Mode Changing in PSR B0844-35 and PSR B1758-29 with Enhanced Emission at the Profile Centers

We have studied the single pulse emission from two pulsars, PSR B0844-35 and PSR B1758-29, over a wide frequency range of 300–750 MHz using the upgraded Giant Metrewave Radio Telescope. The two pulsars have relatively wide profiles with multiple components, which are a result of the line of sight traversing near the center of the emission beam. In both pulsars, the single pulse sequences show the presence of two distinct emission states, where the profiles become much brighter at the center, with prominent core components during one of the modes, while in the other mode the single pulses show odd–even subpulse drifting with a periodicity of around 2P, P being the rotation period of the pulsar. The centrally bright mode was seen for 10% of the observing duration in PSR B0844-35, which usually lasted for short durations of around 10 pulses, but had two longer sequences of around 100 pulses. On the contrary, the centrally bright mode was dominant in PSR B1758-29 and was seen for around 60% of the observing duration. PSR B1758-29 also showed period amplitude modulations of 60P–70P in both modes. The mode changing in these two pulsars facilitates investigation of the sparking process in the inner acceleration region, dominated by nondipolar magnetic fields. The change in the surface magnetic field configurations likely results in the emission mode change.


INTRODUCTION
The single pulse emission from pulsars show several distinct phenomena that include subpulse drifting, seen as systematic variations of the subpulses within the emission window resembling regular drift bands (Weltevrede et al. 2006;Basu et al. 2016Basu et al. , 2019a;;Song et al. 2023); periodic/quasi-periodic modulations where transitions take place between emission states with different intensity levels (Mitra & Rankin 2017;Basu et al. 2017Basu et al. , 2020b)); nulling or disappearance of the single pulse emission for varying durations (Ritchings 1976;Wang et al. 2007;Gajjar et al. 2012;Basu et al. 2017Basu et al. , 2020b)); and mode changing between two or more distinct emission states at regular intervals (Wang et al. 2007;Geppert et al. 2021;Basu et al. 2021).These phenomena are symptomatic of the physical processes in the pulsar magnetosphere that generate the outflowing plasma responsible for the observed radio emission.The outflowing plasma is generated as a non-stationary flow due to sparking discharges in an inner acceleration region (IAR) above the polar cap (Sturrock 1971;Ruderman & Sutherland 1975).The IAR is characterised by highly non-dipolar magnetic fields with large electric potential difference along the magnetic field lines (Geppert 2017;Arumugasamy & Mitra 2019;Sznajder & Geppert 2020;Pétri & Mitra 2020).
A systematic approach towards understanding the sparking process has been developed in recent years where the IAR resembles a Partially Screened Gap (PSG) with a steady outflow of positively charged ions partially screening the gap potential (Gil et al. 2003).The sparks in the PSG develop due to cascading electron-positron pair production in the large potential difference, where the positrons are accelerated to large energies, Lorentz factor γ ∼ 10 6 , away from the star.The electrons are accelerated downwards and heat the surface to critical temperatures of 10 6 K, which causes the positively charged ions to freely escape from the surface and screen the gap potential (Cheng & Ruderman 1980;Jones 1986).The PSG provides the only known physical model for forming a stable two dimensional system of sparks across the polar cap with well defined perpendicular spark size, that is obtained from the thermal regulation criterion of the IAR (Mitra et al. 2020;Basu et al. 2020cBasu et al. , 2022a)).The sparks have typical lifetimes of several tens of microseconds which is the time required to heat the surface to critical temperature.Effective heat regulation in the PSG requires the sparks to be formed in a tightly packed configuration in the IAR.
During sparking the plasma lag behind the rotation of the star, as the charge density is less than the Goldreich-Julian density, shifting the location of maximum heating.The entire polar cap rotates along with the pulsar around the rotation axis, while all the sparks formed inside the IAR above the polar cap also move around the rotation axis, but with a lower speed than the star, such that in the frame of the polar cap they shift opposite to the direction of rotation.Additionally, the sparks cannot be formed in the closed field line region, hence, the boundary of the polar cap also constrains the next spark to be formed along the boundary.In the plane of the polar cap with the axis located at the center, along the outward normal to the plane, and the equator defined as the diameter along the rotation motion cutting across the polar cap, the sparks in the northern half are formed shifted in the clockwise direction around this axis, while those in the southern half are formed shifted in the anti-clockwise direction.At the equatorial boundary the sparks above and below shifts in opposite directions creating an opening that either grows (leading side) or shrinks (trailing side) with time.Sparking is triggered only when the space is large enough for the spark to form.Near the center of the polar cap, around the axis, due to lack of available space, the sparks do not shift in either direction but appears at the same location at regular intervals (see animations in Basu et al. 2022a, for visualization of the sparking evolution in different polar cap configurations).This sets up a steady drift like pattern in the outflowing plasma with a stationary center.
The primary plasma generated in the sparks at the IAR continues to produce secondary pair particles with Lorentz factor γ ∼ 10 2 outside the gap, making up the outflowing plasma clouds.The radio emission is generated due to non-linear instabilities developing in these outflowing plasma clouds that preserve the imprint of the sparks in the observed emission (Melikidze & Pataraia 1980;Melikidze et al. 2000;Gil et al. 2004;Mitra 2017;Lakoba et al. 2018;Rahaman et al. 2020Rahaman et al. , 2022a,b),b).The drift pattern in the spark dynamics is observed as subpulse drifting in the single pulse emission (Basu et al. 2020c).Hence, it is possible to find suitable estimates for the physical parameters of the IAR, like the average screening factor of the electric potential difference in a PSG, the structure of surface non-dipolar magnetic fields, etc., from the pulsar subpulse drifting measurements (see Basu et al. 2023b, for details).The evolution of the sparking system in the IAR is also evident in the average profiles of the pulsar population.The pulsar radio emission beam has been described using the core-cone model, where the average emission has the form of a central core and two rings of nested conal emission, namely, the inner and outer cones (Rankin 1990(Rankin , 1993;;Mitra & Deshpande 1999).The average profile shape depends on the line of sight (LOS) traverse across the beam, with central LOS cuts giving rise to core-cone Triple (T) and core-double cone multiple (M) types, while the shape resembles conal Quadruple ( c Q), conal Triple ( c T), double (D) and conal single (S d ) as the LOS moves further away from the center.It has been observationally confirmed that no drifting behaviour is seen in the central core component and only appears in the surrounding cones (Basu et al. 2019a(Basu et al. ,b, 2020a)), as expected from the evolution of sparking pattern in the PSG.
The other modulation features seen in the single pulse sequence, like mode changing, nulling and periodic modulations, are associated with change in the radio emission behaviour across the entire profile window, usually over timescales of less than a rotation period.It is likely that such variations are a result of small scale changes in the surface non-dipolar field configuration, with the global dipolar magnetic field remaining unchanged.The physical mechanism that can cause such transitions between the different magnetic field configurations is still not well understood.There are proposals for introducing perturbations by the Hall drift and thermoelectrically driven magnetic field oscillations that can account for such fast changes (Geppert et al. 2021).
In this work we investigate the the single pulse behaviour of two pulsars PSR B0844-35 and PSR B1758-29 with multiple components in their average profiles.Both pulsars have been reported to show emission mode changing as well as subpulse drifting in their single pulse sequence (Wang et al. 2007;Basu et al. 2016Basu et al. , 2021)).We have observed the long sequences of single pulses from these two sources over a wide frequency range to explore the connection between these two phenomena.This will enable the characterisation of the surface properties in the IAR, including the PSG parameters and the surface magnetic field configuration.In section 2 we report the observational details.Section 3 presents the single pulse and average profile behaviour of PSR B0844-35 while the equivalent studies for PSR B1758-29 is reported in section 4. Finally, a discussion of the physical properties in these two systems are carried out in section 5, including the changes of the PSG parameters required for the different emission states.However, a detailed modelling of the surface properties based on the observations requires a separate study dedicated to this problem.

