Broadband Radio Study of the North Polar Spur: Origin of the Spectral Turnover with Insights into the X-Ray and Gamma-Ray Spectra

The six all-sky maps from 22 MHz to 2.3 GHz were taken on the ground (Table 1) while data at 23 GHz were obtained with the WMAP satellite. The 30 GHz · 44 GHz · 70 GHz data by the Planck satellite were downloaded from NASA, ³ while the Planck data were obtained from NASA/IPAC. ⁴ The 23 GHz map was already separated into synchrotron and free–free radiation using the maximum entropy method (MEM) analysis in Gold et al. (2011). Table 1 lists the data used in this study.

Table 1. Radio All-sky Data Used in This Study

Product	Release	Observatory	Projection	Resolution (HEALPix)	Data Type
DRAO 22 MHz map	2019	DRAO	12 × 15	nested, res 8 (Nside = 256)	HEALPix
150 MHz map	2019	Parkes,AUS	5°	nested, res 8 (Nside = 256)	HEALPix
Haslam 408 MHz map	2014	GER,AUS,ENG	56'	ring,res 9 (Nside = 512)	Mollweide
Dwingeloo 820 MHz map	2019	Dwingeloo,NLD	12	nested, res 8 (Nside = 256)	HEALPix
1.4 GHz continuum map	2001	Stockert,Villa-Elisa	354	nested, res 8 (Nside = 256)	Mollweide
2.3 GHz continuum map	2019	Hartebeesthoek,ZAF	20'	ring,res 8 (Nside = 256)	Mollweide
23 GHz map	⋯	WMAP	⋯	⋯	Mollweide
30 GHz full channel map	2015	Planck	⋯	nested, res 10 (Nside = 1024)	HEALPix
44 GHz full channel map	2015	Planck	⋯	nested, res 10 (Nside = 1024)	HEALPix
70 GHz full channel map	2015	Planck	⋯	nested, res 10 (Nside = 1024)	HEALPix

References. 22 MHz: Roger et al. (1999); 150 MHz: Landecker & Wielebinski (1970); 408 MHz: Remazeilles et al. (2015); 820 MHz: Paradis et al. (2012); 1420 MHz: Paradis et al. (2012); 2300 MHz: Jonas et al. (1998); 23 GHz: Gold et al. (2011); 30–70 GHz: Planck Collaboration et al. (2014).

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The unit for each all-sky data point is the brightness temperature T_b = I_ν × c²/2k_B ν², where I_ν and k_B denote the brightness and Boltzmann constant, respectively. The brightness temperature is a physical quantity that describes the radiation intensity of an astronomical object. As shown in Table 1, the all-sky map is displayed differently depending on the frequency, such as Mollweide and HEALPix. Therefore, in this study, the all-sky maps were converted to Mercator diagrams (Figure 5 in the Appendix).

The mean of the observed data within a pixel was taken as the measured value, and the standard deviation was the error at that pixel. In addition, the cosmic microwave background (CMB; T_CMB = 2.7 K) was uniformly subtracted from the 22, 150, 408, 820, and 1420 MHz observed data. Because some of the brightness temperature data of Planck contained negative values that were consistent with zero within the uncertainty, all negative values were set to zero. When the lower limit of the error bar was negative, the upper limit was considered for analysis.

