Cyclotron lines in highly magnetized neutron stars

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Table 1.

Magnetic field strength for a few selected sources: comparing measurements based on the observed cyclotron line energy with estimates based on applying accretion torque models.

System	Refer.	μ₃₀(GL)^b	B₁₂ =^d	Cyclotron	B₁₂	B(Wang)	B_torque
	“rotator”^a	or	2 × μ₃₀	line	from	/B(GL)	/B_cyc
		μ₃₀(Wang) =^c	= B_torque	Energy	E_cyc	or
		5 × ϵ₃₀(Wang)		E_cyc	(= B_cyc)	B(Klus)
		[10³⁰ G cm³]	[10¹² G]	[keV]	[10¹² G]	/B(GL)
Her X-1	GL“fast”	0.47^e	0.94	37	3.83	2.2	0.25
″ ″ ″	Wang	1.05	2.10	37	3.83		0.55
GX 301-2	GL “slow”	0.3	0.6	37	3.83		0.16
4U 0115+63	GL “fast”	1.4	2.8	12	1.24	2.1	2.3
″ ″ ″	Wang	2.95	5.9	12	1.24		4.8
4U 1626-67	Wang	4.35	8.7	37	3.83		2.3
A 0535+26	GL “slow”	3.3	6.6	50	5.17	2.1	1.3
″ ″ ″	Klus		14	50	5.17		2.7
Cen X-3	GL “fast”	4.5	9	28	2.90	2.1	3.1
″ ″ ″	Wang	9.55	19.1	28	2.90		6.6
X Per	GL “slow”	4.8	9.6	29	2.19		4.4
″ ″ ″	GL “slow”	4.8	9.6	29	2.19		4.4
″ ″ ″	Klus		42	29	2.19		19.2
Vela X-1^f	GL “fast”	86	172	25	2.60		66
A 0535+26	GL “fast”	148	296	50	5.17		57
GX 301-2	GL “fast”	394	788	37	3.83		206

Notes.

^(a)

“Slow” or “fast” solution according to Ghosh & Lamb (1979a),

^(b)

original values from the literature;

^(c)

the original values of Wang (1987) are ϵ₃₀, μ₃₀ = 5 × ϵ₃₀;

^(d)

we use the definition: B = 2μR⁻³ (unlike Ghosh & Lamb 1979b, see text) and consider this to be the field strength B₀ at the surface of the neutron star at the magnetic poles;

^(e)

we note that μ₃₀ = 0.47 is a valid solution for Her X-1 within the GL-model, but it requires L₃₇ = 2.7 (not 1.0, as in Table 1 of Ghosh & Lamb 1979a);

^(f)

for Vela X-1 the GL “slow” solution yields μ₃₀ = 2.7 10⁻⁵ G cm³, obviously not valid.

References. “GL”: Ghosh & Lamb (1979a), “Wang”: Wang (1987), “Klus”: Klus et al. (2014).

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