The Crab Pulsar at X-ray bands (PDF Download Available)

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Aug 21, 2016 - In its rotating magnetic field, electrons and positrons. are accelerated up to relativistic energies and emit radia-. tion in a cone shaped beam ...
The Crab Pulsar at X-ray bands Project Report for

Vacation Students’ Programme (VSP)-2016 By

Pravir Kumar Indian Institute of Science Education and Research, Bhopal

Under the guidance of

Dipankar Bhattacharya Senior Professor Inter-University Centre for Astronomy and Astrophysics Pune, India

May-July, 2016

Abstract The Indian Astronomy satellite Astrosat has accumulated photon events from the Crab Nebula and its pulsar over a large range of energy bands. In this Project, this data is used to generate the integrated pulse profile of the Crab. Then, We plotted it at several energy bands to find any difference between them. Also, comparison is made with the radio pulses from the Crab pulsar acquired over the same time. Further, Crab Spectrum is determined from the dataset. It is fitted with a simple power-law model to find the spectral index. In the last part, We tried to understand the physical picture behind the emission mechanism by studying different proposed models. This Project is done as a part of IUCAA Vacation Students’ Programme (VSP)- 2016.

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Acknowledgement First of all, I express my heartiest gratitude to Prof. Dipankar Bhattacharya for finding me worthy of doing this summer project. My sincere thanks to Prof. Bhattacharya for the way he put the idea into my head that got me driven into this work. I am deeply indebted to IUCAA VSP Programme for such a pleasant and productive summer. I would like to thank all the people at IUCAA for their hospitality and services.

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Contents 1 Introduction 1.1 Crab Pulsar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Astrosat CZTI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2 Data

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3 Timing Analysis 3.1 Crab Phase . . . . . . . . 3.2 Comparison of Quadrants 3.3 Comparison with Energy . 3.4 Comparison with Radio .

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4 Spectral Analysis 4.1 Phase component definitions 4.2 Phase Resolved Spectrum . . 4.2.1 Pulsar Spectrum . . . 4.2.2 P1 Spectrum . . . . . 4.2.3 P2 Spectrum . . . . . 4.2.4 Ip Spectrum . . . . . .

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5 Pulsar Emission Mechanisms 5.1 Crab Observations . . . . . . . . 5.2 High Energy Emission . . . . . . 5.3 Outer Gap Model . . . . . . . . . 5.4 Synchrotron-Self-Compton Model

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List of Figures 1 2 3 4 5

Crab Nebula and Pulsar composite Multiwavelength Crab Nebula . . . CZTI . . . . . . . . . . . . . . . . . Astrosat . . . . . . . . . . . . . . . Power spectra for the ObsID 118 .

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Pulse profile of the Crab pulsar from ObsID 308-316. 500 bins . . . . . .

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Pulse profile of the Crab pulsar from ObsID 406. 500 bins . . . . . . . .

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Pulse profile for each quadrants of ObsID 308-316. . . . . . . . . . . . .

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Pulse profile for each quadrants of ObsID 406. . . . . . . . . . . . . . . . Phase histograms of PSR B0531+21 (Crab) observed with the CZTI of Astrosat in five energy ranges from 20 to 150 keV. . . . . . . . . . . . . . X-ray pulse profile comparison with radio of Crab observed with the CZTI of Astrosat. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Phase component definitions for the Crab pulsar in this study. . . . . . . CZTI Q0 effective area vs energy used in this study. . . . . . . . . . . . . On-Pulse Spectrum in the energy range 45.0-100.0 keV. Reduced χ2 value = 2.5630 for 49 degrees of freedom; χ2 = 125.59 using 54 PHA bins . . P1 Spectrum in the energy range 45.0-100.0 keV. Reduced χ2 value = 5.3191 for 49 degrees of freedom; χ2 = 260.64 using 54 PHA bins; . . . P2 Spectrum in the energy range 45.0-100.0 keV. Reduced χ2 value = 2.7702 for 49 degrees of freedom; χ2 = 135.74 using 54 PHA bins; . . . Ip Spectrum in the energy range 45.0-100.0 keV. Reduced χ2 value = 4.3728 for 49 degrees of freedom; χ2 = 214.27 using 54 PHA bins; . . . Pulsar emission regions . . . . . . . . . . . . . . . . . . . . . . . . . . . Pulsar magnetosphere(Chiang & Romani, 1992) . . . . . . . . . . . . . .

