# Evidence of jet induced optical microvariability in radio-loud Narrow Line
Seyfert 1 Galaxies

Vineet Ojha1, 2, Vivek Kumar Jha2, 3, Hum Chand2, 4, Veeresh Singh1
1Physical Research Laboratory (PRL), Astronomy and Astrophysics Division,
Ahmedabad, 380 009; India
2Aryabhatta Research Institute of Observational Sciences (ARIES), Manora Peak,
Nainital, 263002; India
3Department of Physics, Deen Dayal Upadhyaya Gorakhpur University, Gorakhpur,
273009; India
4Department of Physics & Astronomical sciences, Central University of Himachal
Pradesh, Dharamshala, 176215; India
E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

To quantify the role of radio jets for Intra-Night Optical Variability (INOV)
in Radio-Loud Narrow-Line Seyfert 1 (RLNLSy1) galaxies, we report the first
systematic comparative INOV study of 23 RLNLSy1 galaxies, with 15 RLNLSy1s
having confirmed detection of jets (jetted) and the remaining 8 RLNLSy1s
having no detection of jets (non-jetted) based on their Very Long Baseline
Array observations. We have monitored these two samples, respectively, in 37
and 16 sessions of a minimum 3-hour duration each. Based upon Fη-test at 99%
confidence level with a typical INOV amplitude ($\psi$) detection threshold of
$>$ 3%, we find the INOV duty cycles of 12% for the sample of jetted RLNLSy1s,
however, none of the sources showed INOV in the sample of non-jetted RLNLSy1s.
Among the jetted RLNLSy1s, we find that the Duty Cycle (DC) for jetted
$\gamma$-ray detected ($\gamma$-ray) RLNLSy1s is found to be 34% in contrast
to null INOV detection in the case of non-$\gamma$-ray RLNLSy1s. It suggests
that instead of the mere presence of a jet, relativistic beaming plays a
significant role for INOV in the case of low-luminous high accreting AGNs such
as NLSy1s in which dilution of the AGN’s non-thermal optical emission by the
(much steadier) optical emission contributed by the nuclear accretion disc is
quite likely. Our study of jetted $\gamma$-ray RLNLSy1s shows more frequent
INOV detection for sources with higher apparent jet speed. Further, our
results also suggest that among the NLSy1s, only jetted $\gamma$-ray RNLSy1
galaxies DC approaches blazar like DC.

###### keywords:

surveys – galaxies: active – galaxies: jets – $\gamma$-ray-galaxies:
photometry – galaxies: Seyfert – gamma-rays: galaxies.

††pubyear: 2022††pagerange: Evidence of jet induced optical microvariability
in radio-loud Narrow Line Seyfert 1 Galaxies– References

##  1 Introduction

Narrow-line Seyfert 1 (NLSy1) galaxies are a subclass of active galactic
nuclei (AGN), emitting electromagnetic radiations from radio to gamma-ray
wavebands. Although in the optical wavelengths, both permitted and forbidden
emission lines are present in their spectra, the width of their broad
component of Balmer emission lines is narrower than the population of general
type-1 Seyfert galaxies, with the full width at half maximum of the broad
component of Balmer emission line (FWHM(H${\beta}$)) being less than 2000 km
s-1 (Osterbrock & Pogge, 1985; Goodrich et al., 1989). Other optical
characteristics such as flux ratio of [O${}_{III}]_{\lambda 5007}/H\beta$ $<$
3, and strong permitted Fe ii emission lines are used in addition to the
criterion of FWHM(H${\beta}$) to characteristically define NLSy1 galaxies
(Shuder & Osterbrock, 1981). Besides, these galaxies also display peculiar
characteristics in other wavelength, especially in X-ray wavelength, such as
strong soft X-ray excess below 2 keV (e.g., Brandt et al., 1997; Vaughan et
al., 1999; Vignali et al., 2004; Ojha et al., 2020b), steep soft X-ray spectra
(e.g., Boller et al., 1996; Wang et al., 1996; Grupe et al., 1998), rapid
X-ray (sometimes optical) flux variability (e.g., Leighly, 1999; Komossa &
Meerschweinchen, 2000; Miller et al., 2000; Klimek et al., 2004; Liu et al.,
2010; Paliya et al., 2013a; Kshama et al., 2017; Ojha et al., 2019; Ojha et
al., 2020a), and blue-shifted emission line profiles (e.g., Zamanov et al.,
2002; Leighly & Moore, 2004; Boroson, 2005; Jha et al., 2021). Furthermore,
NLSy1s are believed to be relatively young AGNs, and they represent an early
phase of their evolution (e.g., Mathur, 2000; Sulentic et al., 2000; Mathur et
al., 2001; Fraix-Burnet et al., 2017; Komossa, 2018; Paliya, 2019).
Observationally, it is suggested that the majority of NLSy1s have relatively
lower Super Massive Black Hole (SMBH) masses of 106 \- 108 M☉ (Grupe & Mathur,
2004; Deo et al., 2006; Zhou et al., 2006; Peterson, 2011; Wang et al., 2014;
Rakshit et al., 2017), and higher accretion rates $\lambda_{Edd}\sim$ 0.05 -
1.00, in contrast to luminous class of AGN such as quasars (Boroson & Green,
1992; Peterson et al., 2000; Ojha et al., 2020b). However, relatively lower
SMBH mass is not uncontested since a systematic underestimation of their SMBH
has been suggested (Decarli et al., 2008; Marconi et al., 2008; Calderone et
al., 2013; Viswanath et al., 2019; Ojha et al., 2020b). These highly accreting
galaxies are generally hosted in spiral/disc galaxies (Deo et al., 2006; Ohta
et al., 2007; Olguín-Iglesias et al., 2020), although in a few $\gamma$-ray
detected NLSy1s, elliptical hosts have been suggested (hereafter
$\gamma$-NLSy1s, D’Ammando et al., 2017, 2018).

Interestingly, although the NLSy1 exhibit both radio-quiet and radio-loud
characteristics, defined by the radio parameter R${}_{5GHz}\equiv
f_{5GHz}/f_{4400\AA}$ with R$\leq$ 10 and $>$ 10 are being used to
parameterized radio-quiet and radio-loud AGNs, respectively (e.g., see, Stocke
et al., 1992; Visnovsky et al., 1992; Kellermann et al., 1994, 1989), the
population is dominated by radio-quiet objects (Kellermann et al., 2016) and
only a small fraction $\sim$ 7% of NLSy1s are radio-loud (hereafter RLNLSy1s,
Komossa et al., 2006; Zhou et al., 2006; Rakshit et al., 2017; Singh & Chand,
2018). This suggests that in a few of these galaxies, jets may be present,
making them radio-loud (Zhou et al., 2003; Yuan et al., 2008). Indeed, Very
Long Baseline Array (VLBA) observations have discovered parsec-scale blazar-
like radio jets in a few RLNLSy1s (Lister et al., 2013; Gu et al., 2015;
Lister et al., 2016).

The existence of relativistic jets in such a subclass of AGN (although in a
few of the sources) that has relatively higher accretion rates and lower black
hole masses contradicts the general trend of the existence of relativistic
jets in larger black hole masses and lower accretion rates (Urry et al., 2000;
Boroson, 2002; Böttcher & Dermer, 2002; Urry, 2003; Marscher, 2009; Chiaberge
& Marconi, 2011), and also objects the theoretical paradigm of jet formation
(e.g., Böttcher & Dermer, 2002). Hence, studying NLSy1s from the standpoint of
jets is essential to understanding the physical processes that can launch
relativistic jets in this subclass of AGN.

Nonetheless, despite a blazar-like double-humped spectral energy distribution
(SED) of a few RLNLSy1s (e.g., Abdo et al., 2009c; Paliya et al., 2013b;
Paliya, 2019), a minuscule fraction of RLNLSy1s, especially very radio-loud (R
$>$ 100) RLNLSy1s exhibit interesting multi-wavelength characteristics such as
compact radio cores, high brightness temperature, superluminal motion, flat
radio and X-ray spectra, and rapid infrared and X-ray flux variability similar
to blazar class of AGN (Boller et al., 1996; Grupe et al., 1998; Leighly,
1999; Hayashida, 2000; Komossa & Meerschweinchen, 2000; Yuan et al., 2008;
Jiang et al., 2012; Orienti et al., 2012; Itoh et al., 2013; Yao et al., 2015;
Berton et al., 2018; Gabanyi et al., 2018; Lister, 2018). All these
characteristics give indirect evidence of the presence of jets in them.
However $\gamma$-ray detection by Fermi-Large Area Telescope (Fermi-
LAT)111https://heasarc.gsfc.nasa.gov/docs/heasarc/missions/fermi.html from
about two dozen RLNLSy1s gives conclusive evidence that $\gamma$-ray detected
NLSy1s are capable of ejecting relativistic jets (Abdo et al., 2009a, b, c;
Foschini et al., 2010; Foschini, 2011; D’Ammando et al., 2012; D’Ammando et
al., 2015; Yao et al., 2015; Paliya et al., 2018; Yang et al., 2018; Yao et
al., 2019).

Variability of an AGN’s optical flux from a few minutes to a day time scales
is variously known as microvariability (Miller et al., 1989), Intraday
Variability (IDV, Wagner & Witzel, 1995) or Intra-Night Optical Variability
(INOV, Gopal-Krishna et al., 1993). This alternative tool is also used to
indirectly verify the presence or absence of jets in other sub-classes of AGN
because of the well established observational fact that for radio-loud jet
dominated sources such as blazars, both INOV amplitude ($\psi$) and the duty
cycle (DC) are found to be distinctively high in comparison to non-blazars,
including weakly polarised flat-radio-spectrum (i.e., radio-beamed) quasars
(Goyal et al., 2013b; Gopal-Krishna & Wiita, 2018). Interestingly, such an
indirect tool has been used for a decade in searching for the Doppler boosted
optical jets in low luminous AGNs such as NLSy1s and weak emission line QSOs
(e.g., see Liu et al., 2010; Paliya et al., 2013a; Kumar et al., 2015; Parveen
et al., 2016; Kumar et al., 2017; Ojha et al., 2018, 2021). However, this
indirect evidence is based upon the observed high amplitude, and duty cycle of
INOV as seen in blazars consisting of strongly Doppler boosted jets. More
importantly, an INOV study comparing a subclass of AGN with jets and without
jets has not yet been explored so far. Therefore, to establish stronger INOV
amplitude ($\psi$) with high DC as evidence of the existence of jet in an AGN,
we have carried out an INOV study with two sub-samples of RLNLSy1s with and
without radio VLBA jets.