The radio data for each frequency in the ground-based observations contained some errors, which, in addition to the errors introduced by data processing in Section 2.1, are mainly classified as scale and zero-level errors. Table 2 summarizes these errors in the observed data. However, Roger et al. (1999) do not mention zero-level or scale errors for the 22 MHz observations; instead, they used a value of ±5000 K as a typical error. For the 150 MHz observations, Patra et al. (2015) calibrated the 150 MHz map by comparing the absolutely calibrated sky brightness measurements between 110 and 175 MHz calculated using the SARAS spectrometer, and Monsalve et al. (2021) proposed a calibration by comparing with absolutely calibrated measurements from the Experiment to Detect the Global Epoch of Reionization Signature (EDGES). We considered which of the three errors (standard deviation during data processing, scale error, and zero-level error) dominated the analyzed domain. Consequently, the standard deviation for each frequency was ≲10% in the NPS region and dominant at 22, 150, 408, and 820 MHz; however, at 1420 and 2300 MHz, the zero-level error was dominant. Therefore, standard deviations were used as errors for ground-based observations from 22 to 820 MHz and for WMAP and Planck, whereas zero-level errors were used for 1420 and 2300 MHz. The original data were used for the two corrections at 150 MHz because they exhibited a minor effect. The WMAP separation of thermal/nonthermal emissions was performed using the MEM of Bennett et al. (2003). This study states that the total observed Galactic emission matched the MEM model by less than 1%, whereas the emission was separated into individual components with low accuracy. Therefore, we considered that these separations are sufficiently reliable.

To compare the differences in the spectral shape between high and low frequencies, we compared the power law using frequency data at 22, 150, 408, 1420, 2300 MHz and 23 GHz. All data were analyzed at a resolution of 5° in both the Galactic longitude and Galactic latitude to align with the 150 MHz resolution.

First, we obtained β maps (T_b = A ν^−β ) using the least squares method with the brightness temperatures measured at different frequencies,

$$\begin{eqnarray}&&\beta =-\frac{{\sum }_{i=1}^{n}\left(\mathrm{ln}{\nu }_{i}-\overline{\mathrm{ln}\nu }\right)\left(\mathrm{ln}{T}_{i}-\overline{\mathrm{ln}T}\right)}{{\sum }_{i=1}^{n}{\left(\mathrm{ln}{\nu }_{i}-\overline{\mathrm{ln}\nu }\right)}^{2}},\end{eqnarray} \tag{ 1 }$$

where ν_i = 22, 150, and 408 MHz for a low-frequency map (Figure 1, top), whereas ν_i = 1420, 2300 MHz, and 23 GHz for a high-frequency map (Figure 1, middle). As shown in Figure 1, the spectral power law of the NPS region (white dotted line in Figure 1) was flatter than that in the other areas for both high and low frequencies. We obtained β ≃ 2.4 to 2.7 at low frequencies and β ≃ 2.7 to 3.2 at high frequencies in the NPS region, indicating that the power law of the spectrum at high frequencies was steeper than at low frequencies.

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Second, to understand the difference in the cutoff frequency of the radio spectrum in the all sky, we obtained a turnover frequency map, as shown in the bottom of Figure 1. This figure plots the frequency at which the two power-law spectra obtained, as shown in the top and middle of Figure 1, intersect. For the two power-law functions obtained from 22 to 408 MHz (${T}_{1}={A}_{1}{\nu }_{1}^{-{\beta }_{1}}$) and from 1420 to 23 GHz (${T}_{2}={A}_{2}{\nu }_{2}^{-{\beta }_{2}}$), the turnover frequency at which the two functions intersect is

$$\begin{eqnarray}&&{\nu }_{\mathrm{turnover}}={\left(\displaystyle \frac{{A}_{2}}{{A}_{1}}\right)}^{\tfrac{1}{{\beta }_{1}-{\beta }_{2}}}[\mathrm{Hz}].\end{eqnarray} \tag{ 2 }$$

As shown in the figure, the NPS spectral turnover was on a lower frequency (<1 GHz) than the other regions (see also Mou et al. 2023). In reality, the turnover frequency in the NPS region for l = 30°–35°, b = 55°–60° was 0.76 GHz, whereas it was 1.1 GHz for l = 40°–45° in the same Galactic latitudes around the NPS.

Next, in order to confirm the spectral turnover of the NPS region in more detail, the NPS spectra for each Galactic latitude are analyzed in the next section.

