Large Scale Structure and Galaxy Evolution

The fascinating observations obtained with the HST, in particular the ongoing analysis of the few thousand galaxies in the Hubble Deep Field shows that there is already significant evolution detectable in the comoving star formation rate density by looking back to a redshift of 1. (Madau, 1998). Already looking back between z = 0.5 and z = 1 (3 - 4 h^-1Gyr) there should be a noticeable increase of a factor 2 - 3 in SFR density. The SFR density appears to peak around z = 1.5 with the most vigorous evolution between z = 1 and z = 3. This analysis is largely based on optical photometry and spectroscopy of galaxies in the HDF.

Little is known, however, about the evolution of the HIin galaxies out to redshifts of 1 and beyond, because present day instruments lack the sensitivity and resolution to directly measure the HIin galaxies at these redshifts. Damped Ly$\alpha$ studies (Lanzetta et al. 1995) indicate that the comoving HImass density is roughly 5 - 10 times the present beyond z = 1 and out to z = 3. This is also the period during which metal-rich gaseous halos appear, confirming that this is an era of strong evolution, where it is imperative to have good insight into the evolution of the HIcontent of galaxies.

The SKA can measure the HIin galaxies back to redshifts of $z \approx 3$ and will revolutionize this area of research. The great potential of SKA is that, unlike optical surveys, it will be able to find galaxies independent of effects of extinction and color using the HI, with the additional advantage that once an object has been found the HI line provides an accurate redshift at the same time. To fully exploit the scientific potential one needs both the HIand optical information. The latter will be coming forward from planned surveys such as the Sloan Digital Sky Survey (SDSS, Gunn and Weinberg 1995) and projects with the Hubble Space Telescope, such as the Hubble Deep Field. The SKA will probe a piece of parameter space, i.e. the neutral gas content, which is absolutely required for understanding galaxy evolution and can only be probed at radio wavelengths.

To fully demonstrate the potential of a large radio telescope facility such as the SKA three specific examples of studies involving measurement of the HI21-cm line in distant galaxies will be described here: (i) a deep ``pencil beam'' survey of an area of one square degree out to redshift of z > 4; (ii) a shallower survey of an area of 1000 square degrees to a limiting redshift of about 1; and (iii) a search for low column density intergalactic HIemission to try to map out the structure of the HIresponsible for the Ly$\alpha$ forest lines.

Before discussing these it should be emphasised that observing the 21-cm HIline in emission has special requirements for the geometry of SKA. HIstudies require high surface brightness sensitivity rather than sub-arcsecond resolution since the brightness temperatures of the emission are at most several tens of Kelvin. Thus there always is a delicate tradeoff between resolution and surface brightness sensitivity. For example: to reach a brightness temperature limit of 0.5 Kelvin in 12 hours of integration time (roughly corresponding to a column density limit of a few 10¹⁹ atoms cm^-2) one requires a resolution of 1-3 arcsec for redshifts below z = 2. This implies that one needs to have most of the collecting area in baselines below 100 km. In contrast to this: continuum emission usually has much higher brightness temperatures and can therefore be observed at much higher resolution.

A Deep SKA HIPencil Beam Survey

Let us consider a 360 hour integration on a single field of one square degree. For HIstudies one requires high surface brightness sensitivity rather than sub-arcsecond resolution. A 1 km² array with baselines up to 100 km will provide a resolution of 1" at 610 MHz (z = 1.3) corresponding to a linear size of 4.4 kpc (for H₀ = 100 km/s/Mpc and $\Omega = 1.0$). Such an instrument will be able to detect L_* galaxies (which typically have HImasses of 3.5x10⁹ h^-2M$_{\odot}$) out to redshifts of z = 3, i.e. beyond the redshift range where the universe shows considerable evolution. Using the HImass function of Zwaan et al. (1997) shown in Fig. 1.3 and assuming no evolution of the HIproperties of galaxies with redshift one can calculate how many galaxies one would expect to detect in a one square degree field of view per redshift interval. Table 1.1 gives a brief summary.

