Formation Rates and Evolution Histories of Magnetars
Pulsar Coffee
15.11.19
Almog Yalinewich
Introduction to Magnetars
Pulsar Magnetic Field
Consistent with flux conservation
B_{NS} < B_{WD,\max} \left(R_{WD}/R_{NS}\right)^2 \approx 5 \cdot 10^{13} G
Magnetar Magnetic Field
Turbulent dynamo
Heuristic for max field:
B_{\max} \approx \frac{M_{\odot}}{m_p} \frac{\mu_N}{R_{NS}^3} \approx 10^{16} \, \rm G
X Ray Luminosity
X ray luminosity
spin
down
luminosity
<<
X ray luminosity powered by magnetic field decay
Giant Flares
Mini EMP from SGR 1806-20
on 21:30:26.5 UT, Dec 27, 2004
10^{46} \, \rm erg
10% of the magnetic energy
Abundance
2700 pulsars vs. 23 magnetars
Competing theories
Rare progenitor theories
Superluminous supernovae
Fast spin
High initial magnetic field
Magnetar Evolution and Age Estimation
Supernova Association
Dynamical time
\tau_d \approx \frac{r}{v}
Upper limit on magnetar creation birth rate
1/100 \, \rm year
Spindown Age
\tau_{\Omega} = \left| \frac{P}{\left(n-1\right) \dot{P}} \right|
n=3
n=5
Demagnetisation Age
\tau_{B} \approx \left| \frac{B}{\dot{B}} \right|
can't be measured
Proxy: X ray luminsity
\tau_{\Omega} \approx \left| \frac{U_B}{L_X} \right|
Correction to spindown
B = B_0 \left(1+\frac{\alpha t}{\tau_B}\right)
\Omega = \Omega_0 \left[\frac{\left(n-1 \right ) \tau_B}{2 \left(\alpha -2\right) \tau_{\Omega}}\left(\left(1+\frac{\alpha t}{\tau_B}\right)-1\right)^{\frac{\alpha-2}{\alpha}} + 1 \right ]^{\frac{1}{1-n}}
Demagnetisation
Buried Magnetic Field?
B \approx B_0 \exp \left(-\frac{\left(t-t_e\right)^2}{2 \tau_B^2}\right)
\Omega = \Omega_0 \left(1+ \frac{\left(n-1\right) \tau_B \pi^{1/2}}{4 \tau_{\Omega}} \left({\rm erf} \left(\frac{t-t_e}{\tau_B}\right)+ {\rm erf} \left( \frac{t_e}{\tau_B} \right)\right)\right)^{\frac{1}{n-1}}
Buried Magnetic Field?
Evolutionary Track
Probability Distribution
Population Synthesis
Setup
-
Natal rotation rate 100Hz
-
Log uniform initial magnetic field 1e14-1e15 G
-
Extinction 1 Mag / kpc
-
Richter like distribution for giant flares
\frac{d N}{d E} \propto E^{-1.4}
P-Pdot curves
Simulated
observed
Flux vs. Numbers
Giant Flare distribution
Conclusion
Magnetar birth rate 2-20 per 1000 years
NS birth rate 17+/-2 per 1000 years
roughly 40% of NS start out as magnetars
1e46 erg giant flare every 200 years
Detectable by swift up to 100 Mpc, 5 every year
Galactic sample is close to complete
magnetar formation rate
By almog yalinewich
