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

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Period Derivative (s/s) 0.001 0.01 0.1 1 10 Period (s)

Radio Fermi NPs Fermi MSPs X-ray Binary RRAT NR AXPs/SGRs

B=10

13

B=10

15

B=10

11

B=10

9

B=10

12

B=10

8

B=10

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τ = 10

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τ = 10

8

τ = 10

6

τ = 10

4

B=10

10

ATNF - http://www.atnf.csiro.au/research/pulsar/psrcat

Binary Pulsars

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Period Derivative (s/s) 0.001 0.01 0.1 1 10 Period (s) B=10

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B=10

15

B=10

11

B=10

9

B=10

12

B=10

8

B=10

14

τ = 10

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τ = 10

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τ = 10

6

τ = 10

4

B=10

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3 2 1

• 1

Log(orbital period) (days) ATNF - http://www.atnf.csiro.au/research/pulsar/psrcat

Normal Pulsars

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Period Derivative (s/s) 0.001 0.01 0.1 1 10 Period (s)

Normal Pulsars

B=10

13

B=10

15

B=10

11

B=10

9

B=10

12

B=10

8

B=10

14

τ = 10

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τ = 10

8

τ = 10

6

τ = 10

4

B=10

10

ATNF - http://www.atnf.csiro.au/research/pulsar/psrcat

Gonthier et al. (2002) — no field decay

Detected Simulated

HB LB

0.01 0.1 1 10 Period Dipole Multipole

Radio Pulsars Radio Loud Gamma Radio Quiet Gamma

Age 108 Age 109 B=1011 B=1012 B=1013 10-19 10-18 10-17 10-16 10-15 10-14 10-13 10-12 10-11 Period Derivative 0.01 0.1 1 10 Period Dipole Multipole Age 109 B=1012 B=1013 B=1011 Age 108

(a) (b)

Death lines - Zhang, Harding & Muslimov (2000)

Gonthier et al. (2004) — Exponential B field decay

Detected Simulated

• 10-19

10-18 10-17 10-16 10-15 10-14 10-13 10-12 10-11 Period derivative 0.01 0.1 1 10 Period (s)

(a)

LF HF

1014G 1013G 1012G 1011G NR ICS CR 105 yr 104 yr 106 yr 107 yr 103 yr Bo = 13.7 Bo = 13.0 Bo = 12.75 Bo = 12.35 0.1 1 10 Period (s)

(b)

NR ICS CR 107 yr 106 yr 105 yr 104 yr 103 yr 1011G 1012G 1013G 1014G Bo = 12.35 Bo = 12.75 Bo = 13.0 Bo = 13.7

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 Bo — Log normal distribution

< log Bo > = 12.8 σlog Bo = 0.46

• For Po — Gaussian distribution — need to explore other

distributions < Po > = 0.11 with Pomin of 1.3 ms σPo = 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)

L =

• 1 + sin2 χ
• Lo
• Magnetic field decay model — Colpi, Geppert & Page (2000)

d B13 d t = −a B1+α

13

(Eq. 2) a = 1 τMyr B13(t) = B13o

• 1 + a α Bα

13o t6

1/α (Eq. 3)

Colpi, Geppert, & Page 2000 - Figure 1

1013 1014 1015 1016 Magnetic Field [G] 1 2 3 4 5 6 7 8 Log Age [yrs] C B A

Colpi, Geppert, & Page 2000, ApJ, 529, L29 – Figure 1 A.) Ambipolar diffusion – irrotaConal mode α = 1.25 a = 0.01 Myr-1 B.) Ambipolar diffusion – solenoid mode α = 1.25 a = 0.15 Myr-1 C.) Crustal Hall cascade α = 1. a = 10. Myr-1

Magnetic field decay — Vigan`

• , Pons, & Miralles 2012

Vigan`

• et al. (2013) —

Figure 10 a = 1 Myr−1 τMyr = 1 Myr α = 0.7 d B13 d t = −a B1+α

13

α =    0 → Ohmic decay 1 → Hall induction 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)

Lν = Lo P αν ˙ P βν mJy · kpc2 · MHz

• Exponents αν and βν are free parameters searched by MCMC

αν = −0.94, βν = 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

Lγ = fγ P αγ ˙ P βγ eV/s αγ = −2.55, βγ = 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

20 15 10 5 Number of Pulsars

• 1.5
• 1.0
• 0.5

0.0 Log( Period ) lnL = -23 χ

2 = 9

25 20 15 10 5 Number of Pulsars

• 16
• 15
• 14
• 13
• 12
• 11

Log( Period Derivative ) lnL = -31 χ

2 = 16

20 15 10 5 Number of Pulsars 14.0 13.5 13.0 12.5 12.0 11.5 11.0 Log( B field ) lnL = -42 χ

2 = 29

25 20 15 10 5 Number of Pulsars 8 7 6 5 4 3 2 Log( Characteristic Age ) lnL = -25 χ

2 = 11

15 10 5 4 3 2 1

• 1
• 2
• 3

Log( S1400 ) lnL = -19 χ

2 = 13

16 14 12 10 8 6 4 2 3.5 3.0 2.5 2.0 1.5 1.0 0.5 Log( DM ) lnL = -23 χ

2 = 10

25 20 15 10 5 4 3 2 1 Log( Slot Gap Flux ) lnL = -20 χ

2 = 11

lnL = -183 Fermi χ

2 = 100 Fermi

lnL = -1064 Radio χ

2 = 702 Radio

lnL = -1247 Total χ

2 = 802 Total

Population synthesis of millisecond pulsars Initial Magnetic Field and Period

• P(B8) ∝ B−1.3

8

• Bmin = 0.9B8
• Pomin = 1.3 ms

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Period Derivative

0.001 0.01 0.1 1

Period

B=10

8

B=10

11

B=10

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B=10

9

12 Gyr 0.1 Gyr

92 detected radio MSPs

Mass accretion lines — Po = 0.18 × 103δ/7 × B6/7

8

ms where δ 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
• f NPs

L ∝ P α ˙ P β

• MCMC searches a 4D model parameter space selecting

αν = −1.07 ± 0.17, βν = 0.59 ± 0.12 αγ = −2.7 ± 1.0, βγ = 1.1 ± 0.4

˙ P − P - TPC

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Period Derivative 0.001 0.01 0.1 1 Period 0.01 0.1 1 54 Fermi Pulsars 11 months Detected 54 Fermi Pulsars TPC Simulated Radio Pulsars Fermi Pulsars Edot (erg/s) 10

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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)?

