NGC 5195 IN M51: FEEDBACK "BURPS" AFTER A MASSIVE MEAL?

The Chandra Advanced CCD Imaging Spectrometer (ACIS) observations of M51 used in this study were obtained from the Chandra archive and are listed in Table 1. Seven long pointings were obtained in Faint mode and total ∼760.2 ks. Three observations, totaling 84 ks, were obtained in Very Faint mode and are discussed in Section 2.2 below. We do not analyze two observations: a short 2 ks observation obtained in Faint mode (ObsID 414) and a ∼10 ks observation (ObsID 12562) obtained in Very Faint mode in which NGC 5195 falls in the gap between the ACIS-I and ACIS-S CCDs. These observations are not included in our analysis as they add little or no signal.

Data preparations were all carried out using the Chandra Interactive Analysis of Observations (CIAO) software package and followed the recommended processing. Each ObsID was examined for times of high particle background. Although no such periods were found, short time intervals were trimmed at the start and end to eliminate possible residuals; the trimmed times sum to <0.1% of the total exposure. Gain calibrations were checked and found to match. The data were energy-filtered to include only events between 0.4 and 8 keV. Given the multiple pointings, the absolute positions of a given ObsID may differ slightly from the others. Consequently, we arbitrarily adopted ObsID 13814 (the longest exposure) as our reference. The CIAO task merge_obs was used to place all frames into a common reference, construct exposure maps for each observation, and merge the exposure maps and event files to build a flux image.

Point sources above a flux of ≈5 × 10⁻¹⁶ erg s⁻¹ cm⁻² (corresponding luminosity at the distance of M51 is ≈4 × 10³⁶ erg s⁻¹) were filtered out from all subsequent analyses. This limit means that the seven bright sources seen in the field are all filtered from the data. Five of the sources are too distant to have any impact on the spectra or profiles of the arcs. A sixth source lies too far west of the western edge of the inner arc to have any impact—the source is ∼15'' W of the edge while the 90% encircled energy radius at its position is ∼4''. The seventh point source sits just south of the nucleus on the east edge of the inner arc. Again, the 90% encircled energy radius of ≈4 arcsec, while contaminating some of the arc emission, remains small relative to the total size of the inner arc. Consequently, the western half of the arc is uncontaminated by point source emission.

The overall field is shown in Figure 1(a). The nuclei of NGC 5194 and NGC 5195 are labeled "A" and "B," respectively. NGC 5194 is nearly centered in the field, so the majority of the galaxy is covered by the image. Also visible is the X-ray emission from a prominent spiral arm lying between the nuclei (discussed in Vega et al. 2016).

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The nucleus of NGC 5195 lies just inside the ACIS field of the merged F-mode exposures (Figure 1). In all subsequent discussion, the two X-ray arcs are labeled as "inner," to describe the one closest to the nucleus of NGC 5195, and "outer." Point sources at the east end of both the inner and outer arcs are removed from the analysis of the spectrum and flux of the respective arc as mentioned previously.

The arcs are separated from the nucleus by ∼780 (∼15'') and 1700 pc (∼30''), respectively (Table 2). The two arcs have broadly comparable curvature: the inner arc spans ∼50°–60° (position angles ∼180°–240° measured eastward from north), while the outer arc spans ∼40°–50° (position angles ∼160°–210°). The curvatures are consistent with an origin at or near the SMBH. The outer arc is approximately centered on a line joining the nuclei of NGC 5195 and NGC 5194, but the inner arc is centered on a line rotated ∼30° counter-clockwise from the NGC 5194/5195 line. Note also that the inner arc is brighter than the outer arc by about a factor of two (Section 2.4.3), consistent with expanding gas. The curvature, coupled with the inner versus outer brightnesses, suggests a nuclear outburst or similar expulsion of matter with the emission becoming fainter as the gas expands. The presence of the two arcs suggests two episodes of SMBH-driven outflows. We discuss other possibilities to explain this structure later in this section.

