Proton CRSF: Magnetar-Field Diagnostics

• Proton CRSF is an X-ray spectral feature produced by resonant scattering off quantized proton Landau levels in magnetar-strength fields.
• The absorption line energy, scaling as 0.63 keV × B₁₄ and modified by gravitational redshift, provides a direct measurement of local magnetic fields.
• Robust identification of proton CRSF relies on narrow line profiles, phase variability, and clear differentiation from atomic transitions or wind features.

Searching arXiv for the cited and closely related proton-CRSF papers to ground the article in current literature. A proton cyclotron resonant scattering feature (CRSF) is an absorption-like spectral feature produced when X-ray photons resonantly scatter off quantized proton Landau levels in a magnetic field. In the non-relativistic limit, the relevant gyrofrequency is $\omega_{\rm c}=|q|B/(mc)$, so the corresponding line energy scales inversely with particle mass; for protons this places the fundamental resonance in the soft X-ray band for magnetic fields of order $10^{13}$–$10^{14}$ G and above (Staubert et al., 2018). In practice, proton CRSFs are of particular interest because they provide a direct probe of magnetar-strength fields near neutron-star surfaces, including local multipolar components that may differ substantially from the large-scale dipole inferred at the magnetosphere (Jayasurya et al., 7 Jun 2026).

1. Physical definition and basic scaling

A charged particle of mass $m$ and charge $q$ gyrates around a magnetic field line of strength $B$ at the cyclotron frequency

$\omega_{\rm c}=\frac{|q|B}{mc}\,.$

In a quantum-mechanical treatment, the motion perpendicular to $\mathbf B$ is quantized into Landau levels separated by $\hbar\omega_{\rm c}$, and photons whose energy matches this spacing are resonantly scattered, producing an absorption-like feature at

$$E_{\rm cyc}=\hbar\omega_{\rm c}=\hbar\frac{qB}{mc}\,.$$

For protons,

$10^{13}$0

with $10^{13}$1 G (Staubert et al., 2018).

In the presence of gravitational redshift, the observed energy is reduced. A convenient form used in recent ultraluminous X-ray source (ULX) analyses is

$10^{13}$2

where $10^{13}$3 (Jayasurya et al., 7 Jun 2026). Solving this expression for an observed line at $10^{13}$4 keV and adopting a fiducial $10^{13}$5 gives

$10^{13}$6

that is, $10^{13}$7 G (Jayasurya et al., 7 Jun 2026).

This scaling is central to the astrophysical significance of proton CRSFs. Electron CRSFs typically lie at $10^{13}$8–$10^{13}$9 keV for fields of several $10^{14}$0 G, whereas proton CRSFs occur at substantially lower energies because $10^{14}$1 (Staubert et al., 2018). A plausible implication is that soft-X-ray absorption lines at a few keV, if securely identified as proton cyclotron features, directly indicate magnetar-strength local fields.

2. Line formation and radiative-transfer conditions

Proton CRSFs are expected to arise in the neutron-star atmosphere or in a thin plasma layer at the magnetic polar cap, covering a small region of order $10^{14}$2 km across (Staubert et al., 2018). In this picture, thermal surface emission is absorbed and re-emitted by protons performing cyclotron transitions. The optical depth at resonance can be written as

$10^{14}$3

so proton densities of order $10^{14}$4–$10^{14}$5 cm$10^{14}$6 and $10^{14}$7–$10^{14}$8 cm yield $10^{14}$9, sufficient to produce an absorption feature (Staubert et al., 2018).

The intrinsic line width expected from proton thermal motion is very small. For $m$0–$m$1 eV, the thermal contribution gives $m$2, which is negligible compared with observed widths such as $m$3 (Staubert et al., 2018). This means that broadening must generally be attributed to magnetic-field inhomogeneity over the emitting cap or to unresolved multiple features, for example harmonic or atomic contributions. In ULX candidates, additional broadening via magnetic-field gradients, phase-averaging, or scattering in an optically thick accretion funnel has also been invoked (Allak et al., 3 Jun 2026).

A useful contrast with electron CRSFs is that proton features appear predominantly at the fundamental, whereas multi-harmonic patterns are often seen in electron CRSF systems (Staubert et al., 2018). This observational asymmetry has become important in evaluating alternative identifications for narrow, harmonic-free absorption features in ULXs (Cruz-Sanchez et al., 11 Mar 2026).

3. Established candidate environments outside ULXs

Before the recent ULX detections, the principal observational context for proton CRSF candidates was provided by nearby, thermally emitting isolated neutron stars. Seven such objects show broad absorption-like features in the $m$4–$m$5 keV band that have been interpreted as proton cyclotron lines: RX J0420.0–5022, RX J0720.4–3125, RX J0806.4–4123, RX J1308.6+2127, RX J1605.3+3249, RX J1856.5–3754, and RX J2143.0+0654 (Staubert et al., 2018).