The general consensus regarding the radio structures of NLSy1s has been that
they harbor sizes of less than 300 pc (Ulvestad et al., 1995; Lister, 2018)
and are generally compact sources with a steep spectrum (Foschini, 2011, 2012;
Berton et al., 2015). The appearance of radio structures in the radio
observations of AGNs depends upon the resolution and sensitivity of the radio
telescopes; therefore, non-detection of the radio jets in the radio images of
RLNLSy1s may not necessarily imply that they do not have jets. Here, we have
selected our sources (see Sect. 2) based on their available observations with
the radio telescopes, which mainly consist of VLBA observations.

Furthermore, as pointed above, $\gamma$-ray detections in several RLNLSy1s
suggest the presence of relativistic jets in them; therefore, a comprehensive
INOV study of the jetted with $\gamma$-ray detected RLNLSy1s (hereafter
J-$\gamma$-RLNLSy1s) and the jetted without $\gamma$-ray detected RLNLSy1s
(hereafter J-RLNLSy1s) is essential to understand the nature of their
variability and jets. Therefore, we have also discussed the INOV nature of
J-$\gamma$-RLNLSy1s and J-RLNLSy1s sub-samples in the present work.

The layout of this paper is as follows. In Sect. 2, we outline the sample
selection procedure. Sect. 3 provides details of our intra-night optical
monitoring and the data reduction procedure. The statistical analysis is
presented in Sect. 4, and our main results, followed by a brief discussion,
are given in Sect. 5. In Sect. 6, we summarize our main conclusions.

Table 1: The present sample of 23 RLNLSy1s galaxies selected for INOV monitoring. SDSS Name,222The SDSS names of the sources with Fermi-LAT detection are suffixed with a “$\blacktriangle$” sign and the references (Abdo et al., 2009a, b; Foschini et al., 2010); (Abdo et al., 2009c); (Foschini, 2011; D’Ammando et al., 2012); (D’Ammando et al., 2015); (Liao et al., 2015); (Yao et al., 2015); and (Ajello et al., 2020) are for the sources, J094857.32$+$002225.6; J032441.20$+$341045.0 and J150506.48$+$032630.8; J084957.98$+$510829.0; J164442.53$+$261913.3; J130522.75$+$511640.2, J122222.99$+$041315.9, and J144318.60$+$472557.0 respectively. | R-mag333Taken from Monet (1998). |  $z$444Emission-line redshifts are taken either from Gu et al. (2015) or from Paliya et al. (2019). |  $R_{1.4GHz}$555$R_{1.4GHz}\equiv f_{1.4GHz}/f_{4400\AA}$ values are taken from Gu et al. (2015) for the sources marked with a ‘†’, and are taken from Ojha et al. (2020a) for the sources marked with an ‘⋆’, except for J120014.08$-$004638.7 for which $R_{1.4GHz}$ is estimated using its total flux density of 27.1 mJy at 1.4 GHz and k-corrected B-band optical flux density of 0.16 mJy (Doi et al., 2012). | Apparent jet speed666The available jet speed of RLNLSy1s from literature which is as follows: for the jet speed of J032441.20$+$341045.0, J084957.98$+$510829.0, J094857.32$+$002225.6, J150506.48$+$032630.8 see Lister et al. (2019), and for J122222.99$+$041315.9, J164442.53$+$261913.3 see Lister et al., 2016, Doi et al., 2012, and. | Optical Polarization777The optical polarization values as reported in these papers: αItoh et al. (2014); βIkejiri et al. (2011); γAngelakis et al. (2018); δMaune et al. (2014); κLeighly (1999). | Radio Polarization888The radio polarization values as reported in these papers: ψNeumann et al. (1994); ΛHodge et al. (2018); τHoman et al. (2001). ⋆fractional radio polarisation images presented in Fig-6 of Gu et al. (2015). | log ($M_{BH}$)999Derived black hole masses of the present sample based upon single-epoch optical spectroscopy virial method were compiled from the literature. The references for the black hole mass are as follows: ∨Zhou et al. (2007); ⋄Yuan et al. (2008); ⋎Yao et al. (2015); ⟂Rakshit et al. (2017); ∔Wang & Lu (2001); ζGreene & Ho (2007). | Observing
---|---|---|---|---|---|---|---|---
|  |  |  |  |  |  | ($M_{\sun}$) | freq. (GHz)
jetted NLSy1s
J032441.20$+$341045.0▲ | 13.10 | 0.06 | 318⋆ | $9.1c\pm 0.3c$ | 1-3%α, 0.7-0.8%β, 1.2%γ | 4%ψ, 0.2-1%Λ | 7.30∨ | 2.2/8.4
J081432.12$+$560958.7 | 18.10 | 0.51 | 339† | - | - | $\star$ | 8.00⋄ | 4.9
J084957.98$+$510829.0▲ | 17.79 | 0.58 | 4496⋆ | $6.6c\pm 0.6c$ | 10%δ, 10%γ | 0.3-3%Λ, 3.3%τ | 7.59⟂ | 5.0/8.4/15.3
J090227.20$+$044309.0 | 18.20 | 0.53 | 1047† | - | - | $\star$ | 7.64⟂ | 4.9
J094857.32$+$002225.6▲ | 18.17 | 0.58 | 846⋆ | $9.7c\pm 1.1c$ | 36%α, 18.8%β, 2.4%γ | 0.2-3%Λ | 7.50⟂ | 22.2
J095317.10$+$283601.5 | 18.60 | 0.66 | 513† | - | - | - | 7.73⟂ | 4.9
J104732.78$+$472532.0 | 18.20 | 0.80 | 7413† | - | - | - | 8.10⋄ | 4.9
J122222.99$+$041315.9▲ | 17.06 | 0.97 | 1534⋆ | $0.9c\pm 0.3c$ | - | 0.2-3.3%Λ | 8.30⋎ | 15.4
J130522.75$+$511640.2▲ | 15.80 | 0.79 | 219† | - | 1.0%γ | $\star$ | 8.15⟂ | 4.9
J142114.05$+$282452.8 | 17.10 | 0.78 | 205† | - | - | - | 7.72⟂ | 4.9
J144318.60$+$472557.0▲ | 17.70 | 0.70 | 1175† | - | - | $\star$ | 7.80⋄ | 4.9
J150506.48$+$032630.8▲ | 17.72 | 0.41 | 3364⋆ | $0.1c\pm 0.2c$ | 4%γ | 0.2-2.5%Λ | 7.26⟂ | 15.3
J154817.92$+$351128.0 | 18.40 | 0.48 | 692† | - | 2.1%γ | $\star$ | 7.84⟂ | 4.9
J164442.53$+$261913.3▲ | 16.60 | 0.14 | 447⋆ | $>1.0c$ | 2.2%γ | - | 7.21⟂ | 1.7
J170330.38$+$454047.3 | 12.80 | 0.06 | 102⋆ | - | 3-5%κ | - | 6.77∔ | 1.7
non-jetted NLSy1s
J085001.17$+$462600.5 | 18.40 | 0.52 | 170† | - | - | - | 7.34⟂ | 4.9
J103727.45$+$003635.6 | 19.10 | 0.60 | 457† | - | - | - | 7.48⟂ | 4.9
J111005.03$+$365336.2 | 19.00 | 0.63 | 933† | - | - | - | 7.43⟂ | 4.9
J113824.53$+$365327.2 | 18.30 | 0.36 | 219† | - | - | - | 7.29⟂ | 4.9
J120014.08$-$004638.7 | 17.70 | 0.18 | 169 | - | - | - | 7.40ζ | 1.4
J124634.65$+$023809.1 | 17.50 | 0.36 | 277† | - | - | - | 7.42⟂ | 4.9
J163323.59$+$471859.0 | 14.50 | 0.12 | 154⋆ | - | 2.4%γ | - | 6.70⟂ | 1.7
J163401.94$+$480940.2 | 19.10 | 0.49 | 204† | - | - | - | 7.56⟂ | 4.9
Table 2: Details of system parameters of the telescopes and detectors used in the observations of 23 RLNLSy1s.  Telescope (s) | No. of sessionse | Detector (s) | Field of view | Readout | Gain | Focal ratio | Pixel size | Plate scale
---|---|---|---|---|---|---|---|---
|  | (arcmin2) | noise | (e- | of | of CCD | of CCD |
|  |  | (e-) | /ADU) | telescope | ($\mu$m) | ( ′′/pixel ) |
1.04-m STa | 2 | 4k$\times$4k | 15.70$\times$15.70 | 3.0 | 10.0 | f/13 | 15.0 | 0.23
1.30-m DFOTb | 47 | 2k$\times$2k | 18.27$\times$18.27 | 7.5 | 2.0 | f/4 | 13.5 | 0.53
3.60-m DOTc | 3 | 4k$\times$4k | 6.52$\times$6.52 | 8.0⋆, 5.0† | 1.0⋆, 2.0† | f/9 | 15.0 | 0.10
2.01-m HCTd | 1 | 2k$\times$2k | 10.24$\times$10.24 | 4.1 | 2.20 | f/9 | 15.0 | 0.30
aSampurnand Telescope (ST), bDevasthal Fast Optical Telescope (DFOT), cDevasthal Optical Telescope (DOT), |
dHimalayan Chandra Telescope (HCT). e No. of intra-night sessions taken from the telescopes. |
⋆Readout noise and corresponding gain at readout speed of 1 MHz and ‘†’ represents the same at readout speed of 500 kHz. |

