Probing star formation in five of the most massive spiral galaxies observed through ASTROSAT UltraViolet Imaging Telescope

We present highly resolved and sensitive imaging of the five nearby massive spiral galaxies (with rotation velocities > 300kms − 1 ) observed by the UltraViolet Imaging Telescope onboard India’s multi-wavelength astronomy satellite ASTROSAT, along with other archival observations. These massive spirals show a far-ultraviolet star formation rate in the range of ∼ 1 . 4 − 13 . 7M ⊙ yr − 1 and fall in the ‘Green Valley’ region with a specific star formation rate within ∼ 10 − 11 . 5 − 10 − 10 . 5 yr − 1 . Moreover, the mean star formation rate density of the highly resolved star-forming clumps of these objects are in the range 0 . 011 − 0 . 098M ⊙ yr − 1 kpc − 2 , signifying localised star formation. From the spectral energy distributions, under the assumption of a delayed star formation model, we show that the star formation of these objects had peaked in the period of ∼ 0 . 8 − 2 . 8 Gyr after the ‘Big Bang’ and the object that has experienced the peak sooner after the ‘Big Bang’ show relatively less star-forming activity at z ∼ 0 and falls below the main-sequence relation for a stellar content of > ∼ 10 11 M ⊙ . We also show that these objects accumulated much of their stellar mass in the early period of evolution with ∼ 31 − 42 per cent of the total stellar mass obtained in a time of ( 1 / 16 )−( 1 / 5 ) th the age of the Universe. We estimate that these massive objects convert their halo baryons into stars with efficiencies falling between ∼ 7 − 31 percent.


INTRODUCTION
Significant progress over the past few decades has been made in the understanding of the formation of galaxies and their evolution with time.However, a fully developed theory of galaxy formation remains one of the significant frontier problems of astrophysics (see Gott 1977;Brodie & Strader 2006;Somerville & Davé 2015;Naab & Ostriker 2017;Robertson 2022 for a review of galaxy formation theories, also see White & Rees 1978;White & Frenk 1991;Fukugita & Peebles 2006;Sommer-Larsen 2006;Cole et al. 2000 for some leading works on galaxy formation).Moreover, explaining galaxy formation and evolution across cosmic time involves understanding processes across many branches of physics, starting from cosmology to plasma physics, which necessarily span a vast range of lengths and timescales.The current galaxy formation scenario is discussed under the hierarchical structure formation model of lambda cold dark matter cosmology ΛCDM (see Benson 2010 for a review).Specifically, it is still uncertain how and when the rare, incredibly massive, rotationally supported spiral galaxies observed in the local Universe, with stellar masses > 10 11 M ⊙ and viral masses > 10 13 M ⊙ , have formed, as it depends on poorly understood non-linear baryonic physics and complex interaction with the dark matter halos.However, based on cosmological simulations, Oser et al. (2010) propose a 'two-phase' evolution of galaxies consisting of a rapid early phase in z > ∼ 2 followed by an extended phase of evolution for z < ∼ 3.They suggest that progenitor of massive galaxies grew considerably in the extended phase by accreting and merging with smaller satellite galaxies formed even before z ∼ 3 around the gravitational well of the central galaxy (see Lackner et al. 2012;Rodriguez-Gomez et al. 2016 also).They also emphasise that the massive galaxies have a considerably higher population of older stars, which is a result of merging with systems that already had 'in situ' star formation before z ∼ 2 and they grew in physical dimension according to hierarchical clustering as proposed by ΛCDM cosmology.Dekel et al. (2009) provide a theoretical background of the formation of massive galaxies at high red-shift, where the interplay between smooth, clumpy cold streams, instability in the disc and bulge formation govern the growth and evolution of the early phase of the galaxies.
Recent observations have found the existence of massive galaxies at the early Universe.For instance, Labbe et al. (2022) reported the finding of six massive galaxies with stellar mass > ∼ 10 10 M ⊙ at redshift 7.4 ≤ z ≤ 9.1, Huang et al. (2023) reported the existence of Ultra Luminous Infrared Galaxies (ULIRG) with infrared luminosity L IR > 10 12.5 L ⊙ and stellar masses ∼ 10 11 M ⊙ at red-shift z ∼ 2, Cheng et al. (2023) found 16 galaxies with stellar mass > 10 10.5 M ⊙ at red-shift 1 < z < 4.5.All these findings indicate that some of these objects had experienced a period of intense star formation and stellar mass growth in a very short period of time in the early Universe.However, the general trend for galaxies, verified by observations, has been that the star formation rate reached its peak at the 'cosmic high noon' or 'cosmic noon' near redshift z ≈ 1 − 2 when galaxies were rapidly building up their stellar masses by converting cosmic baryons to stars, and subsequently, over the next few billions of years the star formation went down drastically (Madau & Dickinson 2014).
Eventually, by the present era, most of the massive galaxies are supposed to have stopped growing (Brinchmann et al. 2004;Renzini & Peng 2015), having reached a state of apparent quiescence (Behroozi et al. 2010(Behroozi et al. , 2019;;Moster et al. 2013).And, for reasons still unknown, in our local universe, some low-mass galaxies are still actively forming stars, while the majority of massive galaxies with halo masses M halo > ∼ 10 12 M ⊙ display a strikingly low specific star formation rate sSFR (where sSFR = SFR/stellar mass; SFR being the star formation rate) compared to less massive galaxies (see Alexander & Hickox (2012) and Wechsler & Tinker (2018) for reviews).One such extremely massive, low star formation rate, 'red and dead' spiral galaxy UGC 12591, was reported in Ray et al. (2022).
The suppression of star formation in these galaxies could be due to multiple factors contributing together and/or functional over different timescales of galaxies' evolution.Further, different quenching mechanisms may dominate at different mass ranges of galaxies (Kaviraj et al. 2007;Cicone et al. 2014;Förster Schreiber et al. 2014;Dhiwar et al. 2023).For massive galaxies with halo mass > ∼ 10 12 M ⊙ , the halo gas gets shocked heated (Rees & Ostriker 1977) while collapsing onto the dark matter halo, which can delay the star-forming activity in the host galaxy's disc (Birnboim & Dekel 2003).For massive galaxies at high red-shift z ∼ 2, Feldmann & Mayer (2015) show that the suppression of star formation happens due to reduced accretion of gas from the intergalactic medium to the galactic dark matter halo, termed as 'Cosmological Starvation' and suggest the presence of additional mechanism such as radio-mode feedback to maintain the quenched state up to the present times (Bower et al. 2006;Croton et al. 2006).Park et al. (2023) found that the massive galaxies at the 'cosmic noon' are formed from a major starburst and are rapidly quenched by AGN feedback.While, from the morphological analysis of the star-forming regions of galaxies with stellar masses > 10 11.3 M ⊙ , Xu et al. (2020) conclude that one-fifth of the massive galaxies are still forming stars, and overwhelmingly most of them have gone through recent mergers.
Moreover, massive galaxies with rotational velocities v rot > ∼ 300kms −1 tend to deviate from the baryonic Tully-Fisher relation, a tight scaling relation between the baryonic mass content and flat rotational velocity of a galaxy (McGaugh 2005), as shown in Ogle et al. (2019b); Dai et al. (2012); Ray et al. (2022).For example, the massive spirals like NGC 1961 and NGC 6753 (stellar mass > ∼ 10 11 M ⊙ ) with moderate star formation of ∼ 15.5M ⊙ yr −1 and ∼ 11.8M ⊙ yr −1 respectively are reported to contain ∼ 30 − 50 per cent fewer baryons in their halos than what is expected from the cosmic baryon fraction (Bogdán et al. 2013a).Similarly, another massive disc galaxy UGC 12591 contains ∼ 85 per cent fewer baryons than that expected from the cosmic mean having a star formation rate of ∼ 0.638M ⊙ yr −1 (Ray et al. 2022).This deficiency in baryons in these galaxies also contributes to their deviations from the baryonic Tully-Fisher relation (Ray et al. 2022), emphasising their inability to condense halo baryons into stars.So, knowing the different assembly histories of such galaxies is extremely important, and to be able to constrain the star formation over the period, starting from the early Universe, of such galaxies would give us a significant understanding of their evolution.
In this paper, we report the ultraviolet observations of five of the most massive spiral galaxies known, in combination with data at other wavelengths, to address some of the most critical questions in this field, like how the cooling of the circum-galactic gas effect star formation in such galaxies, how star formation is fuelled or quenched, and what are the dominant feedback mechanisms for quenching the star formation.These galaxies are extremely massive with stellar masses > 10 11 M ⊙ and they also are fast rotators with rotational velocities > 300km s −1 .Here, we investigate the star formation history, nature of the star-forming regions, signatures and possible AGN/radiative feedback effects on the star formation, etc, accounting for the total baryon budget in these massive, fast-rotating spiral galaxies in the local Universe.
The structure of this paper is as follows: In §2, we describe the observations and data.The data reduction strategy for the UVIT observations, along with the hierarchical structuring of star-forming regions and Spectral Energy Distribution (SED) fitting processes taking FUV to FIR observations of the objects into account, are described in §3.In §4, we present our discussion, and the study's conclusions are outlined in §5.Note that, in our discussion, we explore our objects through the parameters found from direct observations, scaling relations and also from fitting appropriate models to observable data.In our calculations we use the following cosmological parameters; H 0 = 69.6 km s −1 Mpc −1 , Ω M = 0.286 and Ω vac = 0.714.

