Solar Wind Velocities at Comets C/2011 L4 Pan‐STARRS and C/2013 R1 Lovejoy Derived Using a New Image Analysis Technique

The ion tails of bright comets have long been considered as a natural tracers of the solar wind (SW) near these objects. Studies of comets and their ion tails allow inexpensive monitoring of key SW structures in the inner heliosphere, much of which is otherwise only accessible by in situ SW spacecraft measurements. Here, we present a novel technique to mine the rich archive of amateur, professional and spacecraft observations of cometary ion tails. To demonstrate this, we focus on Near‐Sun comet C/2011 L4 (Pan‐STARRS) during Carrington Rotations (CR) 2134 and 2135 and comet C/2013 R1 (Lovejoy) during CR 2118. We outline the technique’s shortcomings, including its geometric limitations, and present a catalog of radial SW velocities derived in the near‐comet environment and information on the heliospheric conditions inferred from the measured SW. Complementary measurements, derived from folding ion rays and a velocity profile map built from consecutive images, are provided as an alternative means of quantifying the SW ‐cometary ionosphere interaction. We find that comets are generally good indicators of SW structure, but the quality of the results is strongly dependent on the observing geometry.

. Illustration of comet-solar wind (SW) paradigm. (Adapted from Brandt & Snow (2000). Smooth, fast SW flow at high solar latitudes lead to largely featureless ion tails. Comets in the solar equatorial region encounter slower and more variable streamer belt flow which have been associated with highly dynamical and variable ion tails which can contain both large-scale and fine structures. Image credit: Courtesy of Gerald Rhemann and NASA/SDO and the AIA, EVE, and HMI science teams).

Isaac Newton Telescope/Wide-Field Camera
The Isaac Newton Telescope (INT) is a 2.5 m optical telescope located at the Roque de los Muchachos, La Palma, Spain. The facility's Wide Field Camera (WFC) is a 4 CCD mosaic covering a 34ʹ × 34ʹ field of view with a chip gap of ∼0.5ʹ. Each CCD pixel corresponds to 0.33ʺ on sky. Y. Ramanjooloo along with K. Birkett, used the WFC to observe comet C/2013 R1 (Lovejoy) using standard broadband photometric filters Sloan R and Harris B (York et al., 2000) from 02 January 2014 to 06 January 2014.

CME Catalog
The CME catalog used here is generated and maintained at the CDAW Data Center by NASA and The Catholic University of America in cooperation with the Naval Research Laboratory (Gopalswamy et al., 2009). The catalog lists all transient ICME events from the SOHO LASCO C2 and C3 coronagraphs (Brueckner et al., 1995). The central position angle (CPA) can be useful in distinguishing between simultaneously occurring ICMEs. This is measured counter-clockwise from solar north in degrees. Once the ICME expansion stabilizes in the C2 FOV, a sky-plane width is measured, when possible. Infrequently, certain ICMEs will exhibit significant acceleration or deceleration, thus reducing the linear speed to merely a guide of the average ICME speed within the LASCO FOV. Combining the date and time of ICME eruption, its linear plane-of-sky speed, width and CPA with the heliocentric distance of our comet and the angle with the solar north pole, we can constrain a list of ICME candidates likely to encounter the comet for a given date.

Technique
An ion tail is always generally oriented in the anti-sunward direction; however it always lags the true anti-solar direction by a few degrees, opposing the direction of the comet's motion. It is well established that SW conditions control and maintain the appearance of the ion tail and that the tail axis is a composite vector of the v sw vector and the comet's orbital motion. An extended ion tail records a time history of SW changes over several hours.
Remote observations of the ion tail are a potentially invaluable resource to probe the high spatial variations of SW structures across a wide range of heliospheric latitudes and distances and over long timescales. We have developed a novel system of extracting valid local estimates, as well as characterizing local parameters for transient interplanetary events near comets, allowing us to use comets as SW monitors within the inner heliosphere. To demonstrate this technique, we investigate amateur images of bright comets with a small geocentric distance and good observing geometry from Earth. By employing measurements from amateur and professionally acquired images, we demonstrate that comet observations can provide reliable estimates of the ambient local v sw at the comet and can lead to the identification of the local parameters of CMEs, the locations of HCS crossings, as well as the locations of CIRs during periods of quiescent solar activity.
When the projected observing geometry is good, that is, when the angle between the Sun, target and the observer (S-T-O angle) is close to 90°, and that the observer is well outside the comet's orbital plane, that is, at a "large enough" orbit plane angle, we can constrain the v sw ( Figure 2). The ideal geometry for comet observations from Earth would occur when the S-T-O angle and orbit plane angle are both near 90°.
The dynamical variations of and plasma density distribution along the tail are controlled by the mass-loading process. Ever-changing, extensive features in the tail such as condensation knots and kinks generally indicate the flow state of the SW, whether the comet is surrounded by quiescent fast SW or traversing a more variable SW flow. Kinks in the tail are often clues that the comet may be moving from one SW regime to another.

Deriving SW Velocities
The ion tail orientation can be exploited to pin down an approximation of the local radial flow of the SW. The aberration angle, ϵ, is defined as the angle between two vectors: the composite vector of the comet's heliocentric orbital motion vector and the SW velocity vector, and the prolonged radius vector from the sun, that is, the radial flow of the SW (Figure 3a). Figure 3 illustrates the slight difference between the two techniques of determining the SW velocities, using a non-study comet as an example. The first technique uses the aberration angle to determine the SW velocity. The second technique is the technique we will present in this paper. The orientation of the ion tail arises from the combination of the comet's orbital velocity and the local SW velocity (Biermann, 1957;Hoffmeister, 1943). The composite vector equation is given by: is the apparent axial vector of the ion tail, is the SW velocity vector, and is the comet's orbital velocity vector. In the top image, it is possible to measure the aberration angle of the ion tail on the plane of the sky. By projecting these vectors onto the comet's orbital plane, as described in Konopleva and Rozenbush (1974), an expression for the aberration angle can be defined. The vector can in principle be resolved into its radial (V r ) and tangential (V ϕ ) components. However, this is challenging as a larger tangential component cannot always be uniquely separated from a radial SW speed change. Rearranging the equation for V r , we obtain: = sin − cosi tan + cos (2) γ is defined as the angle between the extended radial vector of the comet and the vector of the comet's orbital velocity, i is the inclination of the comet's orbital plane to the solar equator, and ϵ is the aberration angle.
In our technique, the images are instead extrapolated along the line-of-sight of the observer and mapped onto the comet's orbital plane; the SW flow is assumed to be purely radial. Once the image is mapped onto the comet's orbit a simplified geometry of the system can be extracted. The aberration angle ϵ can thus be simplified to the equation below, where U ⊥ is the perpendicular component of the comet's velocity to the prolonged radius vector and V r is the radial SW velocity. The radial component of the orbital velocity, and the non-radial components of the SW are both assumed to be negligible here.
The bottom image in Figure 3 encapsulates the adopted sampling method. With cometocentric distances calculated for the image, multiple cuts, shown in red, are taken parallel to the radial vector with set time steps. SW velocities are then calculated from these known quantities. Since each image is projected onto the comet's orbital plane, the best framework to estimate the local SW radial velocity, which we now refer to as for the demonstration of our technique. All the previous considerations ( , i and γ) are factored in within the projection mapping. We also computed V r using the simplified equation for the aberration angle. They both produced SW velocities within the same range, with some erroneous values produced for very small aberration angles, for instances where the ion tail lies close to the extended radial vector. Even under excellent geometrical conditions, without mapping the image onto the comet's orbital plane, precisely measuring the aberration angle can be difficult as the comet's orbital velocity is generally an order of magnitude smaller than the SW velocity (Brandt & Heise, 1970).