##  2 sample selection

The bulk of our sample for intra-night monitoring is drawn from Gu et al.
(2015) where they have reported good quality VLBA observations at 5 GHz for
the 14 RLNLSy1 galaxies having a flux density above 10 mJy at 1.4 GHz and a
radio-loudness parameter101010R1.4GHz is the ratio of the monochromatic rest-
frame flux densities at 1.4 GHz and 4400Å (see Yuan et al., 2008). R1.4GHz >
100\. Out of 14 RLNLSy1s, they confirm the presence of a jet in 7 of the
sources (hereafter, "jetted") based on the detection of a core-jet structure
at 5 GHz, and the remaining 7 sources are termed as "non-jetted" based on the
detection of a compact core only. However, in reference to the jetted nature,
it may be noted that VLBA radio images at typical resolution could generally
resolve parsec scale core jet structures (Lister, 2018) which may not be
relativistically beamed. Hence some of the sources could be steep spectrum
sources as seen in mini-radio galaxies (see Gu et al., 2015). We also note
that the "non-jetted" source J144318.56$+$472556.7 has a $\sim$ 15-mas long
quasi-linear radio component resolved into seven components along the south-
west direction, in addition to diffuse emission extending up to $\sim$ 30 mas
(see figure 12 of Gu et al., 2015). Therefore, we have included this source in
our jetted subsample. We next expanded this sample by including another 9
sources from the VLBA literature, which also satisfy the above twin criteria
(i.e., $f_{\nu\leavevmode\nobreak\ 1.4GHz}\geq$ 10 mJy and
R${}_{1.4GHz}>100$). The jetted (or non-jetted) classification of the 8
sources out of 9 is possible using their published VLBA observations. Thus,
three of these 8 sources, viz., J163323.59$+$471859.0, J164442.53$+$261913.3
and J170330.38$+$454047.3 are taken from the Doi et al. (2011) and the
remaining 5 sources, viz., J032441.20$+$341045.0, J084957.98$+$510829.0,
J094857.32$+$002225.6, J122222.99$+$041315.9 and J150506.48$+$032630.8 are
taken from Zhou et al. (2007), D’Ammando et al. (2012), Giroletti et al.
(2011), Lister et al. (2016) and Orienti et al. (2012), respectively. The
frequencies at which observations of 23 RLNLSy1s were carried out are
tabulated in the last column of Table 1. However, for the NLSy1
J120014.08$-$004638.7, Doi et al. (2012) have confirmed its lobe-dominated
nature based upon its Very Large Array (VLA) 1.4 GHz FIRST images. Note that
this source is also not in the latest sample of Monitoring Of Jets in Active
galactic nuclei with VLBA Experiments (MOJAVE) XVII program (see Lister et
al., 2019). Therefore, we have included this source in our non-jetted set.
Based on the published VLBA observations of 8 sources, 7 sources have a
confirmed jet, and one source falls in the non-jetted category. Thus, overall,
our sample consists of 23 RLNLSy1s, including 15 of which are jetted, and the
remaining 8 RLNLSy1s are non-jetted. Table 1 summarizes the basic properties
of our sample. The SDSS names of the sources with Fermi-LAT detection are
suffixed with a "$\blacktriangle$" sign, and the references are given in the
footnote "b" to Table 1.

##  3 Observations and Data Reduction

###  3.1 Photometric monitoring observations

Intra-night monitoring of all 23 RLNLSy1s of our sample was performed in the
broad-band Johnson-Cousin filter R due to the optimum response of the used
CCDs in this filter. Four telescopes namely, the 1.04 meter (m) Sampurnanand
telescope (ST, Sagar, 1999), 1.30-m Devasthal Fast Optical Telescope (DFOT,
Sagar et al., 2010), 3.60-m Devasthal Optical Telescope (DOT, Sagar et al.,
2012) and 2.01-m Himalayan Chandra Telescope (HCT, Prabhu & Anupama, 2010)
were used for the intra-night monitoring of the present sample. Out of these
four telescopes, the 1.04-m ST is located at Nainital, while the 1.30-m DFOT
and the 3.60-m DOT are located at Devasthal near Nainital, and all the three
are managed by the Aryabhatta Research Institute of Observational Sciences
(ARIES). The fourth telescope, the 2.01-m Himalayan Chandra Telescope (HCT),
is located in Ladakh and operated by the Indian Institute of Astrophysics
(IIA), Bangalore, India. All the four telescopes are equipped with Ritchey-
Chretien (RC) optics and were read out 1 MHz rate during our observations,
except for the 3.60-m DOT, which was read out additionally at 500 kHz. The
monitoring sessions lasted between $\sim$ 3.0 and $\sim$ 5.5 hours (median
3.75 hrs). Our sources were observed in 4$\times$4 binning mode with 1.04-m ST
and the same with the 3.6-m DOT on 2017.04.11. A 2$\times$2 binning mode was
adopted for the remaining sessions with the DOT. No binning was done for the
DFOT and the HCT telescopes observations. The basic parameters of the four
telescopes, the number of monitoring sessions, and the CCDs used in the
present observations are listed in Table 2. In order to improve the INOV
statistics, at least two intra-night sessions were managed for each of our 23
RLNLSy1s. In this work, 1.04-3.60m class telescopes have been used; therefore,
depending on the brightness of the target NLSy1, telescope used, moon
illumination, and sky condition, a typical exposure time for each science
frame were set between 4 and 15 minutes in order to get a reasonable SNR. The
median seeing (FWHM of the point spread function (PSF)) for the sessions
typically ranged between $\sim$ 1 - 3 arcsec, except for a single session
dated 2019.03.25 when seeing became considerably poorer (see Fig. 5).

###  3.2 Data reduction

For each night, sky flat-field images were taken during dusk and dawn, and at
least three bias frames were taken. The dark frames were not taken during our
observations due to the relatively low temperature of the CCD detectors used,
which were cooled either using liquid nitrogen (to about $-120^{\circ}$C) or
using thermoelectrical cooling (to about $-90^{\circ}$C in case of 1.3-m
DFOT). The standard routines within the IRAF111111Image Reduction and Analysis
Facility (http://iraf.noao.edu/) software package were followed for
preliminary processing of the observed frames. Aperture photometry (Stetson,
1987, 1992) was selected in this work for extracting the instrumental
magnitudes of the targets and the comparison stars recorded in the CCD frames,
using DAOPHOT II algorithm121212Dominion Astrophysical Observatory Photometry
(http://www.astro.wisc.edu/sirtf/daophot2.pdf) due to less crowded fields of
the monitored NLSy1s. The prime parameter in the aperture photometry is the
size of the optimal aperture, which is used to estimate the instrumental
magnitude and the corresponding signal-to-noise ratio (SNR) of the individual
photometric data points recorded in each CCD frame. As emphasized in Howell
(1989), the SNR of a target recorded in a CCD is maximized for the aperture
radius $\sim$ PSF. However, as suggested by Cellone et al. (2000) when the
underlying host galaxy significantly contributes to the total optical flux,
its contribution to the aperture photometry can vary significantly due to PSF
variation, mimicking INOV. Possibility of such spurious INOV can be
significant for the lower redshift NLSy1s in our sample, particularly,
J032441.20$+$341045.0 (z = 0.06), J164442.53$+$261913.3 (z = 0.14),
J170330.38$+$454047.3 (z = 0.06), J120014.08$-$004638.7 (z = 0.18) and
J163323.59$+$471859.0 (z = 0.12) (Table 1). This issue is further addressed in
Sect. 5. Nonetheless, bearing the above in mind, we have chosen an aperture
radius equal to 2$\times$FWHM for our final analysis, as already elaborated in
Ojha et al. (2021).

Using the instrumental magnitudes extracted from the aperture photometry, DLCs
of each NLSy1s were derived for each session relative to a minimum of two
(steady) comparison stars that were chosen based on their closeness to the
monitored target NLSy1, both in position and brightness, as recorded in the
CCD frames. The importance of these procedures for genuine INOV detection has
been highlighted by Howell et al. (1988) and further focused in Cellone et al.
(2007). In the case of 12 targets, we could identify at least a comparison
star within $\sim$ 1 instrumental magnitude to the target NLSy1. The median
magnitude offsets ($\Delta m_{R}$) for the remaining 10 targets were also not
significant and within $\sim$ 1.5-mag, except for a source, viz.,
J103727.45$+$003635.6 for which $\Delta m_{R}$ was found to be 1.74 (see Figs
2-6). Table LABEL:tab_jnj_comp_star lists coordinates together with some other
parameters of the steady comparison stars used for all the sessions. It has
been shown in Ojha et al. (2021) that the color differences of such orders can
be safely discounted while analyzing the variability of the DLCs.

