Pristine PSP/WISPR Observations of the Circumsolar Dust Ring near Venus's Orbit

Between 2019 August 17 and 27, PSP approached the Sun from 0.5 to 0.25 au, its roll angle switching between the "rolled" and "unrolled" orientations (see the right panel of Figure 1 for an illustration, and refer to Section 2 for further details). In the upper panels of Figure 2, we show three background-difference snapshots (already corrected by the instrumental artifacts) recorded by WISPR-I on 2019 August 17, 23, and 26, obtained while the S/C was in in the "unrolled" orientation. Corresponding WISPR-O images obtained close in time are shown in the bottom panel. The models to account for the instrumental artifacts on each telescope have been created by taking the minimum of all corresponding "unrolled" background corrected images taken during the nominal science campaign (i.e., here we exploit Case 1).

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On WISPR-I images, we notice the presence of a straight ray extending all the way to the outer edge of the FOV. An extended brightness enhancement is also observed in the WISPR-O frames. A bright object (the planet Venus) wanders along the excess brightness band. The other bright object is Mercury. The black features seen above and below both planets are artifacts of the image processing technique used to estimate the background scene of each individual frame due to the excessive brightness of the object compared to the background. (Here, we want to stress the fact that this extended, stationary, brightness enhancement could be unveiled in all the images taken by both telescopes in the time period between August 17 and 27, regardless of the S/C roll angle). As will be shown next, this ray is seen to continue seamlessly into the WISPR-O frames.

The 2D schematic representation on Figure 3(a) indicates the region of space covered by the PSP/WISPR telescopes in the "unrolled" S/C orientation during this 11 day time frame. The region comprises a section of Venus's orbit between about 65° and 228° ecliptic longitude. The PSP locations at the two extremes are 23° longitude at 0.46 au from the Sun (red dot) and 67° longitude at 0.25 au (blue dot). The green and light blue, hatched regions delineate the FOVs of WISPR-O and -I, respectively, on August 17, while the red and blue hatched regions indicate the respective FOVs on August 27. In Figure 3(b), we show the corresponding PSP/WISPR image composite (one WISPR-I and two WISPR-O) in a celestial coordinate system (GEI; Geocentric Equatorial Inertial), with the orbit of Venus delineated by the red dots. The projection of the invariable plane (inclination i_ip = 158 and ascending node Ω_ip = 10758; see Souami & Souchay (2012)) and of the ecliptic plane are depicted by the yellow dotted line and the orange dashed line, respectively. We choose this inertial coordinate system to display the full coverage of the excess brightness feature in the 11 day time period. The composite reveals a plausible association between the brightness enhancement and the 2D projection of Venus's orbit in the longitude range covered.

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The faint and diffuse nature of the excess brightness observed does not allow us to discern a noticeable change in its location between the beginning and end of the 11 day time window (notice, e.g., the matching of the location of the brightness enhancement at the outer edge and inner edge of the frames from August 27 and 17, respectively, in the composite displayed on Figure 3(b)). This can be simply explained by interpreting the brightness enhancement as the signature of an extended, continuous feature, whose projected location in the FOV of the PSP/WISPR telescopes matches the projected orbital path of Venus.

