Global Deceleration and Inward Movements of X-Ray Knots and Rims of RCW 103

The kinematics of shocks, ejecta knots, and the compact remnant of a supernova remnant give insights into the nature of the progenitor and the surrounding environment. We report on a measurement of the proper motion of X-ray knots and rims of the magnetar-hosting supernova remnant RCW 103. Chandra data obtained in three epochs, 1999, 2010, and 2016, are used. We find a global deceleration of 12 knots and rims in both northern and southern regions within the last ∼24 yr, even though the age of the remnant is thought to be greater than 2 kyr. Some of them even changed their directions of motion from outward (∼1000 km s−1) to inward (∼−2000 km s−1). Our findings can be explained by a collision with a high-density medium at both the northern and southern edges of the remnant, although the remnant may still be expanding in the windblown cavity. The proper motion of the associated magnetar 1E 161348−5055 is possibly detected with a velocity of ≈500 km s−1.


INTRODUCTION
RCW 103 is a young or middle-aged supernova remnant (SNR) hosting the compact object 1E 161348−5055 (Tuohy & Garmire 1980).Its age, i.e., elapsed time after the supernova explosion, is estimated to be 2.0-4.4 kyr (Carter et al. 1997;Braun et al. 2019).It has a nearly circular shape with a spatial extent of ∼ 10 ′ or ∼ 9 pc at the estimated distance of 3.1 kpc (Reynoso et al. 2004).Interestingly, its morphologies are similar among radio, infrared, optical, and X-rays.All show bright emissions in the southern large area and northern small part.Radio continuum observations revealed a smooth structure without clear shells (Dickel et al. 1996).Paron et al. (2006) found an interacting 12 CO cloud in the southern area.Infrared observations also found interacting H 2 gas and other elements (Oliva et al. 1990(Oliva et al. , 1999;;Rho et al. 2001;Reach et al. 2006;Pinheiro Gonçalves et al. 2011).A 1720 MHz OH maser Corresponding author: H. Suzuki hiromasa050701@gmail.com detection from the southern area also supports the cloud interaction (Frail et al. 1996).Carter et al. (1997) detected Hα filaments from both south and north, with the northern filament being much fainter.They estimated the age to be ∼ 2 kyr based on optical proper motions of ∼ 1, 100 km s −1 .
The compact object 1E 161348−5055 has been known as an extraordinary compact object with a very long periodicity ∼ 6.67 h (De Luca et al. 2006).In 2016, it exhibited a bursting activity and began to be recognized as a magnetar (D'Aì et al. 2016;Rea et al. 2016;Tendulkar et al. 2017).Previous X-ray observations shed light on the relation between the progenitor and magnetar (Nugent et al. 1984;Frank et al. 2015;Braun et al. 2019;Zhou et al. 2019).A common conclusion is that the supernova explosion was less energetic (with an explosion energy of 10 49 -10 50 erg) and the progenitor was not very massive (≲ 13 M ⊙ ).Most recently, Narita et al. (2023) identified X-ray emission from shock-heated circumstellar medium (CSM) near the edges of RCW 103.They found an enhanced N/O abundance ratio (∼ 4) of the CSM, and suggested that the progenitor rotation was not rapid (≲ 100 km s −1 ) and a magnetar forma-tion by dynamo effects in massive stars (> 35 M ⊙ ) is unlikely.
From another aspect, constraining the X-ray kinematic properties including movements of forward shocks, ejecta knots, and the associated magnetar is of great importance as well to understand the nature of the progenitor and magnetar.In this paper, we report on proper motion measurements of X-ray bright knots and rims, and the associated magnetar.Out original purpose was to determine the explosion center and obtain tight constraints on the age and kinematics.However, we find a global deceleration and inward movements of the X-ray knots and rims.In Section 2, we summarize the observation log and data reduction processes.Our proper motion analysis and results are described in Section 3. We discuss the origin of the deceleration and inward movements in Section 4, and conclude in Section 5.

