Asteroid 16 Psyche: Shape, Features, and Global Map

We develop a shape model of asteroid 16 Psyche using observations acquired in a wide range of wavelengths: Arecibo S-band delay-Doppler imaging, Atacama Large Millimeter Array (ALMA) plane-of-sky imaging, adaptive optics (AO) images from Keck and the Very Large Telescope (VLT), and a recent stellar occultation. Our shape model has dimensions 278 (-4/+8) km x 238 (-4/+6) km x 171 (-1/+5) km, an effective spherical diameter Deff = 222 -1/+4 km, and a spin axis (ecliptic lon, lat) of (36 deg, -8 deg) +/- 2 deg. We survey all the features previously reported to exist, tentatively identify several new features, and produce a global map of Psyche. Using 30 calibrated radar echoes, we find Psyche's overall radar albedo to be 0.34 +/- 0.08 suggesting that the upper meter of regolith has a significant metal (i.e., Fe-Ni) content. We find four regions of enhanced or complex radar albedo, one of which correlates well with a previously identified feature on Psyche, and all of which appear to correlate with patches of relatively high optical albedo. Based on these findings, we cannot rule out a model of Psyche as a remnant core, but our preferred interpretation is that Psyche is a differentiated world with a regolith composition analogous to enstatite or CH/CB chondrites and peppered with localized regions of high metal concentrations. The most credible formation mechanism for these regions is ferrovolcanism as proposed by Johnson et al. (Nature Astronomy vol 4, January 2020, 41-44).


INTRODUCTION
Asteroid 16 Psyche is the largest Tholen [1984] M-class asteroid and a target of the NASA Discovery mission Psyche [Elkins-Tanton et al., 2017;.
Visible and near-infrared spectra [Bell et al. 1989], optical polarimetry [Dollfus et al. 1979], thermal observations [Matter et al. 2013], and radar observations [Ostro et al., 1985, Magri et al. 2007aShepard et al., 2017] all support the hypothesis that its surface to nearsurface is dominated by metal (i.e., iron and nickel). However, recent spectral detections of silicates [Hardersen et al. 2005;Ockert-Bell et al. 2008Sanchez et al. 2017] and hydrated mineral phases [Takir et al. 2017] have complicated this interpretation and suggest it to be more complex than previously assumed.
Recent studies of Psyche have converged to size estimates (effective diameter) between 220 and 230 km, and to spin poles within a few degrees of (36°, -8°) (ecliptic lon, lat) Drummond et al. 2018;Viikinkoski et al. 2018;Ferrais et al. 2020). Given this size, mass estimates have led to a consensus that Psyche's overall bulk density is between 3,400 and 4,100 kg m -3 [Elkins-Tanton et al. 2020] which places constraints on its internal structure, composition, and possible origin.
Three major hypotheses for the formation and structure of Psyche are currently debated. In simplified terms they are: (1) the early interpretation that Psyche is the stripped remnant core of an ancient planetesimal, dominated by an iron composition [e.g. Bell et al. 1989;Asphaug et al. 2006]; (2) Psyche is a reaccumulated pile of rock and metal, a type of lowiron pallasite or mesosiderite parent body derived from repeated impacts [Davis et al. 1999;Viikinkoski et al. 2018]; and (3) Psyche is either an iron [Abrahams and Nimmo, 2019] or a silicate-iron differentiated body [Johnson et al. 2020] with surface eruptions of metallic iron via ferrovolcanism.
The earliest model for Psyche is that it is a remnant metal core left after a large impact stripped the crust and mantle from an early protoplanet [Bell et al. 1989;Davis et al. 1999]. However, problems with this interpretation have been difficult to overcome. Davis et al. [1999] suggested that an event of this magnitude was unlikely in first 500 Ma of solar system formation and would have left dozens of family fragments that should be detectable but have not been found. The presence of silicates, and especially hydrated phases detected on Psyche has also created doubt. Only recently have new hypervelocity impact experiments on iron bodies suggested a way to systematically explain these signatures [Libourel et al. 2020]. Perhaps the most problematic datum is Psyche's bulk density. Iron has a grain density of ~7,900 kg m -3 , yet multiple estimates of Psyche's mass yield an overall bulk density of half that value [Elkins-Tanton et al. 2020]. If it is a remnant core, it must also be a rubble pile or extremely porous, and it is not known if this is possible for an object as large as Psyche. Although still possible, it is fair to say that this model for Psyche has fallen out of favor [Elkins-Tanton et al. 2020].
As an alternative, Davis et al. [1999] suggested that, while Psyche was shattered by early impacts, it was not completely disrupted. As a result, the surface should preserve a mesosiderite-like mix of metal and silicate material with a still-intact core. The detections of orthopyroxenes and other possible silicates in the spectra of Psyche [Hardersen et al. 2005;Ockert-Bell et al. 2010] are consistent with this. The detection of spectral hydroxyl features [Takir et al. 2017] is inconsistent with this violent early genesis, but easily explained by more recent impacts with primitive objects, similar to the scenario envisioned for Vesta [Prettyman et al. 2012;Reddy et al. 2012;Shepard et al. 2015] and later demonstrated experimentally by Libourel et al. [2020].
Recently, two groups have proposed that Psyche is an object that has experienced a type of iron volcanism, or ferrovolcanism. Abrahams and Nimmo [2019] propose a mechanism in which molten iron erupts onto the brittle surface of a pure iron-nickel remnant as it cools from the outside inward.
They predict that iron volcanos are more likely to be associated with impact craters, or if there is an overlying silicate layer, the iron may be deposited intrusively, as a diapir. Conceivably, these intrusions could later be uncovered by impacts. However, the underlying assumption of this model is that Psyche is largely metallic throughout, possibly covered by a thin layer of silicate impact debris. This seems incompatible with Psyche's overall bulk density. Johnson et al. [2020] propose that Psyche is a differentiated object with a relatively thin silicate mantle and iron core. As it cooled, volatile-rich molten iron was injected into the overlying mantle and, in favorable circumstances, erupted onto the surface. This model is consistent with Psyche's overall bulk density and the observation of silicates on its surface. They make no specific predictions about the location of eruption centers except that they are more likely where the crust and mantle are thinnest.
In both ferrovolcanic models, the presence of volatiles, e.g., sulfur, is critical for lowering the viscosity of the iron melt and providing the pressure needed to drive the melt onto the surface. In the Johnson et al.
model, the thickness of the mantle/crust is also critical; if it is too thick, the melt will never make it to the surface.
In this paper, we refine the size and shape of Psyche using previously published and newly obtained data sets. We examine topographical and optical albedo features discussed in previous work Viikinkoski et al. 2018;Ferrais et al. 2020], produce a global map, and overlay it with radar albedo values, a proxy for metal concentrations in the upper meter of the regolith. We find correlations between centers of high radar and optical albedos and discuss the consequences for these models of Psyche's formation and structure.