Developing the Software
The pointing, field of view, plate scale, and orientation of comet images are essential in order to derive estimates of the SW conditions in a comet's vicinity. These are frequently unknown for amateur observations. Using Astrometry.net source code V0.50 (Lang et al., 2010) has greatly simplified the acquisition of this information, by returning the requisite information almost instantaneously. This robust astronomical image solver computes the equatorial celestial coordinates of each pixel in the original comet images. Hogg and Lang (2008) reported the success rate of Astrometry.net to be >99.9% for contemporary near-ultraviolet and visual imaging survey data, with no false positives. The orbit (red), the extended solar radial vector (black), and the aberration angle (red angle) are labeled in (a). In (b), the image has been transformed so as to keep the sun-comet line fixed with the predicted comet nucleus location as the origin. The horizontal sun-comet line (black) in the second image is the extended radial vector from the sun. The comet's orbit is the red vertical line. The horizontal red lines are extended solar radial vectors originating from where the comet's nucleus would have been at that time. These radial vector cross-sections of the ion tail provide an indication of the distance traveled by each plasma bundle from the comet's orbit to the ion tail.

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Each comet's ephemeris was downloaded from JPL Horizons (Giorgini et al., 1996) in the geocentric equatorial and heliocentric ecliptic coordinate systems (epoch J2000.0). The heliocentric coordinates of the observer's orbit (for this study, the geocenter or STEREO spacecraft) are also downloaded.
The ground-based observations used here were obtained from locations all around the globe. It is not always obvious which time zones were used when the images are made available in online repositories. Moreover, the timing metadata, when provided, was not always accurate nor precise. As an accurate astrometric solution was obtained for the images, an approximate observing time was independently deduced from the comet's orbit; this helped to identify and correct erroneous times. We estimate the percentage of successful solves through this procedure to be >95% after processing over 500 images. Once a time and date of observation for the image has been estimated, each image was converted from celestial coordinates to heliocentric ecliptic longitudes and latitudes, and then to heliocentric ecliptic Cartesian coordinates, as described below.
From the ascending node and inclination of the comet's orbital plane (Figure 4), we define the normal of the comet's orbital plane, . The image and orbit coordinates are converted to ecliptic Cartesian coordinates. The magnitude of the vector to each pixel from Earth, l, is computed from the position of Earth at the time of image exposure and the normal to the comet's orbital plane (Equation 4). Each pixel vector is translated to a new frame of reference using the Sun as origin and accounting for light-travel time.

=
(4) l is the scalar length of the vector of each pixel in the image from Earth. The magnitudes of and are unknown, so a unit vector is assumed for both. is the unit vector to each image pixel from Earth and is the vector from the Sun to the Earth.
The final section of the software computes the vector product of the perihelion vector and the vector perpendicular to the comet's orbital plane to define the x and z axes of a new coordinate system based on the comet's orbital plane. Every object in the previous system is mapped with respect to the comet's plane. The multiple transformations are needed as the comet's orbital plane provides the best framework for estimating v sw .
Each individual image is plotted with its comet's "nucleus" defined as the origin of the frame of reference and the comet's orbit is rotated so that the Sun is always to the left of the image, and the Sun-nucleus line is horizontal. Note that the optocenter (optical center) is not necessarily the true location of the nucleus. The brightness of the coma and only having access to post-processed images online often make it impossible to resolve the comet's nucleus via direct imaging of the comet from Earth. The radius vector from the Sun to the "nucleus" is extended across the image and defines the x-axis. The z-axis is defined as the normal to the comet's orbital plane.
The ion tail center at any position lagging the comet's orbit is set as the point where the extended radial vector intersects the ion tail. Assuming that the SW is always flowing radially, the center of the tail downstream of any position along the orbit that the nucleus has already passed, provides the when the comet was at that orbit location. Rather than regarding the ion tail as a continuous flow of material, for the benefit of simplification of the necessary coding, we instead consider the tail as a set of numerous discrete plasma "packets" flowing radially away from the Sun at the local v sw . By taking multiple cross-sections across the ion tail along the radial anti-sunward direction, we extract multiple velocities across the image along the extended radial vector from the Sun.
We could not automate identification of the ion tail center due to the low relative surface brightness of the tail with respect to the surrounding sky background. An interactive color stretching function with a Graphical User Interface was incorporated into the software. The user can define and store a new color palette for each image to accentuate features of interest. The user then selects the area intersecting the extended radial vector and the ion tail (where the red radial vector overlaps the ion tail in Figure 3), from which a tail center and an uncertainty of ±1/6 of the ion tail coincident with the radial vector were determined. Measurements of the tail center were generally taken from 1 × 10 6 km onwards, as the edges of the ion tail closest to the nucleus merge with light from the coma and dust tail, making the various components difficult to separate. The local is estimated from the distance traveled by the plasma packet, from the position where it left the comet's orbit to the ion tail center, divided by the time difference between the comet's current position in the image and its position when the plasma packet left the vicinity of the comet "nucleus."

Tracking Fast Moving Sub-Structures
An alternative method of quantifying the v sw is to visually track dominant features in consecutive images. These include identifiable kinks, condensation knots, or disconnections. Flow vector maps (hereafter vector maps) are not new in the study of cometary features (e.g., Rauer & Jockers, 1990;Yagi et al., 2015). The criteria employed for the collection of amateur data for this purpose is that the images had to be observed during the same observing night, regardless of location, and with an adequate time separation in between to ensure that we are looking at the same evolving structure and to compensate slightly for errors in the image time.

Tracking of Tail Rays
Tail rays, or tail streamers when within the main ion tail, form much of the fine-scale structure of the ion tail. Typical tail ray lengths are on the order of ∼10 6 km (Minami & White, 1986) with radii ∼2,000-4,000 km (Brandt & Chapman, 2004). Consecutive photographic evidence of tail rays folding around the main tail axis suggests that the ionized plasma can be considered as magnetic tracers of the Heliospheric Magnetic Field (HMF) as it drapes around the comet's nucleus (Moore, 1991;Watanabe, 1991).
To study the motion of features, we overlaid consecutive images and measured the radial velocity shear across the tail ray as it folded. We assumed a simple model of symmetrical pairs of folding rays acting as tracers of the massloaded draped HMF and that measurements of the rays' angular closing rates can reliably constrain the velocity of the mass-loaded SW. If multiple rays were visible in consecutive images, we derived an acceleration of the v sw near the comet head. We expect that as the tail rays curve and lengthen, as they merge with existing plasma along the main tail axis, measurements taken near the nucleus will yield slower velocities than further down the tail streamer. This technique is limited to the region close to the nucleus, ∼1 × 10 5 -1 × 10 6 km and requires an adequate spatial and temporal resolution.
In contrast to previous studies, we did not calculate the angular closing rates of the tail rays. Schlosser (1967) reported 120-170 km s −1 for comet C/1908 R1 (Morehouse). Watanabe (1991) measured the mass-loaded SW and reported 20% lower velocity for comet 23P/Brorsen-Metcalf than v sw derived by radio scintillation. Moore (1991) developed a fairly similar technique to ours but did not project the images onto the plane of the sky at the comet. The tail rays were then measured as they folded about the main tail axis, though no attempts were made at producing a v sw . It can be argued that Moore's approach is safer, since we do not know of any evidence showing that the tail rays are constrained to the comet's orbital plane.

