AN H i COLUMN DENSITY THRESHOLD FOR COLD GAS FORMATION IN THE GALAXY

The diffuse interstellar medium (ISM) contains gas over a wide range of densities, temperatures, and ionization states. These can be broadly subdivided into the molecular phase (e.g., Snow & McCall 2006), the neutral atomic phase (e.g., Kulkarni & Heiles 1988), and the warm and hot ionized phases (e.g., Haffner et al. 2009). The neutral atomic medium (mostly neutral hydrogen, H i) is further usually subdivided into "cold" and "warm" phases (the "CNM" and "WNM," respectively). Typical CNM temperatures and densities are ∼40–200 K and ≳ 10 cm⁻³, respectively, with corresponding WNM values of ≳ 5000 K and ∼0.1–1 cm⁻³. This was originally an observational definition to distinguish between phases producing strong narrow absorption lines toward background radio-loud quasars and smooth broad emission lines (Clark 1965). Later, this separation into cold and warm phases was found to arise naturally in the context of models in which the atomic and ionized phases are in pressure equilibrium. Atomic gas at intermediate temperatures was found to be unstable to perturbations, and to migrate to either the cold or warm stable phases, given sufficient time to attain pressure equilibrium (Field et al. 1969; Wolfire et al. 1995).

Radio studies of the H i–21 cm transition have played a vital role in understanding physical conditions in the neutral ISM. The H i–21 cm excitation temperature of a gas cloud (the "spin temperature," T_s) can be shown to depend on the local kinetic temperature (T_k; Field 1959; Liszt 2001), with T_s ≈ T_k in the CNM and T_s ⩽ T_k in the WNM (Liszt 2001). Since the H i–21 cm absorption opacity for a fixed H i column density varies inversely with T_s, while the emissivity is independent of T_s (in the low opacity limit), H i–21 cm absorption studies against background radio sources are primarily sensitive to the presence of CNM along the sight line, while H i–21 cm emission studies are sensitive to both warm and cold H i. Indeed, the original evidence for two temperature phases in the neutral gas stemmed from a comparison between H i–21 cm absorption and emission spectra (Clark 1965).

Physical conditions in the neutral gas are also known to depend on the gas column density. At the low H i column densities of the intergalactic medium, N_H i < 10¹⁷ cm⁻², the gas is optically thin to ionizing ultraviolet (UV) photons and is hence mostly ionized, giving rise to the so-called Lyα forest (Rauch 1998). At higher H i column densities, 10¹⁷ cm⁻² ≲ N_H i ≲ 10²⁰ cm⁻², the H i is optically thick to ionizing photons at the Lyman limit, and the core of the Lyα absorption line is saturated. Such "Lyman-limit systems" are partially ionized and typically arise for sight lines through the outskirts of galaxies (Bergeron & Boissé 1991). At still higher H i column densities, N_H i ⩾ 2 × 10²⁰ cm⁻², the Lyα line becomes optically thick in its naturally broadened wings and acquires a Lorentzian shape; such systems are called damped Lyα absorbers (DLAs; Wolfe et al. 2005). Damped absorption is ubiquitous on sight lines through galaxy disks and, at high redshifts, has long been used as the signature of the presence of an intervening galaxy along a quasar sight line (Wolfe et al. 1986). Finally, the molecular hydrogen fraction shows a steep transition from very low values to greater than 5% at N_H i ∼ 5 × 10²⁰ cm⁻² in the Galaxy (Savage et al. 1977; Gillmon et al. 2006). Neutral gas is likely to become predominantly molecular at higher H i column densities, N_H i ≳ 10²² cm⁻² (Schaye 2001; Krumholz et al. 2009).

While it is well known that a threshold column density (N_H i ∼ 5 × 10²⁰ cm⁻²) is required to form the molecular phase, for self-shielding against UV photons in the H₂ Lyman band (Stecher & Williams 1967; Hollenbach et al. 1971; Federman et al. 1979), the conditions for CNM formation are less clear. In this Letter, we report results from H i–21 cm absorption studies of a large sample of compact radio sources that indicate the presence of a similar, albeit lower, H i column density threshold for CNM formation in the Milky Way.