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List of Tables 1 2 3 4 5 6 7 8 9

Observation log for the data used in this analysis Radio Timing Parameters of the Crab Pulsar . . . Variation of Peak 1 with Energy . . . . . . . . . . X-ray Radio Comparison parameters . . . . . . . Fit Parameters of Pulsar . . . . . . . . . . . . . . Fit Parameters of P1 . . . . . . . . . . . . . . . . Fit Parameters of P2 . . . . . . . . . . . . . . . . Fit Parameters of Ip . . . . . . . . . . . . . . . . . Spectrum Parameters of the Crab Pulsar . . . . .

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1 Introduction 1.1

Crab Pulsar

Pulsars are rotating, highly magnetized neutron stars. These stars are made of densely packed matter, which gives the entire star a density comparable to an atomic nucleus. They are followed by the death of a massive main sequence star which underwent a core collapse when its internal thermal energy produced by the nuclear fusion processes was not sufficient anymore to counteract the gravitational force against the stars collapse. In its rotating magnetic field, electrons and positrons are accelerated up to relativistic energies and emit radiation in a cone shaped beam which sweeps across the sky like the light from a lighthouse as the star rotates. When the beam sweeps over the earth, it becomes visible as a pulsar, producing light that cycles every few seconds to just a few milliseconds. On July 4, 1054 AD, Chinese astronomers noted a guest star in the constellation Taurus. The cloud of gas which we observe today at the position of this guest star is the Crab supernova remnant. In the optical band the Credit: NASA/CXC/SAO nebula has an extent of 4 × 6 arcmin, corresponding to 3 ∼ 7 × 10 light years for a distance of 2 kpc.(Becker, 2009) Figure 1: Crab Nebula and The observed non-thermal emission required a continPulsar composite uous input of energetic charged particles to keep the nebula emitting. This question of the Crab nebula’s central engine caused to propose that a fast spinning and strongly magnetized neutron star could be the required source which supplies the energy into the nebula.(Pacini, 1967) Indeed, the 33-ms pulsar in the Crab supernova remnant, PSR B0531+21, was the first rotation-powered pulsar from which high energy radiation was detected.

Credit: NASA/CXC/SAO (X-ray), Mt. Palomar Observatories (optical), Caltech/NASA/NSF (infrared), and NRAO/AUI/NSF (radio)

Figure 2: Multiwavelength Crab Nebula

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The Crab is the most powerful rotation-powered pulsar in our galaxy, and it is one of only a few pulsars detected across all wavelengths, from radio up to gamma rays. The pulsar "beams" rotate once every 33 milliseconds, or 30 times each second. Crab pulsar (PSR B0535+21) has been observed in almost every energy band of the electromagnetic spectrum and has been extensively studied to understand the physics of the emission mechanisms. The pulsar’s characteristic pulse profile and its energy spectrum have been measured in detail throughout almost the entire electromagnetic spectrum.

1.2

Astrosat CZTI

Cadmium Zinc Telluride Imager (CZTI) is one among the four X-ray instruments on Astrosat. It is a coded aperture telescope with the primary objective of imaging and spectroscopy of bright X-ray sources in the hard X-ray band (20-150 keV). It has a total active area of 976 cm2 which is achieved by an array of 64 pixelated CZT detector modules. These 64 modules are arranged in four identical and independent quadrants. The source of background in the CZT detector are primarily cosmic diffuse gamma rays and gamma-rays originating Figure 3: CZTI from satellite structure due to interaction of cosmic rays. Cosmic diffuse gamma-ray photons in the energy range (10-100) kev interacts with Tantalum by photoelectric effect and produce fluorescent Kα X-rays. AstrosatHandbook (2014)

Figure 4: Astrosat

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2 Data Data for the analysis were obtained from CZTI detector onboard the ASTROSAT. The field of view of this imaging detector contained both the Crab pulsar and the Crab nebula. The analysis was done using the FTOOLS from the astronomy software HEAsoft -ver 6.18.(Blackburn, 1995) Table 1: Observation log for the data used in this analysis