These systems exhibit line energies from roughly $m$6 eV to $m$7 eV, corresponding to inferred magnetic fields from a few $m$8 G up to $m$9 G when a gravitational redshift factor $q$0 is assumed (Staubert et al., 2018). Several sources show more than one feature. RX J0720.4–3125 and RX J1308.6+2127, for example, display a broad $q$1 eV line together with a narrow phase-variable feature at $q$2 eV, suggesting a stronger local field component superposed on a weaker global field. RX J1605.3+3249 shows two lines at $q$3 eV and $q$4 eV, with the latter implying $q$5 G (Staubert et al., 2018).

Pulse-phase variability is an important part of the phenomenology. In RX J0720.4–3125 and RX J1308.6+2127 the equivalent width of the broad $q$6 eV line varies by $q$7 eV over rotation, while the narrow $q$8 eV feature appears only during $q$9 of phase (Staubert et al., 2018). Long-term changes have also been reported, including a slow increase of line depth in RX J0720.4–3125 over $B$0 yr when the surface temperature rose, followed by gradual cooling. This suggests a link between local temperature, atmosphere ionization, and line strength (Staubert et al., 2018).

These isolated-neutron-star cases define the classical phenomenological template for proton CRSF studies: soft-band absorption, likely surface or polar-cap formation, and sensitivity to local magnetic topology rather than only the dipole field.

4. Candidate proton CRSFs in ultraluminous and hyperluminous X-ray sources

Recent work has extended the proton-CRSF framework into the super-Eddington accretion regime. In NGC 4656 ULX-1, a narrow absorption feature at $B$1 keV was detected in the XMM-Newton/EPIC-pn spectrum. The source exhibits a hard-ultraluminous state, and Monte Carlo likelihood-ratio tests yielded significances from $B$2 to $B$3, depending on the continuum and data selection. Interpreted as a proton CRSF, the line implies a local magnetic field of $B$4–$B$5 G (Cruz-Sanchez et al., 11 Mar 2026).

In NGC 4861 X-2, an absorption-like feature at $B$6 keV was detected in Chandra/ACIS spectra, with significance of $B$7–$B$8 depending on the adopted continuum. The best-fit centroid is $B$9 keV in the diskbb+gabs fit and $\omega_{\rm c}=\frac{|q|B}{mc}\,.$0 keV in the cutoffpl+gabs fit, with $\omega_{\rm c}=\frac{|q|B}{mc}\,.$1 keV and line strengths of $\omega_{\rm c}=\frac{|q|B}{mc}\,.$2 keV and $\omega_{\rm c}=\frac{|q|B}{mc}\,.$3 keV, respectively. The proton-cyclotron interpretation yields $\omega_{\rm c}=\frac{|q|B}{mc}\,.$4–$\omega_{\rm c}=\frac{|q|B}{mc}\,.$5 G (Allak et al., 3 Jun 2026).

In the hyperluminous source 2SXPS J111416.1+481833 in NGC 3583, a narrow absorption line was found in the 2024 XMM-Newton EPIC-pn and MOS2 spectra at $\omega_{\rm c}=\frac{|q|B}{mc}\,.$6 keV with $\omega_{\rm c}=\frac{|q|B}{mc}\,.$7 keV and $\omega_{\rm c}=\frac{|q|B}{mc}\,.$8 eV. Monte Carlo line-scan simulations with $\omega_{\rm c}=\frac{|q|B}{mc}\,.$9 fake spectra, including the look-elsewhere effect, yielded no spurious $\mathbf B$0 larger than observed ($\mathbf B$1), implying a false-alarm rate $\mathbf B$2 and a detection significance $\mathbf B$3. A proton CRSF interpretation gives $\mathbf B$4 G (Jayasurya et al., 7 Jun 2026).

Across these sources, the continuum shape is also noteworthy. NGC 3583 X-1 shows a soft thermal component plus a hard rollover at $\mathbf B$5–$\mathbf B$6 keV, modeled equally well by a cutoff power law, thermal Comptonization, or an advective disk; this low-energy cutoff plus soft excess is typical of the “Hard Ultraluminous” state in super-Eddington accretors (Jayasurya et al., 7 Jun 2026). NGC 4656 ULX-1 likewise exhibits a hard-ultraluminous state (Cruz-Sanchez et al., 11 Mar 2026), while NGC 4861 X-2 is described either by a multicolor disk blackbody with $\mathbf B$7 keV or by a strongly curved continuum with $\mathbf B$8 keV (Allak et al., 3 Jun 2026). This suggests that proton-CRSF candidates in ULXs are preferentially being identified in spectra already indicative of strongly curved, super-Eddington accretion flows.

