2 mm GISMO Observations of the Galactic Center. II. A Nonthermal Filament in the Radio Arc and Compact Sources^*

The first step in the analysis of the emission from the NTF is to extract the brightness profile along the filament. A 9 pixel (54'') wide region is averaged at each latitude. A local background is subtracted by averaging 10 pixel (60'') wide strips located 15 pixels (90'') east and west of the center of the NTF. The backgrounds are taken at the same fixed latitudes as each point along the NTF. The separation places the background regions outside the main bundle of filaments in the Radio Arc. The mean intensity profiles at 2 mm (after dust emission removal), radio wavelengths, and 1.1 mm are shown in Figure 6. The main uncertainty in the measurement of the filament brightness is the subtraction of the background. The dashed line shows the 2 mm brightness profile using a background that is flat, averaged over all latitudes, and provides an indication of the amount of variation that may occur due to confusion. This comparison demonstrates that some of the apparent brightness changes in the filament may be caused by a mismatch in the brightness of the chosen background regions and the actual brightness underlying the corresponding location of the filament. The filament is not detected at 1.1 mm. The brightness profile at that wavelength shows variations that may be ∼5 times larger than the brightness of the filament, if it is comparable to that at 2 mm.

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The main region where the 2 mm emission of the NTF is bright and unconfused spans from −016 < b < −009, which is roughly from the southern edge of the Radio Arc Bubble (seen as a ∼02 diameter ring centered at (l, b) = (015, −01) (Levine et al. 1999; Rodríguez-Fernández et al. 2001; Simpson et al. 2007) to the N3 radio point source at (l, b) = (017, −008) (Yusef-Zadeh & Morris 1987a; Ludovici et al. 2016), which is also coincident with the 2 mm source "A" indicated in Figure 5. To the north of this, between N3 and the Sickle (b = −004), the background becomes brighter and more complex, making it difficult to determine the truly appropriate background for the NTF. To the north of the Sickle, the NTF seems to fade and become confused with the bright thermal emission of the Arches. The apparent brightness of the filament in this region also seems to be diminished by the extrapolation and subtraction of the thermal emission from dust, even though the NTF is not identifiable in the far-IR emission.

The resulting profiles of the spectral indices (α, defined by I_ν ∝ ν^α) are shown in Figure 6. In the relatively clean region, −016 < b < −09, the 2 mm spectral indices seem to show a slight steepening (become more negative) as a function of distance south from the Sickle (at b = −004). The dip in the 2 mm spectral indices at b = −009 may be an artifact of imperfect subtraction of dust emission from the bright molecular cloud that overlaps the NTF here (see Figure 5). The 6–20 cm spectral index lies in the range 0 < α < 0.2, which is consistent with the results found by Wang et al. (2002) in slices across the Radio Arc near N3. It also is similar to the spectral index measured in the northernmost 8' (b > 015) portion of the Radio Arc by Law et al. (2008), who note a steepening of the 6–20 cm spectral index with increasing distance from the Galactic plane.

Figure 7 shows the SED averaged over the −016 < b < −009 range. The 3 mm point is the interferometric measurement of Pound & Yusef-Zadeh (2018), which may be considered a lower limit. Sofue et al. (1992) do not reliably detect the NTF in 7 mm interferometric observations, but they quantify the clear detection in lower-resolution single-dish 7 mm observations (Sofue et al. 1986; Reich et al. 1988) at the level shown in the figure. There is a clear steepening of the spectrum at 2 and 3 mm relative to that at λ > 6 cm, such that the spectral index is α ≲ −1.5 at 2–3 mm. For comparison, we similarly extracted SEDs for known thermal sources: the Sickle and a portion of the Arches. In these cases, a surface brightness limit was used to define an aperture for each source, and a background was subtracted using the same aperture displaced to relatively faint regions 108'' north of the Sickle and 60'' north of the Arches segment, respectively. The 1.1 mm result for the NTF should be interpreted as an upper limit on the emission rather than a detection. The 6 cm image used here does not cover the Arches. At 90 cm, the Sickle is in absorption, and the Arches are too confused for a reliable brightness measurement in the chosen portion.

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After subtraction of the extrapolated dust emission, a number of compact 2 mm sources remain in the region of the Radio Arc. Most notably, there is a source ("A" in Figure 5) that appears to lie on the NTF at the location of the radio source N3. The radio source N3 is very enigmatic, and its physical association with the Radio Arc is unclear. Ludovici et al. (2016) provide a detailed look at the source, ruling out several possible explanations, leaving a microblazar as the remaining best guess.