We extracted the spectrum for each Galactic latitude of the NPS. To eliminate the effects of linear polarization and ensure that it was sufficiently larger than the beamwidth of all frequency maps, the spectral region was 5° in both the Galactic longitude and Galactic latitude. The Galactic longitude was fixed at l = 30°–35° where the NPS radiation is the brightest, and spectra were produced for regions varying in Galactic latitude by 10°. Figure 2 presents the typical spectra for every 10° Galactic latitude in the NPS. The black, green, blue, and red points represent 22–2300 MHz, 23 GHz synchrotron radiation, 23 GHz free–free radiation, and Planck data (30–70 GHz), respectively. The NPS emissions were found to decrease at β ≃ 2.4–2.7(T_b ∝ ν^−β ) power law or α ≃ − 0.4 to −0.7 (I_ν ∝ ν^α , where α = 2 − β), up to a few GHz, regardless of the Galactic latitude. This result is consistent with the values in the literature, β ≃ 2.55–2.65 (Guzmán et al. 2011) or β ≃ 2.3–3.0 (Reich & Reich 1988). Consequently, the electron spectrum indicates a power-law relationship with its index (s) of N(γ) ∝ γ^−s (s ≃ 1.8–2.4, where s = 1–2α) if synchrotron radiation dominated up to a few GHz. In addition, cutoffs were observed around ν_brk ≃ 1 GHz, especially at high Galactic latitudes.

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The synchrotron/free–free data at 23 GHz exhibited a stronger fraction of free–free radiation at low Galactic latitudes, and the contribution of free–free radiation decreased with increasing Galactic latitude. This indicated that synchrotron radiation dominated at high Galactic latitudes. Free–free radiation exhibited a flat power law α ≃ −0.1 in the optically thin region, whereas synchrotron radiation exhibited a significantly steeper power-law behavior with α > −1.0. Therefore, synchrotron radiation clearly dominates at high Galactic latitudes and up to a few GHz.

We consider the 30–70 GHz Planck data where the radiation was consistent with the thermal radiation from dust with α ≃ 2.0 power law. In the optically thin limit, the spectral energy distribution (SED) of the emission from a uniform population of grains is well described empirically by a modified blackbody I_ν = τ_ν B_ν (T), where τ_ν is the frequency-dependent dust optical depth and B_ν is the Planck function for dust at temperature T.

In Section 3.2, we show that the radio emission of the NPS consists of (1) synchrotron radiation, (2) free–free radiation, and (3) dust emission. The characteristics of these types of radiation are described below. Synchrotron radiation decreases following a power-law behavior up to a few GHz and a cutoff at ν_brk ≃ 1 GHz. Synchrotron radiation dominates up to a few GHz, whereas free–free radiation and dust radiation are almost negligible. Free–free radiation theoretically decreases at α_ff ≃ −0.1 power law and can be observed from a few GHz. The contribution of free–free radiation increases, and the amount of radiation even exceeds that of synchrotron radiation, especially at low Galactic latitudes. This is clearly confirmed by the NPS spectra, as shown in Figure 2. Dust radiation is dominant above several tens of GHz. In the optically thin limit, the SED of the emission from a uniform population of grains is well described empirically by a modified blackbody I_ν = τ_ν B_ν (T). Radio emissions of the NPS based on these characteristics are shown in Figure 3.

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The spectral turnover in the NPS can be discussed relative to synchrotron cooling. First, we assume the simplest leaky-box model in which fresh, accelerated electrons are injected into an emission region with a magnetic field B, followed by particle loss due to energy-independent advection and radiative energy loss. Approximating the transport equation for electrons passing through the shock by the leaky-box model, the time evolution of the electron energy distribution N_e (γ) can be expressed as follows (Inoue & Takahara 1996):

$$\begin{eqnarray}&&\displaystyle \frac{\partial {N}_{e}(\gamma )}{\partial t}=\displaystyle \frac{\partial }{\partial \gamma }\left(\displaystyle \frac{\gamma }{{t}_{\mathrm{cool}}}{N}_{e}(\gamma )\right)+{Q}_{0}(\gamma )-\displaystyle \frac{{N}_{e}(\gamma )}{{t}_{\mathrm{adv}}},\end{eqnarray} \tag{ 3 }$$

