Multi-year X-Ray Variations of Iron-K and Continuum Emissions in the Young Supernova Remnant Cassiopeia A

For our study of the year-scale variability in flux, data from the Chandra X-ray Observatory were utilized. Chandra observations of Cassiopeia A have been carried out several times since launch in 1999 (e.g., Hwang et al. 2000, 2004; Patnaude et al. 2011; Hwang & Laming 2012; Patnaude & Fesen 2014). The data used in our analysis are listed in Table 1. Archived data taken with ACIS-S in Timed Exposure mode are gathered. ACIS-S3 is a back-illuminated CCD chip with enhanced soft X-ray response and fairly constant spectral resolution during the course of the mission compared to the ACIS-I array. The satellite and instrument are described by Weisskopf et al. (2002).

We reprocessed the event files (from level 1 to level 2) to remove pixel randomization and to correct for CCD charge transfer efficiencies using CIAO version 4.6 and CalDB 4.6.3. Bad grades were filtered out and good time intervals were reserved. Cassiopeia A is so bright that the data were all taken with the single chip operation mode of S3 to avoid telemetry loss. Cassiopeia A was usually pointed near the center of the ACIS-S3 chip of 1024 × 1024 pixel CCDs, each with 05 × 05 pixels and a field of view of 84 × 84. The pointing position was moderately shifted from the aim-point and its roll angle varied from observation to observation. The effective areas (arf) of individual observations were then calculated for each ObsID using the Chandra standard analysis software package mkwarf in CIAO.

For tracing the non-thermal emission, Suzaku data were utilized. A deep observation with Suzaku was made in 2012. The exposure time was 205 ksec long (XIS0+XIS3). Suzaku has four X-ray CCD cameras (XIS: Koyama et al. 2007; Uchiyama et al. 2007). One of the four XIS detectors (XIS 1) is back-side illuminated (BI) and the other three (XIS 0, XIS 2, and XIS 3) are front side illuminated (FI). In the XIS data taken with the Spaced-row Charge Injection option in normal exposure mode, gap columns due to injected charges appear every 54 lines. The column widths of the FIs are three pixels which are smaller than five for the BI. To minimize flux uncertainty due to the gap, we used only FI data. In the FI CCDs, XIS-2 was not operational in 2012. Data screening was made with standard criteria provided by the Suzaku processing team.

X-ray emissions from Cassiopeia A are known to be a composite of thermal and non-thermal components (e.g., Hughes et al. 2000). The thermal component is characterized by emission lines from highly ionized ions of heavy elements such as iron, accompanied with a continuum emission by a thermal bremsstrahlung. The non-thermal emission is known to be traced by a hard band continuum emission above 10 keV (e.g., Maeda et al. 2009). Figure 1 shows a hard X-ray image (10–12 keV band) with Suzaku. We can see the concentrated hard X-ray distribution from the western region toward the center of Cassiopeia A. Figure 2 shows three color images from Chandra in the 4.2–6.0 keV, the 6.54–6.92 keV (Fe–K line), and the 1.75–1.95 keV (Si–K line) bands overlaid with the Suzaku contour in the 10–12 keV band. The Fe–K emission is believed to originate from optically thin thermal plasma. Using the Suzaku contour map and the Chandra lines, we can segregate the distributions of the thermal and non-thermal X-rays. Based on this information, five local regions and one whole SNR region were selected from the image for our analysis.

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We defined the “east” and the “north west” regions as the “thermal dominant” region (magenta ellipses in Figure 2). The east region has the most abundant X-ray flux of the Fe–K line. Therefore, this region is the best region to discuss the time evolution of the Fe–K line with less of a non-thermal emission contribution. The north west region is the second luminous region of the Fe–K line emission. This region shows a separation from the hard X-ray peak and a separation from continuum X-ray dominant region (DeLaney et al. 2004; Helder & Vink 2008).