OBSERVATION AND DATA REDUCTION
We use five Chandra ACIS-I (Garmire 1997) observations of the RCW 103 region listed in Table 1, which consist of three epochs (1999, 2010, and 2016).The baselines for the proper motion study are ≈ 11 yr and ≈ 6 yr, for the first and second intervals, respectively.The observation log is summarized in Table 1.
We use the analysis software CIAO (v4.15;Fruscione et al. 2006) and calibration database v4.10.2 for the data reduction and analysis.We process the raw data using the standard data reduction method (chandra repro).

ANALYSIS AND RESULTS
We perform a proper motion study on RCW 103.The procedures and results are presented in this section.In our analysis, we use the software HEASoft (v6.30.1;HEASARC 2014), XSPEC (v12.12.1;Arnaud 1996), and AtomDB 3.0.9.Throughout the paper, uncertainties in the text, figures, and tables indicate 1σ confidence intervals.
Figure 1 presents an X-ray image of the whole remnant with our analysis regions.We choose bright knots and sharp edges as our analysis regions.The profile extraction directions are determined by eye to roughly correspond to the directions perpendicular to the boundaries or toward the geometric center of the remnant.

Aspect correction
To maximize the reliability and accuracy of the proper motion measurement, we perform the aspect correction to individual observations.As a large fraction of the central region of the field of view is covered by the bright target source, we only find 7-9 point-like sources with Reg. 1 6.00e-08 6.09e-08 6.28e-08 6.65e-08 7.39e-08 8.89e-08 1.18e-07 1.77e-07 2.96e-07 5.31e-07 9.99e-07 off-axis angles of > 4 ′ .We perform the correction with the CIAO tool wcs match and wcs update.Considering the small number of detected point-like sources and their off-axis positions, we perform coordinate transformations without rotation and scaling.The resultant transformation parameters are listed in Table 1.The relative offsets of 0.1-0.6 pixels, which correspond to 0. ′′ 05-0.′′ 3, are reasonable according to the pointing accuracy of Chandra ACIS-I, ≈ 0. ′′ 67. 1

Proper motions of X-ray knots and rims
We measure proper motions using radial profiles extracted from the regions indicated in Figure 1.The two observations in 2010 are merged after the aspect correction.The same process is done for the observations in 2016.Thus, hereafter, we use three images obtained in 1999, 2010, and 2016.Flux profiles are extracted from the exposure-corrected images in the 0.5-5.0keV energy range.Two examples are shown in Figure 2 (a-1) and (b-1).
We use the same method as that taken in Tanaka et al. ( 2021) and Suzuki et al. (2022) in calculating the velocities.Two profiles obtained from two epochs are used.We artificially shift the second profile by ∆x and evaluate the difference against the first one with χ 2 (∆x), which is defined as where f i and ∆f i indicate the flux and error of the bin number i in the first observation, and g i and ∆g i indi- cate those of the shifted second profile.This calculation is repeated with various values of ∆x and we obtain χ 2 as a function of ∆x.The minimum χ 2 value (χ 2 min ) and corresponding shift (∆x min ) are determined by fitting the χ 2 -∆x plot with a parabola function.We calculate proper motion velocity from the best-fit ∆x min and known baselines.The profile shift is not limited to an integer multiple of the bin width.We re-bin the shifted profile g(∆x) with the same bin arrangement as f with an assumption of a uniform probability distribution inside each bin.Then, the profile-shift ranges that give χ 2 (∆x) = χ 2 min + 1 are calculated from the best-fit parabola functions.These ranges are considered to be 1σ confidence ranges of the profiles shifts.
The χ 2 -∆x plots of Reg. 5 and Reg.6 are shown in Figure 2 (a-2) and (b-2), respectively.The ∆x min values in the second interval (2010 to 2016) are negative, whereas those in the first (1999 to 2010) are positive.These indicate that their movements were outward before 2010 but they changed their moving directions to inward after 2010.We show the calculated velocities of all the analysis regions in the two intervals in Table 2 and Figure 3.One can see a global deceleration from the first to second interval.Among them, Regs.5-8 are firmly found to be moving inward in the second interval.
We here evaluate possible systematic uncertainties.The pointing accuracy of Chandra has to be considered, which would be < 0. ′′ 67 after the aspect correction.Even if we assume that the astrometry offsets between the images are significant, some of the knots or rims still should be moving inward in the second interval, because the analysis regions include both northern and southern edges.The profile extraction directions are determined by eye, and thus the measured velocities will have some uncertainties due to deviations from the true moving directions.We evaluate this uncertainty by slightly changing the extraction direction (±10 deg) of Reg. 6, finding a ≲ 100 km s −1 variation in velocities.This uncertainty is not significant because the statistical uncertainties are much larger.We also repeat the analysis procedure with 1) an alternative aspect correction with an optical source catalog and 2) different extraction energy ranges of 1.0-5.0keV and 1.5-5.0keV.The measured velocities are largely consistent with the ones obtained above with the same tendency (See Appendix A and B).  3 and 4).