Sample selection
Massive galaxies with high rotational velocities (⪆ 300 km s −1 ) have been under study for their departures from the long-established baryonic Tully-Fisher relation.In order to investigate their baryon-to-star conversion, we have observed five such extremely massive galaxies in UVIT (Table .1) as a pilot sample with outer Keplerian disc rotation velocities v rot > 300 km s −1 (Saglia & Sancisi (1988); Rubin et al. (1979); Corradi & Capaccioli (1991); Garrido et al. (2005), Table 2) for this study.These galaxies have K-band stellar masses > 10 11 M ⊙ and virial masses > 10 13 M ⊙ (see Table 2, Section 4.3 and Section 4.5).Previously, we published a detailed analysis of one such massive galaxy, UGC 12591 (Ray et al. 2022), which has v rot ≈ 500 km s −1 .The target galaxies are late-type spirals in the morphological sequence characterised in HyperLeda (Makarov et al. 2014).To see their morphological appearances and other hidden features, we have made color images of these target galaxies in the optical band, which are shown in Fig. 1.These images are made using archival data of z, r and g bands from the Dark Energy Camera Legacy Survey (DECaLS), Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) and Sloan Digital Sky Survey (SDSS).From Fig. 1, it is evident that the object NGC 266 has the face-on view with an inclination angle (the angle between the line of sight and the polar axis of the galaxy) of ∼ 16 degree, and the other objects are almost edge-on with inclination angles of ∼ 47, 63, 68 and 73 degrees for NGC 1961, NGC 4501, NGC 1030 and NGC 5635 respectively.Note that the inclination angles for our objects have opted from HyperLeda, where the apparent flattening (r 25 ) and morphological type (t) of a galaxy are used to find out the inclination (i) from the following relation, where log(r 0 ) = 0.43+0.053tfor t = [−5, 7] and log(r 0 ) = 0.38 for t > 7 (see HyperLeda for more details; Makarov et al. 2014).The dust lanes are clearly visible in NGC 1030 due to its edge on view.It has a rectangular shape with growing asymmetries visible at the edges (Lütticke et al. 2004).NGC 1961 is classified as an intermediate spiral galaxy, objects falling between barred and unbarred spiral galaxies in the morphological classification, with a bar not well defined, which is evident from the optical color image.The highly asymmetric spiral arms of this object are signatures of possible strong recent interaction(s) (Gottesman et al. 1983), specifically due to the stripping of gas from the gravitational potential of the galaxy by ∼ 10 7 K hot intergalactic medium as proposed by Shostak et al. (1982).Any asymmetry in NGC 4501 is not very dominant in the optical image.However, we can see the bright spiral arms embedded into dusty regions throughout the galaxy.However, Vollmer et al. (2008) show the existence of early-stage ram-pressure stripping in the galaxy.A clear asymmetry can be seen in the light distribution for the object NGC 5635, indicating possible recent interaction also shown by Saglia & Sancisi (1988)  We have FUV F154W (∼ 0.1541m) observations for all five spirals and NUV N242W (∼ 0.2420m) observations for the objects NGC 5635 and NGC 266.
In FUV band, the integration times of the objects are T int ∼ 1.9, 1.9, 1.6, 8.1 and 7.4 ks for NGC 1030, NGC 1961, NGC 4501, NGC 5635 and NGC 266 respectively.In NUV band, T int ∼ 8.2, 7.5 ks for NGC 5635 and NGC 266 respectively.Note that, the scale shown in the lower-right of each image is 50 arcsec.
galaxy NGC 266, which is part of a group consisting of six low mass galaxies (Bogdán et al. 2013a), is also found to be interacting with a Seyfert II galaxy Mrk 348 (Hibbard et al. 2001).
In Table 2, we show some important parameters for our sample galaxies.Some are obtained from the literature, shown in the upper panel of the table and these are coordinates of the objects (R.A, Dec.), morphological classification T, redshift z, flat rotational velocity v rot (km s −1 ), central velocity dispersion  (km s −1 ) and activity class  of the active galactic nuclei (AGN) of the objects.In the lower panel, we show a list of parameters derived in this work directly from observations or indirectly using scaling relations.The FUV and NUV magnitudes (m FUV and m NUV ) of the objects are estimated using UVIT data within the apertures estimated following the process described in Section 3.2.The FUV star formation rates SFR FUV are estimated using the corresponding FUV magnitudes/luminosities and the relation provided by Kennicutt (1998) for Salpeter initial mass function (IMF) (Salpeter 1955) (see Section 3.3).The star formation rates corrected for internal dust attenuation of the galaxies are denoted by SFR corr FUV and are estimated considering the total infrared radiations into account following the process described in Section 4.1.The K-band mass to light ratios Υ * K of the objects are calculated using specific colors (Section 4.3) and the scaling relations provided by Bell et al. (2003), and we have used them to calculate the K-band stellar masses M K of our objects from 2MASS K-band luminosities.The specific star formation rates sSFR corr FUV are calculated from the dust-corrected star formation rates and the K-band stellar masses as SFR corr FUV /M K .The neutral hydrogen masses M HI are calculated from 21cm integrated line flux following the relation provided in Section 4.3.On the other hand, the molecular hydrogen masses M H2 are found out using the estimated neutral hydrogen mass multiplied by scale factors provided by Young & Knezek (1989).The black hole masses M bh are calculated indirectly from the central velocity dispersions  or the stellar masses of the objects (see Section 4.4 for the relations used and the references).The halo masses M halo are estimated under the assumption of flat circular velocity upto the virial radius within which the mean density is 200 times that of the critical density of the universe at that redshift (more on this in Section 4.5).T vir denotes the temperature of the gas in the hot halo of the galaxies, which is considered to be a virialized system, calculated using the rotational velocity (see Section 4.3).

Observations
The data were taken by ASTROSAT UVIT under the proposals 04_167 and 05_225 (Principal Investigator Joydeep Bagchi).The objects are observed in the photon counting mode, and the details of the observations are tabulated in Table 1.The observations were carried out to study the young star formation in our objects.UVIT is a versatile instrument designed to see the sky in FUV (130 ⪅  ⪅ 180 nm), NUV (200 ⪅  ⪅ 300 nm) and in the Visible band (VIS) (320 ⪅  ⪅ 550 nm).UVIT is capable of making images simultaneously in a field of view of ∼ 28 arcmins with a resolution of < 1.8 arcsec FWHM.In the two ultraviolet channels, gratings are provided for low-resolution (∼ 100) slitless spectroscopy.The focusing optics is configured as twin R-C telescopes, each with a primary mirror with an effective diameter of ∼ 37.5 centimetre.The FUV and NUV channels provide science observations, while the VIS channel mainly enables corrections for telescope drifts.The NUV and FUV channels provide excellent angular resolutions of ∼1.2 and ∼1.4 arcseconds, respectively, thereby much improving on their predecessor GALEX, In the lower panel, we mention the derived properties of our objects.The mentioned parameters are: m FUV = FUV AB magnitude (corrected for foreground extinction), m NUV = NUV AB magnitude (corrected for foreground extinction), A = aperture area, SFR FUV = star formation rate, SFR corr FUV = star formation rate from corrected FUV luminosty, Υ * K = K-band stellar mass-to-light ratio, M K = K-band stellar mass, sSFR corr FUV = SFR corr FUV /M K , specific star formation rate, M HI = atomic hydrogen mass, M halo = virial/halo mass, T vir = virial temperature of the hot gas.The references for the rotational velocities v rot are, a: Saglia & Sancisi (1988), b: Rubin et al. (1979), c: Corradi & Capaccioli (1991), d: Garrido et al. (2005).
which had a spatial resolution of ∼5 arcseconds.Even though the pixel scale at the detector plane is ∼ 0.42 arcsec/pixel, an onboard algorithm enables incoming photons to be localized on the detector plane with higher accuracy of 1/8 th of a pixel.Due to this higher resolution capability, UVIT is a powerful tool to observe the young star formation in galaxies in a well-resolved manner.
In this study, in addition to ASTROSAT UVIT data we have also used archival data from the following missions: (vii) Infrared Astronomical Satellite (IRAS) (IRAS1, IRAS2, IRAS3, IRAS4).

