.2 |  0011.7 $\pm$ 00.6 |  007.2 $\pm$ 00.8 |  $>$ $-$1.76 |  $-$0.10 $\pm$ 0.09 |  $-$0.65 $\pm$ 0.16 |  $<$ 27.8 | 27.4 | 27.3
n24 | total |  0085.6 $\pm$ 008.6 |  0089.9 $\pm$ 009.2 |  0125.0 $\pm$ 06.3 |  0163.9 $\pm$ 16.4 |  $-$0.06 $\pm$ 0.18 |  $-$0.22 $\pm$ 0.08 |  $-$0.36 $\pm$ 0.15 | 28.0 | 28.2 | 28.3
| A |  0044.5 $\pm$ 004.5 |  0055.9 $\pm$ 005.6 |  0118.4 $\pm$ 05.9 |  0161.2 $\pm$ 16.1 |  $-$0.28 $\pm$ 0.18 |  $-$0.51 $\pm$ 0.08 |  $-$0.41 $\pm$ 0.15 | 27.8 | 28.1 | 28.2
| B |  0029.4 $\pm$ 002.9 |  0022.4 $\pm$ 002.4 |  0004.9 $\pm$ 00.3 |  0002.7 $\pm$ 00.7 |  $-$0.34 $\pm$ 0.18 |  $-$1.04 $\pm$ 0.08 |  $-$0.77 $\pm$ 0.37 | 27.5 | 27.0 | 26.6
| C |  0011.7 $\pm$ 001.2 |  0011.5 $\pm$ 001.9 |  0001.8 $\pm$ 00.2 |  $<$ 0.8 |  $-$0.02 $\pm$ 0.24 |  $-$1.27 $\pm$ 0.13 |  $<$ $-$1.02 | 27.2 | 26.6 |  $<$ 26.2
n25 | … |  0000.9 $\pm$ 000.2 |  0002.4 $\pm$ 000.5 |  0012.8 $\pm$ 00.7 |  013.6 $\pm$ 01.4 |  $-$1.17 $\pm$ 0.34 |  $-$1.14 $\pm$ 0.14 |  $-$0.07 $\pm$ 0.15 | 26.2 | 27.0 | 27.2
n26 | … |  0114.3 $\pm$ 011.5 |  0075.1 $\pm$ 008.0 |  0038.4 $\pm$ 01.9 |  023.8 $\pm$ 02.4 |  $-$0.52 $\pm$ 0.18 |  $-$0.46 $\pm$ 0.08 |  $-$0.63 $\pm$ 0.15 | 28.1 | 27.8 | 27.6
n27 | total |  0485.8 $\pm$ 049.0 |  0285.2 $\pm$ 028.7 |  0077.6 $\pm$ 03.9 |  035.4 $\pm$ 03.5 |  $-$0.68 $\pm$ 0.18 |  $-$0.89 $\pm$ 0.08 |  $-$1.03 $\pm$ 0.15 | 28.9 | 28.4 | 28.1
| A | … |  0072.0 $\pm$ 007.7 |  0016.4 $\pm$ 00.8 |  015.5 $\pm$ 01.6 | … |  $-$1.01 $\pm$ 0.08 |  $-$0.07 $\pm$ 0.15 | … | 27.8 | 27.5
| B | … |  0138.8 $\pm$ 014.0 |  0038.5 $\pm$ 01.9 |  010.1 $\pm$ 01.1 | … |  $-$0.87 $\pm$ 0.08 |  $-$1.75 $\pm$ 0.15 | … | 28.1 | 27.7
| C | … |  0074.3 $\pm$ 007.6 |  0022.7 $\pm$ 01.1 |  09.8 $\pm$ 01.0 | … |  $-$0.81 $\pm$ 0.08 |  $-$1.11 $\pm$ 0.15 | … | 27.9 | 27.5
n28 | … |  0005.6 $\pm$ 000.6 |  0005.7 $\pm$ 000.8 |  0008.2 $\pm$ 00.4 |  018.5 $\pm$ 01.9 |  $-$0.02 $\pm$ 0.22 |  $-$0.24 $\pm$ 0.10 |  $-$1.07 $\pm$ 0.15 | 26.6 | 26.8 | 27.0
n29 | … |  0052.4 $\pm$ 008.7† |  0066.6 $\pm$ 006.7 |  0055.8 $\pm$ 02.8 |  067.6 $\pm$ 06.8 |  $-$0.31 $\pm$ 0.25 |  $-$0.12 $\pm$ 0.08 |  $-$0.25 $\pm$ 0.15 | 27.6 | 27.6 | 27.7
n30 | … | 4122.7 $\pm$ 412.4 | 2750.9 $\pm$ 275.5 | 1165.4 $\pm$ 58.3 | 691.8 $\pm$ 69.2 |  $-$0.50 $\pm$ 0.18 |  $-$0.58 $\pm$ 0.08 |  $-$0.68 $\pm$ 0.15 | 30.1 | 29.7 | 29.5
n31 | … |  0281.5 $\pm$ 028.2 |  0447.6 $\pm$ 044.8 |  0261.7 $\pm$ 13.1 | 143.4 $\pm$ 14.4 |  $-$0.58 $\pm$ 0.18 |  $-$0.37 $\pm$ 0.08 |  $-$0.79 $\pm$ 0.15 | 28.5 | 28.4 | 28.2
n32 | … |  $<$ 39.7† |  $<$ 4.0 |  0016.5 $\pm$ 00.8 |  092.6 $\pm$ 09.3 |  $-$… |  $>$ 0.97 |  $-$2.26 $\pm$ 0.15 |  $<$ 27.6 |  $<$ 27.0 | 27.7
n33 | … |  0315.5 $\pm$ 032.4† |  0357.5 $\pm$ 035.8 |  0181.2 $\pm$ 09.1 | 151.9 $\pm$ 15.4 |  $-$0.16 $\pm$ 0.18 |  $-$0.46 $\pm$ 0.08 |  $-$0.23 $\pm$ 0.15 | 28.6 | 28.4 | 28.3