OBS ID

Exposure time

Date/time start

Date/time end

096 100 104 114 118 122 252 308 312 316 406

41776.9341858 2015-11-12 03-57-33 2015-11-13 03-58-43 15512.4932293 2015-11-14 04-34-09 2015-11-14 12-54-29 21652.9024102 2015-11-14 16-29-10 2015-11-15 04-03-08 14138.0923132 2015-11-23 03-36-42 2015-11-23 14-59-13 23283.7552085 2015-11-24 04-06-00 2015-11-24 15-37-33 9915.10332256 2015-11-25 04-06-11 2015-11-25 09-58-47 59603.0613827 2016-01-07 04:01:30 2016-01-08 11:26:53 58408.428536 2016-02-01 06:38:29 2016-02-02 13:53:38 60829.4635517 2016-02-03 09:37:02 2016-02-04 17:36:30 67214.059277 2016-02-07 14:09:15 2016-02-09 05:54:15 114318.833294 2016-03-31 05:39:19 2016-04-03 03:55:11

The next step is to check the period of the Crab pulsar for each data file. The fundamental frequency in the power spectrum of the data gives the first approximation of the period, which is obtained using the tool powspec. The power spectra for the ObsID 118 obtained using the FTOOLS task powspec is shown below.

Figure 5: Power spectra for the ObsID 118

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3 Timing Analysis Once the pulsar signal has been detected, the next step is to fold the signal at the pulse period. This puts the data in the form of a pulse profile, a sampled waveform of the pulse intensity over its period. Successive individual pulses manifest a wide variety of shapes and strengths, but many thousands of pulses can be averaged to build a unique and consistent pulse profile. Arrival times in the data are in telescope reference frame. But a telescope, sitting on a spinning planet that revolves around the Sun is not in the co-moving pulsar frame. To carry out the transformation from the telescope frame to the pulsar frame, we have to first translate the arrival times to the Solar System Barycenter (SSB). With respect to nearby pulsars, the SSB has roughly zero net acceleration, making it a good approximation to the frame in which the pulses were emitted. The event arrival times at the spacecraft are converted to arrival times at the Solar-system Barycenter using the JPL DE200 Solar-system ephemeris.(Splaver, 2004) The pulsar spin-down mechanism is modeled through a Taylor expansion of the pulse phase in proper time: 1 1 ϕ = ϕ0 + f (Te − T0 ) + f˙(Te − T0 )2 + f¨(Te − T0 )3 (1) 2 6 where ϕ0 is the phase at T0 , Te the barycentric corrected arrival time of the photon, T0 the radio epoch and f = 1/P is the spin frequency. Absolute phase was determined by using the time solution available from the Jodrell Bank Crab Pulsar Monthly Ephemeris.Lyne et al. (1993) The integer part of T0 denotes the barycentric epoch (TDB) of f, f˙ and f¨. The remaining fraction denotes the geocentric arrival time of a pulse. Table 2: Radio Timing Parameters of the Crab Pulsar

Validity

f (s−1 )

T0 (MJD)

57296-57327 (Oct) 57311.000000136 57327-57357 (Nov) 57342.000000350 57388-57419 (Jan) 57403.000000146 57419-57448 (Feb) 57434.000000138 57448-57479 (Mar) 57464.000000166 57479-57509 (Apr) 57494.000000115

29.6607408839888 29.6597515971642 29.6578052059548 29.6568161518166 29.6558590851542 29.6549020938256

f˙(10−10 s−2 ) f¨(10−20 s−3 ) -3.69376 -3.69338 -3.69277 -3.69251 -3.69219 -3.69195

0.704 0.607 0.430 1.81 2.02 4.02

The Barycentered arrival times are finally folded. The (TDB) time to pulse phase conversion taking into account consistent phase alignment for each ephemeris is provided by the above equation. Each detected photon is assigned an arrival phase based on the ephemeris in Table 2. So, from the beginning of the observation, number of pulses "N" is counted at the time when each photon reached. The decimal part of "N" will take numbers from 0 to 1, and mean the phase. The phase of each photon shows where the photon is detected in the pulse.

