Free Access
Issue
A&A
Volume 575, March 2015
Article Number A3
Number of page(s) 88
Section Interstellar and circumstellar matter
DOI https://doi.org/10.1051/0004-6361/201423815
Published online 10 February 2015

Online material

Appendix A: Estimate of the goodness of the fit for each model solution

In this Appendix we describe the calculations used to quantify the relative goodness of the fit solutions obtained between the optimum-model and another model. The method assumes that the optimum-model light curve describes reasonably well the observations and it is based on the evaluation of the standard deviation of all the models, σ, by imposing that the reduced of the optimum-solution is equal to unity. The difference between the values reached for the optimum-model and the other models then provides a measure of the relative goodness of the two solutions.

The χ2 of the optimum-model and of another model, and respectively, are defined as where Nobs,j and Nmod,j are the observed and modelled light curves respectively, and σ the standard deviation of the observed light curve. The difference between these two χ2 can be evaluated from the log-likelihood values given in Tables C.1 and D.1 as Δχ2 = −2 [ln(Lopt) − ln(Lmod)].

With the reduced χ2 of the optimum model set to 1, the standard deviation of the models, σ, is (A.3)

where Nd.o.f. is the number of degrees of freedom of each type of fit (41 for RQ pulsars and 81 for RL pulsars). With the model variance, the of the optimum and other models become: and their difference is (A.6)We have plotted the resulting values in Figs. 3 and 5. The 1σ, 3σ, and 5σ confidence levels plotted in these figures have been obtained from the χ2 probability density function for the appropriate number of degrees of freedom.

Appendix B: Population synthesis results from Pierbattista et al. (2012)

By synthesising a pulsar population we compared theoretical and observed distributions of observable quantities between the Fermi pulsars and the predictions of different γ-ray models. We have assumed low/intermediate and high-altitude magnetosphere emission models PC and SG, OG and OPC respectively, and core plus cone radio emission model. Full details on the population synthesis study can be found in Pierbattista et al. (2012). The plots shown in this Appendix have been obtained as additional results to the population study in Pierbattista et al. (2012) by using the original data at our disposal.

Appendix B.1: α-ζ plane

The α and ζ distributions of the visible component of the simulated population for PC, SG, OG, and OPC models are shown.

Appendix B.2: High-energy cutoff and spectral index as a function of the gap width

High energy cutoff and spectral index as a function of the width of the accelerator gap of the visible component of the simulated population for PC, SG, OG, and OPC. In disagreement with Fig. 15, no Ecut-gap width dependence is predicted from the simulations.

thumbnail Fig. B.1

Number density of the visible γ-ray pulsars obtained for each model as a function of α and ζ in the population synthesis of Pierbattista et al. (2012). The linear grey scale saturates at 1.5 star/bin. The pink contours outline the density obtained for the radio-loud γ-ray sub-sample (at 5% and 50% of the maximum density). The insert gives the set of ζ values measured by Ng & Romani (2008) from the orientation of the wind torus seen in X rays (pink lines) and by Caraveo et al. (2003) from the orientation of the Geminga X-ray tails (green line). The separation in α in the insert is meaningless.

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thumbnail Fig. B.2

Number density of the visible γ-ray pulsars obtained for each model as a function of gap width and high-energy cutoff (left) and of gap width and spectral index (right). The linear grey scale saturates at 8 star/bin. The pink contours outline the density obtained for the radio-loud γ-ray sub-sample (at 5% and 50% of the maximum density).

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Appendix C: The LAT pulsar γ-ray fit light-curve results

Table C.1

Best fit log-likelihood values resulting from the γ-ray fit of the 35 RQ pulsars of the analysed sample.

thumbnail Fig. C.1

Top: PSR J0007+7303; bottom: PSR J0106+4855. For each model the best γ-ray light-curve (thick black line) is superimposed on the LAT pulsar light-curve (shaded histogram). The estimated background is indicated by the dash-dot line.

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thumbnail Fig. C.2

Top: PSR J0357+3205; bottom: PSR J0622+3749. For each model the best γ-ray light-curve (thick black line) is superimposed on the LAT pulsar light-curve (shaded histogram). The estimated background is indicated by the dash-dot line.

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thumbnail Fig. C.3

Top: PSR J0633+0632; bottom: PSR J0633+1746. For each model the best γ-ray light-curve (thick black line) is superimposed on the LAT pulsar light-curve (shaded histogram). The estimated background is indicated by the dash-dot line.

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thumbnail Fig. C.4

Top: PSR J0734-1559; bottom: PSR J1023-5746. For each model the best γ-ray light-curve (thick black line) is superimposed on the LAT pulsar light-curve (shaded histogram). The estimated background is indicated by the dash-dot line.

