Origin of Galactic Spurs: New Insight from Radio/X-ray All-sky Maps

We first compare the radio sky map obtained at 408 MHz (Haslam et al. 1982: contour) and the X-ray map measured at 0.75 keV based on the $ROSAT$ all-sky survey (Snowden et al. 1995: color), as shown in Figure 1. The Galactic spurs analyzed herein are tagged $yellow$, with the projection example for each rectangular region shown separately in the top panels. A significant offset was observed between the radio and X-ray profiles, at least for a certain fixed latitude $b$, as shown in Figure 1. Subsequently, we created a complete list of the radio/X-ray pixel values at the same Galactic position, ($l$, $b$), with a 1^∘ resolution in both the longitude and latitude directions. Next, we defined the source extraction region corresponding to the NPS, SPS, LAS1, and LAS2, as summarized in Table1. Figure 2 shows the close-up view of the radio/X-ray maps for each region.

To be more precise, we first calculated the correlation coefficients $\rho$ between all radio and X-ray pixel values, i.e., $R(l,b)$ and $X(l,b)$, for each spur region. We defined $\rho$[0] for raw radio and X-ray data as follows:

where $cov(R,X)$ is the covariance; $\sigma_{R}$ and $\sigma_{X}$ are the standard deviations of variables $R$ and $X$, respectively. Next, we calculated $\rho$[$\theta$], which is the correlation coefficient between $R$($l$+$\theta$,$b$) and $X$($l$,$b$), wherein the radio data were shifted by $\theta$ [^∘] in the longitude direction. In this context, a “positive” offset is defined as the direction to which the data are shifted toward the center of the Galactic east region (0^∘ $<$ $l$ $<$ 180^∘), and toward the anti-GC for the west region (180^∘ $<$ $l$ $<$ 360^∘).

Figure 3 ($left$) shows $\rho$[$\theta$] as a function of $\theta$ for the NPS, SPS, LAS1, and LAS2, separately. Is it noteworthy that correlations were stronger for the NPS and SPS than for LAS1 and LAS2. Although we did not exclude point sources from all-sky X-ray maps, no such strong sources existed that affected the results of the correlation analysis presented herein. The amount of peak offset is summarized in Figure 3 ($right$) against Galactic longitude $l$. The errors in $\theta$ were estimated by approximating $\rho$[$\theta$] using a single Gaussian function around the peak; hence, the uncertainties of peak positions were estimated in Figure 3 ($right$) . The positional offsets between the radio and X-rays were $\theta$ = 6.31$\pm$0.34^∘ for the NPS and $\theta$ = $-$4.17$\pm$0.83^∘ for the SPS. Meanwhile, the offsets of the LASs were significantly larger, i.e., $\theta$ = 19.35$\pm$0.17^∘ for LAS1 and $\theta$ = $-$10.57$\pm$0.21^∘ for LAS2, respectively. We conclude that in all spurs, the X-ray emission is shifted toward the GC direction compared with the corresponding radio emission by 5$-$20^∘.

It is noteworthy that the observed X-ray all-sky map is generally modified by absorption owing to the interstellar medium (mostly H I gas), particularly in the low latitude regions within or near the Galactic disk and bulge. The amount of absorption depended on the distance to the structure of interest, which is however unknown for the NPS, SPS, and LASs analyzed in this study. Hence, we did not consider such modifications for the correlation analysis in this section. For this reason, we constrained the analysis regions to a relatively high Galactic latitude of $|$$b$$|$ $>$ 15^∘ (see Table 1), where the absorption was almost negligible.

The X-ray emission properties of the NPS/Loop I have been summarized and discussed in our previous papers (Kataoka et al. 2018 and reference therein). Similarly, in this study, we first investigated all the archival $Suzaku$ data whose pointings were situated in the SPS, LAS1, and LAS2 regions, as listed in Table 2. We excluded pointings that contained either bright X-ray sources or extended sources such as Galaxy clusters, whose tailed emission might affect the analysis in the same FOV. Consequently, we discovered that four, five, and two pointings were used in the SPS, LAS1, and LAS2 regions, respectively. The pointing centers of the Suzaku observations and exposure in kiloseconds are listed in Table 2. The analysis procedure used was the same as those provided in the literature; hence, the results of Suzaku observations in the NPS regions (six points in the region defined in Table 1) were reproduced from the data by Kataoka et al. (2013).

