The Infall of the Virgo Elliptical Galaxy M60 toward M87 and the Gaseous Structures Produced by Kelvin–Helmholtz Instabilities

To study the leading edge, we construct circular surface brightness profiles from the background-subtracted, exposure-corrected, coadded 0.5–2 keV image, using logarithmic radial steps. The profiles are each centered on the X-ray peak of M60 ($\alpha ={12}^{{\rm{h}}}{43}^{{\rm{m}}}39\buildrel{\rm{s}}\over{.} 9,\delta =11^\circ {33}^{{\prime} }10\buildrel{\prime\prime}\over{.} 0$) and confined to sectors to the north and west that avoid the wings and exclude the interacting spiral galaxy NGC 4647. We similarly construct the circular surface brightness profile in the eastern (downstream) direction to search for a diffuse, faint tail. These sectors are defined in Table 2 and are shown in Figure 2.

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Our results are shown in Figure 3. Note that the profiles in the N and W sectors are the same in the radial range of overlap. This suggests that they are part of the same leading edge caused by ram pressure, only interrupted in the excluded region by the impending merger of NGC 4647. Due to our Chandra coverage we can study the morphology of the surface brightness profile to larger radii to the north (profile N) than to the west (profile W). We thus confine our analysis to the profile of the N sector of the leading edge, shown in Figure 3, to measure gas properties to larger radii and probe farther from the galaxy into the surrounding Virgo ICM. We see three distinct regions, the characteristic edge profile for galaxy gas for $r\lt 149^{\prime\prime}$ (12 kpc), a very slowly varying, nearly flat surface brightness profile for $r\gt 268^{\prime\prime}$ (22 kpc), and a steeply falling region of excess emission in between. At the 0.97 Mpc distance of M60 from M87, taken to be the center of the Virgo cluster, emission from undisturbed Virgo cluster gas would appear to be flat over the ∼50 kpc scale measured by the profile, consistent with the profile behavior at $r\gt 22\,\mathrm{kpc}$. We take this to be representative of the "free stream region" from Vikhlinin et al. (2001). We suggest the sharply falling surface brightness profile at $12\lt r\lt 22\,\mathrm{kpc}$ may be Virgo gas gravitationally attracted to M60's deep gravitational potential at close radii, i.e., the pile-up region (Vikhlinin et al. 2001). These regions are also shown in Figure 2.

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Vikhlinin et al. (2001) showed that the edge of a cool dense gas cloud moving through surrounding hot gas can be seen in radial X-ray surface brightness profiles as a discontinuity ("edge"), and that the relative velocity of the gas cloud and its surrounding ICM can be determined by the ratio of thermal gas pressures between gas at the stagnation point and cluster gas in the free stream region. If the dense M60 gas were at rest relative to the ICM, the thermal pressures would be equal on both sides of the edge. However, for M60 infalling through the Virgo ICM, where it is subjected to both ram and thermal pressures, this equality is only true at the stagnation point where the relative gas velocity is zero. Following Vikhlinin et al. (2001), we use the gas pressure just inside the edge as a proxy for the pressure at the stagnation point. We then use the pressure ratio between gas at the stagnation point and in the free stream region to derive the relative velocity between M60 and the Virgo ICM, as detailed in Section 3.4.

To calculate pressures, characterize the nature of the edge, and, in the case of ram-pressure-stripping, calculate the velocity of the galaxy, the relative temperatures and electron densities must be obtained for the gas on both sides of the edge.

As in Machacek et al. (2006), we assume spherically symmetric electron power-law density models inside and outside the edge ($r={r}_{e}$)

$$\begin{eqnarray}{n}_{i}(r\lt {r}_{e}) & = & {J}_{d}{n}_{0}{\left(\tfrac{r}{{r}_{e}}\right)}^{-{\alpha }_{i}}\\ {n}_{o}(r\gt {r}_{e}) & = & {n}_{0}{\left(\tfrac{r}{{r}_{e}}\right)}^{-{\alpha }_{o}},\end{eqnarray} \tag{ 1 }$$