OBSERVATION AND ANALYSIS
We have carried out single pulse observations of PSR B0844-35 and PSR B1758-29 using the wideband receivers of the upgraded Giant Meterwave Radio Telescope (u-GMRT, Gupta et al. 2017).The GMRT consists of 30 antennas, with 14 antennas located within a central square kilometer area, while the other 16 antennas are spread out in a Y-shaped array with maximum distance of 27 kilometers.The high time resolution observations for pulsar studies are carried out by combining the signals from several antennas into a Phased-Array, ensuring higher detection sensitivity for the single pulses.It is also possible to form two or more Sub-Arrays from different antenna configurations, where each Sub-Array can operate at different frequency bands.We have used different observing setups to measure the single pulse emission from both pulsars.Initially, the pulsars were observed in the Phased-Array mode comprising of 22 antennas, the 14 central square antennas and first 2/3 arm antennas, over a 200 MHz frequency range between 300-500 MHz, for relatively shorter durations.The single pulses were clearly detected during these studies which prompted subsequent longer observations in the dual Sub-Array mode at two different frequency ranges of 200 MHz bandwidth each, resulting in wider, near continuous, frequency coverage of 400 MHz between 300 MHz and 750 MHz.The first Sub-Array was setup between frequencies of 300-500 MHz, and consisted of 14 antennas equally divided between the central-square and arm antennas.The second Sub-Array operated between the frequency range of 550-750 MHz and consisted of 10 antennas, 7 from the central square and one from each arm.A strong nearby point-like source was observed before the start of the observations to correct for the phase deviations in each antenna response, thereby maximizing the detection sensitivity of the single pulses after the measurements from each antenna were co-added, a process known as phasing of the antennas.Table 1 lists the basic physical properties of each pulsar and the details of the observing setup including the dates of observations, the observing mode and total single pulses recorded during each observation, and emission mode statistics discussed in the next section.PSR B0844-35 was observed in the Phased-Array mode on 27 December, 2018 for a total of 1860 single pulses and later another 3780 single pulses were observed in the dual Sub-Array mode on 17 January, 2020.PSR B1758-29 was observed in the Phased-Array mode on 18 March, 2019 for a total of 2100 single pulses.On 10 February, 2020 the pulsar was once again observed in the dual Sub-Array mode for 5271 single pulses, with a 10 minute phasing interval in between.The lower frequency observations on this day, between 300-500 MHz, were affected by radio frequency interference (RFI) and could not be used for the single pulse studies.
The polarization properties of the incident signals from the pulsars were recorded in the auto and cross-correlated form.The 200 MHz frequency bandwidth was divided into 2048 channels.A number of intermediate analysis were carried out to obtain a properly calibrated polarized single pulse sequence from the time series signals recorded during each observing session.The polarized signals were suitably calibrated and converted into the well known four Stokes parameters (I, Q, U, V), for each spectral channel (see Mitra et al. 2016, for details).Further analysis involved removal of RFI affected signals from the time sequence as well as narrow frequency channels (Mitra et al. 2016;Basu et al. 2016).The delay of the pulse emission across the frequency band due to dispersion in the interstellar medium was corrected using the known dispersion measure of each pulsar (see Table 1), and averaged over five separate sub-bands each of 30 MHz bandwidths centered around 315 MHz, 345 MHz, 397 MHz, 433 MHz and 468 MHz, respectively, for the lower frequency band, and similarly into five sub-bands at the upper frequency band centered around 576 MHz, 610 MHz, 643 MHz, 676 MHz and 709 MHz, respectively, to study the frequency evolution of the emission properties.The sub-bands are not equispaced due to the presence of narrow band RFI that were discarded.The I-Stokes parameter of the single pulse sequence was re-sampled to form a three-dimensional pulse stack and represented in plots with the rotation phase along the x-axis, the pulse number along the y-axis and the intensity level signified by a colour scale (Basu et al. 2016).The single pulse analysis pertaining to subpulse drifting, nulling, periodic modulation and emission mode changing were carried out using the plots of the pulse stacks.On the other hand the average profiles from the remaining three Stokes parameters were used to estimate the linear and circular polarization levels across the emission window, while their single pulse sequences were used for detecting the presence of orthogonal polarization modes and estimating the polarization position angle (PPA) for emission height and LOS geometry studies.Below we report the results of the single pulse analysis of each pulsar.

