A Dynamical Study of Extraplanar Diffuse Ionized Gas in NGC 5775^*

We used the optical and NUV capabilities of RSS (Burgh et al. 2003; Kobulnicky et al. 2003) in longslit mode on SALT (Buckley et al. 2006). We placed one slit on the minor axis (PA = 557, s1) and a second slit parallel to the major axis and offset by Δz = 3.5 kpc on the southern side of the galaxy (PA = 1457, s2; see Figure 1). We used a 125 width for the 8' longslits and the pg2300 grating at an angle of 48875. This produced a dispersion of 0.26 Å pixel⁻¹, a spectral resolution of R = 4830 (σ = 26 km s⁻¹) at Hα, and wavelength coverage from 6100 Å to 6900 Å, including the [N ii]λλ6548, 6583, Hα, and [S ii]λλ6717, 6731 emission lines. We obtained these data between 2017 February 23 and 2017 March 4.

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We also placed a slit perpendicular to the disk at R = 6.5 kpc on the northwest side of the galaxy (PA = 557, s3; see Figure 1). This slit falls along a bright filament detected in Hα imaging by Collins et al. (2000). We obtained two sets of observations at this location: moderate spectral resolution observations of the [O ii]λλ3726, 3729 emission-line doublet (s3uv), and low spectral resolution observations with wavelength coverage from [O ii]λλ3726, 3729 to [N ii]λλ6548, 6583 (s3o). The [O ii] doublet is a powerful eDIG tracer because it is comparably bright to Hα (e.g., Otte et al. 2002) and is found in the NUV regime where the terrestrial sky foreground is minimal compared to the optical.

For the s3uv observations, a 15 slit width and the pg3000 grating at an angle of 3425 yielded a dispersion of 0.24 Å pixel⁻¹ and a spectral resolution of R = 2400 (σ = 53 km s⁻¹) at [O ii]. For s3o, the pg0900 grating at an angle of 13625 produced a dispersion of 0.97 Å pixel⁻¹ and a spectral resolution of R = 620 (σ = 205 km s⁻¹) at [O ii] and R = 1140 (σ = 112 km s⁻¹) at Hα. We obtained these observations between 2015 June 17 and 2015 August 6. For all data, we used 2 × 2 on-chip binning to yield a plate scale of 025 pixel⁻¹. We note the coordinates, position angles, and exposure times in Table 1.

We performed the data reduction using a combination of the PySALT science pipeline⁴ and IRAF software.⁵ We utilized PySALT (Crawford et al. 2010) to apply the bias, gain, and cross-talk corrections, as well as for the image preparation and mosaicking. Using the IRAF L.A.Cosmic package (van Dokkum 2001), we removed cosmic rays from the images. With the IRAF tasks noao.twodspec.longslit.identify, reidentify, fitcoords, and transform, we determined the dispersion solution using Ar comparison lamp spectra for s1 and s2. ThAr and Ar comparison lamp spectra were used for the low and moderate spectral resolution observations of s3.

In s1 and s2, there is a count background of currently unknown origin that varies along both the spatial and spectral axes. The presence of this background—identified as elevated counts above the bias—on both the illuminated and non-illuminated portions of the CCD chip confirm its origin as separate from the sky continuum. It contributes as much as 85% of the sky continuum at the blue end of the spectral range, but less than 20% of the sky continuum near the emission lines of interest. Due to the difficulty in separating the contributions from this background, the sky, and the galaxy, we fit and remove all three contributions to the continuum simultaneously. This is done by modeling the continuum in the spectral direction along every row of pixels in the two-dimensional spectrum using a fifth-order Chebyshev function in the IRAF task noao.twodspec.longslit.background. We assume that the unidentified background, sky, and galaxy continuum all contribute Poisson noise in the error estimation.

Our approach to sky-line subtraction differed depending on the slit position. For s1 and s3, we created median sky spectra from the ends of the slits that were free from galaxy emission. Before performing the sky subtraction, we scaled the sky spectrum by a multiplicative factor that we allowed to vary in the spatial dimension based on the relative strength of the sky lines across the slit. For s2, we did not know beforehand what fraction of the slit would be filled with galaxy emission. We thus obtained a single separate sky observation immediately following the first object observation along a telescope track that replicated the object track, exposure time, and instrument setup. Based on the relative intensities of the sky lines in the object and sky frames, we scaled the sky observation by a multiplicative factor before subtracting it from the object observations. Due to the count background mentioned previously, we fit and removed the continuum from both the sky and object frames before performing the sky-line subtraction.

We stacked the sky-subtracted science frames by aligning them in the spatial dimension based on the location of the peak Hα or [O ii] emission. We then used the IRAF task images.immatch.imcombine to perform a median combine of the images with median scaling and weighting. To extract individual spectra, we performed a median combine over an aperture of 11 pixels; this is a compromise between optimizing the spatial resolution (∼385 pc aperture⁻¹) and the signal-to-noise ratio (S/N), while also mitigating the effects of the curvature of the spectral axis with respect to the CCD chip. We calculated the Poisson error on the raw data frames and propagated the uncertainty through the reduction and analysis.

Using observations obtained on 2016 March 29 and 2017 February 25, we performed the relative flux calibration for s3o and s1/s2 using the spectrophotometric standard stars Hiltner 600 and HR5501, respectively. No relative flux calibration was performed for s3uv due to the small wavelength range of interest around the [O ii] doublet.

Absolute flux calibration cannot be performed with SALT alone due to the time-varying collecting area. We calibrated the Hα intensities along the minor axis using calibrated Hα narrow-band imaging obtained from the Hubble Legacy Archive⁶ (PI: Rossa; Proposal ID: 10416). The observations were taken using ACS/WFC on the Hubble Space Telescope (HST) with the f658n filter. We convolved the image with a two-dimensional Gaussian with full width at half maximum (FWHM) equal to the average seeing at the SALT site (FWHM = 15) using the IDL function Gauss_smooth.

To determine the Hα calibration factor, we computed the mean flux over the bandpass for each extracted spectral aperture in the HST data using the PHOTFLAM keyword. We then compared this to the mean flux in the sky-subtracted SALT spectra convolved with the HST bandpass. We performed the analysis within $| z| \leqslant 5\,\mathrm{kpc}$, but we restricted our determination of a median calibration factor to within $| z| \leqslant 2\,\mathrm{kpc}$ due to declining S/N at large z. The SALT-RSS slit width is sampled by 25 HST pixels, a sufficient number to avoid an infinite aperture correction. We do not account for uncertainty in the flux calibration in the error budget.

