THE STRUCTURE OF THE CIRCUMGALACTIC MEDIUM OF GALAXIES: COOL ACCRETION INFLOW AROUND NGC 1097^*

Searching for Lyα absorption lines at the redshifts of nearby galaxies is hampered by two problems. First, at redshifts close to zero, Lyα lines are unobservable because the QSO flux is completely extinguished by the DLA absorption from our own Milky Way. Second, geocoronal Lyα emission filling the 2.5 arcsec diameter circular COS PSA will contribute additional flux at the wavelengths of the expected extragalactic absorption. This would make lines seem weaker than they really are, and lead to an underestimate of H i column densities. The Lyα airglow is distributed over a wide spectral range, and when observing objects with low count rates, the emission can be a significant additional background source near the rest wavelength of Lyα.

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Portions of the co-added spectra near rest-frame Lyα are shown in Figure 4. At the lowest velocities, geocoronal Lyα emission dominates. The spectrum of Q0244 shows the widest Lyα absorption from NGC 1097 (the extent of which is indicated by orange lines), but there is no flux at the center of the absorption line profile, suggesting that, at least by a redshift of cz = 1270 km s⁻¹, Lyα airglow does not contribute to the spectrum's flux. Additional information comes from the observation of the WD star, S394Z150, where Lyα absorption in the star's atmosphere is so strong that there is no flux over a wavelength range much wider than that which is usually extinguished from interstellar Lyα in the Milky Way. The spectrum of the WD is shown in the bottom panel of Figure 4, where only geocoronal Lyα emission is left at the bottom of the DLA trough (black line). In our sample, the strongest geocoronal Lyα was observed toward Q0244, and Figure 4 shows the extent of the emission toward the WD after the peak of the Lyα emission has been scaled to that of Q0244 (red line). The figure shows that by ≃800 km s⁻¹, any contribution from airglow is negligible and any Lyα absorption lines at those velocities would be unaffected.

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To provide a precise zero-point to the wavelength calibration, we tied the wavelengths of features in the COS data to the velocity of 21 cm emission measured toward the QSOs from H i profiles extracted from the Parkes Galactic All-Sky Survey (GASS, McClure-Griffiths et al. 2009). The median heliocentric velocities of the 21 cm H i emission along all four QSO sightlines were nearly identical, +9 km s⁻¹. We matched this velocity to those of the strongest low-ionization ISM lines seen in the COS spectra, which are expected to arise in the same gas detected at 21 cm, namely Si iiλλ1190, 1193, the S iiλλ1250, 1253, 1259 triplet, Si iiλ1260, and C iiλ1334. In fact, the velocities of these lines did not all agree; in collating line centroids for all four sightlines, differences of 0–12 km s⁻¹ (∼0–2 rebinned pixels) were found between the different ions. There are several possible reasons for this: line centers may be measured incorrectly because of low S/N in the line profile; weaker components of the strongest lines may have different profiles compared to weaker lines where such components are not detected; or errors may arise in the wavelength solution applied to the detectors, or to x-walk along the detector in regions where the gain-sag is high. Without knowing which of these effects dominate, we decided to match the 21 cm emission velocity of +9 km s⁻¹ to the average velocity of all seven MW lines; as a consequence, between 1190 and 1334 Å, the error in measuring the wavelength of any narrow feature ought to be ∼±6 km s⁻¹ or about one rebinned pixel. This wavelength range covers all the lines we expected to see from NGC 1097, except the Si ivλλ1393, 1402 doublet.

The absorption lines seen toward Q0244 are shown in Figure 5. Metal lines are detected toward Q0244 at at least two velocities; in the first case, C iiλ1334, Si iiλ1193, Si iiλ1260, Si iiiλ1206, and Si ivλ1393 are found at a velocity of 1384 km s⁻¹. This component is labelled A3 in Table 3, and categorizes the strongest metal-line absorbers along the sightline. There is also a marginal detection of Si iiλ1190 at this velocity, although its reality is based largely on the presence of the other Si ii lines since its strength is below our detection threshold. As expected therefore, the weakest line of the four Si ii lines, Si iiλ1304, is absent. Si ivλ1403 at 1384 km s⁻¹ is contaminated by an O viλ1032 line at z = 0.35818, from a system that also shows corresponding Lyβ, Lyγ, Lyδ, and O viλ1037. Hence the λ1403 line is not used in the derivation of the Si iv column densities.

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A second component is detected from Si iiiλ1206 at 1227 km s⁻¹; although there are no other metal lines to confirm the reality of this component, there is clear evidence of Lyα at a similar velocity (see below), and so we consider this component to be real. This component is labelled A1.

Finally, a weak feature is detected near the C iiλ1334 A3 component, which, if a lower-velocity C ii absorption feature, would be at v = 1261 km s⁻¹. This velocity is clearly different from that of A1 and A3. We label this possible system A2 in Table 3 and discuss its reality below.

In order to establish the velocity of components A1 and A3, all the metal lines were fit simultaneously. Fits were first made without including the Lyα line. (The Lyα components are clearly blended, so there is little information in the line profile to help establish the components' velocities.) Values of b and N were allowed to vary independently for each component of each species, and while v was also allowed to vary, it was constrained to be the same for each component of each ion.