Uncertainties
The vector map technique suffered from imprecise astrometric mapping. Due to large optocenters, times derived via our software will be slightly limited in precision. The relatively high velocities of the bulk SW and the large FOVs of most images drowned out the timing uncertainty. For the vector maps and tail ray methods, when two consecutive images are considered from different observers, and for small FOVs, this effect becomes considerable as the timing uncertainty will be compounded and cannot be knowingly accounted for. The feature-tracking velocities are calculated from Δr/Δt, where Δr is the distance that the feature has traveled between subsequent images and Δt is the time difference between the two. The error is given by: For the feature tracking, the features were composed of a series of expanding amorphous blobs of varying shapes and sizes and their location is measured by a single position estimated as the feature's center. The error is assumed to be the distance error of the projected pixel vector. The same process was adopted for the tail rays. The error on Δt is given by: The distance error between feature motions in consecutive images can be simplified to the equation below, where σ x and σ y are the pixel distance errors: where 2 Δ ∕ = 2 ∕ 1 + 2 ∕ 2 Vector map analysis was performed on both comets whereas the folding tail rays methodology was only applied to C/2013 R1 for both the amateur and INT observations. A full treatment of the uncertainties is available in the Supporting Information S1.

Orbit Plane Angle and Non-Radial Flows
The orbit plane angle, an important consideration in the comet-Sun-Earth geometry, is the angle between the line of sight from the observer (at Earth) to the comet, and the latter's orbital plane ( Figure 2). A non-zero value indicates that the observer is viewing from a position that is not in the comet's orbital plane. The ideal geometry is when the orbit plane angle is near 90° and the observer is sufficiently far from the comet's orbital plane. Deviations from the ideal geometry will result in an over/under-estimation of the ion tail's true location, which will be dependent solely on the magnitude of the angle and whether the observer is leading or lagging the comet's motion.
The orbit plane angle is equal to zero every 6 months, as the Earth crosses the comet's orbital plane. When the orbit plane angle nears zero, images taken during this period become stretched excessively when mapped onto the comet's orbital plane. The projection mapping technique is a strong function of the orbit plane angle and the distance between the observer and the comet. Extreme scenarios when the observer is far from the comet and the orbit plane angle is low, the pixel vector extrapolation breaks down and results in extremely lengthy vectors stretching out in all directions. Thus, any radial estimates derived from these images would be unreliable and unrealistic. However, we can sometimes resolve the images by zooming in on where the comet's orbit and the Sun-comet line intersect. Figure 5 clearly shows that the mapping technique can sometimes still provide useable results even under these geometric conditions. Images taken during this time period will be recording deviations of the comet along the z-direction, that is, out of the comet's orbital plane. This provides the opportunity to measure the deviation angle of the comet's ion tail from its orbital plane due to the non-radial flow of the SW. Only a small proportion of images can be used for this as demonstrated in Section 4.1.3.1.

Mercator Map
The heliocentric coordinates of each notional plasma packet that reached the comet of interest can be ballistically traced back to its assumed origin at the SW source surface. Its cometocentric coordinates are first converted back into heliographic spherical coordinates (Carrington rotation system). Using the mean sidereal Carrington rotation rate of the sun, we map the plasma back to its source longitudes for possible slow (400 km s −1 ) and fast (800 km s −1 ) approximate speeds at which it left the SW source surface. We assumed typical slow and fast v sw without knowing the true values, and that they remain at this same speed on their path from the Sun to the comet. Figure 6 shows the sources for the notional slow and fast SW. Only the first date and time for a range of plasma packets are plotted for each day. Data points within the black circle represent the first date sampled for this Carrington rotation and the last data points are enclosed by a black square.
The black solid line is the approximate position of the neutral line on the SW source surface as calculated by the Wilcox Solar Observatory research team (Altschuler & Newkirk, 1969;Hoeksema et al., 1991;Schatten et al., 1969). This is a reasonable first-order proxy for the HCS's location. We traced back our measurements to the 2.5 R ⊙ radial solution from the Wilcox observatory.

Integration of SOLARSOFT
High-quality difference images of comet C/2011 L4 (Pan-STARRS) highlighted fainter substructures in the ion tail than our current methodology and were used to produce higher resolution from the images. The Solar- Soft package (http://sohowww.nascom.nasa.gov/solarsoft/), recommended for the data reduction and analysis of the suite of solar instruments available, was integrated to work seamlessly with our software, with both level 1 and 2 (L1 and L2) data from the STEREO Heliospheric Imagers and level 0.5 and level 1 (L0.5 and L1) data from the SOHO LASCO coronagraphs. SOHO L1 data incorporates corrections to photometric calibrations, vignetting, geometric distortion effects, and suppressing stray light (Morrill et al., 2006). STEREO L0 data are the raw, uncalibrated data and L1 contain flat-fielding, alignment and shutterless corrections to the L0 data. L2 data includes the removal of the dust component of the corona-the F corona (Koutchmy & Lamy, 1985)-and is therefore ideal for use. The HI-1 frames are usually 30 min worth of exposures, stacked with 40 min cadences. The error on the observing time is thus taken to be ±15 min.

Data Rejection
The primary reasons for rejecting images were as follows: 1. Image was of poor quality, for example, star trails, saturated image, or incorrect astrometric solutions. 2. Ion tail was too faint to resolve or its edges are poorly defined against the sky background. 3. The image FOV was too large to resolve ion tail. 4. In certain instances, the first measurement was discarded. The proximity of the ion tail to the coma made determining the tail center unreliable. 5. Inaccurate image mapping due to ∼0° orbit plane angle.
Only observations ±2 weeks around its perihelion were analyzed (Ramanjooloo & Jones, 2021b). The set of amateur images were mapped onto the comet's orbital plane with the y-axis defined as the direction to the comet's perihelion ( Figure 7). The comet's orbital plane was inclined by 64°. Amateur images of C/2013 R1 from this period allowed us to probe the inner solar system to intermediate heliographic latitudes from 34°-54°. We obtained 109 estimates from 36 fully processed images out of 123 amateur images with a detectable ion tail. Seven SW estimates did not pass the rejection process and 43 of the remainder are measurements of a sinuous and variable ion tail that were too challenging to interpret with sufficient confidence. The amateur images amassed for this time period were supplemented by our own observations undertaken at the Isaac Newton Telescope in January 2014, presenting a unique opportunity to validate the quality of amateur images using high quality observations from an established scientific observing facility. The comet was at high heliographic latitudes during the INT observations (∼60°).
INT observations were undertaken from 02 January 2014 to 07 January 2014, when the comet was at a heliocentric distance of ∼0.85 and 1.15 AU from Earth. C/2013 R1 was a morning target, limiting observations to 40-60 min. A full list of observations and why they were rejected can be found in Yudish Ramanjooloo's thesis (Ramanjooloo, 2015). Each image consists of four CCD frames. The images were post-processed through a coaddition, dust subtraction, and contrast enhancement pipeline. The result was a set of 11 images showing intricate details of the ion tail's fine structure and the region close to the nucleus. A total of 28 radial velocity estimates were extracted. A total of 19 of these were measured from a dynamic and variable ion tail.
The brightening sky during twilight proved to be a major noise source. For the last few images taken during each night, the signal-to-noise ratio (SNR) was too low to resolve the ion tail. By subtracting the sky contribution from the r filter images, we were able to extract difference images with multiple tail rays and an ion tail fanning out, even in the twilight images. Where feasible, the images were stitched together to create larger mosaics of the coma and ion tail (Figure 8). Multiple pointings were required to image the entire tail. It is important to note that in the time taken for the exposure, image read out, and telescope slew, there was a small angular and positional error between the sections of the ion tail observed due to time elapsed. If the total time between two consecutive images was 2-3 min, this was enough time for the tail dynamics to have also evolved slightly, such that a mosaic of the two images will not be entirely concurrent snapshot. A list of the observations undertaken is given in the Supporting Information S1.
Coadded images were constructed from B and r images taken close to each other in time and reduced using usual flat-fielding techniques to minimize motion blur. Due to short exposure times and the limited number of images in a group, the end results were insensitive to large motion blurs. Figure 8a shows the original coadded CCD images and Figure 8b shows the image following dust continuum subtraction (Wilson et al., 1998). To account for the different pixel locations of the nucleus, each coadded image in a set of difference images was warped using the astrometric parameters of the reference image before mapping onto the comet's orbital plane (Figure 9).
The difference images were chosen for all analysis techniques as they depicted the fine structures more clearly than the calibrated or stacked images. A coadded and dust-subtracted composite image of the nucleus and one of the ion tail, were projected with different observing times onto the comet's orbital plane to create a mosaic stitching image, with the ion tail extending greater than 1°. Different observing times were used to account for the angular and radial motion of the ion tail with respect to the nucleus between exposures. Assuming a SW outflow of 400 km s −1 , the plasma packets in the ion tail would have covered 3.6 × 10 5 km radially. The timing error for each image is assumed to be half of a minute. For the stacked images, the middle image is taken as the observing time so as to retain the correct astrometric parameters associated with that observing time. For the difference images, the WCS coordinates from each stacked B filter image is used and the relevant r images were distorted till they matched the astrometric coordinates of the stacked B image. The distorted r images were subtracted from the B image to remove the dust contribution.