DATA SETS AND SHAPE MODEL
In this section, we briefly describe the datasets used in our shape model, our methods, and final model results. Dataset details are listed in Tables 1-5. Figures 1-6 illustrate both the image datasets and subsequent model fits to them.

Arecibo S-band Delay-Doppler Imaging and Calibrated Echoes
For shape modeling, we use 18 delay-Doppler images acquired by the Arecibo Sband (2380 MHz or 12.6 cm wavelength) radar in 2015 ].
These images have a spatial scale (in range) of 7.5 km/pixel, sample frequency of 50 Hz per pixel (Doppler), and were centered in the southern mid-latitudes of Psyche. Details of those observations are in Table 1 Table 2.  at left is the image data, center is the simulated image data using the model shape and aspect shown in the plane-of-sky view on the right. The images are ordered in rotation sequence, left to right, top to bottom. Run numbers are indicated and can be matched to Table 1 for dates, times, and sub-radar body-centered longitudes. Doppler frequency is along the horizontal axis of the delay-Doppler images (0 in center, positive on the left, ±1000 Hz per image, 50 Hz/pixel), delay increases from top to bottom (307.5 km total per image, 7.5 km/pixel). The spin axis is indicated by the long arrow, the long-axis (lon 0°) is marked by the short (red) peg and the intermediate axis (lon 90°) is indicated by the longer (green) peg. Small white arrows on the images point to the evidence for a large crater (Eros).   Table 2. The March 5 run shows a possible bifurcated echo.

