Probing the Density Fine Structuring of the Solar Corona with Comet Lovejoy

Probing the Density Fine Structuring of the Solar Corona with Comet Lovejoy Giuseppe Nisticò 1,2 , Gaetano Zimbardo 1,2 , Silvia Perri 1,2 , Valery M. Nakariakov 3,4 , Timothy J. Duckenfield 5 , and Miloslav Druckmüller 6 1 Dipartimento di Fisica, Università della Calabria, Via P. Bucci, Cubo 31 C, Arcavacata di Rende, Cosenza, I-87036, Italy; giuseppe.nistico.fi[email protected] 2 National Institute for Astrophysics, Scientific Directorate, Viale del Parco Mellini 84, I-00136, Roma, Italy 3 Centre for Fusion, Space and Astrophysics, University of Warwick, Coventry, CV4 7AL, UK 4 Centro de Investigacion en Astronomía, Universidad Bernardo O’Higgins, Avenida Viel 1497, Santiago, Chile 5 Centre for Mathematical Plasma Astrophysics (CmPA), KU Leuven, Celestijnenlaan 200B bus 2400, B-3001 Leuven, Belgium 6 Faculty of Mechanical Engineering, Brno University of Technology, Technická 2, 616 69 Brno, Czech Republic Received 2022 May 3; revised 2022 August 26; accepted 2022 August 30; published 2022 October 11 Abstract The passage of sungrazing comets in the solar corona can be a powerful tool to probe the local plasma properties. Here, we carry out a study of the striae pattern appearing in the tail of sungrazing Comet Lovejoy, as observed by the Atmospheric Imaging Assembly (AIA)aboard the Solar Dynamics Observatory (SDO)during the inbound and outbound phases of the comet’s orbit. We consider the images in EUV in the 171 Å bandpass, where emission from oxygen ions O 4+ and O 5+ is found. The striae are described as due to a beam of ions injected along the local magnetic field, with the initial beam velocity decaying because of collisions. Also, ion collisional diffusion contributes to ion propagation. Both the collision time for velocity decay and the diffusion coefficient for spatial spreading depend on the ambient plasma density. A probabilistic description of the ion beam density along the magnetic field is developed, where the beam position is given by the velocity decay and the spreading of diffusing ions is described by a Gaussian probability distribution. Profiles of emission intensity along the magnetic field are computed and compared with the profiles along the striae observed by AIA, showing a good agreement for most considered striae. The inferred coronal densities are then compared with a hydrostatic model of the solar corona. The results confirm that the coronal density is strongly spatially structured. Unified Astronomy Thesaurus concepts: Sungrazers (2197);Solar corona (1483);Solar coronal seismology (1994); Magnetic fields (994);Stellar structures (1631);Pickup ions (1239);Collision processes (2286);Computational methods (1965);Space observatories (1543);Solar extreme ultraviolet emission (1493) Supporting material: animations 1. Introduction Daily observations of the white-light solar corona with the Large Angle and Coronal Spectrometer (LASCO)aboard the Solar and Heliospheric Observatory (SoHO)allowed the discovery of more than 3000 comets plunging into the harsh solar atmosphere (Battams & Knight 2017). Because of the proximity of their perihelion, such comets are usually referred to as sungrazers. Jones et al. (2018)gave a more tight classification of comets based on their perihelion distance (q)and distinguished between near-Sun comets (q<66.1 R e fromthecenteroftheSun), sunskirting (3.45 R e <q<33.1 R e ), sungrazing (q=1.0–3.45 R e ),andsundiving (q<1.0 R e )comets. Based on their orbits, sungrazing comets are grouped into families since they are fragments of a common progenitor, like, the Kreutz group. Commonly, sungrazing comets appear in coronagraphs as small and fast-moving bright dots with a short tail, but some of them are outstanding events, with very long tails and bright comas. When approaching the Sun, the majority of these comets are completely dissolved within a couple of solar radii from the Sun’s surface. Nevertheless, two comets were observed in the FoV of the Atmospheric Imaging Assembly (AIA)of the Solar Dynamics Observatory (SDO), hence at distances below 0.7 R e from the solar surface in the extreme ultraviolet wavelengths (EUV):cometsC/2011 N3 (Schrijver et al. 2012)and C/2011 W3 (Lovejoy; Downs et al. 2013). Another comet approaching the Sun in 2013 November, C/2012 S1 (ISON), disregarded