We have used the Westerbork Synthesis Radio Telescope (WSRT, 23 sources), the Giant Metrewave Radio Telescope (GMRT, 10 sources), and the Australia Telescope Compact Array (ATCA, 2 sources) to carry out sensitive, high spectral resolution (∼0.26–0.52 km s⁻¹) H i–21 cm absorption spectroscopy toward 35 compact radio-loud quasars. Most of the target sources were selected to be B-array calibrators for the Very Large Array, and have angular sizes ≲ 5''. Details of the sample selection, observations, and data analysis are given in Kanekar et al. (2003), Braun & Kanekar (2005), N. Roy et al. (2011, in preparation), and N. Kanekar & R. Braun (2011, in preparation). The final optical-depth spectra have root-mean-square (rms) noise values of τ_rms ∼ 0.0002–0.0013 per 1 km s⁻¹ channel, with a median rms noise of ∼5 × 10⁻⁴ per 1 km s⁻¹ channel. These rms noise values are at off-line channels, away from H i–21 cm emission that increases the system temperature, and hence, the rms noise. A careful bandpass calibration procedure was used to ensure a high spectral dynamic range and excellent sensitivity to wide absorption (see Kanekar et al. 2003 and Braun & Kanekar 2005 for details). These are among the deepest H i–21 cm absorption spectra ever obtained (e.g., Dwarakanath et al. 2002; Kanekar et al. 2003; Begum et al. 2010) and constitute by far the largest sample of absorption spectra of this sensitivity. The use of interferometry also implies that the spectra are not contaminated by H i–21 cm emission within the beam, unlike the case with single-dish absorption spectra (Kanekar et al. 2003; Heiles & Troland 2003).

Galactic H i–21 cm absorption was detected against every source but one, B0438−436. We used the Leiden–Argentine–Bonn (LAB) survey (Kalberla et al. 2005)⁶ to estimate the "apparent" H i column density (uncorrected for self-absorption, i.e., N_H i = 1.823 × 10¹⁸ × ∫T_B dV cm⁻² (Wilson et al. 2009), where T_B is the brightness temperature) at a location adjacent to each target. The observational results are summarized in Table 1, whose columns contain (1) the quasar name, (2) its Galactic latitude, (3) the H i column density (uncorrected for self-absorption), in units of 10²⁰ cm⁻², from the LAB survey, (4) the integrated H i–21 cm optical depth ∫τdV, in km s⁻¹, and (5) the harmonic-mean spin temperature T_s in K, estimated assuming the low optical-depth limit (T_s = ∫T_B dV/∫τdV).

Finally, for the one source with undetected H i–21 cm absorption (B0438−436), we quote a 3σ upper limit on the integrated H i–21 cm optical depth, assuming a Gaussian line profile with a full width at half-maximum of 20 km s⁻¹, and the corresponding 3σ lower limit on the spin temperature.

The left panel of Figure 1 shows the integrated H i–21 cm optical depth plotted against H i column density, on a logarithmic scale. It is clear from the figure that the integrated H i–21 cm optical depth has a rough power-law dependence on N_H i for N_H i ⩾ 2 × 10²⁰ cm⁻². However, there is a steep decline in ∫τdV for H i column densities lower than this value. These properties were noted previously by Braun & Walterbos (1992) for individual spectral features (see their Figures 3–6) rather than the line-of-sight integral. A similar pattern is visible in the right panel of the figure, which plots the spin temperature T_s against N_H i. Twenty-four out of 25 sight lines with N_H i ⩾ 2 × 10²⁰ cm⁻² show T_s < 600 K, while all 10 sight lines with N_H i < 2 × 10²⁰ cm⁻² have T_s > 550 K. The median spin temperature for sight lines with N_H i ⩾ 2 × 10²⁰ cm⁻² is ∼240 K, while that for sight lines with N_H i < 2 × 10²⁰ K is ∼1800 K. Thus, there appears to be a physical difference between sight lines with H i columns lower and higher than the column density N_lim = 2 × 10²⁰ cm⁻². Note that the use of apparent N_H i only affects high-opacity sight lines and has no significant effect on our results.

