The first comprehensive spectral and timing study of the ultra-compact X-ray binary 4U 1812-12 with NICER and NuSTAR

Abstract: The source 4U 1812-12 is a persistent, weakly variable low-mass X-ray binary containing a neutron star. The source was observed by NICER between 2019 and 2021 and, more recently, by NuSTAR in 2025. During the NICER and NuSTAR observations, the source was detected in a hard spectral state with a bolometric luminosity of $\sim 1.90\times 10<sup>{36}$ ergs s$<sup>{-1}$. Its $3-70$ keV NuSTAR spectrum is characterized by a soft thermal emission from the disc, a hard Comptonized emission from the corona, and its reflection from the accretion disc. The NuSTAR energy spectrum exhibits the clear presence of disc reflection features, fitted using a self-consistent relativistic reflection model {\tt relxill}. Our reflection modeling indicates a moderately ionized accretion disc (log:$ξ\sim2.72$) extending close to the neutron star surface ($R_{in}\lesssim 1.72:R_{ISCO}$), and viewed through a small inclination angle ($i\sim 25$ degrees). Assuming that the magnetic field ($B$) truncates the disc, we found $B\lesssim 2.54\times 10<sup>{8}$ G, comparable to the typical values observed for NS LMXBs. The $1.0-9.5$ keV NICER spectra are also characterized by a soft thermal component and a dominant hard Comptonized component. During NICER observations, the disc temperature exhibits a small variation within $\sim 0.69-0.84$ keV. In contrast, the power law photon index, $Γ$, exhibits a large variation of $\sim 0.8-1.5$, implying a substantial change in the Comptonized emission. Moreover, NICER timing analysis reveals broadband aperiodic variability with significant QPO-like features at $0.379\pm 0.008$ Hz and $0.724\pm 0.025$ Hz, having fractional rms amplitudes of $2.9\pm 0.6\%$ and $4.1\pm 0.5\%$, respectively.

• The paper presents the first comprehensive broadband spectral and timing study of 4U 1812-12 using 25 NICER observations and a roughly 100 ks NuSTAR exposure, establishing it as a hard-state, Comptonization-dominated atoll source.
• Relativistic reflection modeling detects a broad Fe Kα line and Compton hump, indicating a disc extending to within 1.72 R_ISCO, a low inclination of about 25 degrees, and a neutron-star magnetic field below approximately 2.54 × 10^8 G.
• Timing analysis identifies QPO-like features at 0.379 and 0.724 Hz, while flaring episodes show a roughly 40% disc-temperature increase and threefold 1–10 keV flux enhancement linked to rapid accretion changes.

The neutron star low-mass X-ray binary 4U 1812-12 has long been suspected of being an ultra-compact X-ray binary, but until now it lacked a modern broadband spectral and timing characterization. This paper presents the first comprehensive analysis of the source using 25 NICER observations obtained between 2019 and 2021 and one ~100 ks NuSTAR observation from September 2025 (2608.16841). The principal results are the first detection of disc reflection features (a broad Fe K$\alpha$ line and Compton hump) in this source, self-consistent constraints on the accretion geometry from relativistic reflection modeling, and the identification of two low-frequency QPO-like timing features.

Observations and data reduction

The NuSTAR observation (Obs ID 31101029002) was performed on 2025 September 19 with an effective exposure of ~102 ks per focal plane module and a mean count rate of ~12 counts s$^{-1}$. Spectra from FPMA and FPMB were fitted simultaneously over 3–70 keV, with $N_{\rm H}$ fixed at $0.63\times10^{22}$ cm$^{-2}$ because NuSTAR lacks low-energy coverage. The NICER data set spans 2019 March to 2021 September; observations showing flares or absorption dips were excluded from the persistent-emission analysis, leaving spectra fitted over 1.0–9.5 keV using the scorpeon background model. A narrow Gaussian at ~1.8 keV accounts for the known Si instrumental edge.

Timing behavior

The MAXI/GSC light curve and the individual NICER count rates (~33–55 counts s$^{-1}$) show no secular trend across 2019–2021, indicating that the source remained in the same accretion state throughout. Two observations exhibit intensity excursions lasting ~200–300 s; these are classified as flaring episodes rather than type-I bursts, although for one event the rising phase falls in a data gap and a burst identification cannot be conclusively excluded — a caveat the authors state explicitly.

Power density spectra computed from 0.1-s binned light curves over 102.4-s segments reveal broadband aperiodic variability in most observations. One NICER observation shows two narrow Lorentzian components at $0.379\pm0.008$ Hz ($Q\sim5$, rms $2.9\pm0.6\%$) and $0.724\pm0.025$ Hz ($^{-1}$0, rms $^{-1}$1), interpreted as fundamental and (sub)harmonic QPOs. These are consistent with the ~0.7 Hz QPO reported earlier by RXTE, confirming the atoll-source classification in the hard state.