Here, we take a further look at the spectral properties of source A, in comparison to the other nearby compact 2 mm sources. The other nearby sources are simply the nearest 2 mm pointlike sources, chosen as a comparison sample of sources that are likely to be typical compact sources. Strong similarity of source A to nearby sources would add weight to the argument that it is only coincidentally along the line of sight to the NTF. The sources indicated in Figure 5 and listed in Table 1 all appear compact (≲21'' FWHM) in the residual 2 mm image, and all appear as longer-wavelength radio sources as well. Figure 8 shows cutout images of each of the sources as observed in the various 3.6 μm–90 cm data sets described in Section 2. Figure 9 displays the SEDs at far-IR to radio wavelengths using aperture photometry. A circular 48'' diameter aperture is used for the source, and a 48''–96'' diameter annulus is used for the background at each wavelength. Uncertainties are calculated from standard propagation of errors assuming that the uncertainty for each pixel is given by the measured standard deviation of pixel intensities in the background annulus.

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3.2.1. Source A

3.2.2. Source B

3.2.3. Source C

3.2.4. Source D

3.2.5. Source E

3.2.6. Source F

3.2.7. General

Pound & Yusef-Zadeh (2018) report 3 mm detections of sources C, E, and F (resolved into two sources) as compact or unresolved objects (resolution = 762 × 351) with 3 mm flux densities that are similar to or lower than our 2 mm measurements. In contrast they report sources A (N3) and B (the Pistol Nebula) as extended sources and find flux densities that are ∼2–5 times higher than our 2 mm measurements. Integration of the 2 mm GISMO map over the larger aperture used by Pound & Yusef-Zadeh (2018) does yield a substantially high flux density for source A (N3), though this includes some emission that is not clearly related to the source A (e.g., part of the NTF) and more importantly requires a more distant and fainter region for background estimation that may not properly represent the background at N3.

The diffuse emission and far-IR properties suggest that sources C, E, and F are associated with star formation, and are likely a blend of hot dust and free–free emission surrounding a compact H ii region and cold dust emission from surrounding molecular clouds. Source D would also be consistent with a compact H ii region (ionized gas and hot dust) but shows no indication of emission from cold dust, suggesting a smaller (or no) remaining molecular cloud.

The color–color and color–magnitude diagrams for all sources within 10' of source A in the GLIMPSE II Archive are shown in Figure 10. The locations of sources C and D in the IRAC color–color diagram are consistent with those of the UCHII regions studied by de La Fuente et al. (2009). Sources E and F have somewhat redder [3.6]–[4.5] colors than the UCHII regions, but that could be an effect of stronger foreground reddening for lines of sight toward the Galactic center. The more extended compact H ii regions studied by Phillips & Ramos-Larios (2008) have bluer [3.6]–[4.5] colors on average than the UCHII regions. The colors of sources C, D, E, and F are also consistent with those of candidate YSOs (e.g., Ramírez et al. 2008). The colors of 2MASS J17462113−2850023 (marked as A), which lies within 15 of source A, are consistent with those of a typical red giant. This star's location in the color–magnitude diagram is clearly to the blue side of most of the cataloged stars in the field, suggesting that it may be a relatively nearby foreground star with low extinction.

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A portion of the Radio Arc had previously been observed at 150 GHz (2 mm) by Reich et al. (2000). In the region southward from the Sickle, they detected rather clumpy emission along the Radio Arc, but displaced slightly to the west. The brightest clump, at b ∼ −013, was reported to have a peak brightness near 300 mJy beam⁻¹ (215), compared to a peak brightness in the Sickle region of ∼170 mJy beam⁻¹. The GISMO results present a very different picture. We find that the bright NTF has a relatively smooth profile, which has a brightness of only ∼40 mJy beam⁻¹ (21'') at b ∼ −013, which is several times fainter than the Sickle brightness of ∼200 mJy beam⁻¹. Thus the GISMO results are roughly consistent with the spectral break to α = −1 at ν > 40 GHz as reported by Sofue et al. (1999). We cannot explain why the earlier observations seem to show structure that is absent in the GISMO observations. The GISMO observations do show some bright clumpy emission near the Radio Arc that is well matched as an extension of the far-IR spectrum of dust in molecular clouds, but these do not correspond to features in the Reich et al. (2000) observations. The clear similarities between the GISMO observations and other wider surveys at longer and shorter wavelengths provides confidence that the GISMO results are more reliable.