n34 | … |  0004.0 $\pm$ 000.4 |  0010.5 $\pm$ 001.1 |  0033.2 $\pm$ 01.7 |  035.9 $\pm$ 03.6 |  $-$1.21 $\pm$ 0.18 |  $-$0.79 $\pm$ 0.08 |  $-$0.10 $\pm$ 0.15 | 27.2 | 27.8 | 28.0
n35 | … |  0012.3 $\pm$ 001.2 |  0010.7 $\pm$ 001.5 |  0013.2 $\pm$ 00.7 |  009.2 $\pm$ 00.9 |  $-$0.17 $\pm$ 0.21 |  $-$0.14 $\pm$ 0.10 |  $-$0.48 $\pm$ 0.15 | 27.4 | 27.4 | 27.4
n36 | … |  0037.2 $\pm$ 003.8 |  0025.1 $\pm$ 002.6 |  0021.7 $\pm$ 01.1 |  038.3 $\pm$ 03.9 |  $-$0.49 $\pm$ 0.18 |  $-$0.10 $\pm$ 0.08 |  $-$0.75 $\pm$ 0.15 | 27.9 | 27.8 | 27.8
n37 | … |  0045.9 $\pm$ 004.6 |  0048.9 $\pm$ 005.0 |  0047.5 $\pm$ 02.4 |  045.7 $\pm$ 04.6 |  $-$0.08 $\pm$ 0.18 |  $-$0.02 $\pm$ 0.08 |  $-$0.05 $\pm$ 0.15 | 27.8 | 27.8 | 27.8
n38 | … |  0042.6 $\pm$ 004.3 |  0038.8 $\pm$ 003.9 |  0047.7 $\pm$ 02.4 |  050.2 $\pm$ 05.0 |  $-$0.12 $\pm$ 0.18 |  $-$0.14 $\pm$ 0.08 |  $-$0.07 $\pm$ 0.15 | 28.2 | 28.2 | 28.2
n39 | … |  0010.8 $\pm$ 001.1 |  0013.5 $\pm$ 001.7 |  0012.7 $\pm$ 00.6 |  014.2 $\pm$ 01.4 |  $-$0.28 $\pm$ 0.20 |  $-$0.05 $\pm$ 0.09 |  $-$0.15 $\pm$ 0.15 | 27.1 | 27.1 | 27.2
n40 | … |  0002.8 $\pm$ 000.3 |  0003.2 $\pm$ 000.6 |  0011.0 $\pm$ 00.6 |  009.5 $\pm$ 01.0 |  $-$0.15 $\pm$ 0.28 |  $-$0.84 $\pm$ 0.13 |  $-$0.20 $\pm$ 0.15 | 26.3 | 26.8 | 26.8
n41 | … |  0010.0 $\pm$ 001.0 |  0014.3 $\pm$ 001.4 |  0016.7 $\pm$ 00.8 |  007.5 $\pm$ 00.8 |  $-$0.44 $\pm$ 0.18 |  $-$0.11 $\pm$ 0.08 |  $-$1.05 $\pm$ 0.15 | 27.0 | 27.1 | 26.8
n42 | … |  0136.0 $\pm$ 013.6 |  0080.2 $\pm$ 008.1 |  0022.7 $\pm$ 01.1 |  016.1 $\pm$ 01.6 |  $-$0.66 $\pm$ 0.18 |  $-$0.86 $\pm$ 0.08 |  $-$0.45 $\pm$ 0.15 | 28.2 | 27.7 | 27.5
n43 | … |  0113.5 $\pm$ 011.4 |  0070.2 $\pm$ 007.1 |  0018.9 $\pm$ 01.0 |  011.9 $\pm$ 01.2 |  $-$0.60 $\pm$ 0.18 |  $-$0.89 $\pm$ 0.08 |  $-$0.61 $\pm$ 0.15 | 28.5 | 28.0 | 27.7
n44 | … |  0196.3 $\pm$ 019.8 |  0113.7 $\pm$ 011.6 |  0050.0 $\pm$ 02.5 |  074.2 $\pm$ 07.5 |  $-$0.68 $\pm$ 0.18 |  $-$0.56 $\pm$ 0.08 |  $-$0.52 $\pm$ 0.15 | 28.7 | 28.3 | 28.2
n45 | … |  0002.8 $\pm$ 000.4 |  0007.2 $\pm$ 001.2 |  0043.9 $\pm$ 02.2 |  050.6 $\pm$ 05.1 |  $-$1.18 $\pm$ 0.28 |  $-$1.23 $\pm$ 0.12 |  $-$0.19 $\pm$ 0.15 | 26.8 | 27.6 | 27.8
n46 | … |  0030.3 $\pm$ 003.1 |  0031.6 $\pm$ 003.4 |  0009.5 $\pm$ 00.5 |  007.9 $\pm$ 00.8 |  $-$0.06 $\pm$ 0.18 |  $-$0.82 $\pm$ 0.08 |  $-$0.23 $\pm$ 0.15 | 27.5 | 27.1 | 26.9
n47 | … |  $<$ 25.8† |  0007.5 $\pm$ 001.0 |  0015.2 $\pm$ 00.8 |  013.3 $\pm$ 01.4 |  $>$ $-$1.59 |  $-$0.48 $\pm$ 0.09 |  $-$0.17 $\pm$ 0.15 |  $<$ 27.9 | 27.6 | 27.7
n48 | … |  0015.6 $\pm$ 001.6 |  0011.8 $\pm$ 001.3 |  0036.6 $\pm$ 01.8 |  061.4 $\pm$ 06.2 |  $-$0.34 $\pm$ 0.19 |  $-$0.77 $\pm$ 0.08 |  $-$0.68 $\pm$ 0.15 | 27.4 | 27.6 | 27.9