CR2144
From the Mercator map for CR2144 (Figure 10), there is a reasonable expectation for an observed HCS crossing in mid-December, between 12 December 2012 and 13 December 2012. The observer's projected position onto comet C/2013 R1's orbital plane remained low for the first 2 weeks of December 2013, only rising to ∼20° by late December. The orbit plane angle gradually improved, though it remained fairly low, peaking at ∼30° at the end of the observing period in January 2014. The early set of images, taken in CR 2144, will yield apparent velocities uncharacteristic of the SW due to the low orbit plane angle. The orbit plane angle is <10° for the first half of CR 2144 and between 10° and 17° for the second half from 13 December 2013 to 17 December 2013. We further expect the comet to be immersed in a fast SW region from 26 December 2013 to 09 January 2014. Thereafter, the comet should experience slower slow wind speeds as it approached the neutral line.
The time span from 9 December 2013 to 17 December 2013 were observed at low orbit plane angles, producing estimates in the range of 50-200 km s −1 . The dust tail and ion tail completely overlapped for most of this period, thus our measurements in Figure 11 are ineffective indicators of the . Estimates derived from turbulent ion tail images are highlighted in purple with two DEs identified in the images. Figure 12 is one of the best examples of the highly dynamic variations of C/2013 R1's ion tail, with multiple kinks and a DE. The ion tail's orientation varied numerous times and curved back toward the radial vector generally indicating an acceleration of the lagging end of the ion tail. The orbit plane angle remained just below 10° during this time, thus obfuscating the determination of a realistic radial velocity. The structures visible before the near-90° bend in the ion tail direction at ∼5.5 × 10 6 km, seemed to be entrained almost radially when compared with an image by the same observer half an hour later. Simulations generated by the ENLIL 3D time-dependent heliospheric model (e.g., Jian et al., 2015 and references therein) predicted low SW velocities ∼250 km s −1 at the comet with a small latitudinal component ( Figure 13). The non-radial component included a reversal of the velocity vector acting upon the comet, thus explaining the arced tail in Figure 12.
No velocities were extracted during the expected HCS crossing, as the tail at that time was oriented to actually lead the comet's motion, for which no meaningful radial SW speed could be derived. This unusual orientation was presumably due to a significant non-radial component to the local SW. The first image, taken by Rhemann on 12 December 2013 (Figure 14a), showed wave-like ripples down the tail and an asymmetrical collection of tail rays. A subsequent image by Rhemann a day later (Figure 14b) showed an equally dynamic tail, with a large condensation knot in the middle with a sharp angular change. This tail behavior is reminiscent of DEs observed in other comets. The tail was leading the comet motion in both images. ENLIL predicted the comet would encounter opposite HMF polarities ahead of a CIR between 14 December 2013 at 06:00 UT and 16 December 2013 at 00:00 UT.
Images taken by Jäger and Rhemann on 14 December 2013 exhibited a very extensive ion tail with a large aberration angle, extending into a wide, faintly connected set of ion cloud packets. The plasma packets, constituting the ion tail are expected to have departed from the approximate location of the comet's ionized coma around 12 December 2013 at ∼04:00 UT. There is a large kink evident at the point where the ion tail width dramatically increases, suggesting a large HMF orientation change had occurred upstream of the comet. We are likely viewing the ion tail edge-on in the thin section prior to rotation of the ion tail. Large non-radial components are predicted at the time of observation, though this cannot explain the existing ion tail configuration, considering that a low predicted of ∼250 km s −1 would be insufficient to propagate throughout a 1.2 × 10 7 km tail in time.
ENLIL simulations suggested the comet would encounter the leading edge of a CIR on 16 December 2013. The trend is present in our measurements, though velocities on December 16 and 17 are underestimated by ∼200 km s −1 with respect to ENLIL. The discrepancy throughout this CR is most likely the result of projection effects and the ion tail curving away from the radial direction. This larger perceived aberration would produce much lower apparent SW velocities with this technique.
A collection of ICMEs, traveling in the general direction of the comet, and their Shock Arrival Times [SATs] for the periods mentioned previously are shown in Figure 15 and Table 1. The comet's mean position angle was 343° and the position angle of the solar rotation axis was 13°.