There is a three-day gap in data coverage between August 20 and 22 (see right panel of Figure 1). Therefore, in the following, we restrict the analysis to the observations taken in the S/C "unrolled" orientation between August 23 and early 27 (37 WISPR-I, 16 WISPR-O images). In this time period, the orbit of Venus shifts, in detector coordinates, [6, 9, 11] pixels in the N-S direction at [15°, 45°, 100°] elongation. Under the premise that the brightness enhancement follows the projected orbital path of Venus, this shifting amounts to only a few percent of the observed width of the feature—and therefore allows us to construct a time median image for either telescope, to increase the signal-to-noise and hence help elucidate its spatial extension. In Figure 4, we display a WISPR-I/WISPR-O composite of the median of the images in the time period considered. The composite (displayed in the HPLN-ARC representation (Calabretta & Greisen 2002; Thompson 2006)) highlights the excess brightness along the projected Venus's orbital path (depicted by the red dots). The Sun is to the left of the image, at 0° elongation. The two broken dashed red lines guide the eye to the region of space extending ±0.025 au from Venus's orbital path (a more accurate determination is carried out in Section 4.2). This band places a limit on the width of the brightness enhancement, which is interpreted as the linear, projected extension of the cross section of an excess density feature. The linear extent of the feature in the N-S direction is similar to the value of the cross section of the circumsolar dust ring near Venus orbit detected with both HELIOS (0.048 au; Leinert & Moster 2007) and STEREO (0.055 au; Jones et al. 2013, 2017) observations. The inset is a zoom-in of the region delimited by the red rectangle showing the location of the portion of Venus's orbital path as seen on August 23 (top red line) and 27 (bottom red line). The average N-S displacement in this region is <11 pixels, which corresponds to less than <0.008 au at the location of Venus's orbit.

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During both the inbound and the outbound segments of the extended science window, a few PSP/WISPR images were recorded in the "rolled" S/C orientation (see the right panel of Figure 1). This allowed us to check the consistency of the findings presented in Section 3.1. In this case, to remove the instrumental artifacts from the background-corrected images that were obtained in the S/C "rolled" orientation, we use "grand-minimum" models (one per telescope) created from all the PSP/WISPR images obtained during the inbound segment of the extended science window to treat the images taken during the outbound segment and vice versa (there exists a ∼10° S/C roll difference between the two segments; see the right panel of Figure 1). In other words, we exploit Case 2.

In Figure 5, we show the 2D representation of the viewing geometry of a combined set of "rolled" and "unrolled" observations on August 25 (panel (a)) and on September 12 (panel (b)). On the former date (at 14:00 UT), PSP was located at an heliocentric distance of about 0.284 au (56307 ecliptic longitude, −1872 latitude), and on the latter (at 22:30 UT), at about 0.373 au (257391, 0741). The portion of Venus's orbit in bold orange delineates the part of the orbit captured by the FOVs of the telescopes.

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The corresponding PSP/WISPR composite observations for the two days indicated above are shown in Figure 6, displayed in a helioprojective HPLN-ARC representation. The projected orbital path of Venus is depicted with the red dots, and is seen to match the brightness enhancement (the ecliptic is delineated by the dashed line in orange, and the invariable plane by the dotted line in yellow). Above the images, along the top, we show two additional x-axes. The uppermost top x-axis displays the distance of the observer to Venus's orbit, and the lower top x-axis displays the ecliptic longitudes of the corresponding parts of the orbit in the HAE (Heliospheric Ares Ecliptic) coordinate system. Note that the brightness enhancement caused by the responsible particles is being projected onto the flat detector plane, and apparently follows the projection of the almost circular orbit of Venus. Therefore, under a preliminary assumption that the excess particle density is indeed along Venus's orbit, it appears at a varying distance from the observer depending upon the elongation of the LOS (see the uppermost top x-axis). This would cause some foreshortening at the outer edges, hence the wider, projected latitudinal extension of the feature at larger elongations (Figure 4 clearly shows this effect—compare the latitudinal extent of the region delimited by the dashed red lines at the shortest and longest elongations). On a similar line of argument, and in particular at ∼105° elongation (i.e., the maximum elongation covered by the WISPR outer telescope) the angular latitudinal width corresponding to a portion of a circumsolar ring with a projected cross section of about 0.05 au located at 0.6 au (0.53 au) from the observer is ∼48 (∼54). This explains the slightly wider and more diffuse aspect of the brightness enhancement observed on September 12 compared to August 25 (bottom and upper panels of Figure 6, respectively).

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As a final test to check the consistency of our findings, we create a panorama covering a full 360° range using all the WISPR-I and WISPR-O (both "rolled" and "unrolled") images taken during both the inbound and outbound segments of the extended science window (see right panel of Figure 2). Toward this aim, we map each individual image into a virtual frame in the GEI system, the frame covering [−180°, 180°] in R.A. (akin to longitude) and [−60°, 60°] in decl. (akin to latitude). We then stack the individual frames and take the median.