Note. Columns are as follows: (1) Object ID; (2) subcomponent name of the
sources; (3)–(6) flux densities at 144 MHz, 322 MHz, 1.4 GHz, and 3.0 GHz,
respectively. Reference for columns (3), (5), and (6) are Shimwell et al.
(2022), Becker et al. (1995), and Gordon et al. (2021), respectively. Data in
column (3) indicated by † was obtained from the TGSS at 147.5 MHz (Intema et
al., 2017); (7)–(9) spectral indices between neighbouring bands; (10)–(12) Log
specific luminosity at rest 700 MHz, 3 GHz, and 7.0 GHz calculated by
interpolating the obtained flux densities.

Figure 5:  Radio spectra of the BAL sample. Although error bars are
illustrated for each measurement result, in most cases, they are substantially
smaller than the data points and concealed by the markers. Black circles
represent data obtained by LoTSS (Shimwell et al., 2022), the FIRST survey
(Becker et al., 1995), VLASS (Lyke et al., 2020), and our GMRT observations,
employed in the computation of spectral indices. Crosses and down arrows,
respectively, indicate the flux measurement and its upper limit obtained from
the TGSS (Intema et al., 2017). Gray circles show additional data only
utilised for estimating overall spectral shapes (see Section 3.2 for details).
The results of fitting with a hyperbola, power law, and double power law are
illustrated as red solid, dotted, and dashed lines, respectively. The blue
dotted lines represent the power-law fitting for the data within the optically
thin regime. The spectral indices, $\alpha$, given at each panel was obtained
from the fit. The spectral classification is denoted to the right of the
object name in each panel (see Section 4.2 for more details). As for sources
with a steep/peaked spectrum, the estimated peak frequency,
$\nu_{\mathrm{p}}$, is denoted by a red triangle, and its value is provided in
each panel.  Figure 6:  Radio spectra of the non-BAL sample. Same as Fig. 5.
In the case of n48, because the fitting with the double power law did not
converge, $\alpha=-0.8$ was set as the spectral index for its low-frequency
component.

###  4.2 Spectral classification

To classify the overall spectral shape, we fitted the observed spectra with
the following function:

$\displaystyle\log f_{\nu}=\log
f_{\mathrm{p}}+b-\sqrt{b^{2}+c^{2}(\log\nu-\log\nu_{\mathrm{p}})^{2}},$ (2)

where $f_{\mathrm{p}}$ and $\nu_{\mathrm{p}}$ are the peak flux density and
peak frequency, while $b$ and $c$ represent purely numerical values without
conveying direct physical information (Dallacasa et al., 2000; Tinti et al.,
2005). For objects with spectra lacking significant curvature, we employed a
simple power law model, whereas a double power law model was used for objects
with convex downward spectra. Figs. 5 and 6 also show fitting results. If the
estimated peak frequency was below the observed frequency range, the upper
limit of $\nu_{\mathrm{p}}$ was set by the minimum observed frequency.

Based on the fitting results, we classified the radio spectra of the objects
into steep/peaked or flat/inverted spectra. Following Dallacasa et al. (2000),
for sources fitted with a power law or hyperbolic function, we identified
spectra with a spectral index, $\alpha$, smaller than $-0.5$ in the optically
thin region above the peak frequency as steep or peaked spectra (denoted as
’s’ or ’p’ in Figs. 5 and 6, respectively). In contrast, spectra with
$\alpha>-0.5$ were classified as flat/inverted spectra (denoted as ’f’ in
Figs. 5 and 6). If the number of data points in the optically thin regime was
insufficient to confirm $\alpha<-0.5$, we classified them as flat/inverted
spectra. Our classification was based on the low-frequency component for
sources with two components in their spectra. This focus aligns with the main
objective of this study, aiming to scrutinise low-frequency features that are
less susceptible to relativistic effects and have not been explored in
preceding studies conducted in the GHz regime. These sources with two spectral
components were categorised as sources with steep/peaked spectra (denoted as
’ds’ or ’dp’ in Figs. 5 and 6, respectively), regardless of the value of the
spectral index. Table 7 presents the results of the spectral classification
and estimated physical values. Note that because the distinction between a
steep and peaked spectrum is based on whether the peak frequency lies within
the observed frequency range, the dissimilarity between these two
classifications is a matter of degree.

Table 7: Spectral classification of the BAL and non-BAL samples.