The structure seen in the GISMO observations is also very well matched to the 3 mm observations by Pound & Yusef-Zadeh (2018). The 3 mm interferometric observations have higher angular resolution, but are at lower signal to noise and are insensitive to diffuse large-scale emission. The 3 mm data are much less contaminated by thermal emission from dust in molecular clouds, and therefore the resemblance to the 2 mm data is clearer after the contributions of dust emission have been modeled and subtracted (see Arendt et al. 2019).

Sofue et al. (1992) report a nondetection of the NTF at 43 GHz (7 mm) using the Nobeyama Millimeter-wave Array at <1.4 MJy sr⁻¹ with a 16'' × 10'' synthesized beam. However, they note that single-dish observations at the same wavelength (and 38'' resolution) yield a mean brightness of 16.3 MJy sr⁻¹. This latter brightness is consistent with the other measurements shown in Figure 7.

The GISMO observations of the NTF provide further support for its spectral turnover at ∼40 GHz that was reported by Sofue (1999). The relative brightness of the central NTF and the rest of the Radio Arc, which is only barely visible on the western side of the NTF, indicates that the bulk of the Radio Arc has a steeper spectrum or lower-frequency turnover. Reich et al. (1988) explained the 843 MHz to 43.25 GHz morphology and spectral index of the Radio Arc as a broad component with α = −0.2 and a narrower component with α = 0.3. As these are determined over such a wide frequency range, they are not inconsistent with both components rolling over to a much steeper spectrum at frequencies ≳40 GHz.

Given that the 2 mm data confirm a distinct break in the radio spectrum, it seems unlikely that free–free emission in the vicinity (or foreground) of the filaments would contribute much to the 2 mm emission. Thus, the 2 mm emission effectively sets an upper limit on the free–free at longer wavelengths that is sufficiently low to alleviate the concern that free–free emission may contribute to the flatness of the NTF radio spectrum (Yusef-Zadeh 2003). Dominance by nonthermal synchrotron emission at 2 mm is also supported by the finding that the Radio Arc filaments are one of the few polarized regions in low-resolution 2 and 3 mm observations of the Galactic center (Culverhouse et al. 2011). Furthermore, since our measurements are made using local background subtraction along the filament, any diffuse free–free emission should not contribute to measured brightness unless the emitting gas is also highly confined to the same flux tube.

The key features of the 2 mm emission from the NTF are its relatively steep spectral index compared to the 6 and 20 cm emission, and the observation that this spectral index steepens from north to south along the filament. To gain some insight to the meaning of these results, we compare the observations to theoretically motivated synchrotron spectra.

Consider a source that injects high-energy electrons into a magnetically confined filament with a cross-sectional radius R. We assume that the energy spectrum of the injected electrons remains constant in time, so that the injection rate of electrons per unit volume can be represented by the product of two independent functions

$$\begin{eqnarray}&&{dQ}({E}_{0},{t}_{0})=k({t}_{0})n({E}_{0}){{dE}}_{0},\end{eqnarray} \tag{ 1 }$$

where $n({E}_{0}){{dE}}_{0}$ is the number density of electrons with energies between E₀ and ${E}_{0}+{{dE}}_{0}$, and $k({t}_{0})$ is the injection rate at time t₀.

We assume that the energy spectrum of the electrons is given by a power law with an index p at energies between E₁ and E₂, such that

$$\begin{eqnarray}&&n({E}_{0}){{dE}}_{0}=\displaystyle \frac{{ \mathcal E }}{\left\langle E\right\rangle }\,\xi \,{E}_{0}^{-p}\,{{dE}}_{0},\end{eqnarray} \tag{ 2 }$$

where $\left\langle E\right\rangle =\xi \,\int {E}_{0}^{-p+1}\,{{dE}}_{0}$ and ${ \mathcal E }$ are, respectively, the average energy of the injected electrons, and the total electron energy density over the ${E}_{1}-{E}_{2}$ energy range, and the coefficient ξ is a normalization constant: $\xi ={\left[\int {E}_{0}^{-p}{{dE}}_{0}\right]}^{-1}$.

