A simple relation: Neutron star magnetic field strength and spectral shape at low mass accretion rates

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Table B.1.

Overview of observations and spectral models utilized in this work. Upper part of the table: source and observation information. Lower part of the table: parameters of doublehump spectral fits shown in Fig. 2.

	X Per	GRO J1008−57	IGR J21347+4737	2SXPS	GX 304−1
				J075542.5−293353
Distance [kpc](a)	0.600 ± 0.014	$3 . 52_{- 0.16}^{+ 0.17}$ $Mathematical equation: $ 3.52^{+0.17}_{-0.16} $$	$8 . 5_{- 0.8}^{+ 1.1}$ $Mathematical equation: $ 8.5^{+1.1}_{-0.8} $$	$3 . 29_{- 0.14}^{+ 0.12}$ $Mathematical equation: $ 3.29^{+0.12}_{-0.14} $$	$1 . 85_{- 0.05}^{+ 0.06}$ $Mathematical equation: $ 1.85^{+0.06}_{-0.05} $$
P_orb [d]	250.3 ± 0.6 / De01	249.48 ± 0.04 / Ku13	∼34.3 / Go22	∼260 / Do21	132.189 ± 0.02 / Su15
P_pulse [s]	833.5 ± 0.2 / Ra25	≂93.2 / Lu21	322.738 ± 0.018 / Gh23	308.26 ± 0.02 / Do21	274.9817 ± 0.0001 / Ma15
NuSTAR OBS ID	30401033002	90501357002	90601339002	80102103002	30701015002
				90601322001
NuSTAR date	2019-01-01	2020-01-01	2020-12-17	2016-03-26	2022-01-29
				2020-07-19
Joint with	–	Swift	XMM(b)	Chandra	XMM(c)
NuSTAR exp. [ks] / PI	58.3 / M. Wolff	45.2 / A. Lutovinov (TOO)	27.1 / S. Pike (TOO)	54.7 / V. Kaspi	174.0 / E. Sokolova-Lapa
				49.8 / G. Younes

C_FPMB	0.980 ± 0.003	1.02 ± 0.04	1.02 ± 0.03	1.01 ± 0.03	1.04 ± 0.02
C_{XRT/EPN/FPMA2}	–	0.8 ± 0.3	$0 . 213_{- 0.006}^{+ 0.007}$ $Mathematical equation: $ 0.213^{+0.007}_{-0.006} $$	0.88 ± 0.03	0.84 ± 0.04
C_EMOS1/FPMB2	–	–	0.180 ± 0.007	0.90 ± 0.03	0.72 ± 0.04
C_EMOS2/ACIS	–	–	0.206 ± 0.008	0.24 ± 0.02	0.85 ± 0.04
N_H [10²² cm⁻²]	3.3 ± 0.4	3 ± 2	0.48 ± 0.09	0.8 ± 0.3	1.7 ± 0.3
N_cutoffpl[×10⁻³]	180 ± 9	$2 . 2_{- 0.7}^{+ 1.0}$ $Mathematical equation: $ 2.2^{+1.0}_{-0.7} $$	$0 . 77_{- 0.07}^{+ 0.08}$ $Mathematical equation: $ 0.77^{+0.08}_{-0.07} $$	0.8 ± 0.2	$1 . 8_{- 0.3}^{+ 0.4}$ $Mathematical equation: $ 1.8^{+0.4}_{-0.3} $$
Γ₁	1.43 ± 0.04	1.4 ± 0.4	−0.3 ± 0.2	0.2 ± 0.3	0.1 ± 0.2
E_fold, 1 [keV]	10.1 ± 0.5	$9_{- 3}^{+ 5}$ $Mathematical equation: $ 9^{+5}_{-3} $$	$3 . 4_{- 0.4}^{+ 0.5}$ $Mathematical equation: $ 3.4^{+0.5}_{-0.4} $$	3.0 ± 0.4	2.2 ± 0.2
E_fold, 2 [keV]	15.2 ± 0.6	$(3_{- 2}^{+ 7}) \times 10^{1}$ $Mathematical equation: $ \left(3^{+7}_{-2}\right)\times10^{1} $$	$6 . 3_{- 0.5}^{+ 0.6}$ $Mathematical equation: $ 6.3^{+0.6}_{-0.5} $$	8.7 ± 0.6	7.2 ± 0.5
E_int [keV]	$28 . 1_{- 0.6}^{+ 0.7}$ $Mathematical equation: $ 28.1^{+0.7}_{-0.6} $$	25 ± 5	14 ± 2	13.2 ± 0.6	12.8 ± 0.4

ℒ [10³⁴ erg s⁻¹] (d)	3.23	0.96	6.48	0.38	0.24
χ²/d.o.f.	671/522	195/181	261/213	222/189	280/258
χ_red²	1.29	1.08	1.23	1.18	1.08