On the other hand, we defined “south west,” “inner”, and “forward shock” regions as the “non-thermal dominant” region (light blue regions in Figure 2). Helder & Vink (2008) and DeLaney et al. (2004) show the area dominated by a harder spectrum. As a matter of fact, these regions manifest themselves in hard X-rays. Our image also shows the inner region is bright with hard X-rays. In addition, the forward shock has a featureless non-thermal emission (e.g., Hughes et al. 2000; Bamba et al. 2005). In the forward shock, it was found that the average proper motion of Cassiopeia A is 030 yr⁻¹ (Patnaude & Fesen 2009), so we corrected the forward shock region of each year with this value (see the Appendix).

With the regions defined in the Section 3.1, we extracted spectra using a custom pipeline based on specextract in CIAO script. Here, the background spectra were extracted from outside of the whole SNR region defined in Figure 2. Since X-ray emission from Cassiopeia A is very strong, the background contribution is almost negligible for a time variation estimation. The background fraction of the whole SNR is only ∼3% in the 4.2–7.3 keV band and this is almost constant value from 2002 to 2013. In 2000, this fraction shows a larger value (∼7%) presumably because of an increase in the charged particle flux experienced during this observation. After background subtraction, we fitted the 4.2–7.3 keV band spectra at each epoch with a power-law model and a Gaussian line with XSPEC version 12.8.2. The best-fit parameters are summarized in Table 2.