Proper motion of the associated magnetar 1E 161348−5055
Using the aspect-corrected, 0.5-5.0keV images, we measure the proper motion of the associated magnetar, 1E 161348−5055.For individual observations, we determine the positions of the magnetar and their statistical errors using the CIAO tool wavdetect.The determined locations are presented in Figure 4.The angular displacement between 1999 and 2016 (ObsID 18854) is measured to be 0. ′′ 585 ± 0. ′′ 025, which is converted to 501 ± 21 km s −1 at a distance of 3.1 kpc (Reynoso et al. 2004).We note that this displacement might be insignif- Reg. 5 Reg. 6 if we consider systematic uncertainties due to the pointing accuracy.

DISCUSSION
We find a global deceleration of the X-ray knots and rims in RCW 103 in the last ∼ 24 yrs, even though its age is thought to be larger than 2 kyr.Some of them were even moving inward in the second interval, from 2010 to 2016.We here discuss the origin of this sudden deceleration.Narita et al. (2023) proposed that X-ray emitting plasma near the outer edges are CSM dominated.They also suggested that the remnant is still expanding in the wind-blown bubble based on the derived progenitor properties.The X-ray bright southern and northern edges, on which this work focuses, coincide with the locations of Hα emission (Carter et al. 1997).The southern edge is thought to be interacting with a molecular cloud (Dickel et al. 1996).Considering these facts and suggestions, we propose a scenario that both northern and southern regions interact with molecular or atomic clouds, although the remnant is still expanding in the wind-blown bubble.We assume that the northern part is also interacting with a high-density medium but it is yet to be detected.The weaker Hα emission and slower deceleration in the northern part support an interpretation that the interacting medium there has a lower density than the southern part.Regs.5-8 are found to have decelerated from ∼ +1, 000 km s −1 (outward) to ∼ −2, 000 km s −1 (inward).This can be interpreted as a reflection of the shocks due to a collision with a high-density medium.The shock reflection by an interaction with a high density cloud is studied analytically by Miesch & Zweibel (1994) and Inoue et al. (2012).For a high Mach number incident shock, like an SNR blast wave shock, the relation between the incident/reflection shock velocities and density jump at a cloud surface is given by eq.(A3) of Inoue et al. (2012).In the case of an incident shock velocity ∼ 1, 000 km s −1 and a reflection shock velocity ∼ −2, 000 km s −1 , the required density jump is calculated to be ∼ 36.This is consistent with a typical density jump between a diffuse ISM and HI clouds.We note that a shock wave can be reflected whereas shockheated plasma will not be.The reflected shock enhances thermal X-rays while moving inward, which can be observed as an inward movement if the newly enhanced emission is bright enough.If the observed X-ray radial profiles originate from mixtures of outward-and inwardmoving plasma, actual reflected-shock velocities in the observer's frame might be larger than the measured velocities.
Inward moving filaments were found in a few other young SNRs, such as Cassiopeia A (Sato et al. 2018) and RCW 86 (Suzuki et al. 2022).The inward filaments are interpreted as reverse shocks for Cassiopeia A and reflection shocks for RCW 86.The case of RCW 103 is similar to RCW 86.A large difference is the locations where the inward movements are observed: in the present case, they are at the outer edges of the X-ray emission, whereas they are well behind outermost filaments in the case of RCW 86.This is consistent with our interpretation, a very recent collision in RCW 103.
To summarize, the global deceleration can be understood as a result of a collision of the shocks with a highdensity medium (molecular or atomic cloud), although the X-ray emitting plasma may still be expanding in the wind-blown bubble.