Emission States
The single pulse emission properties of PSR B0844-35 was initially reported in Wang et al. (2007) based on observations at 1.5 GHz using the Parkes 64-m radio telescope.The pulsar was also part of the Meterwavelength Polarimetric Emission Survey (MSPES, Mitra et al. 2016), where polarized single pulses were observed at 325 MHz and 610 MHz using the GMRT, and the mode changing behaviour was studied in Basu et al. (2021).The pulsar has four components in the average profile of the primary emission state termed as mode A, with the second component showing a wider composite structure, and has been tentatively classified as a conal only profile of c Q type.The earlier studies also reported the presence of a short-duration mode B, lasting between 10-20 periods at a time, with the emission becoming brighter for the second component while the remaining components were much weaker during this mode.
We identified the mode changing behaviour in this pulsar over the different observing sessions by careful visual inspection of the single pulse sequences in the pulse stacks and detected the two emission modes.The mode changing was simultaneously seen across the entire frequency range, between 300 MHz and 750 MHz, highlighting its broadband nature.Table 2 shows in detail the sequence of the emission modes during each observing session, and the average statistics of the modes are reported in Table 1.Mode A was seen for around 90 percent of the observing duration and lasted for several hundred periods at a time.In the remaining 10 percent of time the pulsar switched to Mode B, which typically lasted for 20-30 periods.In addition to the short duration modes we also detected two instances, out of 17 transitions to mode B, when the mode was seen for longer durations in excess of hundred rotation periods, once during each observing session.The left panel in Fig. 1 shows a pulse sequence during mode A while the right panel shows the long sequence of mode B during the first observing session.Fig. 2 shows the average profiles of the two modes at two widely spaced frequency bands.The single pulse emission during mode A shows the presence of odd-even drifting pattern (see section 3.2).The wider second component shows bifurcation at the lower frequencies (see Fig. 2, left panel), which suggest the appearance of the central core component which is otherwise masked by the leading inner cone.At higher frequencies there is no clear separation between the inner cone and the core.The single pulse emission also shows certain instances where the core appears to flare up, similar to certain pulsars with partial cone profiles (Mitra & Rankin 2011) and central flaring seen in a few cases with D type profiles (Young & Rankin 2012).The estimated average profile from 41 pulses on the first observing session, where the core emission flares up is shown in Fig. 3.The leading inner cone is much weaker during these pulses, thereby the core becomes clearly visible (see Fig. 3 between longitude range -10 • and -5 • ).The core also appears to be more prominent at the low frequency emission of mode B where the conal components are suppressed (see Fig. 2, right panel, profile at 345 MHz in red).However, due to the differential spectral evolution of the core and the conal components, with the core having a steeper spectral index than the inner cone (Basu et al. 2021(Basu et al. , 2022b)), a clear transition in the mode B profile shape takes place above 450 MHz, with the inner cone becoming comparable and hiding the core.
The evolution of the profile widths as a function of frequency during the two emission states is reported in Table 3, including the width estimated at 5 times the noise rms level (W 5σ ), the width at 10 percent (W 10 ) and 50 percent (W 50 ) of the peak intensity of the outer most components on either side of the profile, and the separation between the inner (W in sep ) and outer (W out sep ) conal pairs, where the peak position of each component is identified by locating the centroid.The effect of radius to frequency mapping along dipolar magnetic field, i.e. lower frequencies originating higher up the pulsar magnetosphere, is evident in the profile widths of mode A as well as the separation between the outer conal components (Mitra & Rankin 2002).However, the separation between the inner cones do not show any significant change with varying frequency, which also agrees with earlier measurements in a number of other pulsars.In case of mode B the conal components become relatively weaker and the separation between the conal pairs could not be measured.The evolution of the profile shape due to the relative spectral difference between the core and conal emission also become evident in the W 50 measurements, which shows an increase between the 433 MHz and 468 MHz profile widths.
In the 2 hour observations of Wang et al. (2007), the authors did not detect the presence of nulling in this pulsar.We did not find any systematic nulling behaviour in this pulsar, even during the more sensitive observations on 27 January, 2018, at the 300-500 MHz band, which agrees with the earlier results.There were 16 pulses where the emission was below the detection limit which puts the upper limit for the nulling fraction to be below 1 percent.However, these were likely a result of the stochastic variations expected from the emission mechanism (Rahaman et al. 2020(Rahaman et al. , 2022a   Mitra et al. 2023a), and not associated with changes in the polar cap configuration, that we believe is the likely cause of nulling in pulsars (Geppert et al. 2021).