UVIT Level-1 data reduction
We obtained the Level-1 (L1) data for our objects from the AS-TROSAT data archive.We used CCDLAB provided by Postma & Leahy (2017) to make observational and detector-related corrections to the L1 data to make it useful for scientific purposes.The L1 files for a particular object contain a FITS binary extension involving a table of the centroid list.Each L1 file may contain multiple observational frames of an object that may be unique or repetitive in nature for each filters.
The image processing by CCDLAB is described in brief as follows: (i) In the first step, all the L1 data files are extracted and checked for their scientific usefulness.All of the duplicate and non-useful data are exempted from further analysis.While observing an object, a short observation of the first 20 seconds is done to test the bright object detection.These observations do not contain enough information to be useful scientifically, and these data are disregarded.All of these are done automatically by CCDLAB.The underlying principle is to create unique subsets of data from the extracted L1 files for each filter based on frame number and frame time of the centroid list, (ii) satellite/telescope drift corrections performed by taking VIS channel observations into account, (iii) exposure array correction, and (iv) finding astrometric solution of World Coordinate System (WCS) to assign a coordinate system to the observed objects.Most of the tasks are automated in the pipeline, although manual intervention is needed for some processing parts.For example, the objects having multiple slices of datasets for a particular band needed to be registered manually with point sources for aligning and merging the images so that translational and/or rotational drifts do not affect the quality of the image.The final calibrated images of our objects from UVIT L1 data are shown in Fig. 2. In this figure, we show the FUV F154W (∼ 0.1541m) observations for all target galaxies and NUV N242W (∼ 0.2418m) observations for the objects NGC 5635 and NGC 266.
In the FUV band, the integration times of the objects NGC 1030, NGC 1961, NGC 4501, NGC 5635 and NGC 266 are T int ∼ 1.9, 1.9 , 1.6, 8.1 and 7.4 ks integration times for objects NGC 5635 and NGC 266 are T int ∼ 8.2, 7.5 ks, respectively.

Aperture photometry
We perform aperture photometry of the objects in each band mentioned in Section 2.2.The apertures for finding out the flux of the objects is estimated with the IRAF task ellipse (Tody 1986).With the UVIT FUV images as the references, the radius of the aperture is defined as the distance at which the intensity of the source matches the background, which is the mean per pixel calculated from regions away from the source.To estimate the background flux per pixel, we use the SAOImageDS9 task region (Joye & Mandel 2003).Depending on the aperture radius, we make image cut-outs for our objects using the IRAF task imcopy.The data preferences are as follows: (a) for FUV and NUV, we use UVIT for all objects except NGC 1030, NGC 1961 and NGC 4501, where in the absence of UVIT NUV, we use GALEX NUV data, (b) for optical bands we use SDSS for NGC 4501, NGC 5635 and NGC 266.In the absence of SDSS images, we use Pan-STARRS images for NGC 1961 and DECaLS images for NGC 1030; (c) for near-infrared, we use 2MASS for all objects; (d) for mid-infrared, we use WISE for all objects except NGC 4501 due to absence of image covering our entire aperture, and in place of that we use IRAS1 and IRAS2, (e) for far-infrared we use IRAS3 and IRAS4 for all our objects.Note that, in the absence of the entire image in our defined aperture, we have used python module reproject to specifically make flux-conserved image mosaics for 2MASS NGC 5635 and 2MASS NGC 266 collecting image frames containing our objects of interest from the corresponding archive.For the same reason, we also use SDSS mosaics, but in this case, we use the SWARP (Bertin et al. 2002;Bertin 2010) script provided by the DR12 Science Archive Server (SAS) to make the mosaics.
To eliminate the contributions from the background sources to the total light within the aperture, we use SExtractor (Bertin & Arnouts 1996) for the image cut-outs with DETECT_THRESH as 3 and subtract their fluxes from the total flux within the defined aperture.To eliminate the effect of overall background contribution, we calculate the background flux per pixel as the mean flux from regions far from any contaminating sources in the images using SAOImageDS9 as mentioned before.The process is carried out for each data mentioned in Section 2.2.Note that, to estimate the fluxes, we use relations provided by Tandon et al. (2017) for UVIT.
Lower wavelength radiations like ultraviolet (UV) light are highly interactive with an interstellar medium consisting of dust grains.The physical dimensions of dust grains are quantified by the power law of Mathis, Rumpl & Nordsieck (1977) to be ∼ 0.005 − 0.25m.Now, with the UV wavelength in the range ∼ 0.01 − 0.4m it can be susceptible to absorption or scattering by dust grains if the grain size is greater or comparable to the wavelength, respectively.The observed UV light from the star-forming regions of galaxies can be thought to be reprocessed in two steps: internal extinction and foreground galactic extinction.To account for the galactic extinction, we consider the dust map of Schlafly & Finkbeiner (2011) and calculate the band extinctions taking individual reddening and Cardelli et al. (1989) extinction law into consideration.The extinction in a particular wavelength is given by, Here,  ( −) is the color excess for the object.The quantity   , the ratio of total to selective total extinction is 3.1 for Milky Way type extinction in V-band (Schultz & Wiemer 1975).

Star formation hierarchy in the galactic discs
Far-ultraviolet radiations (FUV) from a galaxy are useful tracers of young star-forming populations within the galaxy.FUV can locate the clumps which are hosting star formation in the galaxy over the past ∼ 100 Myr.A large star-forming region may contain smaller high-UV-intensity regions with young star formations going on.We consider these star-forming structures to be hierarchical in nature and employ ASTRODENDRO (Robitaille et al. 2019) to identify these regions based on some given constraints.The algorithm of ASTRODENDRO considers an input intensity map (in our case, the UVIT data) to be hierarchical in nature and decompose it like the structure of a tree.The dendrogram is constructed starting with identifying the brightest pixels in the map and progressively adding fainter pixels in the subsequent steps.The dendrogram considered has two types of structures called branches and leaves.A branch can split into another branches and leaves, but leaves do not have any further substructures.All these structures converge into a trunk that has no parent structure (see Robitaille et al. 2019 for more details1 ).The large star-forming regions are considered parent structures in ASTRODENDRO, with smaller regions within these as the child structures.We use ∼ (1.8/0.42) as the minimum number of pixels based on the resolution and pixel scale of UVIT in order to identify the brightest clumps.The detection threshold for the clumps is set at 3 level based on the average noise of the data.The young starforming clumps of the objects identified with 3 detection threshold are shown in Fig. 3 (First row).The parameters derived from the catalogue of star-forming clumps for the objects are shown in Table 3, and their histograms are shown in the second, third, and fourth rows in Fig. 3.In the same figure, fifth row, the variation of the FUV SFR of the identified clumps with radius r d (kpc) from the centre of the galaxy is shown for each object.
A cut-out image of a region (∼ 57 × 57 arcsec 2 ) of the star-forming clumps in NGC 1961 is shown in Fig. 4. The green contours indicate the branches and the red contours indicate the child structures or the leaves.It can be seen that many of the leaves are isolated structures showing isolated regions of young star formation.Note that the image pixel values are in the units of 1.87 × 10 −18 erg s −1 cm −1 Hz −1 .The few parameters of the output catalogue of ASTRODENDRO that were made use of are the position coordinates of the clumps, the exact area of the child structures, the flux enclosed by that area, and the effective radius of the clumps.Note that, we have considered the child structures for estimating our parameters as they are more resolved than the parent structures based on the resolution of UVIT.
The star formation rates for the objects are found out following the relation of Kennicutt (1998) between the SFR and far-ultraviolet luminosity L FUV assuming a Salpeter Initial Mass Function (IMF) with mass limits 0.1−100 M ⊙ which is given below, Note that, we estimate all the SFRs in this paper considering a Salpeter initial mass function (IMF).The magnitude m FUV , SFR and Σ FUV SFR mentioned in Table 3 are corrected for both foreground and internal attenuation of the galaxies.To estimate the corrected magnitude and/or flux of the clumps, the effect of foreground attenuation of radiation is taken into account following the procedure described in Section 3.2 and to eliminate the effect of the internal attenuation within the host galaxies in FUV wavelength, we consider the total extinction A FUV (mag) found out from the best-fit spectral    et al. 2019).The parameters are described below N = the number of clumps, m FUV = magnitude of the identified clumps in the AB system, SFR = star formation rate of the identified clumps in M ⊙ yr −1 , Σ FUV SFR = star formation rate density of the clumps in M ⊙ yr −1 kpc −1 , r eff = effective radius (min value-max value) of the star-forming clumps in pc.All the parameters are derived for the area within the apertures mentioned in Table 2.Note that m FUV , SFR and Σ FUV SFR shown here are corrected for foreground and internal dust attenuation.
energy distribution of the objects using the grid shown in Table 4 and are mentioned in Table 5 (see Section 3.4 for details).

