Investigation of the Mode-Switching Phenomenon in Pulsar B0329+54 Through Polarimetric Analysis

TL;DR

This study investigates the profile mode switching in pulsar B0329+54 by analyzing polarization and geometry, finding that polarization behavior and emission height remain constant across modes, supporting a pair production change model.

Contribution

It provides the first detailed polarimetric comparison of the two profile modes of PSR B0329+54, revealing constant polarization and emission height, and supports a pair production change hypothesis.

Findings

Polarization behavior remains constant between modes.

Emission height remains unchanged across modes.

Supports a pair production change model for mode switching.

Abstract

The phenomenon of profile mode switching in pulsars, where the stable average pulse profile changes to another stable state on the timescale of a pulsar's period, remains poorly understood. We sought to understand how pulsars undergo profile mode switching through a comparative analysis of the polarization and geometry of the two different profile modes of PSR B0329+54. The polarization behavior and fitted parameters of the rotation-vector model remain constant between modes, and the emission height remains constant as well. These similarities lend support to a model of pair production in the surface plasma that would cause a change in the available electrons and therefore the differential emission intensity.

Tables

Table 1. Pulsar characteristics and timing parameters. *See also 2013MNRAS.429..579B ** Previous unconfirmed candidate.
Previous name	Reference	New Name	Start	Finish	Ref.	NTOA	rms	Reduced
			(MJD)	(MJD)	(MJD)		(ms)	${\chi }^2$
J0435+27	1996ApJ...470.1103R	J0435+2749	52854	53785	53400	96	0.12	5.83
J0517+22	2003PhDT.........2C	J0517+2212	53418	53774	53400	98	0.11	2.07
J0627+07*	2003PhDT.........2C	J0627+0706	53418	53675	53400	91	0.26	13.71
J0927+23	1996ApJ...470.1103R	J0927+2345	53318	53858	50000	23	0.47	1.59
J0943+22	1993ApJ...416..182T	J0943+2253	53318	53910	50000	83	0.20	1.80
J0947+27	1996ApJ...470.1103R	J0947+2740	53318	53910	50000	35	0.28	1.88
J1246+22	1993ApJ...416..182T	J1246+2253	53294	53672	53294	88	0.24	1.61
J1404+12	2003PhDT.........2C	J1404+1159	53309	53672	50000	66	0.37	1.98
J1756+18	2003ApJ...594..943N	J1756+1822	52645	53307	52751	89	1.23	2.90
J1935+12	2003PhDT.........2C	J1935+1159	53306	53580	53295	40	2.43	0.70
J2050+13	2003ApJ...594..943N	J2050+1259	52636	53306	52773	27	8.81	6.31
J2052+17**	1996ApJ...470.1103R	J2053+1718	53295	56837	55000	728	0.028	1.34

Table 2. Timing Parameters
Pulsar Name	RA	Dec	$\nu$	$\dot{\nu }$	DM
			(Hz)	(${10}^{-16}$ Hz s-1)	(pc cm-3)
J0435+2749	04 35 51.8178(16)	27 49 1.68(16)	3.06457408039(5)	$-$0.767(4)	53.192(9)
J0517+2212	05 17 17.159(7)(72)	22 12 48.8(1.6)	4.9707996302(9)	$-$2.20(6)	18.691(9)
J0627+0706	06 27 44.2168(15)	07 06 12.67(29)	2.10139608235(13)	$-$1314.82(11)	138.29
J0927+2345	09 27 45.26(4)	23 45 11.(1)	1.3125269006(16)	$-$5.26(5)	17.24(10)
J0943+2253	09 43 32.403(5)	22 53 5.98(11)	1.87626174158(26)	$-$3.168(8)	27.209(17)
J0947+2740	09 47 21.287(13)	27 40 43.48(18)	1.1750682463(7)	$-$5.937(21)	29.09(5)
J1246+2253	12 46 49.3610(28)	22 53 43.12(10)	2.11028093179(6)	$-$3.89(4)	17.793(22)
J1404+1159	14 04 36.961(8)	11 59 14.4(3)	0.3772960811(6)	$-$1.893(18)	18.530(27)
J1756+1822	17 56 17.582(5)	18 22 55.26(13)	1.34408437573(3)	$-$9.266(17)	70.80
J1935+1159	19 35 15.87(23)	11 59 6.(54)	0.5155281800(14)	$-$2.7(11)	191.6(26)
J2050+1259	20 50 57.21(5)	12 59 9.69(14)	0.81898743453(12)	$-$3.38(6)	52.40
J2053+1718	20 53 49.4806(4)	17 18 44.692(7)	8.384495640456(4)	$-$0.002014(7)	26.979

