The data used for this study were obtained http://www.jb.man.ac.uk/pulsar/glitches.html (Basu et al., 2022) and Manchester et al., (2005 - ATNF pulsar catalogue, 2024). There are 471 pulsars whose \(\ddot{\nu }\) were non-zero or given and thus, \(n\) can be estimated from Eq. (2), amongst 471 pulsars, 114 pulsars have record that it has glitched at least once, 56 pulsars have records that they have glitches at least 3 times or more. There were 275 pulsars that have \(n>0\), while 196 have \(n<0\) in our sample (both glitching and non-glitching pulsars). There are 36 pulsars that have glitched once in our sample \(n<0\), among them only 15 have glitched at least 3 times; while there are 78 pulsars with \(n>0,\) among them, 29 pulsars have glitched at least 3 times. Table 1, shows the median and the mean with standard deviation of pulsar parameters (timing and some derived) we studied with \(n>0 \text{a}\text{n}\text{d} n<0\) for a sample of pulsars where \(n\) can be estimated and for a subsample of pulsars that have glitched at least once. Table 1 is the average values (Table 1a – median and 1b – mean with standard error) of the timing and derived parameters of various subsamples of pulsars. Table 1 suggest that glitching pulsars have lower values of \(n\), and is it lower for subsample with \(n>0\) than for subsample with \(n<0\). For pulsars with \(n<0\), the median value are - for \(G=0, {n}_{med}={-2.7\times 10}^{3}\), for \(G\ge 1, {n}_{med}={-1.8\times 10}^{2},\) for\(G\ge 3, {n}_{med}={-8.1\times 10}^{1};\)and for pulsars with \(n>0\), the median value is for \(G=0, {n}_{med}={1.1\times 10}^{3}\), for \(G\ge 1, {n}_{med}={4.6\times 10}^{1},\) for\(G\ge 3, {n}_{med}={4.1\times 10}^{1}\).
Table 1
a: The Median Values of Pulsar Parameters of Various Subsamples
| | \(\varvec{\nu }\) | \(\dot{\varvec{\nu }}\) | \(\ddot{\varvec{\nu }}\) | \(\varvec{n}\) | \(\varvec{P}\) | \(\dot{\varvec{P}}\) | \(\varvec{D}\varvec{M}\) | \(\varvec{R}\varvec{M}\) | \({\varvec{S}}_{400}\) | \({\varvec{S}}_{1400}\) |
All | \(\varvec{n}<0\) | 1.9 | -4.6E-15 | -1.4E-26 | -1.4E + 3 | 0.5 | 1.6E-15 | 83.5 | 6.5 | 12.8 | 1.4 |
\(\varvec{n}>0\) | 2.3 | -1.3E-14 | 5.8E-26 | 2.7E + 2 | 0.4 | 5.0E-15 | 102.7 | 10.1 | 13.5 | 1.4 |
\(\varvec{G}\ge 1\) | \(\varvec{n}<0\) | 3.1 | -4.0E-14 | -3.3E-25 | -1.8E + 2 | 0.3 | 6.1E-15 | 184.7 | 7.1 | 20.8 | 2.1 |
\(\varvec{n}>0\) | 3.3 | -6.6E-13 | 4.5E-24 | 4.6E + 1 | 0.3 | 4.4E-14 | 142.1 | 10.1 | 16.1 | 1.5 |
\(\varvec{G}\ge 3\) | \(\varvec{n}<0\) | 3.9 | -6.0E-13 | -1.0E-23 | -8.1E + 1 | 0.3 | 1.7E-14 | 205.5 | 23.1 | 27.1 | 2.1 |
\(\varvec{n}>0\) | 6.9 | -4.8E-12 | 1.5E-22 | 4.1E + 1 | 0.1 | 9.6E-14 | 194.2 | 5.3 | 25.1 | 1.2 |
\(\varvec{G}=0\) | \(\varvec{n}<0\) | 1.9 | -2.4E-15 | -1.1E-26 | -2.7E + 3 | 0.5 | 1.3E-15 | 66.8 | 6.1 | 11.3 | 1.4 |