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3.1

Crab Phase

The resulting phase histogram with 500 bins is shown below. All four quadrants data is combined in this plot. The folded light curve has an asymmetric, dual-peak shape. The first pulse is stronger than the second pulse. A significant interpeak emission (bridge emission) is also seen. The first peak is referred as "P1" and the second peak as "P2". Crab Pulsar Astrosat CZTI ObsID 308 312 316

Figure 6: Pulse profile of the Crab pulsar from ObsID 308-316. 500 bins

counts

350000

340000

330000

0

0.5

1

1.5

2

phase

Crab Pulsar Astrosat CZTI ObsID 406

Figure 7: Pulse profile of the Crab pulsar from ObsID 406. 500 bins

counts

240000

230000

220000

0

0.5

1

1.5

phase

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2

3.2

Comparison of Quadrants

Now, phase histograms from the four quadrants are plotted seperately. All quadrants are found to be aligned. There is no measurable relative delay between quadrants. Crab Pulsar CZTI Quadrants ObsID 308 312 316 counts

-----Q0 -----Q1

90000

Figure 8: Pulse profile for each quadrants of ObsID 308-316.

-----Q2 -----Q3

85000

80000

0

0.5

1

1.5

2

phase

Crab Pulsar CZTI Quadrants ObsID 406 counts 62000 ----Q0 ----Q1 ----Q2

60000

----Q3

58000

56000

54000

52000

0

0.5

1

1.5

phase

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2

Figure 9: Pulse profile for each quadrants of ObsID 406.

3.3

Comparison with Energy CZTI ObsID 308 312 316

CZTI ObsID 308 312 316

counts

counts

35.0-50.0 keV

20.0-35.0 keV 60000 50000

58000 48000

56000 46000

54000

44000

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

phase

0.6

0.8

1

phase

CZTI ObsID 308 312 316

CZTI ObsID 308 312 316

counts

counts 55000 50.0-70.0 keV

70.0-100.0 keV

54000 70000

53000

68000

52000

51000 66000 50000

0

0.2

0.4

0.6

0.8

1

0

phase

0.2

0.4

0.6

0.8

1

phase

CZTI ObsID 308 312 316 counts

100.0-150.0 keV 68000

67000

66000

65000

64000

0

0.2

0.4

0.6

0.8

1

phase

Figure 12: Phase histograms of PSR B0531+21 (Crab) observed with the CZTI of Astrosat in five energy ranges from 20 to 150 keV.

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The resulting phase histograms in five energy bands from 20 to 150 keV are shown in Fig.12 , with a phase resolution of 250 bins. The well known double peaked structure is prominent in all the bands. It is also evident from above figure that the intensity of P2 and Ip with respect to that of P1 increases with energy. Now, the next thing is to see if there is any variation in the position of the pulse in different energy bands. We have used the peak of the pulse as representative of the X-ray phase. So, a Lorentzian function is fitted to the 1st Peak "P1" to get its phase. The fitted result is in Table 3 with uncertainty corresponding to 90 % confidence range. No measurable variation is found in the position of P1 in different energy bands.

Table 3: Variation of Peak 1 with Energy

Energy Range

Peak 1

Uncertainity

20-35 35-50 50-70 70-100 100-150

0.3427 0.3430 0.3441 0.3429 0.3462

0.7993E-03 1.153E-03 1.811E-03 1.708E-03 2.047E-03

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3.4

Comparison with Radio

We can now compare rotational phases and arrival times of the main peak in the X-ray with phases and arrival times in the radio, reported in the Jodrell Bank Crab Pulsar Monthly Ephemeris website. The fractional part of T0 in the time solution in Table 2 is the radio phase which is shown in blue line in plots below. Crab Pulsar Astrosat CZTI 41 ks ObsID 096

Crab Pulsar Astrosat CZTI ObsID 104

counts

counts

42000 78000

41000

76000 40000

74000

39000

38000 72000

0

0.5

1

1.5

2

0

0.5

phase

1

1.5

2

phase

Crab Pulsar Astrosat CZTI ObsID 114 118 122

Crab Pulsar Astrosat CZTI ObsID 252

counts

counts

90000

116000

88000

114000

112000

86000

110000

84000

108000

82000

106000

0

0.5

1

1.5

2

0

0.5

phase

1

1.5

2

phase

Crab Pulsar Astrosat CZTI ObsID 308 312 316

Crab Pulsar Astrosat CZTI ObsID 406

counts

counts

240000 350000

230000 340000

220000 330000

0

0.5

1

1.5

2

0

phase

0.5

1

1.5

2

phase

Figure 15: X-ray pulse profile comparison with radio of Crab observed with the CZTI of Astrosat.

