Synthetic Absorption Lines from Simulations of Multiphase Gas in Galactic Winds

The cloud in this study reaches maximum compression at t_cc = 2 and completely disintegrates by t_cc = 20. We use 10t_cc for our analysis, as it represents an average state that adequately captures the mixing between the cool and hot gas. Figure 1 shows a simulation snapshot at 10 t_cc. The top panel shows the column density projected on the x–z plane. The lower panels show slices of the density, velocity, and temperature through the center of the domain.

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The cloud material accelerates as momentum is transferred from the hot wind, and enters the outflowing wind with a range of velocities, as can be observed in the velocity slice. The low-density material within the original cloud accelerates much faster than the high-density material, and we see that velocities are anticorrelated with density. The density slice shows that most of the volume is occupied by low-density gas, while the high-density gas is clumped together in small knots, generally seeded by the highest-density regions of the original turbulent cloud. The temperature slice shows that most of the volume is filled with high-temperature gas at approximately T = 10^6.5 K, the temperature of the shocked hot wind. By contrast, the highest-density regions remain at low temperature, driven by efficient radiative cooling of the highest-density cloud gas. By volume, most of the gas in the simulation has a low density, high velocity, and high temperature, but it should be noted that this is partly driven by our selection of a small initial cloud.

The velocity distributions of the gas in the simulation can be quantified via 1D histograms. The distribution of all the gas in the simulation is shown in Figure 2 in mass-weighted (top) and volume-weighted (bottom) 1D velocity histograms. The upper panel shows clear peaks that differentiate the cool and hot gas phases. For the purposes of this discussion, we define the cool phase using the common threshold of T < 2 × 10⁴ K, and we refer to all other material as part of the hot wind. The ratio of mass in low- to high-velocity components also reflects our choice of initial cloud size relative to the domain. By mass, about 90% of the gas in the simulation is part of the hot wind. At this particular cloud-crushing time of 10 t_cc, we find that the total mass of gas at T < 2 × 10⁴ K is approximately 43% of the initial cloud mass, the rest having been heated and mixed into the hot wind earlier in the simulation. The hot wind moves at a high velocity, ∼1000–1250 km s⁻¹. The cooler gas has velocities in the range 30–200 km s⁻¹. This gas is likely comprised of a combination of original cloud mass and material that has been mixed to intermediate temperatures and cooled back down (e.g., Gronke & Oh 2018). The bottom panel in Figure 2 shows the relative contribution of the hot wind and cool cloud to the total volume in the simulation. We can see from this figure that 40% of the gas is unaffected wind material moving at the initial velocity of 1200 km s⁻¹.

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As a simple way to map the gas in our simulation to different absorption lines, we follow Figure 6 in Tumlinson et al. (2017), in which temperature ranges for each ion are given based on the full width at half maximum (FWHM) surrounding the temperature associated with the peak abundance of that ionic species from collisional ionization. Table 1 shows the range of temperatures adopted for each species in this study. Assigning ionization states in this way allows us to study the contribution of each ionic species to the total mass and volume throughout the simulation.

In Figure 3 we show mass-weighted 1D velocity histograms for a representative low, medium, and high ion constructed using these temperature ranges. In general, we see similar behavior between low, intermediate, and high ions and find that Si ii, C iv, and O vi are representative of other ions in these ranges. These histograms show that the higher-ionization species contribute less to the total mass in the simulation. Furthermore, we see that the dense gas traced by the low ions has slower average velocities (see Table 2).

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Column density projections are constructed by integrating along the x-axis, which is the direction of the background wind. Conducting our analysis along this axis allows us to compare our results directly to down-the-barrel observations. Adopting the abundances in Table 1, Figure 4 shows maps of the column density for the three representative low, medium, and high ions. In general, O vi tends to be more spatially extended than the low-ionization ions. Still, the three ions trace each other fairly well, indicating that the gas giving rise to them is generally spatially related. This reinforces the idea that the intermediate- and higher-ionization species are primarily being created as a result of the mixing between the cool cloud and the hot wind.