We determined the detection limits for emission lines as follows. We identified statistically significant fluctuations in the spectra by first fitting and removing any remaining continuum; the fit was performed by masking emission lines and smoothing the spectrum with a broad Gaussian kernel (σ ≳ 15 Å). We then divided the spectrum into intervals equal to the expected FWHM of the emission lines (FWHM = 2.5–6 Å). Within each interval, we summed the counts per Å; we then fit the resulting distribution of integrated intensities with a Gaussian function and determined its standard deviation. We defined detections to be intervals whose integrated intensities were statistically significant at the 5σ level.

We characterized the intensities, velocities, and velocity dispersions of detected emission lines by fitting them with single Gaussians using the IDL function gaussfit. The S/N does not permit reliable identification of multiple Gaussian components. The least-squares fitting routine also returns uncertainties on the best-fit parameters. In the Appendix, we show example spectra from s1, as well as the model fits and their residuals. We also include measured intensities, velocities, velocity dispersions, and emission-line ratios in online-only tables.

Due to partial blending of the [O ii] doublet in the s3uv observations, we fit the doublet with a sum of two Gaussians by minimizing the χ² statistic over a parameter grid (${\chi }^{2}={\rm{\Sigma }}\tfrac{{({I}_{\lambda ,\mathrm{obs}}-{I}_{\lambda ,\mathrm{mod}})}^{2}}{{\sigma }_{\mathrm{obs}}^{2}}$, where ${I}_{\lambda ,\mathrm{obs}}$ and ${I}_{\lambda ,\mathrm{mod}}$ are the observed and modeled specific intensities, σ_obs is the uncertainty on the observed quantity, and the summation is over the relevant wavelength bins). We judge by eye that the blended Gaussian fits are only reliable at detection levels of at least 7σ, and thus we only report the results of these fits. The 1σ error bars on the best-fit parameters were determined from the models within ${\chi }^{2}\leqslant {\chi }_{\min }^{2}+{\rm{\Delta }}{\chi }^{2}$, where Δχ² = 3.53 for three free parameters ($\tfrac{{I}_{\lambda 3726}}{{I}_{\lambda \mathrm{3726,3729}}}$, v_{[O ii]}, and σ_{[O ii]}).

All emission-line widths reported in this paper are the standard deviations of the Gaussian fits and are corrected for the instrumental resolution determined from the comparison lamp spectra. The radial velocities are presented as heliocentric velocities calculated using the IRAF task astutil.rvcorrect. Line ratios are corrected for Galactic extinction using the reddening law of Cardelli et al. (1989) assuming R_V = 3.1 and A(V) = 0.115 (Schlafly & Finkbeiner 2011). We do not correct for internal extinction or for the underlying stellar absorption spectrum.

We fit the Hα intensity, I_Hα, as a function of height, z, along the minor axis. The goal of the fitting is to determine the eDIG electron density, n_e(z), and the exponential electron scale height, h_z,e. Since our observations are integrated in galactocentric radius and n_e(z) and h_z,e may depend on R, we take the best-fit values of these parameters as representative of their characteristic values. We perform the fit along the minor axis because Hα imaging indicates a lack of filamentary structure at this location (Collins et al. 2000), giving us the best sense of the vertical structure of the diffuse layer.

We exclude observations within $| z| \leqslant 1\ \mathrm{kpc}$ to avoid contamination by H ii regions, dust extinction, and underlying stellar absorption in the disk. There is evidence for extraplanar dust in NGC 5775, including polycyclic aromatic hydrocarbon (PAH) and H₂ emission with scale heights of $\sim 0.7\mbox{--}1.1\,\mathrm{kpc}$ (Rand et al. 2011). Molecular gas and dust are also detected to $| z| \leqslant 5\,\mathrm{kpc}$ in discrete locations that appear to coincide with H i supershells (Lee et al. 2002; Brar et al. 2003); however, no such features are seen along the minor axis at the location of s1. Thus, we assume that the impact of dust extinction on the measured eDIG scale height and density distribution above $| z| \sim 1\,\mathrm{kpc}$ is minor.

We perform the fitting using the IDL function mpfitfun. This routine performs a Levenberg–Marquardt least-squares fit of a user-supplied function to a data set. We fit a single exponential function of the form

$$\begin{eqnarray}&&{I}_{{\rm{H}}\alpha }(z)={I}_{{\rm{H}}\alpha }(0){e}^{-| z| /{h}_{z}},\end{eqnarray} \tag{ 1 }$$

as well as a double exponential function given by

$$\begin{eqnarray}&&{I}_{{\rm{H}}\alpha }(z)={I}_{{\rm{H}}\alpha ,1}(0){e}^{-| z| /{h}_{z,1}}+{I}_{{\rm{H}}\alpha ,2}(0){e}^{-| z| /{h}_{z,2}}.\end{eqnarray} \tag{ 2 }$$

Here, ${I}_{{\rm{H}}\alpha }(0)$ is the intensity of the eDIG layer at z = 0 kpc and h_z is the emission scale height. We associate components 1 and 2 with the thick disk and the halo, respectively. As shown in Figure 2, the double exponential provides a much better fit to the intensity profile than the single exponential at large z.

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From the I_Hα(z) profile, we can estimate n_e(z) as follows. I_Hα(z) depends on n_e(z), the electron temperature, T₄, and the volume filling factor, ϕ, according to

$$\begin{eqnarray}&&{I}_{{\rm{H}}\alpha }(z)=\displaystyle \frac{\int \phi {n}_{e}{\left(z\right)}^{2}{dl}}{2.75{T}_{4}^{0.9}}.\end{eqnarray} \tag{ 3 }$$

Using standard units for the emission measure, I_Hα(z) is measured in Rayleighs, $\phi {n}_{e}^{2}$ is given in cm⁻⁶, T₄ has units of 10⁴ K, and the integral is performed over the line of sight ($\int {dl}=L$ for L in parsecs) (e.g., Haffner et al. 1998).

If ϕ and n_e are assumed to be constant along a given line of sight, then we can express the observable quantity $\phi {n}_{e}{(z)}^{2}$ as

$$\begin{eqnarray}&&\phi {n}_{e}{\left(z\right)}^{2}=\displaystyle \frac{{I}_{{\rm{H}}\alpha }(z)(2.75{T}_{4}^{0.9})}{L}.\end{eqnarray} \tag{ 4 }$$

We take the radial extent of the eDIG layer determined by Collins et al. (2000), R = 14 kpc, to estimate L = 2R = 28 kpc (note that R has been adjusted for D).

We do not include any radial dependence, such as a radial scale length of the form ${n}_{e}(R)\propto {e}^{-R/{h}_{R}}$, for the derived densities. Evidence for such a dependence is not clear from existing imaging and spectroscopy. The Hα imaging of Collins et al. (2000) indicates that the eDIG morphology is largely filamentary, with local density enhancements dominating over large-scale trends. The radial density profile derived from Fabry–Perot spectroscopy by Heald et al. (2006) also suggests a clumpy rather than smooth structure. In light of this, we neglect a formal radial density dependence in our analysis and instead briefly consider the impact of including an eDIG radial scale length, h_R, on the success of the dynamical equilibrium model in Section 4.5.