Although A2 is defined only by the possible existence of a weak C ii line, Table 3 lists EW limits and column density limits for the other species at the same velocity. For Si iii, a limit is hard to define, since any absorption would be blended with the A1 component. The Si iii A1 component is broad, and the low S/N of the data makes the profile appear coarse, but there is no obvious need to add an additional component to represent possible absorption at the A2 velocity. We estimate a plausible column density for Si iii based on adding a fictitious A2 (unresolved) component and seeing how the blended profile changes with N(Si iii).

A similar problem exists for defining a C ii column density limit for A1, since any line at that velocity would be blended with the defining A2 C ii component. We again estimate an upper limit to C ii at A1 by blending a hypothetical component (this time with the b value of the broad Si iii component) with the existing C ii component.

The Lyα absorption lines detected from NGC 1097 are complicated by contamination by lines from two higher-redshift systems. One contaminant is Lyλ930 arising from a system at z = 0.31229; the H i from this system is very well constrained, however, since Lyβ, Lyγ, Lyδ, Ly$\epsilon$, Lyλ923, and Lyλ920 lines are all present. Absorption can be fit with a single component to give log N(H i) = 15.88 and b = 38.9 km s⁻¹. With these values we can calculate a profile for Lyλ930 (shown as a dashed line in Figure 5) and remove it from the data. There also likely exists a second contaminant to the Lyα complex, an O viλ1031 line at z = 0.18272. This system is defined primarily by Lyα, Lyβ, and Lyγ lines, and so appears secure. There is a feature at 1227.2 Å that is probably the O viλ1037 line from this system. The O vi absorption is weak and simple, and a fit to the O viλ1037 line gives log N(O vi) = 14.19, b = 20.6 km s⁻¹. We again model the corresponding O viλ1031 line using these values and remove it from the Lyα lines from NGC 1097. Both these interloping Lyλ930 and O viλ1031 lines are relatively weak compared to the strong Lyα lines from NGC 1097 and contribute little to the total EW.

The Lyα profile clearly argues for at least two components, but determining the column density for A3 remains problematic; without including any more information from the metal lines (apart from their velocity) values of log N(H i) = 15.07 and b = 18.9 are obtained (Table 3), but the solution is not unique, and the same profile can be obtained for higher N(H i) and smaller b values. An upper limit for these can be set by the appearance of damping wings, which is not seen in the data, and which occurs when log N(H i) ≳ 17.1 and b ≲ 11 km s⁻¹.

While a two-component fit can adequately represent the observed Lyα absorption, we noted in the previous section the possible presence of an additional C ii component—A2—which could have a corresponding Lyα component. There is no information in the Lyα profile to constrain the physical parameters of a component matching A2, but we can explore how badly the Lyα b-values and column densities of A1 and A3 might be affected by including A2. An upper limit to N(H i) for A2 can be set at log N(H i) ≃ 18.1, when the damping wings of A2 are wider than the entire profile. The maximum b-value of A2 is given by the b-value of the C ii component, which has b = 10.9 km s⁻¹. If b(C ii) was defined purely by turbulent processes, then b(Lyα) would be the same as b(C ii), or 10.9 km s⁻¹. If b(C ii) was entirely a thermal width, then the corresponding temperature would be ∼8.6 × 10⁴ K. The width of a Lyα line at that temperature would be b(Lyα) = 38 km s⁻¹. We can therefore use b = 10.9 km s⁻¹ and b = 38 km s⁻¹ as lower and upper limits to b for A2. We can then fix the velocities of all three components to those of the metal lines, vary N(H i) for A2 in fixed intervals, and then refit, to see how N(H i) and b change for A1 and A3.

In fact, for either value of b for A2, the values of b and N(H i) change little for A1 and A3 until the N(H i) of A2 reaches its upper limit of log N(H i) ≃ 18.1. For N(H i) less than this, most of the optical depth at the velocity of A2 is always taken up by A1, so increasing N(H i) for A2 makes little difference to the optical depth at the velocity of A2. This suggests that N(H i) for A1 and A3 may not be too badly affected by the presence of even a moderately strong Lyα component at the velocity of A2.

Finally, we note the presence of additional weak, higher velocity components, which we label A4 and A5 in Table 3 and Figure 5. The figure shows the Lyα profile after the contaminating O viλ1032 and H iλ 930 lines have been divided out of the data. We find values of N and b from the profile fitting, but the lines are unresolved. The limit of the COS resolution is ∼15 km s⁻¹ FWHM (ignoring the non-Gaussian shape of the LSF) or b ≲ 9 km s⁻¹. The EWs of both Lyα lines lie on the linear part of the Curve of Growth so long as b ≳ 7 km s⁻¹ (i.e., T ≃ 3000 K) with log N(H i) ≃ 13.1. If b is really less than 7 km s⁻¹, however, then N(H i) is a lower limit. As b is unconstrained, we give N(H i) as a lower limit in Table 3.

It is useful to summarize the above discussion in terms of the total N(H i) along the sightline, a value we will use later in this paper. The lower limit to N(H i) is set by A1, and is log N(H i) ≃ 15.6 (Table 3). The upper limit is set by a lack of a damping wing on the red side of A3, log N(H i) ≲ 17.1; however, the possible existence of H i corresponding to the C ii component A2 increases this limit to log N(H i) ≲ 18.1, at which point damping wings would be seen on both sides of the complex.