In summary, we extracted the XIS data from XIS 0, 1, and 3, where XIS 0 and 3 were front-illuminated CCDs (FI-CCDs), and XIS 1 was a back-illuminated CCD (BI-CCD) that possessed better sensitivity than FI-CCDs below 1 keV but less sensitive above 5 keV. We analyzed the $Suzaku$ data using headas software version 6.22, xspec version 12.9 and a calibration database released in April 2016. We applied sisclean to remove hot and/or flickering pixels. Only data with a cutoff rigidity larger than 6 GV as well as day and night Earth data with an elevation angle larger than 20^∘ were used for the analysis. We extracted the spectrum after removing possible point sources within the same FOV and then generated redistribution matrix files and auxiliary response files using xisrmfgen and xissimarfgen (Ishisaki et al. 2007). The non-X-ray background spectra from the night Earth observations were generated with xisnxbgen.

For the spectral analysis, we used the 0.5$-$7.0 keV data for XIS 0 and 3, and 0.4$-$5.0 keV data for XIS 1. We fitted all the spectra using xspec with a model comprising three plasma components, similar to previous studies: apec1 + wabs * (apec2 + pl). The apec model assumes an emission from collisionally ionized diffuse gas. Here, (1) apec1 is an unabsorbed thermal plasma with $kT$ = 0.1 keV that mimics the local hot bubble (LHB), (2) wabs*apec2 is the absorbed thermal plasma emitted from the SPS or LAS, and (3)wabs*pl is an absorbed power-law component representing the cosmic X-ray background (CXB). We assumed metal abundance $Z$ = $Z_{\odot}$ for the LHB, whereas $Z$ = 0.2 $Z_{\odot}$ was assumed for the SPS and LAS, respectively (see Kataoka et al. 2013). For the CXB, we fixed the photon index $\Gamma$ = 1.41, as determined by Kushino et al. (2002).

Table 2 lists the spectral fitting parameters for each analysis region, focusing particularly on the temperature $kT$ and emission measure (EM) of plasma component (2). We first fitted the data with the absorption column density ($N_{\rm H}$) as a free parameter, but the results were not constrained well owing to low photon statistics. Hence, we investigated the following two extreme cases: (1) $N_{\rm H}$ was fixed at the Galactic value provided by Dickey & Lockman et al. (1990); (2) $N_{\rm H}$ was fixed at zero. In each case, the resulting $kT$ value coincided within uncertainties. The reduced $\chi^{2}$ values for the fitting model were listed with the number of degrees of freedom. Figure 4 ($left$) shows the variations in $kT$ in apec2 along the Galactic longitude, whereas Figure 4 ($right$) shows the scatter plots of $kT$ and EM for each Galactic spur. The analysis results in the NPS region ($open$ $magenta$) were from N1 to N6 of Kataoka et al. (2013). It was clear that the $kT$ of the SPS regions was generally $\simeq$0.3 keV, which was higher than those in LAS1 and LAS2 concentrated around $\simeq$0.2 keV, thereby suggesting different emission process origins.

In the previous section, we showed that the diffuse X-ray emission associated with the SPS and LAS was generally reproduced well by a thin plasma model assuming collisional ionized gas, but the temperature in the SPS was slightly higher than that in the LAS. Interestingly, the observed $kT$ $\simeq$ 0.3 keV in the SPS was consistent with those reported in the NPS/Loop I and Fermi bubble edges (Kataoka et al 2018). These results suggested the same physical origin between the NPS and SPS, i.e., the shock heating of the Galactic halo gas through the significant Galactic explosion in the past. This idea was further supported by the recent $eROSITA$ observations, which clearly exhibited X-ray bubbles with sharp edges, both in the north and south of the GC surrounding the Fermi bubbles, where the SPS was situated at the lowest edge of the south bubble (Predehl et al. 2020b).

By contrast, $kT$ $\simeq$ 0.2 keV observed in LAS1 and LAS2 were noteworthy because the temperature was typical of that generally observed in the Galactic halo gas (Yoshino et al. 2008; Nakashima et al. 2018), suggesting that the emissions were from local, unshocked halo gas. It was argued that each spiral arm rendered the local potential minimum on the order of 10$\%$ of the gravitational field of the Galaxy; hence, the interstellar gas will fall into the minimum with a typical velocity of 20$-$30 [km s^-1] (Roberts 1969; Sofue 1973). It is noteworthy that the sound velocity of the interstellar gas is expressed as follows:

where $\mu$ $\simeq$ 0.61 is the mean molecular weight, and $T$ $\sim$ 10⁴ [K] is the temperature of the interstellar gas. Hence, the falling gas causes a strong shock of $M$ $\sim$ 2$-$3, where $M$ is the Mach number, resulting in a significant increase in the star formation rate because the compression of the gas density scales as $n$ $\propto$ $M^{2}$. Moreover, if the Galactic shock is isothermal and the magnetic field $B$ is parallel to the arm, $B$ $\propto$ $M^{2}$, then the radio emissivity scales as $\propto$ $n$$B^{2}$ $\propto$ $M^{6}$. Therefore, the local arms will be sufficiently bright in the radio map, as first confirmed by Mills (1959).

