The Crab Pulsar Experiment

University of Manchester | 3rd Year Laboratory

5.1 Summary of all results

All the final results obtained in the experiment are summarized below.

5.1.1 Dispersion Measures and distances to pulsars

The two tables below are the results obtained from the analysis detailed in the Section 2: Dispersion Measure

Pulsar Names Dispersion Measure
Fitting the curve Fitting the spectrum Monte Carlo
B0329+54 25.6757 ± 3.2703 29.473 ± 2.489 26.0490 ± 0.3591
B0531+21(i) 55.5045 ± 1.1892 55.834 ± 0.410 55.6937 ± 0.0946
B0531+21(ii) 55.8018 ± 1.1892 55.656 ± 0.238 55.8819 ± 0.0805
B0531+21(iii) 56.0000 ± 1.3874 55.725 ± 0.385 55.9550 ± 0.0762
B1642-03 33.3063 ± 6.1441 32.434 ± 1.379 32.0871 ± 0.4578
B1929+10
RFI 1.6116 ± 0.8074
B1933+16 150.9510 ± 7.4074 158.009 ± 7.981 151.1997 ± 1.5803
B2016+28
RFI 1.4712 ± 3.4911
B2020+28 22.7027 ± 2.1802 20.061 ± 3.532 23.3594 ± 0.4248
B2111+46 98.6486 ± 3.4034 too noisy 98.3332 ± 21.4281
Pulsar Names Distance (kpc)
Cordes-Lazio NE2001
(electron density model 1)
YMW16
(electron density model 2)
B0329+54 1.088 ± 0.147 1.162 ± 0.116
B0531+21(i) 1.709 ± 0.298 1.282 ± 0.128
B0531+21(ii) 1.714 ± 0.299
1.286 ± 0.127
B0531+21(iii) 1.715 ± 0.298 1.287 ± 0.129
B1642-03 1.057 ± 0.198 0.973 ± 0. 098
B1933+16 5.484 ± 0.803 4.231 ± 0.423
B2020+28 2.004 ± 0.389 1.617 ± 0.162
B2111+46 3.890 ± 0.458 3.646 ± 0.365

5.1.2 The period of 6 unknown pulsars calculated using Fourier Transform

The final results as quoted in Section 3: Fourier transforms are shown below.

Pulsar Data Period
(seconds)
Width
(ms)
Pulsars
Pulsar 1 0.2265 ± 0.0002 ~ 11 B1929+10
Pulsar 2 0.189 ± 0.003 ~ 2 B1821-19
Pulsar 3 0.476 ± 0.001 ~ 11 B0626+24
Pulsar 4 0.7397 ± 0.003 ~ 19 B1508+55
Pulsar 5 0.2990 ± 0.001 ~ 6 B1702-19
Pulsar 6 0.7146 ± 0.001 ~ 12 B0329+54

5.1.3 Period, Period derivative and magnetic field results obtained from Timing Analysis of 4 pulsars

Pulsar name Period (seconds)
Method 1 Method 2
B0329+54 0.03375705(4) 0.0337570584(1)
B1642-03 0.38771567(1) 0.38771569(3)
B1933+16 0.35879058(3) 0.358790498(7)
B2020+28 0.343445657(5)
Crab (Week 1) 0.033755409(4) 0.03375540740(1)
Crab (Week 2) 0.033755697(3) 0.03375569661(1)
Crab (Week 3) 0.033755950(3) 0.03375595035(7)
Pulsar name Period derivative
Method 1 Method 2
Crab (Week 1) 4.21e-13 4.01e-13
Crab (Week 2) 4.17(3)e-13 4.02e-13
Crab (Week 3) 4.2e-13 4.03e-13

The approximate characteristic age of the Crab pulsar is $Age \approx 1273.85$ years.

The approximate surface magnetic field of the Crab pulsar is $B \approx 1.2 \times 10^8$ T.

5.2 References

[1] R. P. Eatough, E. F. Keane, A. G. Lyne; An interference removal technique for radio pulsar searches, Monthly Notices of the Royal Astronomical Society, Volume 395, Issue 1, 1 May 2009, Pages 410–415

[2] Lyne, A. and Graham-Smith, F., 2012. Pulsar astronomy (No. 48). Cambridge University Press.

[3] Lorimer, D.R. and Kramer, M., 2005. Handbook of pulsar astronomy (Vol. 4). Cambridge university press.

[4] Taylor, J.H., Manchester, R.N. and Lyne, A.G., 1993. Catalog of 558 pulsars. The Astrophysical journal supplement series, 88, pp.529-568.

[5] Davidson, K. and Terzian, Y., 1969. Dispersion measures of pulsars. The Astronomical Journal, 74, p.849.

[6] Cordes, J. M. & Lazio, T. J. W. 2003, “NE2001. II. Using Radio Propagation Data to Construct a Model for the Galactic Distribution of Free Electrons”;

[7] Yao, J.M., Manchester, R.N. and Wang, N., 2017. A new electron-density model for estimation of pulsar and FRB distances. The Astrophysical Journal, 835(1), p.29.

[8] ATNF Pulsar Catalogue, version 1.59, html link: www.atnf.csiro.au/research/pulsar/psrcat/.

[9] Abramowitz, M. and Stegun, I.A., 1965. Handbook of mathematical functions: with formulas, graphs, and mathematical tables (Vol. 55). New York: Dover publications.