The Spectral Energy Distribution
To fit the spectral energy distribution (SED) of the objects, we have made use of data from our UVIT observations as well as other archival data for our objects as mentioned in Section 2.2.The steps followed to estimate the fluxes in FUV-FIR bands of the objects are given in Section 3.2.We used CIGALE (v2022) (Code Investigating GALaxy Emission) (Boquien et al. 2019;Yang et al. 2022) to perform SED fitting, where we utilized multi-band photometry data of the objects given as inputs.The FUV−FIR fluxes are corrected for attenuation due to foreground dust before using them as inputs to CIGALE.The modules used to perform the fitting are described below, (i) Star formation history: The module sfhdelayed is used to model the star formation history of the objects.Here, the star formation model is defined as SFR(t) ∝ t  2 exp (−t/) for t as the variable of time and where  defines the peak of the star-forming history of a galaxy.
(ii) Stellar populations: The module bc03 is used to model the stellar population of the galaxies (Bruzual & Charlot 2003).
(iii) Nebular emission: The module nebular is used to fit the nebular emission (Inoue 2011) in galaxies beyond mid-infrared as a result of heating and ionisation of gas surrounding massive stars, which denotes young star-forming regions within the galaxy.
(iv) Dust attenuation: The module dustatt_calzleit is used to model the attenuation of light in the galaxy.The dust absorbs radiation in shorter wavelengths (ultraviolet and near-infrared) and re-radiates them in mid and far-infrared.Here we use models as per Calzetti et al. (2000) to account for the attenuation.
(v) Dust emission: We use dl2014 to fit the re-processed radiation in mid and far-infrared and beyond (Draine et al. 2014).
(vi) AGN: To account for the effect of the active galactic nuclei (AGN) in the overall SED, we make use of fritz2006 as per Fritz et al. (2006).
We have fitted the spectral energy distribution of each object in our sample individually.The CIGALE grid used to find out the best-fit SEDs for the objects is described in Table 4, where we mention all the free parameters related to the models described above have been used to optimize the fittings.The final best-fit model SEDs for the objects and the observed multi-band photometric data points used as inputs are shown in graphs in Fig. 5.This figure shows CIGALE's best-fit models of the objects' spectral energy distributions.The data points are shown with empty black circles, and the models are shown with black lines.In the lower parts of each graphs, we show the filled transmission curves for the bands used for wavelength references.Filters from left to right: UVIT F154W, UVIT N242W, SDSS u, SDSS g, SDSS r, SDSS i, SDSS z, WISE1, WISE2, WISE, WISE4, IRAS60, IRAS100.Note that we have also made use of DECaLS (g, r, z) and Pan-STARRS1 (g, r, i, z, y) images for NGC 1030 and NGC 1961 respectively (Section 2.2).
As mentioned earlier, the free parameters for the fitting are shown in Table .4 and it is important to note that, we have fitted each of the galaxies individually instead of a batch fitting in order to observe the variations of the parameters more carefully for each galaxies and change them accordingly to optimize the fitting though minimization of reduced chi-square ( 2  ).At first, for each of our objects we start the fitting by the default script generated by CIGALE and then change the free parameters individually and take into account different combinations of them in order to obtain a better fit for each galaxies.This can be noted from the different set of choices for a single parameter (e.g. main ) in case of different galaxies.The free parameters corresponding to the modules described before in this section and also mentioned in the Table.We have employed the following modules to estimate the best-fit results from the FUV-FIR SED: sfhdelayed for star formation history SFH, bc03 for a single stellar population SSP, nebular for nebular emission lines, dustatt_calzleit for dust attenuation, dl2014 for dust emission, fritz2006 for AGN contribution.In the lower part of each graph, we show the bands that have been used to find the SEDs of the objects.Filters from left to right: F154W, N242W, SDSS u, SDSS g, SDSS r, SDSS i, SDSS z, 2MASS J, 2MASS H, 2MASS K, WISE1, WISE2, WISE3, WISE4, IRAS60, IRAS100.The filters with their corresponding colors are also shown in the top right corner of the figure.Note that we have also made use of DECaLS (g, r, z) and Pan-STARRS1 (g, r, i, z, y) images for NGC 1030 and NGC 1961 respectively (Section 2.2). fraction of the late burst population (f burst ), (ii) Stellar population is parameterized by the initial mass function (IMF), metallicity, (iii) dust attenuation is parameterized by colour excess of the stellar continuum light for the young population (E(B − V) young ), Reduction factor for the E(B-V) of the old population compared to the young one (E(B − V) old−factor ), (iv) dust emission is parameterized by mass fraction of Polycyclic Aromatic Hydrocarbon PAH (q PAH ), powerlaw slope  for dU dM ∝ U  .Note that, here, we only mention the parameters that have been varied during the fitting (for more details on each module, see Boquien et al. 2019).
The results of the SED fitting are tabulated in the upper panel of Table 5.We mention the best-fit outputs of some of the parameters of our interest and their parent modules: (i) sfhdelayed: instantaneous star formation rate SFR inst (M ⊙ yr −1 ), e-folding time of the main stellar population model  main (Gyr), (ii) bc03: total stellar mass M ★ (M ⊙ ), stellar mass of the young population M ★,young (M ⊙ ), total stellar luminosity L ★ (L ⊙ ), (iii) dustatt_calzleit: attenuation in UVIT FUV wavelength A FUV (mag), (iv) dl2014: dust mass M dust (M ⊙ ), dust luminosity L dust (L ⊙ ).Note that, in our best-fit SEDs of the objects, we found negligible/ almost no contribution from the AGN, indicating at the present day not much activity is taking place in the galactic nuclei of these massive spirals.In the lower panel of Table 5, we show some more parameters estimated using SEDderived data and other parameters shown in Table 2.We estimate the old to young stellar population ratio  from SED, where we find the mass of the older stellar population M ★,old ∼ M ★ .The stellar mass accumulated up to the peak of the star-forming activity (denoted by  main ) of the corresponding objects are denoted by M ★,peak (M ⊙ ).The total baryonic mass M baryon (M ⊙ ) of these galaxies are estimated using the stellar mass M ★ , dust mass M dust (both shown in upper panel, Table 5) and gas mass M gas (  2021) are also shown.The positions of five target galaxies from the present study are shown with star symbols, with instantaneous SFR and stellar mass from SED using CIGALE.
The light green shadow indicates the green valley region with 10 −11.5 < sSFR(yr −1 ) < 10 −10.5 (Salim et al. 2016).Right panel shows the variation of the star formation efficiency  ★ of the galaxies as a function of its stellar mass  ★ .The black curve is obtained from the relation between halo mass and the corresponding stellar mass provided by Moster et al. (2013) Myr [5,10,25,[1,5,10,[5,10,25,[1,5,10,[5,10,25,50,100] 25,50,100] 50, 100] 25, 50, 100] 50, 100] (d) Age burst Myr [5,10,25,[5,10,25 [5,10,25,[50,100,200,[5,10,25,50,100,200,50,100,200 50,100,200,350,500,750,50,100,200,350,500,750,350,500  Note that  main = 1 − 8000; 20 means that  main is varied between 1 and 8000 with 20 evenly spaced values as inputs.And also, the parameters for which one single value (e.g.q PAH , ) is mentioned, that is, the best fit value for that parameter obtained through multiple iterations.SFR inst = instantaneous star formation rate, M ★ = stellar mass, M ★,young = mass of young stellar population, M dust = dust mass, L ★ = stellar luminosity, L dust = dust luminosity, A FUV = extinction in F154W FUV-band of UVIT,  main = the peak age of star formation of the main stellar population of the objects,  2  = reduced chi-sqaure of the best fit.In the lower panel, we mention some more useful parameters calculated using SED-derived data.We show,  = M ★,old /M ★,young = the ratio of the stellar mass of old to young population, M ★,peak = stellar mass of the objects accumulated by time  main with the percentage of the present day stellar mass M ★ in bracket, M baryon = M ★ + M gas + M dust = total baryonic mass (see Table 2 for M gas ), M expected = baryonic mass of the galaxies expected from the cosmic baryon fraction of 0.167 and the halo mass M halo (see Table 2), f b,r 200 = M baryon /M halo = baryon fraction of the galaxies taking total baryonic mass and the halo mass upto the virial radius and, f ★ = M ★ /f b M halo = star formation efficiency.
fraction is shown by M expected = f b M halo , where f b = 0.167 and the halo mass M halo is shown in Table 2.However, the baryon fraction that is seen in these galaxies within the virial radius r 200 is denoted by f b,r 200 as the ratio of M baryon to M halo .Finally, we mention the star formation efficiency of these objects, which is denoted by f ★ = M ★ /f b M halo , which characterises the efficiency of halo baryons' conversion into stars.It can be seen that all of our spirals have stellar mass > 10 11 M ⊙ (and luminosity > 10 11 L ⊙ ) comparable to high-mass elliptical galaxies.The instantaneous star formation rate of these objects falls in between 1.29 − 12.04M ⊙ yr −1 considering a delayed star formation history model (Section 3.4), where the peak star formation of these objects happened in between 0.843 − 2.750 Gyr after the 'Big Bang'.
The star formation rates of the objects as a function of the stellar mass is shown in (Fig. 6, left panel).In this figure, the variation of specific star formation rate (sSFR in yr −1 ) versus the stellar mass (M ★ in M ⊙ ) is shown for galaxies of various types.The dotted line indicates the star-forming the main sequence from  ∼ 0 (Elbaz et al. 2007).Highly Star-forming ultraviolet luminous galaxies are taken from Hoopes et al. (2007) (filled magenta circles).Super spirals, lenticulars and post-merger galaxies are taken from Ogle et al. (2019a) (orange boxes with red edges).A sample of galaxies with different quenching stages like the star-forming (filled blue circles), mixed (filled orange circles with black edges), nearly retired (filled red circles), fully retired (filled red circles with black edges) and quiescent-nuclear-ring (filled orange circles) taken from Kalinova et al. (2021) have also been shown.The positions of the five target galaxies of the present study are shown with star symbols, with instantaneous SFRs and stellar masses given in Table 5.Despite their high stellar masses, one can see that their sSFR is anomalously low, much below the main sequence, and close to the region of the most massive super spirals of Ogle et al. (2019a), but above the highly quenched, fully retired galaxies.The 'Green Valley' region with 10 −11.5 < sSFR(yr −1 ) < 10 −10.5 (Salim et al. 2016) is shown with light green shadow.
Moreover, we also show the variation of the star formation effi-ciency f ★ of the galaxies as a function of its stellar mass M ★ in (Fig. 6, right panel).Using a multi-epoch abundance matching model, the black curve is obtained from the relation between halo mass and the corresponding stellar mass provided by Moster et al. (2013).The SPARC (Spitzer Photometry and Accurate Rotation Curves) sample of disc galaxies (Lelli et al. 2016;Posti et al. 2019) is shown with black+grey points.In the case of M ★ /M halo = f b , cosmic baryon fraction (CBF), the star formation efficiency f ★ = 1 and is shown with the light grey line.