Table 3: Basic parameters of the comparison stars along with their observation dates used in this study for the 23 RLNLSy1 galaxies. Target RLNLSy1s and | Date(s) of monitoring | R.A.(J2000) | Dec.(J2000) | g | r | g-r
---|---|---|---|---|---|---
the comparison stars |  | (h m s) | (∘ ′ ′′) | (mag) | (mag) | (mag)
(1) | (2) | (3) | (4) | (5) | (6) | (7)
jetted NLSy1s
J032441.20$+$341045.0 | 2016 Nov. 22, 23; Dec. 02; 2017 Jan. 03, 04 | 03 24 41.20 |  $+$34 10 45.00 | 14.50 | 13.70 | 0.80∗
S1 | 2016 Nov. 22, Dec. 02 | 03 24 53.68 |  $+$34 12 45.62 | 15.60 | 14.40 | 1.20∗
S2 | 2016 Nov. 22, Dec. 02 | 03 24 53.55 |  $+$34 11 16.58 | 16.20 | 14.40 | 1.80∗
S3 | 2016 Nov. 23 | 03 24 10.92 |  $+$34 15 01.90 | 16.30 | 15.10 | 1.20∗
S4 | 2016 Nov. 23 | 03 24 14.04 | $+$34 18 20.10 | 15.80 | 15.00 | 1.00∗
S5 | 2017 Jan. 03 | 03 24 14.92 | $+$34 15 21.20 | 15.90 | 15.10 | 0.80∗
S6 | 2017 Jan. 03 | 03 24 08.44 | $+$34 08 15.80 | 15.80 | 14.20 | 1.60∗
S7 | 2017 Jan. 04 | 03 24 38.14 | $+$34 13 53.40 | 15.90 | 15.20 | 0.70∗
S8 | 2017 Jan. 04 | 03 24 14.08 | $+$34 16 48.60 | 15.40 | 14.80 | 0.60∗
J081432.12$+$560958.7 | 2017 Jan. 03; Nov. 20 | 08 14 32.12 |  $+$56 09 58.69 | 18.06 | 18.11 |  $-$0.05
S1 | 2017 Jan. 03 | 08 14 02.78 |  $+$56 11 12.07 | 19.14 | 18.12 | 1.02
S2 | 2017 Jan. 03 | 08 14 53.54 |  $+$56 10 14.14 | 17.96 | 17.35 |  $-$0.61
S3 | 2017 Nov. 20 | 08 13 39.62 |  $+$56 17 55.59 | 19.05 | 17.71 | 1.34
S4 | 2017 Nov. 20 | 08 14 19.58 |  $+$56 06 24.04 | 19.33 | 17.88 | 1.45
J084957.98$+$510829.0 | 2017 Dec. 13, 2019 April 08 | 08 49 57.98 |  $+$51 08 29.04 | 18.92 | 18.28 | 0.64
S1 |  | 08 50 12.62 |  $+$51 08 08.03 | 19.45 | 18.06 | 1.39
S2 |  | 08 50 03.07 |  $+$51 09 12.23 | 17.82 | 17.09 | 0.73
J090227.20$+$044309.0 | 2017 Feb. 22; Dec. 14 | 09 02 27.20 |  $+$04 43 09.00 | 18.96 | 18.63 | 0.33
S1 | 2017 Feb. 22 | 09 02 01.94 |  $+$04 37 32.90 | 19.10 | 17.74 | 1.36
S2 | 2017 Feb. 22 | 09 02 23.40 |  $+$04 35 44.57 | 18.70 | 17.31 | 1.39
S3 | 2017 Dec. 14 | 09 03 04.11 |  $+$04 48 19.65 | 18.85 | 17.95 | 0.90
S4 | 2017 Dec. 14 | 09 03 07.29 |  $+$04 38 57.34 | 18.92 | 17.93 | 0.99
J094857.32$+$002225.6 | 2016 Dec. 02; 2017 Dec. 21 | 09 48 57.32 |  $+$00 22 25.56 | 18.59 | 18.43 | 0.16
S1 |  | 09 48 36.95 |  $+$00 24 22.55 | 17.69 | 17.28 | 0.41
S2 |  | 09 48 37.47 |  $+$00 20 37.02 | 17.79 | 16.70 | 1.09
J095317.10$+$283601.5 | 2017 March 04; 2018 March 23 | 09 53 17.10 |  $+$28 36 01.48 | 18.99 | 18.97 | 0.02
S1 | 2017 March 04 | 09 52 48.09 |  $+$28 29 53.69 | 18.31 | 17.45 | 0.86
S2 | 2017 March 04; 2020 November 21 | 09 53 07.49 |  $+$28 37 17.10 | 18.46 | 17.32 | 1.14
S3 | 2020 November 21 | 09 53 21.03 |  $+$28 34 57.36 | 20.41 | 18.90 | 1.51
J104732.78$+$472532.0 | 2017 April 11; 2018 March 12 | 10 47 32.78 |  $+$47 25 32.02 | 18.97 | 18.76 | 0.21
S1 | 2017 April 11 | 10 47 16.50 |  $+$47 24 47.24 | 18.68 | 17.98 | 0.70
S2 | 2017 April 11; 2018 March 12 | 10 47 27.51 |  $+$47 27 58.94 | 18.79 | 17.87 | 0.92
S3 | 2018 March 12 | 10 48 16.44 |  $+$47 22 42.22 | 18.78 | 17.45 | 1.33
J122222.99$+$041315.9 | 2017 Jan. 03, 04; Feb. 21, 22; March 04, 24 | 12 22 22.99 |  $+$04 13 15.95 | 17.02 | 16.80 | 0.22
S1 |  | 12 22 34.02 |  $+$04 13 21.57 | 18.63 | 17.19 | 1.44
S2 |  | 12 21 56.12 |  $+$04 15 15.19 | 17.22 | 16.78 | 0.44
J130522.75$+$511640.2 | 2017 April 04; 2019 April 25 | 13 05 22.74 |  $+$51 16 40.26 | 17.29 | 17.10 | 0.19
S1 | 2017 April 04 | 13 06 16.16 |  $+$51 19 03.67 | 16.96 | 15.92 | 1.04
S2 | 2017 April 04; 2019 April 25 | 13 05 57.57 |  $+$51 11 00.97 | 16.35 | 15.26 | 1.09
S3 | 2019 April 25 | 13 05 44.25 |  $+$51 07 35.85 | 17.88 | 16.42 | 1.46
J142114.05$+$282452.8 | 2018 May 10; 2019 May 27 | 14 21 14.05 |  $+$28 24 52.78 | 17.73 | 17.74 |  $-$0.01
S1 | 2018 May 10 | 14 20 33.73 |  $+$28 31 10.45 | 18.50 | 17.11 | 1.39
S2 | 2018 May 10; 2019 May 27 | 14 21 08.78 |  $+$28 24 04.99 | 16.16 | 16.21 |  $-$0.05
S3 | 2019 May 27 | 14 21 24.36 |  $+$28 27 16.52 | 16.82 | 16.45 | 0.37
J144318.56$+$472556.7 | 2018 March 11, 23 | 14 43 18.56 |  $+$47 25 56.74 | 18.14 | 18.17 |  $-$0.03
S1 |  | 14 43 37.14 |  $+$47 23 03.03 | 17.51 | 16.82 | 0.69
S2 |  | 14 43 19.05 |  $+$47 19 00.98 | 18.03 | 16.75 | 1.28
J150506.48$+$032630.8 | 2017 March 25; 2018 April 12 | 15 05 06.48 |  $+$03 26 30.84 | 18.64 | 18.22 | 0.42
S1 |  | 15 05 32.05 |  $+$03 28 36.13 | 18.13 | 17.64 | 0.49
S2 |  | 15 05 14.52 |  $+$03 24 56.17 | 17.51 | 17.14 | 0.37
J154817.92$+$351128.0 | 2018 May 17; 2019 May 08 | 15 48 17.92 |  $+$35 11 28.00 | 18.03 | 18.03 | 0.00
S1 |  | 15 47 57.43 |  $+$35 14 05.24 | 18.31 | 17.50 | 0.81
S2 |  | 15 48 02.20 |  $+$35 13 56.16 | 17.37 | 16.98 | 0.39
J164442.53$+$261913.3 | 2017 April 03; 2019 April 26 | 16 44 42.53 |  $+$26 19 13.31 | 18.03 | 17.61 | 0.42
S1 |  | 16 45 20.03 |  $+$26 20 54.55 | 16.56 | 15.89 | 0.67
S2 |  | 16 44 34.40 |  $+$26 15 30.27 | 16.28 | 15.80 | 0.48
J170330.38$+$454047.3 | 2017 June 03; 2019 March 25 | 17 03 30.38 |  $+$45 40 47.27 | 16.12 | 15.41 | 0.71
S1 |  | 17 04 02.02 |  $+$45 42 16.56 | 15.02 | 14.39 | 0.63
S2 |  | 17 04 34.88 |  $+$45 40 08.65 | 15.00 | 13.91 | 1.09
non-jetted NLSy1s
J085001.17$+$462600.5 | 2017 Jan. 01; Dec. 15 | 08 50 01.17 |  $+$46 26 00.50 | 19.12 | 18.82 | 0.30
S1 |  | 08 50 17.69 |  $+$46 20 42.71 | 18.11 | 17.85 | 0.26
S2 |  | 08 49 48.29 |  $+$46 21 11.81 | 18.72 | 17.63 | 1.09
J103727.45$+$003635.6 | 2018 March 11, 22 | 10 37 27.45 |  $+$00 36 35.60 | 19.57 | 19.21 | 0.36
S1 | 2018 March 11 | 10 37 39.63 |  $+$00 38 26.16 | 18.90 | 17.69 | 1.21
S2 | 2018 March 11 | 10 37 28.03 |  $+$00 37 59.88 | 18.97 | 17.52 | 1.45
S3 | 2021 April 08 | 10 36 50.96 |  $+$00 41 25.26 | 18.76 | 17.35 | 1.41
S4 | 2021 April 08 | 10 37 38.72 |  $+$00 40 28.00 | 17.26 | 16.82 | 0.44
J111005.03$+$365336.2 | 2018 March 23; 2019 Jan. 13 | 11 10 05.03 |  $+$36 53 36.22 | 20.60 | 20.49 | 0.11
S1 |  | 11 10 08.50 |  $+$36 50 59.03 | 19.14 | 18.86 | 0.28
S2 |  | 11 10 10.76 |  $+$36 55 26.97 | 19.74 | 18.45 | 1.29
J113824.53$+$365327.2 | 2017 April 17; 2018 March 23 | 11 38 24.53 |  $+$36 53 27.18 | 19.55 | 18.79 | 0.76
S1 |  | 11 38 25.03 |  $+$36 54 44.02 | 18.90 | 17.52 | 1.38
S2 |  | 11 37 56.81 |  $+$36 52 35.56 | 17.91 | 17.41 | 0.50
J120014.08$-$004638.7 | 2018 March 12, May 11 | 12 00 14.08 |  $-$00 46 38.74 | 18.51 | 17.81 | 0.70
S1 |  | 12 00 12.63 |  $-$00 46 07.14 | 17.19 | 16.68 | 0.51
S2 |  | 12 00 25.99 |  $-$00 51 45.21 | 16.73 | 16.37 | 0.36
J124634.65$+$023809.1 | 2017 April 03; 2018 April 12 | 12 46 34.65 |  $+$02 38 09.06 | 18.35 | 18.18 | 0.17
S1 | 2017 April 03; 2018 April 12 | 12 47 00.55 |  $+$02 37 31.37 | 17.91 | 16.89 | 1.02
S2 | 2017 April 03 | 12 47 05.32 |  $+$02 39 06.75 | 16.94 | 16.62 | 0.32
S3 | 2018 April 12 | 12 46 49.50 |  $+$02 37 11.64 | 17.24 | 16.77 | 0.47
J163323.59$+$471859.0 | 2017 May 20; 2019 March 20 | 16 33 23.59 |  $+$47 18 59.04 | 17.25 | 16.95 | 0.30
S1 |  | 16 32 59.26 |  $+$47 26 05.45 | 15.57 | 15.18 | 0.39
S2 |  | 16 32 56.00 |  $+$47 21 01.26 | 15.55 | 15.11 | 0.44
J163401.94$+$480940.2 | 2018 March 22, 26 | 16 34 01.94 |  $+$48 09 40.20 | 19.54 | 19.21 | 0.33
S1 | 2018 March 22 | 16 34 04.24 |  $+$48 11 32.47 | 19.65 | 18.77 | 0.88
S2 | 2018 March 22 | 16 33 50.78 |  $+$48 10 09.78 | 19.04 | 17.86 | 1.18
S3 | 2021 April 09 | 16 33 31.81 |  $+$48 04 31.89 | 19.73 | 18.34 | 1.39
S4 | 2021 April 09 | 16 34 01.24 |  $+$48 08 36.92 | 18.25 | 17.30 | 0.95
The SDSS DR14 catalog (Abolfathi et al., 2018) has been used for getting
optical positions and apparent magnitudes of the sources
and their comparison stars.
∗The USNO-A2.0 catalog (Monet, 1998) has been used in case of non-availability
of the SDSS ‘g-r’ color. The ‘B-R’ color has been
used in such cases.