Atacama Large Millimeter Array
For the first time ever, Psyche was imaged with the Atacama Large (sub-) Millimeter Array (ALMA) in the Atacama Desert in Chile on UT June 19, 2019 over ~2/3 of its rotation at a (model) sub-observer latitude of -14 degrees (de Kleer et al., 2021). Spatially-resolved thermal emission data were obtained in ALMA's Band 6 at a central frequency of 232 GHz (1.3 mm). ALMA was in an extended configuration at the time of observation with a maximum baseline of 16.2 km yielding a spatial resolution of 0.02" or 30 km at Psyche. The data were reduced and calibrated using the ALMA pipeline.
Additional calibration and imaging of the data were performed using the Common Astronomy Software Applications (CASA) package (McMullin et al. 2007), employing a custom iterative imaging and calibration routine. A more extensive description of the observations as well as calibrations and imaging methods is given in de Kleer et al. (2021). In this paper, we use the observations primarily to constrain Psyche's overall shape and size. The observing geometry is summarized here in Table 3 and the image data are shown in Figure 3.

Adaptive Optics Images
We  Table 4 and illustrated in Figure 4.
For our fit, we also included four adaptive optics (AO) images acquired in 2015 Drummond et al. 2018]. These images (Kp band, 2.1 µm) were taken at the Keck II telescope at roughly the same time and aspect (southern midlatitudes) as the 2015 Arecibo radar imaging runs. After the model was completed, we acquired new Keck observations in December 2020 at nearly identical aspects. These were used only to check the model. Details are listed in Table 4 and illustrated in Figure 4.   Sub-observer latitude was -14°; longitudes are noted above the model on select images. Dates, times, resolutions, and aspect information is in Table 3. The approximate beam size (30 km) is indicated and the image scale is 4.4 km per pixel. The cross-hatched pattern visible in the data is an artifact of the imaging process. Arrows with letters indicate the position of features mentioned in the text and Table 6 (first letters only are shown). One feature (Xray) is labeled on ALMA images, but is not seen in the model.   (Table 6). Observations are chronological from top-to-bottom. Alpha, Bravo, Charlie, and the major axis (0°) are indicated on the first of the 2018 observations for reference. Sub-observer longitudes are above the 2019 observations (latitudes -10°). Details are in Table 4. Image scales are 6.0 km/pixel (2018), 4.5 km/pixel (2019). One of the optical "bright spots" reported by Ferrais et al. is visible in the center of the lon=307º image.  Table 4. Image scale is 12 km/pixel.

2019 and 2010 Occultations
On 2019 October 24, Psyche occulted a 10 th magnitude star and a well-organized campaign led by members of the International Occultation and Timing Association (IOTA) generated 15 evenly spaced and highly accurate chords 7 .
This occultation is similar in its equatorial aspect to occultations in 2009 and 2014, but is superior to those in both the quantity and quality of chords. In addition to tightly constraining the c-axis, the 2019 occultation was effectively broadside (shape model sub-observer longitude 95°) and helped to constrain the major (a-) axis. We also include a post-fit comparison to a previous occultation on 21 August 2010 8 which was at a southern aspect (-53º, 350º) and had a dozen chords that spanned the object (Figure 6).