  

Figure 1.3: Lower panel: The distribution of HImasses of the detected galaxies. The error bars are given by Poisson statistics. Upper panel: The thin line is the sensitivity of the survey. The measured HImass function per decade is given by the points. The thick line is a Schechter luminosity function with the parameters given in the upper right corner. (from Zwaan et al. 1997)

 

Table 1.1: Detectable HIMasses for an SKA Deep Pencil Beam Survey

Red-shift	Look Back Time	HIMass Limit	Number of Detections
	(h-1 Gyr)	(h-2 M$_{\odot}$)
0.5 - 1.0	3.0 - 4.2	1.3 108	3.2 105
1.0 - 1.5	4.2 - 4.9	2.8 108	2.5 105
1.5 - 2.0	4.9 - 5.3	5.0 108	9.9 104
2.0 - 2.5	5.3 - 5.6	9.0 108	7.0 104
2.5 - 3.0	5.6 - 5.7	1.4 109	3.6 104
3.0 - 3.5	5.7 - 5.8	2.2 109	2.3 104
3.5 - 4.0	5.8 - 5.9	3.4 109	1.0 104
4.0 - 4.5	5.9 - 6.0	5.1 109	0.8 104

 

Out to a redshift of 2 the resolution will be sufficient to resolve a fair fraction of the galaxies. This implies that one can obtain rotation curves, mass distributions, gas fractions for some 10⁵ galaxies between now and 5 h^-1Gyr ago. One would be in a unique position to trace the evolution of the ISM in galaxies over a substantial fraction of the age of the universe, from the era of strongest evolution and star formation activity until the present. In addition one would learn whether and how the evolution depends on the dark matter content and environment. Low surface brightness galaxies for example appear to be rather unevolved, happen to avoid the denser regions in the universe and probably have low density dark matter halos (de Blok and McGaugh 1997). This notion, however, is based on only a small number of well studied objects and clearly a survey like that described here is required to firmly establish such relationships.

The great advantage of a ``pencil beam'' survey as described here is, of course, that the selection of objects in the field is entirely based on HIcontent and not on the associated stellar component. The selection is therefore independent of the effects of extinction, color and optical surface brightness. The selection does, of course, depend on HIcontent and HIsurface brightness. The combination of deep, HIselected samples and deep, optically selected samples will be extremely powerful for studying galaxy evolution over a large range of redshift.

In addition to the HIcontent the survey will also measure the continuum emission of the galaxies in the field. The continuum emission is known to correlate almost perfectly with the far IR emission of spiral and irregular galaxies (Helou 1991, Condon 1992,Lisenfeld et al. 1996). The FIR emission appears to be a good indicator of massive star formation rate so that one can use the continuum emission to probe the star formation rates of the detected galaxies, independent of the effects of extinction. This information can be used to link the star formation rates to the HIcontents of galaxies as a function of redshift and environment. In addition it will provide an independent estimate of the evolution of the comoving star formation rate density to be compared with the optically determined functions (Madau 1998).

With such a pencil beam survey it will also be possible to verify the characteristics of the Tully-Fisher relation over distances out to z = 2 using the flat part of the rotation curves and establish whether it can be used as a reliable tool for independent distance determinations. Tully-Fisher work will even be possible out to higher redshifts, since all one needs to measure is a redshift and an HIprofile width. An L_* galaxy (assuming no evolution in the gas fraction, which is quite unlikely) can be detected out to redshifts of 3 in a 360 hour integration.

Large scale structure studies from a shallow, wide area survey

  

Figure 1.4: Number of detected galaxies and volume sampled for a number of recent large galaxy redshift survey projects. Optical surveys are shown in blue and HI(HIPASS) surveys in red. The SKA would sample to greater depths than presently possible, and would sample galaxies in atomic hydrogen, thereby viewing galaxian masses independent of stellar content or star formation history.

In addition to a ``pencil beam'' survey one can perform a shallow survey covering a large area of sky to a depth of $z \sim 1$. In 12 months of observing time one could cover 1000 square degrees and be able to detect L_* galaxies out to a redshift of $z \sim 2$ (or about 75% of the age of the universe). Assuming the Zwaan et al. (1997) HImass function one expects to detect $\sim 10^7$ galaxies in a volume of $\sim 10^7$ Mpc³. This is orders of magnitude more than in optical surveys, such as the Sloan Digital Sky Survey (Gunn and Weinberg 1995) and the AAO 2dF Survey (Lahav 1995, Cannon 1995). The properties of the SKA wide field survey are compared to those of large optical surveys in Fig. 1.4.