Table 3. Derived Parameters
Pulsar Name	Galactic Coordinates		$P$	$\dot{P}$	${\tau }_c$	$B_0$	$D$	$\dot{E}$
	$\ell$	$b$	(s)	(${10}^{-15}$s s-1 )	(${10}^9$yr)	(${10}^{12}$G)	(kpc)	(${10}^{31}$erg s-1)
J0435+2749	171 50 32.0	$-$13 04 17.3	0.326279534509(6)	0.00816(5)	0.63	0.052	1.8	0.93
J0517+2212	182 10 37.1	$-$09 00 46.0	0.222366515211(5)	0.01087(28)	0.32	0.050	0.66	3.90
J0627+0706	203 54 25.4	$-$01 59 35.5	0.47587411455(3)	29.7748(24)	0.00025	3.81	4.7	$1.09\times {10}^3$
J0927+2345	205 17 09.1	+44 12 05.6	0.7618891464(9)	0.3051(28)	0.040	0.49	0.66	2.72
J0943+2253	207 53 11.5	+47 27 29.9	0.53297467930(7)	0.09000(23)	0.094	0.22	1.2	2.35
J0947+2740	201 08 31.0	+49 23 04.2	0.8510136770(5)	0.4300(15)	0.031	0.61	1.28	2.75
J1246+2253	288 48 32.7	+85 38 23.7	0.473870556729(13)	0.0874(8)	0.086	0.21	1.5	3.24
J1404+1159	355 04 37.3	+67 06 51.9	2.650438343(4)	1.330(13)	0.032	1.90	1.4	0.28
J1756+1822	43 50 08.5	+20 11 07.1	0.744000910999(17)	0.5129(9)	0.023	0.63	4.2	4.92
J1935+1159	48 36 43.9	$-$04 03 31.7	1.939758172(5)	1.0(4)	0.03	1.4	6.8	0.5
J2050+1259	59 26 11.6	$-$19 14 21.3	1.22101995445(17)	0.504(9)	0.038	0.79	3.1	1.09
J2053+1718	63 33 13.9	$-$17 15 51.8	0.11926775835804(5)	0.0002864(10)	6.7	0.0058	1.9	0.65

Table 4. Polarimetric Observations
Name	MJD		Pulses		Flux Estimates (mJy)		RM
	P-band	L-Band	P-band	L-Band	P-Band	L-Band	(rad-m2)
J0435+2749	53490	54541	1840	3065	—	0.24(3)	+2
J0517+2212	57123	54540	2696	2698	119.(8)	0.52(2)	–16
J0627+0706	57123	57113	518	2520	8(5)0	0.25(4)	+212
J0927+2345	57525	57347	4724	2502	1.9(8)	0.02(2)	–8
J0943+2253	57379		7775		5.3(1)		+8?
J0947+2740	57379	57524	3172	4699	8.8(1)	0.027(9)	+32
J1246+2253	52840	57307	1266	1885	—	0.21(9)	+4?
J1404+1159	55905	57307	509	1591	68.(8)	0.01	+4
J1756+1822	57567	57567	2156	3571	0.008	0.05	+70
J1935+1159	57288	57533	1004	1090	10	0.47(5)	–83
J2050+1259	57524	57525	2046	1966	10.(4)	0.025(8)	–80
J2053+1718	57524	57533	5023	21624	19	0.0006	–5

Table 5. Conal Geometry Models
Pulsar	Class	$\alpha$	$\beta$	$w$	$\rho$	$h$
		(°)	(°)	(°)	(°)	(km)
J0435+2749	T	18	3.4	59.0	10.3	230
J0517+2212	D	31	0	45.2	11.7	205
J0627+0706m	St	90	-7.2	4.54	7.5	131
J0627+0706i	D	90	-6.4	6	6.9	129
J0927+2345m	D/T?	69	3.4	8	5.1	130
J0943+2253	D/T?	42	-5.5	7	5.9	123
J0947+2740	T/M	42	-1.2	18	6.0	205
J1246+2253	St	81	-4.7	6.5	5.7	103
J1404+1159	Sd	25	2.2	5.3	0.88	114
J1756+1822	D	50	2.5	16	6.7	224
J1935+1159	D	10.13	-1.0	50.4	4.3	239
J2050+1259	Sd	27	-2.6	21	5.2	223
J2053+1718	St?	63	-17.2	2.5	17.2	235

