GRMHD Simulations of accreting neutron stars with dipolar and complex magnetic fields Pushpita Das, Oliver Porth, Anna Watts Anton Pannekoek Institute for Astronomy University of Amsterdam Abstract Accreting neutron stars (NS) and accreting millisecond X-ray pulsars (AMXPs) are one of the most interesting laboratories to study the physics of compact objects. Recently, along with providing highly precise mass and radius measurements, NICER also indicted the requirement of complex magnetic field structures to explain the observed X-ray spectra in some of the isolated millisecond pulsars. Rotation-powered millisecond pulsars are assumed to have undergone significant magnetic field evolution during the accretion phase. However, the details of this process are still poorly understood. We performed a suite of GRMHD simulations of accretion onto neutron stars, contrasting dipolar with non- dipolar field structures. Besides exploring processes in different accretion regimes, the simulations inform on the variability properties of the hotspots which can aid in future pulse-profile modeling of accreting sources. Numerical Setup We solve ideal general relativistic magnetohydrodynamic equations using the Black Hole Accretion Code (BHAC) in Schwarzschild coordinates. A few details of the numerical setup is illustrated below. • Effective resolution: 𝑁! × 𝑁" = 1920 × 768 • We initialize the magnetosphere with 𝜎= 100 and 𝛽= 0.01. • We ensure force-free like conditions in the magnetosphere by modifying 𝑝, 𝜌and 𝑢∥following Tchekhovskoy et al., 2013 • At 𝑟= 𝑅⋆, we put outflow boundary conditions at the accreting regions, thus allowing all the materials to pass through the surface undisturbed. Dipoles For reference we show three different accretion states for stars with dipolar magnetic fields rotating at an angular frequency of 0.03𝑐%/𝐺𝑀corresponding to ~572 Hz. Depending on stellar magnetic strength we can push the magnetospheric radius in or out of the corotation radius leading to various accretion states (Parfrey et al., 2017). Figure 1 : Logarithmic density for different values of surface dipolar moment at a fixed snapshot of t = 24570𝐺𝑀/𝑐!. (a) boundary layer, (b) Channeled accretion and (c) propeller regime. Dashed and solid lines represent the corotation and the light cylinder radius respectively (also for all the other density profiles) 𝑟"# 𝑟"# 𝑟"# 𝑟$" 𝑟$" 𝑟$" Conclusions • Hotspot visibility : Number and size of stream are strongly affected by field geometry! • In the parameter regime that we consider, on an average, the neutron star is always spinning down. • The effective spin-down torque at the stellar surface in case of quadrupoles is smaller compared to dipoles for the same surface polar field strength. • Addition of a quadrupolar field enhances the mater torque (causing more spin-up torque) and less spin-down EM torque. • We observe 1ms variability in the temperature profiles. Whether this leads to an observational signature affecting pulse-profile modeling depends on the thermal timescale on the surface and the details of the radiation transport. This is left for future work. Quadrupoles • The initial opposite polarities of the stellar field in the upper and lower hemispheres has a huge impact on the geometry of the accretion flow. • Fig: 2 shows the time evolution of the disk for Q = 70 where the initial disk magnetic field is anti parallel to the stellar field in the northern hemisphere and parallel in the southern hemisphere. • The asymmetric disk-magnetosphere coupling modifies the initial quadrupolar magnetosphere to resemble a quadrudipolar field in the vicinity of the stellar surface. • Fig: 3 shows density profiles for different quadrupolar strengths. Depending upon quadrupolar moment, we get different accretion states. At the lowest quadrupolar moment (Q = 25), the disk crushes the northern closed zone leading to boundary layer accretion. Increasing quadrupolar strength (Q) mainly has two effects. First, it halts the dis