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We used a number of non-parametric two-sample tests (e.g., the Gehan test, the Peto–Prentice test, the log-rank test, etc.), generalized for censored data, to determine whether the spin temperatures of sight lines with N_H i ⩾ N_lim and N_H i < N_lim are drawn from the same parent distribution. All tests used the ASURV Rev. 1.2 package (Lavalley et al. 1992) which implements the methods of Feigelson & Nelson (1985). The use of multiple tests guards against any biases within a given test, resulting from the relatively small sample size (10 systems with N_H i < N_lim) and the presence of censored values (Feigelson & Nelson 1985). Errors on individual measurements were handled through a Monte Carlo approach, using the measured values of T_s and N_H i (and the associated errors) for each sight line to generate 10⁴ sets of 35 pairs of T_s and N_H i values. The statistical significance of each result (quoted below) is the average of values obtained in these 10⁴ trials for each test. The tests found clear evidence, with statistical significance between 4.2σ and 5.3σ, that the spin temperatures for sight lines with N_H i ⩾ N_lim and N_H i < N_lim are drawn from different parent populations. Following Feigelson & Nelson (1985), our final result is based on the Peto–Prentice test, as this has been found to give the best results for very different sample sizes (Latta 1981). The two T_s subsamples (with "low" and "high" N_H i) are then found to be drawn from different parent distributions at 5.3σ significance; the probability of this arising by chance is ∼2 × 10⁻⁷.

It thus appears that sight lines with N_H i < N_lim = 2 × 10²⁰ cm⁻² have systematically higher spin temperatures than sight lines with N_H i > N_lim. The spin temperature measured here is the column-density-weighted harmonic mean of the spin temperatures of different "phases" along the line of sight (e.g., Kulkarni & Heiles 1988). For example, a sight line with N_H i equally divided between CNM and WNM, with T_s = 100 K and T_s = 8000 K, respectively, would yield an average T_s ∼ 200 K, while one with 90% of gas with T_s = 8000 K and 10% with T_s = 100 K would yield an average T_s = 900 K. In other words, a high T_s indicates the presence of a smaller fraction of the cold phase of H i. Thus, the fact that average spin temperatures are significantly higher on sight lines with low H i column densities, N_H i < 2 × 10²⁰ cm⁻², indicates that such low-N_H i sight lines contain low CNM fractions, far smaller than those on sight lines with N_H i ⩾ 2 × 10²⁰ cm⁻².

It is clear from the left panel of Figure 1 that the integrated H i–21 cm optical depth drops sharply at N_H i = N_lim, due to the decline in the CNM fraction at low H i column densities. This can be accounted for by a simple physical model in which a minimum "shielding" H i column density of WNM is needed for the formation of the cold phase in an H i cloud. Assuming that the H i–21 cm optical depth in the WNM is negligible compared to that in the CNM, the equation of radiative transfer for a "sandwich" geometry can be written as

$$\begin{equation} T_B{(V)} = \frac{T_w\tau _w}{2} + T_c (1-e^{-\tau _c}) + \frac{T_w\tau _w}{2} e^{-\tau _c}, \end{equation} \tag{ 1 }$$

where the explicit velocity dependence of τ_W and τ_C has been omitted for clarity and the integrated H i emission profile becomes

$$\begin{equation} \int T_B {dV} = \int T_w\tau _w e^{-\tau _c} {dV} + \int \bigg (T_c + \frac{T_w\tau _w}{2}\bigg) (1-e^{-\tau _c}) {dV} \end{equation} \tag{ 2 }$$

or

$$\begin{equation} N^{\prime }_{{\rm H\,\mathsc{i}}} = N_{0} e^{-\tau _c^{\prime }} + N_{\infty } (1-e^{-\tau _c^{\prime }}) \end{equation} \tag{ 3 }$$

for a measured "apparent" column density, N'_H i (assuming negligible self-opacity), a threshold column density (where τ_c → 0), N₀ ∼ T_wτ_wΔV, a saturation column density (where τ_c → ∞), N_∞ ∼ (T_c + T_wτ_w/2)ΔV, and an effective opacity, τ'_c. The effective opacity is related to the measured integrated opacity by the effective line width, ΔV, as ∫τdV = τ'_cΔV.