While we can measure the length and width of each arc, the thickness thick is unknown. We adopt a thickness of 100 thick₁₀₀ pc at the front edge of the outer arc—a specific thickness at the outer edge leads to a constant opening angle. If the arcs were a very broad angular hemispheric "fan," significant X-ray emission would exist between the arc and the nucleus, but we do not detect such emission. Instead, we detect emission that is length- and width-restricted. The width restriction implies an episode; the length restriction implies an angular constriction in a flow with unknown depth or thickness. An explosion is expected to be azimuthally symmetric, but the arcs to the south are not, appearing instead to be two episodes of a "focused" outflow.

The 85 ks ACIS VF mode data are shown in Figure 1(c). The data provide a glimpse north of the NGC 5195 nucleus; a "glimpse" because the signal-to-noise in the ACIS VF observation is low. X-ray structure exists to the north, however, it does not appear to be arc-like, but instead V- or fan-shaped with the point of the V toward the SMBH. If the density to the north decreases sufficiently quickly, a bubble expanding northward could open, possibly leading to a V- or fan-shaped structure.

Are there alternative explanations at this point? One could interpret the structure as weak point source(s) plus diffuse emission. However, this structure is not consistent with blended point sources, even for the Chandra point-spread function (PSF) ∼4' off-axis. We note, however, that our PSF analysis applies only to sources above ≈100 counts, as fainter ones are inseparable from the diffuse emission at this off-axis angle. A definitive analysis requires an on-axis observation. Another possibility is induced star formation within the arcs; we discuss this interpretation in Section 2.5 after presenting observations in other wavelengths.

A similarly shaped, fan-like structure also appears to the north in a continuum-subtracted Hα image of NGC 5195 presented in Kaisin & Karachentsev (2008) and the Hα image from Hoopes et al. (2001). We discuss the Hα image in Section 2.5.

Figure 2 displays the surface brightness profiles across both X-ray arcs. Each profile was built by extracting counts using an azimuthally constrained annular region similar to that shown in Figure 1(b), but with a larger number of annuli.

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The profiles were extracted by matching angular annuli to the shape of the outer edge, then dividing the region interior to that edge into 20 segments identically shaped. Leaving aside the detector background, there are two source backgrounds to consider: the real cosmic background well-away from M51, and the diffuse background of NGC 5195. The counts in radial bins lying outside the outer edges of the arcs represent the galaxy background. The inner arc borders closely on the outer arc. Consequently the background radial bin of the inner arc is shorter to avoid overlap with the outer arc. Finally, the cosmic background was adopted as a large region WSW of NGC 5195 and sufficiently separated (∼2.5 arcmin) to avoid any contamination from point sources or diffuse emission from the galaxy.

The surface brightness profiles are similar in shape: relatively flat as a function of radius out to the outside edge, then dropping quickly to the level of the ISM. That behavior describes a shock. The large off-axis angle means the PSF is broad at this location (50% encircled energy width of the PSF ∼2–2.5 arcsec; Chandra Proposers Guide). Consequently, the arcs are blurred; to ascertain their shape more accurately will require an on-axis observation.

We extract spectra from the two arcs as well as the nucleus for the purpose of comparing their temperatures and absorption properties.

2.4.1. Overall Spectral Fitting

2.4.2. Nucleus Spectrum and Luminosity

2.4.3. X-Ray Arc Spectra and Luminosities

For the X-ray arc spectra, we adopted an absorbed, optically thin thermal gas model with variable abundances (vapec in XSPEC). We adopted a power-law component to fit any residual nuclear or un-removed X-ray binary emission in the arc spectra. We also adopted a fixed value for the index (1.6; Gilfanov 2004). The resulting fit yields an upper limit on the presence of a power-law component in both arcs. All of the fitted model parameters are listed in Table 3. Initial, fully unconstrained fits to the spectra showed repeated consistency for the arcs' temperatures, normalizations, and abundance values, but not for the column densities.

