Constraints on Cosmic-ray Acceleration Efficiency in Balmer Shocks of Two Young Type Ia Supernova Remnants in the Large Magellanic Cloud

We use the two epoch HST imaging in narrowband Hα of 0509−67.5 that was presented in Hovey et al. (2015), hereafter HHE15. The observations of 0509−67.5 that we use here are from that work. We use two narrowband Hα HST observations of SNR 0519−69.0 separated by ∼1 year (369 days). Our first epoch observation was imaged with the Advanced Camera for Surveys (ACS) Wide-field (WF) camera on 2010 April 17 using the F658N Hα filter for a total integrated exposure time of 4757 s under HST Program number 12107 (PI: J.P. Hughes). The second epoch observation was taken on 2011 April 21 with the ACS/WF camera for an integrated time of 4757 s using the same F658N Hα narrowband filter.⁷

Both epochs of 0519−69.0 were processed using the astrodrizzle and tweakwcs routines, which are a part of the python drizzlepac package. The combined images were drizzled onto a 0025 pixel⁻¹ scale with a pixfrac setting of 0.8 and square convolution kernel. The combined drizzled images were aligned using ∼500 field stars near the center of 0519−69.0 with a positional rms uncertainty of 00028. We take this uncertainty in our alignment to be our systemic uncertainty.

We reanalyzed the FORS2 spectrum of 0509−67.5 from Helder et al. (2010, 2011) (program number 384.D-0518(A), PI: E. A. Helder). These data were taken on 2009 October 16, 2009 October 21, and 2009 November 11 with integration times of 2734 s, 2734 s, and 5468 s respectively. We do not use the data obtained on 2009 October 16 because the seeing deteriorated from 10 to 23 during that observation. The seeing for the other nights was ∼08, which is more suited to our study of the closely spaced Hα filaments in the southwestern portion of 0509−67.5.

The FORS2 data were reduced using standard IRAF⁸ tasks. We subtracted the master bias, used lamp flats to correct for inter-pixel sensitivity, and calibrated the wavelength solution using arc lamp observations. These spectra were flux calibrated using observations of the spectrophotometric standard stars HD49798 (Jaschek & Jaschek 1963) and LTT2415 (Hamuy et al. 1992).

The spectra from SNR 0519−69.0 were taken with the prime focus Robert Stobie Spectrograph (RSS) on the Southern African Large Telescope (SALT) at two different positions with a 2''-wide long-slit and the pg0900 grating. The slit positions are shown in Figure 1 (right). The spectrum from the position labeled slit 1 was taken on 2011 October 03 for 1500 s and on 2014 March 7 for 3000 s. Slit 2 was taken on 2014 March 12 for 1500 s and on 2014 March 19 for 1300 s. The SALT observation in 2011 was taken under proposal ID 2011-3-RU-008 (PI: Hovey) and in 2014 under proposal ID 2013-2-RU-003 (PI: Hughes).

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Each of the four science observations were accompanied by multiple flat-field images as well as unique argon arc lamp observations, with all the long-slit spectra tuned to a grating angle of 1362 to ensure wavelength coverage of Hα. We also observed the standard B1V star Hiltner 600 (Massey et al. 1988; Stone 1996) at the same grating angle on 2014 March 7 that was used to flux calibrate all science spectra. These SALT long-slit spectroscopic data were reduced using our own custom pipeline that incorporates standard tasks from both IRAF/PyRAF as well as PySALT (Crawford et al. 2010). In addition to the standard data reduction steps for long-slit spectra, we also ran a custom version of the LA-Cosmic⁹ routine to remove cosmic rays (van Dokkum 2001) and used PySALT functions to simultaneously derive two-dimensional wavelength calibrations and rectify curved arc and telluric emission lines. The wavelength solution was further refined using the extracted one-dimensional arc lamp spectra. Standard IRAF/PyRAF functions were used to fit and subtract telluric and background emission.