Table 2.  Best-fit Parameters of the ACIS Spectra^a

Epoch		Power-law Model		Fe–K Line			χ2/d.o.f
		Γ	Flux (4.2–6 keV)	Energy	EW	Flux
(Year)			(×10−11 erg cm−2 s−1)	(keV)	(keV)	(×10−3 ph cm−2 s−2)
Whole SNR
	2000.1	2.90 ± 0.02			0.95 ± 0.01	5.27 ± 0.05	347.52/206
	2002.1	2.99 ± 0.02	17.39 ± 0.03		1.00 ± 0.01	5.22 ± 0.04	322.02/206
	2004.1	2.99 ± 0.01			0.98 ± 0.01	5.12 ± 0.03	355.18/206
	2007.9	3.00 ± 0.02	16.52 ± 0.03	6.6377 ± 0.001	1.02 ± 0.01	5.05 ± 0.04	324.81/206
	2009.8	3.00 ± 0.02	16.21 ± 0.03		0.99 ± 0.01	4.79 ± 0.04	321.93/206
	2010.8	2.99 ± 0.02	16.48 ± 0.03		0.97 ± 0.01	4.83 ± 0.04	322.59/206
	2012.4	2.95 ± 0.02	16.44 ± 0.03	6.6503 ± 0.001	1.00 ± 0.01	4.97 ± 0.04	278.20/206
	2013.4	3.00 ± 0.02	16.31 ± 0.03	6.6419 ± 0.001	1.01 ± 0.01	4.93 ± 0.04	268.78/206
East
	2000.1	3.22 ± 0.04	2.52 ± 0.01	6.677	2.53 ± 0.03	1.77 ± 0.02	291.35/206
	2002.1	3.31 ± 0.04	2.45 ± 0.01	6.675	2.67	1.76 ± 0.02	307.28/206
	2004.1	3.29 ± 0.03	2.37 ± 0.01	6.685 ± 0.002	2.66	1.70 ± 0.01	420.74/206
	2007.9	3.30 ± 0.04	2.32 ± 0.01	6.677	2.79	1.75 ± 0.02	299.12/206
	2009.8	3.31 ± 0.04	2.26 ± 0.01	6.679	2.76 ± 0.04	1.68 ± 0.02	278.59/206
	2010.8	3.28 ± 0.04	2.28 ± 0.01	6.672	2.71	1.68 ± 0.02	270.84/206
	2012.4	3.30 ± 0.05	2.17 ± 0.01	6.711	2.82	1.62 ± 0.02	307.66/206
	2013.4	3.40 ± 0.05	2.15 ± 0.01	6.704	2.89	1.61 ± 0.02	292.35/206
North West
	2000.1	2.98 ± 0.03	3.73	6.584	1.61 ± 0.02	1.85 ± 0.02	316.05/206
	2002.1	3.03 ± 0.03	3.66 ± 0.01	6.589	1.66 ± 0.02	1.85 ± 0.02	283.29/206
	2004.1	3.06 ± 0.02	3.63 ± 0.01	6.597 ± 0.001	1.67 ± 0.02	1.83 ± 0.02	389.43/206
	2007.9	3.12 ± 0.03	3.44 ± 0.01	6.596	1.74	1.78 ± 0.02	277.33/206
	2009.8	3.15 ± 0.04	3.26	6.605	1.83 ± 0.03	1.75 ± 0.02	287.39/206
	2010.8	3.17 ± 0.04	3.34 ± 0.01	6.597	1.86 ± 0.03	1.81 ± 0.02	232.13/206
	2012.4	3.01 ± 0.03	3.39 ± 0.01	6.618	1.78 ± 0.02	1.83 ± 0.02	267.84/206
	2013.4	3.04 ± 0.03	3.28	6.604	1.82 ± 0.02	1.80 ± 0.02	290.10/206
South West
	2000.1	2.74 ± 0.03	3.92	6.614	0.60 ± 0.01	0.77 ± 0.02	242.97/206
	2002.1	2.83 ± 0.03	3.90 ± 0.01	6.623	0.62	0.76 ± 0.02	214.20/206
	2004.1	2.78 ± 0.02	3.94 ± 0.01	6.630 ± 0.002	0.59 ± 0.01	0.75 ± 0.01	229.44/206
	2007.9	2.82 ± 0.03	3.65	6.627 ± 0.003	0.62 ± 0.02	0.72 ± 0.02	265.07/206
	2009.8	2.82 ± 0.03	3.61	6.631 ± 0.003	0.62 ± 0.02	0.71 ± 0.02	220.24/206
	2010.8	2.80 ± 0.03	3.63 ± 0.01	6.627	0.62	0.73 ± 0.02	265.88/206
	2012.4	2.80 ± 0.04	3.75 ± 0.01	6.636	0.66 ± 0.02	0.78 ± 0.03	230.55/206
	2013.4	2.82 ± 0.03	3.71 ± 0.01	6.629	0.64 ± 0.02	0.75 ± 0.02	264.19/206
Forward Shock
	2000.1	2.55 ± 0.06	1.57 ± 0.01	6.63	0.22 ± 0.02	0.12 ± 0.02	198.16/206
	2002.1	2.64 ± 0.05	1.562	6.61	0.18 ± 0.02	0.10 ± 0.01	208.52/206
	2004.1	2.69 ± 0.04	1.565	6.627	0.18 ± 0.01	0.092 ± 0.007	199.11/206
	2007.9	2.61 ± 0.05	1.541	6.64 ± 0.02	0.19 ± 0.02	0.10 ± 0.01	229.06/206
	2009.8	2.67 ± 0.05	1.52 ± 0.01	6.62 ± 0.01	0.20 ± 0.02	0.10 ± 0.01	192.79/206
	2010.8	2.55 ± 0.05	1.57 ± 0.01	6.63 ± 0.01	0.20 ± 0.02	0.11 ± 0.01	207.04/206
	2012.4	2.57 ± 0.05	1.585	6.61	0.16 ± 0.02	0.08 ± 0.01	193.40/206
	2013.4	2.65 ± 0.05	1.575	6.64 ± 0.01	0.20 ± 0.02	0.10 ± 0.01	205.78/206
Inner
	2000.1	2.86 ± 0.04	2.409	6.612	0.20 ± 0.01	0.15 ± 0.01	188.96/206
	2002.1	2.93 ± 0.04	2.37 ± 0.01	6.631	0.21 ± 0.01	0.15 ± 0.01	203.19/206
	2004.1	3.01 ± 0.03	2.346	6.625	0.23 ± 0.01	0.17 ± 0.01	236.49/206
	2007.9	2.89 ± 0.04	2.256	6.627	0.26 ± 0.02	0.18 ± 0.01	187.30/206
	2009.8	2.88 ± 0.04	2.24 ± 0.01	6.618 ± 0.009	0.21 ± 0.01	0.15 ± 0.01	181.55/206
	2010.8	2.93 ± 0.04	2.31 ± 0.01	6.649	0.22 ± 0.02	0.16 ± 0.01	230.67/206
	2012.4	2.91 ± 0.04	2.26 ± 0.01	6.655	0.21 ± 0.02	0.14 ± 0.01	215.17/206
	2013.4	2.99 ± 0.04	2.26 ± 0.01	6.632 ± 0.009	0.22 ± 0.02	0.15 ± 0.01	179.23/206

Note.