Full text

††pubyear: 2015††pagerange: No Pulsar Left Behind. I. Timing Solutions, Pulse-sequence Polarimetry, and Emission Morphology for 12 pulsars.–Appendix of Images

1 Introduction and motivation

Since the discovery of the first radio pulsar in 1967 (1968Natur.217..709H), more than 2500 rotation-powered pulsars have been discovered (2005AJ....129.1993M). Of these, more than 400 have no published phase-coherent timing solutions, so that we lack a rudimentary knowledge of their proper motions, spin-down parameters (including characteristic age, magnetic field, spin-down luminosity) and possible orbital elements. Similarly, many newly discovered pulsars lack average polarimetry and fluctuation-spectral analysis, and for many pulsars even basic quantities like flux densities and spectral indices are still lacking. Because of this, the scientific potential for many of these objects is simply not known and is not being exploited.

In this and subsequent papers, we attempt a partial remedy to this situation by characterizing some of these pulsars: we present their timing solutions (with derivations of characteristic ages, surface magnetic field and rotational spin-down) and study some of their radio emission properties. As for all previously well characterized pulsars, the measurements presented here and in subsequent papers will aid future studies of the pulsar population and contribute to the understanding of their emission physics.

In this first paper, we focus primarily on a group of a dozen pulsars discovered with the 430-MHz line feed of the Arecibo 305-m radio telescope in Puerto Rico before the Arecibo upgrade, i.e., pulsars that have been known (and not followed up) for more than 20 years. Most pulsars in this group were discovered in drift-scan surveys: two, J0943+22 and J1246+22, were reported by 1993ApJ...416..182T and three others (J0435+27, J0927+23, J0947+27) were discovered in the completion of that survey by 1996ApJ...470.1103R. Five further pulsars (J0517+22, J0627+07, J1404+12, J1935+12 and J1938+22) were discovered in the Arecibo-Caltech drift-scan survey (2003PhDT.........2C), but again no timing solutions were presented for any of them. Two of these pulsars were later timed by other authors: J0627+0706, which we timed from 2005 Feb. 17 to Nov. 1, was detected by the Perseus Arm pulsar survey and subsequently timed from 2006 Jan 1 to 2011 May 9 (2013MNRAS.429..579B). Their timing results are similar to ours, but more precise given the larger timing baseline. J1938+22, which we did not follow up, was later timed by 2013MNRAS.434..347L, so that it is now known as J1938+2213.

Two other pulsars (J1756+18 and J2050+13) were discovered in the Arecibo 430-MHz intermediate latitude (pointed) survey (2003ApJ...594..943N). They were reported in the above paper describing that survey, but without timing solutions because although they were originally detected on the 19th and 13th of July 1990 respectively, they were confirmed only in January 2003.

Finally, in 1996ApJ...470.1103R an additional pulsar candidate (J2052+17) was listed, but the authors were unable to confirm it because of the start of the Arecibo upgrade. The candidate had a spin period $P$ of 119.26 ms and a DM of $25\pm 3\,\rm cm^{-3}$ pc. In 2004 October we confirmed the existence of this pulsar using the 327 MHz Gregorian receiver of the 305-m Arecibo radio telescope and the Wideband Arecibo Pulsar Processors (WAPPs, 2000ASPC..202..275D) as back-ends. Both the topocentric spin period (119.27 ms) and DM of $27\,\rm cm^{-3}$ pc were compatible with the parameters in 1996ApJ...470.1103R. The pulsar has an exceptionally narrow profile, which represents less than 1% of a rotation cycle as presented in Fig. 1 and in more detail in Fig. A12.

In what follows, we present detailed studies for these objects, both of their timing and emission properties. In §2 we discuss briefly the timing observations and analytical results, §3 describes the pulse-sequence, profile and polarization analyses, §4 discusses the origin of PSR J2053+1718 and §5 summarizes the various results.

2 Timing observations and results

The aforementioned pulsars are relatively bright, and for that reason were used as test pulsars during the very early demonstration stages of the Arecibo 327-MHz drift scan survey (2013ApJ...775...51D). These observations were carried out with the 327-MHz Gregorian feed and one of the four WAPPs as backends. They all were acquired in search mode, with 256 spectral channels, a sampling time of 64$\mu$s and a bandwidth of 50 MHz. They were later dedispersed and folded using the PRESTO routine “prepfold” (2002AJ....124.1788R), and then topocentric pulse times of arrival (TOAs) were derived from the resulting profiles using the FFT technique described by 1992RSPTA.341..117T and implemented in the PRESTO routine get_TOAs.py.