The great potential of such an HIsurvey is the possibility of studying the large scale structure in the universe to greater depth than possible at present. The large coverage in redshift, coupled to the large number of detectable objects makes it possible to trace the evolution of large scale structure with redshift out to at least z = 1.3. Or in other words provide the tools to determine structures and density fluctuations on scales between 10h^-1 and 4800h^-1 Mpc. The evolution of large scale structure with redshift contains information about the different cosmological parameters and is a very powerful tool for testing various structure formation models. Determining clustering properties at the earliest possible epochs will be crucial, as pointed out by Van de Weygaert and Van Albada (1997).

The use of HIas a tracer of the galaxy population offers the additional advantage that for the galaxies with optical photometry one can use the Tully-Fisher method to derive distances independent of redshift and probe the peculiar velocity field to determine the mass density field in the universe. The number of data points from a survey as described above will greatly exceed the present catalogues of peculiar velocities (Dekel 1994, Sigad et al. 1998) and, moreover, have greater precision. A comparison of the mass density field with the actual distribution of galaxies provides a means of putting strong constraints on cosmological parameters.

The Ly$\alpha$ forest seen in the 21-cm HIline

Numerical models suggest that the high redshift Ly$\alpha$ forest is part of a complicated structure of gaseous filaments and sheets formed in the gravitational fluctuations in the underlying dark matter potential (Zheng et al. 1997, Hernquist et al. 1996, Cen et al. 1994). The exact structure of the gas giving rise to the Ly$\alpha$ forest and the precise connection to galaxies formed at early epochs from the original density fluctuations still remains a matter of debate. Lanzetta and coworkers (Lanzetta et al. 1995 and references therein) compare Ly$\alpha$ forest redshifts with the redshifts of galaxies along the same line of sight and find redshift coincidences for galaxies with projected separations of typically 10 to 100 kpc. They argue that the Ly$\alpha$ forest arises from galaxy disks or halos. Shull and van Gorkom and coworkers (Shull et al. 1998, van Gorkom et al. 1996) use the VLA to measure the HIcontent of galaxies along the sight line to fairly low redshift Ly$\alpha$ forest lines ( $z \sim 0.06$) and find much larger projected separations of $\sim$ 400 kpc. These results can no longer be explained as due to galaxy halos, but imply the kind of filamentary structure suggested by the simulations.

Using the inner part of SKA with baselines up to $\sim 10$ km and integrating for 100 hours one can reach limiting column densities of 10¹⁷ atoms cm^-2. The strongest Ly$\alpha$ forest lines correspond to column densities just below 10¹⁷ atoms cm^-2. On the other hand, one might expect to find somewhat higher column densities nearer to the intervening galaxies. Galaxy disks typically truncate at much higher column density levels ( $\sim 10^{19}$ atoms cm^-2), so with observation such as mentioned here one would probe the HIoutside galaxies at levels between 10¹⁷ and 10¹⁹ atoms cm^-2. This is an extremely interesting regime and the structure of the HIin the few 100 kpc vicinity of galaxies will no doubt have clues for resolving the issue of whether the Ly$\alpha$ forest arises in galaxy halos or from filamentary gaseous structures.

High Redshift CO

In order to understand galaxy formation and evolution, as well as the early history of the universe, it is essential to study the properties of galaxies at high redshift. Our knowledge of the processes by which gas becomes stars, and stars become galaxies is seriously incomplete. The primary tools used to study high redshift galaxies, optical and radio continuum observations, provide only an indirect measure of the gas content of early galaxies. CO observations, on the other hand, could provide us with a direct measure of the molecular gas content in high redshift galaxies.

At high redshifts the CO $1\rightarrow0$ line will be sufficiently redshifted to be detected by the SKA. The rest wavelength of the CO $1\rightarrow0$ line is 2.6 mm, which corresponds to a frequency of 115.38 GHz. Figure 1.5 shows the observed wavelengths for the lower CO transition lines as a function of redshift.

  

Figure 1.5: Wavelength of Observable CO transitions as a function of Redshift.

If the SKA has a minimum operating wavelength of 1.2 cm, the CO $1\rightarrow0$ line will be shifted into the observable wavelength band at redshifts greater than or equal to 4. The CO $2\rightarrow1$ line will also be sufficiently shifted at redshifts greater than or equal to 8.

