Unveiling the Nature of Superorbital Modulation of SMC X-1 using NinjaSat

TL;DR

SMC X-1 presents a high-cadence timing and spectral study across nearly a full superorbital cycle using NinjaSat, complemented by MAXI data, to test whether spin evolution tracks accretion-rate changes. The analysis shows a steady spin-up with $\dot{\nu} \approx 2.69\times10^{-11}$ Hz s$^{-1}$ that is largely independent of instantaneous flux, while the 2–20 keV hardness ratio and spectral shape remain stable, supporting a geometric obscuration origin (e.g., a warped inner disk or energy-independent scattering) for the superorbital modulation. Pulse-profile evolution is phase-dependent, with a double-peaked structure whose relative strengths vary with superorbital phase, hinting at variable covering fractions or possible neutron-star spin-axis precession. Collectively, the results argue against the modulation being driven by mass accretion-rate changes and highlight the potential of CubeSat-based observatories for time-domain high-energy astrophysics.

Abstract

We report a long-term, high-cadence timing and spectral observation of the X-ray pulsar SMC X-1 using NinjaSat, a 6U CubeSat in low-Earth orbit, covering nearly a full superorbital cycle. SMC X-1 is a high-mass X-ray binary exhibiting a 0.7 s X-ray pulsar and a non-stationary superorbital modulation with periods ranging from approximately 40 to 65 days. Its peak luminosity of $1.3\times10^{39}$~\lumcgs\ makes it a local analogue of ultraluminous X-ray pulsars powered by supercritical accretion. We find that the spin-up rate during the high state remains consistent with the long-term average, with no significant correlation between spin-up rate and flux. This result indicates that the modulation is primarily geometric rather than accretion-driven. The hardness ratio and spectral shape are stable throughout the entire superorbital cycle, supporting obscuration by optically thick material or energy-independent scattering. In addition, the 2--20 keV pulse profile varies with superorbital phase, which may be explained either by variable covering fraction due to geometric obscuration, or by free precession of the neutron star. This represents the first complete measurement of spin-up rate and spectral evolution across a single superorbital cycle in SMC X-1, highlighting the scientific capability of CubeSat-based observatories.

Figures (7)

• Figure 1: a. Light curve of SMC X-1 obtained with NinjaSat (black dots), MAXI (green triangles), and Swift/BAT (orange squares). NinjaSat data collected during orbital eclipses are shown in green. The light gray shaded regions indicate the superorbital ascending (MJD 60657--60662) and descending (MJD 60688--60695) states, while the dark gray region marks the superorbital low state (MJD 60695--60704). Eleven observed orbital cycles are labeled i to xi. b. Hardness ratio (10--20 keV/2--10 keV) derived from NinjaSat observations. c. Evolution of pulse arrival phases relative to a quadratic ephemeris with $\dot{\nu} = 2.668 \times 10^{-11}$ Hz s$^{-1}$, based on the average spin-up rate during this superorbital cycle. Red curves denote the best-fit quadratic (cycles i to ii) and fourth-order polynomials (cycles iv to ix).d. Spin period deviations relative to the quadratic model. Spin periods for each orbital cycle are derived from TOA fitting (black points) and cross-validated using the $Z_2^2$-test (orange diamonds). e. Evolution of the local $\dot{\nu}$. Red curves in panels d and e are derived from timing solutions in panel c.
• Figure 2: Pulse profile evolution of SMC X-1 observed with NinjaSat. Pulse profiles for 11 orbital cycles (i to xi) are shown sequentially and color-coded, with their corresponding superorbital phase ranges labeled. Photon events from orbital eclipses and pre-eclipse dips were excluded from the folded light curves. The right panel displays the NinjaSat light curve. Black dots indicate data during orbital eclipses, while out-of-eclipse points are color-coded according to orbital cycle. Dotted lines mark the boundaries of the out-of-eclipse intervals for each orbital cycle. Pre-eclipse dips in cycles ix and x are marked by gray-filled regions. Photons collected during these intervals were excluded from the pulse profiles.
• Figure 3: Flux dependence of a. peak ratio, b. pulse fraction of P1, and c. pulse fraction of P2. Gray arrows indicate the evolutionary track of each parameter from orbital cycle i through ix. Right panels show probability density distributions from Monte Carlo simulations (blue) and bootstrapped samples (orange).
• Figure 4: Long-term spin evolution of SMC X-1 observed with NinjaSat and MAXI. a. The 2--20 keV MAXI 6-hr binned light curve is plotted in blue, and the scaled 1-d binned Swift/BAT light curve is plotted in orange. b. Spin frequency ($\nu$) evolution. Blue triangles represent values averaged over individual superorbital high state using MAXI data; gray squares show values computed over 8--12 day intervals; black dots indicate NinjaSat measurements for each binary orbital cycle. The black dashed line is a linear fit to the 8--12 day MAXI $\nu$ measurements. c. Residuals of $\nu$ after subtracting the best-fit linear trend shown in panel b. d. Evolution of the spin-up rate ($\dot{\nu}$). The dashed line represents the best-fit average $\dot{\nu}$ across the nine superorbital cycles, as determined from the linear model in panel b.
• Figure 5: Spectral evolution of SMC X-1 during the NinjaSat monitoring campaign from December 2024 to January 2025. Panel a presents the 2--20 keV light curve as a reference. Panels b--d illustrate the corresponding evolution of spectral parameters derived from the best-fit pcfabs*cutoffpl model: b. $N_{\textrm{H}}$ from the pcfabs component, c. partial covering fraction, d. photon index ($\Gamma$), and e. unabsorbed flux (2--20 keV band).