Marginally stable nuclear burning triggered at different depths of the neutron star surface in Low-mass X-ray binary 4U 1608-52

Abstract

We investigated the timing and spectral properties of the millihertz quasi-periodic oscillations (mHz QPOs) in the neutron-star low-mass X-ray binary 4U 1608-52 using NICER observations. Our analysis reveals a correlation between the QPO frequency and its absolute amplitude, as well as between the frequency and the temperature of the burning layer. Intensity-resolved spectral analysis indicates that the flux modulation of the mHz QPOs is primarily caused by the variations in the blackbody temperature in most observations. Furthermore, for the first time, we report that as the source evolves from the soft spectral state toward the transitional state, the marginally stable burning responsible for the mHz QPOs ignites at deeper layers of the neutron-star surface. The radiation flux associated with the mHz QPOs shows a decreasing trend as the source moves into the transitional state. These two findings support a scenario in which the marginally stable nuclear burning ignites at deeper layers as the temperature decreases, releasing less energy from the nuclear reaction. Finally, we determine that the energy release rate of the marginally stable burning is around 10$^{35}$ erg/s, consistent with the theoretical predictions.

Figures (9)

• Figure 1: The light curve (top) and the Lomb-Scargle periodogram (bottom) of the data set spanning the time interval 0-839 s in Obs 3657025701 with the mHz QPO. We oversampled the frequency by a factor of 100, and marked the 3$\sigma$ significance detection level with a red horizontal dashed line.
• Figure 2: Folded mHz QPO profile in the time interval 22238-23194 s of observation 0050070103. The red and green dashed horizontal lines mark the 2/3 and 1/3 peak photon flux level, which divide the profile into the peak stage (red shadow region), the bottom stage (green shadow region) and the middle stage (the rest). We plot $\sim$1.4 cycles to show the shape of the QPO profile clearly in the plot.
• Figure 3: Long-term 1-day MAXI (top) and Swift-BAT (bottom) light curve of 4U 1608--52. We mark the NICER observations with mHz QPOs in the figure: most of them are indicated with vertical red dashed lines, while Obs 1050070101 (MJD $\sim$ 58022) is marked with a green line, as it is the only detection occurring outside outbursts. For clarity, Obs 8050070103 (MJD $\sim$ 60756) is not shown.
• Figure 4: Hardness-Intensity diagram (HID) of 4U 1608--52 using NICER observations. Each gray point in the plot represents a single NICER observation used in this work, and observations with the mHz QPOs are marked with different symbols. Observations with a QPO time less than 1500 s are marked with green crosses.
• Figure 5: QPO fractional rms amplitude (left) and QPO absolute amplitude (right) vs. frequency of the mHz QPOs in 4U 1608--52. The red dashed lines in the plot correspond to the best-fitting power-law model to the data. All errors in the plots are at the 68% confidence level.