Radio Pulsar Sub-Populations (I) : The Curious Case of Nulling Pulsars

Sushan Konar; Uddeepta Deka

REVIEW 5 major objections 6 minor 79 references

Radio Pulsar Sub-Populations (I) : The Curious Case of Nulling Pulsars

T0 review · 5 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Nulling pulsars are bounded by two death-lines and are likely polar-cap emitters with extremely curved magnetic fields.

desk verdict Useful catalog and a mostly negative correlation result, but the polar-cap/curved-field wedge claim is asserted rather than tested against a non-nulling control. read the letter →

arxiv 1908.07681 v2 pith:67WJ6HHG submitted 2019-08-21 astro-ph.HE

Sushan Konar , Uddeepta Deka This is my paper · ORCID

classification astro-ph.HE

keywords nullingpulsarsfractionpulsardeath-linepolarcapemissionmagneticfieldcurvatureradiopopulationperiod-magnetic-fieldplanemechanism

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Across roughly two hundred known nulling radio pulsars, the fraction of time a pulsar is silent (the nulling fraction) correlates with none of its measured intrinsic properties—spin period $P_s$, inferred surface field $B_s$, spin-down rate $\dot{P}$, characteristic age $\tau_c$, or dispersion measure. This removes age and spin-down as the organizing variables for nulling. On the $P_s$–$B_s$ plane, however, the nulling population occupies a narrow band: nearly none sit above the outer-magnetosphere dipole death-line 5b, and they are bounded below by the polar-cap, very-curved-field death-line 2. The paper concludes that nulling episodes are preferentially experienced by pulsars whose radio emission comes mainly from the polar cap and whose magnetic field lines are extremely curved. If true, this turns nulling from a puzzling side-effect of pulsar ageing into a geometric and emission-mechanism diagnostic.

What carries the argument

The central device is the gridding of the $P_s$–$B_s$ plane by theoretical pulsar death-lines, numbered from 1 to 9b, each derived from a different pair-production model: polar-cap versus outer-magnetosphere emission, central versus offset dipoles, and very curved versus twisted field configurations. The argument turns on two of these lines. Death-line 2 is a polar-cap model with very curved field lines ($r_c\sim R$) and forms the lower bound of the nulling population; death-line 5b is an outer-magnetosphere non-aligned dipole and forms the upper bound, with almost no nulling pulsars above it. The wedge between the two lines is what identifies nulling pulsars as polar-cap, curved-field emitters. The plane's vertical coordinate is not a directly measured quantity but the dipole field $B_s$ inferred from $P_s$ and $\dot{P}$ through the standard spin-down formula, an inference the paper acknowledges is only approximate for the polar-cap death-lines.

What would settle it

A nulling search of pulsars located above death-line 5b—dipolar outer-magnetosphere emitters—that finds a substantial nulling fraction, or a measurement showing that the true surface fields of nulling pulsars deviate from their inferred dipole values by more than about 10 percent, would break the wedge and with it the polar-cap, curved-field conclusion.

Watch

Extended reading notes

Core claim

The central claim is that nulling is a geometric and emission-mechanism signature rather than an age effect. In the $P_s$–$B_s$ plane, nulling pulsars are effectively absent above death-line 5b, which corresponds to a pure dipole field in an outer-magnetosphere emission model, and they are bounded below by death-line 2, which corresponds to polar-cap emission with very curved field lines (curvature radius $\sim$ stellar radius). The authors infer that pulsars whose emission is predominantly from the polar cap, with extremely curved magnetic fields, are the ones that experience nulling episodes. Consistent with this, the nulling fraction $NF$ shows no significant Pearson correlation with $P_s$, $B_s$, $\dot{P}$, $\tau_c$, or $DM$, and the spin-period distributions of high- and low-$NF$ pulsars differ in a Kolmogorov–Smirnov test, so the earlier suggestion that nulling is a late-life phenomenon is not supported by the present population.

Load-bearing premise

The argument assumes that the dipole field $B_s$ inferred from measured $P_s$ and $\dot{P}$ is a fair common coordinate for comparing all pulsars against death-lines whose model field geometries differ, and that any overestimate is no larger than the 10 percent the paper assumes.