5. Identification, alternative explanations, and diagnostic criteria

The central interpretive problem in proton-CRSF work is discriminating cyclotron lines from atomic transitions and absorption in ionized outflows. In NGC 3583 X-1, ionized outflow models using zxipcf or zxipab can formally fit the $\mathbf B$9 keV feature only by invoking extreme blueshifts, $\hbar\omega_{\rm c}$0 or $\hbar\omega_{\rm c}$1, together with high column densities $\hbar\omega_{\rm c}$2–$\hbar\omega_{\rm c}$3 cm$\hbar\omega_{\rm c}$4 (Jayasurya et al., 7 Jun 2026). Such velocities exceed predictions of radiatively driven ULX winds ($\hbar\omega_{\rm c}$5), and in a low-inclination hard-ultraluminous geometry would require unrealistically high mechanical power. No accompanying absorption lines such as blueshifted Mg, Si, or Fe transitions are observed, though such lines would be expected in a bona fide wind (Jayasurya et al., 7 Jun 2026).

Atomic-line explanations are likewise disfavored in the cases summarized here. For NGC 3583 X-1, an identification with blueshifted Mg XI at $\hbar\omega_{\rm c}$6 keV is disfavored by the absence of multiple lines, inconsistent ionization parameters, and the narrowness of the observed feature (Jayasurya et al., 7 Jun 2026). For NGC 4656 ULX-1, an atomic wind-line interpretation, such as S XVI at $\hbar\omega_{\rm c}$7 keV, would require a blueshift of $\hbar\omega_{\rm c}$8 km s$\hbar\omega_{\rm c}$9, yet no companion lines at Si XIV $$E_{\rm cyc}=\hbar\omega_{\rm c}=\hbar\frac{qB}{mc}\,.$$0 keV, S XVI $$E_{\rm cyc}=\hbar\omega_{\rm c}=\hbar\frac{qB}{mc}\,.$$1 keV, or Ca XIX/XX $$E_{\rm cyc}=\hbar\omega_{\rm c}=\hbar\frac{qB}{mc}\,.$$2–$$E_{\rm cyc}=\hbar\omega_{\rm c}=\hbar\frac{qB}{mc}\,.$$3 keV are seen (Cruz-Sanchez et al., 11 Mar 2026).

Electron-cyclotron interpretations provide another comparison standard. In NGC 4656 ULX-1, an electron CRSF at $$E_{\rm cyc}=\hbar\omega_{\rm c}=\hbar\frac{qB}{mc}\,.$$4 keV would imply $$E_{\rm cyc}=\hbar\omega_{\rm c}=\hbar\frac{qB}{mc}\,.$$5 G, but Galactic accreting pulsars’ electron lines are broader, show harmonics, and track pulse phase closely, unlike the narrow, harmonic-free line observed there (Cruz-Sanchez et al., 11 Mar 2026). NGC 4861 X-2 makes the same point quantitatively: electron CRSFs appear at tens of keV, with $$E_{\rm cyc}=\hbar\omega_{\rm c}=\hbar\frac{qB}{mc}\,.$$6 keV, so a $$E_{\rm cyc}=\hbar\omega_{\rm c}=\hbar\frac{qB}{mc}\,.$$7 keV line would correspond to only $$E_{\rm cyc}=\hbar\omega_{\rm c}=\hbar\frac{qB}{mc}\,.$$8 (Allak et al., 3 Jun 2026). This is not impossible in principle, but it sits uneasily with the broader phenomenology of highly luminous, strongly curved ULX spectra and with the absence of the expected electron-CRSF characteristics.

Taken together, the preferred proton-CRSF identification in these systems rests on a convergent set of diagnostics: narrow width, lack of harmonics, stable centroid set by $$E_{\rm cyc}=\hbar\omega_{\rm c}=\hbar\frac{qB}{mc}\,.$$9, absence of companion atomic features, and compatibility with near-surface magnetar-strength fields while allowing a weaker large-scale dipole (Cruz-Sanchez et al., 11 Mar 2026).

6. Timing behavior, accretion geometry, and magnetic-field topology

Proton CRSFs do not by themselves specify the full magnetic configuration; rather, they diagnose the local field in the line-forming region. This distinction is explicit in recent ULX studies. In NGC 3583 X-1, a $10^{13}$00 keV proton CRSF points to magnetar-strength fields near the neutron-star surface, with multipolar components $10^{13}$01–$10^{13}$02 G, while the large-scale dipole can remain $10^{13}$03 G at the magnetospheric radius ($10^{13}$04 km), permitting a super-Eddington funnel/wind structure with $10^{13}$05 (Jayasurya et al., 7 Jun 2026). NGC 4656 ULX-1 reaches a similar conclusion, arguing that a local field of $10^{13}$06–$10^{13}$07 G is consistent with strong fields anchored near the surface even if the large-scale dipole is substantially weaker (Cruz-Sanchez et al., 11 Mar 2026).