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We study absorption-line profiles of six ions that probe different temperatures. As demonstrated by the temperature slice in Figure 1, gas in the simulation has a range of temperatures from 10 to 10⁷ K. We create mock absorption-line profiles using the optical depth of each ionic species, which reflects both total column densities in each map pixel (e.g., Figure 4) and the line-of-sight velocity distribution. The optical depth is computed adopting the Sobolev approximation, which gives τ in terms of the density and radial velocity gradient as

$$\begin{eqnarray}&&d\tau (v;y,z)=\displaystyle \frac{\pi {e}^{2}}{{m}_{{\rm{e}}}c}f{\lambda }_{0}n(v;x,y,z)\displaystyle \frac{{dx}}{{dv}}.\end{eqnarray} \tag{ 2 }$$

Here, the line-of-sight velocity gradient is taken to be in the direction of the background wind (x in the simulation). The oscillator strength (f) and rest-wavelength (λ₀) of each of the six species investigated in this study can be found in Table 1. By integrating the number densities along the x-axis in bins of velocity, we can directly compute the optical depth along each line of sight, giving n_y  × n_z  = 262,144 independent sightlines through the simulation box. We use these to calculate the total flux decrements as a function of velocity for each species through the box; we also use the spatial distribution to assess covering fractions.

The normalized observed flux F(v) is defined as

$$\begin{eqnarray}&&F(v)=\displaystyle \frac{\int {{dydze}}^{-\tau (v;y,z)}S}{\int {dydzS}}={\left\langle {e}^{-\tau (v)}\right\rangle }_{{yz}},\end{eqnarray} \tag{ 3 }$$

where S is the background source brightness (a stellar continuum) and where the average is over the y–z projection of the simulation box. In the limit of low optical depth,

$$\begin{eqnarray}&&F(v)\approx 1-{\left\langle \tau (v)\right\rangle }_{{yz}};\end{eqnarray} \tag{ 4 }$$

from the definition of Equation (2), this involves spatial integration over the whole box. The flux decrement is then proportional to M(v), the distribution of mass as a function of velocity traced by the ion. We do not explicitly model the source brightness in our analysis, but rather use Equation (4) to calculate the flux decrement along each line of sight, which is equivalent to assuming that the source brightness is constant across the y–z extent of the simulation.

Figure 5 shows the normalized flux as a function of velocity for the six ions in Table 1. Typically, down-the-barrel studies do not spatially resolve individual regions of galaxies, and thus the absorption is a result of the integrated continuum and absorption across the entire central starburst region of a galaxy. For our normalized fluxes, the averaging is done over the entire box, so the size and mass of the cloud relative to the simulation box determines how much flux we observe. The larger the simulation box, the more unobstructed sightlines there are in the average, leading to shallower absorption lines. The bigger the clouds and the higher the column density, the more high τ sightlines enter the average, and the smaller the directly computed flux.

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Three commonly measured features of absorption lines in winds are their minimum, central, and 90th percentile velocities. Table 2 lists these velocity statistics for each of the six ionic species in Table 1 using the absorption-line profiles shown in Figure 5, which were calculated using the strong lines. We define v_min as the velocity value corresponding to the minimum flux in the absorption line. v_central is a similar measurement, but is computed by first integrating the flux profiles (see Figure 5) from 0 to 1200 km s⁻¹ and identifying the velocity at which we reach 50% of the area under the curve. Differences between v_min and v_central give some idea as to the non-Gaussian skew of the absorption line—v_central is higher than v_min for all of the lines, reflecting the extended high-velocity tails. v₉₀ is computed similarly to v_central, with the exception that it identifies the velocity that corresponds to 90% of the area under the curve, giving a rough measure of the maximum (observable) velocity of the gas in the wind. From Table 2 we can see an increase in all three velocity statistics as we go from low-ionization ions (Si ii and C ii) to high-ionization ions (N v and O vi).

