Multi-frequency scatter broadening evolution of pulsars - I

We present multi-wavelength scatter broadening observations of 47 pulsars, made with the Giant Metre-wave Radio Telescope (GMRT), Ooty Radio Telescope (ORT) and Long Wavelength Array (LWA). The GMRT observations have been made in the phased array mode at 148, 234, and 610 MHz and the ORT observations at 327 MHz. The LWA data sets have been obtained from the LWA pulsar data archive. The broadening of each pulsar as a function of observing frequency provides the frequency scaling index, $\alpha$. The estimations of $\alpha$ have been obtained for 39 pulsars, which include entirely new estimates for 31 pulsars. This study increases the total sample of pulsars available with $\alpha$ estimates by $\sim$50\%. The overall distribution of $\alpha$ with the dispersion measure (DM) of pulsar shows interesting variations, which are consistent with the earlier studies. However, for a given value of DM a range of $\alpha$ values are observed, indicating the characteristic turbulence along each line of sight. For each pulsar, the estimated level of turbulence, $C^{2}_{n_e}$, has also been compared with $\alpha$ and DM. Additionally, we compare the distribution of $\alpha$ with the theoretically predicated model to infer the general characteristics of the ionized interstellar medium (ISM). Nearly 65\% of the pulsars show a flatter index (i.e., $\alpha < 4.4$) than that is expected from the Kolmogorov turbulence model. Moreover, the group of pulsars having flatter index is typically associated with an enhanced value of $C^{2}_{n_e}$ than those with steeper index.Comment: 13 pages, 4 figures, 3 tables. Accepted for publication in Ap

Simultaneous multi-frequency single pulse observations of pulsars

We performed simultaneous observations at 326.5 MHz with the Ooty Radio Telescope and at 326, 610 and 1308 MHz with the Giant Meterwave Radio Telescope for a sample of 12 pulsars, where frequency dependent single pulse behaviour was reported. The single pulse sequences were analysed with fluctuation analysis, sensitive to both the average fluctuation properties (using longitude resolved fluctuation spectrum and two-dimensional fluctuation spectrum) as well as temporal changes in these (using sliding two-dimensional fluctuation spectrum ) to establish concurrent changes in subpulse drifting over the multiple frequencies employed. We report subpulse drifting in PSR J0934$-$5249 for the first time. We also report pulse nulling measurements in PSRs J0934$-$5249, B1508+55, J1822$-$2256, B1845$-$19 and J1901$-$0906 for the first time. Our measurements of subpulse drifting and pulse nulling for the rest of the pulsars are consistent with previously reported values. Contrary to previous belief, we find no evidence for a frequency dependent drift pattern in PSR B2016+28 implied by non-simultaneous observations by Oster et al. (1977). In PSRs B1237+25, J1822$-$2256, J1901$-$0906 and B2045$-$16, our longer and more sensitive observations reveal multiple drift rates with distinct P3. We increase the sample of pulsars showing concurrent nulling across multiple frequencies by more than 100 percent, adding 4 more pulsars to this sample. Our results confirm and further strengthen the understanding that the subpulse drifting and pulse nulling are broadband consistent with previous studies (Gajjar et al. 2014a; Rankin 1986; Weltevrede et al. 2007) and are closely tied to physics of polar gap.Comment: 22 pages, 44 figures, Single pulse studies of pulsars, accepted by A&

PONDER - A Real time software backend for pulsar and IPS observations at the Ooty Radio Telescope

This paper describes a new real-time versatile backend, the Pulsar Ooty Radio Telescope New Digital Efficient Receiver (PONDER), which has been designed to operate along with the legacy analog system of the Ooty Radio Telescope (ORT). PONDER makes use of the current state of the art computing hardware, a Graphical Processing Unit (GPU) and sufficiently large disk storage to support high time resolution real-time data of pulsar observations, obtained by coherent dedispersion over a bandpass of 16 MHz. Four different modes for pulsar observations are implemented in PONDER to provide standard reduced data products, such as time-stamped integrated profiles and dedispersed time series, allowing faster avenues to scientific results for a variety of pulsar studies. Additionally, PONDER also supports general modes of interplanetary scintillation (IPS) measurements and very long baseline interferometry data recording. The IPS mode yields a single polarisation correlated time series of solar wind scintillation over a bandwidth of about four times larger (16 MHz) than that of the legacy system as well as its fluctuation spectrum with high temporal and frequency resolutions. The key point is that all the above modes operate in real time. This paper presents the design aspects of PONDER and outlines the design methodology for future similar backends. It also explains the principal operations of PONDER, illustrates its capabilities for a variety of pulsar and IPS observations and demonstrates its usefulness for a variety of astrophysical studies using the high sensitivity of the ORT.Comment: 25 pages, 14 figures, Accepted by Experimental Astronom

Detection of long nulls in PSR B1706−-16, a pulsar with large timing irregularities

