Constraints on Cold HI in the Halo of NGC 3079 from Absorption Measurements of Q0957+561
Judith A. Irwin , Lawrence M. Widrow , Jayanne English, PASA, 16 (1), in press.

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Introduction

Primordial nucleosynthesis calculations, together with estimates for the density of luminous matter, indicate that at least some baryonic dark matter is present in the Universe. Baryonic matter has received renewed attention of late (see Carr 1994), especially in the light of recent reports of gravitational lensing events, presumably from massive compact halo objects around the Milky Way. Other possibilities for baryonic dark matter have also been proposed. For example, several authors have investigated the possibility that this matter could be in the form of gas (e.g. Henriksen 1991; Henriksen & Widrow 1995; Pfenniger et al.1994; Pfenniger & Combes 1994).

Dark Matter as Cold Fractal Clouds

Recently, Pfenniger et al. (1994) and Pfenniger & Combes (1994) (hereafter PCM and PC, respectively) proposed a new dark matter candidate: cold primordial H₂ gas in a fractal structure. The gas resides in an extended disk or halo where the only source of heating is the 3 K background. PCM contend that the slow accretion of gas toward the visible disk solves the ``gas consumption problem" (i.e. that the timescale for gas consumption, as implied by current star formation rates, is shorter than the age of the galaxy) as well as the ``disk-halo conspiracy" (i.e. flat rotation curves through the transition region from disk to halo-dominated rotation). The motivation for a fractal-like distribution comes, in part, from observations of the ISM where both atomic and molecular hydrogen clouds exhibit hierarchical structure over a wide range of scales (see, e.g., Diamond et al. 1989, Vogelaar & Wakker 1994, and Elmegreen & Falgarone 1996).

In this paper, we describe our attempt to detect cold HI gas by searching for absorption features against a background continuum source. At the cold temperatures envisaged by PCM and PC, neither HI nor H₂ can be seen in emission. Moreover, if the gas is primordial, it would not be traceable via other molecules such as CO. HI absorption may represent a unique opportunity to constrain, through observations, the PCM and PC hypothesis, provided not all of the hydrogen is converted to molecular form (see below).

Fractal Cloud Parameters

In the PCM and PC scenario, the hydrogen cloud complexes are built out of elementary ``cloudlets" (``clumpuscules" by PC). The size of these objects (determined by setting the free-fall timescale equal to the Kelvin-Helmholtz timescale and assuming virialization) sets a minimum scale below which the gas distribution is no longer described by a fractal. For $T=3\,{\rm K}$ neutral gas, these cloudlets are characterized by the following parameters: mass, $M_*\,=\,0.8$ -

$9.2 \times 10^{-3}~M_\odot$ ; radius, $R_*\,=\,23\,$ -

$\,150~{\rm AU}$ ; number density,

$n_*\,=\,0.25\,$ -

$\,6 \times 10^9~{\rm cm^{-3}}$ ; column density,

$N_*\,=\,0.73\,$ -

$\,2.7 \times 10^{24}~ {\rm cm^{-2}}$ ; and velocity dispersion,

$v_*\,=\,0.10\,$ -

$\,0.14~{\rm km\, s}^{-1}$ . The range is due to departures from spherical symmetry and black body radiation (PC's factor f) as well as differences in mean molecular weight, $\mu$ , between pure HI + He and pure H₂ + He.

A key unknown is the atomic to molecular hydrogen ratio. At the densities found in the cloudlets, the 3-body reactions

${\rm H+H+H}\rightarrow {\rm H+H_2}$ and

${\rm H+H+H_2}\rightarrow {\rm H_2+H_2}$ may be important in converting atomic hydrogen into H₂ (see Palla, Salpeter, & Stahler 1983). Let us assume that at the time when the fractal structure develops, t₀, all of the hydrogen gas is in atomic form, with number density

$n_{\rm HI}(t_0)$ . At late times, t, the number density will be given roughly by

$n_{\rm HI}(t) = \left [ {\cal R}(T)\, (t-t_0)\, n_{\rm HI}(t_0)\right ]^{-1}$ where ${\cal R}(T)$ is the rate constant for the reaction

${\rm H+H+H_2}\rightarrow {\rm H_2+H_2}$ . ${\cal R}(T)$ has been determined only for much higher temperatures ( $\sim$ 3000 K). Extrapolating over 3 orders of magnitude to 3 K gives