^aThe errors are at 1σ confidence level.

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Figure 3 shows the spectra in the 4.2–7.3 keV band taken from the six regions. As described in Section 3.1, the two bright non-thermal dominant regions south west and inner are remarkable in the hard X-ray continuum flux (Figures 1 and 3). Accordingly, the photon indexes of these regions are ∼2.6–3.0 while those of the thermal regions are 3.0–3.4. In the forward shock and whole SNR, photon indexes and evolutions are slightly different from the results in Patnaude et al. (2011). This is probably due to a difference in the energy band used in the spectral fitting. The fit residuals are larger for the thermal dominant regions than for the non-thermal regions. This is because weak thermal lines such as Cr–K (5.6 keV) appeared in the band.

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As shown in Figure 3 and Table 3, we also found an increase of the equivalent width of the Fe–K line of Cassiopeia A for the first time. In the thermal dominant regions, we can see a ∼10% increase of the equivalent width for 13 years, and it is notable that a large evolution of the equivalent width like this is the first detection from all SNRs. In addition, we found the Fe–K line centroid varies among observations. Since there is a calibration uncertainty for Fe K-line centroids of ∼0.3% (or ∼20 eV at Fe–K)¹⁰ , however, it is difficult to discuss its evolution.

From the fitting, we investigated the time variation of the 4.2–6.0 keV band and Fe–K line fluxes. Cassiopeia A flux evolution was well reproduced by linear decline (Patnaude et al. 2011). Therefore, we also fitted flux time variation with a linear model. These fitting results of each region are summarized in Figure 2 and Table 3. In the whole SNR, the 4.2–6 keV band and the Fe–K line fluxes show a significant decline in these ∼10 years with a similar change (∼−0.6% yr⁻¹).

There is a discrepancy between the variation of the 4.2–6 keV band in this work, −0.65 ± 0.02% yr⁻¹, and that in Patnaude et al. (2011), −1.5 ± 0.17% yr⁻¹, in spite of nearly the same data set. Although we tried several analysis methods (see the Appendix), we could not reveal the cause of the discrepancy.

In the local regions, time variation of the 4.2–6.0 keV continuum and Fe–K line fluxes is different from the whole SNR. In Figure 4, we can see larger time variation of the 4.2–6 keV band in the regions which have higher equivalent width of the Fe–K line and a softer photon index. In addition, we also found the forward shock region has no significant change of 4.2–6 keV and Fe–K. From these results, we can interpret that Cassiopeia A is undergoing a flux change in the reverse shock region which has a larger Fe–K line contribution.

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As shown in Figure 4, we found that the east region has the largest decay rate and the largest equivalent width of the Fe–K line. Since the Fe–K line is a tracer of thermal plasma emission, we evaluated emission time variation from the east region via a thermal model. Table 4 shows the results of fitting with a thermal bremsstrahlung instead of the power-law model. We then drew time histories of the resultant temperature and normalization (= emission measure), and fitted them with a linear model. As a result, it is found that the time evolution of the temperature and the emission measure are −(0.4 ± 0.3)% yr⁻¹ and −(0.5 ± 0.5)% yr⁻¹ (90% confidence level), respectively.

Table 4.  Best-fit Parameters of the Bremsstrahlung Model in the East Region^a

Epoch	Bremss Model		χ2/d.o.f
	kT	Normalizationb
(Year)	(keV)
2000.1	2.80	8.65	312.82/206
2002.1	2.69	8.95	307.28/206
2004.1	2.70	8.62	420.74/206
2007.9	2.68 ± 0.09	8.51	299.12/206
2009.8	2.66	8.41	278.59/206
2010.8	2.71	8.25	270.84/206
2012.4	2.67 ± 0.10	8.00	307.66/206
2013.4	2.54	8.63	292.35/206

Notes.

^aErrors are at 1σ confidence level. ^b .

