Inhomogeneity within Local Interstellar Clouds^*

The first measurements of interstellar temperatures, turbulent velocities, and kinematics were for individual bright stars, e.g., Capella (Linsky et al. 1993), Sirius A (Lallement et al. 1994), Procyon (Linsky et al. 1995), CMa (Gry et al. 1995; Gry & Jenkins 2001), α Cen (Linsky & Wood 1996), and β CMa (Jenkins et al. 2000). Redfield & Linsky (2004a) and Redfield & Linsky (2008) provided the first analysis of a large number of sight lines using the spectrographs on board HST. They measured temperatures, nonthermal broadening, and heliospheric velocities for 50 velocity components in the sight lines toward 29 stars located within 100 pc. Fourteen of the sight lines show only one velocity component, nine show two components, and six show three components. All of the stars show at least one interstellar-velocity component. Thus interstellar absorption observed in the H i, D i, and Mg ii lines is ubiquitous with multiple velocity components common even for lines of sight as short as 2.6 pc.

Redfield & Linsky (2004b) found a weighted mean temperature and weighted dispersion $\langle T \rangle ={6680}_{-}^{+}1490$ K. The distribution does not appear Gaussian about the mean value as there are at least eight velocity components with temperatures well below that expected for a Gaussian distribution with this dispersion. Additional observations are needed to better characterize the distribution of temperatures. They also found that the mean value of nonthermal broadening is 〈ξ〉 = 2.24 ±1.03 km s⁻¹ with an apparent excess of large ξ values that could result from unresolved closely spaced velocity components. Subsequently, Redfield & Linsky (2008) found a weighted mean temperature of 7500 ± 1300 K for the 19 LIC stars in their sample. Table 1 compares the weighted mean temperatures and weighted dispersions about the mean temperatures obtained from past and present data sets. For comparison, we include the temperature of neutral helium flowing into the heliosphere from the LIC including corrections for heating and deceleration resulting from elastic collisions in the VLISM (Swaczyna et al. 2021). There is excellent agreement between the new mean temperatures for the LISM and LIC data sets with the temperatures measured for the inflowing neutral helium.

Following the Redfield & Linsky (2008) paper there have been two papers with additional values of T and ξ for other sight lines. Zachary et al. (2018) studied two sight lines each with two velocity components, and Edelman et al. (2019) studied three stars each with three velocity components. The results of these two studies are included in Table 2. The results of our analysis of 27 new sight lines with 31 velocity components are listed in Table 3. In the last column of this table, we list the likely cloud in the sight line; clouds are shown in parenthesis when the sight line passes through its edge. The addition of these 47 velocity components listed in Tables 2 and 3 to the initial list of 50 sight lines obtained by Redfield & Linsky (2004b) warrants a reexamination of the distribution of cloud temperatures and turbulent velocities. The analysis of the new sight lines in this paper followed the approach and used the same software as described in detail by Redfield & Linsky (2004a).

Table 2. Temperature and Turbulent Velocity Measurements since 2008

HD	Name	l	b	d (pc)	〈v〉	T	ξ	Ions Used	Ref
209100	Ind	336.2	−48.0	3.62	−40.4	${8340}_{-440}^{+450}$	${1.97}_{-0.09}^{+0.08}$	H i, Mg ii, Fe ii	4
190248	δ Pav	329.8	−32.4	6.10	−17.2 ± 1.5	${8680}_{-780}^{+740}$	${0.0}_{-0.0}^{+2.18}$	D i, C ii, O i, Mg ii	1
190248	δ Pav	329.8	−32.4	6.10	−9.23 ± 0.58	${9310}_{-7959}^{+10070}$	${2.44}_{-2.44}^{+1.04}$	D i	1
192310	GJ 785	15.6	−29.4	8.81	−30.41 ± 0.57	${8600}_{-1800}^{+2000}$	${3.3}_{-1.3}^{+1.2}$	D i, C ii, Mg ii, Fe ii	2
192310	GJ 785	15.6	−29.4	8.81	−24.24 ± 0.50	${9900}_{-2100}^{+2200}$	${2.2}_{-2.0}^{+1.1}$	D i, C ii, Mg ii, Fe ii	2
192310	GJ 785	15.6	−29.4	8.81	−18.88 ± 0.57	${6900}_{-2300}^{+2600}$	${1.3}_{-1.3}^{+1.6}$	D i, C ii, Mg ii, Fe ii	2
HIP85665	GJ 678.1A	28.6	20.5	10.12	−31.5 ± 2.4	$10,{720}_{-3860}^{+4730}$	${0.0}_{-0.0}^{+1.92}$	D i, Mg ii	1
HIP85665	GJ 678.1A	28.6	20.5	10.12	−23.9 ± 2.4	${8540}_{-2790}^{+3240}$	${0.0}_{-0.0}^{+1.34}$	D i, Mg ii	1
9826	υ And	132.0	−20.7	13.48	9.1 ± 1.2	$10,{400}_{-1900}^{+2000}$	${0.00}_{-0.0}^{+2.4}$	D i, O i, Mg ii, Fe ii	2
9826	υ And	132.0	−20.7	13.48	12.1 ± 1.1	${4000}_{2200}^{+2800}$	${1.8}_{-1.2}^{+0.8}$	D i, O i, Mg ii, Fe ii	2
9826	υ And	132.0	−20.7	13.48	16.45 ± 0.88	${6500}_{-2600}^{+3000}$	${1.3}_{-1.3}^{+0.7}$	D i, O i, Mg ii, Fe ii	2
206860	NN Peg	69.9	−28.3	18.13	−14.68 ± 0.58	${7100}_{-2400}^{+2800}$	${1.4}_{-1.4}^{+0.6}$	D i, Mg ii, Fe ii	2
206860	NN Peg	69.9	−28.3	18.13	−8.0 ± 1.0	${9600}_{-2300}^{+2500}$	${2.11}_{-0.68}^{+0.54}$	D i, Mg ii, Fe ii	2
206860	NN Peg	69.9	−28.3	18.13	−5.44 ± 0.79	${6800}_{-2500}^{+2700}$	${0.80}_{-0.80}^{+0.98}$	D i, Mg ii, Fe ii	2
87901	α Leo	226.4	48.9	24.31	8.8 ± 0.2	${6000}_{-600}^{+600}$	1.78 ± 0.10	C ii, N i, O i, Mg i, Mg ii	3
87901	α Leo	226.4	48.9	24.31	14.4 ± 0.1	${5990}_{-700}^{+700}$	1.85 ± 0.19	C ii, N I, O i, Mg I, Mg ii	3

References. (1) Zachary et al. (2018); (2) Edelman et al. (2019); (3) Gry & Jenkins (2017); Malamut et al. (2014).