with normalization n₀, inner and outer power-law indices ${\alpha }_{i}$ and ${\alpha }_{o}$, respectively, and a discontinuous density "jump" ${J}_{d}={n}_{i}({r}_{e})/{n}_{o}({r}_{e})$ across the edge. We then determine the density by integrating the X-ray emissivity along the line of sight to fit the surface brightness profile, using a multi-variate ${\chi }^{2}$-minimization scheme with the position of the edge (r_e), the density power-law indices ${\alpha }_{i}$ and ${\alpha }_{o}$, and the square root of the surface brightness discontinuity $\sqrt{{J}_{\mathrm{sb}}}\propto {J}_{d}$ across the edge allowed to vary. The measured surface brightness discontinuity J_sb is related to the density jump J_d at the edge through the ratio of X-ray emissivities

$$\begin{eqnarray}&&{J}_{\mathrm{sb}}=\displaystyle \frac{{{\rm{\Lambda }}}_{i}}{{{\rm{\Lambda }}}_{o}}{({J}_{d})}^{2},\end{eqnarray} \tag{ 2 }$$

where ${{\rm{\Lambda }}}_{i}$(${{\rm{\Lambda }}}_{o}$) are the cooling functions for gas inside (outside) the edge, respectively.

At a projected distance of ∼1 Mpc from M87, we expect the X-ray surface brightness of the Virgo ICM to be slowly varying over the angular scales probed by our merged observations. Thus, we extrapolate the flat Virgo surface brightness at $r\gt 22\,\mathrm{kpc}$ to the observed edge and fit the resulting profile to determine the gas density ratio between galaxy gas inside the edge and undisturbed Virgo gas (the free stream region) outside the edge. Our results are shown in Figure 4 and listed in Table 3. We find an edge position at 12.4 ± 0.1 kpc and $\sqrt{{J}_{s}}={10.5}_{-1.1}^{+1.7}$.

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Table 3.  X-Ray Surface Brightness Profile Model

re	${\alpha }_{i}$	${\alpha }_{o}$	$\sqrt{{J}_{\mathrm{sb}}}$
(kpc)
12.4 ± 0.1	$-{1.29}_{-0.08}^{+0.07}$	$-{0.38}_{-0.05}^{+0.09}$	${10.5}_{-1.1}^{+1.7}$

Note. The density model extrapolates the slowly varying Virgo ICM over the pile-up region to the edge. Columns are edge location r_e, power-law indices ${\alpha }_{i}$(${\alpha }_{o}$) inside and outside the edge, and the square root of the surface brightness jump. The density model extrapolates the slowly varying Virgo ICM over the pile-up region to the edge.

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For massive galaxy clusters where ICM gas temperatures are high, the cooling functions in Equation (2) are largely independent of gas abundances and only a weak function of the temperature such that ${{\rm{\Lambda }}}_{i}/{{\rm{\Lambda }}}_{o}\sim 1$ and $\sqrt{(}{J}_{\mathrm{sb}})\sim ({J}_{d})$. The density jump can be inferred from the surface brightness profile fits alone. However, for gas at lower temperatures (≤1–2 kev), X-ray-cooling is line-dominated and the cooling function is strongly dependent on gas metallicity. If these abundances are different, which is likely the case for galaxy gas and ICM gas in the outskirts of a galaxy cluster, the ratio of cooling functions in Equation (2) may deviate significantly from 1 and must be determined from spectral modeling before we can infer the gas density ratio of interest and complete the calculation of the infall velocity for M60. (see, e.g., Machacek et al. 2005).

To determine the mean spectral properties of the gas in M60, we use CIAO tool specextract to extract a mean spectrum in a 200'' circular region centered on the observed X-ray peak. We also extract spectra for the regions N1, N2, and N3 along the northern profile shown in Figure 2 to characterize the Virgo emission (N3) at the position of M60 and to complete the cold front analysis across the leading surface brightness edge (see Figure 4). Point sources above a detection threshold of $\sim 2\times {10}^{37}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ (see Appendix), as well as emission from the interacting companion galaxy NGC 4647, are excluded from the data. The resulting spectra are modeled using XSpec 12.9.0. (See Arnaud 1996.)