\(\varvec{n}>0\) | 1.9 | -5.6E-15 | 1.9E-26 | 1. 1E + 3 | 0.5 | 2.6E-15 | 86.9 | 9.9 | 13.1 | 1.2 |
| | \(\varvec{D}\) | \(\varvec{R}\) | \({\varvec{R}}_{14}\) | \(\varvec{\tau }\) | \({\varvec{B}}_{\varvec{s}}\) | \(\dot{\varvec{E}}\) | \(\ddot{\varvec{E}}\) | \({\varvec{P}}_{\varvec{T}}\) | \({\varvec{V}}_{\varvec{T}}\) | \({\varvec{B}}_{\varvec{L}\varvec{C}}\) |
All | \(\varvec{n}<0\) | 3.4 | 74.2 | 10.8 | 5.1E + 6 | 1.1E + 12 | 4.8E + 32 | 6.4E + 31 | 14.1 | 167.5 | 53 |
\(\varvec{n}>0\) | 3.3 | 90.6 | 15.2 | 2.0E + 6 | 1.7E + 12 | 1.4E + 33 | 2.1E + 32 | 17.1 | 214.9 | 123 |
\(\varvec{G}\ge 1\) | \(\varvec{n}<0\) | 4.2 | 196.2 | 47.5 | 6.1E + 5 | 1.3E + 12 | 3.6E + 33 | 1.9E + 32 | 22.1 | 365.7 | 306 |
\(\varvec{n}>0\) | 3.2 | 93.1 | 17.2 | 1.1E + 5 | 3.1E + 12 | 5.8E + 34 | 6.3E + 33 | 17.5 | 233.9 | 1115 |
\(\varvec{G}\ge 3\) | \(\varvec{n}<0\) | 4.5 | 1184.0 | 104.0 | 6.3E + 4 | 2.6E + 12 | 1.4E + 35 | 8.7E + 33 | 34.1 | 715.6 | 3180 |
\(\varvec{n}>0\) | 3.6 | 112.8 | 17.1 | 2.6E + 4 | 3.6E + 12 | 2.0E + 36 | 8.7E + 34 | 19.1 | 199.2 | 12000 |
\(\varvec{G}=0\) | \(\varvec{n}<0\) | 3.2 | 66.1 | 8.1 | 8.7E + 06 | 9.5E + 11 | 2.5E + 32 | 4.3E + 31 | 12.76 | 154.1 | 43.3 |
\(\varvec{n}>0\) | 3.5 | 88.1 | 13.9 | 4.7E + 06 | 1.3E + 12 | 6.6E + 32 | 5.6E + 31 | 17.1 | 211.8 | 57.2 |
Note: \(\varvec{\nu }\) is the frequency in Hz; \(\dot{\varvec{\nu }}\) is the first time-derivative of frequency in \({\varvec{s}}^{-2}\); \(\ddot{\varvec{\nu }}\) is the second time-derivative of frequency in \({\varvec{s}}^{-3}; \varvec{n}\) is the breaking index; \(\varvec{P}\) is the period in \(\varvec{s}\); \(\dot{\varvec{P}}\) is the first time-derivative of the period; \(\varvec{D}\varvec{M}\) is the dispersion measure in \({\varvec{c}\varvec{m}}^{-3} \varvec{p}\varvec{c}\); \(\varvec{R}\varvec{M}\) is the rotation measure in\(\varvec{r}\varvec{a}\varvec{d} {\varvec{m}}^{-2}\); \({\varvec{S}}_{400}\) is the mean flux density at 400 MHz in mJy; \({\varvec{S}}_{1400}\) is the mean flux density at 1400 MHz in mJy; \(\varvec{D}\) is the distance in kpc; \(\varvec{R}\) is the Radio luminosity at 400 MHz in mJy kpc2; \({\varvec{R}}_{14}\) is the Radio luminosity at 1400 MHz in mJy kpc2; \(\varvec{\tau }=\frac{\varvec{P}}{2\dot{\varvec{P}}}\) is the spin-down age in years; \({\varvec{B}}_{\varvec{s}}\) is the surface magnetic flux density in Gauss; \(\dot{\varvec{E}}\) is the spin down energy loss rate in ergs/s; \(\ddot{\varvec{E}}\) is the energy flux at the Sun in ergs/kpc2/s; \({\varvec{P}}_{\varvec{T}}\) is the total proper motion in mas/yr; \({\varvec{V}}_{\varvec{T}}\) is the transverse velocity - based on \(\varvec{D}\) in km/s; \({\varvec{B}}_{\varvec{L}\varvec{C}}\) is the magnetic field at light cylinder in Gauss; G is number of glitches.