Methods
We utilized the SHAPE modeling software and strategies described by Magri et al. [2007b] and Shepard et al. [2017]. This software simulates the radar image or echo power spectrum for a model shape and spin state and compares it to the images or spectrum taken at the same time. It is also capable of generating synthetic plane-of-sky images that can be compared with images from optical systems. Given an initial shape input, the software uses a gradient search iterative process and adjusts the size, aspect ratios, scattering law(s), spin rate, and pole direction to minimize chi-square, the root-mean-square of the differences between the observations and model.
When beginning the modeling process, we start with ellipsoidal models of many different sizes, aspect ratios, and spin parameters, (i.e., a grid of parameters) and find those combinations that best fit the observations. This reduces the chance of falling into a local minimum solution space.
Once the approximate size, aspect ratios, and spin parameters are better constrained, the ellipsoids are converted into more flexible spherical harmonic shape models to flesh out the gross deviations from an ellipsoid.
When these no longer improve, the best models are converted into faceted vertex models for additional fine tuning. In this case, we also explored the results when starting with the previous shape models of Shepard et al. [2017] and the Ferrais et al. [2020].
With spherical harmonic and vertex models, penalty weights are used to enhance or minimize features on the model, including surface roughness or concavities. Different models may be indistinguishable to the chi-square formalism, so the final model is chosen based on its chi-square and apparent visual goodness of fit to individual features. We also use post-fit comparisons to other datasets that could not be directly used, such as occultations, as a further check on final size and shape.
For our revised shape model, we included the following datasets: from For the occultation, the coverage was extensive enough to generate a planeof-sky silhouette that was used as a plane-of-sky observation (this was not possible with the other occultations). This required artificially moving the Sun for that dataset to put it at opposition and remove any (cast) shadows in the model fit. Similarly, the ALMA images are due to emission (not reflected light) and the position of the Sun for those data was also altered to simulate an opposition view. In both cases, the primary goal was to constrain Psyche's shape outline and dimensions. For all data sets, we allowed radar and optical scattering models to float so that the shape was the primary quantity of interest to the fit.
Psyche is a rapid rotator (period ~4.2h) and some of our data sets were subject to rotational smearing. For example, each radar imaging run integrated 28 minutes of data, corresponding to ~40º of rotation. To minimize the effects of smearing in the final model, we adopted two strategies. First, we had the SHAPE software break up the radar integration time into three snapshots of the model (~13º of rotation between them), synthesize the resulting radar images at each time, and combine them to effectively model the smearing due to rotation during the total integration time. Second, the AO, ALMA, and occultation datasets are snap-shots of Psyche with integration times of a few seconds to a few minutes and little or no smearing. By weighting these datasets more (~75%) than the reduced-smear delay-Doppler images (~25%) in the final model, we effectively reduced any smear to scales on the order of our image resolution.
Our uncertainties reflect our best estimates of the possible range of sizes.
They are asymmetric because, while a range of sizes were found to be compatible with the data, our best model fell in the lower half of that range. Our range of uncertainties along the a-and b-axes are based on the highest resolution AO and ALMA images; our uncertainties along the c-axis are tighter because of the exceptional coverage of the 2019 occultation.
Our model is consistent in size and shape with those of Drummond et al.    Numbers at the bottom indicate the body-centered longitudes facing the viewer. North is up for the left and center views. Numbers to the left indicate the longitude of the axis pointing in that direction. The polar views (right column) are aligned so that the model major axis is horizontal. Note the similarity in a/b extent and shape. However, the Shepard et al. model is approximately 10% thicker (c-axis) than the others and shows slight differences in its polar aspect. Data for the Shepard et al. model

SHAPE AND TOPOGRAPHIC FEATURES
Here we examine the largest topographical features evident in our model and those reported by others, and evaluate whether they are likely to be real or possible artifacts of data processing and inversion. While there are many subtle depressions evident in our model, it is plausible that some are real, and equally plausible that some are noise artifacts. For this reason, we will ignore them unless they are pertinent to the discussion. Where relevant, we will also note optical albedo features reported by others.
To better organize our description of individual features, we adopt names from the International Civil Aviation Organization (ICAO) phonetic alphabet commonly used by radio operators. 9 Details of each feature are listed in Table   6. In Figures 1 and 3-6, topographical features are indicated and identified by their first letter.
We reference Psyche's major features with respect to our shape model bodycentered longitude and latitude, where the +a-axis (major) defines 0° longitude, the +b-axis (intermediate) is at 90° longitude, and the +c-axis (minor) aligns with the spin axis in the positive (north)-polar direction. Figure A.6.) noted three equatorial regions of missing mass relative to an ellipsoidal reference figure, and refer to these "depressions" as A, B, and C. We follow suit but refer to them as Alpha, Bravo, and Charlie, respectively. They are visible in our model and are illustrated in Figure 8. Alpha falls around longitude 270° and is the only one that appears to be a depression while the others are large, flat areas.