Shock speeds for the outer rim and interior filaments of SNRs were measured in HHE15. For the northeast of 0509−67.5, we use the measured value of 6860 ± 307 km s⁻¹, which is the weighted average of the proper motion measurements from outer regions 7, 8, and 9 from Section 4 of HHE15. We break the southwest portion of the remnant into four distinct Balmer filaments that can be seen in the inlay of the left panel in Figure 1. The shock speeds of the outer and inner 1 filaments in the southwest are 8500 ± 1340 km s⁻¹ and 3760 ± 906 km s⁻¹, respectively, which are again drawn from the work done in Section 4 of HHE15. We use the weighted arithmetic mean for inner regions 4 and 5, and then inner regions 1, 2, and 3 from HHE15 to combine the proper motions for the inner filament 2 and inner filament 3 in the southwest of 0509−67.5 respectively. The measured shock speed in the plane of the sky is 5700 ± 1310 km s⁻¹ for the inner filament 2 and 4300 ± 1010 km s⁻¹ for inner filament 3. These results are given in Table 1.

Using the same procedures as HHE15, we measured the shock speeds along various filaments in 0519−69.0 for which we have corresponding spectra. Figure 2 shows the apertures from which we extracted one-dimensional Hα flux profiles in order to measure the proper motions. We show an example of the Hα profiles from region 1 in our slit 1 southern spectral extraction aperture in Figure 3. The first epoch profile is shown in black and the second epoch profile is shown in red. Our best-fit solution for the first epoch profile shifted to the position of the second epoch is shown in blue with the corresponding residuals in purple. In Table 3, we report on the measured proper motions for all filaments that lie in both of our spectroscopic slits, along with the region for which Smith et al. (1991) were able to measure the broad Hα width. The component of the shock speed in the plane of the sky, v_pm, for individual filaments are combined using the measured flux as the weighting factor as,

$$\begin{eqnarray}&&{v}_{\mathrm{pm}}=\displaystyle \frac{{\displaystyle \sum }_{i=1}^{N}{v}_{i}{F}_{i}}{{\displaystyle \sum }_{i=1}^{N}{F}_{i}},\end{eqnarray} \tag{ 2 }$$

where F_i is the integrated flux of a given 1D Hα brightness profile. We choose this particular weighting due to the complicated filamentary structure because we seek to compare these shock speeds with the measured broad Hα widths from optical spectroscopy discussed in Section 3.4. Shock speeds less than 400 km s⁻¹ are excluded from the combination because they are below the spectral resolution of our observations. These combined shock speeds are given in column 7 of Table 1. Note that we investigated other weighting schemes (e.g., using the inverse variance of the individual measured shock speeds), and found that our results were not sensitive to the particular choice of weighting method. As for the quoted uncertainties, we used the larger of the inverse variance combination of the individual filament velocity errors (for the 0519−69.0 Slit 2 North region) or the rms spread of their speeds (all other regions).

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Our goal in the reanalysis of the FORS2 spectrum is to measure the broad Hα widths for the four distinct filaments in the southwest, which HHE15 argued were confused by this complicated multiple filamentary structure. To compensate for these closely spaced shocks, we choose a spectral extraction aperture of 1'', which is slightly larger than the full width at half maximum (FWHM) of the average seeing of the observations and corresponds to the minimum separation between inner filaments 2 and 3. In the northeast, we did not have this constraint, so we use an extraction aperture that is 15 in size to maximize the signal from the faint flux of the broad Hα component.

Standard IRAF procedures were employed to subtract night skylines and stellar continuum flux of the two-dimensional spectra. A 1D spectrum was made for each of the three observations by summing the flux along the spatial extraction region for each wavelength bin. The three resulting 1D spectra were then median combined to produce the final spectrum for analysis.

Smith et al. (1994) measured the widths of the narrow Hα line widths in this remnant, which has a weighted mean of 27.50 ± 2.02 km s⁻¹. We use this value as the fixed FWHM of the narrow component when fitting our Hα spectrum in the NE and SW of 0509−67.5. The spectra are analyzed by first fitting the broad component of the Hα line by fitting a Gaussian, excluding the narrow component (6555–6570 Å). We give the values of the χ² statistic and the corresponding degrees of freedom (d.o.f.) in columns three and four of Table 1. We then subtracted the broad component and fit the narrow component with a Gaussian convolved with a top-hat kernel with a width of ∼10 Å that corresponds to the 16 width of the slit. We find that the narrow Hα component is centered at a wavelength of 6567.5 ± 0.05 Å, which corresponds to a velocity of 213.0 ± 1.8 km s⁻¹. This is roughly consistent with the measured redshift velocity of the LMC, 262 km s⁻¹ (McConnachie 2012).