The best-fit values of ϕn_e(0)² and ${h}_{z,e}$ for the single, thick disk, and halo components are given in Table 2. Note that due to the n_e² dependence of ${I}_{{\rm{H}}\alpha }$, the exponential electron scale height is twice the emission scale height, or $2{h}_{z}={h}_{z,e}$. We quantify the uncertainties on the best-fit values of ϕn_e(0)² and ${h}_{z,e}$ by perturbing the values of I_Hα by increments randomly drawn from Gaussian distributions with standard deviations equal to their 1σ error bars. We then refit the perturbed intensity profile and calculate the difference between the original and perturbed best-fit values. We repeat this process until the median differences converge (10³ iterations); these median values are the uncertainties reported in Table 2. Note that this approach does not account for systematic effects such as the deviation of the inclination angle from 90^◦ and uncertainty in the flux calibration.

Table 2.  Hα Intensity Profile

Model	${h}_{z,e,1}$	$\phi {n}_{e,1}{(0)}^{2}$	${h}_{z,e,2}$	$\phi {n}_{e,2}{(0)}^{2}$
	(kpc)	(cm−6)	(kpc)	(cm−6)
Thick disk (SW)	1.4 ± 0.009	0.029 ± 0.0004	⋯	⋯
Thick disk (NE)	0.8 ± 0.04	0.184 ± 0.003	⋯	⋯
Thick disk + halo (SW)	0.8 ± 0.04	0.069 ± 0.004	3.6 ± 0.2	0.003 ± 0.0004
Thick disk + halo (NE)	0.6 ± 0.04	0.302 ± 0.007	7.5 ± 0.4	0.0006 ± 0.00004

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We also compare our best-fit parameters to past measurements of ${h}_{z,e}$ and $\phi {n}_{e}{(0)}^{2}$ in Table 3. Our scale heights are broadly consistent with the results of these single-component fits, although it is clear that variation exists as a function of R. Our minimum thick-disk scale height (${h}_{z,e}=0.6$ kpc) and our maximum halo scale height (h_z,e = 7.5 kpc) bracket existing measurements of the scale height at various R. Thus, by testing a dynamical equilibrium model of each of our thick-disk and halo components both separately and together, we will assess the success of this model over a representative range of choices for h_z,e.

Table 3.  Past Measurements of Electron Scale Height and Density

${h}_{z,e}$	$\phi {n}_{e}{(0)}^{2}$	Location	Reference
(kpc)	(cm−6)
1.6–1.8	0.0065–0.01	R = 0–2 kpc (−z)	(1)
1.8	0.0055	R = −(8 − 10) kpc	(1)
6.0	⋯	Hα filament (NE side)	(1)
5.0	⋯	Hα filaments (SE, SW sides)	(1)
4.6	⋯	R = 4.5 kpc (+z)	(2)
4.6	⋯	R = 4.5 kpc (−z)	(2)
5.0	⋯	R = −2.8 kpc (+z)	(2)
3.6	⋯	R = −2.8 kpc (−z)	(2)
1.6	⋯	SW side	(3)
1.2	⋯	NE side	(3)

References. (1) Collins et al. (2000), (2) Collins & Rand (2001), (3) Heald et al. (2006).

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We estimate the total mass in the eDIG layer from the observed density distribution and an assumed volume filling factor. For ϕ = 1 (ϕ = 0.1), we find M_eDIG = 1.1 × 10¹⁰ M_⊙ (M_eDIG = 3.5 × 10⁹ M_⊙) on the northeast side of the disk and M_eDIG = 8.4 × 10⁹ M_⊙ (M_eDIG = 2.6 × 10⁹ M_⊙) on the southwest side. Consequently, 65% (54%) of the mass is found in the thick disk on the northeast (southwest) side. These exceed previous estimates of the masses of eDIG layers in other galaxies by more than an order of magnitude (e.g., Dettmar 1990; Boettcher et al. 2017). They are also comparable to the total H i mass (M_{H i} = 9.1 ± 0.6 × 10⁹ M_⊙; Irwin 1994) and more than the total hot halo mass (M_hot = 5.3 × 10⁸ M_⊙; Li et al. 2008).

This suggests that we have overestimated the eDIG mass, implying the need for a very small volume filling factor. Assuming pressure equilibrium between the warm and hot phases does indeed imply an eDIG filling factor of ϕ ∼ 0.1 (Li et al. 2008). Additionally, if the eDIG density decreases exponentially as a function of R, then a reasonable choice of radial scale length (h_R ∼ 3–5 kpc) decreases the total mass estimate by ∼50%.

We use the emission-line ratios to gain a qualitative sense of the physical conditions in the eDIG layer. The emission-line properties have been previously studied in detail by Tüllmann et al. (2000), Collins & Rand (2001), Otte et al. (2002), and others; we confirm their findings at the location of s3, and expand on their results at the locations of s1 and s2. Note that internal extinction and underlying stellar absorption may affect observed line ratios at small z; however, we emphasize interpretation of the line ratios at $| z| \geqslant 1\,\mathrm{kpc}$, where we assume these effects are minimal.

The [O ii]λ3727/Hα, [N ii]λ6583/Hα, and [S ii]λ6717/Hα line ratios depend on temperature, ionization fraction, and elemental abundance as follows (Haffner et al. 1999; Osterbrock & Ferland 2006):

$$\begin{eqnarray}\begin{array}{rcl}\displaystyle \frac{I([{\rm{O}}\,{\rm{II}}]\lambda 3727)}{I({\rm{H}}\alpha )} & = & (4.31\times {10}^{5}){T}_{4}^{0.4}{e}^{-3.87/{T}_{4}}\\ & & \times \,\left(\displaystyle \frac{{{\rm{O}}}^{+}}{{\rm{O}}}\right)\left(\displaystyle \frac{{\rm{O}}}{{\rm{H}}}\right){\left(\displaystyle \frac{{{\rm{H}}}^{+}}{{\rm{H}}}\right)}^{-1},\end{array}\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}\begin{array}{rcl}\displaystyle \frac{I([{\rm{N}}\,{\rm{II}}]\lambda 6583)}{I({\rm{H}}\alpha )} & = & (1.62\times {10}^{5}){T}_{4}^{0.4}{e}^{-2.18/{T}_{4}}\\ & & \times \,\left(\displaystyle \frac{{{\rm{N}}}^{+}}{{\rm{N}}}\right)\left(\displaystyle \frac{{\rm{N}}}{{\rm{H}}}\right){\left(\displaystyle \frac{{{\rm{H}}}^{+}}{{\rm{H}}}\right)}^{-1},\end{array}\end{eqnarray} \tag{ 6 }$$

and

$$\begin{eqnarray}\begin{array}{rcl}\displaystyle \frac{I([{\rm{S}}\,{\rm{II}}]\lambda 6717)}{I({\rm{H}}\alpha )} & = & (7.67\times {10}^{5}){T}_{4}^{0.307}{e}^{-2.14/{T}_{4}}\\ & & \times \,\left(\displaystyle \frac{{{\rm{S}}}^{+}}{{\rm{S}}}\right)\left(\displaystyle \frac{{\rm{S}}}{{\rm{H}}}\right){\left(\displaystyle \frac{{{\rm{H}}}^{+}}{{\rm{H}}}\right)}^{-1}.\end{array}\end{eqnarray} \tag{ 7 }$$