Ferrais et al. [2020] (their
Bravo is the missing mass region first identified by Shepard et al., [2017] and falls between longitudes 340° to 50°. Charlie falls between longitudes 90° and 150°. Although it is common to treat the shape of asteroids as variations on ellipsoids, our model of Psyche is also well described (along the major and intermediate axes) by a rounded rectangular shape with only one corner deviating significantly from this figure (Figure 8). The side lengths differ by only ~10%. From this perspective, Bravo and Charlie disappear, and Alpha remains and becomes considerably wider. We will continue to refer to the smaller region as Alpha and the extended area as West Alpha.  Ferrais et al. [2020] and here referred to as Alpha, Bravo, and Charlie, respectively (see Table 6).
The view on the right shows an alternative rounded rectangular overlay which fits well everywhere except between longitudes 200° to 290°. With this perspective, Bravo and Charlie are not depressions or regions of missing mass, and Alpha becomes considerably larger. The extension of Alpha is referred to as Alpha West or West Alpha.  Table 6 (labels are not present in the animations). The animations cover a full rotation as seen from +20° and -20° latitude. The red peg indicates the +x axis (0°, 0°), and these screenshots are centered on longitude 290°. Both images are oriented with the spin axis up. A Lambertian rendering has been used to emphasize topographic variation.
Asteroids 2867 Steins [Jorda et al. 2012], 101955 Bennu [Barnouin, 2019], and 162173 Ryugu [Watanabe et al. 2019] all display shapes with a significant polygonal character, and for the latter two, this is thought to be a consequence of their rubble-pile nature [Michel et al. 2020]. It is unclear whether that is possible for an asteroid the size of Psyche, some two orders of magnitude larger than Bennu or Ryugu. The surprising fit to a rounded rectangle may be a coincidence, or it may reveal something about Psyche's internal structure. The presence of Alpha is driven primarily by the deconvolved VLT images of the north polar region (Figure 4) and is less obvious in the raw data. This flattened-to-concave area should be visible in the ALMA data but is not (Figure 3). Instead, the ALMA data suggest there is additional topography at this longitude (270°) that is not readily evident in the VLT or Keck data.
The Arecibo observations were not favorably aligned to support either possibility. The ALMA and AO data are complementary in that regions that are dark in visible and near infrared (AO) will be bright in the thermal IR (ALMA), and vice-versa, so perhaps this region is optically dark. We will refer to this possible feature as Xray. Its presence is consistent with the shape outlined by the 2010 occultation (Figure 6), and the Viikinkoski et al.
[2018] albedo map does show a dark region at this longitude. We conclude that the depression Alpha is likely a real feature, though not a certainty, and may include unmodeled topography.
The features referred to as Bravo and Charlie are observed in the radar data, the AO observations from Keck and VLT, and the shape outlined by the 2010 occultation. The evidence for these regions is convincing. Shepard et al. [2017] noted two dynamical depressions in Psyche's southern hemisphere which they labeled D1 and D2. These were regions where the topography, rapid rotation, and estimated gravity of that model conspired to create regions of higher gravitational force, or dynamical depressions. These are locations where fines might preferentially pond and they appeared to correspond with purely topographical depressions. In our model, we find hints but no clear evidence for a topographical depression that coincides with the dynamical depression shown as D1 in that paper (here referred to as Delta) (Figure 9). As a result, we conclude that a significant topographical depression at the south pole is possible, but indeterminate.
The dynamical depression referred to as D2 in the Shepard et al. [2017] model is evident in the topography and is likely to be a large impact crater. It is consistently visible in the delay-Doppler images (Figure 1) as a pocket of low SNR pixels, typically 1-3 standard deviations lower than the surroundings. It is also suggested (a side view) in some of the ALMA images ( Figure 3). We conclude that the evidence for it is convincing and will refer to this depression as Eros 10 . In our model, it is centered at ~longitude 290°, ~latitude -65° and appears to be between 50 and 75 km wide and ~4 km deep (Figure 9). From some viewing aspects, there are indications that it might be two smaller overlapping depressions.
Our model shows a significant topographical depression at the north pole of Psyche and we refer to it as Foxtrot (Figure 9). It was not noted by Viikinkoski et al. [2018] or Ferrais et al. [2020], [2017] model. Evidence of its presence can be seen in the mid-line depression seen in the ALMA images (Figure 3), a few of the 2019 VLT images (Figure 4), and the 2019 occultation (Figure 6). We conclude that the existence of Foxtrot is likely, though not certain. If confirmed, measurements on our model suggest it to be ~50 km wide and a few km deep.
Viikinkoski et al. [2018] described two regions that they referred to as Meroe and Panthia. Meroe is located around longitude 90° just north of the equator and was noted to be significantly darker (optically) than its surroundings. Their model indicated it to be a crater some 80-100 km in size.
Our model shows no significant depression at this location and we conclude that a crater here is possible, but indeterminate.
The region referred to as Panthia is in the northern mid-latitudes from longitudes ~280° to 320° and was found to contain areas much brighter (optically) than the surroundings [Viikinkoski et al. 2018]. Our model also shows this region to contain a relatively wide (~80-90 km) and shallow depression consistent with the Viikinkoski et al. description (Figures 4 and   9). Based on its appearance in both models, we conclude that the evidence for Panthia is convincing.