Following their injection, the electrons lose energy by synchrotron radiation at a rate given by Rybicki & Lightman (1986):

$$\begin{eqnarray}\begin{array}{rcl}-\displaystyle \frac{{dE}}{{dt}} & = & \displaystyle \frac{4}{3}{\sigma }_{{\rm{T}}}\,c\,{U}_{B}\,{\beta }^{2}\,{\gamma }^{2}\\ & \equiv & E/{\tau }_{\mathrm{sync}},\end{array}\end{eqnarray} \tag{ 3 }$$

where σ_T = 6.65 × 10⁻²⁵ cm² is the Thomson cross section, ${U}_{B}={B}^{2}/8\pi$ is the magnetic energy density, B is the magnetic field strength, c is the speed of light, and $\gamma =E/{{mc}}^{2}\,={(1-{\beta }^{2})}^{-1/2}$, where β = v/c ≈ 1, v is the electron velocity, and where the energy loss is averaged over pitch angles ($\left\langle {\sin }^{2}\alpha \right\rangle =2/3$). The parameter τ_sync defined in Equation (3) is the average synchrotron lifetime of the electron.

The specific emissivity of the synchrotron emission per unit volume at frequency ν and time t is then given by

$$\begin{eqnarray}&&\begin{array}{l}{j}_{\nu }(\nu ,t)={\displaystyle \int }_{0}^{t}\,k({t}_{0}){\displaystyle \int }_{{E}_{1}}^{{E}_{2}}\ {P}_{\nu }[\nu ,B,E(t-{t}_{0})]\,n({E}_{0}){{dE}}_{0}\,{{dt}}_{0}\\ \,=\,{\displaystyle \int }_{0}^{t}\,\xi \,\displaystyle \frac{{ \mathcal E }}{\left\langle E\right\rangle }\ k({t}_{0}){\displaystyle \int }_{{E}_{1}}^{{E}_{2}}\ {P}_{\nu }[\nu ,B,E(t-{t}_{0})]\,{E}_{0}^{-p}\,{{dE}}_{0}\,{{dt}}_{0},\end{array}\end{eqnarray} \tag{ 4 }$$

where the synchrotron power per unit frequency interval for a single electron is

$$\begin{eqnarray}&&{P}_{\nu }(\nu ,B,E)=\displaystyle \frac{2}{3}\,{\sigma }_{{\rm{T}}}\,c\,\displaystyle \frac{{U}_{B}}{{\nu }_{{\rm{c}}}}\,{\gamma }^{2}\ \displaystyle \frac{9\sqrt{3}}{4\pi }\,F(x),\end{eqnarray} \tag{ 5 }$$

${\nu }_{{\rm{c}}}=(3/4\pi )({eB}/{mc}){\gamma }^{2}\,\sin (\alpha )$ is a critical frequency, e is the electron charge, α is the pitch angle between the electron velocity and the magnetic field, and F(x) is a function of $x=\nu /{\nu }_{c}$ that can be approximated by (D. Kazanas 2019, private communications)

$$\begin{eqnarray}&&F(x)=2.15\,{x}^{1/3}\,{e}^{-x}.\end{eqnarray} \tag{ 6 }$$

This approximation is accurate within ∼20% for x < 100. The spectrum P_ν is calculated at the energy $E(t-{t}_{0})$, the energy of the electron at time $t-{t}_{0}$ after its injection, which is given by

$$\begin{eqnarray}&&E(t-{t}_{0})=\displaystyle \frac{{E}_{0}}{1+(t-{t}_{0})/{\tau }_{\mathrm{sync}}}.\end{eqnarray} \tag{ 7 }$$

The observed specific flux is given by an integral over the emitting volume

$$\begin{eqnarray}\begin{array}{rcl}{F}_{\nu }(\nu ,t) & = & \displaystyle \frac{1}{4\pi {D}^{2}}\ \displaystyle \int {j}_{\nu }(\nu ,t)\ {dV}\\ & = & \displaystyle \frac{{\rm{\Omega }}}{4\pi }\,{j}_{\nu }(\nu ,t){\ell },\end{array}\end{eqnarray} \tag{ 8 }$$

where Ω is the beam size, and ℓ = 4R/3 is the effective path length through the filament.

To fit the observed spectrum we adopted the following model parameters: E₁ and E₂ equal to 10⁶ and 5 × 10¹⁰ eV, respectively, and assume the magnetic field is uniform with a strength of B = 10⁻³ G (e.g., Yusef-Zadeh & Morris 1987a) along the filament. The flatness of the synchrotron spectrum at ≳6 cm suggests a flat injection spectrum of the electrons with a power-law index of p = 0.92. With this choice of parameters, the average electron energy is $\left\langle E\right\rangle =5.2\times {10}^{9}\,\mathrm{eV}$, with a corresponding synchrotron lifetime of 3200 yr. We took the radius of the filament to be R = 0.15 pc (Morris & Yusef-Zadeh 1985). Our examination is limited to the range −016 < b < −005 where the filament is best seen, corresponding to a length of 4.8 × 10¹⁹ cm, assuming a distance of 8.18 kpc (Abuter et al. 2019).

