J/A+A/700/A70 4U 1538-52 cyclotron lines variability (Maniadakis+, 2025)
How the spin-phase variability of cyclotron lines shapes the pulsed fraction
spectra: Insights from 4U 1538-52.
Maniadakis D.K., Sokolova-Lapa E., D'Ai A., Ambrosi E., Ferrigno C.,
Cusumano G., Anitra A., Burderi L., Del Santo M., Di Salvo T., Fuerst F.,
Iaria R., La Parola V., Malacaria C., Kretschmar P., Pintore F., Pinto C.,
Rodriguez Castillo G.A.
<Astron. Astrophys. 700, A70 (2025)>
=2025A&A...700A..70M 2025A&A...700A..70M (SIMBAD/NED BibCode)
ADC_Keywords: Binaries, X-ray ; Spectroscopy
Keywords: stars: neutron - X-rays: binaries - X-ray: individuals 4U 1538-52
Abstract:
We aim to study the energy-dependent pulse profile of the X-ray
accreting pulsar 4U 1538-52 and its phase-dependent spectral
variability, with particular emphasis on the behavior around the
cyclotron resonant scattering feature at Ecyc∼21keV.
We analyze all available NuSTAR observations of 4U 1538-52. We
decompose energy-resolved pulse profiles into Fourier harmonics to
study their energy dependence. Specifically, we compute pulsed
fraction spectra, cross-correlation, and lag spectra, identifying
discontinuities and linking them to features in the phase-averaged
spectra. We perform both phase-averaged and phase- resolved spectral
analyses to probe spectral variability and its relation to pulse
profile changes. Finally, we interpret our findings via physical
modeling of energy- and angle-dependent pulse profile emission,
performing radiative transfer in a homogeneous slab-like atmosphere
under conditions relevant to 4U 1538-52. The emission is projected
onto the observer's sky plane to derive expected observables.
In contrast to the dips in pulsed fraction spectra observed in other
sources (e.g., Her X-1), we find a broad bump near the cyclotron
resonance energy in 4U 1538-52. This increase is driven primarily by
phase-dependent spectral variability, especially by strong variations
in cyclotron line depth across different phase intervals. We interpret
the observed contrast between dips and bumps in various sources as
arising from phase-dependent variations of cyclotron line depth
relative to the phase-modulated flux. We model the X-ray emission from
an accreting neutron star and find that our simulations indicate high
values of both the observer's inclination and the magnetic
obliquity, along with a ∼10-15° asymmetry between the locations
of the magnetic poles. Assuming this geometry, we satisfactorily
reproduce the observed pulse profiles and introduce general trends in
the observables resulting from the system's geometry.
Description:
This dataset contains observations and modeling results of the X-ray
pulsar 4U 1538-52, as presented in the paper. The observations were
taken with NuSTAR.
Table 1 provides the log of observations including exposure time,
count statistics, flux, luminosity, and timing reference values.
Table 2 presents the best-fit parameters from modeling the pulsed
fraction spectra (PFS), including fits to broad cyclotron-like bumps,
Fe emission/absorption lines (where present), polynomial model orders,
and goodness-of-fit statistics.