The upper and lower dashed curves in the left panel of Figure 1 show the above expression for (N₀ = 10²⁰ cm⁻², N_∞ = 5.0 × 10²¹ cm⁻², ΔV = 20 km s⁻¹) and (N₀ = 2 × 10²⁰ cm⁻², N_∞ = 10²² cm⁻², ΔV = 10 km s⁻¹), respectively. Note that the effective line width only shifts the curves up and down in the figure. The fact that none of the data points of the left panel of Figure 1 lie to the left of the upper curve indicates that a minimum shielding H i column of [N₀/2] ∼ 5 × 10¹⁹ cm⁻² is needed for the formation of the CNM. Note that, in the above "sandwich" geometry, a total WNM column density of ≳ 10²⁰ cm⁻² is needed before any CNM can be formed.

Most theoretical models of the diffuse ISM treat it as a multi-phase medium, consisting of neutral and ionized phases in pressure equilibrium (e.g., Field et al. 1969; McKee & Ostriker 1977; Wolfire et al. 1995). In the McKee–Ostriker model, physical conditions in the ISM are regulated by supernova explosions, whose blast waves sweep up gas in the ISM into shells, leaving large cavities full of hot ionized gas (McKee & Ostriker 1977). Cold atomic gas is then formed by the rapid cooling of the swept-up and shocked gas. Soft X-rays from neighboring hot ionized gas and stellar UV photons penetrate into the CNM and heat and partially ionize it, producing envelopes of warm neutral and warm ionized gas (WIM). Thus, a typical ISM "cloud" (see Figure 1 of McKee & Ostriker 1977) is expected to form at the edges of supernova remnants and super-bubbles containing the hot ionized medium (HIM). Such a cloud consists of a CNM core surrounded by a WNM envelope and a further WIM shell, all of which are in pressure equilibrium. The CNM core is almost entirely neutral, the WNM and WIM are partially ionized, and the HIM is almost entirely ionized (McKee & Ostriker 1977).

A threshold H i column density for CNM formation in an ISM cloud arises quite naturally due to the need for self-shielding against ionizing UV (and soft X-ray) photons (see also Schaye 2004). At low H i columns, UV photons can penetrate all the way into a cloud core and heat (and partly ionize) the H i. Only clouds that self-shield against the penetration of these high-energy photons can retain a stable CNM core. Self-shielding against UV photons is significant once the optical depth at the Lyman limit crosses unity, i.e., for N_H i ⩾ 10¹⁷ cm⁻², and becomes more and more efficient with increasing H i column density. Our results indicate that self-shielding only becomes entirely efficient at excluding UV photons from the interior of H i clouds at a total H i column density of N_H i ∼ 2 × 10²⁰ cm⁻². Below this threshold, sufficient UV photons penetrate into the cloud interior to hinder the survival of the cold phase. The simple "sandwich" model overlaid in the left panel of Figure 1 suggests that a shielding column of ∼(0.5–0.75) × 10²⁰ cm⁻² on each exposed surface of a cloud is sufficient to exclude UV photons, with the rest of the H i then free to cool to lower temperatures.

It is also possible that sight lines with low N_H i are sampling gas at higher distances from the Galactic plane, with lower metallicity and pressure. Two-phase models that incorporate detailed balancing of heating and cooling rates obtain lower CNM fractions at lower pressures and metallicities (Wolfire et al. 1995). Observationally, Kanekar et al. (2009) have found evidence for an anti-correlation between spin temperature and metallicity in high-z DLAs, with low-metallicity DLAs having higher spin temperatures, probably because the paucity of metals yields fewer cooling routes (Kanekar & Chengalur 2001). If low-N_H i sight lines contain "clouds" with systematically lower metallicities (and/or pressures), these could have lower cooling rates and hence lower CNM fractions. Unfortunately, we do not have estimates of either pressure or metallicity along our sight lines and hence cannot test this possibility. We note that all sight lines with high spin temperatures are at intermediate or high Galactic latitudes, b > 40° (see Figure 2), suggesting larger distances from the plane. Conversely, the figure also shows that low spin temperatures (≲ 400 K) are obtained even for sight lines at high Galactic latitudes (b ∼ 40°–70°). Measurements of the metallicity and pressure along the low-N_H i sight lines, through UV spectroscopy, would be of much interest.