##  4 STATISTICAL ANALYSIS

To guarantee the reliability of detection for microvariability events, multi-
testing has mostly been used in recent years (e.g., Joshi et al., 2011; Goyal
et al., 2012; de Diego, 2014; Ojha et al., 2021). Therefore, for unambiguous
detection of INOV in a DLC, we have used in the current work two different
versions of $F$-test, which are the standard _$F$ -test_ (hereafter
$F^{\eta}$-test) and the power-enhanced _$F$ -test_ (hereafter
$F_{enh}$-test). However, in the case of $F^{\eta}$-test, it is suggested that
mismatching in the brightness levels among target AGN (in the current work,
NLSy1 galaxy) and the two chosen steady comparison stars should be within
$\sim$ 1-mag in order to avoid photon statistics and other random-noise terms
(e.g., see Howell et al., 1988; Cellone et al., 2007; Goyal et al., 2012).
Therefore, care was taken while selecting two (non-varying) comparison stars
to be within 1-mag of the respective NLSy1s. Thus, for the present set of
jetted-RLNLSy1s, the median magnitude mismatch of _0.82_ between the reference
star (i.e., the comparison star with the closest match with the target AGN’S
instrumental magnitude) and target NLSy1. The corresponding median values for
the non-jetted-RLNLSy1s and the entire set of 23 NLSy1s are _1.28_ and _0.91_
, respectively. Additionally, while implementing the $F^{\eta}$-test, it is
also crucial to use the correct RMS errors on the photometric data points due
to underestimated magnitude errors by a factor ranging between 1.3 and 1.75,
returned by the routines in the data reduction software DAOPHOT and IRAF
(Gopal-Krishna et al., 1995; Garcia et al., 1999; Sagar et al., 2004; Stalin
et al., 2004; Bachev et al., 2005). Therefore, the ‘$\eta$’ value is taken
here to be 1.54$\pm$0.05, computed using the data of 262 intra-night
monitoring sessions of AGNs by Goyal et al. (2013a).

Following Goyal et al. (2012), $F^{\eta}$-statistics defined as

$F_{s1}^{\eta}=\frac{\sigma^{2}_{(q-cs1)}}{\eta^{2}\langle\sigma_{q-cs1}^{2}\rangle},\hskip
5.69046ptF_{s2}^{\eta}=\frac{\sigma^{2}_{(q-cs2)}}{\eta^{2}\langle\sigma_{q-cs2}^{2}\rangle},\hskip
5.69046ptF_{s1-s2}^{\eta}=\frac{\sigma^{2}_{(cs1-cs2)}}{\eta^{2}\langle\sigma_{cs1-cs2}^{2}\rangle}$
(1)

where $\sigma^{2}_{(q-cs1)}$, $\sigma^{2}_{(q-cs2)}$, and
$\sigma^{2}_{(cs1-cs2)}$ are the variances with
$\langle\sigma_{q-cs1}^{2}\rangle=\sum_{i=1}^{N}\sigma^{2}_{i,\leavevmode\nobreak\
err}(q-cs1)/N$, $\langle\sigma_{q-cs2}^{2}\rangle$, and
$\langle\sigma_{cs1-cs2}^{2}\rangle$ being the mean square (formal) rms errors
of the individual data points in the ‘target NLSy1 - comparison star1’,
‘target NLSy1 - comparison star2’, and ‘comparison star1 - comparison star2’
DLCs, respectively.

The $F$-values were computed in this way for individual DLC using Eq. 1, and
compared with the critical $F$-value, set, viz., $F^{(\alpha)}_{\nu}$, where
$\alpha$ is the level of significance set by us for the $F^{\eta}$-test, and
$\nu$ ($=N_{j}-1$) is the degree of freedom for the DLC ($N_{j}$ being the
number of data points in the DLC). The chance of a false INOV detection signal
becomes lower for a smaller value of $\alpha$. Therefore, in the present work,
similar to our previous work, two critical significance levels, $\alpha=$ 0.01
and $\alpha=$ 0.05 are set by us (e.g., see Ojha et al., 2021). Following Ojha
et al. (2021), a NLSy1 is designated as variable for a given session according
to this test if the computed value of $F^{\eta}$ is found to be greater than
its $F_{c}(0.99)$. Table 4 summarizes the computed $F^{\eta}$-values and the
correspondingly inferred status of INOV detection for all the 53 sessions
(columns 6 and 7).

The second flavor of $F$-test for INOV employed in the present study is the
$F_{enh}$-test (e.g., de Diego, 2014). The statistical criteria for the
$F_{enh}$-test can be described as

$\hskip 7.11317ptF_{{\rm enh}}=\frac{s_{{\rm NLSy1}}^{2}}{s_{\rm
comb}^{2}},\hskip 14.22636pts_{\rm
comb}^{2}=\frac{1}{(\sum_{j=1}^{q}N_{j})-q}\sum_{j=1}^{q}\sum_{i=1}^{N_{j}}B_{j,i}^{2}.$
(2)

here $s_{{\rm NLSy1}}^{2}$ is the variance of the ‘target NLSy1-reference
star’ DLC, while $s_{\rm comb}^{2}$ is the combined variance of ‘comparison
star-reference star’ DLC having $N_{j}$ data points and $q$ comparison stars,
computed using scaled square deviation $B_{{\rm j,i}}^{2}$ as

$\hskip 76.82234ptB_{j,i}^{2}=\omega_{j}(c_{j,i}-\bar{c}_{j})^{2}$ (3)

where, $c_{j,i}$’s is the ‘jth comparison star-reference star’ differential
instrumental magnitudes value and $\bar{c_{j}}$ represent the corresponding
average value of the DLC for its $N_{j}$ data points. The scaling factor
$\omega_{j}$ is taken here as described in Ojha et al. (2021).

The principal feature of the $F_{enh}$-test is that it takes into account the
brightness differences of the target AGN and the selected comparison stars, a
frequently encountered problem with the $C$ and $F$-statistics (e.g., see
Joshi et al., 2011; de Diego, 2014). Thus $F_{enh}$-values were computed using
Eq. 2 for individual DLCs and compared with the set critical values for this
study (see above). Based upon this test, a NLSy1 DLC is assigned a designation
“variable (V)” when the computed value of $F_{enh}$ found for ‘target
NLSy1-reference star’ DLC, is greater than its $F_{c}(0.99)$ (i.e., $F_{{\rm
enh}}>F_{c}(0.99)$), and “probable variable (PV)” if same is found to be
greater than $F_{c}(0.95)$ but less or equal to $F_{c}(0.99)$ (i.e.,
$F_{c}(0.95)<F_{\rm enh}\leq F_{c}(0.99)$). In Table 4, we tabulate the
computed $F_{enh}$-values and the correspondingly inferred INOV status for our
entire 53 sessions in columns 8 and 9.