Table 1
b: The Mean Values of Pulsar Parameters of Various Subsamples
| | \(\varvec{\nu }\) | \(\dot{\varvec{\nu }}\) | \(\ddot{\varvec{\nu }}\) | \(\varvec{n}\) | \(\varvec{P}\) | \(\dot{\varvec{P}}\) | \(\varvec{D}\varvec{M}\) | \(\varvec{R}\varvec{M}\) | \({\varvec{S}}_{400}\) | \({\varvec{S}}_{1400}\) |
All | \(\varvec{n}<0\) | 31.2\(\pm\) 50.3 | -4.8\(\pm\) 8.3E-13 | -7.1\(\pm\) 15.5E-22 | -1.2\(\pm\) 2.4E + 10 | 0.9\(\pm\) 0.8 | 3.2\(\pm\) 6.3E-12 | 158.8\(\pm\) 138.8 | -374.4\(\pm\) 830.3 | 32.1\(\pm\) 32.8 | 4.8\(\pm\) 5.6 |
\(\varvec{n}>0\) | 25.8\(\pm\) 41.3 | -4.6\(\pm\) 7.9E-12 | 2.1\(\pm\) 3.6E-22 | 4.6\(\pm\) 9.1E + 7 | 0.7\(\pm\) 0.5 | 1.4\(\pm\) 2.3E-13 | 172.3\(\pm\) 136.1 | 21.9\(\pm\) 161.5 | 81.2\(\pm\) 109.1 | 12.1\(\pm\) 17.4 |
\(\varvec{G}\ge 1\) | \(\varvec{n}<0\) | 5.1\(\pm\) 3.9 | -2.1\(\pm\) 3.0E-12 | -8.9\(\pm\) 1.5E-22 | -8.5\(\pm\) 10.1E + 2 | 1.2\(\pm\) 1.4 | 1.8\(\pm\) 3.2E-12 | 228.1\(\pm\) 150.4 | 47.8\(\pm\) 216.7 | 46.1 44.2 | 4.1\(\pm\) 3.7 |
\(\varvec{n}>0\) | 6.1\(\pm\) 4.8 | -1.4\(\pm\) 2.2E-11 | 5.5\(\pm\) 9.0E-22 | 1.1\(\pm\) 1.7E + 3 | 0.5\(\pm\) 0.4 | 2.5\(\pm\) 3.4E-13 | 216.9\(\pm\) 158.7 | 28.2\(\pm\) 184.2 | 161.1\(\pm\) 246.2 | 22.3\(\pm\) 35.4 |
\(\varvec{G}\ge 3\) | \(\varvec{n}<0\) | 4.9\(\pm\) 3.5 | -2.2\(\pm\) 2.4E-12 | -2.1\(\pm\) 2.9E-22 | -6.5\(\pm\) 9.5E + 2 | 2.3\(\pm\) 3.3 | 5.6\(\pm\) 9.0E-12 | 281.2\(\pm\) 193.2 | -134.9\(\pm\) 283.9 | 115.0\(\pm\) 120.7 | 5.1\(\pm\) 5.1 |
\(\varvec{n}>0\) | 9.6\(\pm\) 7.2 | -2.8\(\pm\) 3.9E-11 | 1.1\(\pm\) 1.4E-21 | 9.9\(\pm\) 11.1E + 1 | 0.3\(\pm\) 0.2 | 2.5\(\pm\) 2.8E-13 | 249.6\(\pm\) 163.3 | -5.2\(\pm\) 263.3 | 421.3\(\pm\) 627.7 | 51.3\(\pm\) 86.1 |
\(G=0\) | \(\varvec{n}<0\) | 37.1± 59.9 | -1.3± 2.2E-13 | -8.5± 17.1E-21 | -1.5E + 10± 2.9E + 10 | 0.8± 0.6 | 3.6± 7.1E-12 | 144.5± 131.0 | -475.1 1014.±4 | 30.1± 30.9 | 5.1± 6.1 |
\(\varvec{n}>0\) | 33.6± 55.7 | -7.8 13.1E-12 | 6.3E-23± 1.2E-22 | 6.5E + 7± 1.3E + 8 | 0.7± 0.5 | 9.9± 17.1E-13 | 154.7± 124.8 | 19.1± 151.6 | 53.8± 64.1 | 7.3± 9.8 |
| \(\varvec{D}\) | \(\varvec{R}\) | \({\varvec{R}}_{14}\) | \(\varvec{\tau }\) | \({\varvec{B}}_{\varvec{s}}\) | \(\dot{\varvec{E}}\) | \(\ddot{\varvec{E}}\) | \({\varvec{P}}_{\varvec{T}}\) | \({\varvec{V}}_{\varvec{T}}\) | \({\varvec{B}}_{\varvec{L}\varvec{C}}\) |
All | \(\varvec{n}<0\) | 4.2± 2.6 | 426.2± 565.5 | 60.2± 73.4 | 9.6± 19.1E + 10 | 2.2± 3.9E + 13 | 1.5± 2.6E + 35 | 3.2± 5.6E + 34 | 25.7± 20.5 | 263.1± 183.2 | 7.1± 12.1E3 |