The resulting panorama is displayed in Figure 7. The blue (red) dots delineate the projection of Venus's (Earth's) orbit. The vertical dashed–dotted lines at 764 and −1036, respectively, mark the ascending and descending nodes of Venus's orbit. The horizontal dashed lines at ±234 mark the inclination of the ecliptic with respect to the Earth equatorial plane (i.e., the obliquity of the ecliptic). The time direction of the observations is indicated by the two dates on the top axis. The beginning of the sequence starts on 2019 August 17 (the edge of the image at about 100°) and end on 2019 September 18 (edge of the image at about 80°).

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The panorama confirms the coincidence of the excess brightness feature with the projected orbital path of Venus. Note that there seems to be a slight disagreement in the excess brightness and the orbit of Venus between 40° and 80° (as pointed out by the two green arrows). This is because that range is covered in the panorama by WISPR-I images alone, the signal in the inner part of its FOV being dominated by a streamer rather than the circumsolar feature.

The brief analysis above showed that the excess brightness is a signature of a real feature. Moreover, as projected onto the plane of the sky, we have shown that this excess brightness is a signature of a circumsolar dust ring whose projection matches the orbital path of Venus. Thus, without further analysis, we would be tempted to claim that it is indeed a circumsolar dust ring near Venus's orbit. In the following, we will examine the possibility of other alternatives.

The PSP/WISPR images utilized in our study have all been taken from heliocentric distances <0.5 au, i.e., from within the orbit of Venus, comprising a view between about 135 and 108° elongation. Therefore, the lines of sight extend toward the outer Solar System. In the outward direction lie: (1) the circumsolar dust ring associated with Venus's orbit (e.g., Leinert & Moster 2007; Jones et al. 2013, 2017); (2) the Earth's resonant dust ring (Jackson & Zook 1989; Dermott et al. 1994; Reach et al. 1995); and (3) the asteroid dust bands (e.g., Dermott et al. 1984; Low et al. 1984; Reach et al. 1997; Nesvorný et al. 2006a, 2006b), all major dust structures (also circumsolar) whose appearance might resemble the pattern observed in our analysis.

The methodology followed is not sufficient to constrain the exact orbital parameters of the ring (such analysis is beyond the scope of the present work and will be reported elsewhere). It is worth mentioning, however, that a dust ring with orbital parameters such as those reported by Jones et al. (2013, 2017), i.e., i = 21 and Ω_A = 685, displays a projected orbital path in WISPR images that can still be considered to be matching the excess brightness band at the image resolution shown, although not as well.

Our analysis revealed an excess brightness band of the order of 1% in WISPR-O images with respect to the F-corona background, corresponding to a circumsolar feature of about 0.043 au ± 0.004 au in latitudinal extension at FWHM if at the orbit of Venus (see Section 4.2). No other band could be detected at a similar or different brightness level. A close overlap of the brightness band with the projected orbital path of a potentially associated planet/asteroid to a given circumsolar dust ring is the minimum necessary condition to claim that the excess brightness observed is its likely observational signature. All the examples shown in this work clearly show the overlapping of the projected orbital path of Venus with the brightness enhancement, Figures 6 and 7 in particular revealing the matching with Venus's projected orbit and not the ecliptic nor the invariable plane all along the ring's longitudinal extension.

Nesvorný et al. (2006b) showed that the main-belt dust bands are symmetrical with respect to the invariable plane. Although the orbital plane appears very close to the projected orbit of Venus in Figures 3 and 6, the dust band observed (signature of the circumsolar feature) is not aligned with the invariable plane. In particular, Nesvorný et al. (2006b) also showed that the dust bands originating from the Karin asteroid family exhibit a latitudinal extent of ∼42, which corresponds to about 0.2 au. To highlight the nonassociation of the dust band observed in WISPR images with such asteroidal dust bands, we display in Figure 9 a selected couple of frames from Figure 2 (WISPR-I on the left panel and WISPR-O on the right panel) with the projection of a circumsolar ring along: (1) Venus's orbit with a latitudinal extent of 0.043 au (in red color); and (2) an orbital path at the average heliocentric distance of Karin's orbit, inclination of the invariable plane, and 0.2 au latitudinal extent (in yellow color).