CR2145
derived from both the amateur and INT observations are shown in Figure 16. Estimates from turbulent ion tail images are represented as purple dots for amateur images and orange for INT. The range of velocities derived from amateur images is nearly equivalent to the INT images for the period where they both overlap. This fortuitous overlap of observations demonstrates how far consumer technology has come and its benefits to interplanetary heliospheric research.
The data in Figures 16 and 17 suggest that the comet initially encountered slowly decreasing SW velocities. This is supported by ENLIL up to 25 December 2013, though predicted velocities at the comet are ∼100 km s −1 lower. From ENLIL, the comet was expected to encounter flows of opposite magnetic polarity on December 24 and a CIR with large non-radial flow components on December 25. A high contrast enhanced image on December 24 confirmed a HCS crossing within this time frame.   Direct observational evidence of kinks and a DE contradicted the smooth, fast SW outflow predicted at the comet between 26 December 2013 and 28 December 2013. The comet must have either encountered a slow moving disturbed SW, conveniently explaining the decreasing , or the high latitudinal MHD solution is incorrect for this run. The sharp increase in velocity on December 29 likely marked the end of the disturbed SW outflow with velocities at the end matching expected fast SW velocities. The ENLIL fast SW region did not show any velocity gradients.
Observations by Rhemann and Jäger on 03 January 2014 caught the onset of an ICME-related turbulent event, with what seemed like small-scale ion tail variations. These propagated and produced a DE observed 8 hr later in an image by D. Peach. The long, sinuous, disconnected tail was measured traveling radially at ∼450 km s −1 . This was coincident with the INT run where we observed a much closer region of the ion tail. The discrepancy between concurrent results on 03 January 2014 is due to SW measurements extracted from the disconnected ion tail over 1 × 10 7 km versus measurements taken from a newly formed ion tail over 1 × 10 6 km. The comet experienced a decrease in corresponding to a rarefaction region lagging a CIR in the ENLIL model. The velocity samples from both INT and the amateur images are lower than predicted values by ∼200 km s −1 again. The MHD predicted longitudinal velocity component at the comet is ∼20-30 km s −1 .
Images from 06 January 2014 showed a DE related knot moving at ∼40 km s −1 , along and across the tail, and accelerating to ∼150 km s −1 , as measured from knot movement between images. The condensation knot had a of ∼700 km s −1 . There are no CIRs or DEs expected that match our observations, thus this event was likely ICME related. Turbulence in the ion tail persisted until January 07. INT images showed varying tail orientations and a large trackable kink evolving into a DE 0.25 days later (Figure 18). The comet was not expected to have encountered a polarity reversal in the HMF. The ENLIL model shows good agreement for SW velocities on 09 January 2014. For January 10, SW velocities ranged between 250 and 450 km s −1 and were within the predicted 250 km s −1 . There is a slight turbulence and a kink in the ion tail accounting for the range in the velocities reported. There is a small non-radial component to the SW on the 13 January 2014 but this does not account for the large discrepancy in the radial velocity of 150-200 km s −1 between the observed and the predicted lower values.
A list of potential ICME interaction candidates and their expected arrival times at the comet's location is given in Figure 19 and Table 2. Assuming that the fast ICMEs will slow down upon interaction with the solar wind and conversely for slow ICMEs, the unexplained ionic turbulences described for CR 2145 could be explained by interactions with ICMEs.

Low Orbit Plane Angle-Non-Radial Flow
Several observations during CR 2145 were obtained at low orbit plane angles (Ramanjooloo & Jones, 2021c), allowing estimates of the non-radial velocity components (Figure 20). The ion tail overlapped the extended Sun-comet radial vector. Non-radial velocities of ∼45 km s −1 were derived from four images with noticeable deviation from the comet's orbital plane. Figure 15. ICME candidates and their potential interaction with C/2013 R1 and their SATs at the comet. The speed of each ICME is based on its plane-of-sky velocity in coronagraph images. A constant velocity is assumed for each ICME propagation. These interactions may have triggered the unexplained disturbances observed in the comet's ion tail. Interactions (labeled as Int 1-4) marked above are the approximate times at which the images were taken and not the beginning of the interaction of the ion tail the with disturbed SW medium. Each colored line corresponds to a different ICME.

Vector Maps
Non-radial velocity measurements ( Figure 21) were obtained from sequences of images. The velocity profile was observed to increase downtail of the optocenter as expected of an accelerating ion tail to the local radial SW velocity. The first four measurements correspond to two samples from the tracking of a DE and two samples for a large kink in the ion tail. A pair of very slow-moving kinks was tracked, far from the nucleus on 14 December 2013. Measurements were likely impacted by human error due to the large features. A kink was observed to evolve into a slow-moving disconnected tail, with near zero acceleration on 06 January 2014. Bulk radial velocities ranged from 500 to 650 km s −1 . INT observations allowed tracking of a DE knot at short cometocentric distances ∼5 × 10 5 km. The knot accelerated from 40 to 140 km s −1 within minutes. The initial velocities are in the same range as reported by Yagi et al. (2015)-20 and 25 km s −1 along the tail and 3.8 and 2.2 km s −1 across the tail.
Tracking an expanding amorphous cloud proved to be challenging in the absence of information on its expansion rate, direction and center. Tracking an approximate knot center was found to be heuristically better than tracking the feature's edges. Measurements are therefore subjective and slight variations in the feature center can translate to significant changes in the velocity. The feature was observed on 06 January 2014 at ∼1 × 10 6 km from the nucleus. We measured a mostly linear acceleration of the plasma packet down the tail. The trending radial velocity along the tail was ∼60 ± 60 km s −1 and non-radial velocity of 10 ± 54 km s −1 across the tail.

Tail Rays
We define top and bottom tail rays as tail rays located above and below the Sun-comet line, respectively ( Figure 22). The comet exhibited multiple top tail rays close to each other making it difficult to delineate the tail rays positions along the extended radial vector. The bottom tail ray was extensive (∼3 × 10 6 km) and folded quickly about the main tail axis, producing velocities close to the slow v sw . The top tail rays appeared curved. Aside from a few outliers, the v sw increased with both time (Figure 23a) and cometocentric distance (Figure 23b) or remained near-constant. These outliers, mostly in the top tail rays, were measured from curved tail rays indicating a disturbed SW flow interfering with the expected evolution of tail rays. The viewing geometry likely compounded this effect. From 03 January 2014 to 07 January 2014, the folding ion tail rays were evident in the close-up INT images. However, the brightness stretching tool were inefficient at separating the tail rays for reliable measurement. The results shown here should be treated with caution.

Conclusion
measurements near the nucleus were consistently higher than velocities further down the tail contrary to theoretical expectations. We would expect the SW to become mass-loaded through the cometary pick-up ion process as it approaches the comet's nucleus. The mass-loaded SW would then accelerate down the tail until it reaches the surrounding SW velocity. A distinct curvature to the ion tail was present in most of the mapped images, with the Note. The speed, direction, and angular width is expected to vary as the ICME interacts with its surrounding solar wind medium. We identify the possible interactions for each ICME in the last column.

Table 1 The Date and Time of Identified Possible Interplanetary Coronal Mass Ejection (ICME) Interactions at Comet Are Given Below Using the Linear Speed of Observed ICMEs and the Central Position Angle (CPA), Its Direction of Travel, and the Angular Width, the Approximate Expected Region of Interaction
degree of curvature lessening with decreasing cometocentric distance. This unique morphology when mapped is the primary reason for the range of measured velocities. The INT observations were all taken within 1.5 × 10 6 km of the nucleus, with moving features identified and tracked as close as 5 × 10 5 km. During our analysis of the amateur images, the dust tail and ion tail overlapped due to the observing geometry although this was mostly not a hindrance during data extraction. All the velocities derived for this comet were taken when the orbit plane angle was ∼20°. Contrary to previous comets, the ENLIL MHD visualisations offered little insight into the chaotic episodic flows observed at the comet. These sudden deviations from the fast v sw can only be explained by ICME interactions since no HCS crossing or slow winds were expected. We report excellent agreement between the SW velocities derived from amateur images and a professional grade observatory for both the regular SW flow and transient features in the ion tail. This suggests that amateur observations afflicted by inclement weather and subjected to likely worse seeing conditions are as reliable.

Ground Based Observations
Only three samples could be extracted from 1 image out of 41 fully processed images post-perihelion, as most images did not have an observable ion tail. The ion tail, when observed, was extensive, straight, and very close to the radial vector and lacked any features usually associated with a turbulent SW flow. Velocities, measured along the tail, ranged from 1,100 to 1,400 km s −1 . No distinct cause of the extreme high velocities could be identified.
Amateur images of C/2011 L4 were seldom exposed for long enough to image the ion tail. The comet's extensive and bright dust tail overlapped with the ion tail's orientation, further complicating the latter's study. The other images in our catalog were unusable as the Earth traversed the comet's orbit in late May 2013; our technique failed due to the low orbit plane angle.