3.3.1. Mean X-Ray Spectral Properties of M60

We first consider the average spectral properties of M60 as a whole, using the blank-sky background files as in Section 3.1 for backgrounds. This will allow us to determine the mean abundance and temperature of gas within M60. ACIS readout effects redistribute 1.3% of the source counts along the readout direction. Since most of these photons are from the bright core, which is included in our mean spectrum, and inspection of the readout map shows that only 0.3% of the total source counts are redistributed outside the 200'' circular spectral region, readout will not significantly affect the mean spectral fit. We use an absorbed VAPEC model that assumes X-ray emission from collisionally ionized diffuse gas with emission rates calculated from the most current atomic transition data tabulated in AtomDB.⁴ We fix the hydrogen column density at the Galactic value (${N}_{{\rm{H}}}=2.1\times {10}^{20}\,{\mathrm{cm}}^{-2}$). For more information on the VAPEC model, please see XSpec: An X-ray Spectral Fitting Package User's Guide by Arnaud, Gordon, and Dorman.⁵

The gas temperature and abundances for Fe, Mg, Si, and O were allowed to vary. All other abundances were fixed at solar. We find a mean temperature ${kT}=0.906\pm 0.004\,\mathrm{keV}$ and Anders & Grevesse—abundances (Anders & Grevesse 1989) for Fe, O, Mg, and Si of $0.46\pm 0.2\,{Z}_{\odot }$, $0.16\pm 0.04\,{Z}_{\odot }$, ${0.93}_{-0.06}^{+0.05}\,{Z}_{\odot }$, and $0.91\pm 0.05\,{Z}_{\odot }$, respectively, for ${\chi }^{2}/(\mathrm{dof})\,=1989/1516$. The total intrinsic fluxes and luminosities for M60 for the assumed 17.2 Mpc distance are listed in Table 4.

Table 4.  M60 Intrinsic X-Ray Fluxes and Luminosities

Band	Range	Flux	Luminosity
	(keV)	$({10}^{-12}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$)	(1040 $\mathrm{erg}\,{{\rm{s}}}^{-1}$)
Soft	0.5–2.0	3.27	11.56
Hard	2.0–7.0	0.27	0.96
Full	0.5–7.0	3.54	12.53

Note. Flux and luminosities from the best absorbed VApec model fit to the mean spectrum of M60 using a 200'' radius circular region centered on M60's X-ray peak.

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Although a thermal plasma VAPEC model provides an excellent fit to the data, Chandra data measure the X-ray emission from all sources in M60 and along the line of sight. This includes X-ray emission from any unresolved point sources, such as cataclysmic variables (CVs), accreting white dwarfs (ABs), and low-mass X-ray binaries (LMXBs), and Virgo ICM emission along the line of sight, as well as diffuse galaxy gas. We model the relative contribution of each of these unresolved stellar X-ray sources in the Appendix to determine whether these sources significantly affect our spectral measurements of the flux, temperature, and metallicity of M60's diffuse gas. We find that CVs and ABs contribute only 1.5% and LMXB's 2% of M60's total 0.5–2 keV flux. Thus, M60 is still gas-dominated. If these stellar components are included in our spectral model, our results for the temperature and abundance of the diffuse galaxy gas are unchanged. Furthermore, if we allow the normalization of the power-law model for unresolved LMXBs to be a free parameter, the measured 0.5–2 keV flux of unresolved LMXBs in this region is consistent with our predicted value.

3.3.2. Virgo ICM

The final component to model in fitting the spectra is the contribution from the cluster emission. Virgo is a young, dynamically active cluster. Urban et al. (2011) found from XMM-Newton observations that beyond 500 kpc from M87, the X-ray surface brightness of the Virgo ICM is highly variable, varying by as much as a factor 2 at 0.9 Mpc, the projected distance of M60 from M87. Using Suzaku, Simonescu et al. (private communication) further showed that the flux and temperature of Virgo gas at large radius depends strongly on the azimuthal direction of the observation, with higher fluxes and temperatures found along directions that coincide with higher density filaments. We thus choose to measure the spectral properties of the Virgo gas using our combined Chandra data in region N3 (see Figure 2), where the northern surface brightness profile shown in Figure 3 flattens, rather than adopt a model from the literature. We model the spectrum of the Virgo ICM in region N3 using an absorbed thermal plasma APEC model with fixed Galactic hydrogen absorption and $0.1\,{Z}_{\odot }$ abundance (Urban et al. 2011). We find a best-fit temperature, model normalization, and intrinsic 0.5–2 keV flux of ${1.37}_{-0.19}^{+0.35}\,\mathrm{keV}$, $1.75\times {10}^{-5}$ cm⁻⁵, and $8.9\times {10}^{-15}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$ (see Table 5). X-ray emission in the cluster outskirts is faint, contributing only 0.3% of the 0.5–2 keV flux in the 200'' circular region encompassing M60. From the VAPEC model normalization we find a mean electron density for this region of $3\times {10}^{-5}\,{\mathrm{cm}}^{-3}$ with ∼30% uncertainties, yielding a thermal gas pressure of $\sim 1.35\times {10}^{-13}\,\mathrm{erg}\,{\mathrm{cm}}^{-3}$. These results are consistent with Urban et al. (2011), given the measured variability observed at these large radii. Since we directly measure the thermal properties of the Virgo cluster gas, i.e., gas density, temperature, and thermal gas pressure, from the spectral fitting of the X-ray emission of the gas, any evolutionary effects of the ambient cluster magnetic field on determining those thermal properties have implicitly been accounted for in that measurement. Ambient magnetic fields could also contribute an additional non-thermal component to the total pressure in the Virgo Cluster. However, using the simulated magnetic field profile for the Virgo Cluster from Pfrommer & Dursi (2010), the expected non-thermal pressure due to ambient magnetic fields is at most ∼1% of the thermal pressure at these radii and likely could be much less. Thus it does not significantly affect our analysis.

