The appearance of non-spherical systems. Application to LMXB nska 1 Agata R´ o˙ za´ ldycki 1 , Jerzy Madej 2 , Tek P. Adhikari 1 , Bei You 1 Bartosz Be� 1 N. Copernicus Astronomical Center PAS, 2 Warsaw University Observatory Staszic Palace, 31.03.2017, Warsaw, Poland Agata R´ o˙ za´ nska NewCompStar 2017 1 / 15
Jerzy Madej 1 Professor at the University of Warsaw Agata R´ o˙ za´ nska NewCompStar 2017 2 / 15
Jerzy Madej 1 Professor at the University of Warsaw 2 1983 awarded by Ministry of Science for the best PhD Agata R´ o˙ za´ nska NewCompStar 2017 2 / 15
Jerzy Madej 1 Professor at the University of Warsaw 2 1983 awarded by Ministry of Science for the best PhD 3 MIT, USA, postdoc 1 year Agata R´ o˙ za´ nska NewCompStar 2017 2 / 15
Jerzy Madej 1 Professor at the University of Warsaw 2 1983 awarded by Ministry of Science for the best PhD 3 MIT, USA, postdoc 1 year 4 CITA, University of Toronto, postdoc 1 year Agata R´ o˙ za´ nska NewCompStar 2017 2 / 15
Radiative transfer equation Radiation through a foggy atmosphere , A. Schuster, 1905, ApJ, 21, 1. Agata R´ o˙ za´ nska NewCompStar 2017 3 / 15
Radiative transfer equation Radiation through a foggy atmosphere , A. Schuster, 1905, ApJ, 21, 1. Agata R´ o˙ za´ nska NewCompStar 2017 3 / 15
Radiative transfer equation µ dI ν j ν = I ν − = I ν − S ν κ ν + σ ν d τ ν Emission coefficient j ν is the sum of three terms, j ν = j th ν + j sc ν + j fl ν . Agata R´ o˙ za´ nska NewCompStar 2017 4 / 15
Radiative transfer equation µ dI ν j ν = I ν − = I ν − S ν κ ν + σ ν d τ ν Emission coefficient j ν is the sum of three terms, j ν = j th ν + j sc ν + j fl ν . Requires iteration with gas(X,Y,Z) structure due to equilibrium equations: Hydrostatic equil. = > dP dz Agata R´ o˙ za´ nska NewCompStar 2017 4 / 15
Radiative transfer equation µ dI ν j ν = I ν − = I ν − S ν κ ν + σ ν d τ ν Emission coefficient j ν is the sum of three terms, j ν = j th ν + j sc ν + j fl ν . Requires iteration with gas(X,Y,Z) structure due to equilibrium equations: Hydrostatic equil. = > dP dz Radiative equil. = > dT dz Agata R´ o˙ za´ nska NewCompStar 2017 4 / 15
Radiative transfer equation µ dI ν j ν = I ν − = I ν − S ν κ ν + σ ν d τ ν Emission coefficient j ν is the sum of three terms, j ν = j th ν + j sc ν + j fl ν . Requires iteration with gas(X,Y,Z) structure due to equilibrium equations: Hydrostatic equil. = > dP dz Radiative equil. = > dT dz EoS - usually ideal gas Agata R´ o˙ za´ nska NewCompStar 2017 4 / 15
Model atmosphere calculations - glossary of terms 1 Specific intensity I ν , which flows through one cm 2 on the surface of an emitter into a direction. It is an intrinsic property of the source in erg cm − 2 s − 1 Hz − 1 sr − 1 . Agata R´ o˙ za´ nska NewCompStar 2017 5 / 15