4.0 3.5 3.0 2.5 2.0

Log( number of pulsars )

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Log( B field )

4.5 4.0 3.5 3.0 2.5 2.0

Log( number of pulsars )

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Log( B field )

P(B) ∝ B−0.7

NPs MSPs

A natural consequence of the power-law decay of the magnetic field!

B = Bo [1 + a α Bα

• t6]1/α

For large times (a α Bα

• t6) >> 1

A natural consequence of the power-law decay of the magnetic field!

B = Bo [1 + a α Bα

• t6]1/α

For large times (a α Bα

• t6) >> 1

Bα → 1 a α t6

A natural consequence of the power-law decay of the magnetic field!

B = Bo [1 + a α Bα

• t6]1/α

For large times (a α Bα

• t6) >> 1

Bα → 1 a α t6 We are assuming a constant birth rate, therefore the number of present pulsars at time t is N = c t6 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 = Bo [1 + a α Bα

• t6]1/α

For large times (a α Bα

• t6) >> 1

Bα → 1 a α t6 We are assuming a constant birth rate, therefore the number of present pulsars at time t is N = c t6 where c is the constant birth rate of MSPs — c = 4 to 5 per Myr N = B−α a α c

Issues based on previous simulations

Bα

min =

1 a α t6max =

• 9 × 10−6α

If we assume, P(B8) ∝ B−1.3

8

— as we have in previous simulations

• α = 1.3 does not work!

a = 1 1.3 × (9 × 10−6)1.3 × 12000 = 232 Myr−1

• So we take a = 1 Myr−1 and α = 0.7 for NPs

(Vigan`

• et al. 2013) and apply them to MSPs

t6max = 1 0.7 × 1 Myr−1 × (9 × 10−6)0.7 = 4900 Myr

Proposed new simulation

• From NPs α = 0.7 and a = 1 Myr−1 to describe Hall

induction and Ohmic decay of crustal field

• Switch to α = 1.3 and a = 0.01 Myr−1 to describe ambipolar

diffusion of the core field — pure guess, but not sensitive

• Theoretical details pending and the code development
• Redo the MSP simulation to test the scenario with

P(B8) ∝ B−0.7

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• and α = 1.3 and a = 0.01 Myr−1

˙ P − P - TPC

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Period Derivative 0.001 0.01 0.1 1 Period 0.01 0.1 1 54 Fermi Pulsars 11 months Detected 54 Fermi Pulsars TPC Simulated Radio Pulsars Fermi Pulsars Edot (erg/s) 10

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34 10 33

Radio pulsars

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Number of Radio Pulsars

• 3.0
• 2.5
• 2.0
• 1.5
• 1.0
• 0.5

0.0

Log( Period ) Detected Simulated

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• 21
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Log( Pdot )

30 25 20 15 10 5 3.0 2.5 2.0 1.5 1.0 0.5 0.0

Log( DM )

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• 1

Log( S1400 )

40 30 20 10

Number of Radio Pulsars

11.0 10.0 9.0 8.0

Log( Char. Age )

35 30 25 20 15 10 5 11.0 10.5 10.0 9.5 9.0 8.5 8.0

Log( B field )

From αν = −1.07, βν = 0.59, to αν = −0.94, βν = 0.05

Fermi pulsars

20 15 10 5

Number of Fermi Pulsars

• 3.0
• 2.8
• 2.6
• 2.4
• 2.2
• 2.0

Log( Period )

30 25 20 15 10 5

• 21.0
• 20.0
• 19.0
• 18.0

Log( Pdot )

12 10 8 6 4 2 2 1

• 1

Log( S1400 )

20 15 10 5 2.5 2.0 1.5 1.0 0.5 0.0

Log( DM )

16 14 12 10 8 6 4 2 2.0 1.5 1.0 0.5 0.0

Log( Energy Flux )

20 15 10 5

Number of Fermi Pulsars

10.5 10.0 9.5 9.0 8.5 8.0

Log( Age )

25 20 15 10 5 9.5 9.0 8.5 8.0

Log( B )

16 14 12 10 8 6 4 2 36 35 34 33 32 31

Log( Lγ )

From αγ = −2.7, βγ = 1.1, to αγ = −1.77, βγ = 0.23

Conclusions

• Normal pulsars and binary pulsar systems may come from a

similar parent distribution of magnetized neutron stars.

• A log-normal B field distribution of young (normal, isolated)

pulsars can be converted into a power-law B field distribution via standard crustal Hall induction and Ohmic field decay leaving ambipolar diffusion to later play a role within the neutron star core of old dead pulsars that can then be recycled into millisecond pulsars via mass accretion from a stellar companion spinning up the neutron star.

• The cutoff Bmin in the assumed B field birth distribution of

MSPs may be an indication of maximum age and minimum period of active MSPs.

• Detailed theoretical work is pending as well as code

development for an adequate full population simulation.