expectations and failed to show EUV signatures of its passage in the corona, probably because of the lower size of its nucleus that could not withstand the intense heat from the Sun (Bryans & Pesnell 2016). The transit of Comet Lovejoy in 2011 December was exceptional. The comet crossed the corona from east to west, with the perihelion located behind the Sun as observed from Earth, at only ∼0.2 R e from the Sun’s surface. The images recorded by SDO in the different EUV channels of AIA showed a trail of striations, also referred to as striae. Bryans & Pesnell (2012)associated the EUV striae to the temporal evolution of the excited states of oxygen ions released by the comet’s nucleus and guided along the local magnetic field lines, which were emitting in EUV as a consequence of the increase in their relative abundance. Downs et al. (2013)used sophisticated MHD simulations to reproduce the observations and provided estimates of the magnetic field and coronal density of the corona. McCauley et al. (2013)focused on the postperihelion observations of Lovejoy from AIA and included in their analysis X-Ray Telescope (XRT)data from Hinode. They determined the ionization stages in the observed striae and determined other physical parameters, such as the outgassing rate of the nucleus and the mass of the comet. Raymond et al. (2014)also analyzed the striae left by the comet during the outbound phase, estimated the speed of propagation and broadening of the striae along the local magnetic field, and The Astrophysical Journal, 938:20 (13pp), 2022 October 10 https://doi.org/10.3847/1538-4357/ac8e62 © 2022. The Author(s). Published by the American Astronomical Society. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s)and the title of the work, journal citation and DOI. 1 used an MHD model and the theory of pickup ions to compare the measurements with theoretical expectations. They found that cometary ions outline flux tubes with diameters of about 4000 km and that density variations between neighboring flux tubes reach at least a factor of six on a scale of a few thousand kilometers. The measurements were compared with an MHD model and the theory of pickup ions to show that part of the energy of the cometary ions as they isotropize goes to Alfvén waves. However, Raymond et al. (2014)did not consider the Coulomb interaction between oxygen ions and the background coronal plasma when estimating velocities and densities. In general, the relevance of comets relies on the possibility of exploiting them as natural probes of the inner heliosphere and solar corona. In fact, even before the advent of exploration by spacecraft, the direction of plasma tails of comets observed from Earth during their transit was thought to be evidence of solar wind flow (Biermann 1951; Parker 1958). Several studies on comet observations aimed at determining the physical conditions of the interplanetary medium (solar wind speed, density, temperature, etc.)and assessing the physical processes at work in the coupling between the solar wind and comet tails (Vourlidas et al. 2007; DeForest et al. 2015; Nisticò et al. 2018). Along the same lines, sungrazing comets have been used to infer the conditions of the solar corona but at distances much further from the photosphere, using the SoHO/LASCO and UVCS instruments (Bemporad et al. 2007; Raymond et al. 2018). In the case of Comet Lovejoy, the importance of studying the EUV striae concerns the possibility of diagnosing the physical conditions of the low solar corona at distances inaccessible to spacecraft. Even the Parker Solar Probe, which will attain a minimum distance of 9.8 R e , will also not be able to get as close to the solar surface as Comet Lovejoy did. In this work, we aim to study the time evolution of the striae by modeling the propagation of oxygen ions along a magnetic flux tube. The length of a stria is determined by the ion beam velocity, which decays because of collisions, and the ion collisional diffusion. By determining the parameters characterizing the beam slowing down and the collisional dispersion, we can get estimates of the ambient plasma density at the location where the striae are formed. The paper is organized as follows: in Section 2we present the observations of Lovejoy from SDO/AIA; in Section 3we show how the striae of Comet Lovejoy are modeled; Section 4discusses the analysis of the SDO/AIA data and the comparison with the numerical modeling. Finally, the discussion and conclusions are given in Section 5. 2. Observations The perihelion transit of Comet Lovejoy was seen by different space observatories. SDO/AIA recorded the approach to the perihelion between 23:25 and 00:16 UT on 2011 December 15–16. For that occasion, the pointing axis of SDO/AIA was offset by about half a degree to observe the comet entering the corona. Afterward, the comet was seen to re-emerge from the perihelion on the west side between 00:40 and about 01:00 UT. Figure 1shows a composite image taken in the 171 Å channel of SDO/AIA showing the inbound (top panels)and outbound phases of the comet (bottom panels). The images in the top panels are processed with the Noise Adaptive Fuzzy Equalization (NAFE)algorithm (Druckmüller 2013). The trajectory of the comet is superimposed onto the images as a dashed red line and is computed with SPICE: the SPICE kernel file was downloaded from the Horizons System 7 and read with the routines of the Spiceypy Python package (Annex et al. 2020). FITS file images were downloaded from the JSOC service and read using the read_sdo.pro routine in SolarSoftWare (SSW)/IDL. We did not process the FITS files with the standard routine aia_prep.pro because the images of the sequence were not correctly calibrated based on the FITS header information. The images were taken with a 12 s cadence (which was almost uniform during the observations)and a pixel size Δ pix ≈0 56. Some persistent jitter in the inbound phase data was removed by coaligning each image of the sequence to the middle one taken at 23:51:36.58 UT. As shown in Figure 1, the passage of the comet inside the solar corona left a trail of EUV striae. The striae appeared 1 minute after the transit of the comet’s nucleus. In Figure 2we show the intensity profiles versus time extracted from six different locations along the projected path followed by the comet. In each panel, the vertical dashed red line marks the time instant when the comet’s nucleus passed through the point, the dotted black line indicates the time when the EUV intensity starts to increase. Indeed, the stria signature is found as an increase, more or less sharp, in the EUV intensity. The time lag varies between 8 and 9 minutes. These time lags have to be corrected for the light travel time from the Sun to the Earth, which is about 8 minutes. After correction, the definitive time lag between the passage of the comet and the appearance of an EUV stria is within at most 1 minute, thus confirming the estimate provided in McCauley et al. (2013)in different EUV bands. The striae appear different in length and brightness, reflecting the amount of emitting oxygen ions, which in turn depend on the local density of the corona. In Section 3we explain how the striae of Comet Lovejoy are modeled, in order to calculate intensity profiles and compare them with those obtained from the observations. 3. Modeling of EUV Striae 3.1. Theoretical Model Following Downs et al. (2013), we assume that the cometary material is extracted from the comet during its travel through the solar corona, and that this material is rapidly ionized. Once oxygen and other atoms are ionized, they are captured by the magnetic field and start to spiral around the straight field lines, moving along them with a velocity u 0 that can be estimated as the projection of the ion velocity along the magnetic field, u 0 =v i ·B/B. A schematic representation is reported in Figure 3. The initial ion velocity can be seen as the sum of the comet’s velocity v c , and the ion outflow velocity v out , which is usually modeled as radial with respect to the comet’s nucleus (Bryans & Pesnell 2012):v i =v c +v out . As time goes on, oxygen ions reach higher ionization levels until they emit in the 171 Å line and are detected by SDO/AIA. This happens mainly for the ionization states O 4+ and O 5+ (Downs et al. 2013; Pesnell & Bryans 2014)and implies that oxygen ions will be visible in 171 Å only a short time after the comet’s passage, as discussed in Section 2. Later, these ions will be further ionized to O 6+ and more (e.g., by photoionization, charge exchange, electron and proton collisions), so that emission in the 171 Å line fades out. In the meanwhile, oxygen ions move along the magnetic field and slow down because of collisions. They are also undergoing a diffusive spreading 7 https://ssd.jpl.nasa.gov/horizons/app.html#/ 2 The Astrophysical Journal, 938:20 (13pp), 2022 October 10 Nisticò et al. because of their disordered motion, due to the outflow velocity v out and to collisions (Downs et al. 2013, Supplementary Material). The cloud of oxygen ions is spreading in the corona in three dimensions. However, since the Larmor radius is only a few km, which is much smaller than the striae length, we limit ourselves to a one-dimensional modeling with the xdirection along the magnetic field, also considering that (i)the spreading along the line of sight can be taken into account by integrating along it, something which is implicit in the EUV observations; and (ii)the spreading in the plane-of-sky and perpendicular to the xdirection is taken into account by actually summing the EUV signal over a few pixels in that direction (see Section 4), which also allows the improvement of the signal-to-noise ratio. Therefore, we propose a simple modeling of the beam of oxygen ions, which are treated as test particles. The initial velocity along the mean field direction decreases because of collisions as ut ue ,1 t 0slow () ( )=twhere τ slow is the time for the collisional slowing down of a suprathermal ion beam in a field plasma (see below).We consider that v out is symmetric, 〈v out 〉=0, and that for the beam u 0 is given by the average of v i , so that u 0 =v c ·B/B. Then, the position of the beam head x 0 (t)is xt x u t1exp 2 0 00 0 slow slow () [ ( )] ( )tt=+ - - where x 00 is the starting position of the beam, just after the release of ionized material from the comet into the solar corona. Figure 1. Left panels: composite images taken at different times with SDO/AIA in the 171 channel and showing the tail of striae left by Comet Lovejoy enclosed within two continuous red lines before (top panels)and after (bottom)the transit at the perihelion. The orbit of the comet is shown as a dotted red line. Right panels: blow-up view of the regions where striae are formed. The corresponding regions are outlined with a dashed red box in the left panels. The filled green circles labeled by letters mark the locations where intensity profiles are extracted and plotted in Figure 2. 3 The Astrophysical Journal, 938:20 (13pp), 2022 October 10 Nisticò et al. The above expression shows that, basically, the length of a stria is given by u 0 τ slow , to which the spreading due to collisional diffusion has to be added. Here, we study the distribution of material along the magnetic field by a probabilistic description, taking into account both the beam “ordered”motion and the ion diffusive spreading. By using a methodology adopted for the transport of energetic particles accelerated at shock waves (Ragot & Kirk 1997; Perri & Zimbardo 2008; Zimbardo & Perri 2018), we model the number density n(x,t)of ions along the magnetic field as nx t dt dxQx t tPx x t t,,,,3 t 0 () ( )( )() òò =¢ ¢¢¢ -¢-¢ -¥ +¥ where the source of oxygen ions is given by Qx t t t t x x t,, , 4 0 ()()()( ()) ()hd¢¢ = F¢ ¢- ¢ and Px x t t,()-¢ -¢is the probability of observing a particle in (x,t)if it was emitted in xt, ( )¢¢ . Here, Q xtt,,()¢¢ represents the number of ions emitted in the position x ¢ at time t ¢ . The motion of the beam is given by xt 0( ) ¢, i.e., by Equation (2), and the delta function implies that the source is located at xxt 0()¢= ¢. Further, t()F¢models the ion injection from the comet: if injection were sharp and punctual, this could be modeled as tt 0 () d ¢- (see, e.g., Le Roux et al. 2019). However, here we have to take into account that the emission of oxygen ions from the comet is a multistep process that includes solid particles and dust leaving the comet, molecule sublimation and ionization, and then oxygen ions reaching the ionization states O 4+ and O 5+ . These steps require a time of several tens of seconds, as evidenced by the time lags shown in Figure 2, also depending on the coronal density and on the size of the dust grains, and cannot be well described by a sharp injection. Instead, we model the ion injection as a Gaussian function delayed in time by t 0 : ttt 2exp 2.5 tt 00 2 2 00 ⎡ ⎣ ⎢⎤ ⎦ ⎥ () () () ps s F¢= F-¢- In other words, t 0 represents the average time for oxygen ions to reach the O 4+ and O 5+ states, after the comet’s transit, and t0 s the typical half-duration of the injection process. It would be possible to consider an injection process that is not point-like but also spreads out in space. We reserve this for future work. Figure 2. Intensity profiles vs. time taken at six different locations along the path of the comet. The dashed red line marks the time instant of the transit of the comet’s nucleus. The vertical dotted line indicates the moment at which the EUV emission starts to increase, hence when the oxygen ions start to emit. The time lag is calculated between these two vertical lines and must be corrected for the light travel time to the observer. 4 The Astrophysical Journal, 938:20 (13pp), 2022 October 10 Nisticò et al. In addition, we introduce in Q xtt,,()¢¢ afactorη(t)which is not strictly related to ion injection, but rather is a decay factor that corresponds to the ion beam aging. Here, η(t)describes the fact that after some time the oxygen ions pass from O 5+ to O 6+ and therefore the emission in the line 171 Å becomes negligible. Keeping a certain analogy with energetic particle transport, this effect is often modeled as a loss term in the transport equation, i.e., ∂f/∂t;−f/τ L with fthe particle distribution function and with τ L the loss time (e.g., Perri et al. 2016;LeRouxetal.2019).Sucha loss term leads to an exponential decay. Therefore, we model this factor as ttexp L () ( )h t=-, with τ L the ion lifetime, which is obtained from Pesnell & Bryans (2014). The probability Px x t t,()-¢ -¢is given by the Gaussian propagator, which is appropriate in the case of collisional diffusion: Px x t t Dt t xx Dt t ,1 4exp 4 6 xx xx 2 ⎡ ⎣ ⎢⎤ ⎦ ⎥ () () () () () p -¢ -¢= -¢ --¢ -¢ where the diffusion coefficient along the xdirection is given by D v xx D 1 3ran 2t=. Here, v ran is the disordered ion velocity after the ion “first”collision, and τ D the dispersion collision time (see discussion below). We note that the oxygen ion beam represents a strongly nonthermal distribution which can be unstable, so that wave–particle interaction can also contribute to the ion slowing down and diffusive spreading (e.g., Raymond et al. 2014).Here, however, we overlook this possibility and concentrate on collisional effects. By integrating Equation (3)over x ¢ and exploiting the delta function, we obtain nx t t dt t Dt t xu t Dt t ,1 4 exp 1exp 4. 7 t xx xx 0 0 slow slow 2 ⎧ ⎨ ⎩⎫ ⎬ ⎭ () () () () [ ( ( ))] () () ò hp tt =¢F¢ -¢ ´- ---¢ -¢ Further numerical integration over t ¢ gives the density profiles, which can be used for comparison with the striae observations. A summary of the functions and parameters defining the model are given in Table 1. 3.2. Collision Times for Oxygen Ions and Model Parameters The above modeling of the oxygen O 4+ and O 5+ density along the striae depends on a number of parameters. Keeping in mind that several simplifications are needed in order to obtain a manageable treatment, these parameters are determined as follows. The initial beam speed along the magnetic field u 0 is obtained from the projection of the comet’s speed on the magnetic field direction; because of projection effects, the angle θbetween Band v c is not well known. We note that Downs et al. (2013)consider that u 0 may be in the range 100–200 km s −1 , while Raymond et al. (2014)estimate a velocity parallel to the magnetic field of 183 km s −1 for some striae during the egress of comet Lovejoy. Here, we consider similar values of u 0 , of the order of u 0 =100 Figure 3. Scheme of the mechanism for the formation of the striae. Table 1 Description of the Functions and Model Parameters Function or Parameter Description ttexp L 0 () ( )h ht=- Ion beam aging τ L Ion lifetime texp tt 22 tt 0 0 02 0 2 ⎡ ⎣ ⎤ ⎦ () () F¢= - ps s F¢- Ion flux injection τ slow Decay time of the beam t 0 Injection time t0 s Time interval for ion injection xt x u t1exp 00 0 slow slow () [ ( ) ] tt¢= + - -¢ Motion of the beam u 0 Beam speed along the magnetic field D v xx D 1 3ran 2t=Diffusion coefficient v ran Random speed of suprathermal ions τ D Diffusion time 5 The Astrophysical Journal, 938:20 (13pp), 2022 October 10 Nisticò et al. km s −1 , which are determined also with the help of the observed motion of the stria front. We consider that the ion outflow velocity, assumed to spring radially out of the comet, can also causeasignificant spread in the value of u 0 . The temporal evolution of various ion fractional abundances has been studied by Pesnell & Bryans (2014); for O 4+ and O 5+ , which give rise to the emission lines O V and O VI , they find for an electron density n e =10 7 cm −3 a rise time of about 50 and 200 s, respectively, for O 4+ and O 5+ , and an exponential decay time of 300 and 800 s, respectively. Since both ion species contribute to the 171 Å emission line, considering that each oxygen ion goes through successive ionization states, we assume a lifetime for UV emission of τ L ;10 3 s, i.e., roughly the sum of the decay times for O 4+ and O 5+ . On the other hand, the rise times reported by Pesnell & Bryans (2014)and the time lags inferred from Figure 2are used to model the temporal evolution of emitting ion injection, that is, the delay time t 0 after the comet’s transit and the typical half-duration of the injection process: we assume initial values of t 0 =60 s and 80 s t0 s =, and then adjust these values to best match each stria profile (see Table 2). For the elongation and spreading of the oxygen ion beam, basic parameters are the collision times τ slow and τ D , see Equations (2)and (6). Because of the nature of Coulomb collisions, which implies a cross-section decreasing as U −4 , with Uthe relative speed between colliding particles (e.g., Gurnett & Bhattacharjee 2005), the time τ slow for the slowing down of a suprathermal ion beam and the time τ D for dispersion of suprathermal particles are longer than the collision time of thermal particles (e.g., Krall & Trivelpiece 1973; Downs et al. 2013). In turn, the suprathermal ions thermalize with the ambient plasma on a longer timescale than τ slow and τ D (Krall & Trivelpiece 1973). In this case, for an ion beam whose velocity is larger than the ion thermal velocity but slower than the electron thermal velocity, the following expression can be used (Krall & Trivelpiece 1973; Downs et al. 2013) m neq41 1 ln , 8 T eT m mU m m m T slow 2 22 14 32 32 T p T e e e 3 ⎡ ⎣⎤ ⎦ () ()() () t p » +++ L pk with m T and q T the mass and charge of the suprathermal beam particles, Uthe speed of suprathermal particles, ethe elementary charge, m p and m e the masses of proton and electron, κthe Boltzmann’s constant, ln 2 2 Lthe Coulomb’s logarithm. We have also assumed a coronal electron temperature T e ∼1.5 MK. An initial ion speed of the order of U;v c ;500 km s −1 could be taken. Actually, when computing the density of each stria we considered the comet’sspeedv c when it created the stria at a certain distance from the Sun r c . We note that Uis assumed to correspond to the comet’s speed because this is the initial ion speed that is involved in the collision processes, even if the average beam speed along the magnetic field u 0 is lower. In other words, we assume that gyromotion is not modifying the collision time since the gyroradius is very much larger than the interparticle distance. This collision time depends on the electron density n e , whichiskeptasafreeparametertobedeterminedbythefitofthe observed emission profiles. Now, we consider that after the first collision the ions of the beam move in a random direction, that is, are subject to a diffusive motion. In such a scenario, we can assume that the random velocity of dispersive motion v ran decays exponentially from the initial speed of the ions ∼v c to the thermal speed of oxygen, v thO ;40 km s −1 . Here we assume an intermediate value v ran =150 km s −1 , which is close to the geometrical mean of v c and v thO ; indeed, the geometrical mean, rather than the arithmetic mean, represents the fact that in an exponential decay the initial velocity quickly decreases. Then, τ D is determined by fitting the observed emission profiles in the EUV. Indeed, even the dispersion time depends on the local density as (Krall & Trivelpiece 1973) mv neq16 ln ,9 DT eT 2 ran 3 22()tp »L so that determining D v xx D 1 3ran 2t=by fitting the observed brightness profiles, we are able to estimate τ D and then n e . 4. Data Analysis and Comparison with Modeling 4.1. Striae Intensity Profiles from Observations To study the temporal evolution of some of the striae observed in 171 Å, we remapped the image data set into a new 2D grid, having the same pixel size as the original images and with the horizontal axis (x ¢ )parallel to the direction of motion of the comet and the vertical one (y ¢ )strictly perpendicular to its trajectory. Such a perspective is shown in Figures 4and 5. The comet’s path is outlined with a dotted red line and located at y100¢= pix in Figure 4and y150¢= pix in Figure 5. Online animations are also available. Remapping is necessary to trace the striae in the corona. We noticed that the locations where the striae emission starts during the inbound phase of the Table 2 Values of the Parameters Used to Reproduce the Intensity of the Striae Slit t c r c v c u 0 t 0 t0 s τ slow τ D n slow t n D tn e ±Δn e hh:mm:ss (R e )(km s −1 )(km s −1 )(s)(s)(s)(s)(10 7 cm −3 )(10 7 cm −3 )(10 7 cm −3 ) S1 23:53:57 1.57 493 60 90 80 400 40 3.6 6.4 5.0 ±1.4 S2 23:56:00 1.52 500 70 90 80 250 60 5.8 4.3 5.1 ±0.8 S3 23:57:14 1.50 504 80 120 80 400 50 3.7 5.1 4.4 ±0.7 S4 å 00:44:25 1.38 525 250 30 30 150 30 10.7 8.6 9.6 ±1.1 S5 å 00:45:45 1.40 521 200 20 20 200 50 7.9 5.1 6.5 ±1.4 S6 00:50:58 1.50 504 50 80 200 300 100 4.9 2.6 3.8 ±1.2 Note. The two inferred coronal electron densities, namely n slow tfrom Equation (8), and n D tfrom Equation (9), are also shown with their combined average. The symbol å indicates those striae whose intensity profiles are fitted in a less satisfactory way than the others, see Section 4.2. 6 The Astrophysical Journal, 938:20 (13pp), 2022 October 10 Nisticò et al. comet do not lie perfectly on the dashed red line, which outlines the comet’s path, but it is shifted a few pixels outwards. This is probably due to a systematic error in the position of the Sun’s center reported in the header of the FITS files when SDO/AIA was in the off-pointing mode of observations. A physical explanation could also be found in the action of radiation pressure that pushes outwards the fragments and dust grains, before getting sublimated and ionized. However, this effect should be negligible in the present observations. In fact, such a shift is not evident in the outbound observations when SDO/AIA did return to pointing to the Sun center. We manually selected a few bright striae, which are marked by dashed blue lines and labeled as S1,K,S6in Figures 4and 5. The intensity extracted from each slit and averaged over a width of 11 pixels for all the available time steps is stacked into columns forming then a time–distance (TD)map (Figure 6). Time is on the horizontal axis, given in minutes with respect to the time t c when the comet passes through the slit. Distance on the vertical axis, measured with respect to the position where the comet crosses the slit, is given in units of 10 3 km. The analysis of the TD maps can provide some information on the evolution of the oxygen ion emission. The signature of a stria in a TD map is in the majority of the cases pretty diffuse and extends along the positive direction of the vertical axis. We see a sharp boundary denoting the propagating front of the ions and a bright core moving more slowly. In addition, the emission also slowly propagates in the negative direction of the distance axis because of dispersion effects on the moving ions. The emission in the TD maps for slits S4 and S5 is very narrow and straight, indicating that the ions are quickly transported along the magnetic field lines. The emission starts almost 1 minute after the comet’stransitand lasts for a shorter time with respect to the other striae because of the higher collision rate with coronal particles. Given a time interval δt=2 minutes and an apparent distance covered by the emission of Δs∼(20–25)×10 3 km, the slope of the emission in the TD maps for S4 and S5 can be associated with an average ion beam speed of 167–208 km s −1 .Intheother cases, we also see some signatures coming from nearby structures, like a diffuse emission at the right side of the TD maps for the slits S2 and S6. In particular for S3, the shape of the stria signature has an inverted “V”-shape, which is the result of the merging of nearby striae, as it is found by inspecting the animation inbound.mp4. 4.2. Comparison between Observational and Modeling Profiles By focusing on the emission signature, the intensity profile at 171 Å as a function of distance at a given time (i.e., the intensity coming from a vertical line in the TD map)is compared with the squared density from Equation (7)in Figure 7–8. The latter is integrated numerically via Simpson’s rule and is computed over a spatial interval [−5, 5]×10 4 km with an integration step Δx=100 km. The integration in time is performed in a time interval of 600 s spanning the comet’s transit with a time step Δt=12 or 24 s. Figure 4. Reinterpolated image of the transit of Comet Lovejoy during the inbound phase as seen from SDO/AIA in 171 Å. The image is a composition of base ratio frames taken in the time interval indicated at the top of the panel. The red dashed line marks the comet’s path. The analyzed striae are marked by the dashed blue lines, and labeled as S1–S3. The associated animation is available (inbound.mp4). The 6 s video covers the transit of Comet Lovejoy in the corona from 2011 December 15, 23:46 UT to 2011 December 16, 00:16 UT. (An animation of this figure is available.) Figure 5. Same as in Figure 4but for the outbound phase of the comet’s trajectory. The striae marked by blue lines are labeled as S4–S6. The animation of this figure is available (outbound.mp4). The 9 s video covers the transit of Comet Lovejoy on 2011 December 16, from 00:40 to 01:28. (An animation of this figure is available.) 7 The Astrophysical Journal, 938:20 (13pp), 2022 October 10 Nisticò et al. EUV intensity and ion beam density are not directly comparable quantities. The EUV intensity from a pixel at a given wavelength I λ is defined as the convolution of the response function of the EUV filter R λ with the differential emission measure integrated along the line of sight h ¢ (Aschwanden 2004; Boerner et al. 2012): I R TDEMTdT,10 0 () () ( ) ò = ll ¥ where the differential emission measure is defined as D EM T n T h,dh dT 2 () ( )=¢ ¢with nbeing the free electron density of cometary origin, therefore proportional to the oxygen density (Schrijver et al. 2012, Supplementary Material).However,ifwe assume that oxygen ions are formed at a specific temperature value T 0 (see Table 1 of McCauley et al. 2013,wherethe temperature peaks for oxygen ions based on the CHIANTI model under the hypothesis of equilibrium conditions are reported)and that the density is approximately constant through the stria column depth h, the DEM function can ideally be expressed in terms of a delta function D EM T n T T dh dT 20 () ( )d=- ¢,hence: I RTnTdh RTnT dh RThnT,11 h h 0020 0200020 () () () () () () ( ) ò ò = == ll ll ¢ ¢ with hthe column depth of the stria. Therefore, provided the column depth hdoes not vary, under such assumptions, the intensity differs from the squared density only by the multiplicative factor R λ (T 0 )h. On the other hand, the computation of the theoretical intensity fluxes (in units of photons s −1 or DN s −1 )would require that the response function R λ is not based on the ordinary coronal abundances but instead on those of the mixture of coronal and cometary plasma. We avoid this issue by subtracting a background level from the stria intensity profiles and normalizing these to their maximum. The observed intensities and squared density profiles are given as blue and red lines, respectively, in Figure 7for slits S1–S3, S6, and in Figure 8for slits S4–S5. The parameters used to define the computed density profiles are educated Figure 6. Time–distance maps relative to the slits S1–S6 marked in Figures 4and 5. The position of the beam as a function of time obtained from Equation (2)at time steps of 24 s are overplotted as red dots in the TD maps for slits S4 and S5. For details, see Section 4.2. 8 The Astrophysical Journal, 938:20 (13pp), 2022 October 10 Nisticò et al. guesses, obtained by doing several manual trials until the red line does qualitatively fit the observed profiles. More specifically, we followed these steps: 1. Given a set of starting guessed values for the parameters, we numerically integrated Equation (3)and overplotted the computed squared density against the intensity profile; 2. We visually checked the overlap of the profiles, both in time and space; 3. If the profiles did not match well, we proceeded by changing the value of one parameter, we recomputed the modeled density and compared it to the observed intensity profile. If the profiles did not overlap again, we redid the procedure; Figure 7. Intensity profiles for the slits S1–S3 and S6 recorded with SDO/AIA (blue lines)and compared with the squared density profiles obtained from the modeling (red lines). 9 The Astrophysical Journal, 938:20 (13pp), 2022 October 10 Nisticò et al.