Model atmosphere calculations - glossary of terms 1 Specific intensity I ν , which flows through one cm 2 on the surface of an emitter into a direction. It is an intrinsic property of the source in erg cm − 2 s − 1 Hz − 1 sr − 1 . 2 Energy dependent flux is the average of I ν weighted by cos θ (zenithal angle). Integration is over full solid angle 4 π : � F ν = I ν d ω It is an intrinsic property of the source in erg cm − 2 s − 1 Hz − 1 . Agata R´ o˙ za´ nska NewCompStar 2017 5 / 15
Model atmosphere calculations - glossary of terms 1 Specific intensity I ν , which flows through one cm 2 on the surface of an emitter into a direction. It is an intrinsic property of the source in erg cm − 2 s − 1 Hz − 1 sr − 1 . 2 Energy dependent flux is the average of I ν weighted by cos θ (zenithal angle). Integration is over full solid angle 4 π : � F ν = I ν d ω It is an intrinsic property of the source in erg cm − 2 s − 1 Hz − 1 . 3 Infinitesimal energy d F ν can be measured by a distant observer in flat space, over infinitesimal part of full solid angle d F ν = I ν d ω, subtended by the area as seen by an observer. It is NOT an intrinsic property of the source in erg cm − 2 s − 1 Hz − 1 . Agata R´ o˙ za´ nska NewCompStar 2017 5 / 15
Spherically symmetric stars - ideal model of NS θ R NS r To Observer � 2 � 1 � 2 � R NS � R NS F ν, NS = 2 π I ν µ d µ = F ν D D 0 The observed intensity per detector area is proportional to the flux emitted locally from 1 cm 2 of the star’s surface, only due to the spherical shape of the emitting region. Mihalas 1976. Agata R´ o˙ za´ nska NewCompStar 2017 6 / 15
Axially symmetric accretion disk - Shakura & Sunyaev 1973 R out R θ ′ R in To Observer � R out I ν d ω = 2 π sin θ ′ � F ν, AD = I ν RdR , D 2 Ω R in Monochromatic intensity, I ν emitted in the specific direction is integrated over the disk surface from the inner to outer disk radii. Agata R´ o˙ za´ nska NewCompStar 2017 7 / 15
LMXB - neutron star with the accretion disk 4 Accretion disk Accretion disk R out H disk H disk Accretion disk Accretion disk R in = 3 R Schw Neutron star Neutron Star 2 M NS = 1 . 4 M ⊙ Ω θ ′ R NS = 12 km Obs. i line of sight R boost 1 θ ′ 5 � 2 �� 1 � 1 � R NS � F ν, All = π I ν µ d µ + I ν µ d µ D 0 cos θ ′ �� R NS � R NS sin θ ′ � 2 I ν sin θ ′ � � NS sin 2 θ ′ − x 2 dx NS − x 2 dx − R 2 R 2 + I ν D 2 0 0 �� R out � R out � π sin θ ′ + I ν RdR + I ν RdR , D 2 R in R boost Agata R´ o˙ za´ nska NewCompStar 2017 8 / 15
LMXB at different viewing angles θ ′ =50 ◦ θ ′ =90 ◦ F ν, NS θ ′ =70 ◦ θ ′ =10 ◦ θ ′ =30 ◦ θ ′ =90 ◦ 10 1 10 1 θ ′ =30 ◦ θ ′ =10 ◦ 10 0 10 0 10 -1 m =0 . 0008 , T eff , NS =4 . 0 × 10 6 K ˙ 10 -1 m =0 . 001 , T eff , NS =1 . 6 × 10 7 K m =0 . 05 , T eff , NS =1 . 6 × 10 7 K ˙ ˙ 10 -2 θ ′ =50 ◦ θ ′ =90 ◦ F ν, NS 10 2 E*Ph E [keV s − 1 cm − 2 keV − 1 ] E*Ph E [keV s − 1 cm − 2 keV − 1 ] 10 2 θ ′ =70 ◦ θ ′ =10 ◦ θ ′ =30 ◦ θ ′ =90 ◦ θ ′ =30 ◦ θ ′ =10 ◦ 10 1 10 1 10 0 10 -1 m =0 . 003 , T eff , NS =6 . 3 × 10 6 K 10 0 ˙ m =0 . 2 , T eff , NS =2 . 5 × 10 7 K m =0 . 02 , T eff , NS =2 . 5 × 10 7 K ˙ ˙ 10 -2 10 3 10 3 θ ′ =90 ◦ θ ′ =50 ◦ F ν, NS θ ′ =30 ◦ θ ′ =70 ◦ θ ′ =10 ◦ θ ′ =90 ◦ θ ′ =10 ◦ θ ′ =30 ◦ 10 2 10 2 10 1 10 0 m =0 . 01 , T eff , NS =1 . 0 × 10 7 K ˙ 10 1 m =0 . 8 , T eff , NS =4 . 0 × 10 7 K m =0 . 4 , T eff , NS =4 . 0 × 10 7 K 10 -1 ˙ ˙ 10 -2 10 -1 10 0 10 1 10 -2 10 -1 10 0 10 1 E [keV] E [keV] Agata R´ o˙ za´ nska NewCompStar 2017 9 / 15