Table 5.  Northern Edge Spectral Models

Region	kT	Norm	Flux	Λ	${\chi }^{2}/(\mathrm{dof})$
	(keV)	(10−5 cm−5)	(10−14 $\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$)	(10−23 erg cm3 s−1)
N1	1.00 ± 0.02	2.34	3.19	1.36	112/127
N2	${1.6}_{-0.3}^{+0.5}$	1.82	0.93	0.51	186/154
N3	${1.37}_{-0.19}^{+0.35}$	1.75	0.89	0.51	293/243

Note. Spectra were modeled using an absorbed Apec model with Galactic absorption and abundance fixed at $0.5\,{Z}_{\odot }$ for M60 galaxy gas (N1) and at $0.1\,{Z}_{\odot }$ for regions N2 and N3 consistent with Virgo Cluster gas.

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3.3.3. Spectral Fitting across the Edge

To determine the infall velocity of M60 into the Virgo galaxy cluster, we need to measure the temperatures and densities of gas on either side of the edge. We chose the northern profile sector for our analysis because detector coverage allows us to measure gas properties out to greater distances consistent with undisturbed Virgo gas (N3). Additionally the northern sector lies perpendicular to the readout direction, and the inner radius of region N1, the region just inside the edge, lies outside the bright core region, where readout would be greatest, minimizing the contribution of these out-of-time events in these regions. Thus, readout in the spectral analysis of the northern regions (N1, N2, N3) may be neglected. We also note that a comparison of X-ray and kinematical mass measurements for M60 shows that magnetic fields do not contribute significantly to the pressure inside the edge in region N1 ($6.2\lt r\lt 12.4\,\mathrm{kpc}$) (Paggi et al. 2014).

We model the inner two northern regions (N1 and N2), similar to that of N3 in Section 3.3.2, with an absorbed APEC model with fixed Galactic hydrogen absorption and abundances at $0.5\,{Z}_{\odot }$ for region N1 in M60, consistent with our measured mean Fe abundance for M60 galaxy gas, and at the Virgo value ($0.1\,{Z}_{\odot }$) for gas in the pile-up region N2. Our results are given in Table 5.

Since both galaxy and Virgo gas have temperatures of ∼1 keV, the cooling function ${\rm{\Lambda }}(A,T)$ and thus emissivity ${\rm{\Lambda }}{n}_{e}{n}_{p}$ for each depend sensitively on the metal abundance A of the gas. We determine the cooling functions for each of the northern spectral regions (N1, N2, N3) using

$$\begin{eqnarray}&&{\rm{\Lambda }}=\displaystyle \frac{{10}^{-14}{{FD}}_{L}^{2}}{{N}_{\mathrm{APEC}}{[{D}_{A}(1+z)]}^{2}},\end{eqnarray} \tag{ 3 }$$

where F is the unabsorbed model flux in the 0.5–2 keV energy band, to match that of the surface brightness profile, ${N}_{\mathrm{APEC}}$ is the APEC model normalization, z is the redshift, ${D}_{L}({D}_{A})$ are the luminosity (angular size) distances, respectively, and ${D}_{L}^{2}\sim {[{D}_{A}(1+z)]}^{2}$ for $z\ll 1$. Values for ${N}_{\mathrm{APEC}}$, F, and Λ are also given in Table 5.