\(\varvec{n}>0\) | 4.4± 2.7 | 539.5± 689.8 | 115.9± 163.6 | 7.5± 12.2E + 8 | 4.7± 5.3E + 12 | 4.7± 8.6E + 36 | 8.3± 15.2E + 36 | 29.4± 22.9 | 323.6± 227.9 | 2.5± 4.2E3 |
\(\varvec{G}\ge 1\) | \(\varvec{n}<0\) | 5.3± 2.8 | 1027.6± 1233.9 | 84.4± 76.4 | 4.4± 5.8E + 6 | 3.8± 6.4E + 13 | 6.6± 9.9E + 35 | 4.1± 6.1E + 34 | 36.3± 24.9 | 487.6± 279.2 | 6.7± 9.4E3 |
\(\varvec{n}>0\) | 4.9± 3.7 | 671.1± 889.8 | 142.0± 205.4 | 2.7± 4.1E + 6 | 5.5± 4.6E + 12 | 1.6± 2.8E + 37 | 2.7± 5.1E + 36 | 33.8± 25.5 | 333.6± 235.6 | 53.4± 87.1E3 |
\(\varvec{G}\ge 3\) | \(\varvec{n}<0\) | 5.9± 3.6 | 2277.5± 2235.4 | 106.4± 81.4 | 6.2± 8.2E + 5 | 1.1± 1.7E + 14 | 5.9± 6.8E + 35 | 5.6± 7.1E + 34 | 85.7± 72.3 | 607.1± 219.7 | 6.9± 7.5E3 |
\(\varvec{n}>0\) | 5.3± 4.1 | 827.2± 1098.5 | 248.6± 401.8 | 2.4± 3.3E + 5 | 5.6± 3.8E + 12 | 3.6± 6.1E + 37 | 7.1± 13.1E + 37 | 36.7± 29.5 | 264.2± 179.4 | 12.5± 19.2E4 |
\(G=0\) | \(\varvec{n}<0\) | 4.0 2.6 | 341.8± 451.2 | 54.5± 70.6 | 1.2 ± 2.3E + 10 | 1.8 ± 3.2E + 13 | 2.7 ± 4.6E + 34 | 3.1 ± 5.5E + 34 | 23.9± 19.6 | 223.4± 146.9 | 7.2± 12.7E3 |
\(\varvec{n}>0\) | 4.2± 2.4 | 494.4± 617.9 | 104.0± 145.1 | 1.1± 1.6E + 8 | 4.4 5.4E + 12 | 2.± 3.7E + 35 | 3.1± 5.3E + 34 | 27.4± 21.3 | 319.2± 223.1 | 1.4± 2.3E4 |
Table 1 also suggests that the average value of pulsar rotational frequency seems higher for pulsars that have glitched once \(\varvec{\nu }=3.1 Hz \left(for n<0\right)\) and \(\varvec{\nu }=3.3 Hz\) \(\left(for n>0\right)\), and gets larger for more glitching pulsars (for pulsars with \(G\ge 3\), \(\varvec{\nu }=4.1 Hz \left(for n<0\right)\) and \(6.9 Hz\) \(\left(for n>0\right)\) as against when all the glitching pulsars in our sample were considered \(\varvec{\nu }=1.9 Hz \left(for n<0\right)\) and \(\varvec{\nu }=2.3 Hz\) \(\left(for n>0\right)\) and \(\varvec{\nu }=1.9 Hz \left(for n<0 and n>0\right)\) – for completeness – for pulsars that have no record of glitching. It can be inferred from this analysis, that glitching increases the rotational frequency of pulsars, and pulsars with \(n>0\) appear to rotate faster than those with \(n<0\). This trend is similar if the period derivative \(\dot{P},\) the absolute values of \(\dot{\nu }\) and \(\ddot{\nu }\) are considered