ID | method | $\alpha$ | spectral | $S_{\mathrm{p}}$ | $\nu_{\mathrm{p}}$ | $L_{\mathrm{bol}}$ | ID | method | $\alpha$ | spectral | $S_{\mathrm{p}}$ | $\nu_{\mathrm{p}}$ | $L_{\mathrm{bol}}$
---|---|---|---|---|---|---|---|---|---|---|---|---|---
|  |  | type | (mJy) | (GHz) | (W) |  |  |  | type | (mJy) | (GHz) | (W)
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13) | (14)
b01 | P |  $-$0.57 | s |  0$>$ 112 |  $<$ 0.48 |  $<$ 36.3 | n01 | P |  $-$0.46 | f | … | … | …
b02 | P |  $-$0.26 | f | … | … | … | n02 | P |  $-$0.15 | f | … | … | …
b03 | H |  $-$1.16 | s |  0$>$ 174 |  $<$ 0.51 |  $<$ 36.6 | n03 | P |  $-$0.26 | f | … | … | …
b04 | H |  $-$0.83 | p |  00$-$13 |  $-$1.54 |  $-$35.7 | n04 | H |  $-$0.36 | f | … | … | …
b05 | H |  $-$0.82 | s |  00$>$ 82 |  $<$ 0.48 |  $<$ 36.2 | n05 | H |  $-$0.64 | p |  00$-$22 |  0$-$2.23 |  $-$36.1
b06 | H |  $-$1.11 | p |  00$-$82 |  $-$6.78 |  $-$37.4 | n06 | H |  $-$0.62 | p |  00$-$70 |  $-$11.81 |  $-$37.7
b07 | H |  $-$0.93 | p |  00$-$59 |  $-$0.53 |  $-$36.0 | n07 | P |  $-$0.03 | f | … | … | …
b08 | H |  $-$0.33 | f | … | … | … | n08 | P |  $-$0.13 | f | … | … | …
b09 | H |  $-$2.06 | p |  00$-$62 |  $-$4.80 |  $-$37.0 | n09 | P |  $-$0.17 | f | … | … | …
b10 | H |  $-$0.76 | s |  00$>$ 57 |  $<$ 0.18 |  $<$ 35.6 | n10 | H |  $-$0.51 | p |  0$-$183 |  0$-$1.60 |  $-$37.1
b11 | P |  $-$0.60 | p |  00$>$ 28 |  $<$ 4.46 |  $<$ 36.6 | n11 | P |  $-$0.05 | f | … | … | …
b12 | H |  $-$1.78 | s |  0$>$ 797 |  $<$ 0.24 |  $<$ 36.8 | n12 | H |  $-$0.34 | f | … | … | …
b13 | H |  $-$1.16 | dp |  $-$1139 |  $-$1.19 |  $-$37.6 | n13 | P |  $-$0.68 | f | … | … | …
b14 | H |  $-$1.30 | p |  00$-$25 |  $-$5.20 |  $-$36.9 | n14 | P |  $-$0.29 | f | … | … | …
b15 | H |  $-$0.43 | f | … | … | … | n15 | H |  $-$0.65 | p |  0$-$107 |  0$-$0.55 |  $-$36.1
b16 | H |  $-$1.39 | p |  00$-$29 |  $-$3.71 |  $-$36.8 | n16 | H |  $-$0.69 | p |  00$-$78 |  0$-$0.25 |  $-$36.3
b17 | H |  $-$0.68 | p |  00$-$27 |  $-$3.50 |  $-$36.4 | n17 | H |  $-$0.54 | p |  00$-$75 |  0$-$2.62 |  $-$37.0
b18 | H |  $-$1.40 | s |  00$>$ 11 |  $<$ 3.59 |  $<$ 36.5 | n18 | H |  $-$0.19 | f | … | … | …
b19 | P |  $-$0.06 | f | … | … | … | n19 | H |  $-$0.65 | p |  00$-$27 |  0$-$0.94 |  $-$35.7
b20 | P |  $-$0.78 | s |  00$>$ 93 |  $<$ 0.41 |  $<$ 35.9 | n20 | H |  $-$0.61 | p |  00$-$69 |  0$-$1.12 |  $-$36.3
b21 | H |  $-$1.17 | p |  00$-$11 |  $-$4.03 |  $-$35.9 | n21 | P |  $-$0.13 | f | … | … | …
b22 | H |  $-$0.79 | p |  00$-$49 |  $-$2.24 |  $-$36.6 | n22 | P |  $-$0.85 | s |  0$>$ 218 |  0$<$ 0.58 |  $<$ 37.0
b23 | H |  $-$1.20 | p |  00$-$46 |  $-$6.28 |  $-$37.2 | n23 | H |  $-$0.36 | f | … | … | …
b24 | H |  $-$0.43 | f | … | … | … | n24 | H |  $-$0.27 | f | … | … | …
b25 | P |  $-$0.63 | s |  0$>$ 158 |  $<$ 0.15 |  $<$ 35.7 | n25 | H | … | f | … | … | …
b26 | H |  $-$1.72 | p |  00$-$86 |  $-$9.44 |  $-$37.8 | n26 | P |  $-$0.48 | f | … | … | …
b27 | P |  $-$0.14 | f | … | … | … | n27 | P |  $-$0.88 | s |  0$>$ 486 |  0$<$ 0.27 |  $<$ 36.9
b28 | P |  $-$0.55 | s |  00$>$ 68 |  $<$ 0.18 |  $<$ 35.7 | n28 | DP |  $-$0.22 | ds |  000$>$ 6 |  0$<$ 0.42 |  $<$ 34.8
b29 | P |  $-$0.24 | f | … | … | … | n29 | P |  $-$0.07 | f | … | … | …
b30 | H |  $-$0.64 | p |  00$-$42 |  $-$6.83 |  $-$37.3 | n30 | P |  $-$0.53 | s |  $>$ 4123 |  0$<$ 0.22 |  $<$ 37.8
b31 | P |  $-$0.22 | f | … | … | … | n31 | H |  $-$0.79 | p |  0$-$439 |  0$-$1.26 |  $-$37.2
b32 | P |  $-$0.01 | f | … | … | … | n32 | P |  $-$1.03 | f | … | … | …
b33 | H |  $-$0.59 | dp |  00$-$22 |  $-$3.15 |  $-$36.7 | n33 | H |  $-$0.37 | f | … | … | …
b34 | H |  $-$1.07 | p |  00$-$36 |  $-$1.60 |  $-$36.1 | n34 | H | … | f | … | … | …
b35 | H |  $-$1.09 | p |  00$-$25 |  $-$5.18 |  $-$36.8 | n35 | P |  $-$0.06 | f | … | … | …
b36 | H |  $-$1.47 | p |  00$-$50 |  $-$0.53 |  $-$35.8 | n36 | DP |  $-$0.46 | ds |  00$>$ 37 |  0$<$ 0.55 |  $<$ 36.1
b37 | P |  $-$0.56 | s |  00$>$ 59 |  $<$ 0.45 |  $<$ 35.9 | n37 | P |  $-$0.14 | f | … | … | …
b38 | H |  $-$0.35 | f | … | … | … | n38 | P |  $-$0.06 | f | … | … | …
b39 | P |  $-$0.37 | f | … | … | … | n39 | H |  $-$0.17 | f | … | … | …
b40 | H |  $-$0.23 | f | … | … | … | n40 | P |  $-$0.47 | f | … | … | …
b41 | H |  $-$0.52 | p |  00$-$59 |  $-$0.74 |  $-$36.1 | n41 | H |  $-$1.05 | p |  00$-$17 |  0$-$1.71 |  $-$35.9
b42 | DP |  $-$0.44 | ds |  00$>$ 12 |  $<$ 0.58 |  $<$ 35.8 | n42 | P |  $-$0.72 | s |  0$>$ 136 |  0$<$ 0.49 |  $<$ 36.5
b43 | P |  $-$0.19 | f | … | … | … | n43 | P |  $-$0.76 | s |  0$>$ 113 |  0$<$ 0.57 |  $<$ 36.7
b44 | H |  $-$1.90 | p |  00$-$63 |  $-$3.86 |  $-$36.9 | n44 | DP |  $-$0.68 | ds |  0$>$ 196 |  0$<$ 0.57 |  $<$ 36.9
b45 | H |  $-$1.65 | p |  00$-$56 |  $-$3.03 |  $-$37.2 | n45 | H |  $-$0.79 | p |  00$-$55 |  $-$10.63 |  $-$37.4
b46 | H |  $-$1.12 | p |  00$-$43 |  $-$0.76 |  $-$36.3 | n46 | H |  $-$0.64 | p |  00$-$39 |  0$-$0.67 |  $-$35.9
b47 | H |  $-$1.20 | p |  00$-$10 |  $-$5.10 |  $-$36.3 | n47 | P |  $-$0.28 | f | … | … | …
b48 | H |  $-$1.02 | p |  00$-$26 |  $-$1.01 |  $-$35.7 | n48 | DP | … | ds |  00$>$ 16 |  0$<$ 0.50 |  $<$ 35.6