Using the fitted surface brightness jumps $\sqrt{(}{J}_{\mathrm{sb}})$ from Table 3 and the cooling functions given in Table 5 in Equation (2), we calculate the density ratio between galaxy gas inside the edge and free streaming Virgo gas and multiply these by the respective temperature ratios from the spectral fits to obtain the pressure ratio between the stagnation point and the Virgo free stream region. Uncertainties in derived ratios are estimated using the extreme values of the 90% CL uncertainties for measured properties. Our results are listed in Table 6.

Table 6.  M60 Velocity Analysis

${T}_{i}/{T}_{o}$	${{\rm{\Lambda }}}_{i}/{{\rm{\Lambda }}}_{o}$	${n}_{i}/{n}_{o}$	${p}_{i}/{p}_{o}$	${M}_{a}$	v	vt	ξ
					($\mathrm{km}\,{{\rm{s}}}^{-1}$)	($\mathrm{km}\,{{\rm{s}}}^{-1}$)	(deg)
${0.73}_{-0.17}^{+0.13}$	2.66	${6.44}_{-0.67}^{+1.04}$	${4.7}_{-1.4}^{+1.7}$	1.7 ± 0.3	1030 ± 180	${1012}_{-192}^{+183}$	11 ± 3

Note. Velocities assume a sound speed of 604 $\mathrm{km}\,{{\rm{s}}}^{-1}$ for 1.37 keV Virgo gas and M60 radial velocity ${v}_{r}=-190\pm 15\,\mathrm{km}\,{{\rm{s}}}^{-1}$. Uncertainties for derived values assume extremes in the 90% CL uncertainties for measured properties.

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The Mach number ${M}_{a}=v/{c}_{s}$ (where c_s is the speed of sound in the cluster free stream region) for the cold gas cloud moving through the hot ICM is determined from the ratio of pressures (see Equations (4) and (5)).

$$\begin{eqnarray}&&\displaystyle \frac{{p}_{i}}{{p}_{o}}={\left(1+\displaystyle \frac{\gamma -1}{2}{M}_{a}^{2}\right)}^{\tfrac{\gamma }{\gamma -1}},{M}_{a}\leqslant 1\end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray}&&\displaystyle \frac{{p}_{i}}{{p}_{o}}={\left(\displaystyle \frac{\gamma +1}{2}\right)}^{\tfrac{\gamma +1}{\gamma -1}}{M}_{a}^{2}{\left(\gamma -\displaystyle \frac{\gamma -1}{2{M}_{a}^{2}}\right)}^{\tfrac{-1}{\gamma -1}},{M}_{a}\geqslant 1,\end{eqnarray} \tag{ 5 }$$

where $\gamma =5/3$ is the adiabatic index of the monatomic gas.

From the pressure ratios given in Table 6 and Equations (4) and (5), we find M60 moving at Mach 1.7 ± 0.3 relative to the Virgo ICM. The sound speed in completely ionized 1.37 keV Virgo gas in the free stream region is c_s = 604 $\mathrm{km}\,{{\rm{s}}}^{-1}$, such that we find that the speed $v={M}_{a}{c}_{s}$ of M60 relative to the Virgo ICM is 1030 ± 180 $\mathrm{km}\,{{\rm{s}}}^{-1}$.

The physical separation of M60 and M87 is 971 kpc, confirmed with the distance moduli measurements in both Tonry et al. (2001) and Mei et al. (2007). The radial velocity difference between M60 and M87 is ${\rm{\Delta }}{v}_{\mathrm{rad}}=-190\,\pm 15\,\mathrm{km}\,{{\rm{s}}}^{-1}$ (Trager et al. 2000). Taking the Virgo cluster ICM to be at rest relative to M87, we determine the relative transverse component of M60's velocity as ${v}_{t}\,={1012}_{-192}^{+183}\,\mathrm{km}\,{{\rm{s}}}^{-1}$. The components of M60's motion through the Virgo ICM imply an inclination angle with respect to the plane of the sky of $\xi =11\pm 3$ degrees. Nearly all of M60's motion is therefore in the plane of the sky, consistent with the sharp surface brightness edge observed. We estimate the time t_pp for pericenter passage assuming a constant infall velocity and direct projected path toward M87, such that ${t}_{{pp}}\sim 0.971\,\mathrm{Mpc}/{v}_{t}=0.95\,\mathrm{Gyr}$. If the motion of M60 in the plane of the sky is directly toward M87, this will be an upper bound on the infall time.