As shown in Figure 6, Si iiiλ1206 is detected unambiguously at 1240 km s⁻¹ toward S393Z082, a system we label B1. A weak feature is also detected at the wavelength where C iiλ1334 is expected at the same velocity as B1, but the line could be O viλ1032 at z = 0.29863, because there is also a very weak feature that could be Lyβ at that redshift. The corresponding O viλ1037 line is not detected at this redshift, but given the weakness of the λ1032 line, this is not unexpected for unsaturated lines. Fitting Voigt profiles to the Lyβ, O viλ1032, and (to provide an upper limit) O viλ1037, a solution of b = 13.8 km s⁻¹, log N(H i) = 13.7, and log N(O vi) = 13.5 can be found (Figure 7). Although an O vi/H i absorber with such a narrow linewidth is relatively rare, Tripp et al. (2008) have found such systems. Further, the ratio of the column densities in our fit, log[N(H i)/N(O vi)] = −0.17 is consistent with the values found by Tripp et al. for the value of log N(H i) = 13.7 that we find for the system. Given the precise alignment of the two lines, and the plausibility of physical parameters obtained from the profile fits when compared to other O vi systems, we cannot be sure that the line at 1340.1 Å is C ii from NGC 1097 and refrain from using it in our analysis. We note that if the identification is wrong, and the line is indeed C iiλ1334, then the profile fit to the line requires log N(C ii) ≃ 14.0.

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This is the simplest of the Lyα absorption lines associated with NGC 1097, but the physical parameters are not well constrained. The data have the lowest S/N of the four sightlines, and there is some ambiguity over the number of components to fit. A single component, which we label B1 in Figure 6, appears to be adequate; there is a slightly lower "shelf" at 1100 km s⁻¹, and adding a component to match this feature changes N(H i) for B1 by a factor of 4. The MC simulations used to calculate the errors in N(H i) and b-values, however, suggest that the small amount of extra depth may well just be from noise, since in many cases the feature is not replicated in the synthetic spectra. We therefore assume that no additional absorption occurs at this lower velocity.

The Lyα line provides an example of the classic problem of measuring N(H i) and b when its EW lies on the flat part of the Curve of Growth. The line-profile fitting settles on two possible solutions, one with b = 46 km s⁻¹ and log N(H i) = 14.8, and a second one with b = 19 km s⁻¹ and log N(H i) = 17.6. The problem is exacerbated by the low S/N of the data, providing insufficient constraints on the shape of the wings of the line. An analysis in which the width of the line is determined by b_therm and b_turb components (see Appendix C) shows that the change in log N(H i) from 14.8 to 17.6 occurs when T > 1 × 10⁴ K. Figure 6 better shows the problem, where theoretical lines profiles for both the high-N fit (green) and the low-N fit (red) are drawn; the profiles for the two solutions are almost identical.

Along this sightline, Si iii appears to be detected at the redshift of NGC 1097, and being shortward of Lyα, the reliability of its identification is strong. This component is labelled C2 in Table 5 and Figure 8. There is an additional weak Si iii component to the blue side of C2, which is designated as C1.

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Any C iiλ1334 from system C1 is lost in a line that, given its strength and width, is probably Lyα at z = 0.10224 (Figure 8, second panel) although there are no other corroborating lines. C ii from system C2 is expected at 1340.5 Å, and a weak feature is seen very close to that wavelength, although it is nestled next to the high-zLyα line. N(C ii) for the line is given in Table 5, and while we consider the detection to be real, it remains possible that the feature is simply an additional higher-velocity (z = 0.10272) component that is part of the strong high-z Lyα line.

A feature is also seen at 1244.32 Å that could be N vλ1238 from NGC 1097, but there is no N vλ1242 line to confirm this. Fitting the N vλ1238 line gives log N(N v) = 13.50 and b = 20 km s⁻¹; with these values, the N vλ1242 line should be detected, but is not. We therefore list only upper limits in Table 5.

The Lyα absorption from NGC 1097 toward Q0246 comprises three components. Two of these well match the systems C1 and C2 identified in the metals; a third, broader line is evident at a higher velocity, which we label C3 in Figure 8, but which has no corresponding metal-line absorption. The Lyα component in system C2 is another example of a saturated Lyα, and constraining N(H i) is challenging. For this spectrum, the S/N is higher than for S393Z082, which helps constrain the fits of theoretical Voigt profiles; nevertheless, there is still a large uncertainty in N(H i), which is reflected in the errors listed in Table 5.

No metal-line absorption is detected from NGC 1097 along this sightline. The lack of detections is shown in Figure 9, and upper limits are listed in Table 6. Absorption by Si ivλ1393 from NGC 1097 would be blended with a pair of Ly$\epsilon$ lines at z ≃ 0.493, so column density limits are measured for Si ivλ1403 instead.

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Though no metal lines are detected, two Lyα components are seen from NGC 1097. These are labelled D1 and D2 in Figure 9 and Table 6, and lie close to Lyβ lines from a two-component complex at z = 0.18868 and z = 0.18945. D1 Lyα from NGC 1097 is slightly blended with the higher-z of these two Lyβ lines, as can be seen in the figure. Unfortunately, any Lyα components at velocities less than that of D1 will be lost in the Lyβ lines. Neither D1 or D2 can, instead, be an additional Lyβ component at z ≃ 0.189 because the corresponding Lyα lines are not seen at longer wavelengths. We can find no other systems for which D1 and D2 might be metal lines.