The characteristics of the timing observations are given in Table 1, together with the number of TOAs derived for each, the root mean square (rms) of the residuals (measured TOA - model prediction for the respective pulse, depicted graphically in Fig. 2 for PSR J2053+1718 as an example) and the reduced $\chi^{2}$ of each fit. For some pulsars this is much larger than 1, implying the presence of effects that have not been modeled, such as timing noise. This is more prominent for the younger pulsars in this work, in particular for J0627+0706; in agreement with the results of 2013MNRAS.429..579B. The table also gives the new names for these pulsars, now possible given the precise measurements of Right Ascension ($\alpha$) and declination ($\delta$); these names are used throughout the remainder of this paper. The best fit values for $\alpha$ and $\delta$ are presented in Table 2, together with the other numerical parameters of the timing solution such the rotation frequency ($\nu$), its derivative ($\dot{\nu}$), and dispersion measure (DM).

Finally, the derived parameters are given in Table 3: Galactic coordinates ($l,b$) and distance ($D$), derived from the DM using the NE2001 model of the electron distribution of the Galaxy (2002astro.ph..7156C), spin frequency ($P$) and its period derivative ($\dot{P}$), characteristic age ($\tau_{c}$), magnetic field ($B_{0}$), and spin-down energy ($\dot{E}$). The expressions for these quantities were adopted from 2004hpa..book.....L: $\tau_{c}=P/\dot{P}$, $B=3.2\times 10^{19}\sqrt{P\dot{P}}$ and $\dot{E}\,=\,4\pi^{2}\,I\,\dot{P}/P^{3}$, where $I$ is the moment of inertia of the neutron star, which is generally assumed to be $10^{45}\,\rm g\,cm^{2}$. All pulsars in the list are isolated, and most of them belong to the “normal” group, with fairly typical rotation periods (between 0.22 and 2.65 s), characteristic ages (between 0.25 Myr and 0.63 Gyr) and B-fields (from 0.05 to 3.8$\,\times\,10^{12}\,$G). We now discuss the characteristic of the two extreme objects in our sample.

2.1 PSR J2053+1718

PSR J2053+1718 has a much smaller spin period derivative and is clearly much older than the other pulsars in this sample. A first simple fit for $\nu$, $\dot{\nu}$, $\alpha$, $\delta$ and proper motion along these two directions ($\mu_{\alpha}$ and $\mu_{\delta}$) yields a reduced $\chi^{2}$ of 1.80, and visible trends in the residuals. Given the low frequency used in the timing and the relatively high precision of the measurements, these are likely due to variations in DM caused by the Earth’s and the pulsar’s movement through space. We used the DMX model (2013ApJ...762...94D) to measure the DM variations (displayed in Fig. 2) and subtract them; once this is done the reduced $\chi^{2}$ decreases to 1.34. In this model we obtain $\mu_{\alpha}\,=\,1.0\,\pm\,2.3\,\rm mas$ $yr^{-1}$ and $\mu_{\delta}\,=\,+6.9\,\pm\,2.8\,\rm mas$ $yr^{-1}$. The NE 2001 model places this pulsar at a distance of 1.9 kpc, which implies a transverse velocity of $(63\,\pm\,25)\,\rm km\,s^{-1}$, which is typical among recycled pulsars (e.g., 2011ApJ...743..102G). This proper motion allows for a correction of the observed $\dot{P}$, where we subtract the Shklovskii effect (1970SvA....13..562S) and the Galactic acceleration of this pulsar relative to that of Solar System, projected along the line of sight (1991ApJ...366..501D) (this was calculated using the latest model for the rotation of the Galaxy from 2014ApJ...783..130R). These terms mostly cancel each other, so that the intrinsic spin-down, $\dot{P}_{\rm int}\,=\,2.8\times 10^{-19}\,\rm s\,s^{-1}$, is very similar to the observed $\dot{P}$. This implies a low B-field of $\sim\,5.8\,\times\,10^{9}\,$G and a characteristic age of $\sim\,6.7\,$Gyr. The origin of this pulsar is discussed in §4.

2.2 PSR J0627+0706

With a characteristic age of only 250 kyr PSR J0627+0706 is two orders of magnitude younger than any other pulsar in this group; its spin-down power is more than 220 times larger than any other pulsar in this sample. This object displays a prominent interpulse, suggesting an orthogonal rotator. It also has significant timing noise, which is again typical of young pulsars. This is the reason for the very high reduced $\chi^{2}$ of its solution.