Table 4:  Details of the observations and the status of the INOV for the sample of 23 RLNLSy1 galaxies studied in this work (aperture radius used = 2$\times$FWHM). RLNLSy1s |  Date(s)a |  Tb |  Nc |  Mediand |  $F^{\eta}$-test | INOV |  $F^{\eta}$-test | Variability |  $F_{enh}$-test | INOV | $\sqrt{\langle\sigma^{2}_{i,err}\rangle}$ | $\overline{\psi}^{g}_{s1,s2}$
---|---|---|---|---|---|---|---|---|---|---|---|---
(SDSS name) | yyyy.mm.dd | (hrs) |  | FWHM |  $F_{s1}^{\eta}$,$F_{s2}^{\eta}$ |  statuse |  $F_{s1-s2}^{\eta}$ | status of | $F_{enh}$ |  statusf |  (AGN-s)g | (%)
|  |  |  | (arcsec) |  | 99% | 99% |  s1$-$s2 |  | 99% |  |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | (11) | (12) | (13)
jetted NLSy1s |
J032441.20$+$341045.0 | (2016.11.22) | 4.42 | 56 | 2.32 | 14.34, 16.13 | V, V | 00.82 | NV | 17.39 | V | 0.003 | 5.38
| 2016.11.23 | 4.27 | 54 | 2.13 | 03.77, 02.46 | V, V | 00.70 | NV | 05.42 | V | 0.004 | 2.79
| (2016.12.02) | 4.41 | 44 | 2.60 | 85.80, 88.73 | V, V | 00.87 | NV | 98.29 | V | 0.003 | 11.44
| 2017.01.03 | 3.00 | 39 | 2.47 | 04.53, 08.53 | V, V | 00.34 | NV | 13.27 | V | 0.004 | 3.96
| 2017.01.04 | 3.39 | 33 | 2.45 | 21.60, 23.34 | V, V | 00.44 | NV | 49.35 | V | 0.004 | 7.99
J081432.12$+$560958.7 | (2017.01.03) | 3.37 | 19 | 2.69 | 00.33, 00.34 | NV, NV | 00.16 | NV | 01.34 | NV | 0.022 | –
| (2017.11.20) | 4.52 | 32 | 2.79 | 00.86, 00.55 | NV, NV | 00.55 | NV | 05.28 | NV | 0.031 | –
J084957.98$+$510829.0 | (2017.12.13) | 4.42 | 24 | 2.83 | 00.42, 00.51 | NV, NV | 01.06 | NV | 00.77 | NV | 0.033 | –
| (2019.04.08) | 3.04 | 13 | 2.88 | 00.66, 00.89 | NV, NV | 00.62 | NV | 00.62 | NV | 0.032 | –
J090227.20$+$044309.0 | (2017.02.22) | 3.59 | 27 | 2.38 | 00.71, 00.57 | NV, NV | 00.25 | NV | 02.81 | NV | 0.025 | –
| (2017.12.14) | 5.65 | 39 | 2.51 | 00.33, 00.37 | NV, NV | 00.24 | NV | 01.38 | NV | 0.024 | –
J094857.32$+$002225.6 | (2016.12.02) | 4.15 | 17 | 2.58 | 01.71, 01.88 | NV, NV | 00.16 | NV | 10.52 | V | 0.017 | 7.95
| (2017.12.21) | 5.19 | 33 | 2.24 | 13.95, 16.53 | V , V | 00.55 | NV | 25.26 | V | 0.012 | 16.42
J095317.10$+$283601.5 | (2017.03.04) | 3.97 | 29 | 2.41 | 00.36, 00.35 | NV, NV | 00.48 | NV | 00.76 | NV | 0.035 | –
| (2020.11.21) | 3.25 | 11 | 3.10 | 00.77, 00.68 | NV, NV | 00.33 | NV | 02.31 | NV | 0.035 | –
J104732.78$+$472532.0 | (2017.04.11) | 3.75 | 47 | 0.98 | 00.54, 00.53 | NV, NV | 00.53 | NV | 01.03 | NV | 0.035 | –
| (2018.03.12) | 3.82 | 15 | 2.77 | 00.60, 00.63 | NV, NV | 00.38 | NV | 01.58 | NV | 0.028 | –
J122222.99$+$041315.9 | 2017.01.03 | 3.52 | 17 | 2.38 | 00.62, 00.30 | NV, NV | 00.91 | NV | 00.68 | NV | 0.018 | –
| 2017.01.04 | 3.14 | 16 | 2.36 | 00.32, 00.37 | NV, NV | 00.16 | NV | 01.99 | NV | 0.014 | –
| 2017.02.21 | 4.44 | 41 | 2.65 | 00.74, 00.76 | NV, NV | 00.35 | NV | 02.13 | V | 0.020 | 6.36
| (2017.02.22) | 5.50 | 50 | 2.59 | 03.98, 03.60 | V , V | 00.61 | NV | 06.51 | V | 0.017 | 13.33
| (2017.03.04) | 4.93 | 39 | 2.61 | 00.72, 00.86 | NV, NV | 00.53 | NV | 01.36 | NV | 0.019 | –
| 2017.03.24 | 3.94 | 39 | 2.37 | 00.93, 00.75 | NV, NV | 00.56 | NV | 01.66 | NV | 0.020 | –
J130522.75$+$511640.2 | (2017.04.04) | 3.79 | 23 | 2.57 | 00.70, 00.66 | NV, NV | 00.24 | NV | 02.94 | PV | 0.012 | –
| (2019.04.25) | 3.11 | 22 | 2.77 | 01.56, 01.42 | NV, NV | 00.39 | NV | 04.12 | PV | 0.018 | –
J142114.05$+$282452.8 | (2018.05.10) | 4.06 | 26 | 2.83 | 00.55, 00.56 | NV, NV | 00.35 | NV | 01.60 | NV | 0.019 | –
| (2019.05.27) | 3.31 | 18 | 2.68 | 00.86, 00.86 | NV, NV | 00.36 | NV | 02.47 | PV | 0.021 | –
J144318.56$+$472556.7 | (2018.03.11) | 3.05 | 19 | 3.15 | 00.54, 00.56 | NV, NV | 00.21 | NV | 02.59 | PV | 0.022 | –
| (2018.03.23) | 3.13 | 23 | 2.33 | 00.35, 00.36 | NV, NV | 00.35 | NV | 01.00 | NV | 0.018 | –
J150506.48$+$032630.8 | (2017.03.25) | 5.21 | 41 | 2.08 | 00.60, 00.59 | NV, NV | 00.58 | NV | 01.04 | NV | 0.028 | –
| (2018.04.12) | 3.05 | 19 | 2.55 | 00.67, 00.63 | NV, NV | 00.80 | NV | 00.84 | NV | 0.032 | –
J154817.92$+$351128.0 | (2018.05.17) | 3.00 | 19 | 3.08 | 00.40, 00.38 | NV, NV | 00.38 | NV | 01.05 | NV | 0.008 | –
| (2019.05.08) | 3.24 | 14 | 2.79 | 00.60, 00.65 | NV, NV | 00.30 | NV | 01.98 | NV | 0.017 | –
J164442.53$+$261913.3 | (2017.04.03) | 4.37 | 37 | 2.50 | 01.44, 01.28 | NV, NV | 00.41 | NV | 03.53 | V | 0.011 | 5.41
| (2019.04.26) | 3.22 | 24 | 2.27 | 03.06, 03.74 | V , V | 00.48 | NV | 06.40 | V | 0.011 | 7.50
J170330.38$+$454047.3 | (2017.06.03) | 3.76 | 37 | 2.41 | 00.75, 00.67 | NV, NV | 00.64 | NV | 01.17 | NV | 0.004 | –
| (2019.03.25) | 3.13 | 45 | 4.45 | 00.63, 01.08 | NV, NV | 00.90 | NV | 00.70 | NV | 0.010 | –
non-jetted NLSy1s |
J085001.17$+$462600.5 | (2017.01.04) | 3.26 | 13 | 2.28 | 00.39, 00.50 | NV, NV | 00.50 | NV | 00.78 | NV | 0.026 | –
| (2017.12.15) | 3.69 | 20 | 2.89 | 00.80, 00.74 | NV, NV | 00.36 | NV | 02.22 | NV | 0.032 | –
J103727.45$+$003635.6 | (2018.03.11) | 3.30 | 11 | 3.12 | 01.18, 01.22 | NV, NV | 01.08 | NV | 01.09 | NV | 0.030 | –
| (2021.04.08) | 4.96 | 13 | 2.42 | 01.54, 01.77 | NV, NV | 01.00 | NV | 01.53 | NV | 0.043 | –
J111005.03$+$365336.2 | (2018.03.23) | 3.22 | 44 | 0.90 | 00.34, 00.35 | NV, NV | 00.47 | NV | 00.72 | NV | 0.027 | –
| (2019.01.13) | 3.13 | 11 | 3.07 | 02.61, 02.54 | NV, NV | 01.18 | NV | 02.11 | NV | 0.042 | –
J113824.53$+$365327.2 | (2017.04.17) | 4.32 | 20 | 2.11 | 00.32, 00.40 | NV, NV | 00.21 | NV | 01.58 | NV | 0.028 | –
| (2018.03.23) | 4.31 | 21 | 2.53 | 00.36, 00.38 | NV, NV | 00.16 | NV | 02.26 | NV | 0.029 | –
J120014.08$-$004638.7 | (2018.03.12) | 3.83 | 28 | 2.72 | 00.31, 00.22 | NV, NV | 00.19 | NV | 01.63 | NV | 0.011 | –
| (2018.05.11) | 3.13 | 16 | 2.97 | 00.13, 00.25 | NV, NV | 00.33 | NV | 00.39 | NV | 0.018 | –
J124634.65$+$023809.1 | (2017.04.03) | 3.77 | 18 | 2.50 | 00.21, 00.36 | NV, NV | 00.46 | NV | 00.46 | NV | 0.024 | –
| (2018.04.12) | 3.72 | 21 | 2.71 | 00.59, 00.66 | NV, NV | 00.31 | NV | 01.89 | NV | 0.018 | –
J163323.59$+$471859.0 | (2017.05.20) | 4.33 | 36 | 2.26 | 00.85, 00.76 | NV, NV | 00.23 | NV | 03.76 | V | 0.007 | 2.56
| (2019.03.20) | 3.69 | 33 | 2.66 | 01.61, 01.79 | NV, NV | 00.36 | NV | 04.43 | V | 0.016 | 9.52
J163401.94$+$480940.2 | (2018.03.23) | 3.04 | 34 | 0.98 | 00.62, 00.71 | NV, NV | 00.39 | NV | 01.61 | NV | 0.012 | –
| (2021.04.09) | 4.58 | 12 | 2.12 | 01.27, 01.63 | NV, NV | 00.34 | NV | 03.76 | PV | 0.043 | –
aDate(s) of the monitoring session(s). The dates given inside parentheses refer to the sessions we have used here for estimating the INOV duty cycle |
(e.g., see text in Sect. 4.1). bDuration of the monitoring session in the observed frame. cNumber of data points in the DLCs of the monitoring session. |
dMedian seeing (FWHM in arcsec) for the session. ${}^{e,\leavevmode\nobreak\ f}$INOV status inferred from Fη and Fenh tests, with V = variable , i.e. confidence level $\geq$ 99%; |
PV = probable variable, i.e. $95-99$% confidence level; NV = non-variable, i.e. confidence level $<$ 95%. |
gMean amplitude of variability in the two DLCs of the target NLSy1 (i.e., relative to the two chosen comparison stars). |
Table 5: The DC and $\overline{\psi}$ of INOV, for the sample of 23 RLNLSy1 galaxies studied in this work, based on the $F_{enh}$-test and $F^{\eta}$-test. RLNLSy1s | No. of Sources |  $F_{enh}$-test |  $F^{\eta}$-test | Median black hole mass
---|---|---|---|---
|  |  ⋆DC | ${}^{\star}\overline{\psi}^{{\dagger}}$ |  ⋆DC | ${}^{\star}\overline{\psi}^{{\dagger}}$ |  log ($M_{BH}/M_{\sun}$) |
|  | (%) | (%) | (%) | (%) |  |
jetted-RLNLSy1s | 15 |  18 (30)⊥ |  09 (07)⊥ |  12 (30)⊥ |  11 (05)⊥ | 7.72 |
non-jetted-RLNLSy1s | 8 |  05 (16)⊥ |  09 (01)⊥ |  00 (16)⊥ | – | 7.42 |
J-$\gamma$-RLNLSy1s | 8 |  34 (16)⊥ |  10 (07)⊥ |  29 (16)⊥ |  11 (05)⊥ | 7.59 |
J-RLNLSy1s | 7 |  00 (14)⊥ | – |  00 (14)⊥ | – | 7.73 |
⋆We used the 46 sessions for this estimation, as explained in Sect. 4.1. †The mean value for all the DLCs belonging to the type ‘V’. |
⊥Values inside parentheses are the number of observing sessions used to estimate the parameters DC or $\overline{\psi}$. |