Timing results are suggestive but not uniform. NGC 4656 ULX-1 shows a candidate pulsation at $10^{13}$08 Hz, with $10^{13}$09–$10^{13}$10, local significance $10^{13}$11, and pulsed fraction $10^{13}$12 in $10^{13}$13–$10^{13}$14 keV; accounting for trials reduces the global significance to $10^{13}$15, so it remains a “promising candidate” (Cruz-Sanchez et al., 11 Mar 2026). Phase-resolved spectra hint that the $10^{13}$16 keV line is stronger during pulse-off, suggesting an origin close to the accretion column or curtain. NGC 4861 X-2 shows a candidate soft-band period at $10^{13}$17 s with global significance $10^{13}$18 in the same observation that contains the strongest $10^{13}$19 keV line, and the same period appears with global significance $10^{13}$20 in another line-bearing dataset; the co-incidence of period and line suggests a connection to the neutron-star spin and line-forming region (Allak et al., 3 Jun 2026).

By contrast, NGC 3583 X-1 shows no coherent X-ray pulsations, with 90% confidence upper limits on the pulsed fraction of $10^{13}$21 in the $10^{13}$22–$10^{13}$23 keV band and $10^{13}$24 in the $10^{13}$25–$10^{13}$26 keV band (Jayasurya et al., 7 Jun 2026). This non-detection is consistent with multiple scatterings in an optically thick accretion envelope washing out pulses, rapid alignment of the neutron-star spin with the funnel axis in super-Eddington flow, or pulse-phase dilution in a broadband phase-averaged spectrum (Jayasurya et al., 7 Jun 2026). A plausible implication is that the absence of pulsations does not invalidate a neutron-star interpretation when a candidate proton CRSF is present.

The same source also shows extreme long-term variability, from $10^{13}$27 erg s$10^{13}$28 to $10^{13}$29 erg s$10^{13}$30, a factor $10^{13}$31, which hints at transitions into and out of the centrifugal “propeller” regime as the accretion rate falls (Jayasurya et al., 7 Jun 2026). This links proton-CRSF studies to broader questions of magnetospheric gating, super-Eddington funnel geometry, and the observational distinction between neutron-star ULXs and intermediate-mass black-hole interpretations.

7. Open issues and future observational tests

Several open questions remain intrinsic to proton-CRSF identification. In isolated neutron stars, distinguishing pure proton CRSFs from atomic hydrogen features requires higher spectral resolution below $10^{13}$32 keV, with Athena X-IFU explicitly cited as an example of the needed capability (Staubert et al., 2018). At $10^{13}$33 G, bound-bound and bound-free transitions of neutral hydrogen may also produce absorption lines around a few hundred eV if a small fraction of atoms survives in cooler surface layers (Staubert et al., 2018). This complicates the interpretation of broad soft-band features in thermally emitting neutron stars.

In ULXs, the principal challenge is not hydrogen atmosphere physics but the complexity of super-Eddington accretion flows. Detailed radiative-transfer modeling in magnetized atmospheres is needed to predict line profiles, depths, and polarization signatures, while pulse-phase-resolved spectroscopy combined with light-bending calculations can constrain spot geometry and higher-order field components (Staubert et al., 2018). Time-domain studies are likewise important: monitoring the evolution of the spectrum and lines during cooling or outburst episodes can reveal the coupling between crustal heating, atmosphere composition, and local field evolution (Staubert et al., 2018). In the ULX context, analogous monitoring can test whether line appearance correlates with spectral state, soft-band variability, or pulsed emission.

The current observational picture supports a limited but growing class of ULXs and HLXs in which candidate proton CRSFs provide direct magnetic diagnostics. NGC 3583 X-1, NGC 4656 ULX-1, and NGC 4861 X-2 each show narrow absorption features at $10^{13}$34–$10^{13}$35 keV with Monte Carlo significances of roughly $10^{13}$36 and inferred local fields of order $10^{13}$37–$10^{13}$38 G (Jayasurya et al., 7 Jun 2026). This suggests that many hyperluminous, non-pulsing ULXs may nevertheless host magnetar-strength neutron stars whose emission is shaped by multipolar fields, funnel geometry, and scattering envelopes (Jayasurya et al., 7 Jun 2026). Whether these candidates will mature into a robust population depends on repeated detections, phase-resolved confirmation, and improved discrimination against wind and atomic alternatives.