The repertories contain OGIP-compliant FITS files supporting the
spectral and timing analysis presented in the paper. It includes:
- Phase-averaged and phase-resolved spectra for NuSTAR ObsIDs 304 and 3062
- Energy-phase matrices in 32 phase bins for ObsIDs 302, 304, 3062, and 3064
- Background, RMF, and ARF files
Objects:
----------------------------------------------------------------
RA (2000) DE Designation(s)
----------------------------------------------------------------
15 42 23.36 -52 23 09.5 4U 1538-52 = 1RXS J154222.8-522311
----------------------------------------------------------------
File Summary:
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FileName Lrecl Records Explanations
--------------------------------------------------------------------------------
ReadMe 80 . This file
table1.dat 44 4 Observation log
table2.dat 101 4 Best-fit PFS modeling parameters
table3.dat 196 2 Phase-averaged spectral fit (NuSTAR/XMM)
tablec1.dat 190 8 Phase-resolved spectroscopy of ObsID 304
tablec2.dat 202 8 Phase-resolved spectroscopy of ObsID 306-2
list.dat 123 72 List of files
302/* . 4 Files for NuSTAR ObsIDs 302
304/* . 34 Files for NuSTAR ObsIDs 304
3062/* . 34 Files for NuSTAR ObsIDs 3062
3064/* . 4 Files for NuSTAR ObsIDs 3064
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Byte-by-byte Description of file: table1.dat
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Bytes Format Units Label Explanations
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1- 5 A5 --- ObsID Observation ID
7- 11 F5.2 ks Exp Exposure time
13- 16 F4.1 10+4ct Cts Total number of counts in units of 1E+04 counts
18- 20 F3.1 10-13W/m2 Flux Absorbed 4-50 keV flux in 10-10erg/cm2/s
22- 24 F3.1 10+36Lsun Lum Bolometric luminosity (assumed D = 6.6 kpc)
26- 30 F5.3 mHz Freq Pulse frequency
32- 44 F13.3 s Tref Reference time since 2010-01-01 UTC
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Byte-by-byte Description of file: table2.dat
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Bytes Format Units Label Explanations
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1- 5 A5 --- ObsID Observation ID
7- 11 F5.2 keV Ebump Energy of broad bump
13- 16 F4.2 keV e_Ebump 1-sigma uncertainty on Ebump
18- 21 F4.2 keV Sbump Sigma bump
23- 26 F4.2 keV e_Sbump Uncertainty on Sbump
28- 31 F4.2 --- Abump Amplitude of the bump
33- 36 F4.2 --- e_Abump 1-sigma uncertainty on Abump
38- 41 F4.2 keV EFe ?=- Iron line centroid (if present)
43- 46 F4.2 keV e_EFe ?=- 1-sigma uncertainty on EFe
48- 51 F4.2 keV SFe ?=- sigma of Fe line
53- 56 F4.2 keV e_SFe ?=- Uncertainty on sigma of Fe line
58- 63 F6.3 --- AFe ?=- Amplitude of Fe line
65- 69 F5.3 --- E_AFe ?=- Upper uncertainty on AFe
71- 75 F5.3 --- e_AFe ?=- Lower uncertainty on AFe
77- 81 F5.2 keV Esplit Energy at which polynomial split occurs
83 I1 --- npolLow Polynomial order below Esplit
85 I1 --- npolHigh Polynomial order above Esplit
87- 90 F4.2 --- chi2Low Reduced chi2 for low-energy band
92- 93 I2 --- dofLow Degrees of freedom (low band)
95- 98 F4.2 --- chi2High Reduced chi2 for high-energy band
100-101 I2 --- dofHigh Degrees of freedom (high band)
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Byte-by-byte Description of file: table3.dat
