What have we Learned from Fermi Pulsar Light Curve Modelling? - CERN Indico
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What have we Learned from
Fermi Pulsar
Light Curve
Modelling?
Clark et al. (2018)
Christo Venter
Centre for Space Research,
North-West University, South Africa
Collaborators: AK Harding, C Kalapotharakos, Z Wadiasingh,
A Kundu, AS Seyffert, M Barnard, TJ Johnson,
PL Gonthier, I Grenier, …
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg
Outline
hackernoon.com
Brief Observational Context
What have we learned?
1. Spatial Aspects
2. Caustics / Photon Bunching
Interconnected!
3. Pulsar Geometry
4. B & E-field Structure
5. Population Studies
6. Emission Mechanisms
7. Multi-band Fitting
Conclusions www.earthtimes.org
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg
Observations
2PC: 117 pulsars – diversity of LCs
3PC (cf. talk by M. Kerr)
Abdo et al. (2009) Abdo et al. (2013)
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg
Observations Mignani et al. (2017)
Vela Kuiper & Hermsen (2015)
Rudak (2018)
• Broadband spectra
• Light curves
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg
Observations
(Vela) Light curve energy evolution:
P1/P2, φ, W, bridge
Abdo et al. (2010)
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg
1. Probing Spatial Aspects Location and extent of dissipation region: Within light cylinder? Beyond light cylinder? Hybrid accelerator? 9th Fermi Symposium, 12 – 17 April 2021, Johannesburg
1. Probing Spatial Aspects
PC Rmax = 1.2 RLC
Dissipation region:
Within the light cylinder α = 30ο
(PC, OG, SG, TPC, AG) Rmax = 0.8 RLC
Venter et al. (2012)
Rmax = 0.6 RLC
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg
1. Probing Spatial Aspects
PC Rmin = 0.12 RLC
Dissipation region:
Within the light cylinder (OG, TPC) α = 30ο
Rmin = 0.4 RLC
Venter et al. (2012)
Rmin = 0.7 RLC
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg
1. Probing Spatial
Aspects
Dissipation region:
Beyond the light cylinder
(current sheet)
E.g., including GR, 1-photon and
2-photon pair production
PIC model finding current sheet to be the most
significant source of high-energy photons.
Philippov & Spitkovsky (2018)
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg
1. Probing
Spatial
Aspects
Dissipation region:
Beyond the light cylinder
(current sheet)
PIC model with increased rate of injection
from stellar surface:
Gradual screening of accelerating E-field and
formation of force-free current structure.
Brambilla & Kalapotharakos (2018)
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg Cf. Contopoulos & Stefanou (2019)1. Probing Spatial Aspects Dissipation region: Hybrid: E.g., inner / outer gap model Hirotani (2007) E.g., extended SG / separatrix model (cf. A.K. Harding’s talk) Harding et al. (2018) 9th Fermi Symposium, 12 – 17 April 2021, Johannesburg Cf. Yeung (2020)
2. Caustics / Photon Bunching
Traditional models
Morini (1983)
Leading Trailing
Morini (1983) Bunching of photons (from different field lines / heights) in phase due to:
Romani & Yadigaroglu (1995) 1. B-field structure
Dyks et al. (2004) 2. Aberration when transforming from co-rotating to lab frame
3. Time-of-flight delays
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg2. Caustics / Photon Bunching
TPC α = 70o ζ = 80o PSR J0030+0451
OG α = 80o ζ = 70o
Venter et al. (2009)
43rd COSPAR Scientific Assembly, 28/1/2021 – 4/2/2021, Sydney, Australia Cf. Chang et al. (2018)2. Caustics / Photon Bunching
Extended SG / Separatrix models
Calculations in lab frame:
• Go beyond RLC
• No aberration Rmax = 1.2RLC
Sky-map stagnation:
• Force-free B-field approaches split-monopole
solution at large distances
• Bunching of emission from one field line,
different heights
• Geometric model!
Bai & Spitkovsky (2010)
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg2. Caustics / Photon Bunching
FIDO model(s) Kalapotharakos et al. (2014, 2017)
Calculations in lab frame:
• Go beyond RLC
• No aberration
• Force-free-like solution: two-step conductivity
• Sky-map stagnation effect confirmed (but overlapping lines)
• E|| determines emissivity (not cut off at some Rmax)
• High-energy trajectories mostly near leading edge of polar
cap, dominant emission in current sheet
• THUS: B-field structure, time-of-flight effect, E||
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg2. Caustics / Photon Bunching
Current sheet beyond light cylinder: Pulsed SR / IC
Double spiral arm B-field structure
Beaming due to relativistic flow
Generally 2 pulses per period
Geometrically:
Cf. Benli et al. (2021)
Out
Parker spiral /
In
“striped wind”
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg Pétri (2011, 2016)3. Probing Pulsar Geometry
E.g., a single-peaked γ-ray LC
Cut γ-ray caustic almost tangentially
Seyffert (2014)
Use radio light curve information:
rotating vector model (RVM), phase shift
Weltevrede et al. (2010)
Cf. Rookyard et al. (2015)
9th Fermi Symposium, 12 – 17 April 2021, JohannesburgNg & Romani (2008)
3. Probing Pulsar Geometry
E.g., a γ-ray-quiet pulsar
Double-torus fitting: ζ = 32.5o + 4.3o
Thermal pulsed X-rays: low β = ζ − α
Single radio peak: β > 10o
Radio visibility: β < 30o
γ-ray invisibility: α < 55o, ζ < 55o PSR J0855-4644
Best fit radio LC: (α, ζ) = (22o,8o)
Maitra et al. (2017)
X
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg3. Probing Pulsar Geometry
E.g., “quarter-spaced” LCs
Non-thermal X-ray and
γ-ray LCs, radio-quiet
Not due to ingoing
particles in TPC
Caustic γ-ray emission,
X-ray cone at low PSR J1813−1246
altitude (0.2RLC) in
force-free B-field geometry
Marelli et al. (2014)
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg4. B / E-field Geometric
OG
Structure
Offset-dipole fields: geometric /
emission models Geometric
TPC
Barnard et al. (2016)
SG
y
x
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg4. B / E-field Structure
Offset-dipole (vacuum) fields: geometric model
Kundu & Pétri et al. (2019)
θ
φ
y
Shift in PCs
Breaking of N/S symmetry
Radio-to-γ lag
x
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg4. B / E-field Structure
Light curves / curvature radiation spectra using FIDO model
LOW σ = broad, single peaks; HIGH σ: narrow, double peaks
Energy
subbands:
σ = 30 Ω
Yang & Cao (2021) Vela
Cf. Cao & Yang (2019)
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg4. B / E-field Structure
P1/P2 vs. Eγ: P2 correlates with larger ρc
(cf. talk of M. Barnard)
Phase-averaged
Phase-resolved
Barnard et al.