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Table 4: X-ray Radio Comparison parameters

OBS ID

Peak 1

Radio Phase

096 100 104 114 118 122 252 308+312+316 406

0.8020 0.7596 0.7497 0.8379 0.8360 0.8334 0.7147 0.3438 0.7496

0.8969 0.8969 0.8969 0.8969 0.8969 0.8969 0.3741 0.3536 0.2946

Lag time (in µs) 3199 4630 4963 1989 2053 2140 -11482 331 -15340

Again, a Lorentzian function is fitted to the 1st Peak "P1" to get its phase. We have used the peak of the pulse as representative of the X-ray phase. The fitted result of ObsId’s with their respective time difference from the radio is in Table 3. The precise timing of the pulses is important for the understanding of the origin of the emission processes that give rise to the pulses in different parts of the spectrum. Mapping these pulse arrival time differences to radio travel-time differences means that for X-ray and radio pulses the arrival time delay can correspond to a difference in emission heights.

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4 Spectral Analysis 4.1

Phase component definitions

The Phase boundaries we defined for P1, P2, Ip and the Off-Pulse interval for ObsID 308-316, as reported in Fig.17 are (0.24,0.40) for P1, (0.63,0.81) for P2, (0.40,0.63) for Ip and (0.81,1.24) for the Off-Pulse. Similarly, we defined boundaries for all other ObsId, and separated "PI" column from the data in their corresponding phase region. On-Pulse Interval is defined as combined P1, P2 and Ip interval.

Crab CZTI ObsID 308 312 316 counts

350000

340000

Off-Pulse

330000

P1

0

0.2

IP

0.4

P2

0.6

0.8

1

phase

Figure 16: Phase component definitions for the Crab pulsar in this study.

Thus respective PHA files are created for spectral analysis for each ObsID. In other words, we accumulated the spectra in each phase interval, and the aim is to subtract the Off-Pulse contribution from the pulsed component.

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We used XSPEC v12.9(Arnaud, 1996) for the spectral analysis. A background spectrum was obtained from the Off-Pulse Interval, the "Nebular background". This spectrum was used to subtract phase-independent Crab Nebula X-rays, as well as the cosmic and internal backgrounds from each of the remaining pulsar phase intervals. Spectral analysis of P1, P2, Ip and On-Pulse Interval was performed using an appropriate detector spectral response matrix, the background (Off-Pulse Interval), the program XSPEC, and a power-law model. A systematic error of 2% has been applied. PHA files for all ObsID’s are combined. Q0 quadrant data is used for the spectral fitting as auxiliary response file for other quadrants are not available at that time.

Astrosat CZTI Q0 arf SPECRESP (cm^2) 500

400

300

200

100

0 0

100

200

ENERG_LO (keV)

Figure 17: CZTI Q0 effective area vs energy used in this study.

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300

4.2

Phase Resolved Spectrum

4.2.1 Pulsar Spectrum

normalized counts s−1 keV−1

data and folded model

0.05

0.02

normalized counts s−1 keV−1

0.01 4×10−3 2×10−3 0 −2×10−3 −4×10−3 50 Energy (keV)

Figure 18: On-Pulse Spectrum in the energy range 45.0-100.0 keV. Reduced χ2 value = 2.5630 for 49 degrees of freedom; χ2 = 125.59 using 54 PHA bins

Table 5: Fit Parameters of Pulsar

Component Parameter Unit powerlaw powerlaw gaussian gaussian gaussian

PhoIndex norm LinE Sigma norm

keV keV

Table 6: Fit Parameters of P1

Value

Component Parameter Unit

1.73 8.19E-02 62.1 2.14 1.57E-04

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powerlaw powerlaw gaussian gaussian gaussian