The depth of an absorption line depends on both the optical depth τ and the covering fraction C_f of the absorbing gas. The covering fraction accounts for the fraction of the background light source that is obscured by the absorbing gas, while the optical depth measures the total amount of absorption in a given sight line as light passes through the cloud. For example, in Figure 5, the shape of the absorption lines is primarily determined by differences in τ as a function of velocity, while the overall normalization is set by the y–z spatial extent of our cloud (see Figure 4). If the lines are optically thin, the absorption profiles are essentially rescaled inverted profiles M(v), examples of which are shown in Figure 3. When τ > 3, we define the line profile as optically thick, at which point the depth of the observed line will be set exclusively by C_f .

When the line profiles are optically thin, the depth of the line profiles becomes degenerate with C_f and τ. One observational technique to break this degeneracy and separately compute the optical depth and covering fraction takes advantage of doublets of the same ionic species. For example, Figure 6 shows strong and weak absorption lines for O vi. The strong line for O vi has a greater oscillator strength, f, and wavelength coefficients than the weak line. For doublets that have an f-value ratio equal to 2, the relationship between τ_s and τ_w becomes τ_s (v) = 2τ_w (v). This unique ratio allows one to algebraically solve for the covering fraction independently of τ. In order to facilitate a comparison of our results with observations, we now present "empirical" estimates for the optical depth and covering fraction, derived according to this method. In all future discussion, "direct" will refer to the values calculated in Section 3.2, and "empirical" refers to values calculated using the following observational methodology.

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Following Chisholm et al. (2018), empirical equations were derived for the optical depth and covering fraction of each ionic species. From Equation (3), if we consider a fraction C_f (v) of the area as covered by a cloud with optical depth τ(v), and the remaining fraction 1 − C_f (v) as uncovered, the normalized flux would be

$$\begin{eqnarray}&&F(v)=1-{C}_{f}(v)+{C}_{f}(v){e}^{-\tau (v)}.\end{eqnarray} \tag{ 5 }$$

If τ(v) for a weak and strong line is related by fraction 2, the expression for the weak and strong line can be combined to solve for the covering fraction and the optical depth as a function of the flux in each line, assuming each line has the same C_f . The result is

$$\begin{eqnarray}&&{C}_{f}(v)=\displaystyle \frac{{\left(1-{F}_{w}(v)\right)}^{2}}{{F}_{s}(v)-2{F}_{w}(v)+1}\end{eqnarray} \tag{ 6 }$$

and

$$\begin{eqnarray}&&{\tau }_{w,\mathrm{emp}}(v)=\mathrm{ln}\left[\displaystyle \frac{1-{F}_{w}(v)}{{F}_{w}(v)-{F}_{s}(v)}\right],\end{eqnarray} \tag{ 7 }$$

where F_w represents the flux from the weak line, F_s is the flux of the strong line, and τ_w,emp is the empirical optical depth of the weak line.

We can use our directly computed flux for the strong and weak lines and for Equation (6) to calculate an empirical estimate of the covering fraction of each species. In Figure 7 we show this empirically calculated covering fraction and compare it to the directly calculated covering fraction, computed by summing all the lines of sight with τ > 0.1 and normalizing by the total number, n_y  × n_z  = 262,144 lines of sight along the x-direction. There is excellent agreement at all velocities for the low ions, and the modes of the distributions for the direct and empirical method are quite similar for all lines. However, the empirically calculated covering fractions tend to be slightly lower (up to ∼40% difference) than the directly computed values for intermediate- and high-temperature ions.

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Figure 8 shows the empirically calculated optical depth, τ_w,emp, for the six different ions that were used for this study. The low ions, Si ii and C ii, have very similar optical depths. Si ii peaks at τ_w,emp = 3.98 and C ii peaks at τ_w,emp = 3.41; both of these ions also have the same peak velocity of 48 km s⁻¹. This similarity is of course primarily driven by the similar temperature ranges assigned to each ion and by their similar mass fractions under the assumption of solar relative abundances. From this figure, we also see that the velocity range of the low ions is larger than would be captured by a measurement of v₉₀. That is, while most of the mass in these low ions is at low velocity, there is a tail of high-velocity gas even at relatively cool temperatures. The intermediate and higher ions tend to have broader velocity ranges on the whole and are optically thin across the entire range.