Thus, one can infer the glitching in pulsars increases the values of the timing activity parameters and perhaps the magnitude of the timing noise associated with these parameters. Chukwude (2003) reported an exceptionally strong correlation between the magnitude of the observed second derivative of the pulse rotation frequency and phase residuals from 2nd-and 3rd-order polynomial models and conclude that standard timing technique, is reasonably contaminated by effects attributable to pulsar timing irregularity, implying that effective measurement of \(n\) is on how deterministic spin-down effects are decoupled from dominant timing activities.
Carrying similar analysis for the derived parameters, the median values of the dispersion measure and rotation measure showed that pulsars with \(n>0\) or \(n<0\)are located in similar environment, though if we consider only glitching pulsars, the median value \(DM = 184.7 {\varvec{c}\varvec{m}}^{-3} \varvec{p}\varvec{c} and 205.5 {\varvec{c}\varvec{m}}^{-3} \varvec{p}\varvec{c}\) for \(n<0\)for \(G=1and G=3\) respectively; \(DM = 142.1 {\varvec{c}\varvec{m}}^{-3} \varvec{p}\varvec{c} and 194.2 {\varvec{c}\varvec{m}}^{-3} \varvec{p}\varvec{c}\) for \(n>0\) for \(G=1\) and \(G=3\) respectively; a marginal difference. The median values of the mean flux density at 400 MHz (\({\varvec{S}}_{400}\)) and 1400 MHz (\({\varvec{S}}_{1400}\)) seems to suggest higher fluxes from pulsars with \(n<0\) than pulsars with \(n>0\). This is also seen is the radio luminosity at measure 400 MHz and at 1400 MHz, while the reverse is the case for non-glitching pulsars. The median values of the characteristic age of pulsars indicate that non-glitching pulsars are older, and as G increases, the characteristic age of pulsars decreases, also for also the subsamples, the median characteristic age of pulsars indicates that pulsars with \(n<0\) are older than pulsars with \(n>0\), while it appears that the surface magnetic field of pulsars with \(n>0\) are greater that those with \(n<\) 0, also, the median values of the magnetic field of glitching pulsars surface are greater than the median values of non-glitching pulsars in our sample. Table 1 indicates that the spin down energy loss rate, the energy flux at the Sun and the magnetic field at light cylinder are greater in glitching pulsars than non-glitching pulsars and are higher for pulsars with \(n>0\) than pulsars with \(n<0\) for all the subsamples. Furthermore, the median values of the total proper motion and the transverse velocity - based on \(D\) indicated that \({P}_{T}\) and \({V}_{T}\) follow similar trend in our subsamples, higher for pulsars with \(n<0\) than pulsars with \(n>0\) and increases as the number of glitches increases for each subsample.