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Table 3. New Temperature and Turbulent Velocity Measurements

HD	Name	l	b	d (pc)	〈v〉	T	ξ	Ions Used	Ref	Cloud
217987	GJ 887	5.1	−66.0	3.29	−2.74 ± 0.21	${6000}_{-1400}^{+1500}$	${1.65}_{-1.10}^{+0.72}$	D i, Mg ii	1,2	LIC
1326	GJ 15A	116.7	−18.4	3.56	10.91 ± 0.32	${7800}_{-1100}^{+1200}$	${2.81}_{-0.21}^{+0.20}$	D i, Mg ii	1, 2	(Hya)
	GJ 273	212.3	10.4	3.80	18.28 ± 0.92	8620 ± 350	${0.0}_{-0.0}^{+1.32}$	H i, Mg ii	1,2	LIC
	GJ 273	212.3	10.4	3.80	21.38 ± 0.40	${8620}_{-340}^{+350}$	${0.0}_{-0.0}^{+1.59}$	H i, Mg ii	1,2	(Aur)
239960A	GJ 860A	104.7	−0.0	4.01	−0.14 ± 0.67	${4780}_{-1780}^{+2080}$	${2.24}_{-0.51}^{+0.42}$	D i, Mg ii	1	(Eri)
GJ 873	EV Lac	100.6	−13.1	5.0	4.44 ± 0.43	${3030}_{-610}^{+670}$	${2.21}_{-0.23}^{+0.22}$	D i, Mg ii	1	(LIC)
36395	GJ 205	206.9	–19.4	5.70	17.31 ± 0.19	${4200}_{-680}^{+680}$	${2.37}_{-0.24}^{+0.24}$	H i, D i, Mg ii	1, 2	unassigned
36395	GJ 205	206.9	–19.4	5.70	21.93 ± 0.16	${4500}_{-1200}^{+1200}$	${3.64}_{-0.27}^{+0.27}$	H i, D i, Mg ii	1, 2	(LIC)
	GJ 588	332.7	12.1	5.92	−26.58 ± 0.56	${6730}_{-720}^{+700}$	${3.37}_{-0.31}^{+0.32}$	H i, Mg ii	1,2	G
	YZ CMi	215.9	13.5	5.99	18.11 ± 0.31	8930 ± 260	${0.0}_{-0.0}^{+1.18}$	H i, Mg ii, Fe ii	1,2	LIC
	YZ CMi	215.9	13.5	5.99	21.73 ± 0.53	8790 ± 230	${1.59}_{-0.77}^{+0.57}$	H i, Mg ii, Fe ii	1,2	(Aur)
191408	GJ 783	5.2	−30.9	6.01	−25.9 ± 0.42	${7700}_{-1500}^{+1500}$	${3.05}_{-0.86}^{+0.86}$	D i, Mg ii	1	Mic
79210	GJ 338A	164.9	42.7	6.33	12.58 ± 0.09	${6650}_{-1020}^{+970}$	${2.29}_{-0.55}^{+0.61}$	D i, Mg ii, Fe ii	1,2	LIC
115617	61 Vir.	311.9	44.1	8.57	−16.7 ± 0.47	${6600}_{-4400}^{+4800}$	${1.60}_{-1.60}^{+0.83}$	D i, C ii, O i	1	(NGP)
23249	δ Eri	198.1	−46.0	9.04	20.29 ± 0.43	${3650}_{-1110}^{+1200}$	${2.25}_{-0.22}^{+0.19}$	D i, C ii, Mg ii	1	LIC
37394	GJ 211	158.4	11.9	12.3	17.2 ± 0.27	${5600}_{-2500}^{+2200}$	${1.00}_{-1.00}^{+0.71}$	D i, C ii, Mg ii	1	LIC
166	HR 8	111.3	−32.8	13.7	6.50 ± 0.44	${4520}_{-1880}^{+2110}$	${4.39}_{-0.34}^{+0.33}$	D i, C ii, Mg ii	1	LIC
72905	π1 UMa	150.6	35.7	14.5	12.91 ± 0.43	${2450}_{-660}^{+740}$	${2.47}_{-0.11}^{+0.10}$	D i, Mg ii	1	LIC
142373	χ Her	67.7	50.3	15.8	−12.69 ± 0.16	${4700}_{-1100}^{+1200}$	${1.36}_{-0.41}^{+0.31}$	D i, Mg ii, Fe ii	1	(Mic)
43162	GJ 3389	230.9	−18.5	16.7	17.1 ± 0.43	${3200}_{-2330}^{+2680}$	${5.76}_{-0.26}^{+0.25}$	D i, Mg ii	1	LIC
165185	GJ 702.1	356.0	−07.3	17.2	−26.9 ± 0.43	${8610}_{-3340}^{+4150}$	${0.0}_{-0.00}^{+1.76}$	D i, Mg ii	1	(G)
116956	SAO 28753	113.7	59.5	21.7	−0.25	${5160}_{-2680}^{+3420}$	${1.79}_{-1.37}^{+0.69}$	D i, Mg ii	1	(LIC)
116956	SAO 28753	113.7	59.5	21.7	7.7	${2540}_{-1830}^{+2450}$	${1.66}_{-1.66}^{+1.21}$	D i, Mg ii	1	unassigned
59967	GJ 3446	250.5	−09.0	21.8	9.32 ± 0.02	${12400}_{-2700}^{+2900}$	${0.00}_{-0.0}^{+1.9}$	D i, C ii, O i	1	Blue
97334	GJ 417	184.3	67.3	22.6	3.34 ± 0.47	${11000}_{-3000}^{+2400}$	${0.0}_{-0.0}^{+1.4}$	D i, C ii, O i	1	LIC
73350.	GJ 9273	232.1	20.0	24.3	11	${7900}_{-3200}^{+3200}$	${0.68}_{-0.68}^{+1.67}$	D i, Mg ii	1	LIC
82210	DK UMa	142.5	38.9	32.4	9.41 ± 0.61	${4220}_{-430}^{+460}$	${1.86}_{-0.18}^{+0.15}$	D i, Mg ii	1	(LIC)
129333	EK Dra	105.5	49.0	34.6	−2.43 ± 0.32	${2580}_{-250}^{+280}$	${3.13}_{-0.05}^{+0.05}$	D i, C ii, Mg ii	1	(LIC)
93497	μ Vel	283.0	08.6	35.9	−4.38 ± 0.43	${3470}_{-590}^{+580}$	${3.12}_{-0.10}^{+0.11}$	D i, Mg ii	1	G
128987	KU Lib	331.0	30.2	42.3	−20.90 ± 0.62	${6580}_{-3680}^{+4500}$	${3.00}_{-0.10}^{+0.11}$	D i, Mg ii	1	Gem
209458	V376 Peg	76.8	−28.5	48.1	−29.17 ± 0.94	${8500}_{-2850}^{+3280}$	${0.00}_{-0.00}^{+3.02}$	D i, Mg ii	1	unassigned

References. (1) This paper; (2) Wood et al. (2021).

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An important question is whether the cloud temperatures and turbulent velocities within a cloud are roughly constant or distributed in a random or systematic manner. If these properties are random, then their distributions could be Gaussian distributed with perhaps a few outliers. With the 84 sight lines now evaluated for temperature and turbulent velocity, we can address this question. Figure 2 (left) shows the number of temperature measurements in each 1000 K temperature bin. This bin size is appropriate given the typical measurement uncertainties of 500–2000 K. The weighted mean gas temperature is 6838 ± 2455 K, and the solid line in the plot is a Gaussian fit to the data. The fit is reasonably good, although there are seven outliers in the temperature range 12,000–13,000 K. The errors are weighted dispersions about the mean (see Redfield & Linsky 2004b). Table 1 lists the weighted mean temperatures and dispersions measured in different ways. Figure 2 (right) shows the distribution of temperatures for the 36 sight lines that pass through the LIC. While there are fewer sight lines in this plot, the distribution, mean value, and dispersion of the temperatures are similar to the plot that included all sight lines. These data show that the LIC and the other warm clouds in the CLIC have similar wide distributions of internal temperatures.

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Figure 3 (left) shows the distribution of turbulent velocities plotted with a bin size of 0.5 km s⁻¹ as typical measurement uncertainties are in the range 0.2–1.5 km s⁻¹. The weighted mean turbulence is 2.54 ± 1.18 km s⁻¹, and the solid line Gaussian in the figure is also a good fit to the data. The distribution of turbulent velocities for the sight lines that pass through the LIC (Figure 3, right) has similar properties. We conclude that wide ranges of temperatures and turbulent velocities characterize the gas in the nearby warm clouds. As previously noted by Redfield & Linsky (2004a), the turbulent velocities are subsonic and the highest turbulent velocities may result from unresolved velocity components.