We assume ${{\rm{H}}}^{+}/{\rm{H}}\sim 1$ and N⁺/N ∼ 0.8 under typical DIG conditions (Reynolds et al. 1998; Sembach et al. 2000). We also assume O⁺/O = N⁺/N given their similar first ionization potentials. Though the relatively high second ionization potentials of N and O (29.6 and 35.1 eV, respectively) suggest that N⁺⁺/N and O⁺⁺/O are low in the DIG, the lower second ionization potential of S (23.3 eV) means that S⁺⁺/S may be considerable. Thus, we consider models with a range of S⁺/S here. We adopt the solar photospheric abundances of Asplund et al. (2009): N/H = 6.8 × 10⁻⁵, S/H = 1.3 × 10⁻⁵, and O/H = 4.9 × 10⁻⁴. We assume that the emission from different atomic species arises cospatially, and that the temperature, ionization, and abundances do not vary significantly along a given line of sight.

Given these assumptions, we compare the observed and expected emission-line ratios for a range of T₄ and ${{\rm{S}}}^{+}/{\rm{S}}$. In the top panel of Figure 3, we plot [N ii]λ6583/Hα versus [S ii]λ6717/Hα observed along the minor axis in s1. We also show the median and median absolute deviation of these line ratios observed in s2; these ratios do not show a strong trend with slit position at this location. Both line ratios clearly increase as a function of z, a trend commonly observed in the eDIG of edge-on galaxies and often interpreted as evidence of increasing T₄ with z (e.g., Haffner et al. 1999). At $| z| \gt 2\,\mathrm{kpc}$, the line ratios suggest a temperature of T₄ = 0.8–1.0 and an ionization fraction of S⁺/S ∼ 0.5–0.75. There is also a trend toward increasing S⁺/S with z as S⁺⁺ becomes S⁺ in a more dilute radiation field.

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In the bottom panel of Figure 3, we plot [N ii]λ6583/Hα versus [O ii]λ3727/Hα observed along the filament in s3. Since the [O ii] doublet is not resolved in these observations, the [O ii] intensity is integrated over both lines. As N⁺/N and O⁺/O are thought to be comparable in the DIG, these line ratios depend only on temperature for fixed abundances. We compare the observed and predicted line ratios for a range of temperatures, and we find that the observed ratios fall at lower values of [O ii]λ3727/Hα than expected for a given value of [N ii]λ6583/Hα. This may be due to selective internal extinction reddening the [O ii]λ3727/Hα line ratios within the dusty, thick-disk ISM. Additionally, both line ratios may be affected by underlying stellar absorption that reduces the measured Hα intensity. However, it is not clear that the observed and expected line ratios converge at large z where these effects are likely minimal. Thus, it is possible that enhancement in the N abundance with respect to O is also responsible.

From Figure 3, we adopt an eDIG temperature of T₄ = 0.9 for the rest of this paper. As we will see in Section 3.3.2, the turbulent velocity dispersion far exceeds the thermal velocity dispersion, and thus uncertainty in the eDIG temperature on the order of 10%–20% is unimportant for our dynamical equilibrium study. Out of the disk, the observed [S ii]λ6717/[S ii]λ6731 ∼ 1.5 in s1 and [O ii]λ3729/[O ii]λ3726 ∼ 1.5 in s3uv demonstrate that the eDIG is in the low-density limit as expected (e.g., Osterbrock & Ferland 2006).

The emission-line ratios of eDIG layers are also of interest due to the challenge that they present to photoionization models (e.g., Collins & Rand 2001). We comment briefly on that here. In Figure 4, we show [S ii]λ6717/[N ii]λ6583 and [O i]λ6300/Hα as functions of z along the minor axis (s1) and [O iii]λ5007/Hα as a function of z in s3. (Note that detection of the [O i] line in s3 is impeded by sky-line residuals. We also choose to take the ratio of [O iii] to Hα instead of the more traditional Hβ because the latter is not detected at large z and is contaminated by the underlying stellar absorption line at low z).

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In a photoionization model, we expect [S ii]λ6717/[N ii]λ6583 to increase with distance from the ionizing source as ${{\rm{S}}}^{++}\to {{\rm{S}}}^{+}$. We do observe an increase in [S ii]/[N ii] as a function of z. However, the rise in [O iii]λ5007/Hα with z is associated with a need for an additional source of heating and/or ionization, such as shocks or turbulent mixing layers (e.g., Collins & Rand 2001). The presence of shocks is further suggested by the rising [O i]λ6300/Hα. Since the neutral fractions of O and H are coupled via charge exchange, the presence of [O i] emission suggests a multiphase medium, as is found in shock-compressed regions (e.g., Collins & Rand 2001). The need for an additional source of heating and/or ionization that behaves differently than photoionization will be relevant as we consider the dynamical state of the eDIG layer in Sections 4 and 5.

From Figure 4, we can also verify the validity of our assumption that N⁺/N is high by confirming that N⁺⁺/N must be low. Due to the similarly high second ionization potentials of O and N, a low O⁺⁺/O suggests a similarly low N⁺⁺/N. Our observed [O iii]λ5007/Hα line ratios and the electron temperature deduced from Figure 3 (T₄ = 0.9) imply a median value of O⁺⁺/O = 0.1, confirming a low value of N⁺⁺/N. (We thank R. Rand for this suggestion).

3.3.1. Radial Velocities

The heliocentric, line-of-sight Hα velocity, v_Hα, observed in s2 is shown in Figure 5. The Hα rotation curve at z = −3.5 kpc is compared to a model of the H i rotation curve at z = 0 kpc from Irwin (1994). West and east of the minor axis, v_Hα is closer to the systemic velocity than v_{H i} by a median Δv = 71 km s⁻¹ and Δv = 54 km s⁻¹ at $| R| \geqslant 3\,\mathrm{kpc}$, respectively. The eDIG layer thus shows the signature of a lagging gaseous halo that arises as a consequence of the conservation of angular momentum in a disk–halo flow. The larger asymmetric drift of the warmer gas may also contribute to the velocity discrepancy between the two phases.