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Even though PSP/WISPR is looking outward, no other brightness enhancement extending all the way to the end of view of WISPR-O is distinguishable in our images. We give here a plausibility argument as to why the dust ring associated with Earth's orbit is not visible. For instance, at 1.1 au, i.e., a reasonable, average heliocentric distance of Earth's associated dust ring (e.g., Dermott et al. 1994; Kelsall et al. 1998; Reach 2010), the local brightness of the F-corona is only about 38% of the brightness at Venus's average orbital distance, assuming a brightness falloff with heliocentric distance r^−2.3 (the local dust density is about 58%, assuming a falloff r^−1.3). Thus, a dust density enhancement along any LOS from the WISPR instruments would have to be much bigger than the one computed in this work (see Section 4.3) the farther away from the observer they are. For Earth's case, the reported value in the literature is only about 16% of the local dust density value of the zodiacal dust cloud (Kelsall et al. 1998), which, as we saw in the images, will not produce a discernible brightness enhancement.

A similar argument can be applied to explain the absence of the zodiacal dust bands sourced in the asteroid belt. In a direct comparison comprising only a couple of ecliptic longitudes of the asteroidal dust bands in both white light and IRAS IR intensities, Ishiguro et al. (1999) found that the relative brightness increases were below 2% above the background. Further, the location of the relative brightness maxima in the visible and IR were not necessarily at the same ecliptic latitudes. Likewise, the intensity of the relative maxima of each IR wavelength analyzed had wavelength dependence. In spite of these observational findings, we can use their measurements of the absolute white-light intensity of the band closest to the ecliptic to explain why they are not visible in our observations. Ishiguro et al. (1999) reported in their Figure 3 the absolute white-light intensity of several bands at about 1 to 4 S10 units. For a proper comparison with WISPR observations, we first convert the reported intensity of the most intense band (the one closer to the ecliptic) into MSB units (4 S10 = 1.8 × 10⁻¹⁵ MSB). Next, we choose a representative LOS in the FOV of the WISPR telescopes. For simplicity, we choose the same LOS used for the discussion in Section 4.2, i.e., at 67° elongation. (However, the reasoning and conclusion hold regardless of the elongation considered). For the S/C at about 0.3 au (a representative PSP heliocentric distance for the purposes of this argument), this LOS corresponds to an equivalent elongation of about 75 R_☉ or 0.35 au (see, e.g., Stenborg et al. 2021). Therefore, since the absolute brightness of the F corona/zodiacal light at 75 R_☉ is about 2.03 × 10⁻¹² MSB (as inferred from Stenborg et al. (2021)), the effect of the band is not greater than 0.09% of the background brightness; a relative increase that could be too low to be above the digitization threshold of the WISPR detectors (especially of WISPR-I).

The removal of the instrumental artifacts via the approach followed in this article affects the radiometric calibration. Therefore, to measure the relative excess brightness of the observed band and hence help establish the latitudinal extent of the dust ring, we use straight background ratio images (no instrumental background correction) that have been calibrated into physical units in order to keep the processing as simple as possible. Moreover, since the WISPR-I images are much more affected by the K-corona signal, we limited the analysis to WISPR-O data. Note that the determination of the brightness along the band, i.e., of the azimuthal density structure along the ring, is beyond the scope of this work.

A caveat of utilizing this intermediate data product is that the signal is affected by instrumental effects (e.g., row-to-row or column-to-column variations not properly accounted for by the bias correction). In addition, in the rectangular coordinates of PSP/WISPR detectors, the wide-angle optics of the telescopes introduce a certain amount of distortion or warping, which results in an apparent curvature of otherwise linear features. This is especially significant in WISPR-O, which has a much more distorted FOV. In particular, this effect will cause, e.g., a feature that is straight in reality or a structure that is moving straight (in both cases, parallel to the orbital plane of the S/C) to appear increasingly curved as it gets farther from the center of the optical system (see, e.g., the bottom panel of Figure 2).

