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In time-domain radio astronomy with arrays, voltages from individual antennas are added together with proper delay and fringe correction to form the beam in real-time. In order to achieve the correct phased addition of antenna voltages one has to also correct for the ionospheric and instrumental gains. Conventionally this is done using observations of a calibrator source located near to the target field. This scheme is sub-optimal since it does not correct for the variation of the gains with time and position in the sky. Further, since the ionospheric phase variation is typically most rapid at the longest baselines, the most distant antennas are often excluded while forming the beam. We present here a different methodology ("in-field phasing"), in which the gains are obtained in real-time using a model of the intensity distribution in the target field, which overcomes all of these drawbacks. We present observations with the upgraded Giant Metrewave Radio Telescope (uGMRT) which demonstrates that in-field phasing does lead to a significant improvement in sensitivity. We also show, using observations of the millisecond pulsar J1120$-$3618 that this in turn leads to a significant improvement of measurements of the Dispersion Measure and Time of Arrival. Finally, we present test observations of the GMRT discovered eclipsing black widow pulsar J1544+4937 showing that in-field phasing leads to improvement in the measurement of the cut-off frequency of the eclipse., Comment: Accepted for publication in the ApJ

We present the first estimate, based on direct HI 21 cm observations, of the HI mass function (HIMF) of star-forming galaxies at $z\approx1$, obtained by combining our measurement of the scaling relation between HI mass ($M_{HI}$) and B-band luminosity ($M_B$) of star-forming galaxies with literature estimates of the B-band luminosity function at $z\approx1$. We determined the $M_{HI}-M_B$ relation by using the GMRT-CATz1 survey of the DEEP2 fields to measure the average HI mass of blue galaxies at $z=0.74-1.45$ in three separate $M_B$ subsamples. This was done by separately stacking the HI 21 cm emission signals of the galaxies in each subsample to detect, at (3.5-4.4)$\sigma$ significance, the average HI 21 cm emission of each subsample. We find that the $M_{HI}-M_B$ relation at $z\approx1$ is consistent with that at $z\approx0$. We combine our estimate of the $M_{HI}-M_B$ relation at $z\approx1$ with the B-band luminosity function at $z\approx1$ to determine the HIMF at $z\approx1$. We find that the number density of galaxies with $M_{HI}>10^{10} M_\odot$ (higher than the knee of the local HIMF) at $z\approx1$ is a factor of $\approx4-5$ higher than that at $z\approx0$, for a wide range of assumed scatters in the $M_{HI}-M_B$ relation. We rule out the hypothesis that the number density of galaxies with $M_{HI}>10^{10} M_\odot$ remains unchanged between $z \approx 1$ and $z\approx0$ at $\gtrsim99.7$\% confidence. This is the first statistically significant evidence for evolution in the HIMF of galaxies from the epoch of cosmic noon., Comment: 9 pages, 5 figures; minor changes to match version in press at ApJ Letters

We present here estimates of the average rates of accretion of neutral gas onto main-sequence galaxies and the conversion of atomic gas to molecular gas in these galaxies at two key epochs in galaxy evolution: (i) $z\approx1.3-1.0$, towards the end of the epoch of peak star-formation activity in the Universe, and (ii) $z\approx1-0$, when the star-formation activity declines by an order of magnitude. We determine the net gas accretion rate $\rm{R_{Acc}}$ and the molecular gas formation rate $\rm{R_{Mol}}$ by combining the relations between the stellar mass and the atomic gas mass, the molecular gas mass, and the star-formation rate (SFR) at three epochs, $z=1.3$, $z=1.0$, and $z=0$, with the assumption that galaxies evolve continuously on the star-forming main-sequence. We find that, for all galaxies, $\rm{R_{Acc}}$ is far lower than the average SFR $\rm{R_{SFR}}$ at $z\approx1.3-1.0$; however, $\rm{R_{Mol}}$ is similar to $\rm{R_{SFR}}$ during this interval. Conversely, both $\rm{R_{Mol}}$ and $\rm{R_{Acc}}$ are significantly lower than $\rm{R_{SFR}}$ over the later interval, $z\approx1-0$. We find that massive main-sequence galaxies had already acquired most of their present-day baryonic mass by $z\approx1.3$. At $z\approx1.3-1.0$, the rapid conversion of the existing atomic gas to molecular gas was sufficient to maintain a high average SFR, despite the low net gas accretion rate. However, at later times, the combination of the lower net gas accretion rate and the lower molecular gas formation rate leads to a decline in the fuel available for star-formation, and results in the observed decrease in the SFR density of the Universe over the last 8 Gyr., Comment: 8 pages, 3 figures; Accepted for publication in ApJ Letters