2003PhDT.........2C remarked that this pulsar lies, in projection, within $3^{\circ}$ of the centre of the old, large Monoceros supernova remnant (SNR G205.5+0.5); which is located at $\alpha\,=\,06^{\rm h}\,39^{\rm min},\,\delta\,=\,+06^{\circ}\,30\arcmin$. For this reason they proposed that, if PSR J0627+0706 has an age similar to that of SNR G205.5+0.5 (30 to 100 kyr, 1986MNRAS.220..501L), it could be a candidate in association with that SNR (they point out that the positional offset is possible given the age of the SNR and the proper motions of other pulsars observed in the Galaxy).

The age we and 2013MNRAS.429..579B measure for PSR J0627+0706 is larger by a factor of 2.5 to 8. However, this is not very constraining: pulsars can be substantially younger than their characteristic age if they are born with a spin period similar to their current spin period.

Another way of verifying the association is through distance measurements. The estimated distance to the Monoceros SNR, 1.6 kpc (1986ApJ...301..813O), is much smaller than the estimated distance to this pulsar, 4.5 kpc, which is based on its unusually large DM relative to other pulsars in the Galactic anticentre. This, again, is not necessarily an indication that the pulsar is much more distant than the SNR: the large amount of ionized gas in the vicinity of this SNR could be itself an explanation for the large DM of the pulsar.

We note that this area of the Galaxy has an abundance of relatively young pulsars that could potentially be associated with SNR G205.5+0.5. In particular, the “radio quiet” gamma-ray pulsar PSR J0633+0632, discovered in data from the Fermi satellite (2009Sci...325..840A), was listed in the latter paper as a “plausible” association with SNR G205.5+0.5 based on its location within $\sim 1.5^{\circ}$ of the SNR centre. Later 2011ApJS..194...17R measured the characteristic age of PSR J0633+0632 (59 kyr) which is also more compatible with the estimated age of the SNR.

We conclude therefore that PSR J0633+0632 is more likely to be associated to SNR G205.5+0.5 than PSR J0627+0706.

3 Pulse-sequence and Profile Analyses

Recently, we conducted single-pulse polarimetric observations on most of the above pulsars as well as a few others of related interest. The Arecibo observations were carried out at both P band (327 MHz) and L band (1400 MHz) using total bandwidths of 50 MHz and typically 250 MHz, respectively. Four Mock spectrometers were used to sample adjacent sub-bands after MJD 56300 (see 2016MNRAS.460.3063M) and four Wideband Arecibo Pulsar Processors (WAPPs) earlier (2013MNRAS.433..445R) to achieve milliperiod resolution. The observations were then processed to provide pulse sequences that were used both to compute average polarization profiles and fluctuation spectra. Rotation measures (RMs) were determined for each of the pulsars in the course of the polarimetric analyses, and these will be published separately with many others.

A summary of these polarimetric observations are given in Table 4, as described above. Nominal values of the rotation measure are also given in the table, and a complete description of the methods and errors will be given in Rankin, Venkataraman & Weisberg (2017). Below we treat the various pulsars object by object referring to the polarized profiles and fluctuation spectra in the Appendix figures. The analyses proceed from polarimetry to fluctuation spectra and finally to quantitative geometry following the procedures of 1993ApJS...85..145R; 1993ApJ...405..285R. The longitude-resolved fluctuation (LRF) spectra of the pulse sequences (e.g., see 2001MNRAS.322..438D) were computed in an effort to identify subpulse “drift” or stationary modulation associated with a rotating (conal) subbeam system.

3.1 Polarimetry and Fluctuation-spectral Analysis

J0435+2749 has a clear triple profile at both frequencies as shown in Figure A1, though the L-band one is of better quality. The leading and trailing components have very different spectral indices: the trailing component is much stronger at 327 MHz, but the leading is much stronger at L-band. The fractional linear polarization is low in both profiles such that the polarization-angle traverse is well defined only at the higher frequency. The power under the leading component may represent a different orthogonal polarization mode (OPM) than the others, suggesting little position angle (PPA) rotation across the profile. Both fluctuation spectra show broad peaks at about 0.05 cycles/period, primarily in the two outer components, which suggest a 20-period conal modulation.

J0517+2212 has a double component profile at L-band, whereas its P-band profile shows some structure in the second component. The polarization traverse show little rotation at P band apart from the two 90° “jumps” and the behaviour seems similar at L band but less well resolved perhaps because of the diminished fractional linear polarization. The fluctuation spectra show a peaks around 0.12 cycles/period, suggesting an 8 rotation-period modulation.