The estimated median value of the distance parameter \(D\) (kpc), seems to suggest that in glitching pulsars, pulsars with \(n<0\) are located in greater distances than pulsars with \(n>0,\) (for \(G\ge 1\), \(n<0, D=4.2 kpc, n>0, D=3.2 kpc; \text{f}\text{o}\text{r} G\ge 3, n<0, D=4.5 kpc, n>0, D=3.6 kpc,\) while for non-glitching pulsars, \(n<0, D=3.2 kpc kpc, n>0, D=3.5\). We also investigated the seemingly trend observed in the distance\(D\) of pulsars using other distance measure e.g. the parallax (\(PX\)), the distance from the Galactic plane (\(ZZ\)), the \(X\)-distance in the \(X-Y-Z\) Galactic coordinate system and the \(Y\)-distance in the \(X-Y-Z\) Galactic coordinate system. The calculated median (we used absolute values, because we are interested in distances away from the galactic plane) values were shown in Table 2. Table 2 seems to suggest that glitching pulsars exhibit more parallax than non-glitching pulsars (higher values of\(PX\) as \(G\) increases for both \(n>0\) and \(n<0\) subsamples), while non-glitching pulsars and are at larger distances above or below the Galactic plane than the glitching pulsars (lower values of\(ZZ\) as \(G\) increases for both \(n>0\) and \(n<0\) subsamples). The XX values indicate increasing values as G increases for pulsars with \(n<0\), but decreases as G increases for pulsars with \(n>0\), while YY values showed decreasing values as G increases for both pulsars with \(n<0\) and \(n>0\). The median values of YY and ZZ are similar for both pulsars with \(n<0\) and \(n>0\), XX values of subsample with \(n<0\) are higher than those of the subsample with \(n>0\), while PX values are higher for subsample with \(n>0\) (similar trend was observed in the D parameter).
Table 2
Average values of Distance parameters of various subsamples of pulsars in our sample
| PX | abs ZZ | abs XX | abs YY | PX | abs ZZ | abs XX | abs YY |
| mas | kpc | kpc | kpc | mas | kpc | kpc | kpc |
| \(n<0\) | \(n>0\) |
ALL | 0.29 | 0.19 | 1.41 | 6.89 | 0.28 | 0.14 | 1.55 | 6.62 |
\(G=0\) | 0.24 | 0.24 | 1.07 | 6.94 | 0.23 | 0.20 | 1.74 | 6.62 |
\(G\ge 1\) | 0.44 | 0.07 | 2.10 | 5.72 | 0.48 | 0.06 | 1.26 | 5.90 |
\(G\ge 3\) | 1.20 | 0.03 | 2.21 | 4.81 | 2.21 | 0.04 | 1.11 | 5.07 |
Using the mean values, similar trends observed for the various subsamples with the median values were difficult to observe because of large standard errors associated with the mean values due to extreme large values measured or derived in pulsar parameters. We believe that the trends observed in the subsamples using the median values may be significant to pulsar research.