Star formation
The ultraviolet radiation from the young star-forming regions of a galaxy gets absorbed by the dust in the interstellar medium (ISM) and ultimately re-emitted in the thermal infrared.Kennicutt (1998) shows that the far-infrared luminosity integrated over 8 − 1000m is a sensitive tracer of young star formation in a galaxy.Now, to account for the absorbed FUV radiation by the dust in the ISM, we use the relation provided by Kennicutt & Evans (2012) and estimate the corrected FUV luminosity using the following relation, Here, L corr FUV and L obs FUV are the dust corrected and observed luminosity in far-ultraviolet, L TIR = total infrared luminosity over 8 − 1000m.We use the observed luminosity L obs FUV of the objects as per the foreground extinction corrected magnitudes mentioned in Table 2.The integrated luminosity is estimated as, L TIR ∼ 1.75L FIR (Calzetti et al. 2000), where the far-infrared luminosity L FIR is found out using IRAS 60 and 100 m fluxes following Helou et al. (1988).The star formation rates of the objects using the dust-corrected FUV luminosities are shown in Table 2 as SFR corr FUV (M ⊙ yr −1 ).The spirals NGC 1961 and NGC 4501 have the highest FUV star formation of 13.66 and 13.51M ⊙ yr −1 respectively followed by NGC 1030, NGC 266 and NGC 5635.
Massive galaxies often show a quenched state of star formation at low red-shift.The general idea has been that they acquire most of their mass earlier in time compared to the main-sequence galaxies.In Fig. 6 (left panel), we show the variation of the specific star formation rates of the galaxies as a function of their stellar masses for a wide range of samples, including galaxies at different stages of their evolution and properties where we mention ultraviolet luminous galaxies from Hoopes et al. (2007), the super spiral, lenticular and post-merger galaxies from Ogle et al. (2019b) and a mixed group of star-forming, nearly retired and fully retired galaxies from Kalinova et al. (2021).It can be seen that our sample galaxies with stellar mass > ∼ 10 11 M ⊙ fall below the expectation of the main-sequence relation at z ∼ 0 (Elbaz et al. 2007), specifically in the 'Green Valley' region with specific star formation rates in 10 −11.5 < sSFR < 10 −10.5 yr −1 (Salim et al. 2016), confirming the overall trend of lower star formation with increasing stellar mass which is evident from the graph (see Table 5 for M ★ and instantaneous SFR).Even if we consider the specific star formation rates of our objects using FUV dust-corrected star formation rates and their K-band stellar masses (see Table 2 for sSFR corr FUV (yr −1 )), they fall in the 'Green Valley' region indicating they have been in this state for at least the last ∼ 100Myr considering FUV radiation is indicative of star formation in a galaxy in the past ∼ 100Myr (Kennicutt & Evans 2012).The intermediate spiral NGC 1961, which has the highest star formation in our sample, is the closest to the main-sequence relation, followed by NGC 4501.NGC 1030 shows the lowest instantaneous SFR, falling almost at the same place as J2345-0449, which is a spiral galaxy hosting a largescale radio jet (Bagchi et al. 2014).However, our sample of late-type spirals shows a mix of moderate and/or nearly retired instantaneous star formation as opposed to a fully quenched state as shown by the massive isolated S0-a galaxy UGC 12591 (Ray et al. 2022).
In Table 5 (upper panel), we mention the best-fit  main for the objects, which indicates the peak of star formation activity in the galaxies according to a delayed SFR function as described in Section 3.4.Based on our assumed star formation history, we find that all the objects barring NGC 1961 had experienced a peak in their star formation before the peak in the cosmic star formation history, the 'cosmic noon' around 1 < z < 3 translating to a period of ∼ 2.2 − 5.9 Gyr after the 'Big Bang'.We also show that the objects already became massive by the time  main and gained stellar mass M ★,peak of the order of a   × 10 11 M ⊙ before and up to the peak of their star formation histories, corresponding to a growth of ∼ 31 − 42 per cent in a time (1/16)-(1/5) th of the age of the Universe (Table 5).According to our model, the objects that had experienced the peak relatively sooner after the 'Big Bang' show a more suppressed state of star formation in recent times (e.g.NGC 1030, NGC 5635, NGC 266) compared to the objects that had their peak relatively in the later period (e.g.NGC 1961, NGC 4501) are still forming stars (Table 2 and 5).
From the spectral energy distribution of these late-type spirals, we also found the contribution of the older stellar population and the younger stellar population in determining the total stellar mass of these objects.We mention the stellar mass of young population M ★,young in Table 5 (upper panel), and it can be seen that these are much smaller than the total stellar mass of the objects, i.e.M ★,young << M ★ .However, NGC 1961 and NGC 4501, having the highest young star formations among the five objects, have ∼ 10 times more young stellar populations than the other three spirals.We find that these massive galaxies are dominated by older stars, as can be seen from the ratio  between old and young stellar mass ).We plot our objects with galaxies of wide morphologies ranging from ellipticals (red) to late-type spirals (green).
in Table 5 (lower panel) with M ★,old ∼ M ★ .This is also evident from the fact that for our objects K-band stellar mass M K ∼ M ★ (see Table 2, Section 4.3), considering K-band luminosity of a galaxy is primarily dominated by radiations from the galaxy's older stellar population.And objects having a higher population of older stars relative to young stars (hence higher value for ) show lower  main (Table 5) as their main stellar population had peaked sooner after the 'Big Bang'.This is also visible from the graph in Fig. 7, where we show foreground extinction corrected color-color diagram (considering FUV-NUV and NUV-K colors) for elliptical, spiral and irregular galaxies in the nearby Universe from Gil de Paz et al. (2007).In that graph, we find the color NUV-K for our objects increases as  main decreases indicating a relatively more older stellar population in objects with smaller  main , evident from our discussion about  and  main (Table 5).Now, as per the hierarchical structure formation theory of the standard ΛCDM cosmology, where it is assumed that massive systems like these galaxies are formed through the merger of smaller objects over some time, so, they must have more young stellar population instead of older stellar population.The lack of understanding of this well-known problem related to this aspect of galaxy formation theory has also been reported by Man & Belli (2018), Thomas et al. (2005Thomas et al. ( , 2010)).One possible solution to that problem could be that these massive galaxies are formed through merging with relatively more minor objects with their own rapid 'in situ' star formations that occurred in the early universe, and the merged system undergoes negligible new star formation in the later period of evolution as suggested by Oser et al. (2010).However, careful investigation of the high redshift galaxies, more rigorous parameterization of the star formation histories, and detailed understanding of the baryonic processes in the dark matter halos are some of the key aspects to exactly establish and perhaps solve the problem.
However, the recent periods (∼ 100Myr) of star formation seen predominantly in NGC 1961 and NGC 4501 are most probably due to some recent interaction(s) that caused asymmetries in the galactic plane, clearly visible in NGC 1961 optical image as we discussed in Section 2.1.Even though there are no signatures of recent head-on mergers in our objects, the turbulence in the galactic disc provided by strong interaction(s) can make it susceptible to new star formations (Bournaud 2011).In Section 2.1, we mention that all our objects show a varying order of asymmetry and/or interaction, which has helped them to revive star formation to some degree, unlike the quenched disc galaxy UGC 12591 (Ray et al. 2022) situated in an isolated environment devoid of any interaction.However, the exact mechanism of the process is contested (Pearson et al. 2019) and may vary if subjected to morphologically different galaxies and the environment they reside in.Our results are in parallel to the findings of Xu et al. (2020) who show that although the massive galaxies are mostly quiescent in nature, there exists a fraction (∼ 20 per cent) of them that are forming stars and of them, ∼ 85 per cent have asymmetries induced in their structures by recent mergers.

