Star formation rates

 

The work presented in this Chapter is not independent research, but is a project led by Lawrence Cram which is closely related to the work described in this thesis. It follows on from results presented in Chapter 5 and it is particularly relevant to suggestions posed at the end of the previous Chapter.

Radio source populations

In the vast majority of extragalactic radio sources with 1.4 GHz flux density $S_{1.4}{\ifmmode\stackrel{>}{_{\sim}}\else$\stackrel{>}{_{\sim}}$\fi}1$mJy the radio emission is produced by a "monster" emitting a spectral power density $P_{1.4} {\ifmmode\stackrel{>}{_{\sim}}\else$\stackrel{>}{_{\sim}}$\fi}10^{23}$WHz^-1 (e.g. Condon 1989 [17], especially his Fig. 12; Wall & Jackson 1997 [106]). These sources are members of the class of powerful radio galaxies. Their optical hosts are intrinsically bright elliptical galaxies with red colours and optical luminosities of the order of 5 x 10³⁷W [62]. While the monster may stimulate some nuclear star formation, or vice versa, there is not a tight relationship between the radio power and either the number of stars or the current rate of star formation in the host galaxy.

Many of the remaining extragalactic radio sources with $S_{1.4}{\ifmmode\stackrel{>}{_{\sim}}\else$\stackrel{>}{_{\sim}}$\fi}1$mJy, as well as a large fraction of fainter sources, belong to a different population. These have optical counterparts that are spiral (if V ${\ifmmode\stackrel{<}{_{\sim}}\else$\stackrel{<}{_{\sim}}$\fi}18.5$) or blue peculiar (if V ${\ifmmode\stackrel{>}{_{\sim}}\else$\stackrel{>}{_{\sim}}$\fi}18.5$) galaxies with a wide range of optical luminosities, often displaying evidence of current star formation [62,7]. For the brighter members of this population it is known that there is a tight correlation between the far-infrared (FIR) luminosity and the 1.4 GHz radio power (reviewed by Condon 1992 [18]). Astrophysical interpretations of this correlation usually identify both the FIR and the radio emission as the consequence of ongoing star formation. As a corollary, the opportunity exists to determine the current rate of star formation from measurements of the FIR or radio luminosity.

The astrophysical significance of this is heightened by the fact that very sensitive radio surveys can reveal large numbers of star-forming galaxies at redshifts well beyond $z\sim0.1$, at an epoch where there is growing evidence that some classes of galaxies experience star formation at a rate higher than in the local Universe. In this paper we calibrate the relationship between radio luminosity and star formation rate using local star-forming radio galaxies, and apply the calibration to determine the current star formation rate in a sample of galaxies at $0.1{\ifmmode\stackrel{<}{_{\sim}}\else$\stackrel{<}{_{\sim}}$\fi}z{\ifmmode\stackrel{<}{_{\sim}}\else$\stackrel{<}{_{\sim}}$\fi}0.5$.

Estimators of star formation rates

There are several measures of the current star formation rate in galaxies, including the U-band magnitude, the strength of Balmer line emission, the power radiated in the FIR, and the radio luminosity. Here we check empirically the utility of these indicators by using a sample of nearby galaxies for which the radio flux density and several other indicators are available.

Radio continuum emission at 1.4GHz from star-forming galaxies is mainly synchrotron radiation produced by relativistic electrons. It has long been acknowledged that supernovas could play a role in accelerating these electrons [8,59]. This view has been reinforced by the discovery of the tight correlation between radio continuum and FIR emission (reviewed by Condon 1992 [18]). Explanations of the correlation usually suggest that massive stars dominate both radiation mechanisms, and imply that the supernova rate determines the non-thermal radio luminosity. At first sight there is a serious problem with this interpretation, since the total radio luminosity of a galaxy divided by the typical luminosity of a supernova remnant implies supernova rates that are far too high [8,39]. The problem can be resolved consistently with the current understanding of supernova shock acceleration mechanisms by supposing that accelerated electrons, and perhaps the acceleration process itself, endure beyond the $\sim 2 \times 10^4$yr lifetime of detectable remnants [24]. The relationship between the radio luminosity and the supernova rate can then be calibrated using the Galactic values of $L_{1.4} \sim 2.3 \times 10^{22}$WHz^-1 and $\nu_{SN} \sim 1/43$yr^-1. From this Condon (1992) [18] estimates the star formation rate (SFR) for stars massive enough to form supernovas (i.e., $M \ge 8$M$_{\odot}$) and then adjusts this using a model for the initial mass function (IMF) with $\Psi(M) \sim M^{-5/2}$ to obtain

$$SFR_{1.4} (M \ge 5\,{\rm M}_{\odot}) = \frac{L_{1.4}}{4.0 \times 10^{21}\,{\rm WHz}^{-1}}\,{\rm M}_\odot\,{\rm yr}^{-1}.$$ (7.1)

An alternative account of the relationship between the SFR and the radio luminosity rests on the possibility that the major contributors to the non-thermal emission are radio supernovae (with lifetimes of 100yr or so) rather than remnants (with lifetimes of 20000yr) [14]. This model predicts a value of SFR within a factor of $\sim2$ of that given by Equation 7.1.

