Magnetic field decay and unification of young and millisecond pulsar - PowerPoint PPT Presentation

Magnetic field decay and unification of young and millisecond pulsar populations Peter L. Gonthier Hope College Department of Physics June 8, 2016 Physics of Pulsar Magnetospheres NASA Goddard Space Flight Center Collaborators: Alice K. Harding & Elizabeth C. Ferrara — NASA Goddard Space Flight Center Jose Pons — University of Alicante, Alicante, Spain Yew-Meng Koh — Hope College, Department of Mathematics Recent undergraduates: Andrew Johnson & Caleb Billman — Hope College Sara Frederick — University of Rochester Victoria Merten — Washington and Jefferson College

1 Pulsar zoo 2 Population synthesis of normal pulsars 3 Population synthesis of millisecond pulsars 4 The Alicante connection: NPs to MSPs - field decay 5 Proposed new simulation 6 Conclusions

Pulsar Zoo with over 2530 subjects -9 10 15 14 B=10 B=10 -10 10 13 B=10 -11 10 4 -12 τ = 10 12 10 B=10 -13 10 Period Derivative (s/s) -14 11 B=10 10 -15 10 8 τ = 10 6 τ = 10 10 -16 B=10 10 -17 10 10 τ = 10 -18 10 Radio Fermi NPs -19 Fermi MSPs 10 X-ray Binary -20 10 9 RRAT B=10 NR AXPs/SGRs -21 10 8 B=10 -22 10 0.001 0.01 0.1 1 10 Period (s) ATNF - http://www.atnf.csiro.au/research/pulsar/psrcat

Binary Pulsars -9 10 15 14 B=10 B=10 -10 10 13 B=10 -11 10 4 -12 τ = 10 12 10 B=10 -13 3 10 Period Derivative (s/s) Log(orbital period) (days) -14 11 B=10 10 2 -15 10 8 τ = 10 τ = 10 6 10 -16 B=10 10 1 -17 τ = 10 10 10 -18 10 0 -19 10 -20 10 9 -1 B=10 -21 10 8 B=10 -22 10 0.001 0.01 0.1 1 10 Period (s) ATNF - http://www.atnf.csiro.au/research/pulsar/psrcat

Normal Pulsars -9 10 15 14 B=10 B=10 -10 10 13 B=10 -11 10 4 -12 12 τ = 10 10 B=10 -13 10 Period Derivative (s/s) 11 -14 B=10 10 -15 10 8 τ = 10 6 τ = 10 10 -16 B=10 10 -17 10 10 τ = 10 -18 10 -19 Normal Pulsars 10 -20 10 9 B=10 -21 8 10 B=10 -22 10 0.001 0.01 0.1 1 10 Period (s) ATNF - http://www.atnf.csiro.au/research/pulsar/psrcat

Gonthier et al. (2002) — no field decay 10 -11 Detected Simulated (a) (b) B=10 13 B=10 13 10 -12 10 -13 B=10 12 B=10 12 10 -14 Period Derivative HB 10 -15 LB B=10 11 B=10 11 10 -16 10 -17 Age 10 8 Age 10 8 Radio Pulsars 10 -18 Radio Loud Gamma Age 10 9 Age 10 9 Radio Quiet Gamma Dipole Dipole Multipole Multipole 10 -19 0.01 0.1 1 0.01 10 0.1 1 10 Period Period Death lines - Zhang, Harding & Muslimov (2000)

Gonthier et al. (2004) — Exponential B field decay Detected Simulated 10 -11 10 14 G 10 14 G 10 13 G (a) 10 13 G (b) 10 3 yr 10 3 yr 10 -12 10 -13 10 4 yr 10 4 yr HF 10 12 G 10 12 G 10 -14 10 5 yr Period derivative 10 5 yr 10 7 yr 10 -15 10 6 yr 10 6 yr LF 10 11 G 10 11 G B o = 13.7 10 -16 B o = 13.7 B o = 13.0 B o = 13.0 10 -17 B o = 12.75 CR B o = 12.75 CR B o = 12.35 B o = 12.35 10 -18 10 7 yr NR ICS NR ICS 10 -19 0.01 0.1 1 10 0.1 1 10 Period (s) Period (s) � τ = 2 . 8 million years Death lines - Harding, Muslimov & Zhang (2002)