Note. Columns are as follows: (1) and (8) Object ID; (2) and (9) function used
for fitting to the radio spectrum where P, DP, and H represent pawer law,
double power law, and hyperbola, respectively; (3) and (10) estimated spectral
index of the optically thin regime employed for classifying the spectral type;
(4) and (11) result of the spectral classification; (5)–(7) and (12)–(14)
estimated peak flux density, $S_{\mathrm{p}}$, peak frequency,
$\nu_{\mathrm{p}}$, and bolometric radio luminosity, $L_{\mathrm{bol}}$, of
steep or peaked spectral sources.

###  4.3 Comparison of the spectral class composition between the BAL and non-
BAL samples

Table 8 presents the number of sources with steep/peaked spectra and sources
with flat/inverted spectra in the BAL and non-BAL samples. The proportion of
steep/peaked spectra is higher in the BAL sample compared to the non-BAL
sample; the former contains $73\pm 13$ per cent of sources with steep/peaked
spectra, whereas the latter contains $44\pm 14$ per cent, where errors are
given by 95 per cent confidential level. We conducted a chi-square test to
examine the disparities in radio spectra between the BAL and non-BAL samples,
resulting in a $p$-value of 0.0038, which represents the likelihood of
obtaining a result equal to or more extreme than the observed result, assuming
the null hypothesis that the two samples are derived from the same parent
population. The distinction between the two groups is considered significant
at the 5 per cent significance level. Nevertheless, the obtained $p$-value
still corresponds to $\sim 2.9\sigma$. This trend remains even after excluding
objects with spatially resolved source structures (b01, b20, b25, n24, and
n27), candidates showing flux variations (b04 and n24), and objects with no
absorption lines in C IV but absorption lines in Al III (b02, n24), yielding
the $p$-value of 0.0064. Therefore, we have obtained marginal evidence
indicating that BAL quasars harbour more sources with steep/peaked spectra
than non-BAL quasars.

Table 8: Results of spectral classification

| steep/peaked | flat/inverted | total
---|---|---|---
BAL sample | 35 (31) | 13 (12) | 48 (43)
non-BAL sample | 21 0(7) | 27 0(9) | 48 (16)
both samples | 56 (38) | 40 (21) | 96 (59)

Note. The numbers within brackets denote the count of sources for which flux
measurements at 8.4 GHz are available.

Our samples include 43 BAL quasars and 16 non-BAL quasars with data above 8.4
GHz. During the spectral classification, the key criterion for identifying
steep/peaked spectra is to detect high-frequency spectra with $\alpha<-0.5$.
Objects with intrinsically optically thin spectra at high frequencies but no
data available at those frequencies can be classified as sources with
flat/inverted spectra. Hence, the fewer sources with high-frequency data in
the non-BAL sample could introduce a bias towards a reduced count of sources
with steep/peaked spectra compared to the BAL sample. In order to evaluate
this effect, Table 8 also shows statistics confined to sources with flux
density measurements at 8.4 GHz. As a result, 31 out of 43 BAL quasars with
8.4-GHz flux measurements were classified as sources with steep/peaked spectra
($72\pm 13$ per cent). Of 16 non-BAL quasars with flux measurements at 8.4
GHz, eight were classified as a sources with steep/peaked spectra ($44\pm 24$
per cent). The statistics for both sources with and without flux measurements
at 8.4 GHz do not differ significantly. Therefore, the absence of high-
frequency data does not affect our result.

###  4.4 Comparison of the spectral properties between the BAL and non-BAL
samples

In the previous subsection, we described the difference in the compositional
ratios of spectral types within the BAL and non-BAL samples. To investigate
the origins of this difference, we analysed the spectral characteristics of
both samples for each spectral type. This study focused on the peak
frequencies, spectral indices and radio luminosities at the rest frame. In
order to address the challenge posed by sources with only upper or lower
limits on these physical values and to compare them between the BAL and non-
BAL samples, we employed the Kaplan-Meier estimator, which is a non-
parametric, maximum likelihood statistical estimator that estimates the
cumulative distribution of the parent population (Kaplan & Meier, 1958). We
applied the KaplanMeierFitter module from the Python package, lifelines.