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If the line-of-sight velocity samples gas at the tangent point and is thus a measure of the rotational velocity, then this implies a rotational velocity gradient of Δv = −20.3 km s⁻¹ kpc⁻¹ and Δv = −15.4 km s⁻¹ kpc⁻¹ for positive and negative R, respectively. However, this is significantly steeper than the −1 km s⁻¹ arcsec⁻¹ (−7 km s⁻¹ kpc⁻¹) determined by Heald et al. (2006) for this galaxy. These authors demonstrate that quantification of the true rotational velocity gradient is dependent on robust modeling of a three-dimensional, rotating disk in which the density distribution and rotation curve are allowed to vary with distance from the midplane. Thus, we avoid overinterpreting the relatively steep velocity gradients observed here, as they may be biased by local filamentary structure and may not reflect the true rotational velocity of the eDIG layer.

The top panel of Figure 6 shows v_Hα as a function of z observed on the minor axis in s1. There is a spread in v_Hα at small z before it approaches v_sys at larger z. At the largest z, v_Hα is blueshifted with respect to v_sys, moving away from the systemic velocity at increasing distances from the midplane. If the eDIG layer is cylindrically rotating, then we would expect v_Hα ∼ v_sys along the minor axis. Although the spread in v_Hα at small z is likely due to the deviation of the inclination angle from i = 90°, the blueshifted velocities observed at large z merit further discussion in Section 5.

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The bottom panel of Figure 6 again shows v_Hα as a function of z, here observed perpendicular to the disk at R = 6.5 kpc in s3. As previously found at this location by Rand (2000), v_Hα climbs steadily from the rotational velocity in the disk, v_disk ∼ 1550 km s⁻¹, to the systemic velocity, v_sys = 1681 km s⁻¹, as z increases (v_sys is derived using the optical convention from the H i redshift of de Vaucouleurs et al. 1991). v_Hα reaches v_sys around z = 5 kpc, displaying small variations around the systemic velocity at larger z. A similar trend is seen on the southwest side of the galaxy, although v_Hα approaches v_sys at a slower rate and does not reach v_sys over the spatial extent of our emission-line detections. Within $| z| \leqslant 5\,\mathrm{kpc}$, the velocity gradients are approximately Δv ∼ −25 km s⁻¹ kpc⁻¹ and Δv ∼ −6 km s⁻¹ kpc⁻¹ on the northeast and southwest sides, respectively. While this is consistent with the presence of a rotational velocity gradient, we again caution against quantifying this gradient without additional modeling.

It is interesting to ask whether there is any evidence of perturbations to the line-of-sight velocities due to the interaction with NGC 5774. The most likely place to find such evidence would be in s2 where the slit extends across the H i bridge between the galaxies. However, we only detect emission to R = 13.5 kpc on this side of the galaxy, suggesting that any ionized gas in the bridge has too low surface brightness to be detected here. The blueshifted velocities at large z on the minor axis are the subject of further discussion in Section 5, including their possible relationship to an interaction.

3.3.2. Turbulent Velocity Dispersion

The Hα emission-line widths, σ_Hα, are shown as a function of z along the minor axis in Figure 7. These line widths refer to the standard deviation of the Gaussian velocity distribution. In the disk, where we expect σ_Hα to be characteristic of H ii regions (σ_{H ii} ∼ 20 km s⁻¹), the line width is limited by the spectral resolution (σ_res ∼ 26 km s⁻¹). However, σ_Hα smoothly increases with z, reaching values as high as ∼70 km s⁻¹ by $| z| =5\,\mathrm{kpc}$. The median and median absolute deviation observed in s2 (z = −3.5 kpc) is σ_Hα = 58 ± 11 km s⁻¹; there is no obvious trend in σ_Hα with R.

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This is the first clear evidence of an increase in emission-line widths as a function of height above the disk in an eDIG layer. The line widths appear to rise within $| z| \leqslant 4\,\mathrm{kpc}$ and then plateau at some characteristic value. As discussed in Section 3.1, the impact of dust extinction on the observed velocity dispersion is likely to be small, as the increase in σ_Hα with z is observed at several dust scale heights above the disk. Several factors contribute to the line width, including thermal, turbulent, and noncircular motions (note that we have already corrected for the spectral resolution, and rotational motions are minimized on the minor axis). The thermal line width of a gas with T₄ ∼ 0.9 is small compared to the observed line widths (σ_th ∼ 10 km s⁻¹); in the absence of information about contributions from noncircular motions, we take the observed line widths as an upper limit on the turbulent velocity dispersion in the eDIG layer. Here, "turbulence" refers to any random gas motions, including the cloud–cloud velocity dispersion. We discuss possible origins for the z-dependence of σ_Hα in Section 5.

From Equation (10), the thermal gas pressure is given by ${P}_{\mathrm{th}}(z)={\sigma }_{\mathrm{th}}^{2}\rho (z)$, where the thermal velocity dispersion can be expressed as ${\sigma }_{\mathrm{th}}=\sqrt{\tfrac{{kT}}{\alpha {m}_{p}}}$. Here, k is the Boltzmann constant, m_p is the proton mass, and α is a scaling factor. We take α = 0.62 assuming that the gas is 9% He by number, with 100% and 70% of the H and He ionized, respectively (Rand 1997, 1998). For a gas with T₄ = 0.9 (Section 3.2), we find σ_th = 11 km s⁻¹. Assuming that σ_th does not change substantially with z, then the thermal pressure gradient is given by:

$$\begin{eqnarray}&&\displaystyle \frac{{{dP}}_{\mathrm{th}}}{{dz}}=-\displaystyle \frac{{\sigma }_{\mathrm{th}}^{2}}{{h}_{z}}\rho (z).\end{eqnarray} \tag{ 11 }$$

Like the thermal gas pressure, the turbulent gas pressure is given by ${P}_{\mathrm{turb}}{(z)={\sigma }_{\mathrm{turb}}(z)}^{2}\rho (z)$, except here we allow the velocity dispersion to vary with z. By eye, we fit the following functional form to σ_turb(z), assuming isotropic turbulence (see the green dotted line in Figure 7):

$$\begin{eqnarray}{\sigma }_{\mathrm{turb}}(z)=\left\{\begin{array}{ll}{\sigma }_{0}+{m}_{\sigma }z, & \mathrm{if}\ 0\ \mathrm{kpc}\leqslant | z| \leqslant 4\ \mathrm{kpc}\\ {\sigma }_{1}, & \mathrm{if}\ | z| \gt 4\ \mathrm{kpc}.\end{array}\right.\end{eqnarray} \tag{ 12 }$$

Here, we use ${\sigma }_{0}=20$ km s⁻¹, m_σ = 10 km s⁻¹ kpc⁻¹, and σ₁ = 60 km s⁻¹.

