A. Prasad^1,2,3, M. Ranganathan^4,5 , C. Beck⁶ , D. P. Choudhary⁴, and Q. Hu^3,7

1. Rosseland Centre for Solar Physics, University of Oslo, Postboks 1029 Blindern, 0315 Oslo, Norway
2. Institute of Theoretical Astrophysics, University of Oslo, Postboks 1029 Blindern, 0315 Oslo, Norway
3. Center for Space Plasma & Aeronomic Research, The University of Alabama in Huntsville, Huntsville, AL 35899, USA
4. Department of Physics & Astronomy, California State University, Northridge, CA 91330-8268, USA
5. Institute for Particle and Astrophysics, ETH, 8049 Zürich, Switzerland
6. National Solar Observatory (NSO), 3665 Discovery Drive, Boulder, CO 80303, USA
7. Department of Space Science, The University of Alabama in Huntsville, Huntsville, AL 35899, USA

Context: The inverse Evershed flow ^[1] (IEF) is an inflow toward sunspots at chromospheric heights observed as blue/red shift on the limb/center side, which transports materials into sunspots along magnetic field lines (MFLs) that connect the boundary of the moat cell with the outer penumbra.
Aim: In Ref. [2], we combined high-resolution observations of active region (AR) NOAA 12418 on 2015 September 16 from the Dunn Solar Telescope and vector magnetic field measurements from the Helioseismic and Magnetic Imager (HMI) to determine the driver of the IEF.

Figure 1| Magnetic field topology of AR 12418 on 16 September 2015 at 14:48 UT obtained from NFFF extrapolations. Left column: (a) MFLs in the full extrapolation domain with the vertical component of the magnetic field (B_z) overlaid at the bottom boundary, (b) MFLs originating in the sunspot with (B_z), and (c) MFLs overlaid on an Atmospheric Imaging Assembly (AIA) 304 Å image. The black square in panel (b) indicates the area of the seed points for the identification of closed MFLs. Right column: Closed MFLs around the sunspot with the background images showing (d) B_z, (e) the Hα continuum intensity, (f) and the Hα LOS velocity.

Methods: To understand the physics of the IEF, it is necessary to identify the inner and outer foot points (FPs) of the flow channels derived from the chromospheric line-of-sight (LOS) velocities from spectra of Hα and Ca II IR. Here we use the non force-free field (NFFF) extrapolation technique^[3] to retrieve the magnetic connectivity and loop topology associated with the IEF. We selected 19000 closed loops with heights below 7 Mm by an automated procedure, and calculated various physical parameters like pressure (p), magnetic field strength (B), temperature (T) and the photospheric/chromospheric velocities (v) at the inner and outer FPs (Figure 1).

Figure 2| Left column: (a) Top and (b) side view showing properties of MFLs with different ΔB overlaid on B_z. Middle column: (c) Inner and outer FPs for the same ranges in ΔB. (d) Scatter plot of ΔB and 3D loop length. Right column: Scatter plots of (e) ΔB, (f) ΔT and (g) Δp against flow velocities. The green lines show the predicted velocity from the field strength difference for HSRA gas densities at optical depths of log τ = −0.3, −1, and −2. The orange lines in panel (f) show the flow speed predicted by the temperature difference.

Results: We found that the magnetic field lines related to the IEF reach on average a height of 3 Mm over a length of 13 Mm. Their inner (outer) foot points are located at 1.2 (1.9) sunspot radii (Figure 2a-b). The average magnetic field strength difference (ΔB) between inner and outer foot points is around +400 G and shows a strong correlation with the loop length (Figure 2d-e). The temperature difference (ΔT) is anti-correlated with ΔB with an average value of -100 K (Figure 2f). The pressure difference between inner and outer FPs (Δp) is dominated by ΔB and is primarily positive with a driving force toward the inner foot points of 1.7 kPa on average (Figure 2g). The velocities predicted from Δp reproduce the LOS velocities of 2-10 km s^-1 with a square-root dependence (Figure 2g). The comparison of the predicted flow velocities from ΔB (green; for 3 different densities (ρ), ΔT (orange) and Δp (green) with the observed Hα LOS velocities in Figure 2(e-f) shows that the square-root dependence expected from magnetic pressure balance, , is matched but the flow speed is slightly off.

Figure 3| Left column: 3D view of MFLs connecting the sunspot to an opposite-polarity patch on top of (a) the continuum intensity Ic, (b) B_z, and (c) the Ca II IR LOS velocity. Right column: different quantities averaged over the MFLs in the left column as a function of the relative length L. (d) Temperature (blue) and height (red). (e) LOS magnetic flux (Φ_LOS ) (green), B_z (blue) and field strength B (red). (f) LOS velocities of HMI (green), CaII IR (blue), and Hα (red).

Conclusions: We find that the IEF is driven along magnetic field lines connecting network elements with the outer penumbra by a gas pressure difference that results from a difference in field strength as predicted by the classical siphon flow scenario^[4]. Using a combination of high-resolution data and NFFF magnetic extrapolations, we investigated the connectivity of IEF channels that connect the outer penumbra with opposite polarity magnetic elements in the moat (Figure 3a-c). Moving outwards from the sunspot along the closed magnetic loops, we find an increase in T (Figure 3d), a decrease in B (Figure 3e), and a change of flow direction from down flow to up flow (Figure 3f). We conclude that the conditions for a siphon flow are fulfilled (ΔB > 0). The observed velocities have the order of magnitude predicted by the pressure balance equation.

References

[1] Maltby, P. 1975, Sol. Phys., 43, 91
[2] Prasad, A., Ranganathan, M., Beck, C., Choudhary, D. P., & Hu, Q., 2022, A&A, 662, A25
[3] Hu, Q., Dasgupta, B., Derosa, M. L., Büchner, J., & Gary, G. A. 2010, J. Atmos. Sol. Terr. Phys., 72, 219
[4] Thomas, J. H. 1988, ApJ, 333, 407