Editorial extensions

If this is right

Nulling becomes a usable diagnostic: a pulsar that nulls is likely to be a polar-cap emitter with strongly curved field lines, so nulling behaviour can indicate the emission site without detailed pulse modelling.
The claim that nulling is mainly a property of old, low-field pulsars is not supported, so searches and models should stop using characteristic age as the organising variable.
Pulsars above the dipole outer-magnetosphere death-line 5b should not null; finding a nuller there would force a revision of either the death-line models or the wedge interpretation.
Targeted monitoring of slow pulsars between death-lines 2 and 4a is a direct test, since the interpretation predicts these objects should show nulling episodes if observed long enough.
A gap in nulling fraction near 40 percent separates two sub-populations with different intrinsic parameter distributions, implying that $NF$ can define sub-classes even though it is not correlated with any single parameter.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper, the wedge reading suggests that the nulling fraction could serve as a coarse population-level classifier for emission geometry in large pulsar surveys, separating likely polar-cap emitters from likely outer-magnetosphere emitters without per-pulse analysis.
If the wedge is real, the apparent immunity of millisecond pulsars to nulling fits naturally: their low fields and different polar-cap geometry keep them far from the curved-field regime of death-line 2, a link the paper notes but does not draw.
Correcting the inferred $B_s$ for duty-cycle-dependent spin-down in intermittent pulsars may shift individual points within the wedge; the paper assumes the effect is small, but a larger duty-cycle-corrected sample could sharpen or blur the boundaries.
The gap near $NF\sim40\%$ could reflect two genuinely different emission states rather than a detection artefact; simultaneous polarimetric and timing observations of pulsars with $NF$ near the gap would be a testable extension.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The paper is worth reading for the catalog alone: 204 nulling pulsars, nearly double Gajjar's 109, with references and duplicate NF estimates assembled in one place. That is a real resource. The no-correlation result for NF versus intrinsic parameters is also a useful update, and the population split near NF 40% is an interesting observation, even if presented with appropriate caution. I agree with the reader that the central death-line claim is the weak link. The bottom panel of Fig. 5 shows nulling pulsars sitting between death-lines 2 and 5b, and the text concludes they are preferentially polar-cap emitters with extremely curved fields. But there is no control sample. Without asking what fraction of non-nulling pulsars occupy that same wedge, 'preferentially' is unsupported. The upper bound is especially fragile: very few pulsars anywhere lie above 5b, so the absence of nulling pulsars there may just reflect how empty that part of the P-B plane is. The lower bound is undercut by the paper's own admission that the slow pulsars between death-lines 2 and 4a have not been systematically studied for nulling. That is precisely the comparison region, and the authors say they are now starting to monitor it. Until that study is done, the wedge claim is a plausible hypothesis, not a population result. There are also some fixable statistical problems. Table 1 lists sigma=0.044 for NF-Ps and 0.047 for NF-tau_c, yet the text concludes no correlation. Those nominally significant p-values need interpretation, ideally with a multiple-testing correction or an explicit statement that the coefficients are small. The post hoc 40% split should be flagged as such in the table. And the treatment of NF upper limits and conflicting literature values as point estimates could bias the correlation analysis; a sensitivity check would be straightforward. The B_s coordinate issue is acknowledged by the authors, and their 10% overestimate assumption is a guess, but it is a minor concern given the size of the wedge. The paper is honest, the literature coverage is good, and the proposed monitoring of slow pulsars is the right way to test the model. This should go to peer review, but the referee should ask for a quantitative comparison with non-nulling pulsars in the same P-B region, a corrected correlation table, and explicit handling of upper limits. The catalog and the null result are solid enough to survive that revision; the wedge claim may or may not.

Referee Report

5 major / 6 minor

Summary. This paper compiles an updated catalog of approximately 204 nulling pulsars from the literature, examines the distribution of nulling fractions (NF) and their correlations with spin period, dipole surface field, period derivative, characteristic age, and dispersion measure, and overlays the nulling population on theoretical pulsar death-lines in the P_s-B_s plane. The authors report no correlation of NF with intrinsic parameters and identify a 40% gap in NF, and they argue from the bounding of nulling pulsars between death-line 2 (polar-cap, very curved field) and death-line 5b (outer-magnetospheric dipole) that nulling is preferentially experienced by pulsars with polar-cap emission and extremely curved magnetic fields.