STEREO B
A total of 742 estimates were extracted from 190 difference images (Ramanjooloo & Jones, 2021a). Seven images were rejected due to the ion tail's proximity to the dust tail or image defects, which would have rendered the analysis unreliable. C/2011 L4 showed no evidence of folding ion tail rays. There were a number of turbulent periods. This comet was an ideal target for the velocity vector map, as the ion tail was very dynamic, leading a wide and very bright, well-structured dust tail. The ion tail lagged behind what we interpret to be the comet's neutral atom tail (Fulle et al., 2007). We note that Raouafi et al. (2015) in fact interpret the northernmost tail to be the ion tail, with the second, highly structured and dynamic tail studied by that team being dust. The lack of any changes in the northernmost tail are strong indications that it was instead a neutral atom tail. Difference images revealed an aberrant, sinuous ion tail that extended over a large extent of the observations with multiple plasma blobs and DEs as the comet left the STEREO HI-1B FOV. The results oscillated about conventional slow SW velocities. The variations seen in the later measurements corresponded to large orientation changes and increase in turbulent dynamicity in the ion tail. On March 13, the comet appeared to have two ion tails, one stemming from the expected location, the other jutting out from one of the top dust striae. Our period of analysis started shortly after perihelion, and extended from March 10.673 to 16.478 UT, when the comet was moving from southward (blue) to northward of the ecliptic plane (red; Figure 24b). Although this geometry was disadvantageous for ground-based ion tail observations, STEREO B was well positioned on the far side of the Sun from Earth (Figure 24a). An image captured by STEREO B 3 days after perihelion shows a uniform iron (Fe) tail, a striated dust tail with a dynamic and variable ion tail in between (Figure 24c). The orbit plane angle for STEREO B remained stable ( Figure 25b) and large enough to produce reliable SW estimates; that of Earth (Figure 25a) clearly shows the poorer observing geometry.

CR 2134
Assuming a bimodal distribution of of 400 and 800 km s −1 (Figure 26), we can estimate the approximate origins of the SW plasma at its source surface. The predicted sources on the Mercator map corroborate the estimates we derive from comet C/2011 L4 as we expected to mostly encounter a turbulent, streamer belt flow of the slow SW. According to the Mercator map, the comet encountered the HCS between March 14 and 15. STEREO-B images provided continuous monitoring of the comet crossing the HCS and the resultant DE. The tail likely detached around 15 March 2013 at 00:00 UT, followed by an outflow of multiple distinct condensation knots over several hours. A large change in the tail orientation change occurred between 12:09 and 16:09 UT. A data gap occurred around 15 March 2013 at 00:00 UT.
The comet's outbound trajectory sampled SW between heliocentric distance (r H )∼68 R ⊙ (∼0.316 AU) and ∼87 R ⊙ (∼0.405 AU). The velocities match well with the ENLIL predictions. The MHD model predicted a velocity drop from ∼400 to 250 km s −1 , a steady slow SW of ∼250 km s −1 up to March 14, when it would encounter a moderately fast SW. This would correspond to a speed hump of 450-550 km s −1 starting March 14 at ∼12:00 UT and lasting for 2 days. The velocity peak would occur at ∼15 March 2013 at 21:00 UT, when we registered a decreasing SW flow. The start of the enhanced v sw region matched well with our data, though the ensuing period indicated that the comet would have traversed the fast SW region by March 15 at 18:00 UT. It should be noted that this region was associated with notably large longitudinal and latitudinal non-radial velocity components (∼20 km s −1 for both). The expected velocity peak also agreed well with our results (Figure 27). The deviation from the MHD model occurred during the previously described continuous condensation knots at the predicted HCS crossing. It is far more likely that this turbulent period is associated with an ICME-on-ICME interaction from the last two ICMEs reported in Table 3 and Figure 28. In addition, the ICMEs could simply have decelerated, for example, Grison et al. (2018), to the ambient slow v sw of ∼250 km s −1 . The possible merging of the two ICMEs would have resulted in a complex ICME-SW outflow at the comet, which may have compressed the fast SW ahead.
The density enhancements ∼1 × 10 7 km from comet head, observed on March 12 at 22:09 UT, coincided well with the expected arrival of a fast ICME, observed at the comet on March 12 at 10:36 UT (Table 3), at the comet. A double dynamically responsive tail with fairly similar initial propagation direction, was observed emerging in close proximity to the extensive dust tail. The two tails appear to cross over at ∼1.3-1.4 × 10 7 km, followed by Figure 19. ICME candidates and their potential SATs at comet C/2013 R1. Interactions (labeled as Int 1-6) marked above are the approximate times at which the images were taken and not the beginning of the interaction of the ion tail with disturbed solar wind medium. See Figure 15 for more details.

Date
Time ( Note. See Table 1 for more details.

Table 2
The Date and Time of Identified Possible ICME Interactions at Comet Are Given Below a DE. The morphology of the bottom tail is that of a dust stria, which may have undergone a clumping of dust grains. It is unclear whether the second density enhancement is dust or plasma. The CORHEL MHD predicted two polarity reversals at the comet on 12 March 2013 at ∼09:00 UT and 13 March 2013 at ∼15:40 UT ( Figure 29). There are no tail DE identified due to large data gaps and image processing defects during the first period. The second polarity reversal is expected around March 13 18:00 UT, matching well with the observed formation of a DE at 18:49 UT in the STEREO A images (not included in this analysis due to the poor observing geometry). The disconnected tail also coincided with the edge of the merged ICME around the same time. The second highest maxima in the velocity distribution on 13 March 2013 at ∼18:00 UT are velocities from the disconnected tail.
It remains unclear as to why the ion tail underwent a large orientation change on March 15 at 13:29 UT, at a cometocentric distance of ∼6 × 10 6 km. This would have been initiated slightly earlier at the comet's head. A very faint SW plasma cloud can be seen in the larger STEREO HI-1B FOV possibly arriving at the comet at 06:09 UT, while the comet was already displaying turbulent ion tail flow. It is evident that the comet traversed a disturbed medium, which likely corresponds to the merged ICMEs. The link between the two is tenuous, though it is the only obvious SW phenomenon that could account for the atypical ion tail behavior.

Flow Vector Maps: Non-Radial Velocity
Prominent features in the disturbed ion tail maintained their radial motion with no spurious off-radial motions. Most features were hence tracked at a cadence of 80 min. Each feature tracked between consecutive images is represented with the same color and connected with a line. We then group these features per time period for as long as we could track these short-lived features. These are labeled as sets 1-7 (Figure 30a). At certain points, for example, on 13 March 2013 at 00:29-03:29 UT, the comet appeared to have two ion tails (feature set 2). Both were measured in the vector maps, although only the northernmost tail, the real ion tail, was included in the radial velocity investigation. It is difficult to make sense of these velocities, though they mostly show SW velocities centered about reasonable values of ∼300 km s −1 . Feature set 3 followed the acceleration of a kink and a potential disconnected ion tail as it accelerated to ambient v sw . The root cause of this disconnection was not identified. Set 4 corresponds to the HCS tail disconnection. The corresponding tail feature slowed down initially, forming a kinked tail. Once disconnected, the tail section rapidly accelerated to 240 km s −1 , close to the MHD predicted v sw , followed by a decrease in acceleration. A radial velocity interpretation of this image produced a of ∼400 km s −1 , further reinforcing the view that tracking DEs produces slightly erroneous SW velocities. This is because the disconnected tail would appear to momentarily not respond to the radial SW flow. Feature set 5 was taken from a particularly complex difference image, which had been linked to a period of ICME-ICME interaction with the ion tail. The differing trend between different sections of the ion tail is further evidence of a complex non-radial flow at the comet. Small velocity variations could be due to human error. This dataset fills in the velocity data gap in Figure 27, though there is a clear mismatch between the two techniques. The last five features can be separated into two groups. The first (feature set 6) was measured from the second half of the poorly processed difference images and tracked the formation of a newly formed turbulent ion tail. This new tail segment corresponds to the large orientation change, also linked to an interaction with the ICME-ICME disturbed medium. The final feature, set 7, correlates well with the radial velocity technique, supporting our hypothesis that the comet will have traversed the coronal hole more quickly than predicted by the ENLIL model.