Star forming clumps
The UVIT far-ultraviolet images have been spatially resolved into hierarchical star-forming clumps and are shown in Fig. 3 (First row).
We show the statistics of the identified clumps in the consequent rows of Fig. 3.We find the least number of structures in NGC 1030 (Table 3) corresponding to very few regions of ongoing star formation with a radius ranging between 160-317 pc partly due to the edge-on view and the existence of dust lanes as can be seen from the optical image Fig. 1.The identified clumps vary over a magnitude of ∼ 1-mag showing similar star-formation going on in them with mean star formation rate (SFR) of 0.0177 ± 0.0078M ⊙ yr −1 and mean star formation rate density (Σ FUV SFR ) of 0.038 ± 0.008M ⊙ yr −1 kpc −2 .In NGC 1961 we find 393 clumps (Table 3) with magnitude varying over ∼ 3-mag and having the highest SFR and Σ FUV SFR with mean value of 0.0110 ± 0.0079M ⊙ yr −1 and 0.098 ± 0.034M ⊙ yr −1 kpc −2 respectively.Even though the dust-corrected FUV SFR is similar for NGC 1961 and NGC 4501 (Table 2), their clumps statistics differ significantly.NGC 4501 has the highest number of starforming clumps, with 1511 clumps having a radius between 34-168 pc and mean SFR and Σ FUV SFR of 0.0024 ± 0.0020M ⊙ yr −1 and 0.066 ± 0.024M ⊙ yr −1 kpc −2 respectively.The clumps of the object NGC 266 show lower mean SFR and Σ FUV SFR of 0.0021 ± 0.0014M ⊙ yr −1 and 0.014 ± 0.003M ⊙ yr −1 kpc −2 respectively followed by NGC 5635 with the parameters as 0.0017 ± 0.0016M ⊙ yr −1 and 0.011 ± 0.004M ⊙ yr −1 kpc −2 respectively.It can be seen that the mean local dust corrected magnitude m AB and star formation rate density Σ FUV SFR of the clumps tend to vary proportionately with the global dust corrected SFR SFR corr FUV (Table 2) of the corresponding objects rather than the local mean dust corrected SFR of the clumps (Table 3).We have spatially constrained the extent of star-forming regions in these galaxies, which is evident from the variation of clump SFR (M ⊙ yr −1 ) with radius r d (kpc) in Fig. 3 (Last row).NGC 1961 shows a maximum extent of star formation up to ∼ 50kpc with only a few structures after ≳ 30kpc, and on the other extent, NGC 1030 shows very few structures extending only up to ∼ 12kpc.The peaks of the clump SFR variation can be seen from the figure denoting spikes in the number of clumps in the spirals arms of the galaxies, which is more evident for objects like NGC 1961 and NGC 266 due to their face-on view.
It can be seen that the young star-forming clumps in these massive galaxies that are spatially resolved through UVIT FUV images show a local star formation rate density Σ FUV SFR varying over an order or 10, ranging from approximately 10 −2 − 10 −1 M ⊙ yr −1 kpc −2 (Table 2, Fig. 3) even though their global star formation rate density considering the corrected FUV star formation within aperture mentioned in Table 2 varies in the range ∼ 10 −3.7 − 10 −2.7 M ⊙ yr −1 kpc −2 signify the fact that the star formation in these massive spirals are highly localised with young star formation going on only locally throughout the galaxy similar to the giant SB0/a Low Surface Brightness (LSB) galaxy Malin1 (Saha et al. 2021).This can further be investigated in detail with sensitive H observations of these objects.

Stellar and Interstellar components
The less dust-affected near-infrared K-band luminosity can be taken as a proxy for the stellar mass of galaxies.Estimating the mass-tolight ratio Υ ★ K of the objects using Bell et al. (2003) based on their color (B-V) (we use u-g in the absence of B-V for NGC 1030 and NGC 5635), the galaxies are found to be extremely massive with stellar masses of the order of a   × 10 11  ⊙ .The masses M K and the corresponding K-band mass-to-light ratios Υ ★  (each < 1) are shown in Table 2.It is also important to note that the K-band stellar masses show approximately the same results as the masses calculated from the spectral energy distribution of the objects (Table 5, Fig. 5).
The interstellar medium (ISM) of a galaxy consists of atomic HI, molecular H 2 gas components, and dust.Hydrogen gas components in the ISM can be thought to be enveloping the young star-forming regions, with ionised hydrogen gas existing in the inner region surrounding the star-forming cloud and the atomic and molecular hydrogen gas occupying the middle and outer regions, respectively.To calculate the atomic HI gas mass, we consider the HI integrated line flux from the 21 cm line profile (Tifft & Cocke 1988;Springob et al. 2005;Haynes et al. 2011) of the objects.The atomic gas mass M HI can be calculated using the following relation, Here, D is the distance to the object in Mpc, z is the redshift, and ∫ S  d is the integrated line flux in Jy km s −1 .The galaxy HI gas masses are found to be ≈ 10 10 M ⊙ for our objects.The HI gas mass is tabulated in Table 2. Now, to estimate the molecular gas content of our objects, we use the morphology-dependent relation between the molecular and atomic gas mass (M H2 /M HI ) provided by Young & Knezek (1989).Depending on the morphological classifications of the objects as Sa to Sc types (Makarov et al. 2014) we estimate the molecular gas mass to be around ∼ 10 10 M ⊙ (Table 2) for the objects.Note that, here we have assumed that the molecular gas content of an intermediate bar type (SABb) spiral and a barred Sab spiral does not differentiate much from a non-barred Sab spiral to calculate the molecular gas content for the object NGC 1961 and NGC 266.The total gas mass of the objects is then calculated as M gas = 1.38 × (M HI + M H2 ).
The dust mass for the objects is calculated from the spectral energy distribution (Fig. 5) using the model provided by Draine et al. (2014).The estimated mass M dust for the objects fall between ≈ 10 7−8 M ⊙ (Table 5).The total baryonic mass (M baryon = M ★ + M gas + M dust ) of the objects and their baryonic fraction f b,r 200 upto the virial radius are mentioned in Table 5 (Lower panel).It can be seen that the baryon fraction of these objects up to the virial radius varies from ∼ 0.014 − 0.055 indicating ∼ 67−92 per cent fewer baryons ('missing baryons') than expected (see Table 5 for M expected ∼ 10 12 M ⊙ ) according to the cosmic baryon fraction of 0.167.The most significant explanation of these 'missing baryons' has been answered by the X-ray detection of hot gas around these massive galaxies that contribute significantly to the total baryonic mass.Now, if we consider the isothermal (constant temperature) profile of the halo gas, then the virial temperature T vir of the halo gas as a function of the flat circular rotation velocity v c can be expressed as, Using the circular velocities mentioned in Table 2, we estimate the halo gas temperatures to be of the order of a   × 10 6 K translating to 0.3 − 0.5keV (Table 2) for our objects.
According to Kelly et al. (2021), the hot gas (> 5 × 10 5 K) starts to dominate the total baryon fraction of a galaxy for virial mass beyond 10 12 M ⊙ , who investigated the X-ray gas surrounding galaxies with halo mass in the range 10 11 − 10 14 M ⊙ in the cosmological EAGLE simulations.If we consider the virial mass of our objects (∼ 10 13 M ⊙ ), then the ratio of the hot gas to stellar mass component becomes ∼ 5 at red-shift z = 0 (see Figure 1; Kelly et al. 2021), which gives us hot gas mass around ∼ 10 12 M ⊙ for the stellar mass of our objects (Table 5) solving the 'missing baryon' problem keeping in mind uncertainties in individual parameters.But this vast amount of hot gas has not been seen in massive spirals due to the low density of the hot gas limiting X-ray observations to ∼ 1/5th of the virial radius (Mirakhor et al. 2021).In our sample of massive spirals, out of the five objects, two have reported detections of hot (∼ 10 6 K) X-ray halos extending much beyond their optical radius and/or the stellar disc.Bogdán et al. (2013a) detected hot gas emission up to ∼ 60 kpc for NGC 1961 based on XMM-Newton X-ray observations with the hot halo gas mass of ∼ (1.2 ± 0.2) × 10 10 M ⊙ and in Bogdán et al. (2013b) they report hot gas emission upto ∼ 70 kpc containing a mass of ∼ (9.1 ± 0.9) × 10 9 M ⊙ using ROSAT and Chandra X-ray observations of NGC 266.These detections give us a hot halo gas mass of 2 orders of magnitude less than what is expected (∼ 10 12 M ⊙ ).The high temperature (⪆ 10 6 K) (Table 2) and the low-density halo gas significantly affect the star formation in the host galaxy by not being able to settle down in the galactic disc at temperature < 10 2 K necessary for forming molecular clouds capable of forming stars.

