OPTICAL PROPER MOTION MEASUREMENTS OF THE M87 JET: NEW RESULTS FROM THE HUBBLE SPACE TELESCOPE

Because jet components are known to differ in size, intensity, and apparent location with wavelength, we used archival images only in a single filter, F814W (wide I band), which gives the longest possible baseline of 13.25 yr and a dense sampling in time. The total data set is comprised of nearly all the Advanced Camera for Surveys High Resolution Channel (ACS/HRC) and Wide Field Channel (ACS/WFC) archival images as well as those from WFPC2 (PC chip) in this filter. For ACS/HRC, we used 30 (48–50 s) exposures spanning 2002 November to 2006 November. For ACS/WFC, we used 217 dithered exposures (all 360 s) taken in 2006. For WFPC2, we used 161 exposures of 160–600 s, spanning 1995–2008; several shorter exposures of 30–40 s were not used due to poor signal-to-noise ratio.

The general method we have used is similar to that used (and described in detail) in Anderson & van der Marel (2010) and Sohn et al. (2012). The reference frame is based on the positions of hundreds of bright globular clusters associated with the host galaxy which are easily detected in the ACS/WFC images and are effectively stationary to proper motions over the time of this study. As cluster positions do not change with filter, the reference frame was built using 56 (500 s) ACS/WFC exposures of the field in the F606W filter, which has slightly better resolution than F814W. The reference frame was created by first detecting the positions of the globular clusters in each flat-fielded, Charge Transfer Efficiency (CTE)-corrected ACS/WFC image⁴ using a point-spread function peak-fitting routine, then applying the standard (filter-specific) geometric correction to those positions, and then finding the best linear transformation for each image which matches the positions in the individual (geometrically corrected) frames to a master reference frame. This last step is done by a routine similar to MultiDrizzle, but better optimized for astrometry. The process of finding transformations for all frames is iterated so that the master reference frame (super-sampled to a pixel scale of 0025 pixel⁻¹) effectively gives the average position of each reference source in a geometrically corrected frame.

The final reference system consists of positions and magnitudes for 1378 globular clusters within ∼100'' of the M87 core position. Among all clusters, the median one-dimensional rms residual relative to the mean position was 0.05 (reference frame) pixels (1.25 mas), corresponding to a systematic astrometric accuracy (×1/$\sqrt{5}6$) of 0.17 mas; over the 13.25 yr baseline this is equivalent to 0.003c.

Astrometric solutions were then found for all the ACS/HRC, ACS/WFC, and WFPC2 images in F814W, except that the linear transformation solution between the individual (corrected) images and the reference frame was found once rather than iterated. Typical numbers of globular clusters used to match the frames were ∼200–500 for ACS/WFC, ∼15–30 for WFPC2 images, and ∼15–25 for ACS/HRC; corresponding systematic errors were ∼0.006, ∼0.03, and ∼0.05 pixels, or 0.003c, 0.015c, 0.025c over 13.25 yr, respectively.

Because of the difficulty in measuring the diffuse/complex knot structures particularly in the noisy HRC images and shorter WFPC2 images, we chose to first identify the peaks of interest using stacked images. The image stacks include the 2006 ACS/WFC stack, four WFPC2 stacks (epochs 1995–1996, 1998–1999, 2001, and 2007–2008), and three stacks of ACS/HRC exposures (2002 November–2003 November, 2004 July–2005 September, 2005 November–2006 November). The host galaxy was modeled using the ACS/WFC stacked image with the IRAF/STSDAS tasks ellipse and bmodel and then subtracted. Seven jet regions were cut out from these images, corresponding to knots HST-1, D, E, F, I, A+B, and C (see Figure 1).

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A two-dimensional continuous functional representation of the image cutouts was then created using the Cosine Transform function (FourierDCT) in Mathematica, which allowed us to find prominent peaks, as well as contours of constant flux level around those peaks. In general, the number of interesting peaks was chosen by hand, and the contour line levels were at 50% of the flux of the peak, after a "background" level was subtracted, the latter estimated as the minimum flux level between the particular peak and the next nearest peak. The positions defining the contour were "reverse-transformed" from master frame coordinates into each distorted, galaxy-subtracted image so that an intensity-weighted centroid position from the pixels within the contour could be calculated. These final positions were then transformed back into the common reference frame, so that each peak of interest was measured in every exposure, resulting in hundreds of position measurements spread over the 13 yr baseline.

To measure the apparent motion of the jet components over time, we define the x-direction as the line from the core through the center of knot I (position angle of 290°), with y-direction perpendicular. Data were binned into 26 time bins (depicted in Figure 2), and a linear model was fit using standard weighted least squares. The weights were taken to be the inverse of the variance for each time bin, as measured from the 10 nearby globular cluster reference sources (discussed below). For each feature and in each direction, we also attempted to fit the data with a quadratic to look for accelerations. When the analysis of variance favored the quadratic over the linear model at a 95% level or greater, the quadratic fit is noted in Table 1 along with the linear fit. The apparent speed (β_app) in each direction in units of c is also given; where the quadratic fit is favored β_app corresponds to the speed at the mean date of 2004.06.