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Another method for testing whether the temperatures and turbulent velocities within the LIC are constant or have variable properties is to compare the properties of pairs of sight lines as a function of their angular separation. For the 36 sight lines traversing the LIC there are 36 × 35 = 1260 pairs, but only 596 unique pairs after subtraction of pairs for two clouds in the sight line to the same star and pairs that are sampled twice by the search software. Figure 4 (left) shows the temperature differences for these pairs as a function of angular separation between the sight lines. The mean value of these temperature differences is 2845 K, but there are many temperature differences exceeding 6000 K. Since the mean value of the individual measurement uncertainties for these sight lines is 1625 K, most of these sight-line pairs have temperature differences that well exceed the measurement errors.

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Figure 4 (right) plots the same data in angular separation bins 10° wide. The blue line is a least-squares fit to the mean values in each bin. The line slope is 1.96 times its error, indicating a significant increase in the mean temperature differences between zero angular separation (2465 K) and those at the widest separation. This result indicates significant temperature differences on all angular separation scales, even at the smallest separations.

There are many studies of inhomogeneous properties in the ISM; see, for example, the comprehensive review by Stanimirović & Zweibel (2018). Very-small-scale structures of neutral cold gas are inferred from high-resolution absorption lines of neutral carbon (Jenkins & Tripp 2007), sodium (Lauroesch 2007), hydrogen (Stanimirović et al. 2007), and molecules with tiny-scale atomic structures as small as tens of au. Very small structures of ionized gas in the diffuse ISM also show tiny structures with sub-au scales. These very-small-scale structures are identified at radio wavelengths and are caused by variations in the electron density and therefore the refractive index along the sight line that result in diffraction patterns called scintillation; see the reviews by Rickett (2007) and Cordes et al. (2007). Structure sizes as small as 1 au are inferred from the rotation measure structure functions and from scintillation arcs produced by highly turbulent density clumps, called scattering screens, along sight lines to pulsars and quasars. Linsky et al. (2008) found three scattering screens within a few parsecs of the Sun where the edges of two or more partially ionized clouds may interact. These small spatial scales for both neutral and ionized gas refer to density and likely magnetic field fluctuations, and are based on measurements of neutral and ionized gas through long sight lines. With the available data, we can now measure the length scales for temperature fluctuations in the immediate environment of the Sun, including the LIC and other partially ionized clouds, and what these fluctuations suggest could be the timescale of externally driven changes in the heliosphere. Are the length scales for temperature fluctuations in local partially ionized warm clouds similar to the length scales for electron density fluctuations in the ionized ISM?

The least-squares fit in Figure 4 (right) predicts that the mean temperature difference for sight lines with the smallest angular separations should be about 2465 K, but the mean temperature measurement error is only 1625 K. For stars in our data set, the smallest angular scale of 22 is for the Procyon–YZ CMi sight-line pair, which has a temperature difference of 2220 K, but the measurement uncertainty for this pair is only 695 K, a factor of 3.2 smaller. Table 4 lists the four sight-line pairs with the closest angular separations. We note that the H i column densities are the same for the first three pairs, consistent with the shape of the LIC not being highly irregular. The larger and more discordant log N(H i) values for the fourth pair may be due to additional column densities through the edges of the Eri and Hyades clouds. We estimate the path length d(LIC) through the LIC from the neutral hydrogen column densities and n(H i) = 0.20 cm⁻³. The separation, s, of the sight lines halfway through the LIC is then s = 206265 × (d(LIC)/2)tan(θ) au, where θ is the angular separation of the sight lines. The separations range from 5100 au to 17,360 au for these close pairs. These separations could be upper limits to the true inhomogeneity length scale, because there could be unmeasurable but significant temperature variations within the sight lines to even the closest stars and between the stars with the smallest angular separations. Since the Sun moves through the LIC at 5.1 au yr⁻¹, the heliosphere could see changes in local interstellar properties within 1000 yr. We conclude that the linear scale for significant temperature differences in the LIC is at least as small as 5100 au.

Table 4. Sight-line Separations Halfway Through the LIC for the Closest Pairs

Angle	Star 1	Star 2	ΔT	Uncertainty	ΔT/Uncertainty	log N(H i)	d (LIC)	Separation
220	Procyon	YZ CMi	2220 K	695 K	3.2	17.9, 17.89	1.29 pc	5100 au
262	Eri	δ Eri	3760 K	1435 K	2.6	17.88, 17.88	1.29 pc	6,075 au
294	Procyon	GJ 273	1910 K	733 K	2.6	17.9, 17.86	1.23 pc	6,510 au
312	HD 166	PW And	6780 K	2724 K	2.5	18.3 a , 18.1 a	3.09 pc	17,360 au

Note.

^a A portion of log N(H i) for HD 166 may come from the Eri and Hyades clouds.

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This technique for estimating length scales is similar to that described by Spangler (2001), who compared rotation measures as a function of angle between different sight lines. Such measures are proportional to the integral of the product of the electron density and the projection of a magnetic field along a line of sight. There is a break in the difference between rotation measures for sight lines with angular separations less than or about 01, corresponding to a length scale for these plasma fluctuations of about 3.6 pc (Minter & Spangler 1996).

Figure 5 (left) plots temperature versus turbulent velocity for all 84 velocity components. Although there is a large scatter in the data, there is a clear trend of decreasing temperature with increasing turbulent velocity. For the full data set, the least-squares linear fit is in the form T = A + Bv_turb, where A = 8816 ± 449 K and B = −795 ± 220, with the slope 3.6 times its error. For the LIC-only data (Figure 5 (right)), the fit is A = 9350 ± 523 with a steeper slope B = −1523 ± 287 that is 5.3 times its error.

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With the smaller data set then available, Redfield & Linsky (2004b) found a moderately negative correlation between temperature and turbulent velocity with a Pearson r = −0.47 for the entire sample and r = −0.35 for the subsample with more precise parameters. For the larger sample shown in Figure 5 (left) the correlation coefficient is r = −0.37, and for the LIC-only data set the coefficient is larger, r = −0.67, consistent with visual inspection. The covariance for the two data sets are −1077 and −1842, respectively.

This significant correlation of temperature and turbulent velocity, especially in the new LIC data set, could result in part from the absorption-line-fitting procedure, because the fit to low-mass atoms (e.g., D i) and high-mass ions (e.g., Mg ii and Fe ii) depends on the sum of thermal and turbulent broadening. For example, a positive (or negative) error in the temperature measurement can be partially compensated by a negative (or positive) error in the turbulent velocity measurement. The presence of unresolved velocity components would significantly increase the measured turbulent velocities with only a small effect on the temperature measurements. Since the effect of unresolved velocity components is to produce the largest turbulent velocities, the correction of these data points would produce an even steeper correlation. Redfield & Linsky (2004b) discuss other possible causes of the correlation including systematic errors. If the correlation is real and not an artifact of the measurement technique or inadequate spectral resolution, then it could indicate the conversion of turbulent energy to heat. Table 5 summarizes the A and B coefficients and Pearson r values for all of the linear fits. The underlined values of r indicate significant trends.