In this model, we assume an inclined thin disk rotating at a fixed azimuthal speed v_rot. A positive value of v_rot indicates clockwise rotation of the disk shown in Figure 3—the analysis by Quillen et al. (1995) suggests that the southwest (SW) side of the galaxy lies nearer to us than the NE side, and therefore that the galaxy rotates with its spiral arms trailing the rotation. The column density of the disk is assumed to follow an exponential decline with the deprojected (e.g., Williams & Hodge 2001) radius $\widetilde{\rho }\propto \exp (-\tilde{\rho }/{\tilde{\rho }}_{d})$, where the disk scale is ${\tilde{\rho }}_{d}=11\,{\rm{kpc}}$. To model the absorption we assume that microturbulence in the gas produces lines with widths of v_turb = 20 km s⁻¹, which result in the observed line profiles after convolution with the COS LSF.

Our aim is to use the parameters described to predict the line profiles that would be expected along the four QSO sightlines. As there are many parameters that can be varied to produce the predicted profiles, we refrain from, e.g., attempting to minimize a χ² statistic between the theoretical profiles and the data—there is no unique solution for the number of parameters available. Instead, we look for more qualitative agreements that might guide us toward finding a correct scenario for the origin of the absorption.

So, for example, by adopting of value of v_rot ≃ +70 km s⁻¹, we find that our predicted profiles show some agreement with the observed data. (This velocity is smaller than the circular speed of the inner disk observed from measurements of 21 cm emission, which is ∼200–300 km s⁻¹, a point we return to in the next section.) Figure 10 shows the predicted profiles in comparison to the observed profiles. While the impact parameters of the two outer sightlines differ by only 15 kpc, the Lyα line profiles of each are markedly different, with the sightline toward HE0241 showing none of the saturated absorption seen toward Q0246. As the former sightline lies closer to the minor axis of the disk, a lower opacity would indeed be expected. Further, the absorption velocities toward Q0244 and HE0241 are centered around the systemic velocity of NGC 1097, as would be expected for sightlines at opposite ends of the galaxy's minor axis.

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In contrast, the sightlines toward S393Z082 and Q0246 lie close to the opposite ends of the major axis and the absorption ought to be shifted away from the galaxy's systemic velocity, and with the velocities in opposite directions. The implied sense of rotation is consistent with that assumed for the inner disk; for comparison, Figure 10 also shows the results from a disk model where the gas counter-rotates with the galaxy (v_rot = −70 km s⁻¹): here the predicted absorption clearly fails to match the data. As expected, the discrepancies are largest toward the sightlines along the major axis where differences in v_rot would be most noticeable.

To estimate the uncertainties associated with v_rot, we define a minimum fraction of the observed line profile that lies on either side of the centroid velocity of the predicted absorption v_c, i.e., f_min(v_rot) = min[EW(v > v_c(v_rot)), EW(v < v_c(v_rot))]/EW. Hence a model whose predicted velocity is centered around the observed absorption would have f_min ≃ 0.5. For predicted line profiles whose v_c significantly deviates from the observed centroid velocity, f_min ≪ 1. To estimate the uncertainty of v_rot, we calculate f_min for a range of v_rot values, and take the profile to be an acceptable replica of the data if f_min > 0.2. This variation of f_min as a function of v_rot is shown as a dashed line at the bottom of each panel in Figure 10. As noted above, some sightlines are more sensitive to the disk dynamics than others, depending on where they probe the disk. For example, the sightline toward Q0244 is largely insensitive to disk rotation (top left panel of Figure 10), because its sightline passes close to the minor axis of NGC 1097, and hence f_min changes little for any value of v_rot (f_min ≃ 0.5 for −500 km s⁻¹ < v_rot < 500 km s⁻¹). The other sightlines provide more stringent constraints on v_rot, as Figure 10 shows, and the similarity in the velocities at which f_min peaks in the three other panels, ∼70 km s⁻¹, suggests that this is a good estimate of v_rot.

Although this model reproduces some of the absorption line features, there are notable discrepancies between the rotating disk model and the data. For example, the model fails to predict the two-component absorption seen toward HE0241. This might be the easiest discrepancy to understand. One possibility is that a thin disk model might no longer apply at such large radii. In fact, at a radius of ∼200 kpc, the dynamical time $\sim 2\pi \tilde{\rho }/{v}_{{\rm{rot}}}$ is comparable to the Hubble time. Alternatively, the two-component absorption may mean that at large radii, H i clouds no longer form a homogeneous thin disk. Additionally, discrepancies associated with under- and overprediction of the opacity along particular sightlines can be resolved if either v_turb or the column density profile deviates with radius (see, e.g., the variations in the rotation curves around a mean value in Ondrechen et al. 1989; Hsieh et al. 2011). More worryingly, the model predicts only one absorption component toward Q0244, whereas at least two are observed; and the absorption toward S393Z082 is somewhat narrower than the model predicts.

As noted above, the rotation speed of an extended disk with v_rot ≃ 70 km s⁻¹ is significantly smaller than the 200–300 km s⁻¹ rotation speed of the inner disk (Ondrechen et al. 1989, see also Section 9.1). This fact, combined with results from ΛCDM models that imply the existence of cold-flow accretion, leads us to consider a model in which the absorbing gas has an inward radial velocity v_r.