The use of the U-band luminosity to infer a current star formation rate rests on the idea that the emission arises mainly from the photospheres of young, massive stars [27,73]. Cowie et al. (their Equation 1) give an expression involving the UV luminosity L(2500Å) which corresponds to

$$SFR_{U} (M \ge 5\,{\rm M}_{\odot}) = \frac{L_U}{5.9 \times 10^{21}\,{\rm WHz}^{-1}}\,{\rm M}_{\odot}\,{\rm yr}^{-1}.$$ (7.2)

Balmer line emission from star formation in galaxies is the recombination radiation formed in the HII regions excited by early-type stars. Kennicutt (1983) [57] has determined the theoretical relationship between the H$\alpha$ luminosity and the current star formation rate in a galaxy in a form corresponding to

$$SFR_{H\alpha} (M \ge 5\,{\rm M}_{\odot}) = \frac{L(H\alpha)}{1.5 \times 10^{34}~{\rm W}}\,{\rm M}_{\odot}\,{\rm yr}^{-1}.$$ (7.3)

An average correction for extinction of 1.1 magnitude has been applied as suggested by Kennicutt (1983) [57], who also emphasises that variations in extinction imply that individual measurements of H$\alpha$ luminosity must be treated with caution (this point applies also the U-band measurements). Kennicutt points out that the statistical properties of a sample will be considerably more accurate.

FIR emission from star-forming regions is due to the absorption of stellar photospheric radiation by grains, with subsequent re-radiation as thermal continuum in the far infrared. A simple theory relating the FIR power of a galaxy to its current star formation rate can be based on the proposition that essentially all of the UV and much of the blue radiation from massive stars is absorbed by grains, with the associated thermal re-radiation appearing as emission in the $40-120\,\mu$m band. From these ideas Condon (1992) [18] derives a star formation rate equivalent to

$$SFR_{\rm FIR} (M \ge 5\,{\rm M}_{\odot}) = \frac{L_{60 \mu{... ...\times 10^{23}\,{\rm WHz}^{-1}}\,{\rm M}_\odot\,{\rm yr}^{-1},$$ (7.4)

Thronson & Telesco (1986) [99] derive a rate that is $\sim 2.3$ times larger than this, the difference being a fair indication of the unavoidable uncertainty in such theories.

  

Figure 7.1: Comparison of star formation rates deduced from 1.4GHz luminosities (horizontal axis) with the rates deduced using the other luminosities indicated. Solid symbols denote data from the high redshift samples of Benn et al. (1993) [7] (squares), and this thesis (circles).

A comparison of the rates predicted by Equations 7.1 to 7.4 for a sample of local galaxies is illustrated by crosses and open symbols in Figure 7.1, which plots the SFR deduced from U-band, FIR and H$\alpha$ luminosities against the SFR deduced from the 1.4 GHz luminosity. Four "reference" samples have been used to test the relations, as listed in Table 7.1. The data of Kennicutt & Kent (1983) [58] and Lehnert & Heckman (1996) [65] were chosen because these authors tabulate a relatively large number of integrated H$\alpha$ luminosities. Eales et al. (1988) [35] and Condon et al. (1991) [22] were chosen to give good coverage of IRAS galaxies. Values of the H$\alpha$ equivalent widths or luminosities have been taken from the original papers. The NASA Extragalactic Database (NED) has been consulted to obtain U-band and FIR photometry and most of the necessary redshifts, as well as the V-band photometry needed to convert H$\alpha$ equivalent widths to flux densities. Values of the 1.4GHz flux densities are taken from the original papers where available, using a spectral index of $\alpha=-0.8$ ( $S_{\nu}\propto\nu^{\alpha}$) to convert from other frequencies where necessary. The on-line NVSS database [21] was used in the other cases. A point is plotted in the Figure whenever a galaxy has a radio luminosity and at least one other luminosity - we do not require that all SFR indicators be available before plotting a galaxy.

Also plotted on Figure 7.1 as solid symbols are the radio/H$\alpha$ data for two samples of distant star-forming galaxies, namely the objects classified as some variant of "*" in Table 3 of Benn et al. (1993) [7] and the objects described as "Class A" in Chapter 5. It should be recognised that a radio-selected sample of galaxies will contain a significant number of objects in which the radio luminosity is not a measure of the SFR, although the proportion falls in samples restricted to sub-mJy flux densities. The original authors have identified these galaxies on the basis of their colour and/or spectral signature. They are excluded from consideration in this Chapter.

 

 

Table 7.1: Sources of data.