###  4.1 Computation of INOV duty cycle and amplitude of variability

To compute the duty cycle (DC) of INOV for the present sets of RLNLSy1s, we
have adopted, following the definition given by Romero et al. (1999) (see,
also Stalin et al., 2004)

$\hskip 71.13188ptDC=100\frac{\sum_{j=1}^{n}R_{j}(1/\Delta
t_{j})}{\sum_{j=1}^{n}(1/\Delta t_{j})}\hskip 2.84544pt{\rm
per\leavevmode\nobreak\ cent}$ (4)

where $\Delta t_{j}=\Delta t_{j,\leavevmode\nobreak\ observed}(1+$z$)^{-1}$
($z$ being the redshift of the target NLSy1 galaxy in current study) is the
target AGN’s redshift corrected time duration of the $j^{th}$ monitoring
session (see details in Ojha et al., 2020a). For $j^{th}$ session, $R_{j}$ is
considered to be 1 in Eq. 4 only when INOV is detected, otherwise taken to be
zero. Note that to avoid introducing bias, we have used only 2 sessions for
each AGN. For sources observed in more than 2 sessions (e.g., see Table 4),
the computation of DC used only the longest two sessions, as pointed out in
Ojha et al. (2020a); Ojha et al. (2021). The computed INOV duty cycles (DCs)
for the different sets of RLNLSy1s are listed in Table 5, based on two
statistical tests .

To compute the peak-to-peak amplitude of INOV ($\psi$) detected in a given
DLC, we followed the definition given by Heidt & Wagner (1996)

$\hskip 71.13188pt\psi=\sqrt{({H_{max}}-{H_{min}})^{2}-2\sigma^{2}}$ (5)

with $H_{min,\leavevmode\nobreak\ max}$ = minimum (maximum) values in the DLC
of target NLSy1 relative to steady comparison stars and
$\sigma^{2}=\eta^{2}\langle\sigma^{2}_{NLSy1-s}\rangle$, where,
$\langle\sigma^{2}_{NLSy1-s}\rangle$ is the mean square (formal) rms errors of
individual data points. The mean value of ($\overline{\psi}$) for different
sets (e.g., see Table 5) of RLNLSy1 galaxies is computed by taking average of
the computed $\psi$ values for the DLCs belonging to the “V” category. In
Table 5, we have summarized the computed $\overline{\psi}$ values based on the
two statistical tests for the different sets of RLNLSy1s in our sample.

##  5 Results and discussion

The INOV characterization of RLNLSy1 galaxies presented here is likely to be
more representative in comparison to the previous studies based on
significantly smaller samples (Liu et al., 2010; Paliya et al., 2013a; Kshama
et al., 2017). Also, we have paid particular attention to guarding against the
possibility of spurious INOV claims arising from a varying flux contribution
to the aperture photometry from the host galaxy of the AGN caused due to
seeing disc variation during the session. As pointed out by Cellone et al.
(2000), under such circumstances, false claims of INOV can result in $low-z$
AGNs. Based on recent deep imaging studies of NLSy1 galaxies by Olguín-
Iglesias et al. (2020), it can be inferred that any variable contamination
arising from the host galaxy is very unlikely to matter when studying the
variability of AGNs at least at z $>$ 0.5. From Table 4, it is seen that the
INOV detection ($\psi>3$% ) has occurred for just 3 sources in our sample
having z $<$ 0.5. These are: J032441.20$+$341045.0 (at $z=0.06$; 4 sessions),
J164442.53$+$261913.3 (at $z=0.14$; two sessions), and J163323.59$+$471859.0
($z=0.12$, one session). However, since the seeing disk remained steady in all
these sessions (Fig. 1), except for the flickering in the PSF for the 3-4
points only in the case of J164442.53$+$261913.3 for its first session (Fig.
4) and a non-negligible systematic PSF variation in the case of
J163323.59$+$471859.0 (Fig. 6). A closer checkup of these two intranight
sessions shows that either PSF remained fairly steady during the time of AGN’s
flux variations (Fig. 4) or the gradients in the DLCs of the target AGN are
seen to be anticorrelated with systematic variations in the PSF (Fig. 6). This
is opposite to what is expected in case the aperture photometric measurements
were significantly contaminated by the underlying galaxy (see Cellone et al.,
2000). Therefore, the possibility of a significant variation in the fractional
contribution from the host galaxy can be safely discounted. We thus conclude
that the present cases of INOV detection for $low-z$ RLNLSy1s are genuine and
not artifacts of seeing disk variation through the monitoring sessions.

From Table 5, it is seen that the $F_{enh}$-test resulted in the DCs of 18%
and 5% for the jetted and non-jetted-RLNLSy1s sets; however, the DCs of 12%
and 0% are estimated based on the conservative $F^{\eta}$-test for the same
sets. Thus, regardless of which of the two statistical tests is applied, the
INOV DCs for the jetted sample is higher than the non-jetted sample. Since we
are using only two steady comparison stars in this study, therefore power-
enhanced F-test becomes similar to that of the scaled F-test. However, it has
been suggested in Goyal et al. (2013b) that in such a condition power-enhanced
F-test does not follow the standard F-distribution. Therefore, for further
discussion and conclusion, we will be using our results based upon
$F^{\eta}$-test. Additionally, in the case of powerful quasars/blazars, such
DCs characterize non-blazars, including weakly polarised flat-radio-spectrum
(i.e., radio-beamed) quasars (Goyal et al., 2013b; Gopal-Krishna & Wiita,
2018). It is further seen from Table 5 that a higher DC ( $\sim$30%, i.e.,
approaching blazar-like values, e.g., see Goyal et al., 2013b) is only
exhibited by the $\gamma$-ray detected subset, which consists of 8 RLNLSy1s,
all of which belong to the jetted category. This independently reinforces the
premise that $\gamma$-ray detected NLSy1 galaxies emit blazar-like compact
radio jets, which are likely conspicuous due to relativistic beaming. The
absence of $\gamma$-ray detection among the non-jetted RLNLSy1s is interesting
because it suggests the non-detection of jets in these sources. It is probably
related to relativistic dimming (due to misalignment) rather than due to the
jets being beamed but still too small physically to be resolved by VLBA. This
inference is based on the currently popular notion that $\gamma$-rays in AGN
primarily arise from the vicinity of the central engine, i.e., the base of the
jets (e.g., see Neronov et al., 2015). It would then appear that the radio
jets in the non-jetted RLNLSy1s either are not strongly beamed or weak. In
this context, we also note from Table 5, that the DC of 8 J-$\gamma$-RLNLSy1s
is 29% while none of the sources in the sample of 7 J-RLNLSy1s has shown INOV.
As also noted in Sect. 2 that the VLBA detected jets might not be
relativistically beamed, which may result in the non-detection of INOV in
these sources. The higher INOV DC in 8 J-$\gamma$-RLNLSy1s may be related to
the relativistic beaming of jets in these sources, and the mere presence of
jets does not guarantee an INOV detection in NLSy1 galaxies. For instance,
J032441.20$+$341045.0 has lowest polarization value (e.g., see Table 1) and
radio loudness value (e.g., see Zhou et al., 2007) among 8 J-$\gamma$-RLNLSy1s
but shows strong INOV activity which perhaps could be due to very high jets
speed (e.g., see Table 1). This supports our above argument that relativistic
beaming plays a significant role for INOV in the case of gamma-ray detected
radio-loud NLSy1s.