MHD simulations suggest that magnetic fields may wrap around a galaxy during infall, forming a thin draping layer. In this layer ambient cluster magnetic fields may become amplified to a maximum value such that their magnetic pressure equals the ram pressure of the ICM on the galaxy (Lyutikov 2006; Pfrommer & Dursi 2010). Recent simulations also suggest these fields may become tangled and not suppress ram-pressure-stripping (Ruszkowski et al. 2014). For M60 infalling at 1030 $\mathrm{km}\,{{\rm{s}}}^{-1}$ through Virgo gas of electron density $3\times {10}^{-5}\,{\mathrm{cm}}^{-3}$, this would imply a possible maximum magnetic field of $\sim 3.9\,\mu {\rm{G}}$ within a 15 (120 pc) thick draping layer outside the edge. Unfortunately, our combined observations of M60 are not deep enough to constrain the properties of any such layer. (See, e.g., Su et al. 2017, for an analysis of NGC 1404, a similar galaxy, but with a Chandra exposure a factor of 2.6 longer than the one presented here.)

The motion of M60 through the Virgo ICM causes the gas on the northwest side to be stripped and pushed behind the galaxy in the wake of its passage through Virgo, forming the observed "wings" and sharp northwest edge. The coadded images show there are a pair of wings in both the northeast and south directions. These wings align with the direction of the outburst of the AGN at the core of M60 (Paggi et al. 2014).

The double wing structure is shown more clearly by binning to 8 × 8 pixels (4'' × 4'' bins) in Figure 5. The filamentary wings are thin and long, extending at least 150'' in both directions and as wide as the galaxy atmosphere radius (150'' span across each double wing structure). The northeastern wings are of approximately equal length (150'') and separated by a cavity 28'' wide. The wings to the south are less symmetric, with the front wing being shorter than the downstream wing by a factor of 2.

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The dimensions of these filamentary wings were compared with simulations by Roediger et al. (2015a, 2015b) of the Virgo galaxy M89 (NGC4552). The lower panel of Figure 5 shows a soft band X-ray projection of M89 that demonstrates how turbulent stripping can create wings of diffuse gas to the sides of the galaxy, as we observe for M60. The size of the wings scales with the size of the gas atmosphere, hence larger wings are seen in M60, compared to the simulations of the Virgo elliptical M89, since most of M89's gas has already been stripped.

The double wing structure is seen in the simulation image (Figure 5 lower panel). The wings are attached directly to the sides of the galaxy, as is the case for M60, another indicator of motion nearly in the plane of the sky. This can also be explained by the inclination angle; the simulations assume motion purely in the plane of the sky, while M60 has an inclination of 11 ± 3 degrees as shown in Section 3.4. For M89 these features are attached to the upstream edge rather than to the sides (Machacek et al. 2006). Thus, the simulation better represents M60 in this instance.

Two processes can disturb the sharp edge of a cold front; Rayleigh–Taylor instabilities and KHI (Roediger et al. 2012). The Rayleigh–Taylor instability occurs when two fluids of different densities are accelerated into each other. The galaxy gas is accelerating into the ICM, but the Rayleigh–Taylor instability is suppressed by M60's gravity, so the effective acceleration points in the opposite direction.

KHI instabilities, formed at the surface of the cold front edge where velocity shears may produce turbulent motions, are likely the cause of the filamentary wings seen in Figures 1 and 5, perhaps aided by previous AGN outbursts that may have lifted the galaxy gas upward in M60's gravitational potential making it easier to strip.

The simulations predict some faint emission behind the wings downstream leading to a diffuse tail trailing the galaxy. There is a faint excess of emission seen for $r\gt 10\,\mathrm{kpc}$ in the eastern surface brightness profile (Figure 3) over that observed in the northern or western profiles, suggestive of such a tail.

The simulations of M89 predict a downstream edge marking the boundary between the galaxy atmosphere and diffuse tail. We performed our edge analysis as outlined in Section 3.2, on the eastern profile of M60 to look for this downstream edge (See Figures 2 and 3 and Table 2).