CONCLUSION
We examined proper motions of X-ray knots and rims in the southern and northern edges of RCW 103.We found a global deceleration of them within the last ∼ 24 yrs, even though its age is thought to be larger than 2 kyr.Among them, Regs.5-8 were found to have changed the moving directions from ∼ +1, 000 km s −1 (outward) to ∼ −2, 000 km s −1 (inward).We confirmed that the deceleration and inward movements are robust to the uncertainties in the moving directions and the pointing accuracy of Chandra.The inward movements can be understood as a shock reflection due to a collision with a high-density medium.As a conclusion, the global deceleration can be explained as due to a collision with a high-density medium both in the northern and southern regions, although the X-ray emitting plasma may still be expanding in the wind-blown bubble.
We appreciate a fruitful discussion with H. Sano about the surrounding medium.This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France (DOI : 10.26093/cds/vizier).The original description of the VizieR service was published in 2000, A&AS 143, 23.This work was partially supported by JSPS/MEXT grant Nos.JP21J00031 (HS), JP19H01936, JP21H04493 (TT), and JP22H01265 (HU).In order to evaluate systematic uncertainties associated with the aspect correction, we here apply another aspect correction.We use the NOMAD-1 optical source catalog (Zacharias et al. 2004) available via the VizieR service2 (Ochsenbein et al. 2000) to register the point-like sources in the Chandra images.We find 4-6 X-ray sources (depending on observations) which match the catalog sources.After correcting all the images, we measure the proper motions in the same way as in Section 3. The resultant velocities are listed in Table 3. Overall, the velocities are consistent with the ones obtained in Section 3, suggesting that the systematic uncertaintes due to the aspect correction are small compared to the statistical errors.We here check for systematic uncertainties of the proper motions due to the extraction energy range.Because the detector calibration might be less reliable at low energies due to the contamination on the sensor surface (Marshall et al. 2004;O'Dell et al. 2015;Plucinsky et al. 2018), we test two additional cases where we use the 1.0-5.0keV and 1.5-5.0keV energy ranges.The measured velocities are listed in Table 4.In the latter case, velocities are constrained only for Regs.6, 7, and 8, due to the limited statistics.In both cases, one can see that the results are mostly consistent with the ones in Section 3, showing a global deceleration and a change in moving directions.

Figure 1 .
Figure 1.Exposure-corrected Chandra image of RCW 103 in the energy band of 0.5-5.0keV.The radial-profile extraction regions are indicated with the green boxes.

Figure 4 .
Figure 4. Locations of the magnetar 1E 161348−5055 in 1999, 2010, and 2016.The central positions and radii of the ellipses indicate the estimated positions of the magnetar at different times and their statistical errors.

Table 1 .
Chandra observation log ObsID R.A. (2000) Dec. (2000) Date Exposure (ks) ∆x (pixel) a ∆y (pixel) a Coordinate transformation parameters with respect to those of ObsID 11823.Transformation directions +∆x and +∆y correspond to −R.A. and +Dec., respectively.b No correction is performed due to the low quality of point-like sources.

Table 2 .
Proper motion velocities a a A distance of 3.1 kpc is assumed.Minus velocities indicate inward movements (Same for Table

Table 3 .
Proper motion velocities in the alternative aspect correction case B. PROPER MOTIONS IN DIFFERENT ENERGY RANGES