Subpulse Drifting
The presence of subpulse drifting in PSR B0844-35 was detected in drifting studies of the MSPES sample (Basu et al. 2016(Basu et al. , 2019a)).However, these studies did not explore the drifting properties of the individual modes.The periodic variations associated with the subpulse drifting behaviour is measured using the mathematical technique of fast Fourier transforms (FFT).The FFT is carried out for a sequence of numbers signifying the emission intensity of consecutive single pulses at a given longitude in the emission window.This process is repeated for all longitudes within the profile window to form the longitude resolved fluctuation spectra (LRFS, Backer 1973).The LRFS for a sequence of pulses in the two emission modes of PSR B0844-35 is shown in Fig. 4. The periodic behaviour is seen as a peak frequency (f p ) in the LRFS of mode A (left panel).The periodicity of subpulse drifting is P 3 (1/f p ) = 2.03±0.03P, which is visible as a odd-even drift in the single pulse sequence and is consistent with the earlier estimates (Basu et al. 2016).On the contrary no clear periodic behaviour is seen in the LRFS of mode B (Fig. 4, right panel), although there is a possibility of a wide feature between 0.3-0.4cy/P , particularly in the leading side of the window.The presence of clear drifting behaviour cannot be confirmed in this mode.
The LRFS also measures the relative phase variations (ψ) of the subpulses across the longitude range of the profile (see top window in Fig. 4), that represents the relative motion of the sparks in the IAR along the LOS cuts.The phase variations can be measured with more sensitivity using the time varying fluctuation spectra over the entire observing sequence (Basu & Mitra 2018b).The LRFS was initially estimated for 256 pulses from the start of the observing session.The starting point was shifted by 50 periods and the next set of 256 pulses were used for the LRFS, with the process continued till the end of the observing run.The average drift phase, at each pulse longitude, from all these independent measurements has been estimated as shown in Fig. 5, for the two wide frequency bands 300-500 MHz (left panel) and 550-750 MHz (right panel).The pulsar profile at both frequency bands were aligned such that   the central longitude (ϕ = 0 • ) coincided with the profile peak, i.e. the peak of the trailing inner conal component.
We have only included the average phase measurements in the longitudes where significant detection of the drifting behaviour were recorded.Hence, the phase measurements are missing in the central composite component consisting of the leading inner cone and the core, where drifting features are not clearly visible.The increased sensitivity of the wideband observations has revealed more details in the drifting phase behaviour, particularly at the boundary between the components, compared to previous studies (Basu et al. 2019a).he phase variations across the leading outer conal component show a smooth, shallow positive slope.The phase behaviour become more complicated in the trailing half of the profile comprising of the trailing inner and outer cones.On closer inspection two short sections can be seen where the phase variations are roughly linear that coincide with the location of the two component peaks.In case of the third component the linear sections are between ϕ = −1.1 • and ϕ = 1.0 • at 300-500 MHz, and between ϕ = −1.4• and ϕ = 1.0 • at the 550-750 MHz band.While in the trailing fourth component the linear behaviour is seen between ϕ = 3.8 • and ϕ = 7.1 • at the 300-500 MHz frequency band, and between ϕ = 3.6 • and ϕ = 6.9 • in the upper 550-750 MHz band profile.However, at the boundary of the different components the phase behaviour shows deviation from the linear behaviour.At the border between core and the inner cone, around ϕ = −2 • , and at trailing edge of the outer cone only for the lower frequency band, around ϕ = 8 • , the phases show a turnover with a negative slope, while at the boundary between the inner cone and the outer cone, around ϕ = 2 • , the phases show a bell shaped curve.
The variations seen around the boundary do not reflect any systematic variations due to drifting, but arises due to the overlapping nature of these regions with contributions from two disjointed sides.In some single pulses, emission from one side dominate while at other times the other side becomes prominent, resulting in the bell shaped behaviour.Such phase behaviour with a bell shaped or U-shaped curve is also evident in some pulsars with periodic amplitude modulation, like PSR B0823+26, B1642-03, etc., where instead of showing systematic shift of the subpulses across the emission window, the entire emission becomes narrower and wider in a periodic manner (Basu & Mitra 2019).Table 4 reports the measurement of the average drifting properties in the two frequency bands, including f p , P 3 and the width of the drifting frequency feature at 50 percent level of the peak value (F W HM ).The table also lists the longitude range (∆ϕ) across each profile component where the phase behaviour shows linear nature, and the gradient of the phase variations across this longitude range (dψ/dϕ).The phase gradients show evolution between the two frequency bands, with the high frequency measurements showing steeper gradients, almost a factor of two higher.The change in the drift phase behaviour with frequency has been reported in PSR B0809+74 (Hassall et al. 2013), having S d profile shape with peripheral LOS cuts across the emission beam.Our results show that such variations can also be detected in pulsars with central LOS traverse.