Figure 1 is the distribution plot of \(\left|n\right|.\) The plot indicates that the distribution of all the subsamples are lognormal with the peak values of the subsamples with \(n>0\) generally less than the peak values of the subsamples with \(n<0\). Table 3 shows the correlation coefficient results between the braking index and the timing/derived parameters of pulsars. It seems the values of braking indices of pulsars do not depend on any of the measured values of the timing parameters nor the derived parameters. Though the correlation coefficient result between the characteristic age of pulsars and the braking index of pulsars suggests an inverse relationship for pulsars with \(n<0\) and a direct relation for pulsars with \(n>0\), this is simply due to the opposite signs in the values of breaking index. Using the absolute values, the correlation between \(\tau\) and \(\left|n\right|\) follow the similar trends for \(n<0\) and \(n>0\). Also, Table 3 shows that there is no correlation between braking index and pulsar’s glitch parameters for all the subsamples. This null correlation between \(n\)and pulsar parameters indicates that \(n\) values obtained by Eq. 2, may be affected by different factors (for instance, the difficulty in measuring \(\ddot{\nu }\) used in Eq. 2 to estimate \(n\) (Johnston and Galloway, 1999; Alpar and Baykal 2006); pulsar timing activities and timing effects \(\)(Chukwude, 2003; Chukwude, 2007; Zou et al., 2008; Hobbs et al., 2006); pulsars as SOCS (Melatos et al. 2008; Onuchukwu & Chukwude 2016) are expected to have random values of glitch parameters and randomness in timing noises parameters). We also plotted the scatter diagram of \({\text{log}}_{10}\left|n\right|\) and logarithm of the derived parameters. the log-log plots are shown in Figs. 2–8.
Table 3
| \(\varvec{n}<0\) | \(\varvec{n}<0\) | \(\varvec{n}<0\) | \(\varvec{n}<0\) | \(\varvec{n}>0\) | \(\varvec{n}>0\) | \(\varvec{n}>0\) | \(\varvec{n}>0\) |
| All | \(\varvec{G}=0\) | \(\varvec{G}\ge 1\) | \(\varvec{G}\ge 3\) | All | \(\varvec{G}=0\) | \(\varvec{G}\ge 1\) | \(\varvec{G}\ge 3\) |
\(\varvec{n}/\varvec{G}\) | 0.12 | n/a | 0.12 | 0.18 | -0.16 | n/a | -0.16 | -0.08 |
\(\varvec{n}/\varvec{P}\) | 0.05 | 0.07 | 0.07 | 0.06 | 0.01 | 0.00 | 0.27 | 0.34 |
\(\varvec{n}/\dot{\varvec{P}}\) | 0.01 | 0.01 | 0.07 | 0.08 | -0.01 | -0.01 | -0.08 | -0.13 |
\(\varvec{n}/\varvec{\nu }\) | -0.11 | -0.10 | 0.19 | 0.24 | 0.01 | 0.01 | -0.16 | -0.23 |
\(\varvec{n}/\dot{\varvec{\nu }}\) | -0.01 | -0.01 | -0.14 | -0.26 | 0.01 | 0.02 | 0.09 | 0.16 |
\(\varvec{n}/\ddot{\varvec{\nu }}\) | -0.01 | -0.01 | -0.13 | -0.14 | -0.01 | -0.01 | -0.10 | -0.16 |
\(\varvec{n}/\varvec{D}\varvec{M}\) | 0.00 | -0.01 | 0.16 | 0.13 | 0.17 | 0.23 | -0.13 | 0.06 |