where t_cool is the electron-cooling time, t_adv is the advection time, and Q₀(γ) is the electron injection rate. The electron energy steady-state solution can be expressed approximately as a broken power law of the form of Equation (4):

$$\begin{eqnarray}&&\begin{array}{l}{N}_{e}(\gamma \gt {\gamma }_{\min })\\ \quad =\,{N}_{0}{\gamma }^{-s}{\left(1+\displaystyle \frac{\gamma }{{\gamma }_{\mathrm{brk}}}\right)}^{-1}\exp \left(\displaystyle \frac{\gamma }{{\gamma }_{\max }}\right).\end{array}\end{eqnarray} \tag{ 4 }$$

Here, s, N₀, and ${\gamma }_{\min }$ (or ${\gamma }_{\max }$) denote the injection index, normalization constant, and minimum (or maximum) electron energy, respectively. Then, γ_brk corresponds to the energy at which the electron-cooling time and advection time are balanced (t_cool ≃ t_adv), resulting in an electron distribution with a turnover whose power-law index s steepens by one. If the spectral turnover γ_brk originates from synchrotron cooling, the magnetic field B can be estimated by balancing the advection and cooling timescales of electrons.

In a nonrelativistic strong shock wave, the compression ratio is v₂/v₁ = 1/4, where v₁ and v₂ are the upstream and downstream velocities in the rest frame of the shock, respectively. The electron advection time is obtained as follows:

$$\begin{eqnarray}\begin{array}{rcl}{t}_{\mathrm{adv}} & \simeq & \displaystyle \frac{R}{{v}_{2}}\\ & \simeq & 1.23\times {10}^{15}\left(\displaystyle \frac{R}{1\,\mathrm{kpc}}\right){\left(\displaystyle \frac{{v}_{1}}{100\,\mathrm{km}\,{{\rm{s}}}^{-1}}\right)}^{-1}\,[{\rm{s}}],\end{array}\end{eqnarray} \tag{ 5 }$$

where R denotes the thickness of the radiation area. Using the literature value of v₁ ≃ 320 km s⁻¹ (Kataoka et al. 2013) in the GC model, and assuming that the distance to the radiation source was 8000 pc and that the NPS had a spherical structure with an outer diameter R_out ≃ 5 kpc and an inner diameter R_in ≃ 3 kpc (R = R_out − R_in ≃ 2 kpc) (Kataoka et al. 2015), the advection time of an electron was t_adv ≃ 7.7 × 10¹⁴ s ≃ 24.4 Myr. In the supernova remnant (SNR) model, assuming that the distance to the radiation source was 150 pc, we obtained R ≃ 2 kpc × 150/8000 = 38 pc, and the advection time of the electron was t_adv ≃ 1.5 × 10¹³ s ≃ 4.6 × 10⁵ yr.

Meanwhile, the electron-cooling time owing to synchrotron radiation is

$$\begin{eqnarray}\begin{array}{rcl}{t}_{\mathrm{cool}} & \simeq & \displaystyle \frac{E}{{dE}/{dt}}=\displaystyle \frac{\gamma {m}_{{\rm{e}}}{c}^{2}}{\tfrac{4}{3}{\sigma }_{{\rm{e}}}{{cU}}_{{\rm{B}}}{\gamma }^{2}}=\displaystyle \frac{6\pi {m}_{{\rm{e}}}c}{{\sigma }_{{\rm{e}}}{B}^{2}\gamma }\\ & \simeq & \displaystyle \frac{5.1\times {10}^{8}}{{B}^{2}\gamma }\,[{\rm{s}}],\end{array}\end{eqnarray} \tag{ 6 }$$

where σ_e, U_B , and γ denote the Thomson cross section, magnetic field energy density, and Lorentz factor, respectively. A typical synchrotron frequency can be expressed as