Star-forming galaxies are believed to replenish their atomic gas reservoir, which is consumed in star-formation, through accretion of gas from their circumgalactic mediums (CGMs). However, there are few observational constraints today on the gas accretion rate in external galaxies. Here, we use our recent measurement of the scaling relation between the atomic hydrogen (HI) mass $M_{HI}$ and the stellar mass $M_*$ in star-forming galaxies at $z \approx 0.35$, with the relations between the star-formation rate (SFR) and $M_*$, and the molecular gas mass $M_{Mol}$ and $M_*$, and the assumption that star-forming galaxies evolve along the main sequence, to determine the evolution of the neutral gas reservoir and the average net gas accretion rate onto the disks of star-forming galaxies over the past 4 Gyr. For galaxies with $M_* \gtrsim 10^9 M_{\odot}$ today, we find that both $M_*$ and $M_{HI}$ in the disk have increased, while $M_{Mol}$ has decreased, since $z \sim 0.35$. The average gas accretion rate onto the disk over the past 4 Gyr is similar to the average SFR over this period, implying that main-sequence galaxies have maintained a stable HI reservoir, despite the consumption of gas in star-formation. We obtain an average net gas accretion rate (over the past 4 Gyr) of $\approx 6 M_{\odot} yr^{-1}$ for galaxies with the stellar mass of the Milky Way. At low redshifts, $z \lesssim 0.4$, the reason for the decline in the cosmic SFR density thus appears to be the inefficiency in the conversion of atomic gas to molecular gas, rather than insufficient gas accretion from the CGM., Comment: Accepted for publication in The Astrophysical Journal Letters

The atomic hydrogen (HI) properties of star-forming galaxies in the local Universe are known to correlate with other galaxy properties via the ``HI scaling relations''. The redshift evolution of these relations serves as an important constraint on models of galaxy evolution. However, until recently, there were no estimates of the HI scaling relations at cosmological distances. Using data from a deep Giant Metrewave Radio Telescope HI 21 cm survey of the Extended Groth Strip, and the technique of spectral line stacking, we determine the scaling relation between the HI mass and the stellar mass for star-forming galaxies at $z\approx0.35$. We use this measurement, along with the main-sequence relation in galaxies, to infer the dependence of the HI depletion timescale of these galaxies on their stellar mass. We find that massive star-forming galaxies at $z\approx0.35$, with stellar mass $\rm M_* \gtrsim10^{9.5}\:M_{\odot}$, are HI-poor compared to local star-forming galaxies of a similar stellar mass. However, their characteristic HI depletion time is lower by a factor of $\approx 5$ than that of their local analogues, indicating a higher star-formation efficiency at intermediate redshifts (similar to that at $z \approx 1$). While our results are based on a relatively small cosmic volume and could thus be affected by cosmic variance, the short characteristic HI depletion timescales ($\lesssim 3$ Gyr) of massive star-forming galaxies at $z \approx 0.35$ indicate that they must have acquired a significant amount of neutral gas through accretion from the circumgalactic medium over the past four Gyr, to avoid quenching of their star-formation activity., Comment: Accepted for publication in the Astrophysical Journal Letters