From Table 5, the DC estimates, based upon $F^{\eta}$-test for the samples of
jetted and non-jetted RLNLSy1s, have contrasting differences. Thus, our
results suggest that the jetted-RLNLSy1s sample shows higher DC in comparison
to the non-jetted-RLNLSy1s. However, as noted above that, instead of the mere
presence of a jet, relativistic beaming seems to play a dominant role for INOV
in the case of low-luminous high accreting AGNs such as NLSy1 galaxies. As has
been emphasized in Sect. 1 that the central engine of NLSy1s operates in a
regime of a higher accretion rate, and contributions from their host galaxies
are prominent in the case of lower redshift sources (see Sect. 3.2). However,
our method of analysis for INOV detections is very unlikely to be affected by
the host galaxy’s contributions (hence spurious INOV detection) from the
present sources, but due to higher accretion rates of NLSy1s, a relative
enhancement in the AGN’s optical emission (i.e., thermal component) as
compared to its synchrotron emission is expected (e.g., see Zhou et al., 2007;
Paliya et al., 2014). Since AGN’s optical emission is likely to be less
amenable to being variable in comparison to synchrotron emission, resulting
from the Doppler boosted synchrotron jet; therefore the amplitude of INOV is
expected to be suppressed by this thermal contamination. Thus, the DC of the
jetted and non-jetted RLNLSy1s samples would be more robust once it becomes
possible to subtract out thermal contamination originating in NLSy1s from the
disc due to their higher Eddington accretion rates. Furthermore, a relatively
lower DC of the sample of jetted-RLNLSy1s might be either due to the sub-
luminal speed of jets (e.g., see Ojha et al., 2019) or due to their primarily
misaligned relativistic jets towards the observer line of site (Berton et al.,
2018). Therefore, we categorized our sample of jetted-RLNLSy1s into the
subsamples of J-$\gamma$-RLNLSy1s (8 sources) and J-RLNLSy1s (7 sources) based
on their detections in $\gamma$-ray by Fermi-LAT, where detection of
$\gamma$-ray emission supports the scenario of presence of Doppler boosted
relativistic jets (Abdo et al., 2009a, b, c; Foschini et al., 2010; Foschini,
2011; D’Ammando et al., 2012; D’Ammando et al., 2015; Yao et al., 2015; Paliya
et al., 2018; Yang et al., 2018; Yao et al., 2019). It can be seen in Table 5
that we found a lack of INOV detection based upon the $F^{\eta}$-test in the
J-RLNLSy1s subsample in contrast to the DC of $\sim$ 29% for
J-$\gamma$-RLNLSy1s subsample, consistent with the result of Ojha et al.
(2019), where based upon a small sample of three NLSy1s, it was found out that
superluminal motion in the radio jet could be a robust diagnostic of INOV.

To further confirm the above scenario, we compiled the apparent jet speed of
our J-$\gamma$-RLNLSy1s from the literature. We found that out of 8 members of
J-$\gamma$-RLNLSy1s, six members have available apparent jet speeds. These six
J-$\gamma$-RLNLSy1s are: J032441.20$+$341045.0, J084957.98$+$510829.0,
J094857.32$+$002225.6, J150506.48$+$032630.8, with $v_{app}/c$ of $9.1\pm
0.3$, $6.6\pm 0.6$, $9.7\pm 1.1$, $0.1\pm 0.2$, respectively (e.g., see Lister
et al., 2019), and J122222.99$+$041315.9, J164442.53$+$261913.3, with
$v_{app}/c$ of $0.9\pm 0.3$, $>$1.0, respectively (Lister et al., 2016, e.g.,
see, Doi et al., 2012, and). Thus with the current INOV study and available
jet speed of J-$\gamma$-RLNLSy1s, a correlated INOV detection with the
superluminal motion in the radio jet is inferred, except for
J084957.98$+$510829.0. Although, unfortunately, we could not find any INOV in
both $>$ 3 hrs long monitoring sessions of the source, J084957.98$+$510829.0
in the present study, this source has shown in the past a fading by $\sim$ 0.2
mags in its INOV study within just $\sim$ 15 minutes during its high
$\gamma$-ray active phase (see figure 6 of Maune et al., 2014). Other than
this instance, this source previously had also shown significant INOV in all
its six intra-night sessions (e.g., see Paliya et al., 2016). Therefore, the
non-detection of INOV in our current study may be due to currently undergoing
the quiescent $\gamma$-ray phase of this source. Nonetheless, the above
correlation could be firmly established once a more comprehensive INOV
database and apparent jet speeds of J-$\gamma$-RLNLSy1s become available.

On the other hand, in the case of RLNLSy1s (with $R>100$), where most of the
electromagnetic emission (radio, optical, X-ray, and $\gamma$-ray) supposedly
comes from their jets, it is suggested that more massive black holes are more
amenable to launch powerful relativistic jets (Urry et al., 2000; Hyvönen et
al., 2007; Chiaberge & Marconi, 2011; Olguín-Iglesias et al., 2016).
Therefore, we compared the median black hole masses of jetted-RLNLSy1s and
non-jetted-RLNLSy1s samples, derived based upon single-epoch optical
spectroscopy virial method (e.g., see second last column of Table 1). This has
resulted in a nominal difference with the median values of log
($M_{BH}$/$M_{\sun}$) of _7.72_ and _7.42_ for the jetted-RLNLSy1s and non-
jetted-RLNLSy1s samples (see last column of Table 5), respectively. A
contrasting difference has not been found between the black hole masses of the
two sets, which may be either due to smaller sample sizes or due to the use of
the single-epoch optical spectroscopy virial method, which is suggested to
have a systematic underestimation while estimating black hole masses (Decarli
et al., 2008; Marconi et al., 2008; Calderone et al., 2013; Viswanath et al.,
2019; Ojha et al., 2020b). Therefore, to firmly establish the above scenario,
estimation of black hole masses of a large sample of jetted and non-jetted
RLNLSy1s is needed with the method that is less likely to be affected by
underestimation of black hole masses such as the standard Shakura-Sunyaev
accretion-disc model method (Calderone et al., 2013; Viswanath et al., 2019).

##  6 Conclusions

To quantify the role of the absence/presence of radio jets for INOV in the
case of RLNLSy1s, we have carried out a systematic INOV study based on an
unbiased sample of 23 RLNLSy1s. Among them, 15 RLNLSy1s have confirmed
detection of jets (jetted), and the remaining 8 RLNLSy1s have no detection of
jets (non-jetted) with the VLBA observations. Our study spans 53 sessions of a
minimum 3-hour duration each. The main conclusions from this work are as
follows:

  1. 1.

We estimated the INOV DC based upon $F^{\eta}$-test for the sample of jetted
RLNLSy1s to be 12%, however, none of the sources showed INOV in the sample of
non-jetted RLNLSy1s, at the 99% confidence level for a typical threshold
$\psi>3$%.

  2. 2.

Among the jetted RLNLSy1s, the DC for jetted $\gamma$-ray detected RLNLSy1s is
found to be 29% in contrast to null INOV detection in the case of
non-$\gamma$-ray detected RLNLSy1s. It suggests that the INOV detection in
RLNLSy1 galaxies does not solely depend on the presence of radio jets, but
relativistic beaming plays a dominant role.

  3. 3.

The predominance of beamed jet for INOV is also supported in our study based
on the correlation of the INOV detection with the apparent jet-speed available
for 6 jetted $\gamma$-ray detected RLNLSy1s.

  4. 4.

The higher DC of $\sim$ 30%, approaching blazar-like DC, is only exhibited by
the $\gamma$-ray detected subset, suggests that $\gamma$-ray detected NLSy1
galaxies emit blazar-like compact radio jets in which relativistic jet motion
(speed) and/or small jet’s angles to the observer’s line of sight seems to be
correlated with the presence of INOV.

For further improvement, it will be helpful to enlarge the sample and conduct
similar systematic INOV studies for other subclasses of AGN with and without a
confirmed jet, along with the proper estimate of apparent jet speeds.

## Acknowledgements

We are thankful to the anonymous referee for providing comments and
suggestions, which helped us improve the manuscript considerably. This
research is part of the DST-SERB project under grant no. EMR/2016/001723. VKJ
and HC acknowledge the financial support provided by DST-SERB for this work.
We are very grateful to Prof. Gopal-Krishna for his helpful scientific
discussions and important suggestions for this work. We thank the concerned
ARIES and IIA staff for assistance during the observations obtained at the
3.6-m Devasthal Optical Telescope (DOT) and the 2.01-m Himalayan Chandra
Telescope (HCT), which are the national facilities run and managed by ARIES
and IIA, respectively, as autonomous Institutes under Department of Science
and Technology, Government of India.

## Data availability

The data from the ARIES telescopes and the 2.01-m HCT telescope of IIA used in
this paper will be shared on reasonable request to the corresponding author.

Figure 1:  The differential light curves (DLC) for the first 3 jetted-RLNLSy1s
from our sample of 15 jetted-RLNLSy1s are shown here. The name of the RLNLSy1
galaxy, the redshift (z), the name of the telescope used, and the duration of
the observations are shown on the top of each panel. The light curves
generated from the data obtained on the dates given inside parentheses at the
top of each panel were used for the statistical analysis. In each panel, the
DLC on the top is the instrumental magnitude difference between two non-
variable comparison stars, the two DLC in the middle are prepared using the
NLSy1 and the two comparison stars, respectively, while the bottom DLC shows
the variation of the seeing conditions (FWHM in arcseconds) during the
monitoring session. Figure 2: (Continued) DLC for the subsequent 5 jetted-
RLNLSy1s from the current sample of 15 jetted-RLNLSy1s. Figure 3: (Continued)
DLC for another 2 jetted-RLNLSy1s from the current sample of 15 jetted-
RLNLSy1s. Figure 4:  (Continued) DLC for the final 5 jetted-RLNLSy1s from the
current sample of 15 jetted-RLNLSy1s. Figure 5: Similar to Fig. 1, but for the
first 4 non-jetted-RLNLSy1s from our sample of 8 non-jetted-RLNLSy1s. Figure
6: (Continued) DLC for the last 4 non-jetted-RLNLSy1s from our sample of 8
non-jetted-RLNLSy1s.

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