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thumbnail Fig. C.5

Top: PSR J1044-5737; bottom: PSR J1135-6055. For each model the best γ-ray light-curve (thick black line) is superimposed on the LAT pulsar light-curve (shaded histogram). The estimated background is indicated by the dash-dot line.

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thumbnail Fig. C.6

Top: PSR J1413-6205; bottom: PSR J1418-6058. For each model the best γ-ray light-curve (thick black line) is superimposed on the LAT pulsar light-curve (shaded histogram). The estimated background is indicated by the dash-dot line.

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thumbnail Fig. C.7

Top: PSR J1429-5911; bottom: PSR J1459-6053. For each model the best γ-ray light-curve (thick black line) is superimposed on the LAT pulsar light-curve (shaded histogram). The estimated background is indicated by the dash-dot line.

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thumbnail Fig. C.8

Top: PSR J1620-4927; bottom: PSR J1732-3131. For each model the best γ-ray light-curve (thick black line) is superimposed on the LAT pulsar light-curve (shaded histogram). The estimated background is indicated by the dash-dot line.

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thumbnail Fig. C.9

Top: PSR J1746-3239; bottom: PSR J1803-2149. For each model the best γ-ray light-curve (thick black line) is superimposed on the LAT pulsar light-curve (shaded histogram). The estimated background is indicated by the dash-dot line.

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thumbnail Fig. C.10

Top: PSR J1809-2332; bottom: PSR J1813-1246. For each model the best γ-ray light-curve (thick black line) is superimposed on the LAT pulsar light-curve (shaded histogram). The estimated background is indicated by the dash-dot line.

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thumbnail Fig. C.11

Top: PSR J1826-1256; bottom: PSR J1836+5925. For each model the best γ-ray light-curve (thick black line) is superimposed on the LAT pulsar light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. For PSR J1836+5925 the SG is the only model that predicts enough off-pulse emission while OG and OPC models completely fail in explaining the observation probably because they do not predict enough off-pulse emission.

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thumbnail Fig. C.12

Top: PSR J1838-0537; bottom: PSR J1846+0919. For each model the best γ-ray light-curve (thick black line) is superimposed on the LAT pulsar light-curve (shaded histogram). The estimated background is indicated by the dash-dot line.

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thumbnail Fig. C.13

Top: PSR J1907+0602; bottom: PSR J1954+2836. For each model the best γ-ray light-curve (thick black line) is superimposed on the LAT pulsar light-curve (shaded histogram). The estimated background is indicated by the dash-dot line.

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thumbnail Fig. C.14

Top: PSR J1957+5033; bottom: PSR J1958+2846. For each model the best γ-ray light-curve (thick black line) is superimposed on the LAT pulsar light-curve (shaded histogram). The estimated background is indicated by the dash-dot line.

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thumbnail Fig. C.15

Top: PSR J2021+4026; bottom: PSR J2028+3332. For each model the best γ-ray light-curve (thick black line) is superimposed on the LAT pulsar light-curve (shaded histogram). The estimated background is indicated by the dash-dot line.

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thumbnail Fig. C.16

Top: PSR J2030+4415; bottom: PSR J2055+2539. For each model the best γ-ray light-curve (thick black line) is superimposed on the LAT pulsar light-curve (shaded histogram). The estimated background is indicated by the dash-dot line.

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thumbnail Fig. C.17

Top: PSR J2111+4606; bottom: PSR J2139+4716. For each model the best γ-ray light-curve (thick black line) is superimposed on the LAT pulsar light-curve (shaded histogram). The estimated background is indicated by the dash-dot line.

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thumbnail Fig. C.18

PSR J2238+5903. For each model the best γ-ray light-curve (thick black line) is superimposed on the LAT pulsar light-curve (shaded histogram). The estimated background is indicated by the dash-dot line.

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Appendix D: The LAT pulsar Joint fit light-curve results

Table D.1

Best fit log-likelihood values resulting from the γ-ray fit of the 41 RL pulsars of the analysed sample.

thumbnail Fig. D.1

PSR J0205+6449. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.2

PSR J0248+6021. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.3

PSR J0534+2200. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model. See Sect. 2 for a discussion on why we decided to show the joint γ-ray plus Radio fit result for the Crab pulsar.