RADAR PROPERTIES
One of the primary reasons for visiting Psyche is to investigate an object of a type not yet seen -an object that could be the remnant metallic core of an ancient planetesimal. Fortunately, we have 30 calibrated radar echoes that can provide some insight into the potential concentration of metals in the near-surface ( Table 2).
For calibrated radar echoes, we transmit a circularly polarized continuous wave (CW) signal to the asteroid and measure the echo power in the same (SC) and opposite (OC) senses of polarization. The OC echo is dominated by first surface reflections and is typically the stronger. Reported measurements include the OC radar cross-section, σoc, an estimate of the cross-sectional area of a metallic sphere that would produce the same echo power, and the more intuitive OC radar albedo, � , the ratio of the power received from the target relative to that which would be measured from a metallic sphere of the same cross-sectional area at the same distance. To calculate this, we divide the OC radar cross-section by the projected area of the asteroid at the time of its observation.
The ratio of the SC to OC echo is referred to as the circular polarization ratio, or µc. It is generally interpreted to be an indicator of near-surface roughness. A low µc (0.0 to ~0.3) is often interpreted to indicate surfaces relatively smooth at the wavelength scale and dominated by first surface reflections. Higher values are associated with surfaces that are thought to be rough at the wavelength scale, display significant volume or multiple scattering, or some combination of these.
In general, radar albedo is thought to be correlated with the near-surface (upper ~meter) bulk density of an object [e.g., Ostro et al. 1985;Shepard et al. 2015]. Given the assumption that larger main-belt asteroids are generally covered by regolith, higher bulk densities imply a greater concentration of iron-nickel in the regolith. Published radar albedos for asteroids range from lows of � ~0.04 for primitive type (e.g., P) asteroids to highs of ~0.5 for several of the M-class asteroids [Magri et al. 2007a;Shepard et al. 2015].
Using the average of calibrated echo power spectra from 2005, 2015, and 2017, and revised areal cross-sections of Psyche from this shape model, we estimate Psyche's mean OC radar albedo to be � = 0.34 ± 0.08 although there is considerable variation over the surface. This value is slightly lower than previously reported, � = 0.37 ± 0.09 ] because most of the new observations in the northern hemisphere have � < 0.30. Nevertheless, this value is still more than twice as high as the mean MBA S-and C-class radar albedos. The most reasonable interpretation of this observation is that the near-surface (upper ~meter) of Psyche has a bulk density significantly higher than the typical S-or C-class asteroid, probably caused by an enrichment of iron and nickel ].
We estimate the mean circular polarization ratio for the 2017 observations to be µc = 0.1 ± 0.1. This value is consistent with a relatively smooth surface at the wavelength scale and echoes dominated by first surface reflections.
[2018] generated their shape model from AO observations and lightcurves by simultaneously optimizing for both shape and albedo variegations. They allowed albedo variations of ~20% higher or lower than the mean (pv = 0.16) and produced a global albedo map. Figure 10 shows a refinement of that map in Ferrais et al. [2020] (see Figure    [2020] with purported topographical and albedo features labeled ( at least one region where the radar echoes are consistently elevated ( � of 0.3-0.4) and bifurcated ( Table 2, bold/italic entries). As a caveat, we note that radar albedo is a whole-disk average; however, the echo will usually be most heavily weighted by the radar properties of features nearest (within ~30°-40°) the sub-radar point.
The first region of high radar albedo is centered on latitude +37º and longitude 303º and corresponds to the topographical depression and optically bright region of Panthia (Table 6, Figure 9, 10). The regolith may be enriched in metal, or there may be a radar focusing effect because of the depression, or both.
The second region of high radar albedo is centered on latitudes of -45º between longitudes 12º to 50º. Multiple observations on separate dates show it to be a reproducible feature. It falls in an area south of Bravo and we refer to it as Golf. There is some evidence for a broad and shallow depression near this region (centered at longitude ~50º south of the equator, Figure 8) but it also could be an artifact of our fit. Golf is just south of a region much brighter (optically) than the mean (Table 6, Figure 10).
The third region of high radar albedo is centered at (-46°, 128°) and is referred to as Hotel (Table 6, Figure 10). Again, multiple observations on separate dates show it to be a reproducible feature. There is no obvious topographical structure here and the region appears generally flat. Overall, this region is optically darker than the mean except for the nearby bright spots noted by Ferrais et al. [2020].
The fourth area of interest is in the southern midlatitudes between longitudes of 230° and 300°, and we refer to it as India (Table 6, Figure   10). It is notable for two reasons: almost all of the echoes in this region have elevated radar albedos and four of them, between longitudes ~260° and ~280°, are bifurcated ( Table 2, entries with asterisks).
Bifurcated echoes are often associated with a contact binary structure (e.g. Kleopatra, Ostro et al. [2000]; Shepard et al. [2018]), but that is not the case here. Instead, there are likely two or more radar-bright regions separated by a region that is less reflective. As with Golf and Hotel, all the echoes were seen on different dates but fall in the same geographic region, i.e., the behavior is reproducible and is evidence that there is something unusual here.
The bifurcated echoes are centered at the longitude of Alpha, although it is north of our sub-radar points. One echo lobe (on the negative Doppler frequency side) includes reflections from Eros and the bright area and bright albedo spot north of India. The area corresponding to the other lobe (positive Doppler) aligns with the optically bright region just south of West Alpha. There is also some evidence for a broad depression in our model here, just south of the equator and centered at longitude 240°.
There is a possible bifurcated echo in the 2017 observations (northern hemisphere). This echo has an elevated radar albedo like those observed in the south and does fall in a region of modestly higher optical albedo, but there are no obvious structures present.
Based on this admittedly small sample, there appears to be a positive correlation between radar and optical albedos, i.e., the optically brighter regions are more radar reflective and darker regions less so. If confirmed, the most likely reason is that the regolith in the brighter regions has a higher bulk density, and by inference, a higher concentration of metal.