The results of such a model are shown in Figure 11; data toward sightlines that lie in the direction of the minor axis are more sensitive to v_r, and imply v_r < 100 km s⁻¹. We find that a model with v_rot ≃ v_r ≃ 70 km s⁻¹ improves the match between data and model toward some of the sightlines. Toward Q0244, the blue component, A1, is better reproduced by the model, but at the expense of A3, which is not predicted at all. The predicted absorption toward S393Z082 is improved, while the predicted absorption toward Q0246 is unchanged. One of the components toward HE0241, D2, now matches the predictions, but the other component, D1, is still not reproduced.

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The values of v_rot and v_r are not entirely unique, and similar (but not superior) fits can be obtained for other combinations of v_rot and v_r. This model offers an improvement over the simple rotating disk presented above, but still fails to match all the observed features.

NGC 1097 shows moderate amounts of star formation at its center (Calzetti et al. 2010; Hsieh et al. 2011) so it is reasonable to consider the possible effects of an outflow in our models. In several studies where outflows have been traced by gas and dust emission (most notably toward AGNs) a hollow-cone geometry has been inferred whose axis lies along the disk's angular momentum vector (Veilleux et al. 2001, 2005) and where the wind may be detected in emission out to several kiloparsecs above the disk, and potentially out to even larger scales in absorption (Murray et al. 2011).

We consider the effect of adding a hollow-cone model to our rotating–inflowing model by including gas that flows out of the galaxy along radial trajectories at a speed v_rad. This addition is also shown in Figure 11. The most notable result from adding an outflow component is that we can replicate the additional A3 absorption component (Table 3) toward Q0244, using a model that has a cone with v_rad ≃ 300 km s⁻¹ and that is so wide—65° < θ < 70°—that part of the cone wall is still receding from us, providing an absorption component that has a positive velocity (redshift) with respect to the rest of the galaxy. This scheme is highlighted in the inset diagram in Figure 11. Wide-angle outflow cones have been seen in the inner regions of some galaxies, e.g., toward ESO 097-G013 (Greenhill et al. 2003), so a weak outflow that contributes to the absorption is plausible. A wide, amorphous outflow more like the superwind seen toward M82 might be the best analog (e.g., Leroy et al. 2015, and references therein).

Galactic disks are known to exhibit warps, especially in systems undergoing interactions with other galaxies. If the inclination angle of the disk changes with radius, for example, and/or the position angle of the major axis changes with radius, absorption line profiles could be replicated to better match the data with these added variables. For example, the simplest case is where the inclination angle varies with radius, which would allow for a wider range of v_rot at different radii. Among the various possibilities for geometrically thin disks we mention only two: good agreement between data and line profiles can be found when the outer disk has v_rot = 250 km s⁻¹ and i = 10° (i.e., nearly face-on), or v_rot = 60 km s⁻¹, i = 75°, and a very large disk scale of ∼30 kpc. So, given the inclination of NGC 1097 (40° ± 5°), substantial warping would be required to account for the observed absorption. There is some indication from the 21 cm H i maps of Higdon & Wallin (2003) that the outer spiral arms of NGC 1097 are disturbed by tidal interactions (which we discuss later), so distortions in the structure of any extended disk are a possibility. However, far more additional data on the nature of the warps in NGC 1097's disk would be needed before they could be reliably added to our model.

By virtue of isotropy, the absorption line profiles predicted from a spherical outflow model are centered symmetrically around the systemic velocity. For example, expanding shells would generally produce two-component line profiles as the sightlines toward the background QSOs intercept the front and back sides of the outflow. This well matches the double component profile (D1 and D2) toward HE0241, and we used these components to calibrate a thin-shell model with δr ≪ r (a similar approach was adopted by Tripp et al. 2011). Specifically, by matching the model to the D1 and D2 components, we find that the mass in the outflowing shell is >3 × 10⁵η M_⊙, where 1/η is the mass fraction of the gas in the form of H i, a potentially small number related to the uncertainties in the ionization corrections and/or the multiphase nature of the outflow. The mass-loss rate is then of order 4πr²ηN(H i)m_p(v_rad/r) ≃ 10⁻⁴η(r/200 kpc)(N(H i)/10¹⁴ cm⁻²)(v_rad/40 km s⁻¹) M_⊙ yr⁻¹, which is probably much smaller than the current rate of star formation. Irrespective of this argument, thin-shell models fail to explain the decreasing gas opacity with impact parameter—the predicted column densities are always too low to produce the strong absorption seen along all the sightlines. Moreover, the asymmetric absorption around the systemic velocity along sightlines at opposite ends of the disk's major axis (i.e., toward S393Z082 and Q0246) cannot be reproduced.

We find that the simplest models of spherical outflows seem to be inadequate for reproducing the observed absorption, and given the limited set of observational constraints, a more detailed analysis seems unwarranted.

In Section 7.1.2, we showed how adding a polar outflow to the rotating disk models could account for the A3 component seen toward Q0244. In general, however, models that include only polar outflows and no disk component run into difficulties explaining the absorption along the sightlines that lie in the direction of the major axis and are at large impact parameters, unless the opening angle is large or the flow extends far enough above the disk. For example, assuming an outflow that extends out to R_v, an opening angle of >50° is needed to produce absorption toward Q0246.