Significance. The catalog update and the death-line population comparison are potentially useful: if the wedge interpretation survives controls, it would redirect nulling theory toward magnetic geometry and field curvature rather than age or spin-down. The paper's strengths are its careful compilation of heterogeneous literature data, the use of explicit death-line models from the independent literature, and the falsifiable prediction that slow pulsars between death-lines 2 and 4a should be monitored for nulling. However, the central statistical claim is internally inconsistent with Table 1, and the preference claim currently lacks a non-nulling control.

major comments (5)

[Section 2, Table 1; Summary point 4] The claim that NF shows no correlation with intrinsic parameters is not supported by Table 1 as presented: the ALL rows report significance values of sigma=0.044 for NF-Ps, sigma=0.047 for NF-tau_c, and sigma=0.033 for NF-DM, while the NF>40% row reports sigma=0.027 for NF-Ps and the NF<40% row reports sigma=0.0004 for NF-Ps. These conventional significance levels directly contradict the summary statement. Please apply a multiple-testing correction, justify a significance threshold in advance, or soften the claim; as written, the inference is internally inconsistent.
[Section 3, Fig. 5 bottom panel; Summary point 5] The conclusion that nulling pulsars 'preferentially' occupy the wedge between death-line 2 and death-line 5b requires a control comparison that is not provided. The paper does not compute the fraction of non-nulling radio pulsars above death-line 2 and below death-line 5b, nor does it test whether nulling pulsars are overrepresented in that wedge relative to the general pulsar population. Since death-line 2 lies well above the conventional graveyard, a large fraction of all active pulsars is also expected to lie above it; the text itself notes that the slow pulsars in the region between death-lines 2 and 4a 'have mostly not been studied in detail.' Without a control sample, the observed boundaries may reflect selection effects, monitoring incompleteness, or the parameter space of the nulling catalog, and the word 'preferentially' is unsupported.
[Section 3, Eq. (15)] The Chen-Ruderman death-lines (equations 1-5) are defined in terms of the actual surface magnetic field configuration, but Fig. 5 plots them using the dipole estimate B_p obtained from P and Pdot via Eq. (15). The paper acknowledges that this is 'not correct' for those lines and assumes that a 10% overestimate leaves the conclusions unchanged. This is not a derived bound: for very curved or twisted field configurations the relevant surface field can differ from the dipole estimate by more than 10%, and the robustness statement should be quantified, for example by computing how large a fractional change in B_s is needed to move nulling pulsars across death-line 2 or death-line 5b.
[Section 2, Figs. 1-4; Summary point 1] The 40% NF split is identified from the same histogram that is later used to divide the sample for the Kolmogorov-Smirnov test and the split-sample correlations, so the reported P_KS=0.002 is not a valid confirmatory test. The gap around 40% should be treated as an exploratory finding unless the split is justified by a pre-existing criterion or validated on an independent sample; otherwise the significance values in Table 1 and the KS test are inflated by post hoc selection.
[Section 2, Tables 2-5; Table 1] The NF values are heterogeneous: many entries are upper limits (e.g., entries with '≤' in Tables 2-5), and several pulsars have multiple conflicting NF estimates from different references, yet Table 1 treats these as exact point values in a Pearson correlation analysis. This treatment can bias the correlation coefficients and the associated p-values, particularly for the NF-Ps and NF-tau_c results. The authors should either use survival-analysis methods that accommodate upper limits, exclude limits in a sensitivity test, or explicitly justify why treating limits as point values does not affect the no-correlation conclusion.

minor comments (6)