DISCUSSION AND INTERPRETATION
Here we discuss our two main conclusions and briefly discuss their ramifications for the current models of the formation and evolution of Psyche. Shepard et al. [2015] examined radar data from 29 Tholen M-class asteroids,

Psyche is Not Uniformly Radar Bright.
including Psyche, and found that only one-third were "radar-bright", i.e., had mean radar albedos � > 0.30, a property believed to indicate a high metal content in the upper regolith. Psyche and 216 Kleopatra are the largest and most notable of this group. The remaining two-thirds had mean radar albedos �~ 0.25, including 21 Lutetia ( � =0.24). While these values are nearly twice the average value for S-or C-class asteroids, they are inconsistent with a regolith dominated by metal unless it is highly porous ].
Lutetia was later observed by the Rosetta mission and its appearance and spectrum were found to be more consistent with enstatite chondrite or metalenriched chondrites like the CH or CB meteorites than with irons [Coradini et al. 2011]. These analogs are among the most widely suggested alternative compositions for the M-class asteroids [e.g., Gaffey, 1976;Hardersen et al. 2011], and all have the moderately elevated metallic concentrations necessary to explain Lutetia's radar albedo ].
The "background" radar albedo over much of Psyche is � 0.27 ± 0.03, similar to Lutetia and other non-radar-bright M-class asteroids (Table 2, Figure 10).
Standing out from this are several local regions that have up to twice the background value. These regions must have even higher bulk densities (e.g., concentrations of metal), and it is because of these regions that Psyche has a significantly higher average radar albedo than Lutetia. Shepard et al. [2010Shepard et al. [ , 2015 found that nearly all the radar-bright M-class asteroids showed radar scattering behavior like Psyche: rotationally dependent radar albedos, often with bifurcated radar echoes at some aspects indicating distinct radar scattering centers. Except for 216 Kleopatra, none of these objects are known to be contact binaries, and most have the modest lightcurve amplitudes associated with an ellipsoidal shape. A radar image of one of them, 779 Nina, shows an equant object with two separate regions of high radar albedo.
A plausible interpretation of these observations is that Psyche -and possibly any other radar-bright M-class asteroid -has a global silicate regolith with moderately elevated levels of metal, like Lutetia, punctuated with high concentrations of metal in localized regions.