The model shown in Figure 11 assumes outflow from only one side of the galaxy, but a bipolar outflow would produce additional positive velocity absorption. Outflowing gas from the far side of the galaxy would need to extend further than the front-side flow to intercept the sightline. We do indeed see weak components—A4 and A5—at higher velocities, which might fit such a scenario. Whether the extent and covering factor of the outer regions of an outflow could account for such weak absorption is unclear.

We should note that gas outflowing at the observed velocities would need to travel over timescales that are comparable to the dynamical time of the halo, which would most likely invalidate the simple conic geometry. For example, gas may be dragged perpendicular to the outflow if the halo is rotating, or minor mergers may disrupt the geometry of the escaping gas. Again, modeling the absorbing properties of such disrupted outflows is beyond the scope of this paper.

In Figure 12 of Section 8, we showed how Lyα and Si iii column densities and EWs changed with impact parameter. We also introduced a comparison set of data, taken from the COS-Halos program, and in this section we discuss these results further. The properties of Lyα, and of metal lines, from the absorbers were studied by Tumlinson et al. (2013) and Werk et al. (2013), respectively. To compare with our NGC 1097 data, we need to derive galactic virial radii in the same way as we have for NGC 1097. Tumlinson et al. list stellar masses for all their galaxies, derived from SDSS colors, from which we can estimate halo masses, and hence R_v, again using the relationships between the two described by Behroozi et al. (2013).

In Figure 13, the COS-Halos data are shown as light pink squares, while the Si iii values are purple squares. The H i column densities and EWs show a large dispersion, and include a set of sensitive non-detections at very small impact parameters, which Tumlinson et al. suggested was due to the lack of a cool halo around early type galaxies. These non-absorbing galaxies are only a small fraction of the total sample, and the bulk of the absorbers show unity covering fractions out to the ∼0.6 R_v limit of the survey. Our range of N(H i) values, and the inferred covering fraction, appears consistent with the COS-Halos sample.

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For Si iii lines, Werk et al. fitted a power law to the distribution of N(Si iii) and W(Si iii) with ρ/R_v (ignoring both upper and lower limits). These fits are reproduced in the bottom two panels of Figure 13; their fits to N(Si iii) and W(Si iii) are close to what we find for the four sightlines toward NGC 1097. They also calculated a covering fraction for Si iii of ${73}_{-14}^{+9}$% over a radius of 0–160 kpc for galaxies with stellar masses log M_*(M_⊙) ≥ 10.5. This again is consistent with the three or four detections in the halo of NGC 1097 at similar radii and at the same stellar mass limit.

In Figure 14 we introduce the detections and limits for C ii (orange points), Si ii (green points), and Si iv (blue points) for the COS-Halos galaxies. With C ii, Si ii, and Si iv detections toward only Q0244, and a possible C ii detection toward Q0246 (which we include) comparisons with NGC 1097 are tenuous. We note simply that the strengths of the metals toward NGC 1097 are similar to the COS-Halos sample. They lie in regions where the covering fractions of the metals in the COS-Halos sample are less than unity, and our non-detections are compatible with those low values.

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Three background probes were used by Keeney et al. (2013) to probe the edge-on galaxy ESO 157−49, a much less luminous (L/L_* = 0.12) and weaker star-forming galaxy (0.2–1.1 M_⊙ yr⁻¹) than NGC 1097. We assume a viral mass of log M(M_⊙) = 10.6 for the galaxy (the lower limit set by Keeney et al.), which corresponds to R_v = 88 kpc. This puts their sightlines at impact parameters of ρ/R_v ≃ 0.9, 1.1, and 2.0, distances larger than those probed for NGC 1097. We adopt the sum of the three N(H i) components toward the outermost sightline, HE 0435–5304, to be log N(H i) = 14.22 ± 0.11 and calculate the total EW by reconstructing the line profile from their Voigt profile fits, W(Lyα) = 0.63 Å. The Lyα lines toward the inner two sightlines are of similar strength to the inner two sightlines toward NGC 1097, and Keeney et al. had the same problem in determining N(H i) as we have had, with moderately strong W(Lyα) yielding ambiguous column densities. Figure 13 shows these points compared to the NGC 1097 values; although the errors are large, N(H i) (filled cyan squares) appears to continue to decline with ρ/R_v beyond 0.9R_v. Si iii is detected toward the inner two ESO 157–49 sightlines, beyond the last limit from NGC 1097. No C ii or Si ii is detected toward any of the sightlines (open cyan squares) but Si iv is seen at distances beyond where the COS-Halos or the NGC 1097 data probe.

With the absorbers at either side of the major axis of the edge-on galaxy both having negative velocities relative to the galaxy, Keeney et al. concluded that the absorption (at least for one of the sightlines) was unlikely to be associated with any galactic rotation, and that it was more likely to have arisen in material once ejected from the galaxy. This interpretation is clearly quite different from the ones discussed in Section 7 that were designed to account for the absorption toward NGC 1097.