[Figure 3 caption] The caption appears to invert the labels: it reads 'high null (NF < 40%)' while the text and Fig. 4 define low NF as NF < 40%; please correct the caption.
[Section 1] There is a typo in the sentence about associated emission features: 'thedrifting' should be 'the drifting.'
[References] The reference von Mises (1980) is not the standard source for Pearson correlation or the Kolmogorov-Smirnov test; please cite a standard statistics text or the original papers instead.
[Section 3] The text refers to 'death-line 2' and 'death-line 5b' while the numbered list uses equations 02 and 05a/05b; please align the notation for consistency.
[Abstract and Section 2] The abstract says 'About 200 radio pulsars' while the text says 'likely more than 204'; please harmonize these numbers.
[Title page] The title page lists two affiliations but does not indicate which author is associated with the second; please clarify the affiliation details.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found; the central claims rest on independent external data and external death-line theory.

full rationale

The derivation chain is self-contained. The nulling sample (Tables 2-8) is a literature compilation of observed nulling pulsars, the death-lines (Eqs. 1-14) are taken from Chen & Ruderman (1993) and Zhang, Harding, & Muslimov (2000), which are independent of the present authors, and the only equation derived by the paper, Eq. 15, is the standard Manchester-Taylor dipole-field estimate, applied consistently to both the pulsar data and the Zhang et al. death-lines. No parameter is fitted to the nulling data, and no 'prediction' is a renamed input. The central inference that nulling pulsars lie between death-lines 2 and 5b and therefore are consistent with polar-cap, curved-field emission is an interpretive overlay of external theoretical boundaries on an external dataset, not a reduction of the conclusion to its inputs. The paper explicitly acknowledges the coordinate ambiguity for the Chen-Ruderman death-lines and tests the conclusion against a 10% field overestimate, which is a caveat, not a circular step. The self-citations (e.g., Konar 2013, 2017; Konar et al. 2016, and the 'in prep' items) appear only in the introduction or in forward-looking remarks and do not carry the argument. The absence of a non-nulling control in the wedge region is an evidentiary limitation for the word 'preferentially', but it is a statistical or control concern, not a circularity.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

Everything else is pulled from the cited literature: the death-line equations, the pair-production requirement, and the ATNF pulsar parameters. The paper's own analytic contribution is the statistical compilation and the interpretation of pulsar positions, not a derivation, so the ledger is short. The one data-dependent choice is the 40% NF threshold; no new physical entities are introduced.

free parameters (1)

NF split threshold = 40% (hand-selected from histogram)
Selected by inspecting the NF histogram (Fig. 1) and described as a 'likely separation'; the same threshold is then used to split the sample for the KS test on spin-period distributions. It is a data-dependent choice that affects the population split claim.

assumptions (5)

domain assumption The inferred dipole surface field B_s = 3.2e19 sqrt(P Pdot) G (Eq. 15) is the correct coordinate for comparing nulling pulsars to the theoretical death-lines.
Section 3 uses this B_s for all pulsars; the authors state this is unambiguous for Zhang et al. lines but 'not correct' for Chen-Ruderman lines. If the true surface field differs, the wedge placement changes.
domain assumption The death-line models (Chen and Ruderman 1993; Zhang et al. 2000) describe the cessation of pair production relevant to real pulsars.
The central polar-cap/curved-field conclusion is inferred from the position of nulling pulsars relative to these theoretical boundaries.
domain assumption NF values from the literature, including upper limits and multiple conflicting estimates, can be treated as point measurements in Pearson and KS analyses.
Tables 2-5 contain many '<=' entries and duplicate estimates (e.g., J1752+2359, J1703-4851); the paper does not describe a censoring or averaging scheme.
domain assumption The sample of 204 nulling pulsars is representative enough to draw population-level conclusions.
Section 2 acknowledges that only about 8% of known pulsars are monitored and sensitivity affects NF, so selection biases are admitted but not corrected.
ad hoc to paper A 10% overestimate of B_s for nulling pulsars is sufficient to test robustness of the death-line conclusion.
Section 3: 'even with a 10% overestimate (assumed for all the nulling pulsars), we find that our conclusions drawn above remain unchanged.' The value is not derived from measurements.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Radio Pulsar Sub-Populations (I) : The Curious Case of Nulling Pulsars." pith.science (2026). https://pith.science/paper/67WJ6HHG

