The solar-like latitudinal distribution of flaring activities revealed by TESS, APOGEE and GALAH

Abstract

Flare flux reflect contribution from active regions rather than the whole hemisphere of a star. Unlike the amplitude of light-curves caused by starspots, the flare detection is independent of inclination. The two valuable properties of flares can be used to reveal the latitudinal distribution of active regions (LaDAR) given that LaDAR is coupled with inclination and location information in spatially unresolved stars. We detected $\sim 27000$ flares of 1510 flaring stars in the TESS mission with the corresponding inclinations obtained. The detection rate of flaring stars shows that flares are hard to detect on stars with low inclination, indicating that flares occur mainly at low latitudes. Further investigation of the relationship between the apparent flaring activity and inclination along with the rotation period finds that as the rotation period increases from a solar-like rotation to an ultra-fast rotation, the mean latitude of active regions increases from $θ\approx 15^{\circ}$ to $θ\approx 27^{\circ}$, whose trend is in line with the rotation--activity relationship. The LaDAR indicates that flares are attributed to small-scale fields that are formed at low latitudes, while polar spots that are associated with large-scale fields are inactive and are difficult to trigger flares.

Figures (16)

• Figure 1: Top panel: the rotation--flaring activity relationship is shown, which is separated into four regions according to the CgIW scenario. The C region is shown is a log--log plane for clarity, and the other regions are shown in a linear--log plane. The $x$ axis is the Rossby number (Ro; the ratio of the rotation period to the global convective turnover time). The vertical lines are Ro = 0.022, 0.15 and 0.70, respectively. The shapes of symbols refer to the following star types: circle = dwarf; triangle = binary; and five-pointed star = subgiant. The Sun is marked as an $\odot$ symbol. Bottom panel: the Same as the top panel, but is shown in a log--log plane for the whole sample.
• Figure 2: The detection rates of flaring stars along with inclination in the C, g, and I phases. The detection rate is the ratio between the number of flaring stars and the number of rotating stars in a sin$i$ bin. Error bars of each sin$i$ bin were estimated using a square root of the number of flaring star in each bin.
• Figure 3: Inclination sin$i$ vs. the flaring activity in different Ro bins. The size of the circle represents the flaring frequency of a star. The green dashed line represents the best match of the stellar LaDAR. The shaded region represents the uncertainty caused by the maximum and minimum of the solar cycle. The uncertainty of log$R_{\rm flare}$ is 0.26 dex that is from the error propagation of the flare energy. The uncertainty of sin$i$ is from 16th and 84th percentiles of the posterior probability distribution of sin$i$.
• Figure 4: Rossby number vs. the mean latitude of active regions. Each black point represents the best match between the observation and the simulated LaDAR in a Ro bin (the green dashed line in Figure \ref{['fig_sini_fa']}). The blue point is obtained by the upper envelope of the sin$i$--flaring activity relationship in Figure \ref{['fig_sini_fa_ext']}. The Sun is marked with an $\odot$ symbol. The uncertainty of the mean latitude is $\pm 7^\circ$ that is the same as the Sun. The uncertainty of Ro represents the range of each Ro bin used to fit the sin$i$--flaring activity relationship.
• Figure 5: Top panel: the rotation--flaring activity relationship of 26 stars that have the TESS observations and (Z)DI measurements. The symbol of circle represents stars that are found to be high-latitude by the (Z)DI. The symbol of square represents stars that are found to be without high-latitude spots by the (Z)DI. Stars without detectable flares are plotted with downward arrows. Bottom panel: same as Figure \ref{['fig_ro_ladar']} but for stars in the top panel. The green and blue dashed line denote the solar-like and polar latitudinal distribution, respectively.