Meanwhile, the X-ray emitting gas had a sound velocity of $c_{s}$ $\sim$200 km s^-1 for $kT$ $\simeq$ 0.2 keV; hence, it remained unshocked. Even in such a high-velocity gas, an increasing density reflecting the local gravitational potential may occur, although detailed simulations/observations are necessary. Such a gentle pile-up of X-ray emitting gas may account for the observed enhancement around the LAS. Because the EM of thin thermal X-ray gas scales as EM $\propto$ $n^{2}$, only a 20$-$30$\%$ increase in X-ray gas density, $n$, is required to enhance the X-ray gas, whose temperature is $kT$ $\simeq$ 0.2 keV, as indicated from the observation.

We observed a significant offset between the radio and X-ray intensity distributions not only in the NPS but in the SPS and LAS structures, although their origins are likely to be different, as indicated in the previous section. For the NPS/SPS, the situation can be interpreted based on the diffusive shock process. The relativistic electrons accelerated via the forward-shock emit synchrotron radiation in the radio band, whereas swept-up, compressed gas emitted thin-thermal X-ray radiation in the reverse-shocked region. In this context, the observed offset between radio and X-rays might be related to the thickness and positional offset of the forward/reverse shock regions. In fact, X-ray emitting shells are typically observed on the inner side of the radio shell in the case of supernova remnants (e.g., Gaetz et al. 2000 for the case of E0102-72.3).

From Kataoka et al. (2015) we adopt a simple model in which two spherical bubbles that mimic the north and south are embedded in the center of a gaseous halo. The radius of the outer shell corresponding to the NPS/SPS is $R$ $\simeq$ 5 kpc and the shock velocity is $v_{sh}$ $\simeq$ 300 km s^-1, as indicated by X-ray observations. First, the dynamical time scale $t_{dyn}$ in which the bubble expands to radius $R$ is expressed as $t_{dyn}$ $\simeq$ $R/v_{sh}$. For example, $t_{dyn}$ is 16 Myr in case of $R$ = 5 kpc and $v_{sh}$ = 300 km s^-1.

The thickness of forward shock (FS) region can be approximated as follows:

where $k_{1}$ and $k_{2}$ are the diffusion coefficients; $u_{1}$ and $u_{2}$ are the plasma velocities in the upstream/downstream of the FS, respectively; $v_{s}$ is the shock velocity; $r_{g}$ is the gyro radius; $\xi$ ($>$1) is a constant factor (Drury 1983). Furthermore, we assume that the diffusion coefficient $k_{1}$ = $k_{2}$ $\simeq$ $\xi$ $r_{g}$$c$/3. In addition, $v_{s}$= $u_{1}$ = 4$u_{2}$, $r_{g}$ = $\gamma$$m_{e}c^{2}$/$eB$, where $\gamma$ is the Lorentz factor of the accelerated electrons. The acceleration time scale of electrons with energy $\gamma$$m_{e}c^{2}$ is expressed as

For comparison, the radiative cooling time of electrons emitting 408 MHz of radio emission is expressed as

where $m_{e}$ is the rest mass of electron, $\sigma_{T}$ = 6.65$\times$10^-25 cm^-2 is the Thomson cross section, and $U_{B}$ is the magnetic field density. We assume that the shock compression ratio of the magnetic field is $\simeq$ 4. Hence, the cooling time is slightly longer but almost comparable to $t_{dyn}$. Therefore, the thickness of the radio shell, $d_{R}$, is approximated by equating $t_{acc}$ and $t_{dyn}$ $\simeq$ $t_{cool,R}$, resulting in $d_{R}$ $\simeq$ $d_{FS}$ $\simeq$ 1/4 $R$. This is on the order of   1 kpc, which is consistent with the observed thickness of the radio emission region of the NPS/SPS.

