Super-Eddington accretion onto a magnetized neutron star Anna Chashkina, Pavel Abolmasov and Juri Poutanen University of Turku, Nordita and SAI MSU April 18, 2017
Motivation. Ultraluminous X-ray pulsars N X-2 X-1 (Tsygankov et al., 2015) E 5 I M82 X2 (Bachetti et al., 2014). L x 10 40 erg s 1.Spin period p s = 1.37s, ṗ 10 10 s s 1 I NGC 7793 P13 (Israel et al., 2017). L x = 5 10 39 erg s 1. Spin period p s = 0.42s I NGC 5907 (Israel et al., 2016). L x 10 41 erg s 1.Spinperiod p s = 1.13s, ṗ 5 10 9 ss 1
M82 X2: Magnetic field I Standard magnetic field B 10 12 G: I Bachetti et al., 2014 I Lyutikov, 2014 I Low magnetic field B 10 9 G: I Kluzniak and Lasota, 2015 I High magnetic field B & 10 14 G: I Tsygankov et al., 2015
Irradiation from the column. Possible effects I Pressure gradient is important v r @v r @R v 2 R = 1 @P @R GM R 2 I Magnetospheric radius increases µ 2 R in = 2Ṁ p 2GM ns 2/7 µ = BR 3 ns/2 -dipolarmagneticmoment,if B is polar magnetic field at the NS surface (and no higher multipoles present) I Non-local Eddington limit when P rad = P mag.
Magnetospheric accretion: Theory Narrow boundary layer Magnetically-threaded disk: Stellar Wind Interface Alfven Surfaces Ω* Disk Wind IGhosh and Lamb 1979, Wang 1987, Kluzniak and Rappaport 2007 Accretion R * Rt Rco 15 R * Matt and Pudritz 2005, Scharlemann 1978, Anzer and Boerner 1980
Magnetospheric accretion: Simulations Open field lines Lovelace et al. 1995, Parfrey et al. 2016
Our approach (general picture) open lines NS closed lines accretion disc magnetosphere interaction region
Our approach (neglecting radial extention of the transition layer) open lines radiation NS closed lines accretion disc R in magnetosphere boundary
Boundary conditions I Excess angular momentum is removed by magnetic and radiation stresses radiation open lines Ṁ( in ns )R 2 µ 2 H in in = k t R 4 +L in in c 2 H inr in NS closed lines R in accretion disc magnetosphere boundary here k t = B B z I Pressure balance at the boundary P in = P mag + P rad and -prescription: W in r µ 2 H in = 2 8 R 6 in + LH in 4 R 2 in c
Scheme of solution No match Assume R in We got correct R in (to given precision) Match Compare! Calculate in, in,t in at the magnetospheric boundary Calculate the structure of the disc by solving the differential equation for (R) At the magnetospheric boundary find in, in,t in
Disc structure / K 1 10 0.4 0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 10 2 10 3 10 4 r H/R 10 1 10 2 10 3 10 4 r µ = 10 31 Gcm 3, ṁ = 500 Ṁ Edd, = 0.78 Our model, standard Shakura-Sunyaev s radiation pressure dominated and gas pressure dominated discs are shown.
Results. Magnetosheric radius 10 3 1.1 1.0 10 2 0.9 ṁ 10 1 10 0 10 1 10 0 10 1 10 2 µ, 10 30 Gcm 3 0.8 0.7 0.6 0.5 0.4 0.3 White lines correspond to (H/R) max = 0.03, 0.1 and 0.3.
Results. The influence of radiation. ( = 0.1) ( = 0) 10 3 10 2 0.300 0.100 0.042 ṁ 0.016 10 1 0.006 0.002 10 0 10 0 10 1 10 2 µ, 10 30 Gcm 3 0.000 is accretion efficiency
Results. ULXs M82 X2 Without irradiation ' 0.7 andb' 10 14 G. With irradiation ' 0.8 and B ' 7.4 10 13 G H HHHH 0.01 0.05 0.1 0.5 1 0 161 72 51 22 16 0.1 157 62 36 0.2 153 52 10 Table: Magnetic moments µ in units 10 30 Gcm 3 for different values of and. All the calculations were made for ṁ = 500 (L = 10 40 erg s 1 )and p s = 1.37 s, aimed to reproduce the properties of ULX-pulsar M82 X-2. NGC 7793 P13 Without irradiation ' 0.7 andb' 1.4 10 13 G. With irradiation ' 0.7 andb' 1.7 10 13 G
Conclusions I = R in R A accretion rate is not constant. It depends on magnetic field and I is tightly related to inner disc thickness H in /R in and reaches about 1 when H in /R in! 1 I It is important to take into account irradiation by the column when the inner disc becomes thick I irradiation can strongly alter the flows in the magnetosphere I In radiation-pressure-dominated disc R in / 2/9 µ 4/9 30 is independent of Ṁ
Approximations of Boundary condition: Ṁ( in ns )R 2 µ 2 H 2 m in = k t R 4 +L in in c 2 H inr in Gas pressure dominated disc: In dimensionless form: r 3/2 in! in = 2 k tµ 2 30 h in 1 h in /r in ṁr 6 + p in p s Assume! in = 1andlargep s.we have: 1,B (µ 2 30) 2/483 ṁ 26/483 2/69 Radiation pressure dominated disc: 2/9 73 1,A = 2 1/7 ṁ 2/7 24 ( µ 2 30 )4/63 µ 1 = 2 1/7 (2k t ) 2/9 2 4/63 30 h 2/9 in ṁ
Approximasions of 1.2 Gas pressure dominated disc: 1.0 1,B (µ 2 30) 2/483 ṁ 26/483 2/69 Radiation pressure dominated disc: 2/9 73 1,A = 2 1/7 ṁ 2/7 0.2 24 ( µ 2 30 )4/63 0.0 10 2 10 1 100 It is interesting that for radiation dominated disc 2/9 73 r in = 1,A r A = ( µ 2 30 24 )2/9 is independent of ṁ x 0.8 0.6 0.4 (H/R) in
Eddington limits Non-local Eddington limit: P r P mag = L µ 2 4 R 2 in c 8 R 6 in = 2 4/7 µ 2 1/7 30 4 ṁ 8/9 P r 73 = ṁ µ 2 30 P mag 24 1/9 8/9µ 2/9 ' 0.5 30 ṁ 0.1 0.1 ṁ 1 = 1 Local Eddington limit: ṁ 2 ' 4 3 p 1 5 8/9 24 ( µ 2 73 30) 1/9 ' 430 0.1 8/9 0.1 µ 2/9 30 1 2/9 1 73 2/9 p ( µ 2 30) 2/9 4/9 ' 350 µ 30 2 24 0.1