Continuum spectroscopy

For NuSTAR, an absorbed cutoff power law alone fails badly ($^{-1}$2); adding a multicolor disc blackbody improves the fit decisively ($^{-1}$3), yielding $^{-1}$4 keV, $^{-1}$5, and $^{-1}$6 keV. Replacing the phenomenological component with {\tt nthcomp} gives comparable fits with $^{-1}$7 keV and $^{-1}$8, whether seed photons are drawn from the disc or the NS surface/boundary layer; the latter case yields only an upper limit on the seed temperature, so its origin remains ambiguous. The Comptonized component contributes ~90% of the unabsorbed flux, confirming a hard spectral state.

Across all NICER observations, the disc temperature varies only weakly between ~0.69 and 0.84 keV while the power-law photon index varies substantially, $^{-1}$9–1.5. The absence of a clear $N_{\rm H}$0–$N_{\rm H}$1 correlation implies that coronal properties (optical depth, electron temperature, geometry) evolve independently of the thermal disc, though the exact nature of this evolution is left unresolved.

Flaring spectra

Spectra extracted from three flaring intervals in one NICER observation are also Comptonization-dominated (~80% of flux) with $N_{\rm H}$2 keV, but show a disc temperature rising to ~1.12 keV — roughly 40% above the persistent value — and a factor-of-~3 enhancement in 1–10 keV flux. Following prior interpretations of LMXB flaring as disc-instability-driven mass injection, the authors attribute the temperature increase to a rapid rise in the local accretion rate through the inner disc.

Reflection spectroscopy

Residuals to every continuum model show a broad Fe K$N_{\rm H}$3 line at 6–8 keV and a Compton hump peaking near 20 keV — the first detection of reflection in this source. Fitting with {\tt const*TBabs*(diskbb+relxill)} gives $N_{\rm H}$4 (1501 dof) and constrains:

Parameter	Value
Inclination	$N_{\rm H}$5 deg
Inner radius	$N_{\rm H}$6
Ionization	$N_{\rm H}$7
Photon index	$N_{\rm H}$8
High-energy cutoff	$N_{\rm H}$9 keV
Iron abundance	$0.63\times10^{22}$0 solar
Reflection fraction	$0.63\times10^{22}$1

The spin was fixed at zero (justified since NS spins minimally affect the metric for $0.63\times10^{22}$2, and setting $0.63\times10^{22}$3 changes nothing significant). The well-constrained low inclination is consistent with the absence of eclipses and dips, and the inner-radius upper limit indicates the disc extends close to the neutron star with little magnetic truncation. Assuming the disc is truncated at the magnetosphere, the inferred field strength is $0.63\times10^{22}$4 G, typical of NS LMXBs. The bolometric luminosity is $0.63\times10^{22}$5 erg s$0.63\times10^{22}$6 (at 4.1 kpc), corresponding to $0.63\times10^{22}$7 yr$0.63\times10^{22}$8, consistent with previous estimates and supporting the ultra-compact classification via the persistent low luminosity.

Limitations and open questions

Several caveats bear directly on these results. First, the reflection fit depends on a fixed emissivity index $0.63\times10^{22}$9 and fixed spin; while tested to be insensitive to $^{-2}$0, the emissivity assumption is not varied. Second, the physically self-consistent {\tt relxillCP} model could not be used because its hard-coded disc temperature (~0.01 keV) is incompatible with the measured $^{-2}$1–0.85 keV, so the continuum and reflection components are not fully coupled. Third, the seed-photon origin for the boundary-layer scenario is unconstrained. Fourth, the NICER-inferred $^{-2}$2–$^{-2}$3 cm$^{-2}$4 exceeds the Galactic value by more than a factor of two — a discrepancy also seen in MAXI J1957+032 whose physical cause is not addressed. Finally, the tentative ~114-minute orbital period from photometry means the ultra-compact nature itself remains unconfirmed; the paper leaves open whether 4U 1812-12 is a true ultra-compact binary or its progenitor, and what mechanism produces the observed flaring episodes.

Conclusion

This work establishes 4U 1812-12 as a hard-state, Comptonization-dominated atoll source at $^{-2}$5 erg s$^{-2}$6, provides the first detection and self-consistent modeling of disc reflection in the system, and reports two low-frequency QPO-like features consistent with earlier RXTE results. The reflection constraints — a disc extending to within $^{-2}$7, low inclination, moderate ionization, and a weak reflection fraction — place the source among NS LMXBs with weakly truncated inner discs, and the derived magnetic field upper limit is consistent with typical accreting neutron stars.