In the northeast of 0509−67.5, we measured the broad Hα width to be 4000 ± 235 km s⁻¹, which has an uncertainty that is ∼4 times smaller than that reported in Helder et al. (2010, 2011). We report our measured values for the broad Hα width, broad-to-narrow ratios, and line-of-sight velocities (determined by the difference of the broad and narrow Hα line centroids) in Table 1 and our spectra in Figure 8. Table 1 also gives the combined proper motion measurements for the filaments and the combined line-of-sight velocity with the radial speed for the full velocity of the filament. Assuming the shocked gas has an equation of state of γ = 5/3 (Hovey et al. 2015), we boost the bulk velocities by a factor of 4/3, which we then combine with the proper motions to calculate the total velocities reported in Table 1.

In the southwest, we measured broad line widths for the outer rim and three interior filaments. For the outer filament, we measure a broad Hα width of 4000 ± 167 km s⁻¹, though this should be considered a lower limit due to contamination of the spectrum from the brighter interior filament 1. This is due to the fact that inner fillament 1 is moving at a considerably slower speed than the outer filament, which we would expect to a have a brighter broad Hα component. The aperture for the outer filament is placed as far as possible from inner filament 1, but we still expect contamination that would artificially lower the measured width of the fainter, faster moving outer shock. Even though this shock speed should be treated as a lower limit, the value we quote is conservative for the purposes of this study because larger values would only lead to a smaller calculated CR acceleration efficiency than the value that is presented in Section 4.

We measure broad Hα widths of 2900 ± 40.6 km s⁻¹, 3500 ± 117 km s⁻¹, and 3900 ± 136 km s⁻¹ for interior filaments 1, 2, and 3 respectively. Again we quote our measured spectroscopic values in Table 1 and show the spectra in Figure 8. The line-of-sight bulk velocities increase from the outer region progressively to the inner region 3 in the southwest with values of 440 ± 70.7 km s⁻¹, 770 ± 21.4 km s⁻¹, 820 ± 55.1 km s⁻¹, and 1000 ± 65.4 km s⁻¹ for the four filaments.

Slit 1 had three separate exposures and slit 2 had two. The three 2D spectral files for slit 1 were median combined before extracting the final 1D spectrum. For slit 2, the two 2D spectral files were averaged before extracting the 1D spectrum.

We use a fixed narrow Hα line width of 40.30 ± 0.24 km s⁻¹ in our Hα line fitting, which is the statistical mean of the measurements from Smith et al. (1994). The broad Hα line is first fit by excluding the narrow Hα flux. Our χ² values and corresponding d.o.f. are reported in columns three and four, respectively, of Table 1. After this, the broad Hα line flux is subtracted from the spectrum and we fit the narrow line convolved with a Gaussian, which fit the data better than a top-hat kernel. For both of our longslits, we find that the narrow Hα component is centered at a wavelength of 6569.00 ± 0.08 Å, which translates into a redshift velocity of 283 ± 3.7 km s⁻¹. Again this is consistent with the redshift velocity of the LMC reported by McConnachie (2012).

Our spectra for both slits are shown in Figure 4 and the measured Hα broad line widths, broad-to-narrow intensity ratios, and line-of-sight velocities are reported in Table 1. We measure broad Hα widths of 1800 ± 26.0 km s⁻¹ and 2300 ± 27.6 km s⁻¹ for the north and south portions of slit 1 respectively. We divided slit two into four regions: the north, middle 1, middle 2, and south for which we measure broad Hα line widths of 2800 ± 461 km s⁻¹, 1900 ± 51.1 km s⁻¹, 2700 ± 87.1 km s⁻¹, and 2700 ± 131 km s⁻¹ respectively.

In order to place limits on the efficiency of CR acceleration in these shocks, we compare our results with the Balmer shock model from Morlino et al. (2013a). We have chosen to only consider this model in our current analysis, which contrasts with the approach found in Section 4 of HHE15, which additionally considered the Balmer shock model of van Adelsberg et al. (2008) for the comparison of the shock speeds they measured in SNR 0509−67.5 and the spectroscopic measurements of broad line Hα widths from Helder et al. (2010, 2011). The decision to only employ the Balmer shock model found in Morlino et al. (2013a) is based upon the following reasons:

• 1.  
  There is no consideration of efficient CR acceleration or the effects that its precursor might have on the Blamer shock model of van Adelsberg et al. (2008). Furthermore, this model lacks a prescription for the attenuation of broad Hα widths at a given shock speed as CR acceleration increases, like that found in Morlino et al. (2013a).
• 2.  
  The van Adelsberg et al. (2008) model lacks an independent treatment of material upstream from the shock, but rather assumes that it is in an unadulterated thermalized state, which they cite as a weakness that they plan on addressing in the future in their concluding remarks. Morlino et al. (2013a) treats the upstream material separately and found that even in the case of no CR acceleration, the upstream material is affected by the neutral return flux.
• 3.  
  van Adelsberg et al. (2008) also assumes that the populations of post-shock ions and neutrals equilibrate after five charge exchanges, and that both populations will then have the same bulk speed. One of the main results from Morlino et al. (2013a) is that the neutrals do not thermalize and have both a lower temperature and bulk speed than the corresponding population of ions (Morlino et al. 2013b). Again, this is explicitly cited as a weakness in the closing paragraphs of van Adelsberg et al. (2008).

One potential weakness of the Balmer shock model of Morlino et al. (2013a) is their exclusion of helium and its possible effects on the resulting Balmer emission. Morlino et al. (2013a) explicitly address this issue and conclude that their omission of helium does not explain the differences between their model and the one presented in van Adelsberg et al. (2008) and that, in general, helium will have negligible effects on the system. However, it is not clear what role helium may play on attenuating Hα broad line widths once a non-negligible CR acceleration efficiency is included. Given the preponderance of strengths to the sole weakness of the Balmer shock calculations of Morlino et al. (2013a), we only consider this model in the interpretation of our measurements.

Figure 5 shows the Balmer shock model predictions for broad Hα line widths as a function of shock speed for the full range of possible post-shock electron to ion temperature ratios. Black curves are for the case where there is no CR acceleration, while the red curves are for the case of a CR acceleration efficiency of _CR = 20%, where _CR is defined in Morlino et al. (2013a) to be,

$$\begin{eqnarray}&&{\epsilon }_{\mathrm{CR}}=\displaystyle \frac{{P}_{\mathrm{CR}}}{{\rho }_{0,\mathrm{tot}}{{v}_{{\rm{s}}}}^{2}}.\end{eqnarray} \tag{ 3 }$$

The parameter space below the β = 1 curve (shaded yellow) requires CR acceleration (or some other process draining energy from the thermal population). Because all of our data points lie above the line, none of the points require efficient CR acceleration in the limiting case of complete temperature equilibration.

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In order to place an upper bound for CR acceleration efficiency, we fit the ensemble of filaments to the Morlino et al. (2013a) models including the effects of CRs using the conservation assumption that there is no temperature equilibration between post-shock electrons and ions (β = 0.01). We implement a Monte Carlo procedure where we perturb the shock speeds and Hα broad line widths within their respective uncertainties using a Gaussian random variable, running 10⁵ realizations. We find that the CR acceleration efficiency, _CR, must be below 7% at 95% confidence for the full ensemble of filaments.

We have also determined 95% confidence upper bounds for the CR acceleration efficiencies for each remnant separately, and find these to be 6% and 11% for 0509−67.5 and 0519−69.0, respectively.

Using this same Monte Carlo approach, we determine the upper bounds for the CR acceleration efficiencies for the individual filaments again for the case of no temperature equilibration between post-shock ions and electrons (Table 2). The individual _CR values vary broadly from nearly 0%–66%, with an average of 29%. The largest upper limit value comes from the eastern filament studied by Smith et al. (1991). This region has a wide range of shock speeds from the multiple internal features it contains (see Figure 6), which explains its relatively large shock velocity uncertainty and, by extension, its high upper limit on _CR.

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Table 2.  CR Acceleration Efficiency Limits and Temperature Equilibration Ratios for 0509−67.5 and 0519−69.0

Extraction Region	CR;uppera	βupperb
0509−67.5 NE	0.13	0.42
0509−67.5 SW Outer	0.29	⋯
0509−67.5 SW Inner 1	0.28	⋯
0509−67.5 SW Inner 2	0.33	⋯
0509−67.5 SW Inner 3	0.00	⋯
0519−69.0 Slit 1 North	0.21	0.84
0519−69.0 Slit 1 South	0.35	⋯
0519−69.0 Slit 2 North	0.46	⋯
0519−69.0 Slit 2 Middle 2	0.19	0.56
0519−69.0 Slit 2 Middle 1	0.41	⋯
0519−69.0 Slit 2 South	0.13	0.38
0519−69.0 Smith '91 East	0.66	⋯
0509 − 67.5	0.06	0.47
0519 − 69.0	0.11	0.55
All Points	0.07	0.25

Notes.