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Figure 9 shows a comparison between the empirical and direct calculations of the optical depth for the strong lines. For the direct method, the dashed lines show the median value of τ, the bottom of the shaded region shows the 25th percentile, and the upper boundary represents the 75th percentile. The empirically calculated values are shown as solid lines. Examining the two upper left panels, we see that low ions tracing low-temperature gas tend to have τ_s,emp(v) values that underestimate the directly calculated value of τ. Conversely, in the panels that show our medium and high ions, the value of τ_s,emp(v) consistently overestimates τ. Equation (7) can be used to quantitatively explain the cases when the empirically derived values under- or overestimate τ, as follows.

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First, we rewrite Equation (7) in terms of the average flux deficit,

$$\begin{eqnarray}&&{\tau }_{\mathrm{emp}}(v)=\mathrm{ln}\left[\displaystyle \frac{1-\langle {e}^{-{\tau }_{w}(v)}\rangle }{\langle {e}^{-{\tau }_{w}(v)}(1-{e}^{-{\tau }_{w}(v)})\rangle }\right].\end{eqnarray} \tag{ 8 }$$

This equation can now be used to describe the two different behaviors of ${\tau }_{0}(v)$. We define two regimes of τ_emp as τ_low and τ_high, such that $\langle {e}^{-{\tau }_{\mathrm{emp}}}\rangle \sim ({e}^{-{\tau }_{\mathrm{low}}}+{e}^{-{\tau }_{\mathrm{high}}})/2$. These values are an arbitrary representation of the lower and upper 50th percentile of τ₀. In the optically thick case where τ_high and τ_low $\gg \,1$,

$$\begin{eqnarray}&&{\tau }_{\mathrm{emp}}(v)\sim \mathrm{ln}\left[\displaystyle \frac{2}{{e}^{-{\tau }_{\mathrm{high}}}+{e}^{-{\tau }_{\mathrm{low}}}}\right]\sim {\tau }_{\mathrm{low}}.\end{eqnarray} \tag{ 9 }$$

In the opposite, optically thin regime where τ_high and τ_low $\ll \,1$,

$$\begin{eqnarray}&&{\tau }_{\mathrm{emp}}(v)\sim \mathrm{ln}\left[1+\displaystyle \frac{{\tau }_{\mathrm{high}}^{2}+{\tau }_{\mathrm{low}}^{2}}{{\tau }_{\mathrm{high}}+{\tau }_{\mathrm{low}}}\right]\sim {\tau }_{\mathrm{high}}.\end{eqnarray} \tag{ 10 }$$

Equations (9) and (10) can now be used to interpret Figure 9. Equation (9) shows that when the optical depth is large, τ_emp(v) tends to lie near the lower range of τ. Equation (10) shows that when the optical depth is small, τ_emp(v) tends to lie near the upper range of τ. Figure 9 shows that for the low ions such as Si ii and C ii that have direct values of τ > 1, τ_emp indeed underestimates the true value of τ (shown by Equation (9)). Conversely, for intermediate and high-ionization ions such as Si iv, C iv, N v, and O vi, which are optically thin, τ_emp overestimates τ.

The ubiquity of outflows and advancements in telescopes and instrumentation in recent years have made it possible to study this multiphase phenomenon with increasingly large samples of objects and with increasingly detailed spectroscopic coverage. Absorption-line spectra, in particular, have been used to establish an understanding of the kinematics of galactic outflows as a function of different ionic species. In this section, we compare our simulated absorption spectra and kinematics to several representative observational studies. Average characteristics of the galaxies in each study can be found in Table 3.

We begin our comparison with studies that focused on the Na i "D" absorption line (Heckman et al. 2000; Rupke et al. 2002, 2005a, 2005b), which was used to study the warm neutral gas phase in starburst-dominated ultraluminous infrared galaxies (ULIRGs) and infrared galaxies (IRGs). Although we do not attempt to reproduce Na i "D" because of its sensitive dependence on the dust properties of the outflow, these studies are nevertheless a good example of early studies with large samples of objects displaying blueshifted absorption.