####  4.4.1 Sources with steep/peaked spectra

We examined whether there were any distinctions in the spectral features
between the BAL and non-BAL samples for sources with steep/peaked spectra.
Fig. 7 represents comparisons of the peak frequencies, $\nu_{\mathrm{p}}$, and
bolometric radio luminosities, $L_{\mathrm{bol}}$, derived from the model
fitting to the spectra. We approximated $L_{\mathrm{bol}}\simeq 4\pi
D_{\mathrm{L}}^{2}f_{\mathrm{p}}\nu_{\mathrm{p}}$ for the bolometric radio
luminosity (e.g., Feng et al., 2006), where $D_{\mathrm{L}}$ is luminosity
distance. For all steep spectral sources where only an upper limit of
$\nu_{\mathrm{p}}$ was constrained, the spectrum around the lowest observed
frequency was observed as flatter than the spectral index of $-1$ (see Tables
5 and 6). Assuming this trend continues even at lower frequencies, we can
impose an upper limit on $L_{\mathrm{bol}}$. In Fig. 7, we find that the BAL
sample indicates a higher median peak frequency than the non-BAL sample, but a
log-rank test on the distributions of the BAL and non-BAL samples for
$\nu_{\mathrm{p}}$ and $L_{\mathrm{bol}}$ generates $p$-values of 0.28 and
0.87, respectively. These $p$-values indicate the probability of achieving a
result equal to or more extreme than observed, assuming a null hypothesis that
the two distributions originate from the same parent populations. The
statistical tests show no evidence of a distinction between the two groups at
the 5 per cent significance level. Even after excluding objects with spatially
resolved source structures (b01, b20, b25, and n27) and candidates showing
flux variations (b04), these trends do not change, yielding $p$-values of 0.17
and 0.38 for the distributions of $\nu_{\mathrm{p}}$ and $L_{\mathrm{bol}}$,
respectively.

Figure 7:  Cumulative distributions of peak frequency and bolometric
luminosity of sources with steep/peaked spectra for the BAL (blue) and non-BAL
(orange) samples using the Kaplan-Meier estimator with a 95 per cent
confidence interval. (Top) peak frequency, $\nu_{\mathrm{p}}$. (Bottom)
bolometric luminosity, $L_{\mathrm{bol}}$. A log-rank test yields a $p$-value
of 0.28 and 0.87 for $\nu_{\mathrm{p}}$ and $L_{\mathrm{bol}}$, respectively.
These $p$-values indicate the probability of obtaining a result equal to or
more extreme than the observed result, assuming the null hypothesis that the
two samples are drawn from the same parent population.

We also compared spectral indices and luminosities derived from observed flux
densities between the two samples. Fig. 8 displays the cumulative
distributions for spectral indices at low, mid, and high frequencies (labelled
as $\alpha_{\textrm{low}}$, $\alpha_{\textrm{mid}}$, and
$\alpha_{\textrm{high}}$, respectively) that were obtained over the frequency
ranges of 144–322 MHz, 322 MHz–1.4 GHz, and 1.4–3.0 GHz, respectively. These
values are independent of the model applied to the flux measurement data. Our
analysis indicates that the BAL sample exhibits a higher proportion of objects
with optically thick spectral indices at low frequencies than the non-BAL
sample, which aligns with the observation of a higher median peak frequency,
$\nu_{\mathrm{p}}$, in the BAL sample (Fig. 7). Nevertheless, as in
$\nu_{\mathrm{p}}$, a log-rank test on the distributions of the BAL and non-
BAL samples for $\alpha_{\textrm{low}}$, $\alpha_{\textrm{mid}}$, and
$\alpha_{\textrm{high}}$ results in $p$-values of 0.066, 0.23, and 0.33,
respectively, providing limited evidence for the distinction between the two
groups at the 5 per cent significance level. Even after excluding objects
suffering from significant RFI in the 322-MHz data, spatially resolved
sources, and candidates showing flux variations (b01, b04, b18, b20, b25, n10,
and n27; Table 4), these trends remain, yielding $p$-values of 0.052, 0.23,
and 0.32 for the distributions of $\alpha_{\textrm{low}}$,
$\alpha_{\textrm{mid}}$, and $\alpha_{\textrm{high}}$, respectively.

Figure 8:  Cumulative distributions of spectral indices and specific
luminosities for sources with steep/peaked spectra in the BAL (blue) and non-
BAL (orange) samples using the Kaplan-Meier estimator with a 95 per cent
confidence interval. (Top) The distributions of low-frequency spectral index,
$\alpha_{\textrm{low}}$, between 144 and 322 MHz, mid-frequency spectral
index, $\alpha_{\textrm{mid}}$, between 322 MHz and 1.4 GHz, and high-
frequency spectral index, $\alpha_{\textrm{high}}$, between 1.4 and 3.0 GHz
are displayed from left to right. A log-rank test produces a $p$-value of
0.066, 0.23, and 0.33 for $\alpha_{\textrm{low}}$, $\alpha_{\textrm{mid}}$,
and $\alpha_{\textrm{high}}$, respectively. (bottom) The distributions of
rest-frame luminosity at 700 MHz, $L_{0.7}$, interpolated by
$\alpha_{\textrm{low}}$, rest-frame specific luminosity at 3.0 GHz, $L_{3}$,
interpolated by $\alpha_{\textrm{mid}}$, and rest-frame specific luminosity at
7.0 GHz, $L_{7}$, interpolated by $\alpha_{\textrm{high}}$ are displayed from
left to right. A log-rank test produces a $p$-value of 0.19, 0.65, and 0.22
for $L_{0.7}$, $L_{3}$, and $L_{7}$, respectively.