To remove this artificial curvature and get a more accurate representation of the physical features observed, we can create a rectangular grid ¹¹ in the Helioprojective coordinate system, in which every row and column represents a fixed latitude and elongation that covers the entire FOV of the image. Then, we can use the modeled optical properties of the detector to determine the latitude and elongation of each pixel. Using these values, the original image can be interpolated onto the rectangular grid, creating a more accurate representation of the heliosphere as a Cartesian grid. In a sense, these images can be considered "undistorted," as in these images the distortion effects caused by the optics of the instrument are accounted for.

In this new representation, the projected orbital path of Venus in WISPR-O "unrolled" images obtained, e.g., in the time period between August 23 and 27, appears as a straight line inclined ∼15 with respect to the horizontal. We remove this slight inclination by simply rotating the resulting frames by −15. We then stack all these new frames and take the median, in a similar fashion to what we did in Section 3.1. The "undistorted" median image, cropped to a region around the dust band, is displayed on the left panel of Figure 10. On the right panel, we display the median brightness (continuous black line) at each row of the cropped image. The red line delineates a Gaussian fit to the brightness profile (see Equation (1))

$$\begin{eqnarray}&&{\rm{\Delta }}I/I={A}_{0}\,{e}^{-{\left(\displaystyle \frac{x-{x}_{0}}{\sigma }\right)}^{2}}=0.0099\,{e}^{-{\left(\displaystyle \frac{x-777}{24.5}\right)}^{2}}.\end{eqnarray} \tag{ 1 }$$

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The standard error of the fit amounts to 0.1. The amplitude A₀ is an estimate of the median excess brightness ΔI/I at the center of the brightness band. The FWHM of the band is 57 pixels (this extent is indicated on the left panel by the blue dashed lines), which is representative of the median latitudinal extent of the projected dust ring's cross section. To estimate the median latitudinal extent in au, we need both the median distance of the observer and the elongation of the corresponding LOS that would correspond to that distance to the portion of Venus's orbit covered by the WISPR-O FOV in the time period of interest. Figure 11 shows a plot of the PSP–Venus orbit distance as a function of LOS elongation for all the unrolled images in such a time period. We note that, for an LOS at about 67° elongation, the distance is the same regardless of the time of the observation. Therefore, we adopt 0.78 au (at 67° elongation) as the representative distance to estimate the projected latitudinal extent of the ring.

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Under these assumptions, the FWHM = 57 pixels corresponds to 0.043 au ± 0.004 au. (The error is estimated by taking into account the number of pixels the orbital path of Venus shifts in the time period comprised by the images utilized to compute the median image, i.e., 11 pixels; see Section 3.1.) For purposes that will be clearer at the end of this section, 1σ = 24.5 pixels corresponds to about 0.018 au.

The white-light F-coronal brightness can be modeled as the integration along any given LOS of the product of the dust density distribution (ρ[r, β], with r denoting the heliocentric distance and β the latitudinal displacement from the symmetry axis) and a factor related to the efficiency of the scattering at each scattering angle (hereafter Φ[θ], with θ the scattering angle). Lamy & Perrin (1986) showed that the observations from the ZLE on the Helios S/C could be modeled extremely well using an empirical Volume Scattered Function (VSF) to account for the factor Φ[θ]. The physics of the scattering process, the size and composition of the particles, the indices of refraction, etc., are all embedded in this empirical function, the Sun–particle–observer angle being its only dependence. Therefore, to compute the brightness of the F-corona, one only needs to know the dust density distribution along any given LOS. For the modeling of the zodiacal light, several dust density models have been proposed (see, e.g., Giese et al. 1986; Misconi & Rusk 1987). The main difference among these models resides in the radial and latitudinal dependency of the density distribution.