M31 offers an interesting comparison with NGC 1097 in that M31 has a luminosity and halo mass close to that of NGC 1097 (van der Marel et al. 2012a, 2012b). The one important difference is that M31 is interacting with another galaxy of comparable mass only 0.8 Mpc away, with the same halo mass and luminosity—namely the Milky Way; as discussed in Section 2.3, there are no galaxies as bright as NGC 1097 within 4–5 Mpc. Although there are a large number of QSOs that can be found at interesting impact parameters behind M31, the low velocity of the galaxy makes it difficult to study in absorption (Section 1). Nevertheless, Rao et al. (2013) found no absorption beyond 0.2 R_v along the major axis of the disk (assuming R_v = 300 kpc for M31), but low-ionization absorption from four of six sightlines below 0.1 R_v. These data are hard to incorporate in this study because (i) the low resolution of the COS G140L and G230L observations makes it difficult to fully separate out absorption from the strong MW ISM absorption lines, (ii) understanding the relationship between the velocities of the detected lines and the velocity of MS+HVC gas (if any) at the positions probed is beyond the scope of this paper, and (iii) both the Lyα and Si iiiλ1206 lines, which are integral to our study, are not available in their low-resolution data. For these reasons, these data are not plotted in Figures 13 and 14. Nevertheless, Rao et al. drew an important distinction in claiming that M31 is not a typical Mg ii absorbing galaxy compared to higher-redshift samples.

On the other hand, Lehner et al. (2015) used COS G130M and G160M archival data of 18 sightlines passing within 2R_v of M31. They distinguished a specific velocity range over which to measure absorption that they considered sufficient to avoid contamination from MW ISM absorption and the MS. These data are included in Figures 13 and 14 (shown as triangles). Lehner et al. did not provide EW measurements from their data, and so we estimate EWs directly from the column densities, assuming the lines are optically thin. These represent lower limits to the true EWs because not only may some of the lines be mildly saturated, but also because the wings of the absorption profile are often lost in the blended MW ISM and the MS lines either side of the absorption from M31.

Like the COS-Halos sample, the collation by Liang & Chen (2014) is of absorption along single sightlines through many galaxies. Nevertheless, the sample is useful in that the sightlines probe beyond the impact parameters of the COS-Halos galaxies, and measurements of many species of metal lines, as well as Lyα, are provided. This sample of galaxies (hereafter designated as LC14) has a median redshift of 0.02 and samples galaxies with stellar masses of 10⁷–10¹¹ M_⊙. Their derivation of R_v is the same as described above, so we use their tabulated values. Only EWs are given by Liang & Chen, and since these cannot be converted to column densities with any reliability, column densities are not plotted. In Figure 13 all the data for Lyα and Si iiiλ1206 are included, but in Figure 14, most points at ρ/R_v > 1.0 are only upper limits, and not sensitive enough to show any significant decline in EW above those radii. To avoid confusion with points from the other data sets, we show only the median EW limit at ρ/R_v > 1.0 as a gray horizontal bar.

Our fitting of a power law to the data obtained for NGC 1097 shows that the evidence for a decline in H i and Si iii column densities and EWs with ρ/R_v—based only on the four sightlines—is weak. Tumlinson et al. reported no decline in N(H i) or W(Lyα) with ρ/R_v in the COS-Halos sample, which we see recreated in the top panel of Figure 12. However, Figure 13 shows that when we combine the COS-Halos results with the LC14 data it seems more plausible that Lyα and Si iiidecline with impact parameter, and indeed that NGC 1097 follows the same decline. If we exclude the upper limits in the COS-Halos and LC14 data sets, then a linear regression analysis of the two larger samples confirms a strong correlation, with a high probability of being able to exclude the null hypothesis that there is no correlation. A least-squares fit to the W(Lyα) data (shown as a green line in the second panel of Figure 13) has logW* = −0.37 ± 0.02 Å, α = −0.45 ± 0.04; but more importantly, the standard error in the regression, s, is 0.27 dex, while for NGC 1097, s = 0.21 dex. A similar result is found for W(Si iii). This standard error is the average distance that the observed values fall from the fitted line, and conventionally, 95% of all points should fall within 2s. The fact that the values of s for NGC 1097 and the two samples of COS-Halos and LC14 are similar suggests that the overall variability or clumpiness within the halo of NGC 1097 is largely the same as the dispersion seen from the galaxies in the larger single-probe data sets.

Of course, while the Lyα and Si iii absorption in the halo of NGC 1097 may have much the same characteristics as the other data sets, we only know this to be true for impact parameters <0.6R_v. Beyond 1R_v, LC14 have shown that the number of non-detections of Lyα increases rapidly, i.e., the covering fraction declines to ∼60% at an EW threshold of 0.05 Å (their Figure 11). Keeney et al.'s observations of ESO 157–49 do not show such a decrease (and remain as flat as the values for NGC 1097 at smaller ρ/R_v). Whether this represents the way H i is distributed around all galaxies, or whether the detection/non-detection of Lyα points to some other property of a galaxy that influences the extent of H i around its CGM, is not clear. Observations of additional probes beyond 0.6 R_v for NGC 1097 would help to explain how the covering fraction really declines in a single halo at large radii.

We conclude that based on the absorbing column densities and EWs alone, NGC 1097—and probably M31 and ESO 157–49—are "typical" absorbers compared to the COS-Halos and LC14 samples. This is curious, because the structures that have been suggested as origins of the absorbing gas (an isolated galaxy for NGC 1097, an interacting group for the MW–M31–MS system, and post-ejection products from ESO 157–49) are quite different. It may be that while galaxies do indeed possess definable CGMs that decline with radius, some absorption line properties—in this case N and EWs—are relatively insensitive to the structures that contain the baryons. For NGC 1097 we have also used kinematics to attempt to better understand the origin of absorbing gas, leveraging the use of multiple probes of a single galaxy to constrain a model (an approach that is far more ambiguous for single sightlines through single galaxies). Again, though, a similar consideration of the kinematics of the three sightlines toward ESO 157–49 suggests an origin quite different than that for NGC 1097, and it remains to be determined if either set of results is universal for galaxies.