The neutral atomic hydrogen (HI) mass function (HIMF) describes the distribution of the HI content of galaxies at any epoch; its evolution provides an important probe of models of galaxy formation and evolution. Here, we report Giant Metrewave Radio Telescope HI 21cm spectroscopy of blue star-forming galaxies at $z\approx0.20-0.42$ in the Extended Groth Strip, which has allowed us to determine the scaling relation between the average HI mass ($\rm{M_{HI}}$) and the absolute B-band magnitude ($\rm{M_B}$) of such galaxies at $z \approx 0.35$, by stacking the HI 21cm emission signals of galaxy subsamples in different $\rm{M_B}$ ranges. We combine this $\rm{M_{HI}-M_B}$ scaling relation (with a scatter assumed to be equal to that in the local Universe) with the known B-band luminosity function of star-forming galaxies at these redshifts to determine the HIMF at $z\approx0.35$. We show that the use of the correct scatter in the $\rm{M_{HI}-M_B}$ scaling relation is critical for an accurate estimate of the HIMF. We find that the HIMF has evolved significantly from $z\approx0.35$ to $z\approx0$, i.e. over the last four Gyr, especially at the high-mass end. High-mass galaxies, with $\rm{M_{HI}\gtrsim10^{10}\ M_\odot}$, are a factor of $\approx3.4$ less prevalent at $z\approx0.35$ than at $z \approx 0$. Conversely, there are more low-mass galaxies, with $\rm{M_{HI} \approx10^9\ {M}_\odot}$, at $z\approx0.35$ than in the local Universe. While our results may be affected by cosmic variance, we find that massive star-forming galaxies have acquired a significant amount of HI through merger events or accretion from the circumgalactic medium over the past four Gyr., Comment: Accepted for publication in The Astrophysical Journal Letters

We present a comparison between the average atomic gas mass, $\langle M_{Atom}\rangle$ (including HI and He), the average molecular gas mass, $\langle M_{Mol}\rangle$, and the average stellar mass, $\langle M_*\rangle$, of a sample of star-forming galaxies at $z\approx0.75-1.45$, to probe the baryonic composition of galaxies in and during the epoch of peak star-formation activity in the universe. The $\langle M_{Atom}\rangle$ values of star-forming galaxies in two stellar-mass matched samples at $z=0.74-1.25$ and $z=1.25-1.45$, were derived by stacking their HI 21cm signals in the GMRT-CAT$z1$ survey. We find that the baryonic composition of star-forming galaxies at $z\gtrsim 1$ is dramatically different from that at $z\approx0$. For star-forming galaxies with $\langle M_*\rangle\approx10^{10} M_\odot$, the contribution of stars to the total baryonic mass, $M_{Baryon}$, is $\approx61\%$ at $z\approx0$, but only $\approx16\%$ at $z\approx1.3$, while molecular gas constitutes $\approx6\%$ of the baryonic mass at $z\approx0$, and $\approx14\%$ at $z\approx1.3$. Remarkably, we find that atomic gas makes up $\approx70\%$ of $M_{Baryon}$ in star-forming galaxies at $z\approx1.3$. We find that the ratio $\langle M_{Atom}\rangle/\langle M_*\rangle$ is higher both at $z\approx1.0$ and at $z\approx1.3$ than in the local Universe, with $\langle M_{Atom}\rangle/\langle M_*\rangle\approx1.4$ at $z\approx1.0$, and $\approx4.4$ at $z\approx1.3$, compared to its value of $\approx0.5$ today. Further, we find that the ratio $\langle M_{Atom}\rangle/\langle M_{Mol}\rangle$ in star-forming galaxies with $\langle M_*\rangle \approx10^{10} M_\odot$ is $\approx2.3$ at $z\approx1.0$ and $\approx5.0$ at $z\approx1.3$. Overall, we find that atomic gas is the dominant component of the baryonic mass of star-forming galaxies at $z\approx1.3$, during the epoch of peak star-formation activity in the universe., Comment: 9 Pages, 4 Figures; Accepted for publication in ApJ Letters. Updated with minor changes to match version in press

We describe the design, data analysis, and basic results of the Giant Metrewave Radio Telescope Cold-HI AT $z\approx1$ (GMRT-CAT$z$1) survey, a 510-hour upgraded GMRT HI 21 cm emission survey of galaxies at $z=0.74-1.45$ in the DEEP2 survey fields. The GMRT-CAT$z$1 survey is aimed at characterising HI in galaxies during and just after the epoch of peak star-formation activity in the Universe, a key epoch in galaxy evolution. We obtained high-quality HI 21 cm spectra for 11,419 blue star-forming galaxies at $z=0.74-1.45$, in seven pointings on the DEEP2 subfields. We detect the stacked HI 21 cm emission signal of the 11,419 star-forming galaxies, which have an average stellar mass of $M_* \approx 10^{10} M_\odot$, at $7.1\sigma$ statistical significance, obtaining an average HI mass of $\langle M_{HI}\rangle=(13.7\pm1.9)\times10^{9} M_\odot$. This is significantly higher than the average HI mass of $\langle M_{HI} \rangle=(3.96 \pm 0.17)\times10^{9} M_\odot$ in star-forming galaxies at $z \approx 0$ with an identical stellar-mass distribution. We stack the rest-frame 1.4 GHz continuum emission of our 11,419 galaxies to infer an average star-formation rate (SFR) of $8.07\pm0.82 M_\odot yr^{-1}$. Combining our average HI mass and average SFR estimates yields an HI depletion timescale of $1.70\pm0.29$ Gyr, for star-forming galaxies at $z\approx1$, $\approx3$ times lower than that of local galaxies. We thus find that, although main-sequence galaxies at $z\approx1$ have a high HI mass, their short HI depletion timescale is likely to cause quenching of their star-formation activity in the absence of rapid gas accretion from the circumgalactic medium., Comment: 27 pages, 15 figures; The Astrophysical Journal, 937, 103; updated to match published version