Table 3.  Spectral Model Fits: Nucleus and Arc Emission

Parameter	Nucleus	Inner Arc	Outer Arc
χ2/dof; dof	1.31; 490	1.56; 210	1.91; 228
kT (keV)	${0.61}_{-0.05}^{+0.06}$	${0.65}_{-0.04}^{+0.05}$	${0.38}_{-0.03}^{+0.06}$
NH (1022 cm−2)	${0.15}_{-0.05}^{+0.06}$	0.021fa	0.021fa
Norm (×10−6)	${34.5}_{-1.27}^{+1.47}$	${5.02}_{-0.53}^{+0.55}$	${7.97}_{-0.59}^{+0.64}$
Abundance-O (Z⊙)	1.0f	${3.0}_{-0.9}^{+1.2}$	${1.6}_{-0.5}^{+0.7}$
Abundance-Ne (Z⊙)	${3.61}_{-0.90}^{+1.08}$	${4.1}_{-1.0}^{+1.2}$	${3.7}_{-1.0}^{+1.5}$
Abundance-Mg (Z⊙)	1.0f	${1.9}_{-0.5}^{+0.7}$	${2.8}_{-0.9}^{+1.8}$
Powerlaw	${1.17}_{-0.38}^{+0.31}$	1.6f	1.6f
Norm (×10−7)	${6.71}_{-0.21}^{+0.25}$	<7.0	<5.0
Background (used with all components)
Index	${0.24}_{-0.25}^{+0.18}$	⋯	⋯
Index	${4.78}_{-0.98}^{+1.50}$	⋯	⋯
Norms (×10−7):
Power law	${2.64}_{-0.60}^{+0.52}$	⋯	⋯
Power law	${0.82}_{-0.52}^{+0.85}$	⋯	⋯
Gaussian-1: 0.567 keV	${1.56}_{-0.83}^{+0.77}$	⋯	⋯
Gaussian-2: 0.764 keV	${0.62}_{-0.29}^{+0.24}$	⋯	⋯
Gaussian-3: 1.767 keV	${0.43}_{-0.10}^{+0.11}$	⋯	⋯
Gaussian-4: 2.129 keV	${0.63}_{-0.15}^{+0.17}$	⋯	⋯
Measured Flux (×10−14, 0.5–2 keV)
Source	4.42 ± 0.40	3.06 ± 0.28	1.97 ± 0.17
Background	0.11	0.14	0.18
Luminosities (×1038)
Source (absorbed)	3.37	2.33	1.50
Source (unabsorbed)	3.37	2.52	1.62
Background	0.08	0.11	0.14

Note. The "f" on any parameter indicates it was fixed at the value listed. For the power-law index of the background, a fit determined the value, then it was fixed. The energy range used in the spectral fits was 0.4–2.4 keV. Error values represent the 90% contour.

^aFor the column density, see Section 2.4.3 for discussion.

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We initially fixed the column density at a value of 2.1 × 10²⁰ cm⁻², the Galactic column in the direction of NGC 5195 from Schlafly & Finkbeiner (2011). We did so because an unconstrained fit did not converge on a fixed value of the column. Once we reached a "best-fit" state, we also explored fits with the column densities of the arcs fixed between the Galactic column and the nuclear value. The temperatures, abundances, and model normalizations are consistent with any value between the known Galactic column and the fitted nuclear column (0.2–1.6 × 10²¹ cm⁻²). To undertake a proper fit for the column density will require either (i) additional X-ray data; (ii) an on-axis observation; or (iii) additional constraints (such as a measured value for the reddening, E_{B − V}).

The initial fits were also done for temperature and normalization with abundances fixed at solar (=1.0). Then, each abundance in turn was fit. Abundance values that were consistent with 1.0 were fixed at 1.0. Once the abundances were determined, a final fit was done with temperature, normalization, and any non-solar abundances as free parameters. Errors at the 90% level on each parameter were then determined.