We can now compute the specific luminosity at low frequency without making
assumptions based on the acquired spectral index with the newly obtained
322-MHz data. We selected our targets based on the redshift criterion of
$1.68\leq z\leq 4.73$, and the observed redshift range in this study spans
$1.69\leq z\leq 3.38$, resulting in observed rest frequencies of 387–631 MHz,
866–1410 MHz, 3.7–6.2 GHz, and 8.0–13.2 GHz for observations at 144 MHz, 322
MHz, 1.4 GHz, and 3.0 GHz, respectively. Therefore, by using the spectral
indices obtained from the data, we calculated the rest-frame specific radio
luminosities at 700 MHz, 3.0 GHz, and 7.0 GHz through interpolation (labelled
as $L_{0.7}$, $L_{3}$, and $L_{7}$, respectively). Tables 5 and 6 present the
computed values of $L_{0.7}$, $L_{3}$, and $L_{7}$, while the cumulative
distributions of them obtained for both the BAL and non-BAL samples are
depicted in Fig. 8. Our analysis has not revealed any apparent differences
between the plots of the two groups. In order to further evaluate this, we
conducted a log-rank test on the distributions of the two samples for
$L_{0.7}$, $L_{3}$, and $L_{7}$, which produces $p$-values of 0.19, 0.65, and
0.22, respectively, indicating a lack of evidence for a difference between the
two samples. These results persist even when considering only the compact,
non-variable objects without RFI in the 322-MHz data, yielding $p$-values for
$L_{0.7}$, $L_{3}$, and $L_{7}$ as 0.27, 0.89, and 0.51, respectively.

Figure 9:  Cumulative distributions of spectral indices and specific
luminosities for sources with flat/inverted spectra in the BAL (blue) and non-
BAL (orange) samples using the Kaplan-Meier estimator with a 95 per cent
confidence interval. (Top) The distributions of low-frequency spectral index,
$\alpha_{\textrm{low}}$, between 144 and 322 MHz, mid-frequency spectral
index, $\alpha_{\textrm{mid}}$, between 322 MHz and 1.4 GHz, and high-
frequency spectral index, $\alpha_{\textrm{high}}$, between 1.4 and 3.0 GHz
are displayed from left to right. A log-rank test produces a $p$-value of
0.62, 0.22, and 0.73 for $\alpha_{\textrm{low}}$, $\alpha_{\textrm{mid}}$, and
$\alpha_{\textrm{high}}$, respectively. (bottom) The distributions of rest-
frame luminosity at 700 MHz, $L_{0.7}$, interpolated by
$\alpha_{\textrm{low}}$, rest-frame specific luminosity at 3.0 GHz, $L_{3}$,
interpolated by $\alpha_{\textrm{mid}}$, and rest-frame specific luminosity at
7.0 GHz, $L_{7}$, interpolated by $\alpha_{\textrm{high}}$ are displayed from
left to right. A log-rank test produces a $p$-value of 0.27, 0.46, and 0.29
for $L_{0.7}$, $L_{3}$, and $L_{7}$, respectively.

####  4.4.2 Sources with flat/inverted spectra

We also investigated the difference in spectral properties between the BAL and
non-BAL samples for sources with flat/inverted spectra. Fig. 9 displays the
estimated cumulative distribution of the parent population for spectral
indices and specific radio luminosities, respectively, employing the Kaplan-
Meier estimator.

We conducted a log-rank test on the distributions of the BAL and non-BAL
samples for $\alpha_{\textrm{low}}$, $\alpha_{\textrm{mid}}$, and
$\alpha_{\textrm{high}}$, resulting in $p$-values of 0.62, 0.22, and 0.73,
respectively. We do not recognise a significant difference in spectral indices
at the 5 per cent significance level. Even after excluding objects with no
absorption lines in C IV but absorption lines in Al III (b02 and n24), these
trends remain, yielding $p$-values of 0.59, 0.23, and 0.55 for the
distributions of $\alpha_{\textrm{low}}$, $\alpha_{\textrm{mid}}$, and
$\alpha_{\textrm{high}}$, respectively. Additionally, a log-rank test on the
distributions for $L_{0.7}$, $L_{3}$, and $L_{7}$ results in $p$-values of
0.27, 0.46, and 0.29, respectively, indicating a lack of evidence for a
difference between the two samples. These results remain unchanged even when
excluding the objects with no absorption lines in C IV but absorption lines in
Al III, yielding $p$-values for $L_{0.7}$, $L_{3}$, and $L_{7}$ as 0.22, 0.40,
and 0.15, respectively. Consequently, our analyses show no significant
differences in the spectral indices and luminosities of sources with
flat/inverted spectra between the two groups.

##  5 Discussion

Our investigation, involving data down to the 150-MHz band, corresponding to
387–631 MHz in the rest frame, has revealed a higher prevalence of a
steep/peaked spectrum in BAL quasars than their non-BAL counterparts within
flux-limited samples. Because all objects in our samples, except those shown
in Figs. 1 and 4, are point sources at the resolution of the FIRST survey
($\sim$5 arcsecs), most of the sources with steep/peaked spectra identified in
this study can be categorised into GPS/CSS sources (O’Dea, 1998), which are
candidates for lobe-dominated young radio sources observed from a large
viewing angle with respect to the jet axis. On the other hand, point sources
displaying a flat/inverted spectrum are interpreted as core-dominated radio
sources observed from a pole-on perspective (Browne et al., 1982; Orr &
Browne, 1982). Because no significant differences between the two groups have
been observed in the spectral index or luminosity of radio sources with each
spectral class, even at low frequencies, we do not expect any difference in
their intrinsic jet activity between the two samples. These outcomes favour
the orientation scheme for BAL quasars (e.g., Rankine et al., 2020), which is
suggested by a steeper spectral index between 4.9 and 8.4 GHz for BAL quasars
than non-BAL quasars (DiPompeo et al., 2011, 2012).