Discussion
Overall, C/2011 L4 proved to be an interesting probe of the turbulent streamer belt region of the SW usually seen at low heliolatitudes (Figure 31), as solar cycle 24 approached its maximum. The measured SW velocities for comet C/2001 L4 are within expected values for the slow SW. They correlated well with the predicted ENLIL MHD-derived velocities. The STEREO B image archive consisted of numerous images taken at a fixed cadence over several days, allowing the near-continuous monitoring of the comet's behavior near the Sun. The spacecraft data yielded a greater number of data points for the than the amateur observations, as the ion tail extended over greater distances than was typical for amateur images. The velocities were tightly correlated with lower velocity uncertainties over longer cometocentric distances. C/2011 L4 was a near-Sun comet that probed regions of the SW close to the Sun which had been heretofore difficult to sample.

SW Velocity Comparison
There are few published large scale studies of the SW based on comets' ion tails. Brandt and Heise (1970) undertook a statistical analysis of comet ion tail orientations, which suggested mean radial velocities of 450 ± 11 km s −1 with a tangential component of 8.4 ± 1.3 km s −1 . They further proposed a revision of their previously quoted lower bound of the from 150 to 225 km s −1 , which is in accordance with our estimates and in situ values. Figure 22. Measured samples of folding tail rays for comet C/2013 R1 are taken in sets of 3. Measurements are taken from two consecutive images. The red and black dots are positions taken from folding ion tail rays above the Sun-comet line in images 1 and 2, respectively. Blue and purple dots are measured positions below the Sun-comet line from images 1 and 2, respectively. Each set of measurements are connected by a line to represent that they are from the same folding ray. We can thus track the evolution of the tail ray between images.
The data scatter of from spacecraft images was quite well constrained due to the high-quality of consistent observing and data reduction procedures as well as the lack of an atmosphere influencing the image quality. Spacecraft in situ sampling remains the best and most accurate method of providing detailed information on the SW. The remote sensing techniques used in our software provide an alternative inexpensive crowd-sourced solution to increase our spatial and temporal sampling of SW velocities and transient phenomena in the inner heliosphere.
The close agreement between our results and the ENLIL MHD model demonstrate the potential to devolve the dynamical ion tail aberration into a series of velocities as long as we adhere to a strict set of imaging standards and conformity. To account for v sw discrepancies with the CCMC ENLIL model predictions we attempted to identify a cause of transient disturbances in the SW flow. Sizonenko (2007) pointed out similar discrepancies between their SW velocities derived from comet observations and those measured by space-based instruments. They linked these to the low accuracy of cometary observations and to differing SW conditions experienced by Figure 23. v sw with respect to time (a) and radial distance (b) from nucleus. The first (blue), second (purple), and third dot (red) represent the three measurements taken in each set. First is closest to the nucleus and third is furthest along the folding ion ray. As expected, we mostly see an increase in velocity away from the comet.
Earth and the comet, although they had no clear cause. It is unclear how much of an effect the observing geometry contributed toward these discrepancies. Sizonenko (2007) reported that there may be an unaccounted force which could have affected their observed velocities.
A more in-depth study assessing the data quality of spaceborne observations against ground-based amateur images would be useful to further validate this technique. This would require a sufficiently large temporal overlap between the two vantage points. This is difficult to achieve as the solar-observing spacecraft will image comets at low solar elongation when they are at their most difficult to observe from Earth.
Tracking the radial evolution of folding tail rays using the mapped images is a theoretically sound concept. Accurately pinpointing the radial locations of the tail rays requires a smaller scale contrast between the tail rays and the image FOV than is available with amateur images. A series of images taken with an hourly cadence, or better, and small FOV is highly recommended for this technique.

Low Orbit Plane Angle
It is notable that there is a systematic overestimation or underestimation of the v sw . This is likely due to the orbit plane angle and the observing geometry. At low angles, the projection mapping breaks down as the pixel vectors are stretched to near-infinity when the orbit plane angle approaches zero.  In the JPL Horizons data, positive values of the orbit plane angle indicate that the observer is above the comet's orbital plane along the positive z-axis in the inertial reference frame. Our orbit plane angle plots only show the absolute value, as it is assumed that the observer's location above or below the comet's orbital plane is irrelevant. In an idealized scenario for a straight ion tail with no complications, the geometry reduces to the three-dimensional position of the observer with respect to the comet and the extended Sun-comet radial vector. Assuming the anti-sunward SW flow at the comet is purely radial, the ion tail will be constrained to the plane of the comet's orbit. When the observer is ahead of the comet, with the Sun-comet line between the observer and the ion tail, the projected uncertainty will always be underestimated, regardless of the observer's z-position with respect to the comet's orbital plane. Vice versa, when the observer is lagging the comet's motion such that the ion tail flows between the observer and the Sun-comet vector, the projected ion tail will appear to have a smaller aberration angle. In a realistic situation, factoring in a curving ion tail from radial speed variations and non-radial plasma flows, the orbit plane angle becomes an important criterion in the distorted projection.
Unless this angle is near 90°, there will always be an element of over-or under-estimation. For non-radial tails, it is evident that the three-dimen-  Note. See Table 1 for more details. The comet is between position angles 95°-55°. sional location of the observer with relation to the comet's tail will be a contributing factor toward the disparity between the measured and observed values. To truly test this technique, spacecraft observations with high temporal resolution of a comet's ion tail with a near 90° orbit plane angle would help to remove geometrical perspective effects.  . ICME candidates and their potential SATs at comet C/2011 L4. The start and end of the STEREO B observations are marked as red dotted lines. These interactions may have triggered the dynamically variable ion tail structures observed during this period. Each colored line corresponds to a different ICME. The overlap between the first two ICME paths suggest they may have interacted with each other, slowed down and could have interacted further with ICME 3 and 4.