Measurements of the atomic hydrogen (HI) properties of high-redshift galaxies are critical to understanding the decline in the star-formation rate (SFR) density of the Universe after its peak $\approx8-11$ Gyr ago. Here, we use $\approx510$ hours of observations with the upgraded Giant Metrewave Radio Telescope to measure the dependence of the average HI mass of star-forming galaxies at $z=0.74-1.45$ on their average stellar mass and redshift, by stacking their HI 21 cm emission signals. We divide our sample of 11,419 main-sequence galaxies at $z=0.74-1.45$ into two stellar-mass ($M_*$) subsamples, with $M_*>10^{10} M_\odot$ and $M_*<10^{10} M_\odot$, and obtain clear detections, at $>4.6\sigma$ significance, of the stacked HI 21 cm emission in both subsamples. We find that galaxies with $M_*>10^{10} M_\odot$, which dominate the decline in the cosmic SFR density at $z\lesssim1$, have HI reservoirs that can sustain their SFRs for only a short period, $0.86\pm0.20$ Gyr, unless their HI is replenished via accretion. We also stack the HI 21 cm emission from galaxies in two redshift subsamples, at $z=0.74-1.25$ and $z=1.25-1.45$, again obtaining clear detections of the stacked HI 21 cm emission signals, at $>5.2\sigma$ significance in both subsamples. We find that the average HI mass of galaxies with $\langle M_* \rangle\approx10^{10} M_\odot$ declines steeply over a period of $\approx1$ billion years, from $(33.6\pm6.4) \times 10^9 M_\odot$ at $\langle z\rangle\approx1.3$ to $(10.6\pm1.9)\times10^9 M_\odot$ at $\langle z\rangle\approx1.0$, i.e. by a factor $\gtrsim3$. We thus find direct evidence that accretion of HI onto star-forming galaxies at $z\approx1$ is insufficient to replenish their HI reservoirs and sustain their SFRs, thus resulting in the decline in the cosmic SFR density 8 billion years ago., Comment: 11 Pages, 7 Figures; Astrophysical Journal Letters, 931 L34; a minor typographical error is fixed in this version

We study the relationship between the H{\sc i} specific angular momentum (j$_{\rm g}$) and the H{\sc i} mass (M$_{\rm g}$) for a sample of galaxies with well measured H{\sc i} rotation curves. We find that the relation is well described by an unbroken power law \jg $\propto$ \mg$^{\alpha}$ over the entire mass range (10$^{7}$-10$^{10.5}$ M$_{\odot}$), with $\alpha = 0.89 \pm 0.05$ (scatter 0.18 dex). This is in reasonable agreement with models which assume that evolutionary processes maintain H{\sc i} disks in a marginally stable state. The slope we observe is also significantly different from both the $j \propto M^{2/3}$ relation expected for dark matter haloes from tidal torquing models and the observed slope of the specific angular momentum-mass relation for the stellar component of disk galaxies. Our sample includes two H{\sc i}-bearing ultra diffuse galaxies, and we find that their angular momentum follows the same relation as other galaxies. The only discrepant galaxies in our sample are early-type galaxies with large rotating H{\sc i} disks which are found to have significantly higher angular momentum than expected from the power law relation. The H{\sc i} disks of all these early-type galaxies are misaligned or counter-rotating with respect to the stellar disks, consistent with the gas being recently accreted. We speculate that late stage wet mergers, as well as cold flows play a dominant role in determining the kinematics of the baryonic component of galaxies as suggested by recent numerical simulations., Comment: Accepted for publication in MNRAS.15 pages, 22 figures, 6 tables