Polarization Properties and Emission Height
The polarization behaviour across the average profiles of PSR B0844-35 is shown in Fig. 6, where both emission modes are shown in the same plot, with left panel showing the average behaviour over 300 to 500 MHz frequency range while the right panel between 550 and 750 MHz.Each panel in the figure comprises of three parts, representing the total intensity profiles (top window), the linear polarization (middle window), and the circular polarization (bottom window) across the two profiles.The presence of the core emission at the center of the profile is highlighted by the decrease in the linear polarization level as well as change in the sign of the circular polarization (Mitra et al. 2007;Smith et al. 2013).The profiles of both emission modes at each frequency range have been aligned with respect to a common center, identified from the polarization position angle (see below) to compare their relative locations.The figure shows that the emission window, including the location of the individual components, remains the same in both modes A and B, suggesting that the location of the radio emission is not affected by mode changing in this pulsar.
The polarization position angle (PPA) for the single pulse time samples with significant polarization detection is shown in Fig. 7 (see Mitra et al. 2023a,b, for more details about making these plots).The average PPA resemble the  characteristic S-shaped curve that follows the rotating vector model (Radhakrishnan & Cooke 1969), although certain deviation from the RVM nature is seen particularly in the core region due to presence of orthogonal polarization modes (Mitra et al. 2007;Smith et al. 2013;Brinkman et al. 2019;Mitra et al. 2023a,b).The single pulse plots of the PPA generally show time samples with significant detection of polarization power.In case not enough such time samples are available, the orthogonal polarization modes are not clearly visible in these plots, although the deviations of the average profile PPAs from the RVM can still be a result of these invisible orthogonal mode mixing.More sensitive observations are required in such cases to detect the polarization modes in the single pulse plots.The RVM, in the static dipole approximation, gives an estimate of the PPA, χ, as a function of the pulse longitude, ϕ, using the angle between the magnetic and rotation axes, α, and the angle of closest approach of the LOS to the magnetic axis, β, in the form : Here, χ • and ϕ • are the arbitrary phase offsets in the PPA and the profile longitude, respectively.The RVM model for the PPA are also shown in Fig. 7 (pink dashed line) and closely matches the observed behaviour, except the core region in mode B. Although the geometrical angles, α and β, cannot be fixed from RVM fits due to highly correlated solutions (Everett & Weisberg 2001;Mitra & Li 2004), the steepest gradient (SG) of the RVM, | dχ/dϕ | max , and its location specified by ϕ • (black point with error bar in Fig. 7) can be used to find estimates of the radio emission height.It has been shown that for the emission heights less than 10% of the light cylinder distance, the aberration and retardation effects, arising from pulsar rotation, causes a positive shift in ϕ • with respect to the the center of the profile, ϕ c , and the shift ∆ϕ = ϕ • − ϕ c , is proportional to the emission height, h A/R , (Blaskiewicz et al. 1991;Dyks 2008) The estimation of ϕ c requires identifying two longitudes, ϕ l and ϕ t , at the leading and trailing edge of the profile corresponding to the last open field line, such that ϕ c = ϕ l + (ϕ t − ϕ l )/2.In practice ϕ l and ϕ t are identified as the longitudes on either edge of the profile that are above the detection limit, i.e. above five times the baseline noise rms level.Table 5 shows the measurement of the relevant quantities and emission heights for the two modes A and B, estimated over the two observing frequency ranges, 300-500 MHz and 550-750 MHz.In both modes the radio emission originates a few hundred kilometers above the neutron star surface, that is consistent with the height estimates in the normal pulsar population (Mitra 2017;Mitra et al. 2023b).The height estimates are affected by errors arising from identifying the SG point due to depolarization of the core component, particularly in mode B, as well as the identification of the profile edges due to detection sensitivities.Although the wideband measurements provide improved sensitivity for the edge detections, the emission heights should be used as suggestive for the location of the radio emission in the pulsar magnetosphere, rather than exact estimates.

Emission States
PSR B1758-29 was observed at 325 MHz and 610 MHz as part of the MSPES sample for around 2000 pulses at both frequencies (Mitra et al. 2016).The average profile was classified as type T with a central core component and one pair of conal emission on either side of the core.Basu et al. (2021) reported the presence of two emission modes in the MSPES single pulse sequence, classified as bright (B) mode and quiet (Q) modes.The emission in the central core region dominates during mode B but becomes greatly reduced during the Q mode.Further analysis of the mode behaviour, including mode statistics, was not possible due to the the weaker detection sensitivity of the single pulse emission, particularly during mode Q, from these narrow band observations.The higher sensitivity wideband observations have allowed a detailed study of mode changing in this pulsar.
Fig. 8 shows two pulse sequences representing the two emission states, mode B (left panel) with bright central core, and mode Q (right panel) where both the core and the trailing conal components become much weaker, average of the intensity of the core and the conal emission, where the cores have a steeper spectra compared to the cones, with a relative difference in the spectral index ∆α core/cone = −0.9(see Basu et al. 2021Basu et al. , 2022b, for details).
After perusing through the single pulses on each observing session we have identified the sequences of the two modes as reported in Table 9, while Fig. 10 shows the mode length distributions, combining the two observing sessions.The average statistics of the modes are reported in Table 1 and unlike PSR B0844-35 the durations of the two modes are more comparable, with mode B being about 40-50 percent longer than the Q mode on an average.PSR B1758-29 spends around 60 percent of its time in mode B and the remaining 40 percent in mode Q.The mode lengths usually lasted for a few hundred pulses for both modes and did not exceed 500 pulses during the two observations (see Fig. 10).
The evolution of the profile widths as a function of frequency during the two emission states is reported in Table 7, including the width estimated at 5 times the noise rms level (W 5σ ), the width at 10 percent (W 10 ) and 50 percent (W 50 ) of the peak intensity of the outer most components on either side of the profile, and the separation between the outer (W out sep ) conal pair.The inner conal pair was visible in the Q mode and we estimated the separation between them (W in sep ), however, due to the lower intensity of the trailing outer cone the W 10 could not be estimated in this case.The effect of radius to frequency is once again visible in the frequency evolution of W 10 , W 50 and W out sep .The separation between the inner conal pair usually do not show any change with frequency.At the higher frequency range above 550 Hz W in sep remains constant, but shows a jump below this frequency.This is due to the difficulty in identifying the location of the inner conal component peaks as the they become relatively weaker, compared to the core and the outer cones at lower frequencies, and merge with the outer cones.The W 50 and W out sep estimates show that the profile window becomes wider as the pulsar transitions from the B mode to the Q mode.
The average energy distribution of the single pulses in the B and the Q modes is estimated for the two frequency bands and shown in Fig. 11.The pulse energies show a log-normal distribution in both emission states with a prominent tail.The plots also highlight the B mode to be more energetic than the Q mode with a much longer tail in the distribution.The distribution of the B mode at both frequencies show a bimodal structure with a second peak coincident with the baseline noise distribution, estimated in the off-pulse region, suggesting the presence of nulling.However, the presence of numerous lower energy pulses did not allow the identification of the individual null pulses within the B mode sequences, either using statistical estimates or visual inspection.The nulling fractions can be estimated using Gaussian fitting techniques to the off-pulse and the null distributions of the B mode (Basu et al. 2017).We found the upper limits of the nulling fraction to be 4.9±0.6 percent at the lower frequency and 4.1±0.4percent at the higher frequency.The nulling fractions over the two observing sessions are consistent within measurement errors and the variations can be attributed to the different observing durations and detection sensitivities.There were no clear separation between the null and the burst pulses in the Q mode distributions.Although it is likely that the Q mode also exhibits nulling, more sensitive observations are required to study the nulling behaviour in this mode.