X-ray observations of XTE J1709-267 by XMM-Newton XTE J1709-267 MOS unfolde d da ta T ota l Mode l 10 -3 Powe rla w LMXB Absorbe d LMXB E*Ph E [keV s − 1 cm − 2 keV − 1 ] Absorbe d powe rla w 10 -4 10 -5 10 -6 10 -3 10 -2 10 -1 10 0 10 1 Ene rgy [ke V] Agata R´ o˙ za´ nska NewCompStar 2017 10 / 15
X-ray observations of XTE J1709-267 by XMM-Newton Parameters from the fitting of XTEJ1709-267 XMM-Newton MOS1 data. The reduced χ 2 of the fit is equal 1.32 Model Parameter Value Error 2 . 67 × 10 21 cm − 2 tbabs N H ± 0 . 22 6 . 335 × 10 6 K ± 0 . 105 × 10 6 lmxb T eff , NS lmxb m ˙ 0.0104 ˙ m Edd ± 0 . 0019 θ ′ 70 . 6 ◦ – lmxb 5 . 33 × 10 − 5 ± 0 . 27 × 10 − 5 lmxb Norm. Γ 0.36 – powerlaw 1 . 79 × 10 − 5 powerlaw Norm. – Agata R´ o˙ za´ nska NewCompStar 2017 11 / 15
X-ray observations of XTE J1709-267 by XMM-Newton Parameters from the fitting of XTEJ1709-267 XMM-Newton MOS1 data. The reduced χ 2 of the fit is equal 1.32 Model Parameter Value Error 2 . 67 × 10 21 cm − 2 tbabs N H ± 0 . 22 6 . 335 × 10 6 K ± 0 . 105 × 10 6 lmxb T eff , NS lmxb m ˙ 0.0104 ˙ m Edd ± 0 . 0019 θ ′ 70 . 6 ◦ – lmxb 5 . 33 × 10 − 5 ± 0 . 27 × 10 − 5 lmxb Norm. Γ 0.36 – powerlaw 1 . 79 × 10 − 5 powerlaw Norm. – Our fit is consistent with the BB fit by Degenaar et al. (2013). We obtained 3.5 times hotter star, but the warm absorption column is by 0.2 smaller. Agata R´ o˙ za´ nska NewCompStar 2017 11 / 15
Summary 1 Overall continuum shape from non-spherical LMXB shows two peaks. The lower energy peak is caused by the accretion disk emission, whereas higher energy bump is due to the neutron star. Published in Acta Astronomica 2017, vol. 67 Agata R´ o˙ za´ nska NewCompStar 2017 12 / 15
Summary 1 Overall continuum shape from non-spherical LMXB shows two peaks. The lower energy peak is caused by the accretion disk emission, whereas higher energy bump is due to the neutron star. Published in Acta Astronomica 2017, vol. 67 2 X-ray binaries: Zhang et al. 2000, GRS 19151+105 Agata R´ o˙ za´ nska NewCompStar 2017 12 / 15
Summary 1 Overall continuum shape from non-spherical LMXB shows two peaks. The lower energy peak is caused by the accretion disk emission, whereas higher energy bump is due to the neutron star. Published in Acta Astronomica 2017, vol. 67 2 X-ray binaries: Kolehmainer et al. 2011, GX 339-4 Agata R´ o˙ za´ nska NewCompStar 2017 13 / 15
Summary 1 Seyfert galaxies: Jin et al. 2012, J112328+052823, PG 1415+451 Agata R´ o˙ za´ nska NewCompStar 2017 14 / 15
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