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The method was tested using 10 globular clusters near to the jet, each of which was measured as described above, with contour levels drawn at 50% of the peak intensity. Each set of cluster positions was binned into the 26 time bins spread between 1995 and 2008, and for each bin the mean position for all 10 clusters was subtracted from the positions so that the variance in the estimates could be measured from all clusters as a function of epoch for use in the weighted linear least-squares fit. The measured variance was essentially constant across all epochs at ∼0.1 reference pixels. Linear fits to the x- and y-direction positions versus time in all cases were consistent with a slope of zero, with typical errors on the order of 0.003 pixels yr⁻¹ or 0.02c.

Knot D is the most consistently bright feature after the knot A/B/C complex, and significant proper motions were measured in both previous studies.⁵ As suggested by the contours overlaid on Figure 1, D-Middle is one of the fastest components with a speed of 4.27 ± 0.30c along the jet, while the brighter D-West shows evidence of deceleration radially, slowing to a near stop by the final epoch in 2008, while maintaining one of the largest transverse speeds of −0.59 ± 0.05c (see Figure 2). These measurements are consistent with the results of B99 (5.26 ± 0.92c and 2.77 ± 0.98c for D-Middle and D-West, respectively), where we compare with our estimated velocity of D-West in 1996 of 2.73 ± 0.40c from the quadratic fit.

Previous results on knot D-East have been conflicting: B95 found that it moved inward along the jet at 0.23 ± 0.12c (possibly consistent with being stationary), while B99 found a large outward apparent velocity of 3.12 ± 0.29c; our result of 0.28 ± 0.05 is more in line with B95. It is possible that there is a stationary feature at D-East, through which components emerge (analogous to what is seen in HST-1). In that case, the higher-resolution Faint Object Camera was perhaps tracking an emerging bright component, while over longer periods the global feature at D-East is stationary.

As shown in the central lower panel of Figure 1, the main knot structure of knot E (E-West) is complex, with a moderately superluminal speed of 1.91 ± 0.14c, about half of that found in B99 (4.07 ± 0.85c). In addition to the 50% intensity contrast contour line shown, a lower-intensity contour at 30% has been drawn around this area to illustrate the morphological changes of this feature over time. To the west there appears a bright extension in the 1995 epoch which advances westward faster than the brightest part, and rapidly fades in the later epochs. Interestingly, a new component appears to the east in 2008, suggesting again the possibility of a favored location or stationary feature, which should be checked with future observations.

Like knot E, the next feature in the jet, knot F, is diffuse, faint, and apparently complex. We track two broad features, F-East and F-Middle, as shown in the lower right of Figure 1. As B99 were unable to measure proper motions for anything beyond knot E, the only previous measurement gives 0.90 ± 0.23c in B95, for the entire diffuse feature seen in the radio. This is slightly faster than the value we measure for the most prominent component F-Middle (0.36 ± 0.14c); however, the epochs of observation are not contemporaneous and slight deceleration is possible.

Finally, knot I has a slight negative velocity along the jet axis, of −0.23 ± 0.12c. The knot clearly fades steadily with time, as shown in the upper left of Figure 3. This knot is the clearest case of a possible stationary feature in the jet outside of the upstream component HST-1d which has been extensively observed with VLBI (β_app < 0.25c; Cheung et al. 2007).

The outer part of the jet looks very different from the evenly spaced knots discussed previously. Knot A is the brightest feature in the entire jet, excepting HST-1 during its remarkable flare of 2002–2008 (Harris et al. 2006). It has been suggested that knot A is an oblique shock which precipitates the breakup of the orderly structure of the jet, thus resulting in the complex knot B region downstream, and the final knot C feature which is considerably off the main jet axis (Bicknell & Begelman 1996). Within the bright but extended knot A, we track two features which appear on top of this more diffuse emission (see Figure 3). For A1, we find a relativistic velocity of 1.32 ± 0.12c; however, it is not clear that this feature is really a single component, as the western side of it appears to move slowly, if at all. For A2, we measure a much slower radial velocity of 0.31 ± 0.06c, consistent with the previous results of 0.4–0.6c from B95.

Qualitatively, the A/B complex is surprisingly "active" with new features brightening up and moving with high speeds relative to other nearby components. A good example is pointed out by the arrow in the last epoch of the central panel in Figure 3, where a "bar" has formed between B3 and B4. At the same time, within region B4 a separation is taking place, leaving a small knot behind to the northeast. While B4 is probably a complex of at least two to three "subknots," we used the inner contour (at 80% median flux), giving us an apparent speed of 1.66 ± 0.11c along the jet direction. B1, B2, and B3 as well as the final knot C show significant apparent velocities in both directions, on the order of 0.5–1.5c.

The final terminus of knot B is particularly interesting, as a new distinct component (which we have labeled B5-n) appears in the northern half in the 2001 epoch. Using data from 2001–2008 only (the time when this component was detected), we measure an apparent velocity of 2.16 ± 0.35c along the jet direction and 1.30 ± 0.31c in the transverse direction. Qualitatively, the northern end of B5 seems to continuously brighten while the whole feature stretches up toward the northwest. In knot B, generally there is a repeating motif of two bright regions connected by a fainter "bar"; this is apparent between knots B1 and B2, between B3 and the remnant of B4, and the two halves of B5.

The most striking finding of the outer jet component velocities is depicted in the lower panel of Figure 3, where the velocity vectors are plotted from the center of each knot. There is a conspicuous "tip-to-tail" alignment of almost all the vectors within the outer knot A/B/C complex, strongly suggestive of a flattened view of a helical motion which might result in such a "zig-zag" pattern, though this should be checked with theoretical modeling.