EUV Doppler Maps: Diagnosing Solar Flows

• EUV Doppler Maps are two-dimensional representations of line-of-sight plasma velocities in the solar atmosphere derived from extreme ultraviolet emission-line spectroscopy.
• They employ rigorous calibration, spectral fitting, and rasterization techniques to accurately capture small- and large-scale flow phenomena such as jets and CMEs.
• The maps enable 3D vector flow reconstructions and provide critical diagnostics for understanding coronal heating, magnetic reconnection, and dynamic solar events.

EUV Doppler maps are two-dimensional representations of plasma flow velocities in the solar atmosphere, constructed from extreme ultraviolet (EUV) emission-line spectroscopy. These maps are foundational diagnostics for quantifying mass motions, heating events, and magnetic reconnection sites in the corona and transition region, enabling precise discrimination of upward (blueshifted) and downward (redshifted) flows on spatial and temporal scales set by the instrument and observing strategy.

1. Principles and Physical Basis

EUV Doppler mapping relies on the measurement of the centroid shift of optically thin emission lines, primarily from iron ions (e.g., Fe VIII–Fe XIV), to infer line-of-sight (LOS) plasma velocities via the standard Doppler formula: $$v = c\,\frac{\lambda_{\text{obs}} - \lambda_0}{\lambda_0}$$ where $c$ is the speed of light, $\lambda_{\text{obs}}$ is the observed centroid, and $\lambda_0$ is the rest wavelength (Yang et al., 2011, Sterling et al., 2 Dec 2025, Kitagawa et al., 2015). Positive velocities indicate redshifts (downflows), while negative values denote blueshifts (upflows).

EUV Doppler maps transcend intensity imaging by isolating bulk motions regardless of line brightness. Multi-wavelength capability allows mapping of flows across a broad temperature range ($0.05-10$ MK), thus providing constraints on the thermal structuring and heating mechanisms in coronal and transition region plasma (Cozzo et al., 17 Jun 2024).

2. Methodologies for Map Construction

The construction of EUV Doppler maps consists of several rigorously calibrated steps:

a) Data Preparation and Calibration:

• Standard procedures involve dark-current subtraction, cosmic-ray interpolation, flat-fielding, and detector-bias correction. Precise rest wavelength determination uses spatial or temporal averaging over quiet-Sun regions or center-to-limb calibration to enforce $v=0$ at the limb (Yang et al., 2011, Kitagawa et al., 2015, Sterling et al., 2 Dec 2025).

b) Spectral Fitting:

• Gaussian (or multi-Gaussian for blends) fits are performed for each spatial pixel and chosen EUV emission line, extracting intensity, centroid, and line width. The centroid yields the LOS velocity, while the observed line width is decomposed into thermal, instrumental, and non-thermal (turbulent) contributions:

$$\xi_{\rm nt} = \sqrt{\Delta V_{\rm obs}^2 - \Delta V_{\rm th}^2 - w_{\rm inst}^2}$$

with thermal and instrumental broadening subtracted in quadrature (Yang et al., 2011, Chan et al., 19 Apr 2024, Cozzo et al., 17 Jun 2024).

c) Rasterization:

• The spectrometer slit is scanned over the FOV, with exposures at each positional increment (e.g., $2''$ steps, $5$–$20$ s exposures) to build a 2D velocity array $v(x, y)$. Advanced systems using multiple slits or simultaneous full-disk coverage accelerate this process and minimize temporal smearing (Chan et al., 19 Apr 2024).

3. Instrumentation and Observational Platforms

EUV Doppler mapping has been implemented using:

• Hinode/EIS: Single-slit rastering with high spectral resolution ($\Delta\lambda \sim 0.06$ Å), enabling velocity accuracies of $\sim3$ km s$^{-1}$ over a wide wavelength range (Yang et al., 2011, Kitagawa et al., 2015, Sterling et al., 2 Dec 2025).
• Multi-slit Spectrographs: A five-slit configuration spanning 184–197 Å realizes full-disk ($2400''\times2400''$) maps with $4''$–$8''$ spatial resolution in $\sim 5$ min, relying on numerical decomposition algorithms to disambiguate overlapping spectra (Chan et al., 19 Apr 2024).
• MUSE (upcoming): Designed for rapid, simultaneous multi-wavelength imaging spectroscopy, with $0.17''\times 0.4''$ spatial sampling and cadence of $12$ s, tuned for Fe IX 171 Å, Fe XV 284 Å, and Fe XIX 108 Å (Cozzo et al., 17 Jun 2024).
• Stereoscopic Platforms: Solar Orbiter/SPICE and coordinated Hinode or IRIS observations enable 3D vector reconstruction using LOS Doppler shifts from widely separated vantage points (Podladchikova et al., 2021).