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thumbnail Fig. D.4

PSR J0631+1036. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.5

PSR J0659+1414. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.6

PSR J0729-1448. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.7

PSR J0742-2822. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.8

PSR J0835-4510. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.9

PSR J0908-4913. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.10

PSR J0940-5428. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.11

PSR J1016-5857. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.12

PSR J1019-5749. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model. Because of the low statistics of the γ-ray light curve, the best-fit solution of each model is dominated by the radio light curve. The optimum-solution is given by the SG model but it represents an unreliable result since the best fit γ-ray light curve corresponds to a flat profile.

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thumbnail Fig. D.13

PSR J1028-5819. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.14

PSR J1048-5832. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.15

PSR J1057-5226. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.16

PSR J1105-6107. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.17

PSR J1112-6103. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.18

PSR J1119-6127. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.19

PSR J1124-5916. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.20

PSR J1357-6429. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.21

PSR J1410-6132. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model. For this pulsar the SG model gives the optimum-solution but it represents an unreliable result since the best fit γ-ray light curve correspond to a flat profile.

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thumbnail Fig. D.22

PSR J1420-6048. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.23

PSR J1509-5850. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.24

PSR J1513-5908. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.25

PSR J1648-4611. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.26

PSR J1702-4128. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.27

PSR J1709-4429. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.28

PSR J1718-3825. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.29

PSR J1730-3350. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.30

PSR J1741-2054. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.31

PSR J1747-2958. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.32

PSR J1801-2451. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.33

PSR J1833-1034. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.34

PSR J1835-1106. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.35

PSR J1952+3252. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.36

PSR J2021+3651. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.37

PSR J2030+3641. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.38

PSR J2032+4127. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.39

PSR J2043+2740. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.40

PSR J2229+6114. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. D.41

PSR J2240+5832. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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Appendix E: Joint fit of radio and γ-ray light curves of the radio-faint pulsars J0106+4855 and J1907+0602

In this Appendix we give the results of the joint-fit of radio and γ-ray light curve for the 2 RF pulsars J0106+4855 and J1907+0602.

Appendix E.1: J0106+4855

Figure E.1 shows the best-fit radio and γ-ray light curves for pulsar J0106+4855 while its best joint-fit parameters are given in Table E.1. The PC joint-fit solution is characterised by lower α and ζ angles and similar | αζ | and fΩ values when compared with the γ-ray only fit solution, while the SG model joint-fit solution is overall consistent with the γ-ray-only fit results. For OG and OPC models, the joint-fit α values are larger than the values obtained through γ-ray only fit. This implies a lower joint-fit | αζ | value that favours simultaneous γ-ray and radio emission. Moreover the OG and OPC joint-fit values of fΩ are larger than the values obtained with the γ-ray only fit and this favours the overlapping of γ-ray and radio beam to give a RL pulsar.

Concerning the best fit radio and γ-ray light curves, the largest PC likelihood value shown in Table E.1 is fictitious since the PC γ-ray fit shown in Fig. E.1 explains just one of the two γ-ray peaks. In agreement with the γ-ray only fit that predicts a two peaks γ-ray light curve just for PC and SG models (Fig. C.1), the SG is the model that best explains simultaneous γ-ray and radio emission from pulsar J0106+4855.

Appendix E.2: J1907+0602

Figure E.2 shows the best-fit radio and γ-ray light curves for pulsar J1907+0602 while its best joint-fit parameters are given in Table E.2. Both PC and SG model best joint-fit parameters are consistent with the γ-ray-only fit results. As for pulsar J0106+4855, the OG and OPC models best-fit results predict α values larger than the values obtained through γ-ray only fit and larger values of fΩ. The lower | αζ | joint-fit values and the larger fΩ joint-fit values favour the overlapping of γ-ray and radio beam to give a RL pulsar.

In agreement with the γ-ray only fit that predicts a γ-ray light curves with two peaks connected by a high bridge just for OG and OPC models (Fig. C.13), the OG is the model that best explains simultaneous γ-ray and radio emission from pulsar J1907+0602.

Table E.1

Best fit parameters resulting from the joint fit of radio and γ-ray light curves of pulsar J0106+4855.

Table E.1

Best fit parameters resulting from the joint fit of radio and γ-ray light curves of pulsar J1907+0602.

thumbnail Fig. E.1

PSR J0106+4855. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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thumbnail Fig. E.2

PSR J1907+0602. Top: for each model the best joint fit solution γ-ray light-curve (thick black line) is superimposed on the LAT pulsar γ-ray light-curve (shaded histogram). The estimated background is indicated by the dash-dot line. Bottom: for each model the best joint fit solution radio light-curve (black line) is superimposed on the LAT pulsar radio light-curve (grey thick line). The radio model is unique, but the (α,ζ) solutions vary for each γ-ray model.

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© ESO, 2015

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