Table 5. Linear Least-squares Fits for y = A + Bx

Plot for parameters y versus x	Data set (2σ)	A	B	Pearson r
Temperature versus turbulent velocity	All	8816 ± 449	−795 ± 220	–0.371
Temperature versus turbulent velocity	LIC	9350 ± 523	−1523 ± 287	–0.672
Temperature versus distance	All	6969 ± 379	28.7 ± 15.0	+0.207
Temperature versus angle from Galactic Center	All	6804 ± 614	7.20 ± 5.86	+0.135
Temperature versus angle from CMa	All	7704 ± 627	2.53 ± 6.42	−0.044
Temperature versus angle from CMa	LIC	7342 ± 1010	−2.83 ± 11.90	−0.041
Temperature versus angle from inflow direction	All	6669 ± 635	8.42 ± 5.96	+0.154
Temperature versus angle from LIC core	LIC	6127 ± 1032	17.01 ± 16.16	+0.178
Temperature versus angle from magnetic field	All	6352 ± 741	11.39 ± 6.97	+0.178
Temperature versus angle from magnetic field	LIC	7298 ± 1530	−1.549 ± 13.031	−0.020
Temperature versus N(H i)	All	7657 ± 13068	−9.81 ± 731.1	−0.001
Temperature versus N(H i)	LIC	171434 ± 19113	−560 ± 1067	−0.090
Temperature difference versus angle from LIC core	LIC	2465 ± 236	4.72 ± 2.40	+0.452
Turbulent velocity versus distance	All	1.764 ± 0.180	−0.00468 ± 0.00713	−0.072
Turbulent velocity versus angle from Galactic Center	All	1.612 ± 0.289	0.000722 ± 0.00276	+0.029
Turbulent velocity versus angle from CMa	All	1.952 ± 0.291	−0.00310 ± 0.00298	−0.114
Turbulent velocity versus angle from CMa	LIC	1.239 ± 0.444	0.00289 ± 0.00524	+0.094
Turbulent velocity versus angle from LIC core	LIC	1.596 ± 0.463	−0.00228 ± 0.00724	−0.054
Turbulent velocity versus angle from inflow direction	All	1.623 ± 0.300	0.000592 ± 0.00281	+0.023
Turbulent velocity versus angle from magnetic field	All	1.661 ± 0.351	0.00019 ± 0.00330	+0.006
Turbulent velocity versus angle from magnetic field	LIC	1.157 ± 0.673	0.00271 ± 0.00574	+0.081
Turbulent velocity versus angle from magnetic field (bins)	All	1.250 ± 0.462	0.00385 ± 0.00445	+0.311
Turbulent velocity versus angle from magnetic field (bins)	LIC	0.496 ± 0.727	0.00993 ± 0.00701	+0.472
Turbulent velocity versus N(H i)	All	−4.33 ± 6.20	0.335 ± 0.347	+0.106
Turbulent velocity versus N(H i)	LIC	−4.69 ± 8.41	0.339 ± 0.470	+0.123
Mean density versus thermal pressure	16	0.0338 ± 0.0312	(4.48 ± 4.79) × 10−6	+0.243
Mean density versus thermal+turbulent pressure	16	0.0336 ± 0.0291	(2.84 ± 2.81) × 10−10	+0.261

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We searched for evidence of whether the distance to the star at the end of the sight line influences the properties of the intervening interstellar gas. Figure 6 (left) plots temperature versus the distance to the star at the end of a given sight line. The absence of a significant trend in the data supports the assumption that background stars only serve as illumination sources. The fit parameter for the turbulent velocity data in Figure 6 (right) also shows no significant trend. A possible trend with distance to stars with very strong extreme-UV (EUV) emission is tested in Section 3.6. We can therefore combine sight lines of near and more distant stars when studying individual clouds.

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The heliosphere is now located near the edge of the LIC and will likely leave the LIC in less than 2000 yr (Redfield & Linsky 2004b; Frisch et al. 2011; Linsky et al. 2022). The trajectory is in the direction of the G Cloud, but whether the heliosphere will directly enter the G Cloud or an intercloud boundary consisting of Local Cavity gas or compressed partially ionized gas has been a matter of speculation. Very recently, Swaczyna et al. (2022) proposed that the heliosphere is now surrounded by overlapping LIC and G Cloud plasma with an average temperature intermediate between the two clouds and n(H i) = 0.20 cm⁻³, the sum of the densities of the two clouds. With our new data set, we can test whether the LIC and G Cloud have different properties. Table 6 lists the weighted mean values and weighted dispersions of the temperatures and turbulent velocities of the two clouds measured by Redfield & Linsky (2008) and measured in this paper. There are measured parameters for six sight lines through the G Cloud, but only four sight lines have temperatures that meet the 2σ criterion (α Cen A, α Cen B, 30 Oph, and μ Vel). As shown in Table 6, the weighted mean temperature is cooler and the weighted mean turbulent velocity is higher in the G Cloud than in the LIC, but the large weighted dispersions encompass the parameters for the two clouds.

Inflowing interstellar ions and ions produced by charge exchange reactions with inflowing interstellar neutrals are constrained by the heliospheric magnetic field to flow around the heliosphere away from the inflow direction. We therefore ask whether there are correlations of the measured temperatures and turbulent velocities with angle from the inflow direction. The upwind direction of interstellar gas flowing into the heliosphere is the vector sum of the interstellar gas flow in the local standard of rest and the Sun's motion relative to the local standard of rest. The upwind velocity, temperature, and direction have been studied using observations with the EUVE, IBEX, Ulysses, and STEREO spacecraft. A recent analysis of IBEX data by Swaczyna et al. (2021) gives T = 6400 K, v = 25.85 km s⁻¹ and inflow Galactic coordinates (l = 35, b = +152) (Swaczyna et al. 2018). The temperatures and turbulent velocities in Figure 7 show no trend with angle θ from the upwind direction.

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The strongest source of EUV radiation that ionizes hydrogen (λ < 912Å) is the star CMa (Galactic longitude l = 2398 and Galactic latitude b = −113), but there are other stellar (Vallerga 1998) and hot white dwarf (Welsh et al. 2013) EUV sources distributed across the sky. Since β CMa, the second brightest EUV source, and Sirius B, the closest white dwarf, are in a similar direction as CMa, we searched to see whether there are correlations of temperature and turbulent velocity with angle from CMa. Figure 8 (left) shows the dependence of temperature and on angle from CMa for the full data set, and Figure 8 (right) shows the dependence for the LIC-only data set. We see no such effect for the temperature data or the turbulent velocity data (see Figure 9), with respect to the angle from CMa. The absence of any correlation with direction from CMa could be due to the many EUV sources distributed over the sky and the main heating source in the ISM being the photodissorption of electrons from dust grains that can be liberated by lower-energy photons.

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Spangler et al. (2011) suggested that turbulence in the local warm clouds could be anisotropic with velocity fluctuations that are larger perpendicular to the magnetic field direction than in the parallel direction. The basis for this suggestion was that in the solar wind and corona fluctuations in the magnetic field and plasma flow velocity are highly correlated and predominately perpendicular to the magnetic field direction. While this anisotropy decreases with heliocentric distance and likely decreases further as a result of ion-neutral collisions in the local clouds, Spangler et al. (2011) searched for but found no conclusive evidence for anisotropy in the data then available and encouraged a search in larger data sets as they become available. With the larger data set now available, we investigated the dependence of turbulent velocity on the angle from the magnetic field direction using the magnetic field direction l = 2598, b = 5009 in Galactic coordinates that Zirnstein et al. (2016) obtained from analysis of the IBEX ribbon data. They proposed that this direction is valid for the interstellar magnetic field at a distance of 1000 au.

Figure 10 shows the angular distribution of turbulent velocities relative to the magnetic field direction in 20° wide bins for the entire data set and for only those sight lines that traverse the LIC. In both plots there is no significant enhancement in the turbulent velocities near 90°, perpendicular to the magnetic field direction. A similar analysis of the temperatures also reveals no enhancement near 90°.

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Figure 11 addresses the question of whether the temperatures and turbulent velocities depend on whether sight lines penetrate through the core of the LIC (approximate coordinates l = 145° and b = 0°) or its edge. There are no significant trends in the temperature or turbulent velocity on direction of sight lines through the LIC, indicating that self-shielding from external EUV radiation sources is not important for determining the temperature or turbulent velocity of the LIC plasma.