PhoIndex norm LinE Sigma norm

keV keV

Value 1.85 0.166 62.8 0.174 1.33E-04

4.2.2 P1 Spectrum

data and folded model

normalized counts s−1 keV−1

normalized counts s−1 keV−1

0.1

0.05

0.02

0.01 5×10−3

0

−5×10−3

50 Energy (keV)

Figure 19: P1 Spectrum in the energy range 45.0-100.0 keV. Reduced χ2 value = 5.3191 for 49 degrees of freedom; χ2 = 260.64 using 54 PHA bins;

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4.2.3 P2 Spectrum

data and folded model

normalized counts s−1 keV−1

normalized counts s−1 keV−1

0.1

0.05

0.02

4×10−3 2×10−3 0 −2×10−3 −4×10−3

50 Energy (keV)

Figure 20: P2 Spectrum in the energy range 45.0-100.0 keV. Reduced χ2 value = 2.7702 for 49 degrees of freedom; χ2 = 135.74 using 54 PHA bins;

Table 7: Fit Parameters of P2

Component powerlaw powerlaw gaussian gaussian gaussian

Parameter Unit

Value

PhoIndex norm LinE Sigma norm

1.73 0.115 61.9 9.34E-02 1.91E-04

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keV keV

4.2.4 Ip Spectrum

normalized counts s−1 keV−1

data and folded model

0.02

0.01

normalized counts s−1 keV−1

5×10−3 2×10−3

0

−2×10−3 50 Energy (keV)

Figure 21: Ip Spectrum in the energy range 45.0-100.0 keV. Reduced χ2 value = 4.3728 for 49 degrees of freedom; χ2 = 214.27 using 54 PHA bins;

Table 8: Fit Parameters of Ip

Component powerlaw powerlaw gaussian gaussian gaussian

Parameter Unit

Value

PhoIndex norm LinE Sigma norm

1.54 2.10E-02 61.6 2.78 1.08E-04

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keV keV

Table 9: Spectrum Parameters of the Crab Pulsar

phase

α

P1 1.85 P2 1.73 IP 1.54 Pulsar 1.73

Table 9 reports the resulting spectral indexes for the different regions. We conclude that the single power law well describes the source emission in each energy band. Local residuals mainly due to the calibrations uncertainties are responsible for the high χ2 in the fits. There is also a gaussian line fitting around 62 keV, due to the photoelectric effect by Tantalum from the spacecraft. The two Kα X-ray lines should be around 57 keV and 65 keV and that has been taken care in the auxiliary response file but, it is averaging around 62 keV. A more precise arf file and background are needed for further analysis.

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5 Pulsar Emission Mechanisms 5.1

Crab Observations

The High-energy observations provide the key for the understanding of the pulsar emission mechanisms. The high energy radiation detected has been attributed to non-thermal emission from charged relativistic particles accelerated in the Pulsar Magnetosphere. As the energy distribution of these particles follows a power-law, the emission is also characterized by power-law-like spectra in broad energy bands. The emitted radiation can be observed from optical to the gamma-ray band. As far as the pulsars emission mechanisms are concerned, it is very well established that magnetospheric emission from charged particles, accelerated in the neutron star magnetosphere along the curved magnetic field lines, dominates the radiation from the Crab pulsar. Accordingly, the radiation of Crab-like pulsars is characterized by a power-law spectrum, dN photons cm−2 keV −1 ∝ E −α , (2) dE in which α is called photon-index. This implies that the energy distribution of the charged particles emitting this radiation also follows a power-law in a broad energy range. For the Crab pulsar the slope of its photon energy spectrum slowly increases with photon energy the photon index varies from α = 1.6 at E ∼ 1 keV to α = 2.1 at E ∼ 1010 eV.(Becker, 2009)