$$\begin{eqnarray}&&{\nu }_{\mathrm{syn}}=\displaystyle \frac{{eB}}{2\pi {m}_{{\rm{e}}}}{\gamma }^{2}\simeq 1.2\times {10}^{6}B{\gamma }^{2}\,[\mathrm{Hz}],\end{eqnarray} \tag{ 7 }$$

where B denotes the magnetic field in units of Gauss. Then, by substituting Equation (7) into Equation (6), we obtain

$$\begin{eqnarray}\begin{array}{rcl}B & \simeq & 5.9\times {\left(\displaystyle \frac{{\nu }_{\mathrm{syn}}}{1\,\mathrm{GHz}}\right)}^{-1/3}\\ & & \times \,{\left(\displaystyle \frac{{v}_{1}}{100\,\mathrm{km}\,{{\rm{s}}}^{-1}}\right)}^{2/3}{\left(\displaystyle \frac{R}{1\,\mathrm{kpc}}\right)}^{-2/3}\,[\mu {\rm{G}}].\end{array}\end{eqnarray} \tag{ 8 }$$

Figure 2 shows the presence of a cutoff at ν_brk ≃ 1 GHz, which indicates that the electron-cooling time and advection time are balanced (t_cool ≃ t_adv). Thus, by substituting the cutoff frequency ν_syn ∼ ν_brk ≃ 1 GHz and the electron advection time t_adv into Equation (8), the magnetic field of the NPS can be obtained, the values of which are 8 μG and 114 μG for the GC and SNR models, respectively. Note that the NPS radius varies by a few kiloparsecs in the literature for the GC model (see Predehl et al. 2021). When the shell thickness is doubled, B ≃ 5 μG and B ≃ 72 μG for the GC and SNR models, respectively, but we do not believe that these errors affect the discussion.

Last of all, we note that such spectral turnover may be owning to various other models. First, if the low-energy electrons do not have sufficient time to establish a steady state relative to synchrotron cooling, but radiation loss time is sufficiently short for high-energy electrons, a similar turnover could be observed around the GHz energy band. In such a case, we can no longer assume exquisite balance between t_adv and t_cool; however, Equations (6) and (7) still hold, which leads to $B\simeq 68\times {\nu }_{\mathrm{syn}}^{1/3}\,[\mathrm{GHz}]\times {{\rm{t}}}_{{cool}}^{-2/3}\,[\mathrm{Myr}]$. Therefore, if the NPS is a GC structure over ≃10 Myr ago and the cooling time is comparable, B ≃ 10 μG is naturally obtained. Similarly, we obtained B ≃ 100 μG in the case of a nearby SNR. Hence, we infer that our discussion will not be affected provided the cooling time is comparable to the dynamical timescale (or age) of the NPS.

Second, the bremsstrahlung energy losses may play a significant role in including spectral breaks, particularly in regions with high gas densities (Crocker et al. 2010). However, the bremsstrahlung energy loss timescale in the case of the NPS is approximately three orders of magnitude longer than the synchrotron timescale, advection time, and age of the NPS because of its notably thin gas density of n ≃ 10⁻³ cm⁻³ (e.g., Sofue et al. 2019) compared to the GC. Consequently, the effect of the bremsstrahlung energy losses can be regarded as negligible.

Finally, although there is certainly a steady state, bremsstrahlung collisions experienced by the electrons in the interstellar medium gas are the dominant loss process for low-energy electrons. In fact, bremsstrahlung emission from nonthermal electrons is observed in a few SNRs, where a hard spectrum is possibly owing to the interaction of electrons with a thick interstellar medium and a gas density of approximately n ≃ 10 −100 cm⁻³ (Uchiyama et al. 2002; Tanaka et al. 2018). Compared to this, the gas density in the NPS is sufficiently low, where n ≃ 10⁻³ cm⁻³ and n ≃ 1 cm⁻³ for the GC and SNR scenarios, respectively. Therefore, we infer that the contamination of the bremsstrahlung emission from nonthermal electrons cannot account for the spectral turnover as observed in the GHz band.