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Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 5 A5 --- ObsID Observation ID
7- 11 F5.2 keV Ecut Cutoff energy
13- 16 F4.2 keV e_Ecut Lower uncertainty on Ecut
18- 21 F4.2 keV E_Ecut Upper uncertainty on Ecut
23- 27 F5.2 keV Efold Folding energy
29- 32 F4.2 keV e_Efold Lower uncertainty on Efold
34- 37 F4.2 keV E_Efold Upper uncertainty on Efold
39- 43 F5.3 --- Gamma Power-law photon index
45- 49 F5.3 --- e_Gamma Lower uncertainty on Gamma
51- 55 F5.3 --- E_Gamma Upper uncertainty on Gamma
57- 62 F6.4 --- Nnewhcut Normalization of the cutoff model
64- 69 F6.4 --- e_Nnewhcut Lower uncertainty on Nnewhcut
71- 76 F6.4 --- E_Nnewhcut Upper uncertainty on Nnewhcut
78- 80 F3.1 10-4 Nbbody Blackbody normalization (in units of 1E-04)
82- 84 F3.1 10-4 e_Nbbody Lower uncertainty on Nbbody
86- 88 F3.1 10-4 E_Nbbody Upper uncertainty on Nbbody
90- 94 F5.2 keV Ecyc Cyclotron line energy
96- 99 F4.2 keV e_Ecyc Lower uncertainty on Ecyc
101-104 F4.2 keV E_Ecyc Upper uncertainty on Ecyc
106-109 F4.2 keV Scyc Width of cyclotron line
111-114 F4.2 keV e_Scyc Lower uncertainty on Scyc
116-119 F4.2 keV E_Scyc Upper uncertainty on Scyc
121-125 F5.3 --- Dcyc Depth of cyclotron absorption
127-131 F5.3 --- e_Dcyc Lower uncertainty on Dcyc
133-137 F5.3 --- E_Dcyc Upper uncertainty on Dcyc
139-142 F4.2 keV SFe Fe line width
144-147 F4.2 keV e_SFe Lower uncertainty on SFe
149-152 F4.2 keV E_SFe Upper uncertainty on SFe
154-156 F3.1 10-4 AFe Fe line amplitude (in units of 1E-04)
158-160 F3.1 10-4 e_AFe Lower uncertainty on AFe
162-164 F3.1 10-4 E_AFe Upper uncertainty on AFe
166-170 F5.3 --- Cfpmb Cross-normalization FPMB
172-176 F5.3 --- e_Cfpmb Lower uncertainty on Cfpmb
178-182 F5.3 --- E_Cfpmb Upper uncertainty on Cfpmb
184-186 F3.1 10-10 Flux Absorbed 4-50 keV flux
188-192 F5.3 --- Wstat W-statistic
194-196 I3 --- dof Degrees of freedom
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Byte-by-byte Description of file: tablec1.dat
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Bytes Format Units Label Explanations
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1- 11 A11 --- Phase Spin phase bin
13- 16 F4.1 keV Ecut Cutoff energy
18- 20 F3.1 keV e_Ecut Lower uncertainty on Ecut
22- 24 F3.1 keV E_Ecut Upper uncertainty on Ecut
26- 30 F5.2 keV Efold Folding energy
32- 35 F4.2 keV e_Efold Lower uncertainty on Efold
37- 40 F4.2 keV E_Efold Upper uncertainty on Efold
42- 45 F4.2 --- Gamma Photon index
47- 50 F4.2 --- e_Gamma Lower uncertainty on Gamma
52- 55 F4.2 --- E_Gamma Upper uncertainty on Gamma
57- 62 F6.4 --- Nnewhcut Normalization of the cutoff model
64- 69 F6.4 --- e_Nnewhcut Lower uncertainty on Nnewhcut
71- 76 F6.4 --- E_Nnewhcut Upper uncertainty on Nnewhcut
78- 81 F4.1 10-4 Nbbody Blackbody normalization (in units of 1E-04)
83- 85 F3.1 10-4 e_Nbbody Lower uncertainty on Nbbody
87- 89 F3.1 10-4 E_Nbbody Upper uncertainty on Nbbody
91- 95 F5.2 keV Ecyc Cyclotron line energy
97-100 F4.2 keV e_Ecyc Lower uncertainty on Ecyc
102-105 F4.2 keV E_Ecyc Upper uncertainty on Ecyc
107-110 F4.2 keV Scyc ?=- Width of cyclotron line (if fit)
112-115 F4.2 keV e_Scyc ?=- Lower uncertainty on Scyc