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We show plots of the temperature (Figure 12) and turbulent velocity (Figure 13) versus N(H i) for the full data set and the LIC-only data set. There are no significant trends of either the temperatures or turbulent velocities on N(H i). One might expect higher temperatures in low-N(H i) sight lines that would be in closer proximity to the external EUV radiation field or perhaps hot gas surrounding the clouds, but there is no evidence that either scenario is the case.

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Line-of-sight measurements of interstellar absorption provide information on the interstellar properties of gas in front of a star, but not where the cloud's absorbing gas begins and ends along the sight line. For stars within about 10 pc of the Sun, the detection of Lyα absorption blueshifted relative to the interstellar hydrogen absorption indicates the presence of interstellar neutral hydrogen that has charge exchanged with energetic stellar wind protons (Wood et al. 2005a). This shows that the star is embedded in an interstellar cloud containing neutral hydrogen. The absence of this blueshifted astrospheric absorption could be explained by the star being embedded in fully ionized interstellar gas or the sight line being near the downwind direction. Table 7 lists the stars within 10 pc for which astrospheric absorption has been detected or definitely not detected. In the 15 cases where there are detections of blueshifted astrospheric absorption, the star must be located within the cloud identified in the sight line. In three cases where there are more than one cloud, there is uncertainty as to which of the two or three clouds envelopes the star, but one of them must. For the eight cases where no astrospheric absorption has been reported, it is likely that no detected cloud extends as far as the star.

Table 7. Fill Factors for Sight Lines to Stars within 10 pc of the Sun

HD	Star	l	b	d (pc)	Number	log N(H i)	Filling	Clouds	Astro-	Ref.
	Name				Clouds		Fraction	in Front	sphere
128620	α Cen ABC	315.7	−0.7	1.35	1	17.61	0.49	G	Yes	1
GJ 699	Barnard's star	31.0	14.1	1.83	1	17.72	0.46	G	No	3
95735	GJ 411	185.1	65.4	2.55	1	17.84	0.44	(LIC)	No	3
48915	SiriusAB	227.2	−8.9	2.64	2	17.4,17.2	0.25	(LIC), (Blue)	⋯	8
22049	Eri	195.8	−48.1	3.22	1	17.88	0.32	LIC	Yes	4
217987	GJ 887	5.1	−66.0	3.29	1	18.10	0.62	LIC	Yes	2
201091	61 Cyg A	82.3	−5.8	3.50	2	17.8,17.8	0.58	Eri, Aql	Yes	8
61421	Procyon	213.7	13.0	3.51	2	17.9,17.6	0.55	LIC, Aur	⋯	8
1326	GJ 15A	116.7	−18.4	3.56	1	18.02	0.48	(LIC), (Hya)	Yes	2
209100	Ind	336.2	−48.0	3.64	1	17.95	0.45	(LIC)	Yes	5
10700	τ Cet	173.1	−73.4	3.65	1	18.01	0.44	LIC	No	1
⋯	GJ 273	212.3	10.4	3.79	2	17.86,17.78	0.57	LIC, Aur	⋯	2
GJ 191	Kapteyn's star	250.5	−36.0	3.93	1?	17.98	0.39	Blue	⋯	3
239960A	GJ 860A	104.7	−0.0	4.01	1	17.78	0.24	(Eri)	Yes	2
GJ 388	AD Leo	216.5	54.6	4.97	1	18.47	0.96	(LIC), (Leo)	No	1
26965	40 Eri A	200.8	−38.1	4.98	1	17.8	0.21	LIC	No	6
GJ 873.	EV Lac	100.6	−13.1	5.05	1	17.97	0.32	(Hyades)	Yes	1
165341	70 Oph A	29.9	11.4	5.08	3	17.8,17.1,17.5	0.34	G, (Aql), (Mic)	Yes	8
187642	α Aql	47.1	−8.9	5.13	3	17.9,17.9,17.5	0.60	Aql, Eri, (Mic)	⋯	8
36395	GJ 205	206.9	–19.4	5.70	2	17.60,17.24	0.16	(LIC), unassigned	Yes	2
⋯	GJ 754	352.4	−23.9	5.91	2	18.16,17.62	0.51	Unassigned, (Aql)	⋯	9
⋯	GJ 588	332.7	12.1	5.92	1	18.12	0.36	G	⋯	2
155886	36 Oph A	358.3	6.9	5.96	1	17.85	0.17	G	Yes	7
GJ 285	YZ CMi	215.9	13.5	5.99	2	17.89,17.45	0.29	LIC, (Aur)	Yes	2
191408	GJ 783A	5.2	−30.9	6.02	1	18.31	0.55	(Mic)	⋯	11
20794	82 Eri	250.7	−56.7	6.04	1?	18.33	0.57	G	⋯	3
190248	δ Pav	329.8	−32.4	6.10	2	17.82,17.55	0.18	Unassigned, (Vel)	⋯	9
79210	GJ 338A	164.9	42.7	6.33	1	17.79	0.16	LIC	Yes	2
152751	GJ 644B	11.0	21.1	6.50	1	18.40	0.63	(Mic)	⋯	2
131156	ξ Boo A	23.1	61.4	6.73	1	17.92	0.19	Gem	Yes	1
H iP86287	GJ 686	42.2	24.3	8.16	1	18.28	0.38	LIC	⋯	9
115617	61 Vir	311.9	44.1	8.57	1	18.01	0.19	(NGP)	Yes?	11
39587	χ1 Ori	188.5	−2.7	8.66	1	17.93	0.12	LIC	No	1
192310	GJ 785	15.6	−29.4	8.81	3	17.96,17.90,16.17	0.32	(Vel), (Mic), (LIC)?	⋯	10
23249	δ Eri	198.1	−46.0	9.04	1	17.88	0.14	LIC	Yes	1
20630	κ1 Cet	178.2	−43.1	9.14	2	17.5,17.5	0.11	LIC, (Hyades)	No	8
197481	AU Mic	12.7	−36.8	9.72	1	18.36	0.26	(Mic)	No	1

References. (1) Wood et al. (2005b); (2) Wood et al. (2021); (3) Youngblood et al. (2022); (4) Dring et al. (1997); (5) Wood et al. (1996); (6) Wood & Linsky (1998); (7) Wood et al. (2000); (8) Redfield & Linsky (2008); (9) Zachary et al. (2018); (10) Edelman et al. (2019); (11) This paper.

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The one-dimensional extent of a cloud along a given line of sight is more complicated. Since the Sun is embedded in the outer region of the LIC, other clouds detected in the same sight line must lie beyond the LIC. It is likely that the G Cloud also lies in front of other clouds as most of the sight line to the nearest star, α Cen, is in the G Cloud with no detected absorption at the LIC cloud's velocity. If one assumes that n(H i) in a cloud is the same as in the LIC (about 0.20 cm⁻³; Slavin & Frisch 2008; Swaczyna et al. 2020), then a cloud's path length along the sight line is given by the ratio N(H i)/0.20. While neutral hydrogen column densities N(H i) can be measured with modest precision, there are no accurate methods for measuring n(H i) in clouds other than the LIC.

High-resolution spectra of the Mg ii and Fe ii interstellar absorption lines observed toward nearby stars, primarily M dwarfs, provide a tool for identifying the filling fraction of a cloud along the sight line to the star. Table 7 lists all of the stars within 10 pc of the Sun with measured N(H i) and the number of clouds identified in each sight line. For each sight line, we identify the clouds located in front of the star by matching two criteria: (1) that the measured interstellar radial velocities lie within 2 km s⁻¹ of the velocities predicted from the cloud's velocity vector, and (2) the star lies within the cloud's morphological outline (Redfield & Linsky 2008). Cloud names are placed in parentheses when the star is located at or just beyond the cloud edge.