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Young SNRs like Cassiopeia A are experiencing a drastic expansion due to the high speed of their ejecta. Plasma formed by shock heating should then be adiabatically expanded. Adiabatic expansion causes cooling of the plasma, too. Therefore, the change of X-ray flux from the thermal component must be first examined with an adiabatic cooling. Laming & Hwang (2003) suggested that Cassiopeia A is currently transitioning from the ejecta-dominated to the Sedov–Taylor phase, and hence it is natural to assume that Cassiopeia A is experiencing an adiabatic evolution without radiative cooling.

Here, we evaluate the time decay of regions where the thermal emission is dominant by assuming that their entire emission is of purely thermal origin. Bremsstrahlung X-ray flux from a thermal plasma is described as

where EM, h, k_B, and are the emission measure, Planck constant, Boltzmann constant, and Gaunt factor, respectively. The Gaunt factor is given by (see Rybicki & Lightman 1979)

where the constant ζ = 1.781. In the case of Cassiopeia A, a typical electron temperature is in the range of 1–3 keV (Hwang & Laming 2012). Therefore, we can use Equation (2) because the energy band we chose (4.2–6.0 keV) is above the spectrum cut-off.

First, we calculate the time evolution of the emission measure. We assume the number of particles nV = constant. Using the expansion parameter m (r ∝ t^m), we can describe , around a dynamical timescale or in the beginning of the Sedov–Taylor phase, and then

where we assume n_e ∼ n_i. In the case of Cassiopeia A, the emission measure change rate is

where we normalized m by 0.66 (Patnaude & Fesen 2009) and t by the remnant age of 340 year.

Next, we calculate the thermal decay rate by taking adiabatic cooling into account. For adiabatic gas, PV^γ = const. By the same token, we can estimate temperature evolution along with the plasma volume as

where γ = 5/3 is the heat capacity ratio. Thus, we can estimate the rate of decline of temperature as

Here we can describe and . In order to calculate flux evolution including both of these effects, , and then

We measured a typical electron temperature of Cassiopeia A to be k_BT ∼ 2.5 keV. This is about twice as low as the mean photon energy of the 4.2–6.0 keV band. Thus we can estimate the thermal component flux change rate as

The variation in the east region (=−1.03; see Table 3) is closest to this. Also, the predicted rates of the emission measure and temperature (see Equations (5) and (7)) are consistent with observational values in the east region; −(0.4 ± 0.3)% yr⁻¹ for the emission measure and −(0.5 ± 0.5)% yr⁻¹ for the temperature. Thus we conclude that flux variation in the east region of Cassiopeia A could be explained by thermal variation due to adiabatic expansion.

On the other hand, change rates in the other regions are much smaller than the value predicted by Equation (9). In particular, variations in the non-thermal dominant regions (<−0.6% yr⁻¹) could not be explained by adiabatic expansion.

Cosmic-ray electrons are considered to be accelerated in the shock front by diffusive shock acceleration (DSA; Bell 1978; Blandford & Eichler 1987). In the Sedov phase, the blast wave is decelerated by sweeping up ambient interstellar matter. This effect causes flux decay of synchrotron X-rays. In addition to this, evolution of the magnetic field and the electron injection rate also changes the flux of synchrotron X-rays. Here, we investigate whether the evolution of these parameters could explain the time variation of Cassiopeia A or not.

X-ray synchrotron emission is well approximated analytically. The electron energy spectrum is generally given by

where A, E_b, and are a normalization factor, the break energy, and the maximum energy of electrons, respectively. In the case of Cassiopeia A, the radio index (Baars et al. 1977). The break energy expresses the spectrum shape which suffers synchrotron cooling. During acceleration, electrons with E > E_b are losing their energies via synchrotron cooling, which provides a steepened energy spectrum. From this electron distribution, we can calculate the approximate formula of the X-ray luminosity as shown in the Equation (5) of Nakamura et al. (2012),

where B_d, ν_b, and ν_roll are the downstream magnetic field, break frequency, and roll-off frequency, respectively. In this calculation, Nakamura et al. (2012) assumed photon energy is larger than break photon energy (ν > ν_b), and break frequency depends on the downstream magnetic field (). This assumption could be adapted for young SNRs (t_age ≲ 10³ year) due to their amplified magnetic field. Here, we attempted to estimate the time variation of the synchrotron X-ray in the case of Cassiopeia A by transforming this equation into our time evolution formulation framework.