We performed an SED analysis for the high Galactic-latitude region, where synchrotron radiation is dominant. We used the area (l, b) = (30°–35°, 55°–60°), where the spectral region is 5° in both the Galactic longitude and Galactic latitude. Fitting was performed on data from 22 MHz–23 GHz, which is pure synchrotron radiation, assuming distances to the NPS for each GC (8000 pc) and SNR (150 pc). The leptonic model was used for the fitting (Inoue & Takahara 1996; Kataoka et al. 1999), assuming the electron distribution as in Equation (4) and using the magnetic field obtained in Section 4.2.

The fitting results under these conditions are shown in Figure 4. The green, red, and blue lines represent synchrotron radiation, inverse Comptonization (IC) when the CMB photons are knocked, and synchrotron self-Compton (SSC) scattering. The yellow dotted line indicates the dust radiation, represented as I_ν = τ_ν B_ν (T), whose optical thickness and temperature are τ_ν ∼ 10⁻⁶–10⁻⁵ and T ∼ 20 K, respectively, from the literature (Planck Collaboration et al. 2014). Yellow is the IC when the dust radiation is knocked. In addition, the purple dotted lines and plots depict the SED of the Fermi bubbles fitted in the one-zone leptonic model (Kataoka et al. 2013). The GeV data plots correspond to the emissions of the entire bubble structure, following Su et al. (2010). The radio data plots correspond to the WMAP haze emissions averaged over b = −20° to −30° for ∣l∣ < 10°. The bow tie centered at the 23 GHz K band indicates the range of synchrotron spectral indices allowed for the WMAP haze, following Dobler & Finkbeiner (2008). The parameters used for the fitting and the corresponding results are listed in Table 3. Note that the best fit parameter, the hard electron spectrum s ≃ 1.9, cannot be easily explained by the standard shock model. Although this is a very interesting topic, we simply adopted this value as it is beyond the scope of this study.

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Table 3. Comparison of the Fitting Parameters of the SED

Parameter	NPS/GC	NPS/SNR	Bubbles
Distance [pc]	8000	150	8000
B [ μG]	8	114	10
Region radius [cm]	2.2 × 1020	4.0 × 1018	1.2 × 1022
Bulk Lorentz factor	1	1	1
Q0 [cm−3 γ−1 sr−1]	4.0 × 10−4	5.2 × 10−4	1.7 × 10−4
${\gamma }_{\min }$	1.0	1.0	1.0
γbrk	1.0 × 104	2.7 × 103	1.0 × 106
${\gamma }_{\max }$	2.5 × 104	6.0 × 103	1.0 × 107
Index s	1.9	1.9	2.2
Brightness index β	2.45	2.45	2.6
Intensity index α	−0.45	−0.45	−0.6
Ue [erg cm−3]	1.2 × 10−12	1.2 × 10−12	1.8 × 10−13
UB [erg cm−3]	2.5 × 10−12	5.2 × 10−10	4.0 × 10−12
Pn/th [erg cm−3]	1.2 × 10−12	1.7 × 10−10	1.4 × 10−12

Note. For the electron energy distribution, we assumed a standard broken power-law form ${N}_{e}{(\gamma \gt {\gamma }_{\min })={N}_{0}{\gamma }^{-s}(1+\gamma /{\gamma }_{\mathrm{brk}})}^{-1}\times \exp (-\gamma /{\gamma }_{\max })$. U_e , U_B : electron and magnetic field energy densities, U_e = ∫d γ m_e c² γ N_e (γ) and U_B = B²/8π. P_n/th: the nonthermal pressure P_n/th = (U_e + U_B )/3.