The cloud-identification process is somewhat subjective as the cloud morphologies are not precisely known given the limited number of stars that were used to construct these morphologies. However, in all but three of the 52 velocity components in the 37 sight lines to stars within 10 pc, the number of measured interstellar-velocity components is the same as the number of previously known clouds identified by the two-step procedure just described. For the sight line to GJ 15A one absorption component was observed but two clouds meet both selection criteria. This could result from both clouds being in the sight line, or errors in the cloud outlines as the star is located at the edge of both the LIC and Hyades clouds. The agreement between the number of interstellar-velocity components and the number of identified clouds for 14 of the 15 new sight lines that were not available when the cloud outlines were constructed by Redfield & Linsky (2008) provides strong support for the cloud outlines obtained at that time. The identification of a cloud near its edge is a strong determination that the cloud is actually in the sight line, since there is no alternative cloud that meets both criteria of measured radial velocity and fitting within the cloud boundary. We conclude that nearly all velocity components identified so far correspond to previously identified warm clouds.

The only cloud in the CLIC for which the neutral hydrogen density has been measured is the LIC, or more precisely the outer edge of the LIC where the heliosphere resides. Measurements of the inflowing neutral helium consistently predict n(H i) ≈ 0.20 cm⁻³. Slavin & Frisch (2008) developed theoretical models for the LIC just outside of the heliosphere consistent with this neutral hydrogen density and other empirical constraints. For other clouds in the CLIC, there are measurements of the neutral hydrogen column density, N(H i), but not the number density, n(H i). It is tempting to assume initially that n(H i) is roughly the same in the other CLIC clouds as in the LIC. If so, then it is simple to determine the extension of a cloud along a sight line from the measured N(H i) assuming n(H i) = 0.20 cm⁻³.

We can now test this assumption with data for 37 stars within 10 pc of the Sun. Table 7 lists the neutral hydrogen column densities for each cloud detected in the sight lines to all stars within 10 pc of the Sun that have measured N(H i). The eighth column lists the filling fractions of the clouds along each sight line determined from the cloud extensions (assuming that n(H i) = 0.20 cm⁻³) divided by the distance to the star. The ninth column lists the cloud(s) in the sight line to the star; clouds in parenthesis are viewed through their edges. For sight lines with multiple clouds, the filling fraction is the sum for all of the clouds. Figure 14 plots the filling fractions for the 37 sight lines. The least-squares fit to the data (the solid curve in the figure) shows a clear decrease in filling factor with distance to the star. The Pearson correlation coefficient r = −0.45 confirms the decrease. There are several interesting results shown in this figure:

• 1.  
  The value of n(H i) entering the heliosphere and astrospheres plays a critical role in both ionization and heating because n(H i) sets the charge exchange rate with protons throughout the astrosphere and thus the relative fraction of suprathermal ions compared to the stellar wind ions. A higher number of suprathermal ions leads to more energy dissipation at the termination shock and beyond (see Swaczyna et al. 2020). It is therefore critical to obtain realistic estimates of n(H i).
• 2.  
  With the exception of AD Leo (see Section 3.13), all of the sight lines have filling fractions smaller than 0.63. This maximum filling factor could be explained either by a sparcely filled CLIC with highly ionized gas located between the clouds observed along the sight line, or with clouds that entirely fill the sight lines but with smaller densities than the LIC value of n(H i) = 0.20 cm⁻³, or by a combination of the two possibilities. The large sample of 37 relatively short sight lines with 53 absorption components and the detection of 15 astrospheres provides an opportunity to distinguish between these possibilities.
• 3.  
  Sight lines to 11 of the 13 stars within 4 pc of the Sun have filling factors in the range 0.38 to 0.62. Also, an additional five more distant stars have filling factors that lie within this range. This result could be explained by the clouds having typical densities of n(H i) ≈ 0.10 cm⁻³ that fill the sight lines. The alternative explanation of sight lines to a large number of stars all being about 50% filled seems contrived and less likely. The short sight line with the smallest fill factor (0.25) is toward Sirius AB (2.64 pc). This is not surprising because Sirius B is a hot white dwarf with a surrounding H ii region of fully ionized hydrogen.
• 4.  
  There are four stars within 4 pc of the Sun ( Eri, GJ 887, GJ 15A, and Ind, ) that have only LIC absorption in their sight lines and also astrospheric H i Lyα absorption that requires that these stars are located inside of a cloud containing neutral hydrogen. The simplest model for these sight lines is that the LIC extends from the heliosphere to the astrosphere of each star and perhaps beyond. In this case, the mean filling factor toward these four stars is 0.47 and the mean neutral hydrogen density in the LIC is 0.094 cm⁻³. The density n(H i) = 0.20 cm⁻³ in the immediate environment of the Sun, therefore, appears to be unrepresentative of the mean neutral hydrogen density in the LIC.
• 5.  
  Other clouds in the CLIC may have similar densities to n(H i) ≈ 0.10 cm⁻³ for the LIC. For example, the sight line to the nearest stellar binary system α Cen AB shows no evidence for LIC absorption, only G Cloud absorption and astrospheric absorption likely produced by neutral hydrogen in the G Cloud. After a minimal amount of LIC gas, the complete sight line to α Cen could be filled with G Cloud gas with n(H i) = 0.10 cm⁻³. We conclude that within 4 pc of the Sun the clouds appear to be tightly packed, and that typical densities are n(H i) ≈ 0.10 cm⁻³. However, a "Swiss cheese" model with high-density gas separated by voids cannot be ruled out by the available data.
• 6.  
  Beyond 4 pc, there is a wider range of filling fractions with a clear trend of decreasing filling fraction with increasing distance, as shown by the least-squares linear fit shown in Figure 14. For the sight lines between 4 pc and 7 pc the filling fractions have a wide range (0.16–0.63), but the seven sight lines in the range 8–10 pc all have filling fractions less than 0.38, and four of the sight lines have filling fractions of about 0.15. Gry & Jenkins (2017) found that the warm gas filling factor in the sight line to α Leo (23.8 pc) is about 0.13. This trend of decreasing filling fraction with distance suggests that the CLIC clouds are becoming more widely separated with distance from the Sun, as was suggested by Redfield & Linsky (2008), and that the intercloud gas with fully ionized hydrogen is occupying a larger fraction of sight lines to the more distant stars. The intercloud gas may be the same as the gas that fills most of the Local Cavity (Linsky et al. 2019).

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Although the model just described fits the data very well, it has been suggested to explore an alternative model in which warm clouds fill the entire space well beyond 4 pc. If filling factors are close to unity along these longer sight lines, then one might expect that the thermal plus turbulent pressure to be roughly constant despite the inhomogeneous temperatures and turbulent velocities. Values of variable magnetic and other pressure terms are not available for individual sight lines. We therefore looked for correlations of the mean neutral hydrogen density 〈n(H I)〉 = N(H I)/d with thermal pressure, proportional to T, and with the sum of thermal and turbulent pressure, proportional to ${kT}+1.4m({\rm{H}}){v}_{\mathrm{turb}}^{2}$. We selected 16 sight lines, listed in Table 7, that have only a single cloud. In Figure 15 there is a Pearson correlation coefficient, r = 0.24, for the correlation of 〈n(H I)〉 with thermal pressure, and a correlation coefficient, r = 0.26, for the correlation of 〈n(H I)〉 with the sum of thermal and turbulent pressures. The slopes of the least-squares fits are less than their errors in both plots. The larger correlation coefficient for filling factor with distance in Figure 14, r = −0.45, supports the previous model of warm clouds completely filling space out to 4 pc with decreasing filling fraction beyond.