Instrument	Spatial Res.	Spectral Res.	Coverage/Mode
Hinode/EIS	$1''$–$2''$	0.06 Å ($\sim90$ km/s)	Raster, small FOV
5-slit (Chan+24)	$4''$ ($8''$ eff.)	0.1 Å	Full-disk, $\sim5$ min cadence
MUSE	$0.17''\times0.4''$	10–15 km/s (FWHM)	Fast raster imaging
SPICE	$4''$	0.04–0.07 Å	Raster, moderate FOV

4. Diagnostics and Interpretive Applications

EUV Doppler maps reveal:

a) Small-Scale and Large-Scale Flows:

• Recurring active-region jets exhibit elongated blueshifted outflows and compact redshifted footpoints, with $v$(Fe XII 195 Å) spanning $-25$ to $-121$ km s$^{-1}$ (spires) and $+11$ to $+38$ km s$^{-1}$ (bases). He II 256 Å reveals even larger blueshifts up to $-232$ km s$^{-1}$ (Yang et al., 2011).
• Full-disk maps resolve coronal mass ejections (CMEs) and flaring cores with blueshift ranges to $-100$ km s$^{-1}$, surrounded by redshifted envelopes (Chan et al., 19 Apr 2024).

b) Non-Thermal Motions:

• Non-thermal velocities extracted from line-width analysis reach $181$ km s$^{-1}$ (Fe XII, jet spires) and $399$ km s$^{-1}$ (He II, spires), diagnosing turbulence, unresolved flows, and reconnection-driven motions (Yang et al., 2011, Cozzo et al., 17 Jun 2024).

c) Sensitivity to Subtle Phenomena:

• EUV Doppler mapping detects "dark jets": high-speed ($\sim200$ km s$^{-1}$) Doppler shifts from jets that remain undetected in direct EUV images, highlighting the method's superior sensitivity to faint and rapid mass flows (Sterling et al., 2 Dec 2025).

d) Thermodynamic Structuring:

• Temperature dependence of bulk flows: averaged Doppler velocity at jet bases decreases as maximum ionization temperature increases, constraining the altitude and type of reconnection site (Yang et al., 2011, Kitagawa et al., 2015).

5. 3D Vector Velocity Mapping and Stereoscopy

The combination of multiple LOS Doppler maps enables 3D velocity vector reconstruction in coronal loops:

• Stereoscopic techniques use simultaneous or temporally separated observations from spatially separated spacecraft (e.g., Solar Orbiter, Hinode/EIS, IRIS). For a feature identified in both images, LOS velocities $v_1$, $v_2$ are mapped with knowledge of respective viewing geometries to recover the flow vector $V_{3D}$ via analytical geometry in the local epipolar plane (Podladchikova et al., 2021).
• Deprojections onto loop directions utilize tie-pointing of loops in co-aligned EUV images, constraining flows to modeled field directions (straight/open or circular/closed). Resulting $|V_{3D}|$ values quantitate true plasma speeds and directions in complex magnetic topologies.

6. Calibration, Validation, and Accuracy

Rigorous wavelength and velocity calibration is paramount:

• Reference-wavelength determination demands quiet-Sun or limb fitting, imposing $v=0$ at the limb or at known rest regions (Yang et al., 2011, Kitagawa et al., 2015, Sterling et al., 2 Dec 2025).
• Instrumental drifts, temperature-induced shifts, and slit tilts are corrected by polynomial fitting or software routines (e.g., SolarSoft's "eis_tilt_correction", "eis_orbit_spline").
• Error budgets account for formal fitting uncertainties ($\sim3$ km s$^{-1}$ for Hinode/EIS Fe XII 195 Å), calibration systematics ($<5$ km s$^{-1}$), and S/N-driven thresholds. Full-disk inversions using sparse Lasso regularization yield typical velocity uncertainties $\lesssim5$ km s$^{-1}$ in strong signal regions (Chan et al., 19 Apr 2024, Kitagawa et al., 2015).

Validation against numerical MHD forward models demonstrates root-mean-square velocity differences $\lesssim5$ km s$^{-1}$ for S/N(Fe XII 195 Å)$>20$ (Chan et al., 19 Apr 2024). Stereoscopic reconstruction propagates pixel, tie-point, and orientation uncertainties analytically (Podladchikova et al., 2021).

7. Scientific Impact and Future Developments

EUV Doppler mapping is critical for:

• Determining the locations, velocities, and turbulence of jets and eruptions, including sub-EUV-threshold ("dark") jets contributing to solar wind mass and energy (Sterling et al., 2 Dec 2025).
• Tracing coronal heating and energy-release scenarios (e.g., nanoflare storms, current sheet dissipation), with specific signatures such as footpoint evaporation (Fe IX upflows of $50$–$100$ km s$^{-1}$) and fast localized events (Fe XIX flashes to $100$ km s$^{-1}$) (Cozzo et al., 17 Jun 2024).
• Calibrating theoretical models via the observed v–T dependence, bulk flows, and non-thermal widths, challenging MHD simulations where observed blueshifts exceed model predictions in the $1$–$2$ MK range (Kitagawa et al., 2015, Cozzo et al., 17 Jun 2024).
• Enabling time-dependent and stereoscopic 3D velocity reconstructions, unlocking vector flow measurements and dynamic analyses impossible with single-slit raster scans alone (Podladchikova et al., 2021).

Advances in multi-slit, wide-field, and high-cadence spectroscopic missions are expected to further increase spatial/temporal resolution, sensitivity, and 3D flow diagnostic capability, solidifying EUV Doppler mapping as a cornerstone of solar atmospheric plasma diagnostics.