Radar Albedo is Correlated with Optical Albedo
Given the coarse nature of a radar albedo measurement, this conclusion is necessarily tentative, but appears credible. If correct, it provides a clue about the processes operating on Psyche that give rise to localized concentrations of metal. In general terms, this finding seems counterintuitive because meteoritic iron minerals tend to have dark optical albedos [Cloutis et al. 2010 and references therein]. It may be that the region is brighter because of another mineral phase associated with the process that produced this concentration. Alternatively, there may be a difference in the regolith texture. In general, fine-grain silicates are optically brighter than their coarse-grained equivalents. However, laboratory experiments have found coarse-grained or coherent slabs of meteoritic iron to be optically brighter than fine-grained samples, just the opposite of silicates [Cloutis et al. 2010].

Consequences for Psyche Model Interpretations
Based on the consensus bulk density measured for Psyche, the model of a remnant core is effectively ruled out unless it is a highly porous (~50% microporosity) object [Elkins-Tanton et al., 2020;Siltala and Granvik, 2021]. The unusual shapes of Ryugu and Bennu have been explained as the result of their rubble pile structure [Michel et al. 2020], but it is not known whether metals are strong enough to support a porous structure of Psyche's size [Elkins-Tanton et al. 2020]. The curious fit of our shape model to a rounded rectangle (Figure 8) suggests this still may be worth further exploration.
The mechanisms for impact generated regolith on an iron body are still poorly understood, but recent experiments have shown that all the spectral characteristics noted in the past, including the presence of silicates and hydrated phases, are consistent with the formation of glass coatings during hypervelocity impacts of silicates on iron [Libourel et al. 2020]. If composed of pure iron-nickel, Psyche's background radar albedo suggests the upper ~meter of regolith would have to be highly porous (>60% using the model of Shepard et al. [2010]), but this may be consistent with the formation of "foamy" impact melt and carapaces also found in their experiments [Libourel et al. 2020]. Our finding of regional concentrations of metal is also consistent with a hypervelocity impact origin and subsequent evolution.
However, of the three highest radar albedo regions, only Panthia has an associated impact structure, although we noted a possible depression at Golf.
Hypervelocity impacts might also explain the association of high radar and optical albedos as those experiments found scenarios leading to both darker and brighter optical albedos.
It is conceivable that an impact-gardened silicate-metal regolith [e.g., Davis et al. 1999] would have localized concentrations of metal, but there are several difficulties. If these concentrations are randomly distributed because of some reaccumulation process, it is not readily evident why they are optically brighter. If impacts are invoked, one must explain how they concentrate metal. Impacts could explain the optical brightening as the associated ejecta blanket covers the region in relatively bright silicate fines. However, the rate of space weathering becomes important here [e.g., Clark et al. 2002], for these ejecta fines must stay bright as long as the concentrations are visible.
The interpretation that best appears to fit our observations is that Psyche is a differentiated silicate world, albeit one with elevated metal concentrations consistent with an enstatite or CH/CB chondritic regolith. The radar-bright regions are local ferrovolcanic eruptions of metal as proposed by Johnson et al. [2020], and the surface is optically brighter in these regions because of this process. The iron flow itself might raise the optical albedo because slabs of meteoritic iron have significantly higher albedos than fine grains [Cloutis et al. 2010]. Alternatively, there may be bright secondary materials associated with an eruption, including the volatiles that caused the eruption, compounds derived from them, or materials entrained in the melt from deep in the mantle. Or, like impacts, an eruption may cover a broad area in silicate fines, raising the optical albedo. Here again, the rate of space weathering becomes important.

SUMMARY AND FUTURE WORK
The earliest interpretation of M-class asteroids like Psyche is that they are the remnant metal cores of ancient protoplanets [Bell et al. 1989]. The consensus after many years of data gathering is that this is unlikely [Elkins-Tanton et al. 2020]. Nevertheless, given the recent experiments of high velocity impacts on metal substrates [Libourel et al. 2020], we find that our results cannot rule it out.
If Psyche is a mixed silicate-metal world, our results are best explained by a differentiated object with a mixed silicate and metal regolith (e.g., enstatite or CH/CB chondritic analogs), peppered with local regions of high metal content from ferrovolcanic activity as proposed by Johnson et al. [2020]. This model provides both a mechanism for concentrating metal in local