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In the GC model, the IC of the CMB is dominated by high-energy radiation, with a peak in the 100–1000 keV range and a flux of 10⁻⁹ erg s⁻¹cm⁻² sr⁻¹, whose brightness is almost equal to that of the high-energy band of the Fermi bubble. However, the IC of the CMB is dominant in the SNR model, similar to the GC model, but with a peak below 10 keV and a flux of approximately 10⁻¹² erg s⁻¹cm⁻² sr⁻¹. This value is several orders of magnitude lower than the detection limits of modern astronomical satellites. More accurate fitting will be possible if all-sky observations of gamma-rays progress in the future and the NPS is discovered.

In Section 4.3, owing to the distance to the two different NPSs, we obtained the parameters shown in Table 3, where U_e and U_B are electron and magnetic field energy densities.

$$\begin{eqnarray}&&{U}_{e}=\int d\gamma {m}_{e}{c}^{2}\gamma {N}_{e}(\gamma )\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&{U}_{B}={B}^{2}/8\pi .\end{eqnarray} \tag{ 10 }$$

P_n/th is the nonthermal pressure, P_n/th = (U_e + U_B )/3. The total energy can be estimated by assuming the NPS volume. In the GC model, the total volume of the NPS can be calculated as $V=4\pi /3\times ({R}_{\mathrm{out}}^{3}-{R}_{\mathrm{in}}^{3})\sim 1.2\,\times \,{10}^{67}\,{\mathrm{cm}}^{3}$ using R_out ≃ 5 kpc and R_in ≃ 3 kpc (Kataoka et al. 2015). Thus, we estimated that the nonthermal energy of the NPS was E_n/th = V × (U_e + U_B ) ≃ 4.3 × 10⁵⁵ erg, which was consistent with the literature values E_n/th ∼ 10⁵⁵⁻⁵⁶ erg (Sofue 1984; Kataoka et al. 2018; Sofue & Kataoka 2021). It is notable that the NPS radius contains an error of several kiloparsecs in the GC model. When the shell thickness is doubled, some of the parameters listed in Table 3 change to Q = 1.0 × 10⁻³ cm⁻³ γ⁻¹ sr⁻¹, γ_brk = 1.2 × 10⁴, U_e = 2.9 × 10⁻¹² erg cm⁻³, and U_B = 9.9 × 10⁻¹³ erg cm⁻³, and the nonthermal energy is estimated to be E_n/th ≃ 1.3 × 10⁵⁶ erg. However, we do not believe that these errors affect the discussion.

The thermal pressure of the NPS was estimated by Kataoka et al. (2013) using X-ray Suzaku observations. It should be noted that they are estimated using 8° < l < 16°, 42° < b < 48° observation data, and yielded P_th ≃ 2 × 10⁻¹² erg cm⁻³. It was found to be in close agreement with the nonthermal energy determined for the first time from the radio spectrum of the NPS. Therefore, this can be interpreted as natural in the case of the GC.

In contrast, in the SNR model, the volume of the NPS was V ∼ 7.9 × 10⁶¹ cm³, and the nonthermal energy was estimated to be E_n/th ≃ 4.1 × 10⁵² erg. When the shell thickness is doubled, the parameters change to Q = 1.2 × 10⁻³ cm⁻³ γ⁻¹ sr⁻¹, γ_brk = 3.4 × 10³, U_e = 2.8 × 10⁻¹² erg cm⁻³, and U_B = 2.1 × 10⁻¹⁰ erg cm⁻³, and the nonthermal energy is estimated to be E_n/th ≃ 4.8 × 10⁵² erg. Compared to the GC, the distance to the NPS was approximately ∼1/50 times larger, and the number density of the gas was ∼1/7 times greater. Thus, the thermal pressure was estimated to be P_th ≃ 1.4 × 10⁻¹¹ erg cm⁻³, which was approximately ten times larger than the nonthermal pressure. Therefore, the pressure balance was found to be disturbed in the SNR model. In addition, the typical energy of an SNR is E ∼ 10⁵¹ erg, which is unnatural, at least for a single SNR. Therefore, if the NPS is a local structure, it could be a massive structure associated with a super bubble (Krause et al. 2018).