To date, there have only been a handful of CO detections at high redshift. The most significant of these are shown in Table 1.2. It should be noted that the detections of CO in IRAS F10214+4724 and the Cloverleaf QSO were aided by amplification due to gravitational lensing, and that the detection in PC 1643+4621A is somewhat controversial.

Table 1.2: CO Detections at High Redshift

 

Table 1.2: CO Detections at High Redshift

Object	z	Ref.	Line	$L^{\prime}$	$S \cdot \Delta \nu$	Speak
				(h-2Kkms$^{-1}\,$pc2)	(Jykms-1)	(mJy)
IRAS F10214+4724	2.29	1	$1\rightarrow0$	$1.4\times10^{11}$	2.4	13.3
PC 1643+4621A	3.14	2	$1\rightarrow0$	$9.4\times10^{11}$	10	$\approx 15$
53W002	2.39	3	$1\rightarrow0$	$1.2\times10^{11}$	1.9	5.0
BR 1202-0725	4.69	4	$5\rightarrow4$	$1.8\times10^{10}$	2.7	9.3
Cloverleaf QSO	2.56	5	$3\rightarrow2$	$6.1\times10^{10}$	8.1	23

 

Here we consider two scenarios in predicting the detectability of CO at high redshifts: The first requires a burst of initial star formation at an early epoch, and has been modeled theoretically by several authors. The second is a constant luminosity model in which a typical spiral galaxy is observed at large redshifts.

Evans  et al.,  (1996) reported negative CO detection from 11 high redshift powerful radio galaxies in the range 1<z<4. To account for these non-detections, it has been suggested (Ikuta  et al.,  1997) that the content of CO in galaxies with redshifts below 4 is intrinsically less that those with redshifts above 4. This is supported by galactic wind models for formation of elliptical galaxies (Arimoto & Yoshii 1987), and bulge-disk models for formation of spiral galaxies (Arimoto & Jablonka 1991). In these models, the formation epoch of galaxies is assumed to be z=10, with the galactic wind occurring 0.85 Gyr after formation, when the thermal energy released from supernovae explosions exceeds the binding energy of the gas. The initial masses are taken to be $M_{init} = 2 \cdot 10^{12} M_{\odot}$ and $2 \cdot 10^{11} M_{\odot}$ for the ellipticals and bulge-disk galaxies, respectively. The bulge-disk galaxies are considered to behave like modified, small ellipicals.

  

Figure 1.6: CO Luminosity as a Function of Redshift. Observations from Table 1.2 are shown as asterisks; open circles are upper limits observed by Evans   et al.,  1996

Figure 1.6 shows the CO luminosities predicted by a galactic wind model for elliptical galaxies (Ikuta  et al.,  1997), compared to a model with a constant luminosity of $1.5 \times 10^{9}$ h^-2Kkms^-1pc². The latter value is representative of an average Sb or Sc galaxy (Solomon  et al.,  1992), and is taken as the ``standard galaxy'' for the constant luminosity case.

Observed luminosities for IRAS F10214+4724, PC 1643+4621A, 53W002, BR 1202-0725, and the Cloverleaf QSO are shown on the plot with asterisks. BR 1202-0725, and the Cloverleaf QSO are observed in high-J states. The assumption has been made for the plot in Figure 1.6 that the ratios with the $\rm J = 1\rightarrow0$ line is about 1 (see Solomon  et al.,  (1992) and the discussion below). The CO non-detections observed by Evans et. al (1996) are also shown on the plot with open circles. (These indicate an upper limit to the CO luminosity.)

Figure 1.7 shows the integrated flux density as a function of redshift for a source with a CO luminosity as given by the galactic wind model, as well as for the standard galaxy (constant luminosity with z) with a CO luminosity of $1.5 \times 10^{9}$ h^-2Kkms^-1pc². The same observational data for the sources in Figure 1.6 are also shown in Figure 1.7. The integrated flux density, was derived from the expression,

$$S \cdot \Delta \nu = \frac{L^{\prime} \, h^{2} \, \nu_{rest}^{2} \, q_{0}^{4} \, (1+z)}{2.92 \times 10^{14} \, Q^{2}},$$ (1.13)

where $L^{\prime}$ is the luminosity in h^-2Kkms^-1pc², $\nu_{rest}$ is the rest frequency in GHz, z is the redshift, q₀ is the deceleration parameter, and Q is the cosmological term associated with luminosity distance:

$$Q = q_{0}z + (q_{0} - 1)\left( \sqrt{ 1 + 2q_{0}z } - 1 \right).$$ (1.14)

