# Evolution of Spin, Orbital, and Superorbital Modulations of 4U 0114+650

## TL;DR

This study systematically analyzes the complex spin, orbital, and superorbital modulations of the high-mass X-ray binary 4U 0114+650, revealing dynamic spin behavior, variable superorbital modulation linked to accretion disk presence, and stable orbital period with changing profiles.

## Contribution

It provides the first detailed analysis of the long-term modulation evolution in 4U 0114+650, highlighting the connection between superorbital modulation and accretion disk dynamics.

## Key findings

- Spin period varies dramatically and anti-correlates with X-ray flux.
- Presence of two ~1000-day spin-down epochs linked to accretion disk absence.
- Orbital period remains stable, but orbital profile varies significantly.

## Abstract

We report a systematic analysis of the spin, orbital, and superorbital modulations of 4U 0114+650, a high-mass X-ray binary consists of one of the slowest spinning neutron stars. Utilizing the dynamic power spectrum, we found that the spin period varied dramatically and anti-correlated with the long-term X-ray flux variation that can be observed using RXTE ASM, Swift BAT, and MAXI. The spin-up rate over the entire dataset is consistent with previously reported values; however, the local spin-up rate is considerably higher. The corresponding local spin-up timescale is comparable to the local spin-up rate of OAO 1657-415, indicating that 4U 0114+650 could also have a transient disk. Moreover, the spin period evolution shows two ~1000-day spin-down/random-walk epochs that appeared together with depressions of the superorbital modulation amplitude. This implies that the superorbital modulation was closely related to the presence of the accretion disk, which is not favored in the spin-down/random-walk epochs because the accretion is dominated by the direct wind accretion.The orbital period is stable during the entire time span; however, the orbital profile changes with time significantly. We found that the depth of the dip near the inferior conjunction of the companion is highly variable, which disfavors the eclipsing scenario. Moreover, the dip was less obvious during the spin-down/random-walk epochs, indicating its correlation with the accretion disk. Further monitoring in both X-ray and optical bands could reveal the establishment of the accretion disk in this system.