Heckman et al. (2000) investigated 32 far-IR-bright starburst galaxies drawn from parent samples in previous studies (Armus et al. 1989; Lehnert & Heckman 1995). The authors found that the absorption-line profiles of Na i D in these outflow sources exhibit high maximum velocities that range from 400 to 600 km s⁻¹. In comparison to our lowest-energy ions, we find that our maximum velocities for Si ii of 400 km s⁻¹ and for C ii of 448 km s⁻¹ are within the range of velocities computed in their study, although our v₉₀ values tend to be significantly lower.

Using the Echellette Spectrograph and Imager (ESI) instrument on Keck II, Rupke et al. (2002) studied 11 ULIRG from the IRAS 1 Jy survey that have visible Na i D absorption. The authors measured a "typical" outflow speed of 300 km s⁻¹, which is consistent with our low ion values for v₉₀, but significantly higher than our values for v_central. Rupke et al. (2005a, 2005b) studied 78 ULIRGs and IR galaxies at z < 0.5. Because of the large sample size, the authors were able to study the evolution of winds as a function of host galaxy properties. The sample was split into three different categories: IRGs (z < 0.5), low-z ULIRGs (z < 0.25), and high-z ULIRGs (0.25 < z < 0.50). ULIRGs (L_IR > 10¹² L_⊙) are host to starbursts and power star formation with the large amount of dense molecular gas found in their cores. By contrast, IRGs (10¹⁰ L_⊙ < L_IR < 10¹² L_⊙) host fewer starbursts and have a lower wind detection rate than ULIRGs (Heckman et al. 2000; Rupke et al. 2002; Martin 2005). Each of the three samples were selected from three different surveys; the IRGs from the Infrared Astronomical Satellite (IRAS) Revised Bright Galaxy Sample (RBGS) and Warm Galaxy Sample (WGS), the low-z ULIRGs from the IRAS 1 Jy survey, and the high-z ULIRGs from the FIRST/FSC survey. We compare our maximum velocities for Si ii and C ii with the average maximum velocities for the three samples, which are 308, 401, and 359 km s⁻¹ for IRGs, low-z ULIRGs, and high-z ULIRGs, respectively. Our maximum velocity for Si ii (400 km s⁻¹) closely matches that of the low-z ULIRGs, while our maximum velocity for C ii (448 km s⁻¹) exceeds the average maximum velocity computed in this study for all three samples.

Starting with stacks of galaxies at intermediate redshift and later individual galaxies at lower redshifts, Weiner et al. (2009), Rubin et al. (2010, 2014), and Heckman et al. (2015) used starburst galaxies to study UV absorption lines of the warm ionized gas (10⁴–10⁵ K) in outflows. Weiner et al. (2009) studied Mg ii absorption in the stacked spectra of 1406 starburst galaxies at z ∼ 1.4 from the DEEP2 redshift survey. With an ionization potential of 15.0 eV, Mg ii does not photodissociate as easily as Na i D, which leads to smaller ionization corrections. This study found central outflow velocities that range from 250 to 300 km s⁻¹. Our v_central for Si ii, C ii, Si iv, and C iv are 132, 144, 156, 156 km s⁻¹, respectively, which are consistently lower than the velocities found in this study. In a similar study, Rubin et al. (2010) investigated Mg ii and Fe ii absorption in the stacked spectra of 468 galaxies from the Team Keck Treasury Redshift Survey (TKRS) at slightly lower redshift. The authors found central velocity offsets of ∼250 km s⁻¹ for Fe ii and Mg ii, with slightly larger offsets for Mg than for Fe. These values are again slightly higher than our v_central values for the low ions.

Rubin et al. (2014) used redshift surveys of the Great Observatories Origins Deep Survey (GOODS) fields and the Extended Groth Strip (EGS) to analyze the individual spectra of 105 galaxies using the Mg ii (λ2796 and λ2803) and Fe ii (λ2586 and λ2600) doublet absorption-line profiles at 0.3 < z < 1.4. Two distinct models were used in this study in order to quantify the kinematics and strength of each line profile. The "one-component" model follows the same approach as Rupke et al. (2005b) and parameterizes the normalized flux as a function of wavelength. The "two-component" model assumes that the same line profile comes from two velocities as opposed to one. We compare our v_central with the two-component model, for which most of the calculated v_central values are <150 km s⁻¹, and find that our values for Si ii, C ii, Si iv, and C iv of 132, 144, 156, 156 km s⁻¹, respectively, are within the range of velocity values calculated in this study.