Note again that the observed σ(z) is an upper limit to the true σ_turb(z) due to possible contributions from noncircular motions. We have also not corrected the observations for the (small) contribution from thermal motions. This yields the following turbulent pressure gradient:

$$\begin{eqnarray}&&\begin{array}{l}\displaystyle \frac{{{dP}}_{\mathrm{turb}}}{{dz}}\\ =\,\left\{\begin{array}{ll}2{m}_{\sigma }{\sigma }_{\mathrm{turb}}(z)\rho (z)-\displaystyle \frac{{\sigma }_{\mathrm{turb}}{\left(z\right)}^{2}}{{h}_{z}}\rho (z), & \mathrm{if}\ 0\ \mathrm{kpc}\leqslant | z| \leqslant 4\ \mathrm{kpc}\\ -\displaystyle \frac{{\sigma }_{1}^{2}}{{h}_{z}}\rho (z), & \mathrm{if}\ | z| \gt 4\ \mathrm{kpc}.\end{array}\right.\end{array}\end{eqnarray} \tag{ 13 }$$

To estimate the magnetic field and cosmic-ray pressure gradients, we turn to the radio continuum observations discussed in Section 1. Krause et al. (2018) characterize the magnetic field strengths in the disks and the synchrotron scale heights of galaxies in the CHANG-ES sample, including thin disk and halo components. For NGC 5775, they find a disk field strength of B₀ = 14.8 μG and halo synchrotron scale heights of h_z,syn = 1.46 ± 0.13 kpc (C-band D-array; centered at 6 GHz) and h_z,syn = 1.98 ± 0.35 kpc (L-band C-array; centered at 1.5 GHz). We discuss the thin synchrotron disk in Section 5.

To estimate the magnetic pressure gradient in the halo of NGC 5775, we assume energy equipartition between the magnetic field and cosmic-ray energy densities (see Section 5 for a discussion of the merits of this assumption). Under this assumption, the synchrotron scale height is related to the magnetic field scale height via the nonthermal spectral index: h_z,B ∼ h_z,syn(3 + α) (Beck 2015). Note that h_z,B may be even larger due to energy losses of cosmic-ray electrons lowering the synchrotron scale height.

For α = 1.09 (Krause et al. 2018), h_z,B = 6 kpc and h_z,B = 8.1 kpc determined from the 6 GHz and 1.5 GHz observations, respectively. We adopt the latter value here, as lower frequency emission arises from lower energy cosmic rays that undergo fewer losses than their higher energy counterparts. The vertical distribution of lower-energy cosmic-ray electrons therefore better approximates the distribution of (lossless) cosmic-ray protons; the cosmic-ray pressure, of interest in Section 4.4, arises from this latter component.

We assume a simple, plane-parallel geometry for the halo component of the magnetic field, where

$$\begin{eqnarray}&&B(z)={B}_{0}{e}^{-| z| /{h}_{z,B}}.\end{eqnarray} \tag{ 14 }$$

Therefore, given ${P}_{B}=\tfrac{B{\left(z\right)}^{2}}{8\pi }$, the magnetic pressure gradient can be written as

$$\begin{eqnarray}&&\displaystyle \frac{{{dP}}_{B}(z)}{{dz}}=-\displaystyle \frac{2}{{h}_{B}}{P}_{B}.\end{eqnarray} \tag{ 15 }$$

The observed "X-shaped" morphology of the halo magnetic field suggests that it becomes increasingly vertical at large z (Soida et al. 2011). However, the likely presence of a significant turbulent component to the field mitigates the effect of the field geometry on the magnetic pressure gradient.

To determine the cosmic-ray pressure gradient, we again assume equipartition between the magnetic field and cosmic-ray energy densities. Since the majority of the cosmic-ray energy density is believed to be due to only mildly relativistic protons (Ferrière 2001), we take P_cr = 0.45U_cr = 0.45U_B and find

$$\begin{eqnarray}&&\displaystyle \frac{{{dP}}_{\mathrm{cr}}(z)}{{dz}}=0.45\displaystyle \frac{{{dP}}_{B}(z)}{{dz}}.\end{eqnarray} \tag{ 16 }$$

We first test the dynamical equilibrium model for an initial choice of parameters: a volume filling factor of ϕ = 1 (no gas clumping) and the magnetic field properties discussed in Section 4.3. We restrict our analysis to $| z| \geqslant 1\,\mathrm{kpc}$, as the nature of the gas density profile within $| z| \lt 1\,\mathrm{kpc}$ is not well characterized due to obscuration by dust and H ii regions and the slight inclination of the disk from edge-on. We thus assume that some boundary condition governs the meeting of the eDIG layer with the thin-disk ISM at small z. We analyze each side of the galaxy individually, assessing the dynamical state of the thick disk and halo both together and separately.

We calculate the thermal, turbulent, magnetic field, and cosmic-ray pressure gradients and compare the total observed gradient with the required gradient (in other words, with the right-hand side of Equation (8)). We consider the model satisfied if the observed pressure support equals or exceeds the required support at $| z| \geqslant 1\,\mathrm{kpc}$. We do so at every galactocentric radius between the center and the edge of the eDIG layer (0 kpc ≤ R ≤ 14 kpc, in steps of ΔR = 1 kpc), and we determine the minimum radius at which the dynamical equilibrium model is satisfied, R_eq.

In Figure 8, we present the observed and required pressure gradients at R_eq for each side of the galaxy and each eDIG component considered. The halo components are most easily supported in dynamical equilibrium, with R_eq = 8 kpc (R_eq =9 kpc) on the northeast (southwest) sides of the galaxy. Both thick disk components have a similar result (R_eq = 9 kpc). Combining the components renders the model more difficult to satisfy, pushing R_eq to R_eq = 10 kpc on the northeast side and to R_eq = 11 kpc on the southwest side.

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It is clear that there is insufficient vertical pressure support to satisfy dynamical equilibrium except in the shallowest parts of the galactic gravitational potential. In other words, R_eq is a significant fraction of the radial extent of the eDIG layer for all components considered. The success of such a model thus requires placing the gas in a ring geometry at moderate to large R, perhaps over star-forming spiral arms. It is the magnetic pressure gradient, followed by the cosmic-ray pressure gradient, that provides the most substantial source of vertical support.

Note that there is a discontinuity in $\tfrac{{{dP}}_{\mathrm{turb}}}{{dz}}$ at $| z| =4\,\mathrm{kpc}$, where the turbulent velocity dispersion transitions from a rising to a flat regime. This discontinuity is most prominent in the halo component. At $| z| \leqslant 4\,\mathrm{kpc}$, $\tfrac{{{dP}}_{\mathrm{turb}}}{{dz}}$ is positive; this is because σ(z)² rises more quickly than ρ(z) falls due to the large-scale height of the halo. At $| z| \gt 4\,\mathrm{kpc}$, $\tfrac{{{dP}}_{\mathrm{turb}}}{{dz}}$ becomes negative as σ(z)² becomes constant and ρ(z) continues to fall. The total pressure gradient remains negative at all z due to contributions from the magnetic field and cosmic rays.