Birth distributions — a more recent study • Born in the spiral arms using the electron density model NE2001 — Cordes & Lazio (2003). Spiral arm system rotates with the speed of the density waves • Trajectories are evolved in the Galactic potential — Paczy´ nski (1990) • For B o — Log normal distribution < log B o > = 12 . 8 σ log B o = 0 . 46 • For P o — Gaussian distribution — need to explore other distributions < P o > = 0 . 11 with P o min of 1 . 3 ms σ P o = 0 . 14 • Four free parameters to define the means and widths — searched in MCMC chains

Spin-down and field decay • Spitkovsky (2006) • Contopoulos, Kalapotharakos & Kazanas (2014) • Tchekhovskoy, Philippov & Spitkovsky (2016) 1 + sin 2 χ � � L = L o • Magnetic field decay model — Colpi, Geppert & Page (2000) d B 13 = − a B 1+ α (Eq. 2) 13 d t 1 a = τ Myr B 13 o B 13 ( t ) = (Eq. 3) � 1 /α 1 + a α B α � 13 o t 6

Colpi, Geppert, & Page 2000 - Figure 1 10 16 A.) Ambipolar diffusion – irrotaConal mode α = 1.25 a = 0.01 Myr -1 Magnetic Field [G] 10 15 B.) Ambipolar diffusion – solenoid mode α = 1.25 a = 0.15 Myr -1 10 14 C.) Crustal Hall cascade A B α = 1. a = 10. Myr -1 C 10 13 0 1 2 3 4 5 6 7 8 Log Age [yrs] Colpi, Geppert, & Page 2000, ApJ, 529, L29 – Figure 1

Magnetic field decay — Vigan` o, Pons, & Miralles 2012 Vigan` o et al. (2013) — Figure 10 a = 1 Myr − 1 τ Myr = 1 Myr α = 0 . 7 d B 13 = − a B 1+ α 13 d t  0 → Ohmic decay  1 → Hall induction α = 2 → Ambipolar diffusion  private communication, Jos´ e Pons

Radio and γ -ray beam geometry and emission • Harding, Grenier & Gonthier (2007) and • Pierbattista, Grenier, Harding, & Gonthier (2012) • Core and conal beams • Conal — altitude dependent — Kijak & Gil (2003) • Empirical radio luminosity — P and ˙ P dependence Arzoumanian, Chernoff, Cordes (2002) P β ν mJy · kpc 2 · MHz L ν = L o P α ν ˙ • Exponents α ν and β ν are free parameters searched by MCMC α ν = − 0 . 94 , β ν = 0 . 41 • Threshold characteristics of a select group of ten radio surveys • γ -ray sky maps — Extended Slot Gap emission — Muslimov & Harding (2004) • Empirical γ -ray luminosity L γ = f γ P α γ ˙ P β γ eV / s α γ = − 2 . 55 , β γ = 0 . 63

B field power-law decay model Detected Simulated The Structure and Signals of Neutron Stars, from Birth to Death , March 24 - 28, 2014, Florence, Italy

