1. Pulse Profile Decomposition: Geometry and Beam Patterns of EXO 2030+375 and 4U 0115+63
Manami Sasaki
Ute Kraus, Isabel Caballero, Dmitry Klochkov, Carlo Ferrigno, Andrea Santangelo
2/23/2019
Manami Sasaki

2. Outline Pulse Profile Decomposition Method EXO 2030+375 4U 0115+63
Beam Patterns, Models for Pulse Formation
2/23/2019
Manami Sasaki

3. Pulse Profile Decomposition Method
Developed by Ute Kraus and applied to Her X-1 and Cen X-3.
Possible explanation for asymmetric observed pulse profiles is a distorted magnetic dipole field in which the two magnetic poles are not located opposite to each other.
Assumption: two symmetric and identical emission regions. Asymmetry in geometry results in asymmetric total pulse profile.
Fits the pulse profiles with a sum of symmetric functions by Fourier analysis and get two symmetric functions that together describes the observed total pulse profiles.
2/23/2019
Manami Sasaki

4. Assumed Geometry of the Neutron Star
Two magnetic poles, the magnetic axes most likely do not coincide with the rotation axis.
Polar angles of the magnetic poles: 1, 2.
Symmetry points 1, 2 in the pulse profile corresponds to the rotation angles of the two poles.
Angle  between the first magnetic pole and the line of sight also changes with .
2/23/2019
Manami Sasaki

5. Assumed Geometry of the Neutron Star
The second magnetic pole is not located on the axis through the first magnetic pole and the center of the neutron star. Instead, it has an offset of .
For the phase it causes a shift  between the symmetry points of the emission:
 =  - (1 - 2).
2/23/2019
Manami Sasaki

6. Run the Decomposition
1, 2, (or 1, ), and the inclination angle between the rotation axis and the line of sight are a complete set of angles to define the geometry of the neutron star.
Search for good (1, ) values.
Criteria for good decompositions:
Since the functions describe the flux of emitting regions they have to be positive.
There should be no small scale structures in the pulse profiles that cancel out in the sum.
Values for (1,) must be consistent for all energy bands and observations.
2/23/2019
Manami Sasaki

7. Giant Outburst of EXO 2030+375 in 2006
RXTE
RXTE
INTEGRAL
INTEGRAL
2/23/2019
Manami Sasaki

8. Observed Total Pulse Profiles of EXO2030+375
Before maximum
(RXTE)‏
After maximum
(RXTE)‏
End of decay
(INTEGRAL)‏
Maximum (INTEGRAL)‏
2/23/2019
Manami Sasaki

9. Accepted 1-
2/23/2019
Manami Sasaki

10. Accepted 1-
2/23/2019
Manami Sasaki

11. Decompositions
INTEGRAL - maximum
2/23/2019
Manami Sasaki

12. Reconstruction of Beam Patterns
Two beam patterns are obtained from the decomposition for each pair of single pole pulse profiles.
During one revolution of the neutron star, there may be a range of the viewing angle  in which the observer sees emission from both emission regions.
If, in addition, the two emission regions on the neutron star have the same beam pattern, the emission that one sees at  from one pole is the same emission as what one sees at ' from the other pole.
This means that the visible beam patterns of the two poles must partly overlap. If we find such an overlap of the beam patterns of the two single pole pulse profiles we can overlay them.
2/23/2019
Manami Sasaki

13. Beam patterns of EXO
2/23/2019
Manami Sasaki

14. Possible Geometry of EXO 2030+375
2/23/2019
Manami Sasaki

15. Asymptotic Beam Patterns of EXO 2030+375
2/23/2019
Manami Sasaki

16. Giant Outburst of 4U in 1999
Beppo SAX
2/23/2019
Manami Sasaki

17. Observed Total Pulse Profiles of 4U 0115+63
Before maximum
After maximum
2/23/2019
Manami Sasaki

18. Decompositions
After maximum
2/23/2019
Manami Sasaki

19. Beam Patterns of 4U
2/23/2019
Manami Sasaki

20. Possible Geometry of 4U 0115+63
2/23/2019
Manami Sasaki

21. Asymptotic Beam Patterns of 4U 0115+63
2/23/2019
Manami Sasaki

22. Kraus 2001: Thin Hollow Column
Beam patterns for thin hollow column, assumed  = i = 0.1.
rn/rS = , 3.3, 2.5, 2.2, 2.1, and 2.
Upper panel: absolute values.
Lower panel: normalized to show the shape more clearly.
Combined emission from the inner and the outer column wall causes two maxima.
2/23/2019
Manami Sasaki

23. Kraus et al. 2003: Halo + Column
Assuming isotropic emission from the column.
Top: compact neutron star rn/rS = 2.
Bottom: less compact rn/rS = 2.4
Photon energies = 1, 5, 10, and 20 keV.
Kraus et al., in prep.: if scattering in the upper accretion stream is included, accretion column emission is significant only up to ~160°, steep increase of flux from the upper stream for > 160° for > 20 or 30 keV.
2/23/2019
Manami Sasaki

24. Comparison to Beam Patterns
EXO 4U
2/23/2019
Manami Sasaki

25. Solution for EXO
No overlap between the beam patterns of the two emission regions.
1 = 40°, 2 = 140°,  = 40° for O = 50°.
The main peak at phase = 0.2 is cased by the 'anti-pencil' from the upper accretion stream when the pole is on the back + halo emission from the pole which is facing to us.
Sharp minima when the accretion columns are seen from the side.
2/23/2019
Manami Sasaki

26. Solution for 4U
Overlap between the beam patterns of the two emission regions.
1 = 30°, 2 =100°,  = 60° for O = 60°.
At lower energies, halo emission dominates at phase = 0.3 – 0.7. This component is stronger in the data before (near) maximum (consistent w/ Ferrigno et al. 2009).
Additional emission from the accretion column causes increase in flux (at phase = 0.2, 0.8).
At higher energies, significant emission from the upper accretion stream around phase = 0.2 – 0.5.
Additional small minima and maxima in beam patterns. Hollow column?
2/23/2019
Manami Sasaki

27. Conclusions EXO 2030+375: no overlap for the beam patterns.
4U : beam patterns overlaid.
Slightly distorted magnetic field in both systems.
Strong evidences for halo emission (< 10 keV) and scattering in the upper accretion stream (> 30 keV).
Indications for hollow column or other complicated geometries.
More detailed analysis of < 10 keV band might be interesting!
To pin down the values for the polar angles of the magnetic poles 1, 2, and thus the exact geometry, an independent measurement of the angle between the rotation axis of the neutron star and the line of sight is still necessary.
2/23/2019
Manami Sasaki