J0627+0706 has a bright interpulse, a component-peak separation of 177° (main pulse minus interpulse peak longitudes) as can be seen in Fig. A3. Because both features have structure, more detailed interpretation is needed to assess how close to 180° they fall; however, given the narrowness of both features, it seems likely that they represent emission from the stars two poles, implying an orthogonal geometry where $\alpha$ is close to 90°. PPA tracks give hints about the geometry only at L band, and here little to go on apart from a probable 90° “jump” under the main pulse. The main pulse might have three components and the interpulse two. The fluctuation spectra are not displayed because they showed only flat “white” fluctuations.

J0927+2345 shows an interesting feature at P-band approximately 180° away from the main pulse (Fig. A4). This apparent interpulse is discernible only in the P-band profile, and disappears in the L-band profile. Again, both profiles show so little linear polarization that a reliable PPA rate can be estimated for only a narrow longitude interval at P band. The main pulse appears to have three closely spaced features. The fluctuation spectra are not given for this pulsar either because they showed no discernible features.

J0943+2253 nulls as seen in Fig. 1 above, but the fluctuation spectra show no quasiperiodic behavior. The polarization is slight and the PPA track shows what appears to be a 90° “jump” within the narrow interval where it is clearly defined.

J0947+2740 shows three components at both frequencies, though the leading region may be more complex at the lower frequency, probably representing a core and closely spaced inner cone. At L-band the conal components are weaker, and the PPA traverse is more complex, perhaps showing a 90° “jump” in the region of rapid PPA rotation. RVM behaviour, and the slope of it’s polarization traverse could not be determined. This pulsar is also known to exhibit sporadic emission between intervals of weakness or nulls as in Fig. 1. The fluctuation spectra seem to hint at fluctuation power at periods longer than about 3 or 4 pulses.

J1246+2253 has a single component at P band, which develops into a resolved triple form at L band in what may be the characteristic core-single manner. The fractional linear polarization at both frequencies is low, so little can be discerned reliably from the PPA tracks. Also no clear features are seen in the fluctuation spectra as is often the case for core-single profiles.

J1404+1159 exhibits a narrow peak in its fluctuation spectra around 0.2 cycles/period, suggesting a modulation period $P_{3}$ of some 5 rotation periods. A display of its individual pulses bears this out, and a display of the its emission folded at $P_{3}$ shows that the modulation is highly regular. The PPA rate at the profile center suggests an outside sightline traverse as is usual for conal single “drifters”. See Figure A8.

J1756+1822 appears to have two profile components, and its profile broadens perceptibly with wavelength, suggesting a conal double configuration. The P-band polarization is negligible, whereas a hint of a moderately steep negative PPA traverse is seen at L-band. The fluctuation spectra showed no features and were thus omitted.

J1935+1159’s long nulls (see Fig. 1) make this pulsar difficult to observe sensitively, and neither clear profile structure nor polarization signature is seen at either frequency. Similarly, fluctuation spectra showed nothing useful.

J2050+1259 also exhibits frequent nulls as seen above in Fig. 1. However, its single profile at L band broadens and bifurcates at P band in the usual conal double manner, and a steep PPA traverse is seen at the lower frequency. Finally, here we do see strong low frequency features in the fluctuation spectra indicative of modulation on a scale of 50 rotation periods or longer.

J2053+1718 Our P and L band observations do not provide much polarization information or fluctuation-spectral information apart its having a single profile at both frequencies.

3.2 Quantitative Geometry

We have also attempted to classify the profiles where possible and conduct a quantitative geometrical analysis following the procedures of the core/double-cone model in Rankin (1993a,b; hereafter ETVI). Outside half-power (3-db) widths are measured for both conal components or pairs—and where possible estimated for cores. Core widths can be used to estimate $\alpha$, PPA-traverse central rates $R=\sin\alpha/\sin\beta$ can be used to compute $\beta$, and the conal widths can be used to compute conal beam radii using eqs. (1) through (6) of the above paper.

The notes to Table 5 summarize our measurements, and the table values show the results of the geometrical model for the pulsar’s emission beams. The profiles class is given in the first column, $\alpha$ and $\beta$ in next two per the $R$ value when possible. The conal component profile widths $w$, conal beam radii $\rho$, and characteristic emission heights $h$ are tabulated in the rightmost three columns.

J0435+2749’s average profile has a triple component configuration at both frequencies, and the observed conal spreading suggests a core/outer cone geometry. The core width can only be estimated at the higher frequency at perhaps 9° maximum, implying that $\alpha$ is less that some 1.4° per ETVI, eq.(1).