Radio pulsars

Fermi pulsars ln L = -1064 Radio ln L = -183 Fermi ln L = -1247 Total 2 = 702 Radio 2 = 100 Fermi 2 = 802 Total χ χ χ 25 20 ln L = -42 ln L = -23 20 ln L = -31 2 = 29 2 = 9 χ χ 20 2 = 16 χ Number of Pulsars 15 Number of Pulsars Number of Pulsars 15 15 10 10 10 5 5 5 0 0 0 -1.5 -1.0 -0.5 0.0 -16 -15 -14 -13 -12 -11 11.0 11.5 12.0 12.5 13.0 13.5 14.0 Log( Period Derivative ) Log( B field ) Log( Period ) 25 25 16 ln L = -19 ln L = -25 ln L = -23 ln L = -20 2 = 13 2 = 11 14 15 χ χ 2 = 10 20 χ 2 = 11 20 χ 12 Number of Pulsars 15 10 15 10 8 10 10 6 5 4 5 5 2 0 0 0 0 2 3 4 5 6 7 8 0.5 1.0 1.5 2.0 2.5 3.0 3.5 -3 -2 -1 0 1 2 3 4 0 1 2 3 4 Log( Characteristic Age ) Log( DM ) Log( S1400 ) Log( Slot Gap Flux )

Population synthesis of millisecond pulsars Initial Magnetic Field and Period -16 10 10 B=10 11 B=10 92 detected radio MSPs -17 10 0.1 Gyr 9 B=10 Period Derivative -18 10 • P ( B 8 ) ∝ B − 1 . 3 8 • B min = 0 . 9 B 8 -19 10 12 Gyr • P o min = 1 . 3 ms -20 10 8 B=10 -21 10 0.001 0.01 0.1 1 Period Mass accretion lines — P o = 0 . 18 × 10 3 δ/ 7 × B 6 / 7 ms where δ 8 dithered between 0 and 2.8 — Lamb & Yu (2005)

MCMC - Radio and γ -ray Luminosities • Assuming empirical radio and γ -ray luminosities as it the case of NPs L ∝ P α ˙ P β • MCMC searches a 4D model parameter space selecting α ν = − 1 . 07 ± 0 . 17 , β ν = 0 . 59 ± 0 . 12 α γ = − 2 . 7 ± 1 . 0 , β γ = 1 . 1 ± 0 . 4

˙ P − P - TPC -16 10 54 Fermi Pulsars 54 Fermi Pulsars 11 months TPC 34 10 35 Detected 33 10 E dot (erg/s) Simulated 10 -17 10 Period Derivative -18 10 -19 10 -20 10 Radio Pulsars Fermi Pulsars -21 10 0.001 0.01 0.1 1 0.01 0.1 1 Period

Summary of Population Synthesis of MSPs Catalog Period Detected Simulated TPC OG RALTPC PSPC BSL 3 months 13 29 30 27 29 1FGL 11 months 54 54 54 54 54 2FGL 2 years 68 76 77 80 80 3FLG 4 years 82 107 106 110 109 5 years 119 118 121 122 10 years 162 153 170 160

The Alicante connection: NPs to MSPs - field decay How do we go from a log-normal B distribution (NPs) to a power law B distribution (MSPs)? 4.5 4.0 NPs MSPs 4.0 Log( number of pulsars ) Log( number of pulsars ) P ( B ) ∝ B − 0.7 3.5 3.5 3.0 3.0 2.5 2.5 2.0 2.0 11 12 13 14 15 8 9 10 11 Log( B field ) Log( B field )

A natural consequence of the power-law decay of the magnetic field! B o B = o t 6 ] 1 /α [1 + a α B α For large times ( a α B α o t 6 ) >> 1

A natural consequence of the power-law decay of the magnetic field! B o B = o t 6 ] 1 /α [1 + a α B α For large times ( a α B α o t 6 ) >> 1 1 B α → a α t 6

A natural consequence of the power-law decay of the magnetic field! B o B = o t 6 ] 1 /α [1 + a α B α For large times ( a α B α o t 6 ) >> 1 1 B α → a α t 6 We are assuming a constant birth rate, therefore the number of present pulsars at time t is N = c t 6 where c is the constant birth rate of MSPs — c = 4 to 5 per Myr

A natural consequence of the power-law decay of the magnetic field! B o B = o t 6 ] 1 /α [1 + a α B α For large times ( a α B α o t 6 ) >> 1 1 B α → a α t 6 We are assuming a constant birth rate, therefore the number of present pulsars at time t is N = c t 6 where c is the constant birth rate of MSPs — c = 4 to 5 per Myr N = B − α a α c