Amateur Versus Professional Observations
Spacecraft data are consistently recorded with the same equipment and manner with little external influence on the way the data is processed and saved. Equally, sources of noise for the spacecraft instruments, commissioned by professional scientists, will be better constrained and more consistently removed from the data. Amateur observers are much less coordinated in this respect. They are limited by the consumer technology available and their individual budgets. This leads to a wide array of telescopes, detector types, and FOVs being used to monitor the target, often without the use of any filters. There is no method of ensuring the equipment set up and data reduction are performed in a consistent manner. Though most amateur images of comets are likely to be calibrated, they will not be subjected to the same scientific rigor as observatory processing pipelines or spacecraft observations and may not have obtained all the necessary calibration frames. Furthermore, there tends to be an observational bias in the ion tail images gathered by amateur observers. Most of these images were acquired by volunteer astrophotographers and thus will publish their most aesthetically pleasing and dynamic ion tail images. The timescales for the observations also differ. Spacecraft observations have delivered a high cadence of observations from the same instrument over a short period of time. Amateur astronomers tend to observe in short bursts over long periods of time. Inclement weather can often stymie consecutive observations leading to large data gaps in our resulting plots. Optical observations are prone to distortions. Astrometry.net calculates a Simple Imaging Polynomial (SIP) to represent image distortion (Shupe et al., 2005) of order 2, which is applied when mapping the photographs into their equatorial coordinates. Considering the maximum FOV astronomical images are a few degrees apart, with the comet often covering a subsection of that, the optical distortion should not cause a large discrepancy in the orbital plane mapping.
Knowing the accuracy of the image time is paramount to the success of our software. The unknown timing information played a larger role than had been initially anticipated in determining accurate v sw estimates. The range of possible times for optocenters covering a large pixel area can lead to incorrect image projection. In such instances, the ion tail will appear closer or further from the solar radial vector leading to over/under-estimations of the SW velocities. This is a likely strong source of the data scatter in our results. While the amateur community is getting better at reporting this information, our professional-amateur collaboration would benefit immensely by organizing mass requests of images and being specific about the information required including standardised metadata.

Turbulent Events/Non-Radial Flows
Transient interplanetary events were partially responsible for deviations from the modeled SW velocities. Large radial velocities exceeding 1,000 km s −1 , peaking at ∼1,650 km s −1 , were recorded. Velocity vector maps of turbulent ionic features in consecutive images suggested that it was possible to at least constrain the velocity and expansion of the interaction region between ICMEs and the comet's ion tail. By comparing our image catalog, our velocity estimates, MHD SW velocities and the CME catalogs, we can identify the list of likely transient phenomena. Some disturbances in the ion tail can often look like ICME-related turbulent events, appearing as a kink or a "double ion" tail, in certain instances. These could be due to the perspective viewing of a fast ion tail packet catching up with an earlier, slower moving condensation cloud.

Conclusions
We have demonstrated a new technique to extract v sw estimates, as well as characterizing general local parameters for transient interplanetary events near comets, allowing us to use comets as SW monitors throughout the inner heliosphere. The techniques demonstrated here rely heavily on high production rate comets that were close enough to the Sun to form a bright, observable ion tail. Nonetheless, the frequency of bright comets is significant enough to create a catalog of SW velocities in the inner heliosphere. The big picture was to build a comprehensive view of the large scale and small scale variations throughout the inner heliosphere over past solar cycles.
Uncertainties in the SW velocities may arise from a number of identified and quantified error sources, chief amongst which are non-radial components of v sw . Mapping the images onto the comet's orbital plane provides a good estimate of but the inherent uncertainties always need to be borne in mind. To summarize our caveats: 1. The core technique is the determination of multi-point, multi-latitudinal radial mass-loaded v sw at the comet. 2. Ground-based observations are at the mercy of the elements and there is not much that amateur astrophotographers can do to minimize this effect on data quality. 3. It is unclear which amateur images have been calibrated and treated with due scientific rigor. This will only get better by improving collaborations between professional and amateur observers, and informing the amateur community of best practices for scientific analysis, including accurate and precise recording of the times at which images were obtained. 4. Our technique seems to be impeded by a recurring curving ion tail. It remains to be determined whether this is a characteristic of all comets or whether the technique will incorrectly underestimate SW velocities far from the nucleus and overestimate values close to the comet head. 5. Infer general SW variations with solar cycle. 6. Detection of transient events such as HCS crossings, CIR, and ICME interactions.
Our results of the global structure of the SW were mostly limited to the equatorial plane, which showed large spikes in . They do not always match the extrapolated near-Earth data or ENLIL MHD model perfectly. However, the close correlation during quiescent SW periods and the identified transient SW phenomena for most of the non-corresponding periods clearly show that the technique holds potential to diminish our knowledge gap of the SW variation in the inner heliosphere, as a complementary dataset to MHD models. The large error bars for the estimates arise either due to poor image quality, the plasma tail sampling technique or wide and diffuse plasma tails.
The results of this work do not entirely support our original hypothesis that amateur images of comets can be used as a reliable source for remote investigation of the SW. Though they can provide a rough indication of the bulk plasma flow velocity, though at times this is marred by the numerous heliospheric phenomena causing turbulence in the cometary ion tail. The observing geometry is an unexpectedly large factor in controlling the quality of the results. When applied to professional spaceborne observations, the technique yields comparable estimates of the v sw . In stark contrast, the spacecraft data yielded a mostly smooth variation for the SW velocities. A high orbit plane angle of near 90° is considered to be the optimal observing scenario to produce high-quality, reliable estimates of the v sw . In conclusion, v sw estimates derived for amateur images are useful hints as to the SW behavior as long as they are strictly considered under the caveats discussed previously.

Future Work
The software and technique presented here is being been adapted to an online web service. Once fully operational, amateur observers will be able to contribute images for analysis. If successful, it could be beneficial to coordinate a select group of skilled amateur astrophotographers dispersed globally and equip them with a red and blue broadband filter at a minimum and ideally also with narrowband filters. Interesting to pursue would be to characterize the SW-geometrical dependency with a three dimensional triangulation of the plasma tail. This is achievable by comparing simultaneous observations of the ion tail from different vantage points. A similar study was done by Thompson (2009). They could only apply their technique to the dust tail as there were no stereoscopic observation of the ion tail until C/2011 W3 (Lovejoy) was observed. The technique could not be translated to the ion tail due to the complexity of the ion tail's non-radial motion and the observer's geometrical perspective. Another avenue worth investigating would be to identify the causal factor for the arcing nature of the ion tail. Simply determining whether the decreasing velocity trend downtail is a physical manifestation of the interaction between the massloaded SW and the charged dust tail, or whether it is an artifact of this technique, would be very informative.

Data Availability Statement
The processed data for the comets studied in this project and a description of the data can be found at https:// doi.org/10.6084/m9.figshare.17197595.v4, https://doi.org/10.6084/m9.figshare.17197685.v1, and https://doi. org/10.6084/m9.figshare.17197757.v1. also acknowledges the UK Institute of Physics for support. The excellent and very proactive community of amateur astronomers have helped make this project very interesting. Their willingness to contribute their data freely towards science has been near unanimous and we would like to thank them for making this research possible. This research made use of data processed through Astrometry.net. Yudish Ramanjooloo is grateful to Chris Arridge, Gethyn Lewis, and Lin Gilbert for help with the programing. Wilcox Solar Observatory (currently supported by NASA) data used in this study was obtained via the web site http://wso. stanford.edu courtesy of J. T. Hoeksema. We extend our gratitude to the SOHO/ LASCO and UK SECCHI science team at RAL for the data, advice and timely assistance and are grateful to R. Howard (NRL), PI of both the LASCO and SECCHI instruments. The CME catalog employed is generated and maintained at the CDAW Data Center by NASA and The Catholic University of America in cooperation with the Naval Research Laboratory. We also used data from the CACTus CME catalog, generated and maintained by the SIDC at the Royal Observatory of Belgium. A critical aspect of this project would have been unfeasible without the training and data acquired during both INT discretionary times and our own proposal. Simulation results have been provided by the Community Coordinated Modeling Center at Goddard Space Flight Center through their public Runs on Request system (http://ccmc. gsfc.nasa.gov). The CCMC is a multiagency partnership between NASA, AFMC, AFOSR, AFRL, AFWA, NOAA, NSF, and ONR. The ENLIL Model was developed by D. Odstrcil at University of Colorado at Boulder.