Single pulse observations, characterizing in detail, the nulling behaviour of PSR B1706$-$16 are being reported for the first time in this paper. Our regular long duration monitoring of this pulsar reveals long nulls of 2 to 5 hours with an overall nulling fraction of 31$\pm$2\%. The pulsar shows two distinct phases of emission. It is usually in an active phase, characterized by pulsations interspersed with shorter nulls, with a nulling fraction of about 15 \%, but it also rarely switches to an inactive phase, consisting of long nulls. The nulls in this pulsar are concurrent between 326.5 and 610 MHz. Profile mode changes accompanied by changes in fluctuation properties are seen in this pulsar, which switches from mode A before a null to mode B after the null. The distribution of null durations in this pulsar is bimodal. With its occasional long nulls, PSR B1706$-$16 joins the small group of intermediate nullers, which lie between the classical nullers and the intermittent pulsars. Similar to other intermediate nullers, PSR B1706$-$16 shows high timing noise, which could be due to its rare long nulls if one assumes that the slowdown rate during such nulls is different from that during the bursts.Comment: Accepted for publication in MNRA

Multi-frequency scatter broadening evolution of pulsars - II. Scatter broadening of nearby pulsars

We present multi-frequency scatter broadening evolution of 29 pulsars observed with the LOw Frequency ARray (LOFAR) and Long Wavelength Array (LWA). We conducted new observations using LOFAR Low Band Antennae (LBA) as well as utilized the archival data from LOFAR and LWA. This study has increased the total of all multi-frequency or wide-band scattering measurements up to a dispersion measure (DM) of 150~pc\,cm$^{-3}$ by 60\%. The scatter broadening timescale ($\tau_{sc}$) measurements at different frequencies are often combined by scaling them to a common reference frequency of 1\,GHz. Using our data, we show that the $\tau_{sc}$--DM variations are best fitted for reference frequencies close to 200--300\,MHz, and scaling to higher or lower frequencies results in significantly more scatter in data. We suggest that this effect might indicate a frequency dependence of the scatter broadening scaling index ($\alpha$). However, a selection bias due to our chosen observing frequencies can not be ruled out with the current data set. Our data did not favour any particular model of the DM -- $\tau_{sc}$ relations, and we do not see a statistically significant break at the low DM range in this relation. The turbulence spectral index ($\beta$) is found to be steeper than that is expected from a Kolmogorov spectrum. This indicates that the local ISM turbulence may have a low wave-number cutoff or presence of large scale inhomogeneities in the line of sight to some of the reported pulsars.Comment: Accepted for publication in Ap

Lie Symmetry Analysis of the Black-Scholes-Merton Model for European Options with Stochastic Volatility

We perform a classification of the Lie point symmetries for the Black--Scholes--Merton Model for European options with stochastic volatility, $\sigma$, in which the last is defined by a stochastic differential equation with an Orstein--Uhlenbeck term. In this model, the value of the option is given by a linear (1 + 2) evolution partial differential equation in which the price of the option depends upon two independent variables, the value of the underlying asset, $S$, and a new variable, $y$. We find that for arbitrary functional form of the volatility, $\sigma(y)$, the (1 + 2) evolution equation always admits two Lie point symmetries in addition to the automatic linear symmetry and the infinite number of solution symmetries. However, when $\sigma(y)=\sigma_{0}$ and as the price of the option depends upon the second Brownian motion in which the volatility is defined, the (1 + 2) evolution is not reduced to the Black--Scholes--Merton Equation, the model admits five Lie point symmetries in addition to the linear symmetry and the infinite number of solution symmetries. We apply the zeroth-order invariants of the Lie symmetries and we reduce the (1 + 2) evolution equation to a linear second-order ordinary differential equation. Finally, we study two models of special interest, the Heston model and the Stein--Stein model.Comment: Published version, 14pages, 4 figure

A Search for Pulsars in Steep Spectrum Radio Sources

We report on a time-domain search for pulsars in 44 steep spectrum radio sources originally identified from recent imaging surveys. The time-domain search was conducted at 327 MHz using the Ooty radio telescope, and utilized a semi-coherent dedispersion scheme retaining the sensitivity even for sub-millisecond periods up to reasonably high dispersion measures. No new pulsars were found. We discuss the nature of these steep spectrum sources and argue that majority of the sources in our sample should either be pulsars or a new category of Galactic sources. Several possibilities that could hinder detection of these sources as pulsars, including anomalously high scattering or alignment of the rotation and magnetic axes, are discussed in detail, and we suggest unconventional search methods to further probe these possibilities.Comment: Accepted for publication in Ap

Scatter broadening measurements of 124 pulsars at 327 MHz

We present the measurements of scatter broadening time-scales ($\tau_{sc}$) for 124 pulsars at 327 MHz, using the upgraded Ooty Radio Telescope (ORT). These pulsars lie in the dispersion measure range of 37 $-$ 503 pc cm$^{-3}$ and declination ($\delta$) range of $-$57$^{\circ} < \delta< 60^{\circ}$. New $\tau_{sc}$ estimates for 58 pulsars are presented, increasing the sample of all such measurements by about 40% at 327 MHz. Using all available $\tau_{sc}$ measurements in the literature, we investigate the dependence of $\tau_{sc}$ on dispersion measure. Our measurements, together with previously reported values for $\tau_{sc}$, affirm that the ionized interstellar medium upto 3 kpc is consistent with Kolmogorov spectrum, while it deviates significantly beyond this distance.Comment: 19 pages, 4 figures, accepted for publication in Ap