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5.2

High Energy Emission

The emissions ranging from radio to γ -rays are produced in different regions of the pulsar magnetosphere.The pulsars may be considered as a rotating magnet with a very strong surface magnetic field, and the magnetosphere is completely dominated by electromagnetic forces. Due to this, there must be a fully conducting plasma surrounding the neutron star. If the component of the electric field E∥ along the magnetic field direction (B) is non-zero in the pulsar magnetosphere, then this can accelerate particles to ultrarelativistic energies. The accelerated particles emit γ -rays due to curvature emission and other processes, e.g., inverse Compton scattering. Some of these are absorbed giving rise to secondary electron-positron pairs. The created electron- positron pairs screen the electric field E∥ in the pulsar magnetosphere everywhere except for certain compact regions. The regions where E∥ is not screened are called accelerators or gaps. These gaps serve as an engine which is responsible for the pulsar non thermal radiation. There are two kinds of magnetosphere gaps: polar gaps and outer gaps, their location and potential drop being determined by the dipolar magnetic field, the rotation speed Ω and the angle beCredit: MAGIC Collaboration tween them called the inclination angle (α). Figure 22: Pulsar emission The polar gaps place the source of the emission imregions mediately above a magnetic pole near the surface of the neutron star. The outer gap place the source of emission far out in the magnetosphere, close to the velocity of light cylinder (Fig:23).(Cheng, 2009)

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5.3

Outer Gap Model

As proposed by (Cheng et al., 1986) (Romani, 1996), the "outer gap" model is widely used in explaining gamma-ray emission of pulsars. According to the this model, the emission is generated in the outer magnetosphere gap which is located above the nullcharge surface (Null-charge surface is where Ω.B = 0) towards the RLC . The lower surface of the gap is the last closed field lines and the upper surface is defined with a fractional gap width (Fig:23).

Figure 23: Pulsar magnetosphere(Chiang & Romani, 1992)

The primary particles are accelerated in this charge-depleted region and radiate primary curvature photons. These primary photons have moved away from the field line due to pulsar rotation and then the secondary pairs are produced with a considerable pitch angle. Consequently, the secondary pairs radiate synchrotron photons. Due to pair production, the charged particle density increases in the gap, so that the upper boundary depends on the pair cascade. The curvature photons contribute to the hard gamma-ray region and synchrotron photons contribute to the soft gamma-ray region of the spectrum.(Perera, 2013)

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5.4

Synchrotron-Self-Compton Model

Geometrical models, based on the outer gap successfully explains the basic features of the observed light curves (Romani & Yadigaroglu, 1995). However, the emission locations in the magnetospheres are still not clearly understood. (Cheng et al., 1986) concluded that Crab primary outer gap e+ /e− lose most of their energy to curvature γ-rays. Thus, Curvature radiation has remained as the preferred gamma-ray emission mechanism. But Detection of Crab above 150 GeV excludes curvature emission as the main emission mechanism (Lyutikov et al., 2012). So, the observed Spectral break in Crab is not due to curvature emission. (Lyutikov, 2013) argued that the IC(Inverse-Compton) scattering may be the dominant source of high energy photons in a majority of pulsars. He developed the IC model to include a modeling of the broadband SED, from UV to very high energy -rays, covering nearly ten decades in energy. The lower energy UV-X-ray peak is due to the cyclotron emission by the secondary particles, Doppler boosted by the parallel motion of the plasma to the X-ray range, while the GeV component is due to the scattering of the cyclotron photons by the counter-streaming beam. The Crab (SED) has two spectral bumps, a broad UV-X-ray-soft γ-ray bump, ∼ 1 eV10 MeV, and a high energy γ-ray bump, ∼ 100 MeV- 100 GeV. (Lyutikov et al., 2012) identify the broad soft UV-X-ray peak in the SED of the Crab pulsar as a synchrotron emission from the secondary plasma(formed as a result of the pair-production from the photons of Primary radiative processes) boosted by the large parallel velocities of emitting particles. This creates target photons for IC scattering both by the primary beam and by the secondary plasma. Within the framework of the SSC model the power emitted by IC is related to the power of the seed photons. Photons of different energies that are emitted by the same particles should in principle produce similar pulse profiles. In this model, the pulse profiles in X-ray and gamma-rays are similar because the secondary plasma emits synchrotron radiation in X-rays and IC scatters UV photons into the VHE band. Since within the SSC model the soft and hard photons are related, there is some γ-ray - X-ray correlation.

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