117-120 F4.2 keV E_Scyc ?=- Upper uncertainty on Scyc
122-125 F4.2 --- Dcyc Cyclotron line depth
127-130 F4.2 --- e_Dcyc Lower uncertainty on Dcyc
132-135 F4.2 --- E_Dcyc Upper uncertainty on Dcyc
137-140 F4.2 keV SFe Fe line width (if fit)
142-145 F4.2 keV e_SFe Lower uncertainty on SFe
147-150 F4.2 keV E_SFe Upper uncertainty on SFe
152-154 F3.1 10-4 AFe Fe line amplitude (in units of 1E-04)
156-158 F3.1 10-4 e_AFe Lower uncertainty on AFe
160-162 F3.1 10-4 E_AFe Upper uncertainty on AFe
164-168 F5.3 --- Cfpmb FPMB cross-normalization
170-174 F5.3 --- e_Cfpmb Lower uncertainty on Cfpmb
176-180 F5.3 --- E_Cfpmb Upper uncertainty on Cfpmb
182-186 F5.3 --- Wstat W-statistic from fit
188-190 I3 --- dof Degrees of freedom
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Byte-by-byte Description of file: tablec2.dat
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Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 11 A11 --- Phase Spin phase bin
13- 16 F4.1 keV Ecut Cutoff energy
18- 20 F3.1 keV e_Ecut Lower uncertainty on Ecut
22- 24 F3.1 keV E_Ecut Upper uncertainty on Ecut
26- 30 F5.2 keV Efold Folding energy
32- 35 F4.2 keV e_Efold Lower uncertainty on Efold
37- 40 F4.2 keV E_Efold Upper uncertainty on Efold
42- 46 F5.3 --- Gamma Photon index
48- 52 F5.3 --- e_Gamma Lower uncertainty on Gamma
54- 58 F5.3 --- E_Gamma Upper uncertainty on Gamma
60- 65 F6.4 --- Nnewhcut Normalization of the cutoff model
67- 72 F6.4 --- e_Nnewhcut Lower uncertainty on Nnewhcut
74- 79 F6.4 --- E_Nnewhcut Upper uncertainty on Nnewhcut
81- 86 F6.3 10-4 Nbbody ?=- Blackbody normalization (in units of 1E-04)
88- 92 F5.3 10-4 e_Nbbody ?=- Lower uncertainty on Nbbody
94- 98 F5.3 10-4 E_Nbbody ?=- Upper uncertainty on Nbbody
100-104 F5.2 keV Ecyc Cyclotron line energy
106-109 F4.2 keV e_Ecyc Lower uncertainty on Ecyc
111-114 F4.2 keV E_Ecyc Upper uncertainty on Ecyc
116-119 F4.2 keV Scyc ?=- Width of cyclotron line (if fit)
121-124 F4.2 keV e_Scyc ?=- Lower uncertainty on Scyc
126-129 F4.2 keV E_Scyc ?=- Upper uncertainty on Scyc
131-134 F4.2 --- Tau Optical depth (CompTT)
136-139 F4.2 --- e_Tau Lower uncertainty on Tau
141-144 F4.2 --- E_Tau Upper uncertainty on Tau
146-149 F4.2 keV SFe Fe line width
151-155 F5.3 keV e_SFe Lower uncertainty on SFe
157-161 F5.3 keV E_SFe Upper uncertainty on SFe
163-166 F4.1 10-4 AFe Fe line amplitude (in units of 1E-04)
168-170 F3.1 10-4 e_AFe ?=- Lower uncertainty on AFe
172-174 F3.1 10-4 E_AFe ?=- Upper uncertainty on AFe
176-180 F5.3 --- Cfpmb FPMB cross-normalization
182-186 F5.3 --- e_Cfpmb Lower uncertainty on Cfpmb
188-192 F5.3 --- E_Cfpmb Upper uncertainty on Cfpmb
194-198 F5.3 --- Wstat W-statistic from fit
200-202 I3 --- dof Degrees of freedom
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Byte-by-byte Description of file: list.dat
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Bytes Format Units Label Explanations
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1- 33 A33 --- FileName Name of the file
35-123 A89 --- Title Title of the file
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Acknowledgements:
Dimitrios Maniadakis, dimitrios.maniadakis(at)inaf.it
(End) Patricia Vannier [CDS] 24-Jun-2025