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The short (4.97 pc) sight line to AD Leo is interesting for several reasons. The Galactic coordinates of AD Leo (l = 2165, b = +546) place it at the edge of the LIC, Leo, and north Galactic pole (NGP) clouds (Redfield & Linsky 2008), but its interstellar radial velocity of 13.13 km s⁻¹ is inconsistent with the predicted radial velocities of the LIC (7.23 km s⁻¹), Leo (9.21 km s⁻¹) and NGP (16.22 km s⁻¹) clouds, using the LISM Dynamical Model Kinematic Calculator. ⁴ As a result, AD Leo is not assigned to any known cloud and the high H i column density may result from the sight line passing through a shock. Since the LIC and Leo clouds have essentially the same velocity amplitudes, the shock would not be from these two clouds. Instead, the NGP cloud has a velocity vector amplitude 13 km s⁻¹ different from the LIC and Leo clouds and thus could be responsible for the shock.

Gry & Jenkins (2017) found interstellar absorption toward the star Regulus (α Leo) at 8.8 ± 0.2 km s⁻¹, which they assigned to the LIC, and a second component at 14.4 ±0.1 km s⁻¹. Since Regulus and AD Leo are separated by only about 10° and the radial velocity of the second component is similar to that seen toward AD Leo, it is likely that these two components are formed in the same unassigned structure in front of AD Leo and thus closer than 4.97 pc. Although the Local Leo Cold Cloud (LLCC; Peek et al. 2011) is in the same direction as Regulus (and AD Leo) with a similar radial velocity (9.3 km s⁻¹), Gry & Jenkins (2017) argue that the LLCC lies beyond Regulus at a distance of 33.5 ± 11.3 pc. Thus the anomalously large value of N(H i) in front of AD Leo is not the LLCC, but some other perhaps very interesting feature.

If the high value of N(H i) in front of AD Leo is produced in a shock between the NGP and either the LIC or Leo clouds, then the radial velocity of the shock should be intermediate between the NGP and the other two clouds. The halfway radial velocity between the NGP and LIC is 11.7 km s⁻¹ and between the NGP and Leo clouds is 12.7 km s⁻¹. Both velocities are consistent with the observed interstellar velocity of 13.13 km s⁻¹ toward AD Leo. This spatial agreement between AD Leo and the cloud interfaces and the velocity agreement provides evidence for a shock in the sight line to AD Leo. This would be a second shock in the LISM, the first being the Cetus ripple discovered by Gry & Jenkins (2014) located mostly in the southern Galactic hemisphere.

Empirical studies of the local ISM can be viewed as having proceeded through three stages driven by the increasing availability of high-resolution UV spectra and the constraint of matching the properties of the plasma flowing from the LISM into the heliosphere. The first stage consisted of studies of individual sight lines to nearby bright stars, first by analyzing ground-based observations of the Ca ii H and K lines, and then by analyzing UV spectra from the Copernicus satellite and the HRS instrument on HST. These studies provided measurements of radial velocities, temperatures, turbulent broadening, hydrogen and metal column densities, and electron densities of interstellar matter in these sight lines. Subsequently, Redfield & Linsky (2004b) measured the properties for 50 velocity components along the sight lines to 29 stars using high-resolution spectra from the STIS instrument on HST. These studies could not determine where along the sight line the absorption occurs or whether these properties are homogeneous or the mean of variations along the sight line.

The recognition that the flow of interstellar gas is in the form of comoving structures, now called clouds, is the second stage in the empirical study of the LISM. It began with the discovery by Crutcher (1982) that radial velocities in many sight lines in directions away from the Galactic Center are consistent with a coherent flow from the direction of the Scorpio-Centaurus Association, and that the properties of the gas in this flow are consistent with the properties of neutral helium atoms flowing into the heliosphere from the LISM (Witte et al. 1993). The region from which this flow originates is now called the LIC. Subsequently, Lallement & Bertin (1992) found that the flow of gas observed for sight lines in the Galactic Center direction are consistent with a different flow vector that they named the Galactic cloud, and which is now called the G Cloud. Lallement et al. (1994) noted that the sight line to Sirius A shows a second velocity feature at −5.7 ± 0.2 km s⁻¹ relative to the LIC absorption. A similar blueshifted absorption component in the direction of CMa observed by Gry & Jenkins (2001) confirmed that this extra absorption is from a third cloud called the Blue Cloud.

With the accumulated database of 270 radial velocity measurements toward 157 stars within 100 pc of the Sun, Redfield & Linsky (2008) identified 15 velocity vectors. The validity of these clouds and their morphologies was confirmed by Malamut et al. (2014), who found that nearly all of the newly observed velocity components that lie within the morphologies of clouds previously identified by Redfield & Linsky (2008) have radial velocities consistent with these cloud vector velocities. Further support for the multicomponent model comes from the scintillation of radio emission from point-source quasars (Linsky et al. 2008). In the present paper we find that the radial velocities of 49 out of 52 velocity components toward stars within 10 pc have radial velocities consistent with the clouds in their directions. Although the multicloud model fits essentially all of the available data, the assumption of discrete clouds with constant internal flows and finite edges may be unrealistic. An alternative model proposed by Gry & Jenkins (2014) in which the LISM consists of one cloud with internal velocity gradients filling all of space within 9 pc may be more realistic, although it does not fit the data as well as the multicomponent model (Redfield & Linsky 2015).

The third stage in the development of empirical LISM studies, beginning with this paper, is the recognition that the temperatures and turbulent velocities within the LIC and other clouds are not homogeneous but have a wide range of values. Whether or not this distribution is random remains to be seen. A future stage in understanding of the LISM would be the identification of the physical causes responsible for these variable parameters on the basis of observations. A related question is whether the clouds completely fill space within about 4 pc, as discussed in Section 3.12, or whether an intercloud medium separates the clouds especially at larger distances. Breitschwerdt et al. (2000) proposed that the LIC and other warm clouds are produced by fragmentation due to hydromagnetic Rayleigh–Taylor instabilities that occur where the Local Bubble and Loop I interact. This formation mechanism would be consistent with the clouds being isolated structures separated from other clouds by an ionized intercloud medium.

In parallel with the empirical studies, theoretical models and physically based simulations have developed in two stages. The first stage involved models that included many heating and cooling processes, but assumed that there is energy and pressure balance in an assumed quiescent and static ISM. Theoretical models of a multicomponent ISM (Field et al. 1969; Wolfire et al. 1995, 2003) assume that the balance between heating and cooling processes plays the critical role in identifying the likely temperature-pressure structures in the ISM. In these models, warm interstellar gas is usually modeled as two stable phases: the warm neutral medium (WNM), consisting of neutral hydrogen and other species, and the warm ionized medium (WIM) in which hydrogen is fully ionized. The WNM and WIM can coexist at the same thermal pressure given the model assumptions. The WIM is often called an H ii region ora Strömgren sphere surrounding a star emitting strong EUV radiation (see Linsky et al. 2019).

Since there is strong evidence that near the heliosphere the LIC is partially ionized, n_e /n_H = 0.07 cm⁻³/0.195 cm⁻³ = 0.35 (Slavin & Frisch 2008), neither of the two warm models may provide a useful prototype for the properties of the LIC and other nearby clouds. Our data on temperatures in the LIC and nearby partially ionized clouds can test these models.

In the second stage, numerical simulations of the ISM powered by supernova explosions and winds and radiation from hot stars predict a very different ISM. The simulations of de Avillez & Breitschwerdt (2005) and de Avillez & Breitschwerdt (2012), for example, show that dynamical phenomena resulting from shock waves and instabilities create a time-dependent nonequilibrium ISM in which there are no steady-state phases and all parameters (temperatures, turbulent velocities, densities, and magnetic fields) have a wide range of values both spatially and over time. Also, highly nonlinear heating and cooling processes mean that time-independent energy balance is not realistic. In these simulations more than half of the mass is in thermally unstable phases predicted by the steady-state models. Are these simulations relevant for describing the LISM embedded inside an old supernova remnant, or are the steady-state theoretical models of a more quiescent LISM a better approximation? The diverse properties of the LIC and the nearby warm clouds provides an opportunity to begin testing these very different models.