(in prep.)
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg5. Population Approach
∆-δ for young pulsars
Kalapotharakos et al. (2014)
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg6. Multi-wavelength LCs
Harding et al. (2018)
Optical photons:
E.g., extended SG model: pair SSC
primary SC, pair SR,
primary IC on pair SR, etc.
(cf. talk of A.K. Harding)
E.g., OG model:
primary IC on pair SR,
pair IC on thermal X-rays, TeV photons: primary IC on pair SR
pair SSC
Rudak & Dyks (2017)
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg6. Multi-wavelength LCs
Need statistic to properly weight
contributions from different Single-
subbands (cf. talk by A.S. Seyffert) band
Only:
Non-colocation of single-band
best fits of (α,ζ)
Error disparity between bands
Corongiu et al. (2021)
Seyffert et al (in prep.) Joint Fit of
Radio / γ-rays:
Cf. Johnson et al. (2014)
Cf. Pierbattista et al. (2015, 2016)
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg6. Multi-wavelength LCs Kalapotharakos et al. (2021)
One of the main NICER goals is the
precise determination of M and R of
several MSPs (Gendreau et al. 2016)
Miller et al. (2019) and Riley et al. (2019)
reported strong evidence of multipolar
B-fields via X-ray LC modelling
Dual-band LC fitting (X-ray & γ-ray)
proved constraining for an 11-parameter
model that assumes offset-dipole and
offset-quadrupole B-field components
(Cf. talk by C. Kalapotharakos)
Cf. Chen et al. (2020)
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg7. Emission Mechanisms
Traditional / extended SG / Current-sheet models: SR (γe ~ 104-6)
FIDO / PIC: CR (γe ~ 107-8)
PIC: Need to scale down B-field and γe;
Use realistic P, B to scale up γe crude resolution in R*/RLC
Kalapotharakos et al. (2018)
α = 30o
Cf. Chang
et al.
(2019) Philippov &
Spitkovsky (2018)
Cf. Petri α = 60o
(2019) Cf. Cerutti et al.
(2016)
Cf. Chang & Zhang (2019): IC
9th Fermi Symposium, 12 – 17 April 2021, Johannesburg7. Emission Mechanisms Fundamental Plane – radiation-reaction regime (cf. poster by C. Kalapotharakos): Fit: 88 pulsars (2PC) Kalapotharakos et al. (2019) 9th Fermi Symposium, 12 – 17 April 2021, Johannesburg
7. Emission Mechanisms Synchro-curvature emission: encapsulates perpendicular (SR) and longitudinal (CR) limits Many single-particle contributions Can help to fill out GeV spectrum and create sub- exponential high-energy tail to better match data Effect on LCs? Cheng & Zhang (1996) Vigano et al. (2014, 2015) Torres (2018) Harding et al. (2018) 9th Fermi Symposium, 12 – 17 April 2021, Johannesburg
7. Emission Mechanisms Pulsed γ-rays detected by MAGIC from Geminga Second light curve peak: 15 – 75 GeV Smoothly connected to Fermi spectrum Overlapping radiation components? E.g., CR / IC Acciari et al. (2020) 9th Fermi Symposium, 12 – 17 April 2021, Johannesburg
Combining Datasets
Phase-resolved spectroscopy (FIDO)
Polarisation
Harding & Kalapotharakos (2017)
Vela
Brambilla et al. (2015)
9th Fermi Symposium, 12 – 17 April 2021, JohannesburgConclusions What have we learned? 1. Spatial Aspects Probe dissipation region (location, extent) 2. Caustics / Photon Bunching Trajectories, TOF effects, acceleration, energetics 3. Pulsar Geometry Constrain α, ζ within certain framework 4. B & E-field Structure Force-free-like; multipoles for MSPs? 5. Population studies Uncover trends, e.g., ∆-δ or α/ζ distribution 6. Emission Mechanisms CR vs. SC vs. SR vs. … LC discrimination (e.g., P1/P2) 7. Multi-band Fitting Stronger constraints; robust statistic needed Convolution of effects creates imprints on light curves Future: Combine with phase-resolved spectral / polarisation studies 9th Fermi Symposium, 12 – 17 April 2021, Johannesburg
This work is based on the
research supported wholly/in
part by the National Research
Foundation (NRF) of South Africa
Thanks!
(grant number 99072). The
grantholder acknowledges that
opinions, findings, and
conclusions or recommendations
expressed in any publication
generated by the NRF supported
research is that of the author(s),
and that the NRF accepts no
liability whatsoever in this regard.
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