${\cal R}(T)\,=\,2.3\times 10^{-30}\,{\rm cm}^6 {\rm s}^{-1}\,<br /> (3 K/T)$ . Taking

$t-t_0\sim 10\,{\rm Gyr}$ , then

$n(\rm HI)_*\sim 550\,$ - 5500 cm^-3. This corresponds to HI optical depths of 0.5 to 13. Rawlings (1988) quote a reaction rate 2 orders of magnitude lower which increase the HI fraction and optical depth proportionately. We will therefore consider

$n(\rm HI)_*/n_*$ to be a free parameter, $f_{\rm HI}$ , with HI and H₂ coexisting throughout the cloudlets. In this initial treatment, we consider optically thick HI, assume no departures from spherical symmetry (PC's parameter, f = 1) and let $\mu\,=\,2.3$ . The cloudlet parameters are then

$M_*\,=\,0.8 \times 10^{-3}~M_\odot$ ,

$R_*\,=\,23~{\rm AU}$ ,

$n_*\,=\,6 \times 10^9~ {\rm cm^{-3}}$ ,

$N_*\,=\,2.7 \times 10^{24}~ {\rm cm^{-2}}$ , and

$v_*\,=\,0.10~ {\rm {\rm km\, s}^{-1}}$ .

The cloudlets combine in a fractal structure to form clouds (denoted with subscript, c, below) which have parameters related to the parameters of the cloudlets via,

$\displaystyle M_c = {\cal N}_c M_* = \left (\frac{R_c}{R_}\right )^D M_$		$\displaystyle n_c = \left (\frac{R_c}{R_}\right )^{D-3} n_$
$\displaystyle N({\rm HI})_c = \left (\frac{R_c}{R_}\right )^{D-2} \,f_{\rm HI}\, N_$		$\displaystyle v_c = \left ( \frac{R_c}{R_}\right)^{(D-1)/2}v_$	(1)

Here ${\cal N}_c$ is the number of cloudlets in a cloud, the quantity, R_c/R_* is the scale over which fractal structure exists and D is the fractal dimension. We expect

$D\,\,\hbox{\raise 0.5 ex \hbox{$<$}\kern-.77em \lower 0.5 ex \hbox{$\sim$}$\,$}\,2$ since for $D\,>\,2$ , collisions tend to dissipate the cloud (PC). $D\,=\,2$ corresponds to an area covering factor of unity and we therefore assume that cloudlets within a single cloud do not shadow one another. For simplicity, we also extend the no-shadowing assumption to velocity space and to cloud/cloud shadowing. For clouds of equivalent mass, a lower value of D implies that the cloud will be larger and less dense.

The NGC 3079 - Q 0957+561 Pair

A fortuitous alignment of the extension of the major axis of the galaxy, NGC 3079, with the background quasar, Q0957+561 (Fig. 1, Left) has provided the opportunity to search for cold gas in an extended halo or an extended disk around the foreground galaxy. NGC 3079 (D = 15.6 Mpc; H₀ = 75 km s^-1 Mpc^-1) has been mapped in HI by Irwin & Seaquist (1991). The outermost point at which emission is observed is denoted by a small star in Fig. 1. Q0957+561 is a gravitationally lensed system (Walsh et al.1979) at a redshift of z = 1.4 (see Schmidt & Wambsganss 1998 and references therein). The projected separation between the center of NGC 3079 and Q0957+561 is 64.1 kpc at the distance of NGC 3079. A dark matter halo may extend between 100 and 200 kpc in radius (see Ashman 1992). For our purposes, we consider the lensed quasar to be simply a source of background radio continuum emission.

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ASKAP

Public

$\displaystyle M_c = {\cal N}_c M_* = \left (\frac{R_c}{R_}\right )^D M_$		$\displaystyle n_c = \left (\frac{R_c}{R_}\right )^{D-3} n_$
$\displaystyle N({\rm HI})_c = \left (\frac{R_c}{R_}\right )^{D-2} \,f_{\rm HI}\, N_$		$\displaystyle v_c = \left ( \frac{R_c}{R_}\right)^{(D-1)/2}v_$	(1)

Australia Telescope National Facility

Introduction

Dark Matter as Cold Fractal Clouds

Fractal Cloud Parameters

The NGC 3079 - Q 0957+561 Pair