Δχ_cutoffpl²	2764	35	163	285	667
	SRGA J124404.1-632232	MAXI 0655−013	A0535+26	Cep X-4
Distance [kpc](a)	$5 . 8_{- 0.0}^{+ 0.8}$ $Mathematical equation: $ 5.8^{+0.8}_{-0.0} $$	$3 . 44_{- 0.21}^{+ 0.26}$ $Mathematical equation: $ 3.44^{+0.26}_{-0.21} $$	$1 . 77_{- 0.06}^{+ 0.07}$ $Mathematical equation: $ 1.77^{+0.07}_{-0.06} $$	$7 . 2_{- 0.7}^{+ 0.8}$ $Mathematical equation: $ 7.2^{+0.8}_{-0.7} $$
P_orb [d]	138 ± 1 / Mr21	27.9 ± 1.7 / Ra23	110.3 ± 0.3 / Fi94	20.85 / Mc07
P_pulse [s]	538.70 ± 0.05 / Do22	1129.09 ± 0.04 / Pi23	103.3890 ± 0.0009 / Ba17	66.3336 ± 0.0002 / Vy17
NuSTAR OBS ID	80660301002	31001020002	90401370001	90901322002
NuSTAR date	2021-01-30	2024-10-02	2018-12-26	2023-07-07
Joint with	NICER	XMM-Newton	Swift	Swift
NuSTAR exp. [ks] / PI	54.0 / V. Doroshenko (TOO)	84.1 / C. Malacaria	54.9 / S. Tsygankov (TOO)	26.5 / R. Ballhausen (TOO)
C_FPMB	1.02 ± 0.04	1.05 ± 0.04	0.97 ± 0.02	1.01 ± 0.04
C_XTI/EPN/XRT	$1 . 02_{- 0.09}^{+ 0.10}$ $Mathematical equation: $ 1.02^{+0.10}_{-0.09} $$	0.76 ± 0.04	0.8 ± 0.2	0.6 ± 0.3
C_EMOS1	–	$0 . 67_{- 0.03}^{+ 0.04}$ $Mathematical equation: $ 0.67^{+0.04}_{-0.03} $$	–	–
C_EMOS2	–	0.72 ± 0.04	–	–
N_H [10²² cm⁻²]	1.4 ± 0.4	0.9 ± 0.2	$0 . 2_{- 0.2}^{+ 0.8}$ $Mathematical equation: $ 0.2^{+0.8}_{-0.2} $$	0.8(e)
N_cutoffpl[×10⁻³]	$0 . 6_{- 0.2}^{+ 0.3}$ $Mathematical equation: $ 0.6^{+0.3}_{-0.2} $$	0.33 ± 0.04	$1 . 9_{- 0.5}^{+ 0.7}$ $Mathematical equation: $ 1.9^{+0.7}_{-0.5} $$	$0 . 6_{- 0.4}^{+ 0.7}$ $Mathematical equation: $ 0.6^{+0.7}_{-0.4} $$
Γ₁	0.1 ± 0.6	$- 0 . 6_{- 0.3}^{+ 0.2}$ $Mathematical equation: $ -0.6^{+0.2}_{-0.3} $$	−0.6 ± 0.4	−1 ± 2
E_fold, 1 [keV]	$2 . 9_{- 0.9}^{+ 1.5}$ $Mathematical equation: $ 2.9^{+1.5}_{-0.9} $$	2.0 ± 0.3	$2 . 1_{- 0.2}^{+ 0.3}$ $Mathematical equation: $ 2.1^{+0.3}_{-0.2} $$	$1 . 7_{- 0.5}^{+ 1.0}$ $Mathematical equation: $ 1.7^{+1.0}_{-0.5} $$
E_fold, 2 [keV]	$6_{- 2}^{+ 3}$ $Mathematical equation: $ 6^{+3}_{-2} $$	$5 . 4_{- 0.9}^{+ 1.2}$ $Mathematical equation: $ 5.4^{+1.2}_{-0.9} $$	6.2 ± 0.2	$5 . 3_{- 0.4}^{+ 0.5}$ $Mathematical equation: $ 5.3^{+0.5}_{-0.4} $$
E_int [keV]	$13_{- 3}^{+ 4}$ $Mathematical equation: $ 13^{+4}_{-3} $$	12 ± 2	10.6 ± 0.3	$7 . 9_{- 0.5}^{+ 0.7}$ $Mathematical equation: $ 7.9^{+0.7}_{-0.5} $$
ℒ [10³⁴ erg s⁻¹] (d)	2.84	0.40	1.41	6.06
χ²/d.o.f.	144/130	201/183	438/317	127/149
χ_red²	1.10	1.10	1.38	0.85
Δχ_cutoffpl²	40	172	441	78

Notes. (a) Photogeometric distances from Gaia DR3 (Gaia Collaboration 2016, 2023; Bailer-Jones et al. 2021). (b) The XMM-Newton observation of IGR J21347+4737 was not performed simultaneous to the NuSTAR observation, but at similar luminosity. (c) The XMM-Newton observation of GX 304−1 was not performed simultaneous to the NuSTAR observation, but at the same orbital phase and similar luminosity. (d) Absorbed luminosity in the observer’s frame in the 5–50 keV energy band. (e) Galactic absorption column density N_H from HI4PI Collaboration (2016).

References. Ba17: Ballhausen et al. (2017), De01: Delgado-Martí et al. (2001), Do21: Doroshenko et al. (2021), Do22: Doroshenko et al. (2022), Fi94: Finger et al. (1994), Gh23: Ghising et al. (2023), Go22: Gorban et al. (2022a), Ku13: Kühnel et al. (2013), Lu21: Lutovinov et al. (2021), Ma15: Malacaria et al. (2015), Mc07: McBride et al. (2007), Mr21: Mroz & Udalski (2021), Pi23: Pike et al. (2023), Ra23: Rai et al. (2023), Ra25: Rai et al. (2025), Su15: Sugizaki et al. (2015), Vy17: Vybornov et al. (2017)

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