We found the gas temperatures for the two arcs differ, with the outer arc cooler (${0.41}_{-0.03}^{+0.06}$ keV) than the inner arc (${0.65}_{-0.03}^{+0.04}$ keV) (Figure 3)—the outer arc has had a longer time to expand and to cool, as well as plowing into more material that enhances the cooling. The fitted model normalizations also support one's visual impression that the outer arc is fainter—they differ by a factor of ≈1.5 with the outer arc having a smaller normalization. The 0.5–2 keV luminosities calculated from the fitted models are L₃₈ ∼ 1.5 (outer) and L₃₈ ∼ 2.3 (inner) in 10³⁸ erg s⁻¹ units.

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The nucleus and both arcs exhibit Ne enhanced relative to a solar value. While the arc values are higher, within the errors, they are consistent with the nuclear value. However, both arcs also exhibit enhanced values for Mg of 2.5–3.5 times solar. Additionally, the inner arc has an enhanced value for oxygen of 3.3 (Table 3). That the arcs exhibit enhanced O and Mg abundances suggests the outflow has swept up material from prior phases of stellar mass loss. The enhanced Ne found in the nucleus and the arcs could indicate some nucleosynthetic processing occurred before the gas was expelled.

The X-ray observations are more easily interpreted if placed in context with the emission from other wavelengths. The position of the NGC 5195 nucleus is sufficiently well-determined, in spite of its near CCD-edge position, that it and the arc structures may be compared with images at other wavebands. The nuclear source corresponds within a few arcseconds to the positions of the nuclear source in the data sets from the Swift UVOT, DSS2 (blue), WISE6 μm, and VLA FIRST images (Figure 4).

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Most other wavelengths reveal little structure at the location of the arcs, particularly if the band is a continuum or has a wide wavelength coverage. Necessarily, that statement depends on the degree to which the images in other bands provide sufficient dynamic range in the area of the sky where the arcs are located (e.g., WISE6 μm image has insufficient resolution to discern; DSS2 is over-exposed in the same region).

However, three images are intriguing. First, the 6 cm VLA image (Figure 4) shows a broad arc SE of the nucleus of NGC 5195 at approximately the distance of the outer X-ray arc. The breadth of the radio arc is likely tied to the resolution of the configuration used (VLA configuration "D") for the observation. Second, the Swift UVOT image (Figure 4) exhibits a structure to the north of NGC 5195 at a distance from the nucleus comparable to the distance between the nucleus and the inner arc. The UVOT structure resembles a single broad arc, suggesting a possible symmetric expulsion of matter. That interpretation leaves a puzzle: why are there two X-ray-visible arcs to the south and a single UV-visible arc to the north?

The third interesting image is Hα (Hoopes et al. 2001; retrieved from the NASA Extragalactic Database; Figures 4, 5). A slender Hα arc and a second, less well-defined structure are visible near the regions of the X-ray arcs. The slender Hα arc lies outside the outer X-ray arc, implying "snow-plowed," or swept-up material by the expanding plasma driven by the AGN outflow. Based on a single spectrum obtained in 1998 with the spectrograph's slit lying approximately across the H_α arc (their "slit 4"), Hoopes & Walterbos (2003) conclude that the spectral behavior is indicative of an expanding structure or outflow, but that "the mechanism for such an outflow is unclear." The same authors also note that this region exhibits high [N ii]/Hα, [S ii]/Hα, and [O iii]/Hβ, with values higher than in the diffuse gas elsewhere in the galaxy. Those emission lines are indicative of shocked emission.

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The presence of the Hα emission plus the shock indicators support an interpretation of the X-ray arcs as resulting from shocks driving the Hα emission outward. Earlier, we raised the possibility that the arcs originate from collision-induced star formation. We interpret the shape of the Hα emission and its location immediately outside the outer X-ray arc as support for the outgoing blast wave interpretation, rather than in situ collision-induced star formation activity.