A flat universe ( q₀ = 0.5) was assumed in all calculations. The Hubble constant is given by $H_{0} = h \times$100 km s^-1 Mpc^-1. $L^{\prime}$ may be related to the luminosity L, which has units of solar luminosity, by the formula:

$$L = \left( \frac{ 8 \pi \, k_{b} \, \nu_{rest}^{3} }{ c^{3} } \right) L^{\prime}.$$ (1.15)

  

Figure 1.7: Integrated ( right) and peak ( left) flux densities of CO as a Function of Redshift for both constant luminosity and galactic wind evolution.

A useful quantity in determining the ability of the SKA to detect CO at high redshift, however, is the predicted peak flux density of CO at a given redshift. This can be approximated by dividing the integrated flux density $S \cdot \Delta \nu$ by the average velocity width. Based on existing data, a reasonable value for the average velocity width is 300 km s^-1. Estimates of peak flux densities based on the galactic wind model, as well as a constant luminosity model, are shown in Figure 1.7. Existing data are again shown with asterisks.

Between redshifts of about 4 and 8, the galactic wind model peak flux densities are between about 0.1 and 1 mJy. For a 24 hour observing run, with a bandwidth of 2 MHz (28 km s^-1 at $\lambda = 1.4$ cm, at a system temperature of 70 K, the SKA would have a flux density sensitivity of $\Delta S = 0.8216 \,\mu$Jy. (A bandwidth of 2 MHz would allow 10 points across a line spectrum integrated over a galaxy with a velocity width of 300 km s^-1). Using the conservative estimate of S_peak=0.25 mJy for the peak flux density, the signal-to-noise ratio for a CO detection would be $\frac{S_{peak}}{\Delta S} \approx 300$.

This result indicates that, for the galactic wind model at least, the CO flux densities at redshifts observable by the SKA (z>4) would easily be high enough for the SKA to detect. In this simulation, CO line is undetectable beyond z = 10, since z=10 is the epoch of galaxy formation for this model.

The signal-to-noise ratio is much lower for the constant luminosity model, as shown in Figure 1.8. Nonetheless, the plot indicates that an average spiral galaxy could be detected in CO (at $5\sigma$) out to a redshift of about 20.

  

Figure 1.8: The signal-to-noise ratio for detection of CO in a 24 hour observations as a Function of Redshift. A bandwidth of 28 km s^-1 is assumed.

In comparison, for a similar observing run at its system temperature of 160 K, the VLA would have a flux density sensitivity of $\Delta S = 141.7 \,\mu$Jy. This gives a signal-to-noise ratio that is too low for detection of both the constant luminosity CO line and the galactic wind model CO line. It is thus not surprising that the data points in Fig. 1.7 are above the model curves. It is possible that a large number of sources emit CO at flux densities matching the model, but since such low flux densities cannot currently be detected, only the more outstanding data values are seen.

For very high redshifts we would expect the higher J lines to be excited as a result of the higher microwave background temperature, which increases with redshift as ${\rm T_{cmb}} = 2.7(1+z)$. At $z \approx 4.5$, this temperature becomes comparable to the mean gas temperature of lower-redshift CO clouds. This results in a change in the relative populations of the CO states, increasing the strengths of the higher-frequency CO lines, and reducing the strengths of the lower-frequency CO lines. Solomon  et al.,  predict that the CO $3\rightarrow2$ line is always comparable in strength to the CO $1\rightarrow0$ line for all very high redshift galaxies, because of the warmer microwave background.

The analysis of Solomon  et al., demonstrates that the relative strength of the higher excitation lines of CO is very dependent on gas density. Thus observations of a range of CO transitions is critical to sample the full range of gas conditions An analysis by Silk & Spaans (1997) for high-density gas, $\rm 2 \times 10^6~cm^{-3}$ suggests that the population of the J=1 state decreases by a factor of about 3 as z goes from 5 and 30.

In conclusion, the SKA will to be able to observe redshifted CO lines beyond z =10 from both large spirals and ellipticals. Starburst galaxies will be observable, although these galaxies will also be well observed using the large millimeter arrays (MMA/LSA). The SKA and the MMA/LSA will be complementary instruments to fully sample the range of physical conditions (density and temperature) of the CO that are expected to exist during the era of galaxy formation.