Next, we consider the dynamics of the X-ray shell. First, the radiative cooling time scale of the X-ray emitting gas can be expressed as

where $n$ is the number density of the X-ray emitting gas, $T_{6}$ is the temperature in the unit of $10^{6}$ K (Eq. 34.4 of Draine (2011)). We further modified the above equation assuming subsolar metallicity $Z$ $\simeq$ 0.2 $Z_{\odot}$ (Kataoka et al. 2013), which leads to

(see also Inoue et al. (2017)). We assume a The X-ray-emitting gas does not cool during the expansion time, $t_{dyn}$; hence, the thickness of the X-ray shell is determined by the amount of halo gas piled up in the reverse shock (RS) region to form the NPS.

As the underlying halo gas density profile, we assume a hydrostatic isothermal model expressed as

where $n(r)$ is the gas density [cm^-3] at radius $r$ from the GC; $n_{0}$ is the density at $r$ = 0; $r_{c}$ is the core radius, which we set as $r_{c}$ = 0.5 kpc from the observation (Kataoka et al. 2015). The thickness of the X-ray shell, $d_{X}$, can be determined from the conservation of the swept gas mass as follows:

where 4$n(R)$ is the density of the shocked halo gas in the downstream, assuming the strong shock of a specific heat ratio of 5/3. Using Eq. (8), we obtained $d_{X}$ $\sim$ 1/4 $R$ $\sim$ 1.3 kpc for $R$ = 5 kpc. This is consistent with the observed thickness of the NPS/SPS, as shown in the X-ray map, and explains the approximate similarity between the radio/X-ray thicknesses, $d_{R}$ $\sim$ $d_{X}$. Hence, the observed offset of $\sim$5^∘, which corresponds to  0.7  kpc between the radio and X-ray NPS, may indicate that the FS is located outside the RS by 0.7 kpc on average; however, approximately half of the FS/RS regions may have been overlapped. This is because the radio emission becomes maximum around the forefront of the FS owing to compressed magnetic field via the synchrotron emission, whereas the X-ray emission would have a broad maximum in the RS reflecting a density gradient of the swept up halo gas.

As reviewed in $\S$1, the radio emissions associated with the LASs have been well known since the 1950s; however, the origin of radio spurs in the tangential direction of the local arm is yet to be elucidated. Sofue (1973;1976) suggested that spurs immediately above the Galactic shock may be generated by the inflation of magnetic fields through the Parker instability triggered by the Galactic shock wave. Such an inflation is promoted by the strong compression of the gas and magnetic fields; subsequently, the magnetic force lines above the shock lane will be stretched into the halo perpendicular to the Galactic plane. This is consistent with measurements of vertically extended magnetic fields, as inferred from polarized far-infrared dust emissions in the local arm directions (Mathewson & Ford 1970; Planck Collaboration et al. 2015).

In such a scenario, the formation of radio spurs may be substantially delayed after the Galactic shocks are being activated. First, shock-compressed interstellar gas (mostly H I and H₂), increases the magnetic field strength along the arm, and increases the rate of star formation at the shock front. Thus, the regions of the newly born stars (or H II regions) lies just outside the shock front. Typical time-scale for the evolution of massive stars is $t_{SF}$ $\sim$ 10^6-7 years, thus the H II region $lags$ $behind$ the shock by $\simeq$ $t_{SF}$$\times$($v_{\rm rot}$ $-$ $v_{\rm\Omega}$) $\simeq$ 1 kpc along the direction of Galactic rotation, where $v_{\rm rot}$ $\simeq$ 220 km s^-1 is the rotation speed of the Galaxy and $v_{\rm\Omega}$ $\sim$ 100-150 km s^-1 is the pattern speed of the spiral density wave. Accordingly, offset by $\sim$ 1 kpc $\times$ sin($p$) $\sim$ 100 pc is anticipated in the direction perpendicular to the Galactic arm for a pitch angle of $p\sim 12^{\circ}$. When the stars end their lives, supernovae happen to accelerate cosmic-ray electrons, which may take 10^4-5 years further. Then accelerated electrons propagate into the nonthermal bank perpendicular to the disk along the arm within a timescale of $h$/$v_{A}$ $\simeq$ $\sim$ 10⁶ yr, where $h$ $\simeq$ 100 pc is the height of non-thermal bank and $v_{A}$ $\simeq$ 10$-$100 km s^-1 is the Alfven velocity.