^aUpper limits at 95% confidence for CR acceleration efficiency assuming no equilibration between electron and ion temperatures (β = 0.01). ^bUpper limit values at 95% confidence for β, unless it cannot be unconstrained between the limits of 0.01 ≤ β ≤ 1.

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We compare these results to those of Tycho's SNR, which has a similarly young age, 445 years, as the LMC remnants and also exhibits BD shocks (albeit over only a very small portion of the rim). Using their CR-hydro NEI model constrained by the structure and broadband spectrum of Tycho's SNR, Slane et al. (2014, 2015) found that 16% of the kinetic energy in the remnant has been converted into relativistic particles, with 11%, of those escaping as CRs. They find the present diffuse shock acceleration (DSA) efficiency in Tycho's SNR to be 26%. The DSA CR efficiency is equivalent to the ion acceleration efficiency, ${\epsilon }_{\mathrm{CR}}^{* }$, from Morlino et al. (2013a) defined as,

$$\begin{eqnarray}&&{\epsilon }_{\mathrm{CR}}^{* }=\displaystyle \frac{{P}_{\mathrm{CR}}}{{\rho }_{0,\mathrm{ion}}{{v}_{{\rm{s}}}}^{2}}\equiv \displaystyle \frac{{\epsilon }_{\mathrm{CR}}}{\chi },\end{eqnarray} \tag{ 4 }$$

where χ is the ionization fraction of the pre-shock medium. In HHE15, we constrained this ionization fraction to be in the range of 0.4–0.7 for plausible evolutionary models that mimic a range of CR acceleration efficiencies at the forward shock through the use of an effective equation of state. In the following, therefore, we use an ionization fraction of 1/2, for which the ion acceleration efficiency becomes ${\epsilon }_{\mathrm{CR}}^{* }=2{\epsilon }_{\mathrm{CR}}$. This gives us upper limits at 95% confidence of ${\epsilon }_{\mathrm{CR}}^{* }=12 \%$ for SNR 0509−67.5, ${\epsilon }_{\mathrm{CR}}^{* }=22 \%$ for SNR 0519−69.0, and ${\epsilon }_{\mathrm{CR}}^{* }=14 \%$ using the ensemble of all data points.

It is apparent that neither 0509−67.5 nor 0519−69.0 is as efficient as Tycho's SNR at accelerating CRs. As mentioned above, the BD shocks in Tycho's SNR cover only a very small fraction of the remnant (mostly in the northeastern region of the rim), while such shocks cover the entire extent of both LMC remnants. This difference could be the key to the difference in the CR acceleration efficiencies. BD shocks require a partially neutral upstream medium where processes such as ion-neutral wave damping could suppress CR acceleration if the ambient magnetic field of the upstream material is sufficiently weak (O'C Drury et al. 1996).

Another plausible reason for the brighter Hα emission and smaller CR acceleration efficiencies in SNRs 0509−67.5 and 0519−69.0 compared to Tycho's SNR, is that a stronger CR precursor exists in Tycho that is ionizing the upstream ambient medium to a greater degree, hence suppressing Hα emission in the remnant. Knežević et al. (2017) found a global Hα narrow line width in the northeastern region of 54.8 ± 1.8 km s⁻¹ for Tycho's SNR, whereas Smith et al. (1994) measured narrow line widths of 25–31 km s⁻¹ and 39–42 km s⁻¹ for SNRs 0509−67.5 and 0519−69.0 respectively. The relatively smaller narrow line widths for 0509−67.5 and 0519−69.0 suggests that a stronger CR precursor is likely for Tycho's SNR compared to the LMC remnants we have studied.

We can use the Balmer shock models of Morlino et al. (2013a) to place constraints on the degree to which the temperatures of post-shock electrons and ions have equilibrated under the assumption of no CR acceleration. The temperature ratio of post-shock electrons to ions, β, for several regions are given in Table 2. In many of the regions, we are unable to constrain the value of β. For the ensemble of all data points we find an upper limit to the temperature ratio of β ≤ 0.25 at 95% confidence. This upper limit is consistent with the $\beta \sim {v}_{{\rm{s}}}^{-2}$ relationship between shock velocity and β established by Ghavamian et al. (2007).