Subpulse Drifting and Periodic Modulation
The presence of subpulse drifting in PSR B1758-29 was reported in the MSPES study of Basu et al. (2016), where periodic repetition with P 3 ∼ 2.5P was found without any significant change in the drift phase across the pulse window.We have used the LRFS technique to measure the periodic variations of the wideband observations at the two frequency ranges.The two emission modes show different periodic behaviours in their pulse sequences.Fig. 12(a) shows the LRFS corresponding to a pulse sequence in mode B and has a clear low frequency feature across the entire profile window, with relatively flat phase variations.This feature confirms the presence of periodic modulation in this pulsar that has not been reported in earlier studies.The short duration drifting feature is not visible in the LRFS suggesting the absence of systematic drifting during mode B, although the pulse sequence (see Fig. 8, left panel) might exhibit short bursts of periodic behaviour during this mode.Fig. 12(b) shows the average LRFS of mode Q from the 18 March, 2019 observations in the lower frequency band and shows the presence of prominent peak in the spectra around f p ∼ 0.4 cy/P .This is primarily seen in the bright leading conal component with a flat phase variation across it, and The pulse between 15 and 185, in mode Q, showing the presence of both subpulse drifting as well as periodic modulation.The phase behaviour corresponding to subpulse drifting in this pulsar is also flat but limited to primarily the leading component.
is consistent with the subpulse drifting behaviour reported in the earlier work.Fig. 12(c) shows the LRFS of a pulse segment during Mode Q, with both subpulse drifting, seen as a high frequency peak, as well as periodic modulation as a low frequency feature, being present.The periodic modulation, that is usually a quasi-periodic behaviour, is seen across both modes of the pulsar, but systematic subpulse drifting is only present during the Q mode.The periodic modulation in pulsars is further divided into two categories, periodic nulling, where the single pulses transition between null and burst states in a quasi-periodic manner, and periodic amplitude modulation, where the transition happens between two emission states of varying intensity (Basu et al. 2020b).There are around 30 pulsars that have periodic nulling in their pulse sequence while around 20 with periodic amplitude modulation.Out of these there are around 15 pulsars that have both period modulation and subpulse drifting in the same system.PSR B1758-29 is another addition to this select group.In almost all of these cases periodic nulling and subpulse drifting coexist, with the only exception being PSR B1737+13 (Force & Rankin 2010), also with an M type profile, where periodic amplitude modulation and subpulse drifting are seen together.In case of PSR B1758-29 we were not able to clearly identify the null pulses due to the presence of low intensity single pulses.It is more likely that the low frequency periodic modulation are a form of periodic amplitude modulation and not periodic nulling.In case of the Q mode the low frequency feature is most prominent when the short bursts of centrally bright pulses appear (see Fig. 8, right panel).These bursts typically repeat at intervals of 50-80P that matches the periodic modulation feature.Similarly, in case of the B mode there are regular intervals of bright and weaker pulses, where the weak regions may have some nulls in them but also exhibit low level emission.However, studies with higher sensitivity will be required to clearly identify the null pulses in both emission modes and find conclusive evidence for the exact nature of periodic modulation in this pulsar.
Table 8 reports the measurement of the periodic behaviour in the two frequency bands.This include f p and F W HM for both the subpulse drifting and periodic modulation, the periodicity of drifting, P 3 , the longitude range of the leading component where the drifting behaviour is seen with sufficient sensitivity, ∆ϕ, as well as the slope of the drift phase over this range, dψ/dϕ, and the periodicity of amplitude modulation, P M .The estimated P 3 is around 2.4P which matches earlier estimates and dψ/dϕ is close to zero at both frequencies, underlying the flat nature of the phase variations.The P M at both emission modes varies between 60-70P and shows fluctuations with the feature becoming stronger at certain intervals and less prominent at other times.

Polarization Properties and Emission height
The average polarization behaviour of PSR B1758-29 is shown in Fig. 13, for the 300-500 MHz frequency band (left panel) and the 550-750 MHz band (right panel).Both the B and the Q mode properties are superposed on the same plots showing the total intensity profiles (top window), the linear polarization behaviour across the profile (middle window) and the circular polarization (bottom window).The primary difference between the two modes is encapsulated by the presence of the core component during mode B and its absence during the Q mode, and the associated depolarization at the center of the profile in mode B as well as the sign changing circular polarization behaviour.The profiles of the two modes were aligned using a common reference point estimated from the SG point of the PPA obtained from highly polarized time samples, to minimize the effects of polarization mode mixing (see Mitra et al. 2023a, for a detailed discussion).Similar to PSR B0844-35 we find the emission region to remain identical in the two modes, both for the average profile and the individual components, with the exception of a slight flaring seen in the trailing edge of the 550-750 MHz profiles of the Q mode.These results show that the location of the emission region remains unchanged during the mode transition in PSR B1758-29.
Fig. 14 shows the PPA estimates from the significant time samples of the single pulses, both both modes and frequency bands.The average PPA in all cases could be estimated using the RVM and the fits are shown in the plots (dashed pink line) along with the SG point (black dot with error bars).Table 9 reports the measurement of the different quantities associated with the emission height estimates of modes B and Q at 300-500 MHz and 550-750 MHz frequencies, including ϕ o , ϕ l , ϕ t , ϕ c , ∆ϕ and h A/R .The estimated emission heights are around few hundred kilometers and agrees with the general trend.The height estimates of mode Q at 550-750 MHz are indeterminate because of the flaring in the trailing side of the profile which shifts ϕ c towards ϕ o , thereby reducing ∆ϕ (see eq. 2).