Note that our BAL and non-BAL samples are constructed to have similar
luminosity distributions based on flux density at 1.4 GHz (Fig. 2). On the
contrary, whole non-BAL quasars are known to be brighter than our current
samples (e.g., Shankar et al., 2008). These bright quasars in the radio may
experience more intense relativistic beaming effects in their jets (cf. Orr &
Browne, 1982). It would be crucial to investigate the fraction of
flat/inverted spectra in those bright non-BAL quasars to test the orientation
scheme further.

While we have found a difference in the composition of the spectral classes
between the two samples, the BAL and non-BAL samples also include a
considerable number of sources with flat/inverted spectra and sources with
steep/peaked spectra, respectively. Therefore, a simple orientation scheme may
not comprehensively account for the distinction between BAL and non-BAL
quasars (cf. Matthews et al., 2017; Yong et al., 2018). Similar issues have
been raised regarding radio morphology (Kunert-Bajraszewska et al., 2015;
Cegłowski et al., 2015; Nair & Vivek, 2022) and radio flux variations (Zhou et
al., 2006; Ghosh & Punsly, 2007; DiPompeo et al., 2011; Cegłowski et al.,
2017), pointing towards the possibility of polar BAL quasars (Punsly & Lipari,
2005; Brotherton et al., 2006; Wang et al., 2008; Reynolds et al., 2013;
Berrington et al., 2013).

As a complement to the orientation scheme, an intermittent BAL phase
associated with periods of restarting jet activity was proposed to explain
multiple spectral components at low frequencies (Bruni et al., 2015). However,
we have found that the number of sources with multiple spectral components is
comparable between the two samples; three and four sources are identified as
having a spectral classification of ’dp’ or ’ds’ in our BAL and non-BAL
samples, respectively. Therefore, it is challenging to infer factors beyond
the orientation scheme from the results of low-frequency observations in this
study.

Previous VLBI observations have revealed that a subset of GPS/CSS sources
associated with radio-loud BAL quasars demonstrates characteristics of lobe-
dominated young radio sources in terms of little flux variability, a two-sided
structure on a VLBI scale, and unpolarised radio emission in the core region
(e.g., Bruni et al., 2013; Doi et al., 2013; Hayashi et al., 2013).
Nevertheless, flat spectral radio quasars can exhibit a peaked spectrum during
a flare (Tornikoski et al., 2001; Torniainen et al., 2005; Torniainen et al.,
2007), and GPS sources may involve core-jet objects resembling blazars
(Stanghellini et al., 1997, 2001). Therefore, VLBI observations are crucial to
ascertain whether the identified sources with steep/peaked spectra genuinely
represent lobe-dominated compact radio sources. We are currently conducting a
VLBI program on the samples in this study, the results of which will be
presented in a forthcoming paper.

##  6 Conclusions

We have performed new GMRT observations on 48 radio-loud BAL quasars, chosen
from Gibson et al. (2009), and a corresponding number of radio-loud non-BAL
quasars. Using these observational data in conjunction with previous flux
measurements, we have studied low-frequency spectra of the two samples. Our
key findings are as follows:

  1. 1.

In our BAL sample, $73\pm 13$ per cent of objects exhibit a steep/peaked
spectrum, in contrast to $44\pm 14$ per cent for the non-BAL sample, with
errors reported at the 95 per cent confidence level. While the statistical
evidence is limited to a $\sim 2.9\sigma$ level, the BAL sample reveals a
higher incidence of steep/peaked spectra than the comparison sample.

  2. 2.

No significant difference between the two quasar groups is found in peak
frequencies ($\nu_{\mathrm{p}}$) and bolometric radio luminosities
($\nu_{\mathrm{bol}}$) of the sources with steep/peaked spectra. Additionally,
no significant distinctions between the two samples are observed in spectral
indices ($\alpha_{\mathrm{low}}$, $\alpha_{\mathrm{mid}}$, and
$\alpha_{\mathrm{high}}$) and specific radio luminosities ($L_{0.7}$, $L_{3}$,
and $L_{7}$) of sources with steep/peaked spectra and sources with
flat/inverted spectra.

The orientation scenario of BAL quasars can account for these spectral
features, attributing the higher prevalence of steep/peaked spectra in the BAL
sample to a relatively edge-on perspective. Nevertheless, more than the
orientation scheme is also needed to explain all the observational results,
including the presence of flat/inverted spectra in the BAL sample.
Additionally, our analyses do not rule out the possibility that peaked
spectral sources in both samples are contaminated by blazars in a flaring
state. In this regard, acquiring more densely packed data along the time
direction and implementing high-resolution observations with VLBI would
provide substantial advantages.

## Acknowledgements

We express our gratitude to the anonymous reviewer for their invaluable
feedback, which has contributed to enhancing the quality of the paper. We
thank the staff of the GMRT that made these observations possible. The GMRT is
run by the National Centre for Radio Astrophysics of the Tata Institute of
Fundamental Research. This work was partially supported by a Grant-in-Aid for
Scientific Research (C; 21540250, A.D.), Global COE Program "the Physical
Sciences Frontier" from the Japanese Ministry of Education, Culture, Sports,
Science and Technology. We used the NASA/IPAC Extragalactic Database (NED),
which the Jet Propulsion Laboratory, California Institute of Technology
operate. This research used the VizieR catalogue access tool, CDS, Strasbourg,
France. This research also made use of Montage, which is funded by the
National Science Foundation under Grant Number ACI-1440620. It was previously
funded by the National Aeronautics and Space Administration’s Earth Science
Technology Office, Computation Technologies Project, under Cooperative
Agreement Number NCC5-626 between NASA and the California Institute of
Technology.

## Data Availability

The raw data underlying this article are available via the GMRT online archive
facility: https://naps.ncra.tifr.res.in/goa/data/search. All data analysis
packages used in this work are publicly available.

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