From Equation (8), a discontinuity in $\tfrac{{dP}}{{dz}}$ implies a jump in ρ(z) (in this case, an increase in ρ(z) at $| z| =4$ kpc). This is an unstable configuration. Thus, we interpret the total observed pressure gradients in Figure 8 not as the true pressure gradients that we seek to reproduce with a density model, but instead as an indication of the maximum available pressure support in the eDIG layer. This allows us to assess the viability of the dynamical equilibrium model without claiming a precise characterization of the true pressure profile. We also note that the turbulent motions in the halo component may differ from those in the thick disk; since the latter dominate the line profiles, we do not wish to overinterpret $\tfrac{{{dP}}_{\mathrm{turb}}}{{dz}}$ in the halo.

We now explore how variations in ϕ, B₀, and h_z,B affect the success of the dynamical equilibrium model. We vary ϕ from 0.01 (highly clumpy) to 1 (no clumping) and B₀ and h_z,B both by 50% (7.4 μG ≤ B₀ ≤ 22.2 μG, 4.05 kpc ≤ h_z,B ≤ 12.15 kpc). Within this parameter space, we conduct the analysis described above for the thick disk and halo combined and determine the value of R_eq.

We show results in this parameter space in Figure 9 for the northeast (top) and southwest (bottom) sides of the galaxy. In the top two panels for each side, we display R_eq in the ϕ, B₀ (h_z,B = 8.1 kpc) and ϕ, h_z,B (B₀ = 14.8μG) planes. Everywhere in these planes, R_eq ≥ 7 kpc; this confirms the need for a ring geometry for the dynamical equilibrium model to succeed.

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In general, for the gas to be supported at a given galactocentric radius, a higher magnetic field strength (a steeper $\tfrac{{{dP}}_{B}}{{dz}}$) is required for a smaller ϕ (a steeper $\tfrac{d\rho }{{dz}}$). Likewise, a smaller h_z,B (a steeper $\tfrac{{{dP}}_{B}}{{dz}}$) is needed to support the gas given a smaller ϕ. As the eDIG scale height begins to exceed the magnetic scale height, it is more difficult to support the eDIG at $| z| \gt {h}_{z,B}$, and larger values of ϕ are again required.

We briefly consider the impact of a radially dependent eDIG density distribution on the success of the dynamical equilibrium model. For radial dependence of the form ${n}_{e}(R)\propto {e}^{-R/{h}_{R}}$, a reasonable choice of h_R (i.e., a few kpc, comparable to the stellar scale length) has only a small effect on the model's success. For example, a choice of h_R = 4 kpc mildly reduces R_eq to 8 kpc from 10 and 11 kpc for the combined thick disk and halo models on the northeast and southwest sides of the disk, respectively. This minor reduction in R_eq is expected if the gas surface density decreases with R, rendering the model easier to satisfy at large galactocentric radii. In the absence of a comparable radial dependence in the magnetic field strength, such a radial fall-off in the density distribution produces a magnetic pressure comparable to the gas pressure (thermal and turbulent) at small R, but in excess of the gas pressure by an order of magnitude at R = 10 kpc. In a model lacking radial dependence, the magnetic pressure exceeds the gas pressure by a factor of ∼2, more consistent with approximate energy equipartition.

The magnetic buoyancy instability first described by Parker (1966) presents another challenge to the success of our dynamical equilibrium model. Although Parker considered cosmic rays as a fluid with an adiabatic index γ_cr = 0, we allow for cosmic-ray coupling to the gas either via extrinsic turbulence or via the streaming instability for high- and low-energy cosmic rays, respectively (γ_cr = 1.45 given P_cr = 0.45U_cr; Zweibel 2013). This allows the cosmic rays to act toward stabilizing the gas as well as elevating it above its natural scale height.

These considerations yield the following stability criterion (Newcomb 1961; Parker 1966; Zweibel & Kulsrud 1975):

$$\begin{eqnarray}&&-\displaystyle \frac{d\rho }{{dz}}\gt \displaystyle \frac{{\rho }^{2}{g}_{z}}{{\gamma }_{g}{P}_{g}+{\gamma }_{\mathrm{cr}}{P}_{\mathrm{cr}}}.\end{eqnarray} \tag{ 17 }$$

To determine whether the eDIG layer is robust against the instability, we calculate the minimum value of γ_g required to satisfy this criterion for both γ_cr = 0 (no cosmic-ray coupling) and γ_cr = 1.45 (cosmic-ray coupling). An adiabatic index of γ_g = 5/3–2 may be characteristic of the star-forming, turbulent ISM (Zweibel & Kulsrud 1975); however, values as low as γ_g = 1 may be found in the eDIG (Parker 1966). Therefore, we define a stable model as that for which the minimum value of γ_g that satisfies the stability criterion is γ_g ≤ 1.

Heintz & Zweibel (2018) have recently demonstrated the potential importance of cosmic-ray streaming to the stability of the magnetized ISM. They illustrate that inclusion of cosmic-ray streaming can be destabilizing due to cosmic-ray heating. This effect is mitigated in the isothermal case (γ_g = 1). Future work will explore the implementation of cooling and the characteristic wavelength of the instability in the nonlinear regime, potentially shedding light on the impact, if any, of cosmic-ray heating on the electron temperature and/or ionization structure of the eDIG. However, it is important to note that even if a model satisfies the stability criterion above, the model may be unstable if heating via cosmic-ray streaming is important.

We perform the stability analysis between $1\ \mathrm{kpc}\leqslant | z| \,\leqslant 10\ \mathrm{kpc}$. Note that our treatment of the instability is based on a one-dimensional model and may fail at large z. In Figure 10, we present the minimum values of γ_g required to satisfy the stability criterion for the thick disk and the halo, separately and combined. Models with γ_cr = 0 are not stable at all z for the relevant R; thus, it is clear that the cosmic rays must be coupled to the gas to achieve a stable model.

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Allowing γ_cr = 1.45, the thick disk is stable at all radii at which the dynamical equilibrium model succeeds. In contrast, the halo on the northeast (southwest) side of the disk is not stable at all z until R > 14 kpc (R ≥ 10 kpc). The instability of the halo is exacerbated by the large-scale height on the northeast side. A gas cloud perturbed upwards will be buoyant if the rate at which its internal density decreases is faster than the rate at which the background density decreases. This is more likely to occur in a medium in which the gas density profile changes only slowly, rendering the halo less stable than the thick disk. While the coupled cosmic rays can "stiffen" the equation of state of the medium and thus decrease the minimum galactocentric radius at which a stable model can be achieved, this effect is insufficient to produce stable models outside of a thin ring, or at all, on the southwest and northeast sides of the disk, respectively.