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There have been earlier suggestions, based on semi-analytical or numerical treatments of self-shielding, that H i clouds are predominantly neutral for N_H i ≳ 10²⁰ cm⁻² (e.g., Viegas 1995; Wolfe et al. 2005). However, this is the first direct evidence for a change in physical conditions in H i clouds at this column density. Note that this is a factor of several lower than the known threshold of N_H i ∼ 5 × 10²⁰ cm⁻² for the formation of molecular hydrogen in Galactic clouds, set by the requirement of self-shielding against UV photons at wavelengths in the H₂ Lyman band (Savage et al. 1977). Thus, there appear to be three column densities at which phase transitions occur in ISM clouds, at N_H i ∼ 2 × 10²⁰ cm⁻² resulting in the formation of cold H i, at N_H i ∼ 5 × 10²⁰ cm⁻² resulting in the formation of molecular hydrogen, and finally, at N_H i > 10²² cm⁻², when most of the atomic gas is converted into the molecular phase.

In this context, it is vital to appreciate that the abscissa of Figure 1 refers to apparent H i column density under the assumption of negligible self-opacity of the H i profile. The saturation column density, N_∞, is an observational upper limit to ∫T_BdV and does not represent a physical limit on N_H i. In fact, the widespread occurrence of the H i self-absorption phenomenon within the Galaxy (Gibson et al. 2005) and the detailed modeling of high-resolution extragalactic H i spectra suggest that self-opacity is a common occurrence (Braun et al. 2009) which can disguise neutral column densities that reach N_H i ∼ 10²³ cm⁻².

The original definition of a DLA as an absorber with N_H i ⩾ 2 × 10²⁰ cm⁻² was an observational one, based on the requirement that the damping wings of the Lyα line be detectable in low-resolution optical spectra of moderate sensitivity (Wolfe et al. 1986). With today's 10 m class optical telescopes, it is easy to detect the damping wings at significantly lower H i column densities, ∼10¹⁹ cm⁻² (e.g., Péroux et al. 2003); such systems are referred to as "sub-DLAs." There has been much debate in the literature on whether or not DLAs and sub-DLAs should be treated as a single class of absorber and on their relative importance in contributing to the cosmic budget of neutral hydrogen and metals (e.g., Péroux et al. 2003; Wolfe et al. 2005; Kulkarni et al. 2010). Wolfe et al. (2005) argue that DLAs and sub-DLAs are physically different, claiming that most of the H i in sub-DLAs is ionized and at high temperature, while that in DLAs is mostly neutral; this is based on numerical estimates of self-shielding in DLAs and sub-DLAs against the high-z UV background (Viegas 1995). Our detection of an H i column density threshold for CNM formation that matches the defining DLA column density indicates that DLAs and sub-DLAs are indeed physically different types of absorbers, with sub-DLAs likely to have significantly lower CNM fractions than DLAs, at a given metallicity.

In summary, we report the discovery of a threshold H i column density, N_H i ∼ 2 × 10²⁰ cm⁻², for cold gas formation in H i clouds in the ISM. Above this threshold, the majority of Galactic sight lines have low spin temperatures, T_s ≲ 500 K, with a median value of ∼240 K. Below this threshold, typical sight lines have far higher spin temperatures, >600 K, with a median value of ∼1800 K. The threshold for CNM formation appears to arise naturally due to the need for self-shielding against UV photons, which penetrate into the cloud at lower H i columns and heat and ionize the H i, inhibiting the formation of the CNM.

We thank the staff of GMRT and WSRT for help during the observations. GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research. WSRT is operated by ASTRON with support from the Netherlands Foundation for Scientific Research (NWO). N.K. acknowledges support from the Department of Science and Technology through a Ramanujan Fellowship. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.