@misc{pith2026190807681,
  author       = {Pith},
  title        = {Pith review of: Radio Pulsar Sub-Populations (I) : The Curious Case of Nulling Pulsars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/67WJ6HHG}},
  note         = {Machine review of arXiv:1908.07681}
}

read the original abstract

About 200 radio pulsars have been observed to exhibit nulling episodes - short and long. We find that the nulling fraction of a pulsar does not have any obvious correlation with any of the intrinsic pulsar parameters. It also appears that the phenomenon of nulling may be preferentially experienced by pulsars with emission coming predominantly from the polar cap region, and also having extremely curved magnetic fields.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

79 extracted references · 79 canonical work pages

[1]

C., 1970, , 228, 42

Backer D. C., 1970, , 228, 42

work page 1970
[2]

Basu R., Mitra D., 2018, , 476, 1345

work page 2018
[3]

I., 2017, , 846, 109

Basu R., Mitra D., Melikidze G. I., 2017, , 846, 109

work page 2017
[4]

Bhattacharyya B., Gupta Y., Gil J., 2010, , 408, 407

work page 2010
[5]

D., 1992, , 394, 574

Biggs J. D., 1992, , 394, 574

work page 1992
[6]

Brinkman C., Freire P. C. C., Rankin J., Stovall K., 2018, , 474, 2012

work page 2018
[7]

Burke-Spolaor S., Bailes M., 2010, , 402, 855

work page 2010
[8]

et al., 2011, , 416, 2465

Burke-Spolaor S. et al., 2011, , 416, 2465

work page 2011

Show all 79 references

[9]

et al., 2012, , 423, 1351

Burke-Spolaor S. et al., 2012, , 423, 1351

2012
[10]

M., Chatterjee S., Johnston S., Demorest P., 2012, , 746, 63

Camilo F., Ransom S. M., Chatterjee S., Johnston S., Demorest P., 2012, , 746, 63

2012
[11]

Chen K., Ruderman M., 1993, , 402, 264

1993
[12]

M., Shannon R

Cordes J. M., Shannon R. M., 2008, , 682, 1152

2008
[13]

221, American Astronomical Society Meeting Abstracts \#221, p

Crawford F., Lorimer D., Ridley J., Madden J., 2013, in American Astronomical Society Meeting Abstracts, Vol. 221, American Astronomical Society Meeting Abstracts \#221, p. 412.04

2013
[14]

Deneva J. S. et al., 2016, , 821, 10

2016
[15]

S., Stovall K., McLaughlin M

Deneva J. S., Stovall K., McLaughlin M. A., Bates S. D., Freire P. C. C., Martinez J. G., Jenet F., Bagchi M., 2013, , 775, 51

2013
[16]

A., Rankin J

Deshpande A. A., Rankin J. M., 2001, , 322, 438

2001
[17]

M., Large M

Durdin J. M., Large M. I., Little A. G., Manchester R. N., Lyne A. G., Taylor J. H., 1979, , 186, 39P

1979
[18]

Dyks J., Zhang B., Gil J., 2005, , 626, L45

2005
[19]

G., Graham-Smith F., Kramer M., Manchester R

Esamdin A., Lyne A. G., Graham-Smith F., Kramer M., Manchester R. N., Wu X., 2005, , 356, 59

2005
[20]

Faulkner A. J. et al., 2004, , 355, 147

2004
[21]

V., Radhakrishnan V., 1982, , 263, 828

Filippenko A. V., Radhakrishnan V., 1982, , 263, 828

1982
[22]

Gajjar V., 2017, arXiv:1706.05407

2017 arXiv
[23]

C., Kramer M., 2012, , 424, 1197

Gajjar V., Joshi B. C., Kramer M., 2012, , 424, 1197

2012
[24]

C., Kramer M., Karuppusamy R., Smits R., 2014, , 797, 18

Gajjar V., Joshi B. C., Kramer M., Karuppusamy R., Smits R., 2014, , 797, 18

2014
[25]

P., Yuen R., Wen Z

Gajjar V., Yuan J. P., Yuen R., Wen Z. G., Liu Z. Y., Wang N., 2017, , 850, 173

2017
[26]

Gil J., Mitra D., 2001, , 550, 383

2001
[27]