A single-phase solution (i.e., a single cloud with a uniform density) for this component that satisfies all the observational constraints is obtained for n ≲ 7 × 10⁻⁴ cm⁻³ and Z ≲ 0.3 Z_⊙, which yields log N(H) ≳ 18 (Figure 18). Taking the extreme values of this solution, the resulting length scale is 0.5 kpc ≲ l ≲ 10 kpc, which implies that the gas occupies only a small fraction of the volume as l/ρ < 0.2.

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The contribution of NGC 1097 to the flux ionizing the absorbing gas along this sightline may not be negligible, given the relatively small impact parameter of Q0244. Assessing the galaxy's contribution is difficult because the UV and X-ray flux that the absorbers see may depend on the galaxy's inclination relative to where the clouds are, on their distance and orientation to star-forming regions in the disk, and on any contribution from the central AGN (all of which are highly uncertain). The SED of the UV background, which is dominated by galaxies at z = 0, will likely have, to first order, a similar shape to that of NGC 1097, so the contribution from the galaxy can be accounted for by simply scaling-up the background flux level. In this case, a solution is obtained for the same ratio of photon density to particle density, and the allowed density range scales with the flux level (by roughly +0.6 dex given the luminosity of NGC 1097).

Alternatively, we can at least qualitatively assess the effects of assuming that the SED below the He ii edge is similar to that of the Milky Way (Fox et al. 2005), by using a flux below the He ii edge that is twice as high as that given by the HM SED (and which includes a contribution from both quasars and galaxies); the results are shown in Figure 18, where a single-phase solution can only be found if the upper limit to the Si iv column density is underestimated by 0.1 dex. The resulting model then has n ∼ 10⁻³ cm⁻³, Z ∼ 0.5 Z_⊙, log N(H) = 18.0 (l ∼ 0.3 kpc), which implies slightly higher gas metallicities and slightly more compact absorbers.

We also consider the possibility that the elements might be depleted onto dust grains. Adopting any depletion patterns that are similar to the Milky Way is difficult, since these are known to differ widely for, e.g., disk and halo gas (e.g., Savage & Sembach 1996). CLOUDY offers a compromise of using an average of values from both warm and cold gas, and we use these to see how our calculations might change with dust included. Ignoring any contribution to the UV flux from NGC 1097, using all the available column density ratios and limits, there is no single-phase solution. Only if we raise the upper limits on column density by a factor of 2, and use ±2σ intervals around the measured values, do we find a solution that has Z ∼ 3 Z_⊙ and n ≳ 1 × 10⁻⁴ cm⁻³. We consider it unlikely, however, that the errors and upper limits for the metal lines in A1 are so badly determined by our analysis, and we reject these values.

The analysis of this component yields no single-phase solution that can simultaneously account for all the observational constraints. The phase spaces for many line ratios are shown in Figure 19, and we see that none of the regions intersect. Considering the N(C ii)/N(H i) ratio alone (for example), the phase space available is completely ruled out because the allowed area is completely outside the region plotted in Figure 19 (unless Z > 10 Z_⊙). As discussed in Section 5.3, N(H i) is poorly constrained for this component (although apparently less so than A1), which certainly adds to the difficulty in finding a suitable solution. Nevertheless, even allowing for a wide range of N(H i), there is no single-phase solution that accounts for all the metal line ratios alone (Figure 19).

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This problem remains even if additional flux is added from NGC 1097, or if the absorbing gas is assumed to be depleted by dust like the Galactic ISM, and it persists even when pure collisional heating is considered instead of photoionization. The difficulties can be seen most acutely when considering low-ionization line ratios (in particular the N(Si ii)/N(C ii) ratio, which seems to be more shifted toward lower densities than the other line ratios), which suggests that the problem is not simply because we have searched for a single phase to explain all the line ratios simultaneously. For the particular case of N(Si ii)/N(C ii), if carbon is underabundant by a factor of ∼3 compared to the solar value, then the phase-space traced by this ratio is in better agreement with those of other metal-line column density ratios.⁸

We can further attempt to constrain the physical conditions of the absorber by narrowly focusing on only the silicon lines, for which three ionization levels are observed: the gas density is then restricted by N(Si iv)/N(Si ii) to be 10⁻⁴ cm⁻³ ≲ n ≲ 10⁻³ cm⁻³ over nearly three decades in metallicity. Constraints for all silicon column density ratios yield a single-phase solution at 2 × 10⁻⁴ cm⁻³ < n < 3 × 10⁻⁴ cm⁻³ with 1.4 Z_⊙ < Z < 3 Z_⊙. The total hydrogen column density depends on the uncertain N(H i), but is in the range 17.3 < log N(H) < 19.5, which gives a scale length l ∼ 0.2–50 kpc.

In conclusion, the physical parameters of the A3 absorbing cloud remain far from clear. It is possible, for example, that the gas is not in equilibrium. In that case, a more detailed treatment of this system would require additional data.