In this context, we can qualitatively interpret the offset between radio and X-rays in the LAS as follows. The position of the radio spur may include an offset compared with the Galactic shock position because we expect a $\sim 10^{6-7}$ years of delay for their formation. Radio spurs originate in synchrotron emission by cosmic-ray electrons, which are likely generated by supernova remnants. Hence, time delays due to stellar evolution, particle acceleration, and diffusion should occur. By contrast, the LAS diffuse X-ray emission may be associated with the Galactic shock region if the Galactic halo gas is trapped by the local potential minimum of the spiral arm. Such an association is often observed in nearby galaxies (Tyler et al. 2004; Long et al. 2014). In such cases, the X-ray emission from the LAS is expected to $lead$ the radio emission by $\sim$ a few 10⁶ years. Assuming a typical distance of $\simeq$ 1 kpc to the regions of the Orion–Cygnus arm, which primarily contributes to the radio/X-ray emissions of the LAS, the observed 10$-$20^∘ offset corresponds to $\sim 100$ pc, which is approximately consistent with the horizontal size ($\sim$30^∘ from Figure 1) of the radio bank in the all-sky map, where we assumed $\sim$ 100 pc.

Finally, we revisit some aspects related to the distance and possible origin of the NPS. As noted in §1, the NPS was initially thought to be the remnants of an old supernova close to the Sun rather than a distant structure associated with the GC activity. Although this idea is not well supported by a number of recent X-ray and gamma-ray observations, it was recently claimed that the NPS distance between 70 and 135 pc depends on the galactic latitudes, according to near-infrared and optical photometry, and Gaia DR2 (Das et al. 2020). However, note that Das et al. (2020) observed the extinction of stars toward the NPS; thus, they measured the distance to the cold dust (typical temperature $T$ $\simeq$ 10³ K) rather than the X-ray brightness of the NPS itself ($T$ $\simeq$ 10^6-7 K). In fact, such foreground dust absorption in the Aquila Rift is generally used to provide a lower limit on the distance to the NPS (e.g., Sofue 1994, 2015; Lallement et al. 2016), but it is unlikely that cold dust and the hot X-ray plasma of the NPS coexist. Similarly, a wide range of the distance depending on the position in the NPS, as proposed by Das et al. (2020), is also unlikely if the NPS is a single continuous structure.

However, let us consider the situation if the NPS is really a structure close to the Sun, in the context of observed thickness and offset, as discussed in §3.2. Now, the radius of the NPS is as small as $R$ $\simeq$ 100 pc, and the width of the forward shock, $d_{FS}$, is $\simeq$ 1/4 $R$, as anticipated from $t_{dyn}$ $\simeq$ $t_{acc}$ $\simeq$ 0.3 Myr (see Eqs. (4) and (5)). Assuming a typical magnetic field strength of $B$ $\simeq$ 10 $\mu$G for an old SNR (e.g., Loru et al. 2020), the cooling time of electrons, $t_{cool,R}$, is much longer than $t_{acc}$; thus, the accelerated electrons remain uncooled, and the radio-bright NPS would be more spherical in shape rather than forming a shell. In contrast, the X-ray shell is formed as previously mentioned, i.e., by sweeping up the interstellar medium. We would expect quite different morphologies for the radio (sphere-like) and X-ray (shell), which are far from the observation. This is an indirect but additional reason supporting why we think the NPS is a giant structure associated with the GC.

Finally, note that the most recent observation by HaloSAT enabled coverage of the entire bright NPS through 14 observations of approximately 30 ks each (LaRocca et al. 2020). These observations provide the first complete survey of the NPS thanks to a wide field of view. While the observed X-ray spectrum is well fitted by two thermal components of $kT_{cool}$ $\simeq$ 0.1 keV and $kT_{hot}$ $\simeq$ 0.3 keV, there is a gradient of temperature across the NPS such that the inner arc temperature is slightly warmer ($kT_{hot}$ $\simeq$ 0.31 keV) than the outer arc ($kT_{hot}$ $\simeq$0.26 keV). For comparison, the NPS results presented in Figure 4 ($kT$ = 0.30$\pm$0.01 keV) were extracted from Kataoka et al. (2013), in which all Suzaku pointings were arranged in the inner arc of the NPS. Moreover, LaRocca et al. (2020) provided a new indication that the cool component also belongs to the NPS rather than to local hot bubbles (LHB). Similarly, even the modeled hot component of $kT$ $\simeq$ 0.30 keV further complicated the analysis by adding a halo gas emission of $kT$ $\simeq$ 0.2 keV in addition to the NPS (e.g., Gu et al. 2016; Miller & Bregman 2016). Although the same conclusion is always reached, i.e., the NPS is a distant object in the kpc range, future deep observations by wide-field satellites such as $HaloSAT$ and $eROSITA$ will provide a new insight to resolve such complexity in the modeling of NPS spectra.