Heckman et al. (2015) studied the kinematics of the warm gas phase found in supernova-driven winds of 39 low-redshift (z < 0.2) objects using UV absorption lines. This study used two samples of galaxies: the stacked spectra of 19 galaxies observed with the Far Ultraviolet Spectroscopic Explorer satellite (FUSE), and the individual spectra of 21 Lyman Break Analogs (LBAs) observed with COS on HST. We compare our absorption-line profiles of Si ii, C ii, and Si iv with those computed in this study and find that our v_min values of 84, 96, 133 km s⁻¹ are systematically lower than those found in this study. The v_min values that Heckman et al. (2015) find for the same species (Si ii, C ii, and Si iv) are 200, 150, and 300 km s⁻¹, respectively.

Using COS spectra, Chisholm et al. (2017) investigated seven starburst galaxies using UV absorption lines. Using the Si iv doublet, they derive and solve a system of two equations for the velocity-resolved optical depth and covering fraction, as described in Section 3. We compare our optical depth and covering fraction results for Si iv to those from this study. The peak τ values for Si iv in this study range from τ ∼ 0.5–2.7, comparable to our τ_emp value for Si iv, which peaks at 0.75. A notable difference between our work and this study is the assumption in Chisholm et al. (2017) that the Si iv absorption is produced exclusively by cool photoionized gas, while we assume that it is produced exclusively by warm collisionally ionized gas. Our covering fractions are of course much smaller than those computed in this study due to the small area of the cloud in our simulation.

In a particularly instructive single-object study, Chisholm et al. (2018) used data from the Magellan Evolution of Galaxies Spectro-scopic and Ultraviolet Reference Atlas (MEGaSaURA) to study O vi 1032 Å absorption from a gravitationally lensed high-redshift galaxy (z ∼ 2.9) with a star formation rate of >48 M_⊙ yr⁻¹ as measured by spectral energy distribution (SED) fitting. O vi in winds likely probes gas transitioning between a warm 10⁴ K gas and a hot <10⁷ K, allowing the kinematics of distinct gas phases to be studied. This study examined absorption-line profiles of many lower ions (see Table 3) and compared them to O vi, finding two "regimes" for the O vi line—at low velocities, its profile resembles that of the optically thick low ions, while at high velocities, its profile resembles that of the optically thin lines. In general, we find that the optical depth of our lines is smaller than those shown in their work. This is partly due to the fact that the depth of our normalized flux is affected by the size of our simulation and the size of our cloud. When calculating our flux, we average over the entire simulation box, so there are many unobstructed sightlines in our average, leading to shallow absorption lines. However, we can more fairly compare the quantities v_central and v₉₀ from the studied metal absorption lines. In contrast to the previous studies mentioned, when comparing our computed velocity values to the derived quantities from Chisholm et al. (2018), we find that our values do not match the observations well. In this study, the central velocities for the strong lines of Si ii, C iv, and O vi are 201, 130, and 246 km s⁻¹, while our values are systematically lower, at 132, 156, and 180 km s⁻¹, respectively. Our v₉₀ values for the same three species (228, 264, and 300 km s⁻¹) also underpredict those seen in this object—Chisholm et al. (2018) find values corresponding to these same species of 585, 455, and 532 km s⁻¹.

Generally speaking, our lowest-ionization state gas appears to match the kinematics of the low-z observed absorption-line systems better than the high-z systems. Our numerical study is based on the canonical low-z starburst galaxy M82 and assumes a lower star formation rate (and thus less extreme hot wind properties) than many of the high-z systems discussed here, which may account for the better match to the systems observed a lower redshift. On the other hand, our higher-ionization lines consistently underpredict the observed values for all studies. In particular, our higher-ionization lines tend to have lower central and maximum velocities than those that are observed.