Furthermore, collision-induced star formation often occurs in tidal debris or along the bridges/tails linking the interacting pair (Machacek et al. 2009). The simulations to date either demonstrate a glancing collision with NGC 5195 passing by on a hyperbolic trajectory (Toomre & Toomre 1972), or that there have been multiple encounters with the two galaxies in high-eccentricity orbits (Salo & Laurikainen 2000). None of the simulations we have seen to date have been done with sufficient resolution to investigate detailed gas motions.

The outer Hα arc is ≈1660 pc in length (Table 2). Along the length of the arc, the width is ≈5'' or ≈200 pc. Measured velocities ranged from 500–600 km s⁻¹. This arc also exhibits what appear to be two or three small H ii regions, suggesting the outer arc has plowed sufficient material to trigger star formation.

The data at present are limited, so many of the estimates must be order-of-magnitude. There are also a number of quantities that cross-feed into the estimates. As we want to avoid creating confusion in the reader's mind, the overall path is as follows: determine the mass of the SMBH, then L_Edd, then an age estimate for the outbursts from the velocities, followed by a density estimate, which leads to the mass of the arcs, followed by an estimate of the cooling time of the arcs.

From the velocity dispersion σ of 124.8 km s⁻¹ for NGC 5195 (Ho et al. 2009), the ${M}_{{\rm{BH}}}\mbox{--}\sigma$ relation yields M_BH ∼ 3.8 × 10⁷ M_⊙ (M₇ = 3.8), assuming σ^α = σ^4.4 (Ferrarese & Merritt 2000; Gebhardt et al. 2000). The Eddington luminosity for NGC 5195 is

$$\begin{eqnarray*}&&{L}_{{\rm{Edd}}}=4\pi {GcM}/\kappa \approx 1.3\times {10}^{45}({M}_{{\rm{BH}}}/{10}^{7}\;{M}_{\odot })\end{eqnarray*}$$

where κ = electron scattering opacity; with values inserted for NGC 5195, we have L_Edd = 4.9 × 10⁴⁵ erg s⁻¹ compared to the observed 0.5–2 keV luminosity of ∼5 × 10³⁸ erg s⁻¹ (Section 2.4.2). To reiterate, that value means the NGC 5195 SMBH is in a radiatively inefficient state of L_obs = f L_Edd with f ∼ 10⁻⁷.

A measure of the velocities of the arcs could lead to their estimated age. Unfortunately, the velocities of the arcs and their surroundings likely have not been measured. The velocity measured from the Hoopes et al. (2001) Hα spectrum, ∼500–600 km s⁻¹, was obtained from a long-slit spectrograph and represents an average over a range of velocities (Section 2.5). The velocity of NGC 5195 itself is ∼470 km s⁻¹ (NED). With uncertainties included, these two values are comparable. Further, if the gas is confined to the interaction plane, then any measured velocity is a projection into our line of sight. Absent a good measure of the projection angle, measured velocities have a wide range.

Can limits on the velocity of the arcs be set or inferred? Hoopes et al. (2001) measured line ratios from optical spectra from which they inferred that the ratios are consistent with a shock velocity of "several hundred kilometers per second." Additionally, a lower limit on the arcs' motion is set by considering the time from the interaction of NGC 5195 and NGC 5194 based on models: ∼50–100 Myr (Salo & Laurikainen 2000). Given the present positions of the arcs, this leads to velocities of ∼8–15 (inner) and ∼17–35 (outer) km s⁻¹. However, velocities this low would not generate shock emission consistent with the Hoopes et al. (2001) values.