Black hole and its effect on star formation
The massive galaxies are often hosts to supermassive black holes at their centres (Magorrian et al. 1998;Gebhardt et al. 2000).It is extremely difficult to constrain the black hole masses of galaxies observationally.So, in order to estimate the black hole mass of the target objects, we use the tight correlation between the mass of the black hole M bh and the central velocity dispersion  of the spirals (Gültekin et al. 2009).The relation is shown below, log( M bh M ⊙ ) = (8.12± 0.08) + (4.24 ± 0.41)log(  200km s −1 ) (7) The central velocity dispersion  of the objects is mentioned in Table 2.In case the information about the central velocity dispersion is not available for the objects, such as the case for NGC 1030 and NGC 5635, we estimate the black hole mass M bh from the relation provided by Reines & Volonteri (2015) correlating the black hole mass with the stellar mass (see Table 5 for stellar mass).From these relations, we show that the black hole mass of our objects is in the range of a   × 10 7−8 M ⊙ and is tabulated in Table 2.
The star formation in massive galaxies (≥ 10 11  ⊙ ) is still and primarily an unexplored phenomenon; galaxies of such types can be broadly classified into two groups where a group of galaxies showing extremely quenched SFRs and the other group showing a moderate star formation (Fig. 6, Left panel) for a similar mass range.The massive galaxies are supposed to have acquired much of their stellar mass content before normal main-sequence spirals, which are still actively forming stars, which also determined their growth of central black hole at a faster rate, which is evident from the study carried out by Reines & Volonteri (2015) on a sample of 341 galaxies including galaxies hosting active galactic nuclei (AGN) and inferred that, the growth of black hole mass is accompanied by the growth of stellar mass of the host galaxy, i.e.M ★ ∝ M bh .As we have discussed in Section 4.1 that, depending on our assumed models, these massive galaxies have experienced their peak in the star-forming activity approximately in the period of red-shift z ∼ 2.4 − 6.5 (Table 5), reaching up to the 'cosmic high noon' at z ∼ 1 − 3, which overlaps with the 'quasar epoch' around red-shift z ∼ 2. This suggests the coexistence of the era of intense star formation with the 'quasar epoch' in the universe (Shaver et al. 1999).However, from the star formation history of our objects, it is evident that there existed a period of rapid star formation assisted by the black holes' growth as well as rapid stellar mass growth in the pre-quasar era leading up to the 'quasar epoch' (Alexander et al. 2005).It indicates the possibility that the rise of star formation in these galaxies and the steep growth of the central black hole mass stops at around the peak of the star formation history of the galaxies, as by then, the black hole must have experienced a growth upto ∼ 10 7 − 10 8 M ⊙ to be able to regulate star formation of the host galaxies efficiently.Now, we discuss the possible growth scenario of the central black holes in these massive galaxies in their early period of evolution.If the black hole mass at time t is M bh (t), then the dimensionless Eddington luminosity ratio (= L/L Edd ) can be defined as (Shapiro 2005;Hopkins et al. 2006), Here, M bh (0) is the initial black hole mass at time t = 0,  r = 0.06 − 0.42, for spin 0 − 1 respectively, denotes how efficiently can the accreted mass be converted into radiative energy, t sal = 0.45 Gyr, the Salpeter timescale.For a scenario of the rapid growth of stellar mass (hence high SFR) and M bh , we expect the radiative efficiency  r to be smaller as higher  r will lead to lower growth rate for the black hole mass following above equation, dM bh /dt ∝ (1/ r − 1).In our calculations we consider,  r ∼ 0.1 and M bh (0) to be 10 2 M ⊙ , a Population-III seed black hole.If we consider the central black holes of our spirals to have grown up to ∼ 10 8 M ⊙ around the peak of their consequent star formations, then we estimate the ratio  to be in the range ∼ 0.25 − 0.86 for  main ∼ 2.8 − 0.8 Gyr (Table 5), i.e. with  ∼ (1/ main ) the accretion approaches the near-Eddington limit ( ∼ 1) for galaxies experiencing star forming peak sooner (< 10 9 yr) after the 'Big Bang'.So, It can be seen that the black hole growth and the star formation in a galaxy are closely related to each other, and our results follow the findings of Martín-Navarro et al. (2018), who suggest that the black hole growth in the early universe is proportional to the gas cooling rate and hence the star-forming activity and galaxies hosting more massive black holes experience the suppression of star formation earlier than the others in their later period of evolution.However, from the SED fitting of these objects, we find almost no activity of the active galactic nuclei of these objects in the present time, which is also evident from the AGN class of the objects as mentioned in Table 2.As we do not see any large-scale radio jets from the centre of these objects, we infer that these AGNs are presently in radio-quiet mode, with possibly weak and smallscale outflows, with no significant effect on the star formation in the galactic disc.

Star forming efficiency
How efficiently the hot halo baryonic mass is converted into the stellar mass of a galaxy can be characterised by star formation efficiency.The star formation efficiency SFE of a galaxy is defined as the following (Posti et al. 2019), Here, M ★ and M halo are the stellar and halo mass of a galaxy, whereas f b is the cosmic baryon fraction taken as 0.167 in our calculations (Komatsu et al. 2011).To calculate SFE, we use the stellar masses from the best-fit SEDs of the objects (Table 5), and the halo masses of our objects are estimated using the following relations, Here, we assume that the density of the halo is Δ c  c with Δ  ∼ 200 and  c as the critical density of the universe.Under the assumption of flat circular rotational velocity v rot up to the virial radius r vir , the halo mass can be written as, M halo = v 3 rot 10GH(z) ; G = Gravitational constant and H(z) = Hubble parameter.Expressing the redshift dependent Hubble parameter as, H(z) = H 0 [Ω M (1 + z) 3 + Ω vac ] 1/2 , the halo masses are estimated as   × 10 13 M ⊙ (see Section 1 for H 0 , Ω M and Ω vac ).The estimated halo masses and SFEs are shown in Table 2 and Table 5, respectively.The star-forming efficiency of our sample of the massive spirals is shown in (Fig. 6, right panel) along with other massive spirals like UGC 12591 (Ray et al. 2022) and J2345-0449 (Bagchi et al. 2014;Nesvadba et al. 2021).We also show the SPARC (Spitzer Photometry and Accurate Rotation Curves) sample of disc galaxies from Lelli et al. (2016) having stellar mass in the range of ∼ 10 7 to > 10 11 M ⊙ in the graph.The star formation efficiency of the galaxies is supposed to peak around the stellar mass of M ★ ∼ 10 10.2−10.3M ⊙ with f ★ ∼ 20 per cent (Moster et al. 2013).This means that massive galaxies in their evolution towards the stellar mass of ∼ 10 11 M ⊙ can only experience a maximum ∼ 20 per cent SFE with most of their baryons not converted into stars.However, the massive spirals from Lelli et al. (2016); Ogle et al. (2019b), as shown in the graph, depict a contradictory trend at the high mass end where the SFE increases with increasing stellar mass upto > 10 11 M ⊙ and corresponding f ★ reaching ≈ 0.3−1 indicating the conversions of the most (30 − 100 per cent) of their baryons into stars.In contrast to this, an extremely massive, quenched and isolated spiral like UGC 12591 shows an SFE of ∼ 3 − 5 per cent and falls in the place expected from Moster et al. (2013) model for red-shift z ∼ 0. Our sample set of massive spirals with even greater stellar masses than the other samples mentioned before shows a star-forming efficiency of ∼ 7−30 per cent with NGC 4501 and NGC 5635 having the highest and the lowest f ★ respectively (Table 5) indicating a moderate to low ongoing (z ∼ 0) conversions of baryons into stars.As we have discussed before in Section 4.1, our objects fall in the 'Green Valley' region considering some signatures of recent star formation as evident from Fig. 6 (left panel) arguably induced by interactions.However, they fall below the star formation efficiency line for f ★ = 1, the line showing all baryons have been converted into stars.Moreover, they have higher SFEs than expected from the stellar-to-halo mass relation provided by Moster et al. (2013) by abundance matching model (Fig. 6, right panel).This indicates the possibility that the stellar masses of these objects may have grown recently due to turbulenceinduced star formation in the disc and possible gas inflow to some extent; however, large-scale baryon cooling and/or halo gas (∼ 10 6 K) condensation in the galactic disc is not very predominant provided their baryon fractions f b,r 200 (Table. 5) are much less than the cosmic baryon fraction.