There are two possible reasons for this. First, the maximum velocities we observe in these simulations do increase slightly with time. That is, analysis of a later snapshot in the simulation would yield velocity profiles with slightly higher maximum velocities. So it is possible that the cloud gas at this point simply has not had enough time to be accelerated to the maximum velocities observed. However, even at the latest times in these simulations, when the cloud gas has mostly been destroyed, the maximum velocities do not reach the highest values of the observed velocities. In a number of recent studies, several authors have demonstrated that additional momentum can be transferred to gas in the warm photoionized phase and intermediate hotter phases via mixing with the hot wind, and that the amount of momentum transferred is a function of the amount of mixing that has occurred, and thus the distance that the gas has traveled (e.g., Fielding et al. 2018; Gronke & Oh 2018, 1970; Schneider et al. 2020; Vijayan et al. 2020). Because the simulation used in this study consisted of a small (5 pc) cloud in a relatively small (160 pc) box, there is simply not enough room for the higher-ionization state gas to have achieved the velocities commonly observed. In larger-scale simulations, this gas experiences further acceleration, and the higher-ionization state profiles may be a better fit (Schneider et al. 2020). This is an avenue we will explore in future work.

In addition to the many observational studies, the past several years have seen a substantial effort on the theoretical side to better understand the physics of outflows through the use numerical simulations (e.g., Cooper et al. 2009; Scannapieco & Brüggen 2015; Brüggen & Scannapieco 2016; Schneider & Robertson 2017; Cottle et al. 2018; Fielding et al. 2018; Gronke & Oh 2018; Kim & Ostriker 2018; Kim et al. 2020). Most of these studies did not include absorption spectra, and we therefore do not compare the results here, but we can compare to Cottle et al. (2018), who included a thorough examination of blueshifted absorption from an idealized wind simulation very similar to that presented in this work.

Cottle et al. (2018) used adaptive mesh refinement 3D hydrodynamic simulations from Scannapieco & Brüggen (2015) and Brüggen & Scannapieco (2016) to study a cool cloud in a hot wind. These simulations included the effects of radiative cooling, thermal conduction, and an ionizing background characteristic of a starburst galaxy in varying combinations. The authors used the TRIDENT code (Hummels et al. 2017) to produce synthetic column densities of 10 different species from the simulations: H i, Mg ii, C ii, C iii, C iv, Si iii, Si iv, N v, O vi, and Ne viii. The physical volume of the simulation box hosting the interaction between these two phases is −800 × 800 pc along the x–y direction and −400 × 800 pc along the z direction, which is the direction of the hot wind. The simulations used a cloud with an initial temperature of T = 10⁴ K, radius of R_cloud = 100 pc, and a mass density of ρ = 10⁻²⁴ g cm⁻³ (substantially larger than the cloud in this work), and allowed cooling down to 10⁴ K. The study included results at four characteristic times in the cloud destruction that correspond to when 95%, 75%, 50%, and 25% of the mass fraction of the cloud remains at or above one-third of the clouds original density. Here we compare our results to their t₅₀, which is most similar to our 10 t_cc snapshots.

We compare our column densities of C iv and O vi to those computed in this study and find that similar to our findings, O vi tends to be more spatially extended than the lower ions. As in our simulation, the column density profiles of all the ions in Cottle et al. (2018) trace each other fairly well, indicating that the species are spatially related and have a similar creation mechanism. Comparing this to our normalized flux results, we find similar results only for N v—all other ions in our study have much smaller depths than theirs, and their lowest-ionization states are completely saturated. This can primarily be attributed to the much larger cloud used by Cottle et al. (2018), which leads to larger column densities, optical depths, and covering fractions. When comparing our velocities with those in this study, we see that for both our model and Cottle et al. (2018), the velocities increase with ionization state. This stands in contrast to the velocities shown in Chisholm et al. (2018), Table 1, where there is not a clear correlation of increasing ionization states and velocities. Additionally, we compare our covering fraction results to those from this study and find that our values are smaller than those presented in this study. Although the shapes of our velocity profiles differ from those presented in Cottle et al. (2018), we do find similar v_min values—our velocities all fall within their peak range of ∼50–200 km s⁻¹ for the various ions.