We assume that the electrons are injected into the filament at some time t = t₀, and that their energies evolve due to synchrotron losses as described in Equation (7). Fitting the data allows us to estimate the time elapsed since their injection. Figure 11 depicts the fits of this model at the opposite endpoints of this segment of the filament, where the spectral indices are distinctly different. The fits suggest ages of 2500 and 5000 yr and electron energy densities of 1.3 and 2.1 × 10⁻¹⁰ erg cm⁻³ at the north and south ends, respectively.

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If the electrons are injected into the filament near the northern position, and the age difference corresponds to the electron diffusion time to the southern position, then the implied velocity is ∼6100 km s⁻¹. As in an ionized medium this velocity is limited to the Alfvén velocity, ${v}_{{\rm{A}}}\approx 2\times {10}^{11}B\,{n}_{{\rm{H}}}^{-1/2}$ cm s⁻¹ (Wentzel 1974; Longair 1981), we derive an average density of nuclei in the filaments of n_H = 0.1 cm⁻³.

The total energy contained in this segment of the filament is E_tot ≈ 5.7 × 10⁴⁵ erg. If the filament is not a transient phenomenon, then the luminosity required to sustain the emission from the filament is approximately given by E_tot/τ_sync ≈ 15 L_☉. This luminosity is very similar to the independently obtained value obtained by Serabyn & Morris (1994). However, it depends on our choice of the magnetic field strength and the value of E₂. For example, for a fixed magnetic field strength, we find that the filament's luminosity scales as $\sim {E}_{2}^{1.5}$. A detailed examination of the the model scenario and parameter space will be a subject of future studies.

A number of models for electron acceleration giving rise to the synchrotron emission in the Galactic center filament were summarized by Morris (1996). One hypothesis by Serabyn & Morris (1994) invoked acceleration by magnetic field line reconnection at the surface of the molecular cloud that is ionized by UV radiation from the Quintuplet Cluster. They had found reconnection plausible because the magnetic fields inside and outside of the molecular cloud are orthogonal to each other, and they can be mixed and reconnected in the turbulent, ionized cloud surface. They also noted that there are particular molecular clumps associated with each of the primary bundles of filaments in the Radio Arc (see Figure 2 of that paper). That, and the fact that several of the filaments undergo a discontinuity in either brightness or direction (slightly in the case of direction) at the location of the ionization front, suggested an association of the production sites for relativistic particles with the ionized surfaces of the molecular clumps. However, we do note that at 90 cm, the Sickle appears in absorption against the Radio Arc filaments, suggesting that it lies in front, at least in part (Figure 4). This was noted by Anantharamaiah et al. (1991), who also point out likely absorption by the Pistol Nebula as well (source B in Figure 4). There are other clear cases where an ionized surface on a molecular cloud is associated with a filament, as studied by Uchida et al. (1996) and Staguhn et al. (1998).

Alternately, production of the relativistic electrons may arise in shocked stellar winds as proposed by Rosner & Bodo (1996) and Yusef-Zadeh (2003). In the case of single adiabatic diffusive shock acceleration, the spectral index is α = −0.5. Having multiple shocks flattens the distribution of the energy spectrum of the particles. Winds from different stellar sources may be responsible if they collide and get shocked multiple times (Pope & Melrose 1994). The shocks would be due to the collective winds from all the stars in the Quintuplet Cluster, which is more compact than the scale of the ionization front/shock (i.e., the Sickle). While the Radio Arc NTFs have a flat spectrum at longer wavelengths, most other nonthermal filaments have steep spectra (Law et al. 2008). However, this model does not give an obvious reason why the prominent filament bundles in the Radio Arc are associated with molecular clumps. From this, one might expect that electrons would be accelerated across the shock all the way along the Sickle, rather than in just a few choice places.

The interaction of a Galactic wind with dense clouds has also been proposed by Shore & LaRosa (1999) as a means of creating NTFs, with more detailed development by Dahlburg et al. (2002). Given the large number of filaments in the Galactic center, a global wind is needed and at the sites where the wind gets shocked, producing relativistic particles. In the case of the Radio Arc, the wind could come from the Quintuplet Cluster.