CONCLUSIONS
In this paper, we study the aspects related to star formation in massive spirals (> L ★ ) with a focus on five late-type galaxies NGC 1030, NGC 1961, NGC 4501, NGC 5635 and NGC 266 observed in Ul-traViolet Imaging Telescope onboard ASTROSAT.In addition to analysing the UVIT data, we used the archival data of GALEX, SDSS, PanSTARRS, DECaLS, 2MASS, WISE and IRAS in our analysis.The significant results of our analysis are listed below: (i) The late-type spiral galaxies show a mix of moderate to nearly quenched young (∼ 100 Myr) FUV star formation.Taking dust correction into account NGC 1961 show the highest star formation of SFR corr FUV = 13.66 ± 2.04 followed by NGC 4501 with SFR corr FUV = 13.51 ± 2.24M ⊙ yr −1 and the other three galaxies NGC 1030, NGC 5635 and NGC 266 show SFR corr FUV = 5.15 ± 0.87, 1.43 ± 0.13 and 2.54 ± 0.25 M ⊙ yr −1 respectively.
(ii) We identify the young star-forming regions in the galaxies within a defined aperture, considering them to be hierarchical in nature and segregating them into clumps.We find that the star formation in these galaxies is highly localised with star formation rate density Σ FUV SFR in the range of ∼ 10 −2 − 10 −1 M ⊙ yr −1 kpc −2 as opposed to a global star formation rate density of ∼ 10 −3.7 −10 −2.7 M ⊙ yr −1 kpc −2 .
(iii) From the FUV-FIR multi-wavelength SED fitting of each of the galaxies, we find the stellar mass M ★ of the objects to be of the order of a   ×10 11 M ⊙ with instantaneous star formation falling in the 'green valley' region with 10 −11.5 < sSFR(M ⊙ yr −1 ) < 10 −10.5 and with SFR inst in the range ∼ 1.7 − 12.0 M ⊙ yr −1 .We find no significant AGN contributions affecting the star formation of these objects in the present era.However, all our objects show a varying degree of asymmetry/interactions, which most probably explains the recent star formation activity in these objects.
(iv) Based on a delayed star formation history model, the peak of the star formation history of the objects is found to be in the range ∼ 0.8 − 2.8 Gyr after the 'Big Bang' expanding throughout pre-cosmic 'high noon' and pre-quasar era (1 < z < 3).The galaxies that had experienced peaks sooner after the 'Big Bang' show relatively low star formation at low redshift (z ∼ 0) than the others.For example, NGC 1030 and NGC 5635 experienced their peak ∼ 0.843 Gyr after the 'Big Bang' have low instantaneous star formation rates of 1.66 ± 0.08 and 1.29 ± 0.06 M ⊙ yr −1 , whereas, NGC 1961 shows a relatively higher instantaneous star formation of 12.04 ± 2.48 M ⊙ yr −1 having experienced the peak ∼ 2.75 Gyr after the 'Big Bang'.
(v) We show that the objects had gained much of their stellar mass (> 10 11 M ⊙ ) very rapidly in the early period of their evolution, acquiring almost ∼ 31 − 42 per cent of the present-day stellar mass in a period of ∼ (1/16) − (1/5) th of the age of the Universe.We argue that the early period of growth of the central black holes in these objects occurred rapidly with star formation and stellar mass growth in these objects.We show that the black holes must have accreted at near Eddington limit for objects that had their peak in the star formation at around < ∼ 10 9 yrs after the 'Big Bang' to be able to grow up to 10 8 M ⊙ and affect star formation activity of the host.
(vi) We find that these spirals have baryonic mass (a   × 10 11 M ⊙ ) of ∼ 67 − 92 per cent less than what is expected (a   × 10 12 M ⊙ ) from the cosmic baryon fraction of 0.167.X-ray hot halo mass detected in two objects, NGC 1961 and NGC 266, tries to compensate for the 'missing baryons'; however, they still are far less than what is expected.These objects have star-forming efficiency, the baryon-to-star conversion efficiency in the range ∼ 7 − 31 per cent with halo mass of > 10 13 M ⊙ and hot halo gas temperature of ∼ 10 6 K.With baryon fraction f b , r 200 far less than 0.167, we conclude that there is no large scale baryon cooling happening in these extremely massive objects.

Figure 1 .
Figure 1.In the above figure, we show the RGB images of the five massive late-type spirals (Table 1).The images are made using optical data (∼ 0.4 − 0.9m) in the following configurations: (a) NGC 1030: DECaLS z+r+g, (b) NGC 1961: PanSTARRS1 z+r+g, (c) NGC 4501: SDSS z+r+g, (d) NGC 5635: SDSS z+r+g and (e) NGC 266: SDSS z+r+g.Note that, the scale shown in the lower-right of each image is 50 arcsec.

Figure 2 .
Figure 2. Here, in the above figure, we show the calibrated images of our objects from UVIT Level-1 data processed in CCDLAB (Postma & Leahy 2017).We have FUV F154W (∼ 0.1541m) observations for all five spirals and NUV N242W (∼ 0.2420m) observations for the objects NGC 5635 and NGC 266.In FUV band, the integration times of the objects are T int ∼ 1.9, 1.9, 1.6, 8.1 and 7.4 ks for NGC 1030, NGC 1961, NGC 4501, NGC 5635 and NGC 266 respectively.In NUV band, T int ∼ 8.2, 7.5 ks for NGC 5635 and NGC 266 respectively.Note that, the scale shown in the lower-right of each image is 50 arcsec.

Figure 3 .
Figure3.First row: Here, we show the young star-forming clumps based on the UVIT far-ultraviolet (FUV) data of the objects that are identified with 3 detection threshold considering the star-forming clumps to be hierarchical in nature(Robitaille et al. 2019) (Section 3.3).Second row: Here, we show the histogram of FUV magnitude (m FUV ) of the identified clumps in the AB system for the objects with the mean  with 1 uncertainties mentioned in the respective plots.Third row: Here, we show the histogram of the FUV star formation rate SFR(M ⊙ yr −1 ) of the identified clumps of the objects with mean  and 1 uncertainty.Fourth row: Here, we show the distribution of FUV star formation rate density Σ FUV SFR (M ⊙ yr −1 kpc −2 ) of the objects with the mean  and 1 uncertainty.Fifth row: Here, the variation of the FUV SFR of the identified clumps with radius r d (kpc) from the centre of the galaxy is shown for each object.

Figure 4 .
Figure 4. Here, we show a cut-out region (∼ 57 × 57 arcsec 2 ) of star forming clumps (Fig. 3) of the object NGC 1961.The green contours indicate the branches and the red contours indicate the child structures or the leaves.It can be seen that many of the leaves are isolated structures showing isolated regions of young star formation.Note that the image pixel values are in the units of 1.87 × 10 −18 erg s −1 cm −1 Hz −1 .

Figure 5 .
Figure5.The best-fit models of the spectral energy distributions of the objects using CIGALE are shown.The data points are shown with empty black circles, and the models are shown with black lines.We have employed the following modules to estimate the best-fit results from the FUV-FIR SED: sfhdelayed for star formation history SFH, bc03 for a single stellar population SSP, nebular for nebular emission lines, dustatt_calzleit for dust attenuation, dl2014 for dust emission, fritz2006 for AGN contribution.In the lower part of each graph, we show the bands that have been used to find the SEDs of the objects.Filters from left to right: F154W, N242W, SDSS u, SDSS g, SDSS r, SDSS i, SDSS z, 2MASS J, 2MASS H, 2MASS K, WISE1, WISE2, WISE3, WISE4, IRAS60, IRAS100.The filters with their corresponding colors are also shown in the top right corner of the figure.Note that we have also made use of DECaLS (g, r, z) and Pan-STARRS1 (g, r, i, z, y) images for NGC 1030 and NGC 1961 respectively (Section 2.2).
(a)   = E-folding time of the main stellar population model, (b) Age = Age of the main stellar population in the galaxy, (c)  burst = E-folding time of the late starburst population model, (d) Age burst = Age of the late burst, (e) f burst = Mass fraction of the late burst population, (f) IMF = Initial Mass Function (Salpeter; Salpeter 1955), (g) Metallicity, (h)  ( −  ) young = Colour excess of the stellar continuum light for the young population, (i)  ( −  ) old−factor = Reduction factor for the E(B-V) of the old population compared to the young one, (j)  PAH = Mass fraction of PAH, (k)  = Power-law slope for dU dM ∝ U  .

Figure 7 .
Figure7.Here, we show the color-color diagram taking foreground extinction corrected (FUV-NUV) and (NUV-K) colors into account from the GALEX ultraviolet ATLAS of nearby galaxies (Gil dePaz et al. 2007).We plot our objects with galaxies of wide morphologies ranging from ellipticals (red) to late-type spirals (green).

Table 1 .
The details of observations for the five massive spiral galaxies are mentioned here.

Table 2 .
Here, in the upper panel of the table, we mention some properties related to the galaxies.The mentioned parameters are: R.A. = Right Ascension (J2000), Dec. = Declination (J2000), T = morphology, z = red-shift, v rot = rotational velocity and,  = central velocity dispersion and,  = activity class of AGN as per HyperLeda where S2, S3 and S3b denote Seyfert II, LINER and LINER with broad Balmer lines classes of AGNs respectively.

Table 3 .
. In the above table, we mention the mean () and 1 uncertainty of the parameters derived from the catalogue of star-forming clumps of the objects identified with 3 detection threshold in ASTRODENDRO (Robitaille

Table 2 )
. The expected baryonic mass these spirals should have as per the mean cosmological baryon Hoopes et al. (2007)Variation of specific star formation rate (sSFR in yr −1 ) versus the stellar mass (M ★ in M ⊙ ) is shown for galaxies of various types.The dotted line indicates the star-forming the main sequence from  ∼ 0(Elbaz et al. 2007).Highly Star-forming ultraviolet luminous galaxies are taken fromHoopes et al. (2007)(filled magenta circles).Super spirals, lenticulars and post-merger galaxies from Ogle et al. (2019a) (orange boxes with red edges).A sample of galaxies with different quenching stages like the star-forming (filled blue circles), mixed (filled orange circles with black edges), nearly retired (filled red circles), fully retired (filled red circles with black edges) and quiescent-nuclear-ring (filled orange circles) taken fromKalinova et al. (

Table 4 .
Here, we mention the grid used in CIGALE to find out the best-fit parameters.The parameters are as follows:

Table 5 .
Here, in the upper panel of the table, we mention the best-fit output parameters for SED fitting in CIGALE.The mentioned parameters are as follows: