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plasma tails of comets and their time variations potentially provide crucial information on solar winds and magnetic fields in the solar system ( e.g. , * ? ? ? * ; * ? ? ? * ; * ? ? ? short - time variations in plasma tails , however , are not yet fully understood . indeed , most previous studies observed tails and structures at far distances ( @xmath3 km from the nucleus ) with a time resolution of an order of an hour .    regarding the speed of movement along the tail , @xcite studied 72 disconnection events ( des ) of various comet tails and found @xmath4 100 km s@xmath2 at @xmath5 km from the nuclei . their initial speeds before des are around 44 km s@xmath2 and the typical acceleration is 21 cm s@xmath6 . @xcite analyzed a knot in the plasma tail of comet 1p / halley and derived its average velocity of 58 km s@xmath2 at 49 @xmath1 km from the nucleus . @xcite observed c/1996 b2(hyakutake ) and measured the speed of a knot of 99.2 km s@xmath2 at 5.0 @xmath7 km from the nucleus . @xcite investigated de of c/1995 o1 ( hale - bopp ) and obtained the speed of @xmath0 500 km s@xmath2 at @xmath0 7@xmath8 km from the nucleus . @xcite analyzed several knots in comets c/2001 q4(neat ) and c/2002 t7(linear ) using the solar mass ejection imager . they found the speed to be 50100 km s@xmath2 around @xmath9 km from the nucleus . these previous studies did not catch the moment immediately after the formation of knots or the detachment of knots from the tail . the initial speed at these critical times was only an extrapolation from later observations relatively far away . in this letter , we report detections of knots in the plasma tail 3@xmath1 km away from the nucleus of c/2013 r1(lovejoy ) and a direct measurement of their initial motions . we adopt the ab magnitude system throughout the paper . the comet was observed on 2013 december 4 ( ut ) using the subaru prime focus camera ( suprime - cam ; * ? ? ? * ) mounted on the subaru telescope at mauna kea ( observatory code 568 ) . the camera consists of a 5 @xmath10 2 array of 2k @xmath10 4k ccds . the pixel scale is 0.202 arcsec pixel@xmath2 . the field of view is about 35@xmath1028 arcmin . we used two broadband filters : w - c - ic ( i - band : center=7970  , full width at half maximum ( fwhm)=1400 ) and w - j - v ( v - band : center=5470  , fwhm=970 ) filters . both bands trace the plasma tail . i - band includes predominantly h@xmath11o@xmath12 line emissions , while v - band includes co@xmath12 and h@xmath11o@xmath12 line emissions . the observation log is given in table [ tab : obslog ] . the total observing time of 24 minutes was spent after main science targets of the observing run were set . the start time of the exposures have an uncertainty of about 1 second . the position angle and the pointing offset were adopted to catch the comet nucleus at the bottom - left corner and to have the tail run diagonally across the field - of - view so that the maximum extent of the tail is framed in each exposure . the subaru telescope s non - sidereal tracking mode@xcite was used so that the comet was always observed at the same position on the ccd array . for the observing run , the comet s coordinates were calculated using the nasa / jpl horizons system with the orbit element of jpl#22 . we used an ephemeris of one - minute step . unfortunately , the values of jpl#22 were not recorded . in the following , we instead used newer orbital elements ( jpl#55 ) . the values are given in table [ tab : orbit ] . the positions calculated from jpl#22 and jpl#55 have an offset by 0.34 arcsec in right ascension and -1.88 arcsec in declination but show no drift during the observation . the offset of the absolute celestial coordinate does not affect in this study , since our analysis is on relative position of structures inside of the comet . at the time of the observations , the observercentric and heliocentric distance to the comet were 0.55230.5526 and 0.88120.8811 au , respectively . in the sky projection , the conversion from the angular to the physical scales was 400.6400.8 km arcsec@xmath2 . considering the phase angle ( sun - target - observer angle ) of 83.5 degrees at the time of the observations , we adopt the physical scale along the tail of 403.3 km arcsec@xmath2 in the following discussion . the heliocentric ecliptic coordinate of the comet nucleus was ( @xmath13,@xmath14)=(87.5,30.7 ) . the comet was located before the perihelion passage , and its heliocentric velocity was -12.6 km s@xmath2 .    the seeing size is estimated from short ( two - second ) exposures and was 1.0 and 1.1 arcsec in i and v - bands , respectively . the movement of the comet in the celestial coordinate was about ( dra@xmath10cos(d)/dt , d(d)/dt)=(283 284,-115 ) arcsec hr@xmath2 during the observations . due to the non - sidereal tracking , stars move in an exposure , but this motion does not affect the measurement of the seeing size significantly since the shift is only about 0.17 arcsec in a two - second exposure .    the data was reduced in a standard manner ; the steps include overscan subtraction , crosstalk correction @xcite , flat fielding using twilight flat , and distortion correction . the relative flux and relative position among the ccds are calibrated using other dithered datasets taken in the same night . the mosaicked image of v1 ( table [ tab : obslog ] ) is shown as figure [ fig : v1 ] as an example . the flux was calibrated against stars in the field using the eighth data release of the sloan digital sky survey ( sdss dr8 ; * ? ? ? * ) catalog in the same way as in @xcite . we first used sextractor @xcite for object detection in the suprime - cam images and astrometric calibration was performed to the center of the elongated stars against the guide star catalog 2.3.3 @xcite . then , we measured aperture fluxes at each position of sdss star whose r - band magnitude is 16@xmath15r@xmath1520 . the aperture radius was 40 , 50 , and 60 pixels , and we used @xmath16\ ] ] as the background - corrected aperture flux of an elongated star , where @xmath17 is the aperture flux of @xmath18 radius . photometric zero point was estimated from the instrument flux @xmath19 and the catalog magnitude converted to the suprime - cam ab system . the color conversion coefficients from sdss to suprime - cam magnitudes are given in table [ tab : colorcoeff ] . the k - correct @xcite v4 offset for sdss is applied ; @xmath20=0.012 , 0.010 and 0.028 for @xmath21 , @xmath18 and @xmath22 , respectively . the number of stars used for calibration was @xmath23 in v and @xmath24 in i. the measured photometric zero - point of chip 2 ( reference chip ) was 27.36(i ) and 27.15(v ) ab mag per 1 adu s@xmath2 , and the peak - to - peak variation among exposures were smaller than 0.02 mag in each band . these zero points are comparable to the ones derived typically under photometric conditions , and thus we regard the data as having been obtained under photometric conditions . to investigate the fine structures in the plasma tail , additional image processing was applied . first , we rotate the image counterclockwise by 50 degrees so that the plasma tail aligns to the y - axis , and the region around the plasma tail within full width of 1000 pixels ( 3.4 arcmin ) was extracted . the position angle of the image to the north is the same among the nine images ( 160.0 degree ) . in the coordinate , the sun lay in the direction of ( x , y)=(-0.014,+1.000 ) . the nuclei position was measured in short exposures ( i2 and v2 ) . the relative positional consistency among the images depends on the accuracy of the non - sidereal tracking mode of the subaru telescope . as we used the ephemeris of a one - minute step , enough accuracy is guaranteed . we then applied an unsharp masking technique to each image ; we convolved the extracted images with various sizes of gaussian filter ( @xmath25=10 , 20 , 30 , 50 , 75 pixels ) and subtracted the smoothed image from the original ones . the details are presented in appendix a. this processing removes larger structures and enhances fine structures . to differentiate the processing with different kernel sizes , we refer to each as highpass@xmath26 , e.g. , highpass10 when processed with the gaussian with @xmath25=10 pixels . bright stars in the background contaminate small features associated physically with the cometary tail ( e.g. , knots ) , and hence , we iteratively masked them . finally , we binned the image by 5@xmath105 pixels ( 1.01 arcsec square ) . figure [ fig : knots ] shows six longer - exposure images after the processing . these images show the gaps between ccd chips as gray bands . brightening / darkening around chip edges are artifacts . these do not affect the following analyses . we can visually see two knots moved downstream around the distance of @xmath0 3@xmath1 km from the nucleus ( indicated by arrows in figure [ fig : knots ] ) . the closeup images are shown as figure [ fig : closeup ] . one of the knots first appears to be connected to the global filamentary structures running along the tail . it later becomes detached from the structures . the positions of the knots are measured by running sextractor @xcite on the 5@xmath105 binned unsharp masked images . we measured in highpass30 , highpass50 , highpass70 , and highpass90 images . as examined in appendix b , an unsharp masking with a smaller kernel may introduce larger positional errors . meanwhile , the knot may not be detected after an unsharp masking with a large kernel because it is buried in global features . we therefore adopted the position from the largest kernel in which the peak of the knot is detected . the root mean squares ( rms ) of the position was @xmath27 km . distances from the nucleus ( along the tail ; y - axis ) and offsets from the tail axis ( perpendicular to the tail ; x - axis ) are plotted as a function of time in figure [ fig : speed ] . 20 and 25 km s@xmath2 along the tail and 3.8 and 2.2 km s@xmath2 across the tail , respectively . the motion should make the shape of the knots elongated in a two - minute exposure by 67 arcsec along the tail and 1.3 or 0.7 arcsec across the tail . since the size of the knots is at least 1015 arcsec in diameter , elongation by the motion had little effect on the size estimation . these knot motions show tilts from the central axis of the tail by about 0.10.2 radians ( 611 degrees ) . we note that the direction to the sun is 0.014 radians ( 0.8 degrees ) from the axis , and therefore , the knot motions are not in a perfect alignment to the direction to the sun .    the distances to the knots from the nucleus change almost linearly with time in figure [ fig : speed ] . the effect of acceleration is therefore small in the short duration of our observations ( 23 minutes ) . the clear detection of the spatial motions , however , indicates the potential for direct measurements of the acceleration in future . if we can take the accelerations of previous measurements of other comets by @xcite ( 21 cm s@xmath6 ) , the expected change in the speed is only 0.3 km s@xmath2 in 23 minutes . if we adopt 17 cm s@xmath6 , which is calculated from figure 4 of @xcite as 2.4 km s@xmath2 increment is seen in four hours , the expected change in the speed during our observation is even smaller ( 0.2 km s@xmath2 ) . therefore , a sequence of few hours observations of a knot would permit us to measure the acceleration . we found that the width of the plasma tail also rapidly changed . in the analysis , the original images before the unsharp masking were used . in figure [ fig : itail ] and figure [ fig : width ] show spatial surface brightness profiles across the tail and their time variation . since we have measured the motions of the knots ( presumably the motion of the tail ) , we can track the variation in the tail width at a comoving position as the tail would flow at the speed of @xmath0 22 km s@xmath2 . in a sequence of images ( i1 , i3 , and i4 ) , we measured a profile at the distance of 6@xmath1010@xmath28 km in i1 . we then tracked the location of the material initially at this distance , but at later times using the flow speed , and plotted the profiles of ( presumably ) the same material in i3 and i4 . the tail width is determined at the surface brightness of 21.3 ab magnitude arcsec@xmath6 in i - band . it narrowed from 2.4@xmath29 to 2.0@xmath29 , and then to 1.8@xmath29 km for i1 , i3 , and i4 , respectively .    from this measurement , the speed of the narrowing motion across the tail is @xmath0 8 km s@xmath2 at each edge . the center of the light distribution , meanwhile , did not show any notable change ( figure [ fig : width ] ) . this narrowing speed is larger than those of the knots in the same direction perpendicular to the tail ( 3.8 and 2.2 km s@xmath2 ; section [ sec : knots ] ) . this apparent difference could be attributed to a projection of the motion of the knots in the sky . if we assume every fine structure ( filamentary structure ) in the tail is moving at @xmath0 8 km s@xmath2 perpendicular to the tail , the amount of spatial shift would be about 2.5 arcsec within the 120-second exposures . on the other hand , the fine structures appear to be a typical 5 10 arc sec width in short exposures ( i2 , v2 ) . therefore , the blur due to the motions during a single 120-second exposure should not affect the positional measurements of the structures much . the initial speeds of two moving knots ( @xmath0 22 km s@xmath2 ) are significantly slower than the ones measured by @xcite ( 44 km s@xmath2 ; rms of 10.9 km s@xmath2 ) . this speed is also smaller than that measured in comet halley by @xcite ( 58 km s@xmath2 ) , who suggested that the velocity was constant at 49 @xmath1 km from the nucleus . though it is not clear what the dominant factor of the initial speed of knots is , we can compare several parameters of the comets . as the data used by @xcite include information from various comets , we compare parameters with the single case of the comet halley by @xcite . at the observation by @xcite , the heliocentric distance to comet halley was 1.016 au , the heliocentric ecliptic coordinate was ( @xmath13,@xmath14)=(30.1,8.8 ) , and the heliocentric velocity was -26.5 km s@xmath2 . compared with c/2013 r1(lovejoy ) in this study , a part of the difference in the initial speed may be explained by the difference in the heliocentric velocity of the nucleus , -12.6 km s@xmath2 versus -26.5 km s@xmath2 , if we assume that the initial speed of the knots might be comparable in heliocentric frame . it , however , does not fully explain @xmath0 40 km s@xmath2 difference . another difference is heliocentric ecliptic latitude , 30.7 vs 8.8 , which may result in the difference in the speed of the solar wind at the comet position . yet another point is that we have compared the speeds of our relatively faint and small knots with more prominent knots / kinks and des in the previous studies . the relevance of this comparison might be debated in light of future studies . in addition , we analyzed only one comet tail observed in a relatively short duration . a more systematic investigation is obviously needed as to the distribution of the initial speed of the tail as a function of the heliocentric velocity , the heliocentric distance , and the ecliptic position of the comet .    in summary , we found two knots that were just formed at 3@xmath1 km from the nucleus of c/2013 r1(lovejoy ) . their initial speed was smaller than the ones measured in previous studies , and a physical interpretation requires a more statistically significant sample at various heliocentric positions . we also found a rapid variation in the tail width in seven minutes , which implies a rapid change in ambient solar winds and magnetic field . these results strongly suggest that the variations in comet plasma tails , especially in their fine structures , require high time resolution observations with a large aperture telescope such as subaru . this work is based on observations obtained with the subaru telescope . we acknowledge david thilker , alexandre y. k. bouquin , fumiaki nakata , and yutaka komiyama for their help . we thank miriam forman for suggestive comments . we also thank anonymous referee for useful comments . this work has made use of sdss dr8 database , horizons ephemerides service in nasa / jpl , and the computer systems at astronomical data analysis center of naoj . jk is supported by the nsf through grant ast-1211680 and by nasa through grants nnx09af40 g , nnx14af74 g , a herschel space observatory grant , and a hubble space telescope grant .
we report short - time variations in the plasma tail of c/2013 r1(lovejoy ) . 
 a series of short ( two to three minutes ) exposure images with the 8.2-m subaru telescope shows faint details of filaments and their motions over 24 minutes observing duration . 
 we identified rapid movements of two knots in the plasma tail near the nucleus ( @xmath0 3@xmath1 km ) . 
 their speeds are 20 and 25 km s@xmath2 along the tail and 3.8 and 2.2 km s@xmath2 across it , respectively . 
 these measurements set a constraint on an acceleration model of plasma tail and knots as they set the initial speed just after their formation . 
 we also found a rapid narrowing of the tail . after correcting the motion along the tail 
 , the narrowing speed is estimated to be @xmath0 8 km s@xmath2 . 
 these rapid motions suggest the need for high time - resolution studies of comet plasma tails with a large telescope .