Refined Orbital Period of MASCARA-1 b

• The paper presents updated measurements of MASCARA-1 b’s orbital period with a statistically significant 4σ offset compared to earlier reports.
• It applies multi-wavelength transit photometry and MCMC modeling to reduce uncertainties and refine the exoplanet’s ephemeris.
• The findings underscore that small-aperture instruments, like ONC-T, can achieve high precision in exoplanet transit timing.

MASCARA-1 b is an ultra-hot Jupiter first discovered orbiting a bright, rapidly rotating A8 star ($m_V=8.3$) by the Multi-site All-Sky CAmeRA (MASCARA). The planet exhibits a near-polar, highly misaligned orbit and is subject to intense irradiation from its host. Recent multi-instrument datasets have enabled significantly refined measurements of its orbital period, most notably identifying a statistically significant offset—at the 4σ level—between the updated value and previous literature reports. This article provides a comprehensive overview of the evolving determination of MASCARA-1 b’s orbital period, the methodologies underpinning its measurement, and the broader implications for exoplanetary studies.

1. Discovery and Early Orbital Characterization

The initial discovery of MASCARA-1 b (Talens et al., 2017) was based on joint transit photometry from MASCARA and NITES. Analysis via a Markov Chain Monte Carlo (MCMC) framework, with transit models following Mandel & Agol (2002), yielded a period $P=2.148780\pm8\times10^{-6}$ days. Key parameters from these observations include:

• Transit duration: $T_{14}\approx4.05$ hr
• Impact parameter: $b\approx0.2$
• Circular orbit: $e=0$ (fixed)

The host star’s mass and radius ($M_*=1.72\pm0.07\,M_\odot$; $R_*=2.1\pm0.2\,R_\odot$) enabled calculation of the semi-major axis using Kepler’s third law:

$a^3 = \frac{G M_* P^2}{4\pi^2}$

yielding $a=0.043\pm0.005$ AU.

Spectroscopic analysis revealed a pronounced projected obliquity ($\lambda=69.5^\circ\pm3^\circ$), indicative of a misaligned orbit relative to the stellar rotation axis.

2. Refined Period Measurements from Space-Based Photometry

Advances in transit and phase-curve photometry, particularly with CHEOPS and Spitzer (Hooton et al., 2021), yielded a new period measurement:

$$P = 2.14877381^{+8.8\times10^{-7}}_{-8.7\times10^{-7}}\,\text{days}$$

This precision (better than $10^{-6}$ relative error) draws on several advantages:

• High-cadence CHEOPS data captured both transit and occultation with distinct gravity-darkening-induced asymmetries, allowing precise timing and improved constraints on $t_0$, transit duration, and impact parameter.
• Nearly continuous Spitzer coverage at $4.5\,\mu$m anchored the phase lag between transit and occultation, further refining the ephemeris.

Joint modeling of multi-wavelength data significantly diminishes correlations among transit parameters and, when expanded with priors from Doppler tomography, constrains the true spin-orbit angle to $\Psi=72.1^{+2.5}_{-2.4}$ deg. These measurements affirm a near-polar orbit, further refining the system’s 3D geometry.

3. Updated Period from ONC-T and TESS and the 4σ Discrepancy

The most recent update to the planetary ephemeris (Yumoto et al., 16 Oct 2025) is distinguished by the use of the 15-mm aperture Optical Navigation Camera (ONC-T) on Hayabusa2 and complementary TESS photometry. Four ONC-T transit events and 20 TESS transits enabled a linear ephemeris fit:

$T_\mathrm{C}(N) = T_0 + N \cdot P$

with

• $T_0 = 2458833.488125 \pm 0.000079$ (BJD$_\mathrm{TDB}$)
• $P = 2.14876998 \pm 0.00000013$ days

Comparison with the CHEOPS/Spitzer-derived value ($P=2.14877381^{+0.00000088}_{-0.00000087}$ days) shows a period difference $\Delta P \approx 3.83 \times 10^{-6}$ days, corresponding to $\sim4\sigma$ when uncertainties are propagated:

$$\sigma_{\Delta P} = \sqrt{(1.3 \times 10^{-7})^2 + (8.8 \times 10^{-7})^2} \approx 8.9 \times 10^{-7}\,\text{days}$$

$$\left| \Delta P / \sigma_{\Delta P} \right| \approx 4$$

This result indicates that earlier ephemerides may now be inaccurate for future transit predictions. The systematic offset may reflect, among other possibilities, transit timing variations (TTVs), unrecognized instrumental biases, or data reduction differences.

4. Methodological Innovations and Instrumental Impact

The ONC-T dataset (Yumoto et al., 16 Oct 2025) marks the first definitive detection of an exoplanet transit with a space-based instrument aperture $<60$ mm. Each MASCARA-1 b transit was measured with timing precision of $6$–$7$ minutes. Comparison to TESS mid-times revealed agreement to within $2$ minutes, and planet-to-star radius ratio precision reached $0.004$ (absolute, 6% relative), with relative agreement to TESS results within $0.002$ (3%).

This demonstrates the capabilities of miniature instrumentation for precise transit timing:

Instrument	Aperture (mm)	Period Precision (days)	SNR (per event)
MASCARA/NITES	>100	$8\times10^{-6}$	—
CHEOPS/Spitzer	200-300	$\sim10^{-7}$	—
ONC-T/Hayabusa2	15	$1.3\times10^{-7}$	8–16

A plausible implication is that small-aperture spacecraft and CubeSats are now viable for monitoring transiting exoplanets, including those on long-period orbits that are otherwise underrepresented.

5. Astrophysical and Observational Implications

The 4σ period discrepancy has several astrophysical ramifications. The ongoing refinement of the MASCARA-1 b ephemeris is essential for planning and interpreting future transit and occultation observations. Drift in predicted mid-times accumulates rapidly (up to several minutes per year), potentially resulting in missed transit observations if not corrected.

The detection of such discrepancy opens discussions about the potential for TTVs—in other systems, such variations can reveal the presence of additional planetary or stellar bodies. For MASCARA-1 b, it remains unclear whether this offset is astrophysical or instrumental in origin. Continuous, multi-instrument monitoring is therefore crucial both for accurate transit prediction and for investigating possible dynamical interactions in the system.

6. Broader Impact on Exoplanet Research Methodologies

The progression in period measurement accuracy, culminating in miniature space-based detection, reflects methodological evolution in exoplanet characterization. Studies highlight the importance of joint, multi-wavelength analyses to resolve parameter degeneracies—particularly in systems transiting fast-rotating, early-type stars where gravity darkening and spin-orbit misalignment complicate modeling.

The successful use of ONC-T suggests similar optical navigation cameras may be deployed on nanosatellites for exoplanet monitoring and ephemeris refinement, supporting more efficient use of flagship telescopes and optimizing transit windows for atmospheric studies.

A plausible implication is that the confirmation of precise periods for planets like MASCARA-1 b will increase detection completeness and promote more systematic investigations of migration and alignment in hot Jupiter populations—key drivers in understanding planetary system evolution.