First, we considered the time evolution of the normalization factor A in Equation (11). We assumed that the amount of accelerated particles is proportional to the product of the fluid ram pressure and the SNR volume, as assumed in Nakamura et al. (2012). Then, we can describe , where v_s is the shock velocity and we assume the shock is moving through the progenitor wind of the supernova: ρ ∝ r⁻². Then the decay of this term is sensitive to the value of m. In the case of Cassiopeia A (m = 0.66), we find that this normalization is almost constant with time.

Second, we considered the time evolution of the term in Equation (11). The magnetic energy density is amplified to a constant fraction of : case (a) or : case (a′) (e.g., Bell 2004; Vink 2006, 2008), and we can interpret the magnetic energy density evolution as a function of time as

Hereafter we denote . If we neglect the time evolution of ν_roll for the time being, the discussion so far results in synchrotron intensity at the forward shock as L_ν ∝ t^X. Thus, we can estimate the time variation of the synchrotron radiation by the evolution of the magnetic field as . In the case of Cassiopeia A, m = 0.66: Patnaude & Fesen (2009), α = 0.77: Baars et al. (1977), and t_age = 340 year predicts the variation of −0.08% yr⁻¹ for case (a) and −0.09% yr⁻¹ for case (a′), whose difference is quite small. From this result, we find that the contribution of the magnetic field evolution to the X-ray variation is small.

Finally, we consider the time evolution of the term in Equation (11). Assuming that ν_roll is determined by a balance between the acceleration rate and synchrotron loss (Aharonian & Atoyan 1999; Yamazaki et al. 2006), we obtain

From the discussion of time evolution of all parameters (A, B_d, and ν_roll), the logarithmic derivative of Equation (11) results in (see also Katsuda et al. 2010)

In the case of Cassiopeia A, roll-off energy hν_roll is suggested to be ∼2.3 keV in the outer shock filament (Grefenstette et al. 2015). This implies (ν/ν_roll) ≃ 2 for the band 4.2–6 keV. Thus, we can estimate the variation in the outer filament as , and then a change rate is about −0.26% yr⁻¹ for both cases (a) and (a′).

Consequently flux variability is sensitive to the value of the expansion parameter m. If we adopt m = 0.66, variation in the band 4.2–6 keV is estimated to be −0.26% yr⁻¹. Figure 5 shows a comparison between the predicted rate and the observed time variation of the 4.2–6 keV continuum in the forward shock region. We found the model rate well fits observations from 2000 to 2010. The parameter m could be interpreted as a deceleration of the shock velocity. If we assume 5000 km s⁻¹ as the shock velocity of Cassiopeia A, m = 0.66 means a deceleration of ∼5 km s⁻¹ yr⁻¹. In Figrue 5, however, the data points after 2010 do not follow the m = 0.66 line. For reference, we draw another line of m = 0.8 that is closer to the data after 2010. In this case the deceleration is ∼3 km s⁻¹ yr⁻¹. This means a strong braking in the shock velocity has not been occurring in the forward shock region (at most ∼5 km s⁻¹ yr⁻¹). We can see a flux jump between 2010 and 2012. Several non-thermal filaments in Cassiopeia A have a flickering of X-ray flux with a timescale of ∼year, and this jump might also be able to be explained by that feature.

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Particle acceleration and synchrotron cooling in the reverse shock are very complicated. The continuum emission seems to be decreasing gradually in the south west and inner regions. However, these regions have a number of flickering filaments and a large thermal X-ray contribution. In addition, the dynamical evolution of the reverse shock inward of the remnants have not been well understood. Zirakashvili et al. (2014) investigated particle acceleration in the forward and reverse shock of Cassiopeia A by using numerical calculations. They predicted the change rate of the synchrotron X-ray in the reverse shock to be ∼−0.9% yr⁻¹ at least because ejecta density drops proportional to t⁻³ (=−0.9% yr⁻¹). However, we cannot see such a large decrease in the south west and inner regions, and cannot explain the details of the acceleration in the reverse shock at present.