If we instead assume that "several hundred" translates to ≈300 km s⁻¹, then the arcs require ∼2.5 × 10⁶ (inner) and ∼5.6 × 10⁶ (outer) years to reach their current positions and the episodes are separated by ≈3 × 10⁶ years. Adopting the definition of terminal velocity from King (2010; Equation (37) in that paper), and assuming this value is the velocity of the arcs, then with σ₂₀₀ = 0.624, the terminal speed is ${v}_{e}\sim 875{\sigma }_{200}^{2/3}$ km s⁻¹ ≈ 620 km s⁻¹. (We note that the ≈300–600 km s⁻¹ range fits within the simulations of Salo & Laurikainen 2000.) This value leads to dynamical ages of ∼1.2 × 10⁶ (inner) and ∼2.7 × 10⁶ (outer) years. The episodes are then separated by ≈1.5 × 10⁶ years. Consequently, if we assume the interaction actually occurred ≈50 MYr ago, then the observed feedback took some time to develop, with the arcs emerging over the past ≈10^6–7 years.

One significant question then arises: what was the material doing for ≈40 MYr, the time between the interaction of NGC 5195 with NGC 5194 and the outbursts? The answer could be "infalling": if we assume material started from rest and was located ≈1500 pc distant (approximately the current separation of the arm of NGC 5194 from the nucleus of NGC 5195), then ≈65 MYr must elapse before the gas reaches the nucleus. With an arbitrary initial speed of 100 km s⁻¹, that time would be reduced to ≈15 MYr. Absent additional constraints, this estimate may be the best we can do.

We now move to estimating gas densities with the goal of calculating masses and cooling times for the arcs to compare with the dynamical age estimate. The H_α (Figure 5) arc provides one route to the matter density. The flux in the line emission, integrated over a rectangular region matching the H_α arc, and again adopting a thickness = 100 thick₁₀₀ pc, leads to a volume V of 1.3 thick₁₀₀ × 10⁶³ cm³. Assuming the Lyman H lines are optically thick ("Case B" recombination) then L = nΛV and adopting an emissivity Λ of 2.59 ×  10⁻¹³ cm³ s⁻¹ (Osterbrock & Ferland 2005, Table 2.1), leads to a number density of ∼5/thick₁₀₀ cm⁻³ or a mass estimate of ≈4 × 10⁶ M_⊙. That value is mid-range for typical interstellar molecular clouds (Murray 2011).

A second estimate of the number density in the X-ray arcs follows from the X-ray vapec model normalization:

$$\begin{eqnarray*}&&\mathrm{normalization}=\displaystyle \frac{{10}^{-14}}{(4\pi {({D}_{A}(1+z))}^{2}}\;\int \;{n}_{e}\;{n}_{p}\;{dV}\end{eqnarray*}$$

(Arnaud 1996). Assuming n_e = n_p, z = 0.002, D_A =8 d₈ Mpc, and using the volume V as defined in the prior paragraph, then ${n}_{e}\approx 0.06(0.09){\mathrm{thick}}_{100}^{-1}$ cm⁻³ for the outer (inner) arc. The mass in each of the X-ray-emitting arcs is then ≈5.5 × 10⁴ M_⊙ (5.7 (outer) and 5.3 (inner)) or about 1% of the Hα arc.

Given the mass disparity, can the X-ray arcs be pushing the Hα arc? Assuming the gas in the X-ray and the Hα arcs may be described by the ideal gas law, then the pressures for the Hα, outer, and inner X-ray arcs are 3.5 × 10⁻¹², 1.9 × 10⁻¹¹, and 4.3 × 10⁻¹¹ dyn cm⁻², respectively. The X-ray arcs then have about a factor of 5–12 times higher pressure than the Hα arc, driving material outwards. The total kinetic energy of the X-ray arcs is ≈2 × 10⁵³ erg.