We now consider the effect of stability on the parameter space study discussed in the previous section. We ask where in parameter space a stable, successful dynamical equilibrium model is found, and show the results in Figure 9. For the northeast side of the disk, R_eq increases to R_eq ≥ 14 kpc as compared to R_eq ≥ 7 kpc in the slices of parameter space previously considered; this is due to the instability of the halo at large z seen in Figure 10. On the southwest side of the disk, for which the halo scale height is a factor of ∼2 smaller than on the northeast side, the areas of parameter space over which the dynamical equilibrium model succeeds and over which it succeeds and is stable are much more comparable. The instability of the dynamical equilibrium model at almost all galactocentric radii on the northeast side effectively rules out this model for this side of the galaxy.

In Figure 11, we show example spectra from the minor axis on the northeast side of the galaxy (s1). In the top panel, the Gaussian fits for detected Hα and [N ii]λ6583 lines are shown; the corresponding residuals are given in the bottom panel. In general, the emission-line profiles are well characterized by a single Gaussian fit. However, at high S/N, low- and/or high-velocity wings are apparent in some locations. This is particularly evident for the red wing seen in both the Hα and [N ii] residuals at $z=1.2\,\mathrm{kpc}$. While detection of such wings is challenging at high $| z|$ due to the low S/N, the detection of these wings at low $| z|$ suggests the presence of gas at more extreme velocities than are considered in this work. Higher S/N spectra that can better characterize the emission-line wings would help to determine whether there is an additional, low-surface-brightness component with a higher velocity dispersion than quantified here.

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We provide the best-fit Gaussian parameters in machine-readable tables available online (see Tables 4–7). Portions of these tables are given below for guidance with respect to their form and content.

Table 4.  Best-fit Emission-line Properties: s1

z	IHα	${v}_{{\rm{H}}\alpha }$ a	${\sigma }_{{\rm{H}}\alpha }$ b	$\tfrac{[{\rm{O}}\,{\rm{I}}]\lambda 6300}{{\rm{H}}\alpha }$	v[O i]	${\sigma }_{[{\rm{O}}{\rm{I}}]}$	...c
(kpc)	(10−17 erg cm−2 s−1 arcsec−2)	(km s−1)	(km s−1)		(km s−1)	(km s−1)
8.1	0.5 ± 0.1	1637 ± 7	42 ± 7	0	0	0	...
...	...	...	...	...	...	...	...

Notes.

^aThe heliocentric radial velocity. ^bThe line width corrected for the spectral resolution. σ refers to the standard deviation and not the FWHM of the Gaussian fit. ^cThe remaining columns give the line ratio with respect to Hα, velocity, and velocity dispersion for the [N ii]λ6583 and [S ii]λ6717 lines. Null entries indicate locations where the relevant emission line was not detected.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image

Table 5.  Best-fit Emission-line Properties: s2

R	IHα	${v}_{{\rm{H}}\alpha }$ a	${\sigma }_{{\rm{H}}\alpha }$ b	$\tfrac{[{\rm{N}}\,{\rm{II}}]\lambda 6583}{{\rm{H}}\alpha }$	v[N ii]	${\sigma }_{[{\rm{N}}{\rm{II}}]}$	...c
(kpc)	(10−17 erg cm−2 s−1 arcsec−2)	(km s−1)	(km s−1)		(km s−1)	(km s−1)
13.5	1.1 ± 0.1	1532 ± 5	46 ± 5	0	0	0	...
...	...	...	...	...	...	...	...

Notes.

^aThe heliocentric radial velocity. ^bThe line width corrected for the spectral resolution. σ refers to the standard deviation and not the FWHM of the Gaussian fit. ^cThe remaining columns give the line ratio with respect to Hα, velocity, and velocity dispersion for the [S ii]λ6717 line. Null entries indicate locations where the relevant emission line was not detected.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image

Table 6.  Best-fit Emission-line Properties: s3uv

z	I[O ii]	$\tfrac{[{\rm{O}}\,{\rm{II}}]\lambda 3729}{[{\rm{O}}\,{\rm{II}}]\lambda 3726}$	v[O ii]a	${\sigma }_{[{\rm{O}}{\rm{II}}]}$ b
(kpc)	(SALT ADU)		(km s−1)	(km s−1)
5.8	11 ± 9	${2.0}_{-0.83}^{+0.83}$	${1651}_{-16}^{+16}$	${30}_{-16}^{+26}$
...	...	...	...	...

Notes.

^aThe heliocentric radial velocity. ^bThe line width corrected for the spectral resolution. σ refers to the standard deviation and not the FWHM of the Gaussian fit.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image

Table 7.  Best-fit Emission-line Properties: s3o

z	${I}_{{\rm{H}}\alpha }$	vHαa	$\tfrac{[{\rm{O}}\,{\rm{II}}]\lambda 3727}{{\rm{H}}\alpha }$	$\tfrac{[{\rm{O}}\,{\rm{III}}]\lambda 5007}{{\rm{H}}\alpha }$	$\tfrac{[{\rm{O}}\,{\rm{I}}]\lambda 6300}{{\rm{H}}\alpha }$	$\tfrac{[{\rm{N}}\,{\rm{II}}]\lambda 6583}{{\rm{H}}\alpha }$
(kpc)	(SALT ADU)
8.1	96 ± 17	1714 ± 23	0	0	0	0
...	...	...	...	...	...	...

Note.

^aThe heliocentric radial velocity. Null entries indicate locations where the relevant emission line was not detected.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

Download table as:  DataTypeset image

To determine the galactic gravitational potential of NGC 5775, we follow Collins et al. (2002) in adopting the mass model presented in the Appendix of Wolfire et al. (1995). This model consists of a disk, spherical bulge, and logarithmic halo; although it is developed for the Galaxy, it can be adapted to other systems by adjusting the v_circ parameter. We take ${v}_{\mathrm{circ}}=195$ km s⁻¹ to match the H i rotation curve of NGC 5775 (Irwin 1994), and we compare the adapted Wolfire et al. (1995) and Irwin (1994) rotation curves in Figure 12. The rotation curves are in good agreement at large R; discrepancy at small R may be due to lack of H i in the inner part of the galaxy. For the disk, bulge, and halo components, the gravitational potential, ${\rm{\Phi }}(z,R)$, and the gravitational acceleration, $-{g}_{z}=-\tfrac{d{\rm{\Phi }}(z,R)}{{dz}}$, are given in Equations (A1)–(A3) and (A7)–(A9) of Wolfire et al. (1995).

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