L., Rankin J

Herfindal J. L., Rankin J. M., 2007, , 380, 430

2007
[28]

L., Rankin J

Herfindal J. L., Rankin J. M., 2009, , 393, 1391

2009
[29]

A., Bailes M., Ord S

Jacoby B. A., Bailes M., Ord S. M., Edwards R. T., Kulkarni S. R., 2009, , 699, 2009

2009
[30]

G., Manchester R

Johnston S., Lyne A. G., Manchester R. N., Kniffen D. A., D'Amico N., Lim J., Ashworth M., 1992, , 255, 401

1992
[31]

Joshi B. C. et al., 2009, , 398, 943

2009
[32]

M., 2010, Proceedings of the National Academy of Science, 107, 7147

Kaspi V. M., 2010, Proceedings of the National Academy of Science, 107, 7147

2010
[33]

8, Das S., Nandi A., Chattopadhyay I., ed, Astronomical Society of India Conference Series, p

Konar S., 2013, in Astronomical Society of India Conference Series, Vol. 8, Das S., Nandi A., Chattopadhyay I., ed, Astronomical Society of India Conference Series, p. 89

2013
[34]

Konar S., 2017, Journal of Astrophysics and Astronomy, 38, 47

2017
[35]

Konar S., 2019, in prep

2019
[36]

et al., 2016, Journal of Astrophysics and Astronomy, 37, 36

Konar S. et al., 2016, Journal of Astrophysics and Astronomy, 37, 36

2016
[37]

Konar S., Roy J., Bhattacharyaa B., 2019, in prep

2019
[38]

G., O'Brien J

Kramer M., Lyne A. G., O'Brien J. T., Jordan C. A., Lorimer D. R., 2006a, Science, 312, 549
[39]

et al., 2006b, Science, 314, 97

Kramer M. et al., 2006b, Science, 314, 97
[40]

N., Qian M

Li J., Esamdin A., Manchester R. N., Qian M. F., Niu H. B., 2012, , 425, 1294

2012
[41]

R., Camilo F., Xilouris K

Lorimer D. R., Camilo F., Xilouris K. M., 2002, , 123, 1750

2002
[42]

R., Lyne A

Lorimer D. R., Lyne A. G., McLaughlin M. A., Kramer M., Pavlov G. G., Chang C., 2012, , 758, 141

2012
[43]

Lynch R. S. et al., 2013, , 763, 81

2013
[44]

Lyne A., Hobbs G., Kramer M., Stairs I., Stappers B., 2010, Science, 329, 408

2010
[45]

G., McLaughlin M

Lyne A. G., McLaughlin M. A., Keane E. F., Kramer M., Espinoza C. M., Stappers B. W., Palliyaguru N. T., Miller J., 2009, , 400, 1439

2009
[46]

Lyne A. G. et al., 2017, , 834, 72

2017
[47]

N., Hobbs G

Manchester R. N., Hobbs G. B., Teoh A., Hobbs M., 2005, VizieR Online Data Catalog, 7245, 0

2005
[48]

N., Taylor J

Manchester R. N., Taylor J. H., 1977, Pulsars . W. H. Freeman, San Francisco, San Francisco, p. 36

1977
[49]

McLaughlin M. A. et al., 2006, , 439, 817

2006
[50]

B., 2017, Reviews of Modern Plasma Physics, 1, 5

Melrose D. B., 2017, Reviews of Modern Plasma Physics, 1, 5

2017
[51]

Meyers B. W. et al., 2018, , 869, 134

2018
[52]

I., 2009, , 696, L141

Mitra D., Gil J., Melikidze G. I., 2009, , 696, L141

2009
[53]

C., Manoharan P

Naidu A., Joshi B. C., Manoharan P. K., KrishnaKumar M. A., 2017, , 604, A45

2017
[54]

C., Manoharan P

Naidu A., Joshi B. C., Manoharan P. K., Krishnakumar M. A., 2018, , 475, 2375

2018
[55]

T., Kramer M., Lyne A

O'Brien J. T., Kramer M., Lyne A. G., Lorimer D. R., Jordan C. A., 2006, Chinese Journal of Astronomy and Astrophysics Supplement, 6, 4

2006
[56]