DISCUSSION
The analysis of the single pulse behaviour in PSR B0844-35 and PSR B1758-29 have revealed the properties of the emission modes, with certain similarities that are seen on rare occasions in pulsars.Both pulsars have the presence of    two distinct emission modes, with one mode showing increased intensity of the core component in the profile center.
In both cases subpulse drifting is seen in the emission mode with the lower intensity core emission, with periodicity close to 2P .The single pulse emission becomes more chaotic with increased core activity and the well ordered drifting behaviour vanishes.Additionally, in the weaker state the core emission is usually faint, but shows short bursts of flaring from time to time.There are many similarities between the mode changing behaviour of these two pulsars and PSR B1237+25, that also has a M type profile (Srostlik & Rankin 2005;Smith et al. 2013).The leading part of the profile in PSR B1237+25, including the core component, shows increased emission during the abnormal mode, but the central core emission is much weaker during the normal mode apart from instances of flaring.The pulsar also shows the presence of subpulse drifting with large phase variations similar to PSR B0844-35.Another prominent example of M type profile associated with mode changing is PSR B2003-08 (Basu et al. 2019b), where the pulsar has four emission modes, modes A and B with central core and showing subpulse drifting, mode D also with prominent core and showing periodic modulation in the form of periodic nulling, and an additional mode C with weaker core but the single pulses have periodic nulls.Our studies have now doubled this unique set of pulsars that exhibit mode changing and subpulse drifting in a system that has core component in the average profile.
In both modes of the two pulsars we have found profile widths to change with frequency (see Table 3 and 7), representing the so called radius to frequency mapping, where the lower frequency profiles become progressively wider (Mitra & Rankin 2002).The radius to frequency mapping is a feature of the coherent curvature radiation along the diverging dipolar open magnetic field lines (Gil et al. 2004;Mitra et al. 2009), where the characteristic frequency (ν) of emission is ν ∼ γ 3 /ρ c , here γ is the Lorentz factor of the plasma responsible for the emission and ρ c is the radius of curvature of the dipolar field lines.As the magnetic field lines diverge with distance from the neutron star surface, ρ c increases.If we consider γ to be constant, i.e., the same plasma is responsible for all frequencies, then the lower frequencies are associated with higher values of ρ c , and are emitted further away from the surface.If we assume the profile edges to be associated with the last open field lines then the radius to frequency mapping is a result of the lower frequency emission being emitted at higher heights due to the curvature radiation mechanism.
We also found the location of the radio emission region in the two pulsars to remain largely unchanged during the mode transition.This result is consistent with previous reports of mode changing behaviour in several pulsars like, PSR B0329+54 (Brinkman et al. 2019), PSR B1819-22 (Basu & Mitra 2018a), PSR B2003-08 (Basu et al. 2019b), and PSR B2319+60 (Rahaman et al. 2021), where the radio emission heights were also shown to be constant in the different modes.We detected short duration flaring in the core region of the Q mode profile of PSR B1758-29, as well as the trailing edge of the profile, primarily at the higher frequency range.There are intriguing possibilities regarding the origin of such flaring, with the emission arising at slightly different heights in certain parts of the emission beam, or possibility of partial illumination of the emission beam as seen prominently in the partial-cone pulsars (Mitra & Rankin 2011).In the PSG model the properties of the outflowing plasma, including the Lorentz factor, is determined by the screening factor (η) in the IAR.It has been suggested that the mode changing arises as a result of changes introduced in the local magnetic field configuration of the IAR, due to perturbations introduced by Hall drift and thermoelectrically driven magnetic field oscillations (Geppert et al. 2021).These changes are likely to change the η in the gap which in turn can result in different values of γ for the two modes.Further exploration of these ideas, including flaring at different parts of the profile, would require rigorous works concerning the the nature of the outflowing plasma arising due to thermal regulation in the PSG.
The wideband observations have allowed a detailed characterisation of the subpulse drifting behaviour in the mode A of PSR B0844-35.The pulsar shows large phase variations across the different profile components, in the leading outer cone as well as the trailing conal pair.These measurements have also revealed the effect at the component boundaries, where jumps and reversals in the phase variations are seen.These effects seem to be different from the bi-drifting and phase switching behaviour seen in certain pulsars, where the phase behaviour across the entire component show reversal or jumps compared to other components and not just at the boundary between components (Champion et al. 2005;Weltevrede 2016;Szary & van Leeuwen 2017;Basu & Mitra 2018b;Basu et al. 2019a).The most likely explanation for the boundary jumps in the drifting phase is the overlapping of the subpulses belonging to two different drift sequences in the adjoining components, that are unconnected in their phase behaviour.Similarly, flaring of the emission at the extreme edge of the profile at certain intervals lead to additional reversals in the phase at the profile boundaries.The drift phase behaviour in the Q mode of PSR B1758-29 could only be measured in the leading component and shows flat behaviour across it, which is very different than PSR B0844-35.However, it is possible that the inner components may have large phase variations, like the drifting behaviour in PSR B2003-08 (see Fig. 9 in Basu et al. 2019b), and would require more sensitive observations for detection.
The complex phase behaviour in PSR B0844-35 suggests that surface magnetic field configuration is non-dipolar in nature.A prescription for modelling the non-dipolar magnetic field configuration of surface polar cap with an elliptical boundary has been proposed by Basu et al. (2023b), where the complicated bi-drifting behaviour in PSR J1034-3224 has been reproduced from the sparking mechanism developing in a PSG (Mitra et al. 2020;Basu et al. 2020c).Additional constraints to this model is provided by the frequency evolution of subpulse drifting measured in this pulsar, where the phase variations across each component show steeper gradient with increase in frequency.This effect can once again be related to the radius to frequency mapping, where at higher frequencies the LOS traverses the outer region of the emission beam, and thereby samples a different trajectory across the evolution of the sparking pattern in the IAR.Thus in effect the measurement of the drifting features at multiple frequencies builds up a two dimensional map of sparking process in the IAR and shows the importance of multifrequency studies in understanding the drifting behaviour in pulsars.A detailed modelling of the drifting behaviour in PSR B0844-35 using the PSG model would need to incorporate the various observational details uncovered in this work and requires a separate dedicated study.