We construct mass models of eight gas rich dwarf galaxies that lie in the Lynx-Cancer void. From NFW fits to the dark matter halo profile, we find that the concentration parameters of halos of void dwarf galaxies are similar to those of dwarf galaxies in normal density regions. We also measure the slope of the central dark matter density profiles, obtained by converting the rotation curves derived using 3-D (\fat) and 2-D (ROTCUR) tilted ring fitting routines, into mass densities. We find that the average slope ($\alpha = -1.39 \pm 0.19$), obtained from 3-D fitting is consistent with that expected from an NFW profile. On the other hand, the average slope measured using the 2-D approach is closer to what would be expected for an isothermal profile. This suggests that systematic effects in velocity field analysis have a significant effect on the slope of the central dark matter density profiles. Given the modest number of galaxies we use for our analysis, it is important to check these results using a larger sample., Comment: Accepted for publication in MNRAS, 24 pages, 58 figures, and 6 tables

We present statistical analysis of a fluence limited sample of over 1100 giant pulses from the Crab pulsar, with fluence > 130 Jy ms at ~1330 MHz. These were detected in ~260 hours of observation with the National Centre for Radio Astrophysics (NCRA)-15m radio telescope. We find that the pulse energy distribution follows a power law with index $\alpha\approx$-3 at least up to a fluence of ~5 Jy s. The power law index agrees well with that found for lower energy pulses in the range 3-30 Jy ms. The fluence distribution of the Crab pulsar hence appears to follow a single power law over ~3 orders of magnitude in fluence. We do not see any evidence for the flattening at high fluences reported by earlier studies. We also find that at these fluence levels, the rate of giant-pulse emission varies by as much as a factor of ~5 on time-scales of a few days, although the power law index of the pulse-energy distribution remains unchanged. The slope of the fluence distribution for Crab giant pulses is similar to that recently determined for the repeating FRB 121102. We also find an anti-correlation between the pulse fluence and the pulse width, so that more energetic pulses are preferentially shorter., Comment: 5 pages, 6 figures

We have used the upgraded Giant Metrewave Radio Telescope to carry out a deep (117 on-source hours) L-band observation of the Extended Groth Strip, to measure the average neutral hydrogen (HI) mass and median star formation rate (SFR) of star-forming galaxies, as well as the cosmic HI mass density, at $0.2 < z < 0.4$. This was done by stacking the HI 21cm emission and the rest-frame 1.4 GHz radio continuum from 445 blue star-forming galaxies with $\rm M_B \leq -17$ at $z_{\rm mean} \approx 0.34$. The stacked HI 21cm emission signal is detected at $\approx 7\sigma$ significance, implying an average HI mass of $\rm \langle M_{HI} \rangle = (4.93 \pm 0.70) \times 10^9 \: M_{\odot}$. We also stacked the rest-frame 1.4 GHz radio continuum emission of the same galaxies, to obtain a median SFR of $(0.54 \pm 0.06) \: {\rm M}_\odot$ yr$^{-1}$; this implies an average atomic gas depletion time scale of $\rm \langle \Delta t_{HI}\rangle \approx$ 9 Gyr, consistent with values in star-forming galaxies in the local Universe. This indicates that the star-formation efficiency does not change significantly over the redshift range $0 - 0.4$. We used the detection of the stacked HI 21cm emission signal to infer the normalized cosmic HI mass density $(\rm \rho_{HI}/\rho_{c,0})$ in star-forming galaxies at $z \approx 0.34$. Assuming the local relation between HI mass and absolute B-magnitude, we obtain $\rm \rho_{HI}/\rho_{c,0} = (4.81 \pm 0.75) \times 10^{-4}$, implying no significant evolution in $\rm \rho_{HI}/\rho_{c,0}$ from $z \approx 0.4$ to the present epoch., Comment: 7 pages, 4 figures