Using the power-law model from Equation (1), the eastern profile is well fit with upstream and downstream power-law slopes of ${\alpha }_{i}={1.42}_{-0.04}^{+0.03}$ and ${\alpha }_{o}={1.86}_{-0.32}^{+0.38}$, respectively. We find a small jump $\sqrt{(}{J}_{\mathrm{sb}})={1.43}_{-0.17}^{+0.23}$ at $r={12.9}_{-0.5}^{+0.4}$ kpc downstream from the center of M60. Since we expect from simulations that the near tail is composed of galaxy gas displaced but not yet completely stripped from M60 (Roediger et al. 2015a), the abundances across the eastern edge should be the same. Thus, $\sqrt{(}{J}_{\mathrm{sb}})={J}_{d}$, the ratio of the gas density across the eastern downstream edge. Figure 6 shows the extracted surface brightness profiles for both the upstream (northern cold front) and downstream (eastern tail) edges. The simulations generally find the downstream edge at a larger radius than the upstream edge, even more so than is observed for M60.

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The surface brightness profiles are symmetric in both radial directions until each respective edge. In the simulations of M89, the upstream edge of the cold front and wings look sharper than the downstream edge, consistent with what we see in Figure 6.

There are several factors that could keep the tail of M60 faint. A steep initial gas density profile for M60 would mean there was less gas to strip at larger radii and the stripped gas may mix quickly with the surrounding ICM. The large distance of M60 from M87 (971 kpc) and the galaxy velocity of ${v}_{{\rm{M}}60}=1030\pm 180\,\mathrm{km}\,{{\rm{s}}}^{-1}$ suggest multiple possibilities. First, we could be witnessing the very early stages of the M60–Virgo interaction, thus sufficient gas has not yet been stripped to form a clear tail, as was observed in M89, which is located far closer to M87 (390 kpc) and therefore has undergone a much longer gas-stripping period. Alternatively, M60 may already have passed through the Virgo system once and we are observing it shortly upon completing a turn around in its orbit. This would suggest stripping is occurring primarily from KHI, such that no large volumes of gas are being pushed behind the galaxy. In either case, stripping may be less efficient in the low-density Virgo outskirts, requiring gas to first be uplifted by periodic AGN activity before being pushed back into the tail.

Based on X-ray observations of M32, Revnivtsev et al. (2007) found that unresolved stellar objects may provide a large fraction of the diffuse X-ray emission in low-mass galaxies. In their follow-up paper, Revnivtsev et al. (2008) showed that the old stellar populations in galaxies can be characterized by a universal value of X-ray emissivity per unit stellar mass or per unit K-band luminosity.

From studying the K-band images of M60 taken with the 2MASS survey, we determined the stellar mass and implied X-ray luminosity of the stars. The K-band luminosity measured in a 200'' radius region centered on the X-ray peak is ${L}_{{\rm{K}}}=2.90\times {10}^{11}\,{L}_{{\rm{K}},\odot }$. Bell et al. (2003) showed that the relation between the galaxy's stellar mass and the K-band luminosity can be expressed as

$$\begin{eqnarray}&&\mathrm{log}\left(\displaystyle \frac{{M}_{* }}{{L}_{{\rm{K}}}}\right)={a}_{{\rm{K}}}+{b}_{{\rm{K}}}\times (B-V),\end{eqnarray} \tag{ 6 }$$

where M_* is in units of ${M}_{\odot }$ and ${L}_{{\rm{K}}}$ is in units of ${L}_{{\rm{K}},\odot }$. Using ${a}_{{\rm{K}}}=-0.206$, ${b}_{{\rm{K}}}=0.135$ (Bell et al. 2003) and the extinction-corrected color for M60 $B-V=0.95$ from RC3 data (de Vaucouleurs et al. 1991 NED) in Equation (6), we find a stellar mass of ${M}_{* }=2.4\times {10}^{11}\,{M}_{\odot }$, where systematic uncertainties in the M/L relationship may be as high as 25%.

Revnivtsev et al. (2007) give the relation between X-ray luminosity and stellar mass in the soft (0.5–2.0 keV) energy band as follows:

$$\begin{eqnarray}&&{L}_{{\rm{X}}}^{0.5-2.0\mathrm{keV}}=7\times {10}^{38}\left(\displaystyle \frac{{M}_{* }}{{10}^{11}{M}_{\odot }}\right)\,\mathrm{erg}\,{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 7 }$$

Using Equation (7), the stellar contribution to the soft X-rays is therefore ${L}_{{\rm{X}}}^{0.5\mbox{--}2.0\mathrm{keV}}=1.68\times {10}^{39}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$, such that the stellar component is 1.5% of the total 0.5–2 keV emission. One should note, however, that there is of order a factor 2 scatter in the ${L}_{{\rm{X}}}\mbox{--}{L}_{{\rm{K}}}$ relation for these components in early-type galaxies (see, e.g., Bogdan & Gilfanov 2011).