The PPA traverse shows a much more complex behavior than the Rotation Vector Model (RVM) describes; however, the roughly 90° rotation near the center of the pulse may be so interpreted. The spherical geometric beam model in Table 5 seems compatible with a core-cone triple T classification.

J0517+2212’s profile shows two primary components. There is more structure at L-band, as well as overall pulse narrowing. These factors, along with the lack of PPA traverse suggest that $\beta\sim 0$ and imply the outer conal beam geometry shown in Table 5.

J0627+0706’s main-pulse profile may have two or three closely spaced components. The pulse width at half maximum interestingly widens from P-band to L-band suggesting a core-single configuration where the conal emission is seen mainly at high frequency. The polarization traverse is clearer at L-band, marked by prominent 90° modal “jumps”. It thus seems likely that $\beta$ is small for the main pulse and perhaps larger for the inter pulse, but that $\alpha$ is close to 90°, yielding the classifications and model values in Table 5. The emission heights given for both the main pulse and interpulse suggest that it is inner conal emission.

J0927+2345’s average profile has two clear components and possibly an unresolved trailing one as well. Its half width interestingly broadens from P-band to L-band suggesting a core single evolution where conal “outriders” appear or become more prominent at high frequency. The polarization traverse is well defined only for a short interval at L band, which provides a useful $R$ value that leads to the geometric beam model in Table 5. If this profile were triple, the central component would be $2.8\degr$ wide.

J0943+2253’s average profile also has two closely spaced components and perhaps and unresolved weak feature on its leading edge, suggesting a double or triple configuration. We only have a P-band observation so cannot see how the profile evolves, and the linear polarization is slight and difficult to interpret. However, we can guess a central PPA rate of 7°/° in order to compute the geometric model parameters in Table 5, which suggest an inner-conal configuration.

J0947+2740’s profile is comprised by three main components, and the fact that its width increases with wavelength indicates an outer-conal configuration. Its PPA traverse seems interpretable per the RVM model at P band, but its L-band traverse seems to be distorted by what may be a 90° “jump” just prior to the profile center. Its profile then seems to be a core/outer cone triple, and the quantitative beam geometry model is shown in Table 5. The core width is estimated around $2.65\degr$, which is much more narrow than the central component of the profile ($7.92\degr$ at P-band and $10.08\degr$ at L-band), which indicates that the central component contains both core and conal emission.

J1246+2253’s single profile at P band becoming triple at L band strongly suggests a core single configuration. Despite the low fractional linear polarization, the trailing positive traverse through roughly 90° was used to computer the geometrical model in Table 5. The core width is estimated at $3.55\degr$.

J1404+1159 has a single component profile at both frequencies, and its narrow fluctuation feature identifies it as having regular drifting subpulses as shown in Fig. A8. The pulsar then appears to have a classic conal single profile. Both PPA tracks show a negative-going traverse with a central slope of about –12°/°. Here we also give short pulse-sequences folded at the modulation period of some 0.2 rotation-periods/cycle.

J1756+1822 has an interestingly shaped profile that appears to have two separate components. The P and L-band profiles have similar forms with the longer wavelength one somewhat broader in the usual pattern of the conal double class. The fractional linear profiles is low at both frequencies, but at L-band there seems to be a hint of a traverse through more than 90° across the profile. The fluctuation spectra are not shown as no features could be discerned.

J1935+1159 Appears to be a five component pulsar; even though only two individual components can be resolved, it appears to be filled which could hide additional components. According to the emission heights, and the profile narrowing from P-band to L-band, indicate that this is an outer cone which is filled with inner conal and/or core emission. For the geometric computations, we have estimated a central traverse of $10\degr/\degr$.

J2050+1259’s profile has a single component at Lband and two closely spaced components at P band as seen in Figs. 1 and A11. Its profile is broader at the lower frequency, and strong hints of a roughly 180°PPA traverse are seen in both profiles, suggesting that this is a conal single profile with a small impact angle with the beaming parameters as given in Table 5.

J2053+1718 show a single component at both frequencies, though in the higher frequency observation the time resolution was poor with only 232 samples across the rotation cycle. The polarization information and fluctuation spectra do not give much to go on either. Curiously, this pulsar has a wider profile in L-band than in P-band, however much of this can probably be attributed to the quality of the observation. Its short 119-ms rotation period and single profile do suggest a core-single classification.