Carbon Radio Recombination Lines trace the interface between molecular and atomic gas. We present GMRT observations of Carbon Radio Recombination Lines (CRRL), C$\alpha$244-C$\alpha$250 towards Cassiopeia A. We use a novel technique of stacking the emission lines in the visibility domain to obtain, for the first time, sub-pc resolution optical depth maps of these CRRLs. The emission shows a wide range of spatial and velocity structures, some of which are unresolved within our synthesis beam of 0.29 pc and velocity channel of 0.55 km/s. These variations in the emission optical depth and line width are indicative of inhomogeneity and fragmentation in the intervening Perseus Arm gas. We compare the distribution of the CRRL emission with that of diffuse and dense molecular gas using existing CO and H$_2$CO studies. We find that the CO emission in the -47 km/s Perseus Arm component is primarily concentrated along an elongated structure detected in our CRRL maps, to the south of which lies the high-density molecular clumps traced by H$_2$CO. This spatial distribution of CRRL and molecular tracers is similar to what one would observe for a Photo Dissociation Region (PDR). In the other Perseus Arm component centered at -37 km/s, there is evidence for high column density (N$_{H_2}$ ~ $10^{22}$cm$^{-2}$) molecular clumps embedded in diffuse CO as well as CRRL emission towards the center of Cassiopeia A. We propose that the CRRL emissions coincident with molecular tracers originates from the line of sight integrated component of the C$^{+}$ envelope of the molecular gas., Comment: 11 pages, 7 figures. Accepted for publication in MNRAS

We present a detailed analysis of post-correlation beamforming (i.e. beamforming which involves only phased sums of the correlation of the voltages of different antennas in an array), and compare it with the traditionally used incoherent and phased beamforming techniques. Using data from the GMRT we show that post-correlation beamformation results in a many-folds increase in the signal-to-noise for periodic signals from pulsars and several order of magnitude reduction in the number of false triggers from single pulse events like fast radio bursts (FRBs). This difference arises primarily because the post-correlation beam contains less red-noise, as well as less radio frequency interference. The post-correlation beam can also be more easily calibrated than the incoherent or phased array beams. We also discuss two different modes of post-correlation beamformation, viz. (1) by subtracting the incoherent beam from the coherent beam and (2) by phased addition of the visibilities. The computational costs for both these beamformation techniques as well as their suitability for studies of pulsars and FRBs are discussed. Techniques discussed here would be of interest for all upcoming surveys with interferometric arrays. Finally, we describe a time-domain survey with the GMRT using the post-correlation beamformation as a case study. We find that post-correlation beamforming will improve the current GMRT time-domain survey sensitivity by ~ 2 times for pulsars with periods of few 100s of millisecond and by many-folds for even slower pulsars, making it one of the most sensitive surveys for pulsars and FRBs at low and mid radio frequencies., Comment: 24 pages, 9 figures, accepted for publication in The Astrophysical Journal

We present high resolution H{\sc i} 21cm Giant Meterwave Radio Telescope (GMRT) observations of the superthin galaxy FGC1540 with a spatial resolution of 10$''$ $\times$ 8$''$ and a spectral resolution of 1.73 kms$^{-1}$ and an rms noise of 0.9 mJy per beam. We obtain its rotation curve as well as deprojected radial H{\sc i} surface density profile by fitting a 3-dimensional tilted ring model directly to the H{\sc i} data cubes by using the publicly-available software, Fully Automated Tirrific (FAT). We also present the rotation curve of FGC1540 derived from its optical spectroscopy study using the 6-m BTA telescope of the Special Astrophysical Observatory of the Russian Academy of Sciences. We use the rotation curve, the H{\sc i} surface density profile together with Spitzer 3.6 $\mu$m and the SDSS $i$--band data to construct the mass models for FGC1540. We find that both the Pseudo-isothermal (PIS), as well as Navarro-Frenk-White (NFW) dark matter (DM) halos, fit the observed rotation curve equally well. The PIS model indicates a compact dark matter halo ($R_{\rm C}/R_{\rm D}$ < 2), with the best-fitting core radius ($R_{\rm C}$) approximately half the exponential stellar disc scale length ($R_{\rm D}$), which is in agreement with the mass models of superthin galaxies studied earlier in the literature. Since the vertical thickness of the galactic stellar disc is determined by a balance between the net gravitational field and the velocity dispersion in the vertical direction, the compact dark matter halo may be primarily responsible in regulating the superthin vertical structure of the stellar disc in FGC1540 as was found in case of the superthin galaxy UGC7321., Comment: Accepted for publication in MNRAS