In fitting the X-ray spectra, this component is modeled with a mekal model plus power law with a fixed temperature ${kT}=0.5\,\mathrm{keV}$, Anders and Grevasse abundance $A=1.0\,{Z}_{\odot }$, and power-law exponent ${\rm{\Gamma }}=1.9$ (Revnivtsev et al. 2008). The relative normalization of the two components is fixed by setting the ratio of the mekal model to power-law fluxes to be 2.03 in the 0.5–2 keV band and the overall normalization is fixed such that the contribution of CV and AB stars is 1.5% of the 0.5–2 keV flux.

A second component to the X-ray emission is required to account for unresolved LMXBs below the individual source detection threshold that contribute to the overall diffuse X-ray luminosity. The azimuthally averaged spatial distribution of the number of LMXBs for most normal galaxies follows closely the distribution of the near-infrared light (Gilfanov 2004). The combined luminosity functions of LMXBs for such galaxies are

$$\begin{eqnarray}\displaystyle \frac{{dN}}{{{dL}}_{38}}=\left\{\begin{array}{ll}{K}_{1}{\left(\tfrac{{L}_{38}}{{L}_{{\rm{b}},1}}\right)}^{-{\alpha }_{1}}, & {L}_{38}\lt {L}_{{\rm{b}},1}\\ {K}_{2}{\left(\tfrac{{L}_{38}}{{L}_{{\rm{b}},2}}\right)}^{-{\alpha }_{2}}, & {L}_{{\rm{b}},1}\lt {L}_{38}\lt {L}_{{\rm{b}},2}\\ {K}_{3}{\left(\tfrac{{L}_{38}}{{L}_{\mathrm{cut}}}\right)}^{-{\alpha }_{3}}, & {L}_{{\rm{b}},2}\lt {L}_{38}\lt {L}_{\mathrm{cut}}\\ 0, & {L}_{38}\gt {L}_{\mathrm{cut}}\end{array}\right.,\end{eqnarray} \tag{ 8 }$$

$$\begin{eqnarray}{K}_{2} & = & {K}_{1}{\left(\tfrac{{L}_{{\rm{b}},1}}{{L}_{{\rm{b}},2}}\right)}^{{\alpha }_{2}},\\ {K}_{3} & = & {K}_{2}{\left(\tfrac{{L}_{{\rm{b}},2}}{{L}_{\mathrm{cut}}}\right)}^{{\alpha }_{3}},\\ {L}_{38} & = & \tfrac{{L}_{{\rm{X}}}}{{10}^{38}}\mathrm{erg}\,{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 9 }$$

The average normalization is ${K}_{1}=440.4\pm 25.9$ per ${10}^{11}\,{M}_{\odot }$, ${\alpha }_{1}=1.0$, ${\alpha }_{2}=1.64$, ${L}_{{\rm{b}},1}=0.19$, ${L}_{{\rm{b}},2}=5.1$ (Gilfanov 2004). The total number of LMXBs and their collective luminosity is directly proportional to the stellar mass of the host galaxy. In regions without significant diffuse X-ray emission, 7 counts is typically sufficient to detect a point source with Chandra. Assuming a power-law LMXB spectrum with a slope of ${\rm{\Gamma }}=1.56$, and the combined exposure time of 262 ks, the estimated source detection sensitivity would be $6\times {10}^{36}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$. However, due to the presence of copious diffuse emission in M60, the actual source detection sensitivity is significantly higher than this. Based on a sensitivity map that was computed using the CIAO lim_sens task, we estimate that in most regions of M60 we detect sources brighter than ${L}_{\mathrm{lim}}=2\times {10}^{37}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$. Based on this source detection sensitivity and Equations (8) and (9),we predict that the X-ray luminosity of unresolved LMXBs in M60 is ${L}_{\mathrm{LMXB}}^{200^{\prime\prime} }=2.6\times {10}^{39}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$ in the 0.5–2 keV band, approximately 2% of of the total X-ray luminosity within the 200'' radius region.