Figure 1 .Figure 2 .
Figure 1.The left panel shows the single pulse sequence corresponding to mode A of PSR B0844-35, observed on 27 January, 2018, and represents the pulse range between 625 to 725 from the start of the observing session averaged over the 300-500 MHz frequency band.The right panel shows the 300-500 MHz frequency averaged pulse sequence also observed on 27 January, 2018, between pulses 280 and 360, belonging to mode B.

Figure 3 .
Figure3.The average profile from selected pulses where there is flaring in the core emission.

Figure 4 .
Figure 4. Longitude resolved fluctuation spectra (LRFS) to estimate the drifting behaviour in the two modes of PSR B0844-35.The left panel shows the LRFS for a pulse sequence of 180 periods in mode A and the right panel shows the LRFS of mode B for 102 pulses.A peak frequency due to subpulse drifting with periodicity ∼ 2P is seen during mode A, while mode B do not show any clear periodic behaviour.

Figure 5 .
Figure 5.The phase variations across the emission window corresponding to the subpulse drifting behaviour in PSR B0844-35 during emission mode A. The left panel shows the phase variations in the low frequency range between 300 and 500 MHz while the high frequency behaviour between 550 and 750 MHz is shown in the right panel.The average profiles are shown in the background to highlight the phase behaviour across each component.

Figure 6 .
Figure6.The polarization behaviour across the average profiles of PSR B0844-35, with the two modes A and B shown in the same plot.The left panels show the average profiles over the 300-500 MHz frequency range and the right panels show the corresponding profiles averaged between 550-750 MHz.The top window in each panel represents the total intensity profiles, the middle window shows the variation of the linear polarization across the profile and the bottom window the circular polarization behaviour.

Figure 7 .
Figure 7.The figure shows the polarization position angle (PPA) distribution of the single pulse time samples of PSR B0844-35.The top windows (a) and (b) shows the behaviour of mode A and B, respectively, at the 300-500 MHz frequency range.The bottom windows (c) and (d) shows the PPA of the two modes averaged between 550 and 750 MHz.The top panel in each window shows the average profile (black), the average linear (red) and circular polarization (blue) properties of the radio emission.In the bottom window the distribution of the single pulse PPA is shown as a colour scale, representing the number of points in each location, as well as the average PPA behaviour across the window (red error bars).The rotating vector model (RVM) fits to the PPA is also shown in the figure (pink dashed line), along with the steepest gradient point of the RVM fit (black error bar).

Figure 8 .Figure 9 .
Figure 8.The left panel shows the single pulse sequence corresponding to the Bright mode of PSR B1758-29, observed on 18 March, 2019, and represents the pulse range between 260 to 460 from the start of the observing session.The right panel shows the pulse sequence between pulses 870 and 1070, belonging to the Quiet mode.

Figure 11 .
Figure 11.The distribution of the average energies of single pulses in the two modes of PSR B1758-29.The left panel shows the distribution in the lower frequency band, between 300 and 500 MHz, while the upper band distribution, averaged over 550 and 750 MHz, is shown in the right panel.The Gaussian noise distribution in the off-pulse region is also shown in each plot.

Figure 12 .
Figure 12.The LRFS across the single pulse sequences of PSR B1758-29 during the observations on 18 March, 2019, showing the different periodic behaviour.(a) The pulse sequence between 1700 and 1850 in mode B showing the low frequency periodic modulation seen in this mode.The phase variations corresponding to the periodic modulation feature (top window) are flat with close to zero slope across the profile.This highlights that the emission across the entire window changes simultaneously during periodic modulations.(b) The average LRFS estimated in mode Q showing the subpulse drifting behaviour with P3 = 2.4P .(c)The pulse between 15 and 185, in mode Q, showing the presence of both subpulse drifting as well as periodic modulation.The phase behaviour corresponding to subpulse drifting in this pulsar is also flat but limited to primarily the leading component.

Figure 13 .
Figure13.The polarization behaviour across the average profiles of PSR B1758-29, with the two modes B and Q shown in the same plot.The left panels show the average profiles over the 300-500 MHz frequency range and the right panels show the corresponding profiles averaged between 550-750 MHz.The top window in each panel represents the total intensity profiles, the middle window shows the variation of the linear polarization across the profile and the bottom window the circular polarization behaviour.

Figure 14 .
Figure 14.The figure shows the polarization position angle (PPA) distribution of the single pulse time samples of PSR B1758-29.The top windows (a) and (b) shows the behaviour of mode B and Q, respectively, at the 300-500 MHz frequency range.The bottom windows (c) and (d) shows the PPA of the two modes averaged between 550 and 750 MHz.The top panel in each window shows the average profile (black), the average linear (red) and circular polarization (blue) properties of the radio emission.In the bottom window the distribution of the single pulse PPA is shown as a colour scale, representing the number of points in each location, as well as the average PPA behaviour across the window (red error bars).The rotating vector model (RVM) fits to the PPA is also shown in the figure (pink dashed line), along with the steepest gradient point of the RVM fit (black error bar).

Table 1 .
Observing Details

Table 3 .
Average Profile properties in the emission modes of PSR B0844-35

Table 4 .
Subpulse Drifting Estimates in Mode A of PSR B0844-35

Table 5 .
Estimation of radio emission height in PSR B0844-35

Table 7 .
Average Profile properties in the emission modes of PSR B1758-29

Table 9 .
Estimation of radio emission height in PSR B1758-29