Modeling isolated magnetar spin-down evolution and implications for long-period radio transients

Abstract

Long-period radio transients (LPTs) are a new class of radio sources characterized by long spin periods ($P_{\text{spin}}>10^3$ s) and highly variable radio emission. While known magnetars are relatively young ($τ<10^5$ yrs) with spin periods clustered between $1-10$ sec, it has been proposed that LPTs may be linked to a missing population of older magnetars. In this paper, we present an extensive parametric analysis of isolated magnetar spin evolution using various propeller spin-down models. In general, at higher initial magnetar B-fields ($B_0>\sim10^{15}$ G) and larger ambient densities ($n_0>\sim10^2$ cm$^{-3}$), magnetars will transition to the propeller phase earlier, and they start accreting gas from the ISM or molecular clouds after $τ\sim10^8$ yrs. We found that a transition from the pulsar to the propeller phase is required to reach the observed LPT period range of $P>10^3$ s. More specifically, our population synthesis study based on Monte-Carlo simulations shows that two propeller models can account for most of the observed LPT periods ($P\sim1-400$ [min]) and their period derivative constraints ($\dot{P}<10^{-9}$ s s$^{-1}$). Our spin-down models predict that (1) nearby radio-quiet neutron stars with the estimated dipole $B$-field range of $B\sim(1-5)\times10^{13}$ G will transition to the propeller phase eventually after $τ>\sim10^7$ yrs; (2) thermal X-ray emission from accretion-phase magnetars becomes too faint for detection after traveling ($d>\sim10$ kpc) from their birth places; (3) sporadic radio outbursts observed from LPTs may not be explained by regular radio pulsar and magnetar emission mechanisms that operate during the propeller phase.

Figures (14)

• Figure 1: NS spin evolution for $B_0=10^{15}$ G, $v_0=100$$\mathrm{km}\,\mathrm{s}^{-1}$, $n_0 = 1$ cm$^{-3}$ in case of the propeller model E. The vertical dashed lines indicate the four transition points as detailed in the text. In the rightmost panel, the typical LPT period range ($P = 10^3 - 10^4$ s) has been indicated in gray.
• Figure 2: A comparison of the six propeller spin-down models for the same input parameters ($B_0=10^{15}$ G, $v_0=100$$\mathrm{km}\,\mathrm{s}^{-1}$, and $n_0 = 1$ cm$^{-3}$), including the case where only dipole spin-down is considered. In the rightmost panel, the typical LPT period range ($P = 10^3 - 10^4$ s) has been indicated in gray.
• Figure 3: A qualitative study of the parameter space for the propeller model E, which traces the evolution of an NS in the $P-\dot{P}$ space. The leftmost plot varies the initial B-field $B_0$, the center plot varies the translational velocity of the NS $v_0$, and the right column varies the density of the surrounding material $\rho_0$. The remaining parameters, which are not being varied, are fixed to $B_0=10^{15}$ G, $v_m = 200$$\mathrm{km}\,\mathrm{s}^{-1}$ and $n_0$ = 1 cm$^{-3}$. Similar results for the remaining models can be found in appendix \ref{['app:qual_par_study']}.
• Figure 4: Population synthesis results for the various propeller models plotted in $P$--$\dot{P}$ space. The black dots with downward arrows are the six yet unidentified LPTs with known $\dot{P}$ upper limits (CHIME J0630+25, GLEAM--X J1627--52, GPM J1839--10, ASKAP J1832--09, ASKAP J1935+21, and ASKAP J1839--08).
• Figure 5: Fraction of simulated NSs in different phases (pulsar phase in blue, propeller phase in green, and accretion phase in orange) at different time-slices for models E and F.