One of the predictions of the steady-state theoretical models is that temperatures in both the WNM and WIM lie in the thermally stable range 5040–8310 K (Wolfire et al. 2003) with wider limits depending on the rates of heating and cooling. Lower temperatures should be unstable due to rapid cooling to very low temperatures becoming CNM gas. By contrast, the probability distribution function for temperatures is roughly flat between 100 K and 10⁶ K in the Breitschwerdt & de Avillez (2021) simulations. We measured temperatures in a number of clouds with T > 10,000 K, the highest temperature with small uncertainty being $T=12,{050}_{-790}^{+820}$ K for the sight line to V368 Cep through the LIC. These high temperatures are probably inconsistent with steady-state energy balance in the WNM and WIM models and the rapid increase of Lyα cooling with increasing temperature.

Table 8 lists the sight lines through clouds with low interstellar gas temperatures. There are 13 velocity components in 10 sight lines with temperatures below 3500 K, but many have large uncertainties. Four velocity components have temperatures including 1σ positive errors that lie below 3500 K: HD 72905 (π¹ UMa), HD 129333 (EK Dra), and HD 220657 (υ Peg). These stars do not lie in similar directions, but both EK Dra and υ Peg are at the edges of clouds and the sight line to π¹ UMa passes close to the center of the LIC. These velocity components provide evidence for interstellar matter somewhat cooler than T < 3500 K, well below the nominal temperature regime for WNM models. The low temperatures are distributed among seven known clouds and two sight lines without known clouds. In most cases the sight lines pass through the edges or just outside of clouds. We note that the sight line to 70 Oph includes low temperatures through three clouds, and the sight line to υ Peg contains low temperatures through two clouds. These two stars are well separated in Galactic coordinates. However, the sight lines to SAO 28753, η UMa, and EK Dra are in similar directions, suggesting that these low temperatures could have a common origin. Since two of these identifications are unassigned to any known cloud and the sight line to the third (EK Dra) passes through the edge of or just outside of the LIC, the low temperatures may occur in interstellar matter outside of partially ionized clouds, perhaps in the WNM. The LLCC, located between 11.3 pc and 24.3 pc from the Sun according to Peek et al. (2011), has a temperature of 15–30 K, which is definitely CNM. None of the low-temperature sight lines listed in Table 7 is near the LLCC (centered at l = 222°, b = 44°).

Table 8. Low-temperature Sight Lines

HD	Name	l	b	d (pc)	〈v〉	T	ξ	Ref.	Cloud
48915	α CMa	227.2	−8.9	2.6	12.70	${3000}_{-1000}^{+2000}$	2.7 ± 0.3	2	Blue
GJ 873	EV Lac	100.6	−13.1	5.0	4.44 ± 0.43	${3030}_{-610}^{+670}$	${2.21}_{-0.23}^{+0.22}$	1	(Hyades)
165341	70 Oph	29.9	11.4	5.1	−26.50 ± 0.07	${2700}_{-2300}^{+3000}$	${3.64}_{-0.44}^{+0.42}$	2	G
165341	70 Oph	29.9	11.4	5.1	−32.53 ± 1.30	${1700}_{-1700}^{+2100}$	3.3 ± 1.1	2	(Oph)
165341	70 Oph	29.9	11.4	5.1	−43.34 ± 0.92	3300 ± 2100	2.31 ± 0.37	2	(Aql)
72905	π1 UMa	150.6	35.7	14.5	12.91 ± 0.43	${2450}_{-660}^{+740}$	${2.47}_{-0.11}^{+0.10}$	1	LIC
43162	GJ 3389	230.9	−18.5	16.7	17.1 ± 0.43	${3200}_{-2330}^{+2680}$	${5.76}_{-0.26}^{+0.25}$	1	LIC
116956	SAO 28753	113.7	59.5	21.7	7.7	${2540}_{-1830}^{+2450}$	${1.66}_{-1.66}^{+1.21}$	1	Unassigned
120315	η UMa	100.7	65.3	30.9	2.6 ± 3.4	${0}_{-0}^{+4400}$	${5.6}_{-1.1}^{+0.9}$	2	Unassigned
129333	EK Dra	105.5	49.0	34.6	−2.43 ± 0.32	${2580}_{-250}^{+280}$	${3.13}_{-0.05}^{+0.05}$	1	(LIC)
93497	μ Vel	283.0	08.6	35.9	−4.38 ± 0.43	${3470}_{-590}^{+580}$	${3.12}_{-0.10}^{+0.11}$	1	G
220657	υ Peg	98.6	−35.4	53.1	8.8 ± 1.2	${1000}_{-1000}^{+1900}$	${3.46}_{-0.63}^{+0.61}$	2	(Hyades)
220657	υ Peg	98.6	−35.4	53.1	1.73 ± 0.39	${1700}_{-900}^{+1100}$	3.93 ± 0.22	2	(Eri)

References. (1) This paper; (2) Redfield & Linsky (2004b).

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The observed diversity of temperatures inside the LIC and in other partially ionized clouds raises the question of what physical processes could be responsible. Localized heating by hydromagnetic shocks is an obvious candidate that needs to be pursued with high-spatial-resolution observations. Another possibility is a change in the energy balance on small spatial scales resulting from a change in the local heating or cooling rates driven by local changes in the ionization. Cooling per unit volume by the emission of optical and UV photons following electron collisional excitation of atoms and ions is proportional to the product n_e n_{H i} (Draine 2011). If the dominant heating process is from photoelectrons emitted by dust grains following absorption of UV photons, then the heating rate per atom is proportional to the dust density and thus the heating rate per unit volume is proportional to n_{H i} ². If these two processes dominate the energy balance, then n_e plays a critical role. Higher electron densities lead to enhanced cooling and thus lower temperatures, while lower electron densities lead to decreased cooling and thus higher temperatures. Support for this prediction comes from the Gry & Jenkins (2001) analysis of the CMa sight line, where n_e is lower in the Blue Cloud than the LIC but the temperature of the Blue Cloud is higher.

All previous analyses of absorption lines in the LISM and the present work have assumed that the component of line broadening that depends on mass is thermal, so that line widths measure gas temperatures. Studies of the heliosphere indicate that small-scale nonthermal processes such as shocks and charge exchange produce pickup ions that create a plasma with both thermal and suprathermal velocities. Suprathermal velocities are most easily detected in lines of low-mass atoms such as D i (m = 2), because turbulent broadening dominates over thermal broadening for high-mass ions such as Mg ii (m = 24). Thus what we have called temperature may in fact be a combination of thermal and suprathermal velocities, and the observed inhomogeneous "temperatures" may be due in part to spatial differences in the suprathermal broadening. Also, the different timescales for ionization and recombination for warm gas in the ISM cause the plasma to be out of equilibrium such that the electron temperature responsible for line broadening can be very different from a "temperature" characterizing ionization balance (e.g., de Avillez & Breitschwerdt 2012).

Small-scale variations in the thermal and suprathermal velocity structure can be maintained for a long time by inhomogeneous magnetic fields, since the Larmor radius of a 7000 K thermal electron in a 3 μG magnetic field is 0.2 km and for a thermal proton is 350 km. Thus inhomogeneous structures smaller than 5000 au can be maintained by random magnetic fields much smaller than 3 μG even for protons with energies much larger than thermal.