A second check on our mass estimates is possible. If the outer arc swept clear the gas in the halo along that vector, then the mass in the second arc is an approximate measure of the rate of accumulation. We acknowledge that the second arc is not moving through precisely the same space, but the question remains: is it possible to sweep up the observed mass? Above, we estimated the mass in the second arc as ≈5.3 × 10⁴ M_⊙ and the interval between episodes as ≈1.3 × 10⁶ years. Those values lead to an accumulation rate of ≈4 × 10⁻² M_⊙ yr⁻¹. Magorrian et al. (1998) developed a bulge mass-SMBH mass relation with updates by McConnell & Ma (2013) and Belfiori et al. (2012) and environmental dependencies explored by McGee (2013). The value of σ₁₀₀ and the SMBH mass yield an estimated bulge mass/SMBH mass ratio of ≈1000, or a bulge mass of ≈(2–4) × 10¹⁰ M_⊙.⁵ If we assume most of that mass is composed of ≤1 M_⊙ stars given the color of NGC 5195, then some of those stars will have evolved off the main sequence to at least the asymptotic giant branch (AGB). AGB stars have typical mass loss rates of ≈10⁻⁸ M_⊙ yr⁻¹ (De Beck et al. 2010). If just 0.1% are AGB stars, then the mass available per year is ≈10⁻¹ M_⊙, more than sufficient to provide the swept-up mass observed. As a by-product, we would expect sector-to-sector differences in gas density and metals in these regions, a potential test of the overall interpretation described in this paper.

With densities in hand, we can estimate the cooling time for comparison with the dynamical time. We use Figure 1 of Gehrels & Williams (1993) which displays, for an optically thin gas with solar abundances, the cooling curve as a function of temperature for several processes (two-photon, recombination, bremsstrahlung, and line emission). For the measured temperatures of the arcs of ∼0.4 and 0.65 keV, line emission dominates the cooling (the next largest contributor, bremsstrahlung emission, contributes ≤10%). The cooling time is defined as

$$\begin{eqnarray*}&&{t}_{\mathrm{cool}}=(3/2){kT}/({n}_{e}{\rm{\Lambda }}(T))\end{eqnarray*}$$

where Λ(T) is the cooling function. With values inserted, we obtain an estimated cooling time of ≈1–1.6 × 10⁷ years for the X-ray arcs. This estimated cooling time is about an order-of-magnitude larger than the dynamical time. We then expect X-ray spectra should be dominated by line emission, a prediction that could be checked using Hitomi (Takahashi et al. 2014).

To summarize, we can place a crude limit on the age of the arcs (∼1–3 × 10⁶ years) that is an order-of-magnitude lower than the cooling time for the arcs based on crude estimates of their velocities. Estimated densities (≈0.1–5 cm⁻³) lead to the masses of the arcs, which combined with the arcs' velocities (adopted as ∼600 km s⁻¹), carry sufficient momentum to sweep up the Hα arc. The estimated densities are supported by an estimate of the normal stellar mass loss within the galaxy's nuclear volume over the lifetime of the arcs.

3.2.1. Transition Radius from Momentum- to Energy-driven Flow?

With regard to AGN feedback, we can estimate the radius of transition from momentum- to energy-driven flow (KP2015):

$$\begin{eqnarray*}&&{R}_{{\rm{crit}}}\sim 500\;{M}_{8}^{1/2}\;{\sigma }_{200}\;{\rm{pc}}.\end{eqnarray*}$$

Assuming their approach is valid for NGC 5195, the critical radius is ≈230 pc or ≈58 at the adopted distance of M51. For comparison, the sphere of influence for the SMBH is

$$\begin{eqnarray*}&&{R}_{{\rm{inf}}}\sim \displaystyle \frac{3{M}_{7}}{{\sigma }_{100}^{2}}\sim 9\;{\rm{pc}}\approx 0\buildrel{\prime\prime}\over{.} 2.\end{eqnarray*}$$

The X-ray arcs both lie outside of this critical radius and, within the context of KP2015, both arcs would fall into the energy-driven regime. R_crit could easily be constrained with current-generation telescopes provided the extreme luminosity contrast of the nucleus versus its surroundings is overcome.

3.2.2. Another Burst?

3.2.3. Star Formation?

3.2.4. Azimuthally Limited Arcs?

3.2.5. Similar Objects?