4 On the origin of PSR J2053+1718

In double neutron star systems, the first-born neutron star was recycled by accretion of mass from the progenitor of the second-formed neutron star. This accretion spun up the first formed NS to spin periods between 22 and 186 ms (for the known DNSs, likely faster right after they formed) and, by mechanisms that are not clearly understood, it induced a decrease in its magnetic field to values between $10^{9}\,<\,B_{0}\,<\,10^{10}$ G. Such pulsars spin down very slowly and therefore will stay in the active part of the $P$ - $\dot{P}$ diagram for much longer than non-recycled pulsars; this is the reason why we mostly see the recycled pulsars in these systems (the second-formed non-recycled pulsars are observed in two DNSs only).

Some isolated pulsars like PSR J2053+1718 are in the same area of the $P$ - $\dot{P}$ diagram as the recycled pulsars in DNSs, but have no companion to explain the recycling. The conventional explanation for their formation is that, like the recycled pulsars in DNSs, they were spun up by a massive stellar companion; the difference is that when the latter star goes supernova and forms a neutron star, the systems unbinds, owing to the kick and mass loss associated with the supernova (e.g., 2010MNRAS.407.1245B). For this reason they have been labelled “Disrupted Radio Pulsars”, or DRPs.

We should keep in mind the possibility of alternative origins for these pulsars: some NSs observed in the center of supernova remnants, despite being obviously young, have small B-fields and large characteristic ages similar to those of DRPs — these objects are known as Central Compact Objects, or CCOs (see e.g., 2010ApJ...709..436H). Therefore, one could expect that some DRPs formed as CCOs. However, 2013ApJ...773..141G find after extensive study of DRPs in X-rays that none appears to have thermal X-ray emission, implying that there is likely no relation between CCOs and DRPs. This results in a mystery: a substantial fraction of neutron stars appear to form as CCOs, which one might reasonably expect to form DRP-like radio pulsars, some of them with strong thermal X-ray emission, but these large numbers of DRPs (and “hot” DRPs) are not observed. Either, for some unknown reason, they never develop radio emission, or their B-field increases significantly after birth, making them look more like normal pulsars. In any case, the results of 2013ApJ...773..141G seem to exclude the possibility that DRPs such as PSR J2053+1718 formed from central Compact Objects.

Any model that explains quantitatively the observed distribution of orbital eccentricities and spatial velocities of DNSs should also be able to explain the relative fraction of DRPs to DNSs and, furthermore, the velocity distribution of the two classes of objects. As already discussed by 2010MNRAS.407.1245B, the relative number of DNSs and DRPs implies that the second SN kick must be, on average, significantly smaller than that observed for single pulsars. The evidence for this among DNSs has been growing in recent years and is now very strong (see summary in Tauris et al. 2017). It is therefore clear that more measurements of proper motions, spin periods, ages and B-fields of DRPs such as those presented here give us important clues for understanding the formation of DNS systems.

5 Discussion

In the foregoing sections we have characterized a group of pulsars that had not been the target of any previous detailed studies. We determined timing solutions for them; most are normal, isolated pulsars. One of them, PSR J0627+0706, is relatively young ($\tau_{c}\,=\,250$ kyr) and is located near the Monoceros SNR, however it is not clear whether the pulsar and that SNR originated in the same supernova event. We confirmed a candidate from a previous survey, PSR J2053+1718; subsequent timing shows that, despite being solitary, this object was recycled; it appears to be a member of a growing class of objects that appear to result from the disruption of double neutron stars at formation. We highlight that measurements of the characteristics of these objects (spin period, age, B-field, velocity) are important for understanding the formation of double neutron star systems.

As part of our characterization, we have also observed these pulsars polarimetrically with the Arecibo telescope at both L and P band in an effort to explore their pulse-sequence properties and quantitative geometry. Three of them (PSRs J0943+2253, J1935+1159 and J2050+1259) have strong nulls and sporadic radio emission, several others exhibit interpulses (PSRs J0627+0706 and J0927+2345) and one shows regular drifting subpulses (J1404+1159). All these measurements will contribute to future, more global assessments of the emission properties of radio pulsars and studies of the NS population in the Galaxy.

Acknowledgments

The authors sincerely thank Dr. Paulo Freire of the Max Planck Institute for Radioastronomy in Bonn for his generous assistance with the timing analyses. Much of the work was made possible by support from the US National Science Foundation grant 09-68296 as well as NASA Space Grants. One of us (JMR) also thanks the Anton Pannekoek Astronomical Institute of the University of Amsterdam for their support. Arecibo Observatory is operated by SRI International under a cooperative agreement with the US National Science Foundation, and in alliance with SRI, the Ana G. Méndez-Universidad Metropolitana, and the Universities Space Research Association. This work made use of the NASA ADS astronomical data system.

Appendix of Images