Therefore, to estimate the overdensity along the LOS due to the dust ring, if ΔI/I = 0.01, we can write

$$\begin{eqnarray*}&&{\int }_{{\tilde{r}}_{0}}^{{\tilde{r}}_{1}}{\rm{\Delta }}\rho (\tilde{r})\,{\rm{\Phi }}({\tilde{r}}_{\theta })\,d{\tilde{r}}_{\theta }=0.01\,I,\end{eqnarray*}$$

where Δρ represents the overdensity in the ring necessary to produce a relative increase in brightness of ∼1%. For simplicity, we assumed β = 0 and expressed the parameters involved as a function of the distance $\tilde{r}$ along the LOS, explicitly denoting the dependence of the VSF with the scattering angle Φ through $\tilde{r}$. The limits $\tilde{{r}_{0}}$ and ${\tilde{r}}_{1}$ of the integral indicate the extension of the ring along the LOS.

To estimate the excess dust density necessary to produce a 1% brightness increase, we (1) assume it to be uniform in the $[\tilde{{r}_{0}},\tilde{{r}_{1}}]$ interval and symmetrically distributed along the LOS from Venus's orbital path (i.e., ${\rm{\Delta }}\rho (\tilde{r})={\rm{\Delta }}\rho \,=$ constant); and (2) consider the VSF ${\rm{\Phi }}({\theta }_{\tilde{r}})$ as defined in Lamy & Perrin (1986) (this choice is motivated by its use in reproducing the observations performed by the ZLE on the Helios spacecraft). Therefore, for our rough estimate, we can consider it constant and hence write

$$\begin{eqnarray*}&&C\,{\rm{\Delta }}\rho \,(\tilde{{r}_{1}}-\tilde{{r}_{0}})\approx 0.01\,I,\end{eqnarray*}$$

where C is a constant representing the approximate constant value of the scattering function in the integration range. The PSP orbit—in particular, the WISPR viewpoint from inside the orbit of Venus—only allows us to estimate the extension of the ring in the direction transverse to its plane. Therefore, to estimate the extent $(\tilde{{r}_{1}}-\tilde{{r}_{0}})$ of the ring along the LOS, we assume it to be similar to the extent exhibited by the latitudinal cross section measured at 2.58σ (i.e., 99% of the dust ring population along the LOS). We estimate this extent as $(\tilde{{r}_{1}}-\tilde{{r}_{0}})={\rm{\Delta }}({x}_{0}\pm 2.58\sigma )$ ≈ 126 pixels ≈ 0.093 au (0.108 au if we consider the extent of the overdensity defined at 3σ, i.e., 99.7%). We note that, at the range supposedly covered by the density enhancement, the scattering angle θ varies from 1536 to 1574 (or 1514 to 1594 for 3σ). This range of scattering angles implies a relative variation of ±1.8% (or ±2.0% for 3σ) in the VSF between the extremes $\tilde{{r}_{1}}$ and $\tilde{{r}_{0}}$. Under all these assumptions, the Δρ overdensity necessary to produce a relative brightness increase of ∼1% ranges between about 8.6% and 10.8% of the local density of the smooth component of the zodiacal dust cloud, depending upon at which location the extent of the ring is defined.

As we can see, the disentanglement of the fractional contribution of the dust distribution along a given LOS is a difficult (if at all possible) process. However, both the spatial localization (Section 4.1) and restricted extension along the LOS of the dust enhancement facilitate the analysis, and under certain assumptions, allow us to constrain the excess density necessary to explain the observed excess brightness.

Theoretical modeling of resonant dust rings (e.g., Kuchner & Holman 2003), predicts an asymmetric azimuthal distribution of dust particles as well as a preceding and trailing gap in dust density following the planet. The manner in which we have analyzed the images, however, restrains us from elaborating on the analysis of the azimuthal dust density distribution, which is nevertheless beyond the scope of this work. A more detailed, quantitative analysis supported by modeling is underway and will appear elsewhere. Therefore, at this stage, we cannot elaborate on the nature of the ring, i.e., whether it is a resonant dust ring (an interpretation in agreement with, e.g., Jones et al. (2013, 2017)), or simply due to Venus's co-orbital dust particles, as in Pokorný & Kuchner (2019).