\(\varvec{n}/\varvec{R}\varvec{M}\) | -0.03 | -0.03 | -0.14 | -0.30 | 0.25 | 0.32 | 0.13 | -0.23 |
\(\varvec{n}/{\varvec{S}}_{400}\) | 0.05 | 0.05 | 0.25 | 0.49 | -0.01 | -0.02 | -0.08 | -0.05 |
\(\varvec{n}/{\varvec{S}}_{1400}\) | 0.03 | 0.03 | 0.14 | 0.22 | -0.01 | -0.01 | -0.04 | 0.19 |
\(\varvec{n}/\varvec{D}\) | -0.06 | -0.07 | -0.75 | -0.64 | 0.08 | 0.13 | -0.08 | -0.11 |
\(\varvec{n}/\varvec{R}\) | 0.03 | 0.03 | -0.86 | -0.98 | -0.03 | -0.03 | -0.09 | 0.83 |
\(\varvec{n}/{\varvec{R}}_{14}\) | 0.03 | 0.03 | -0.55 | -0.01 | 0.01 | 0.02 | -0.02 | 0.87 |
\(\varvec{n}/\varvec{\tau }\) | -0.99 | -0.99 | -0.43 | -0.88 | 0.15 | 0.15 | 0.65 | 0.94 |
\(\varvec{n}/{\varvec{B}}_{\varvec{s}}\) | 0.01 | 0.01 | 0.08 | 0.08 | -0.02 | -0.02 | -0.10 | -0.08 |
\(\varvec{n}/\dot{\varvec{E}}\) | 0.01 | 0.02 | 0.15 | 0.26 | -0.01 | -0.02 | -0.07 | -0.14 |
\(\varvec{n}/\ddot{\varvec{E}}\) | 0.01 | 0.01 | 0.17 | 0.16 | -0.01 | -0.01 | -0.06 | -0.11 |
\(\varvec{n}/{\varvec{P}}_{\varvec{T}}\) | 0.08 | 0.08 | 0.37 | 0.47 | -0.06 | -0.06 | -0.14 | 0.02 |
\(\varvec{n}/{\varvec{V}}_{\varvec{T}}\) | 0.09 | 0.09 | 0.20 | 0.74 | -0.04 | -0.04 | -0.13 | -0.35 |
\(\varvec{n}/{\varvec{B}}_{\varvec{L}\varvec{C}}\) | 0.01 | 0.01 | 0.00 | 0.24 | -0.01 | -0.02 | -0.07 | -0.14 |
\(\varvec{n}/\varvec{\varDelta }\varvec{T}\) | | | 0.09 | -0.16 | | | 0.01 | -0.09 |
\(\varvec{n}/\left|\varvec{\varDelta }\varvec{\nu }/\varvec{\nu }\right|\) | | | -0.11 | -0.03 | | | -0.05 | 0.03 |
\(\varvec{n}/\left|\varvec{\varDelta }\dot{\varvec{\nu }}/\dot{\varvec{\nu }}\right|\) | | | -0.06 | -0.01 | | | -0.02 | 0.01 |
\(\varvec{\varDelta }\varvec{T}/\left|\varvec{\varDelta }\varvec{\nu }/\varvec{\nu }\right|\) | | | 0.05 | 0.00 | | | 0.01 | -0.03 |
\(\varvec{\varDelta }\varvec{T}/\left|\varvec{\varDelta }\dot{\varvec{\nu }}/\dot{\varvec{\nu }}\right|\) | | | -0.06 | -0.03 | | | -0.02 | -0.03 |
Note: \(\varvec{\varDelta }\varvec{T}\) is the waiting time estimated for sources that have glitched for more than once; \(\left|\varvec{\varDelta }\varvec{\nu }/\varvec{\nu }\right|\) is the magnitude of the glitch size in frequency; \(\left|\varvec{\varDelta }\dot{\varvec{\nu }}/\dot{\varvec{\nu }}\right|\) \(\left|\varvec{\varDelta }\varvec{\nu }/\varvec{\nu }\right|\) is the magnitude of the glitch size in first-time derivative of frequency. |
Figure 6: Plot of log-log values of \({\varvec{P}}_{\varvec{T}}\) against\(\left|\varvec{n}\right|\)
Figure 8: Plot of log-log values of \({\varvec{B}}_{\varvec{L}\varvec{C}}\) against\(\left|\varvec{n}\right|\)
Figure 8 is the plot of log-log values of \({B}_{LC}\) against \(\left|n\right|\). The plot indicates that on the average, the subsample with \(n>0, G\ge 1\) appear to have higher values of \({B}_{LC}\) than other subsamples. This was also indicated in Table 2