13, Astronomical Society of India Conference Series, p

Rajwade K., Gupta Y., Kumar U., Arjunwadkar M., 2014, in Astronomical Society of India Conference Series, Vol. 13, Astronomical Society of India Conference Series, p. 73

2014
[57]

M., 1986, , 301, 901

Rankin J. M., 1986, , 301, 901

1986
[58]

M., Rathnasree N., 1995, Journal of Astrophysics and Astronomy, 16, 327

Rankin J. M., Rathnasree N., 1995, Journal of Astrophysics and Astronomy, 16, 327

1995
[59]

M., Wright G

Rankin J. M., Wright G. A. E., 2007, , 379, 507

2007
[60]

M., Wright G

Rankin J. M., Wright G. A. E., 2008, , 385, 1923

2008
[61]

M., Wright G

Rankin J. M., Wright G. A. E., Brown A. M., 2013, , 433, 445

2013
[62]

L., Rankin J

Redman S. L., Rankin J. M., 2009, , 395, 1529

2009
[63]

T., 1976, , 176, 249

Ritchings R. T., 1976, , 176, 249

1976
[64]

et al., 2013, , 768, 85

Rosen R. et al., 2013, , 768, 85

2013
[65]

A., Sutherland P

Ruderman M. A., Sutherland P. G., 1975, , 196, 51

1975
[66]

et al., 2014, , 791, 67

Stovall K. et al., 2014, , 791, 67

2014
[67]

P., Joshi B

Surnis M. P., Joshi B. C., McLaughlin M. A., Gajjar V., 2013, in IAU Symposium, Vol. 291, IAU Symposium, p. 508

2013
[68]

Tan C. M. et al., 2018, , 866, 54

2018
[69]

N., 2010, , 408, L41

Timokhin A. N., 2010, , 408, L41

2010
[70]

Vivekanand M., 1995, , 274, 785

1995
[71]

Academic Press, New York

von Mises R., 1980, Mathematical Theory of Probability and Statistics . Academic Press, New York

1980
[72]

N., Johnston S., 2007, , 377, 1383

Wang N., Manchester R. N., Johnston S., 2007, , 377, 1383

2007
[73]

M., Armstrong B

Weisberg J. M., Armstrong B. K., Backus P. R., Cordes J. M., Boriakoff V., Ferguson D. C., 1986, , 92, 621

1986
[74]

Yang A., Han J., Wang N., 2014, Science China Physics, Mechanics, and Astronomy, 57, 1600

2014
[75]

J., Stappers B

Young N. J., Stappers B. W., Weltevrede P., Lyne A. G., Kramer M., 2012, , 427, 114

2012
[76]

J., Weltevrede P., Stappers B

Young N. J., Weltevrede P., Stappers B. W., Lyne A. G., Kramer M., 2014, , 442, 2519

2014
[77]

J., Weltevrede P., Stappers B

Young N. J., Weltevrede P., Stappers B. W., Lyne A. G., Kramer M., 2015, , 449, 1495

2015
[78]

Zhang B., Gil J., Dyks J., 2007, , 374, 1103

2007
[79]

K., Muslimov A

Zhang B., Harding A. K., Muslimov A. G., 2000, , 531, L135

2000

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

C., 1970, , 228, 42

Backer D. C., 1970, , 228, 42

work page 1970

[2] [2]

Basu R., Mitra D., 2018, , 476, 1345

work page 2018

[3] [3]

I., 2017, , 846, 109

Basu R., Mitra D., Melikidze G. I., 2017, , 846, 109

work page 2017

[4] [4]

Bhattacharyya B., Gupta Y., Gil J., 2010, , 408, 407

work page 2010

[5] [5]

D., 1992, , 394, 574

Biggs J. D., 1992, , 394, 574

work page 1992

[6] [6]

Brinkman C., Freire P. C. C., Rankin J., Stovall K., 2018, , 474, 2012

work page 2018

[7] [7]

Burke-Spolaor S., Bailes M., 2010, , 402, 855

work page 2010

[8] [8]

et al., 2011, , 416, 2465

Burke-Spolaor S. et al., 2011, , 416, 2465

work page 2011