		Numbers of galaxies
Authors	Selection criteria	1.4GHz	H$\alpha$	60$\mu$m	U-band
Kennicutt	optical mag limited,	78	69	73	58
& Kent (1983)	mostly spirals
Lehnert	IR-selected starbursts	28	13	27	19
& Heckman (1996)	(edge on)
Eales et al. (1988)	representative sample	63		59
	of IRAS galaxies
Condon et al. (1991)	complete sample of	40		40
	ultra-luminous IRAS
	galaxies
Benn et al. (1993)	VLA & WRST	50	39
	1.4GHz, 3 deep
	surveys
This thesis	ATCA 1.4GHz,	24	24
	deep survey

Radio luminosity as an SFR estimator

Firstly the "nearby" sample, in which several different estimators of SFR are often available for a single galaxy, is considered. Figure 7.1 indicates that SFR estimates based on the various indicators are in broad agreement with one another, but also points to the existence of systematic differences between different estimators of the SFR, as well as several objects in which at least one indicator is discordant.

The tightness of the relationship between SFR_1.4 and $SFR_{\rm FIR}$ reflects the well-studied radio/FIR correlation. A line of best fit to these points would imply that values of SFR deduced from 1.4GHz luminosities using the equations presented above are about a factor of 2 lower than those deduced from 60$\mu$m luminosities. This level of disagreement is consistent with the uncertainties in the theory underlying Equations 7.1 and 7.4. Apart from this systematic discrepancy there is a tight correlation between the two estimates, with the exception of a small number of galaxies in which the radio prediction is too high. These objects are NGC 4374 (M83) and NGC 4486 (M87) from Kennicutt & Kent (1983) [58] and IRAS 0421+040 from Eales et al. (1988) [35]. In each of these sources there is evidence that some of the radio emission is not related to star formation.

Estimates of SFR based on H$\alpha$ luminosities follow the trend of those predicted by L_1.4 or $L_{\rm FIR}$, but tend to lie above the trend at low SFR and below the trend at high SFR. A similar conclusion could have been drawn from Figure 1 of Devereaux & Young (1990) [32]. As noted by these authors, the general correlation supports the view that both the H$\alpha$ and the FIR luminosity are produced mainly by massive stars. The systematic deviations at low radio luminosity could be related to the difficulty of correcting for possible underlying H$\alpha$ absorption in the presence of weak H$\alpha$ emission. The deviations at high radio luminosities could result from a relatively larger amount of extinction in those objects undergoing the most vigorous star formation, or from the loss of Ly$\alpha$ photons by free escape or grain opacity as an alternative to recombination, or from an IMF which weights differently the high-mass stars mainly responsible for H$\alpha$ and the lower mass stars which dominate the supernova numbers (or to a combination of these factors).

Estimates of SFR based on U-band observations exhibit the greatest scatter with respect to the radio estimates. Like the estimates based on H$\alpha$ they tend to lie above the trend line at low SFR and below it at high SFR. Since even old stellar populations emit some U-band light (e.g., Bruzual & Charlot 1993 [10], Figure 1) we would expect to see the former trend; the latter could reflect enhanced extinction in vigorous starbursts.

The filled symbols in Figure 7.1 correspond to galaxies selected from very deep radio surveys. At present, only the radio luminosities and the H$\alpha$ luminosities are available. The H$\alpha$ values have sometimes been derived from quite noisy spectra which were obtained to determine redshifts rather than line fluxes, and hence they are expected to show significant scatter. The expedient of rejecting radio-selected objects that are red and/or show absorption line spectra has led to a sample which follows a trend in Figure 7.1 that is similar to the "local" sample. It is reasonable to hypothesise that the radio luminosities of these type of galaxies provide estimates of their current star formation rates according to Equation 7.1. One corollary of this is that the faint radio-selected galaxies have star formation rates comparable with those of the intrinsically luminous IRAS galaxies.

While the SFR of a galaxy is a property of interest in its own right, the ratio of the current SFR to the total number of stars that have been formed in a galaxy offers additional insight the potency of the bursts. The total mass of stars being formed in the faint radio galaxies, M, can be estimated by using the R-band luminosities in the relation

$$M = \frac{L_R}{3.4 \times 10^{11}\,{\rm WHz}^{-1}}\,{\rm M_{\odot}\,{\rm yr}^{-1}}.$$ (7.5)

Here, we have used the approximation (deduced from Bruzual & Charlot 1993 [10]) that steady star formation, with a standard IMF and occurring over a period of many Gyr, will produce an R-band absolute magnitude R$\sim5$M$_{\odot}^{-1}$. Since this approach fails to account for the contribution of the current star burst on the R-band luminosity it underestimates the significance of the burst.

  

Figure 7.2: The current star formation rate inferred from the 1.4GHz luminosity versus the total mass of stars inferred from the R-band luminosity for the objects contained in the radio-selected samples of Benn et al. (1993) [7] and this thesis.

Figure 7.2 exhibits the relationship between the SFR deduced from the radio luminosity and the total mass of stars deduced from Equation 7.5. There is a tendency for galaxies that have already formed many stars to support a higher rate of current star formation. There is also a wide scatter in the ratio of SFR to total mass at any chosen size, not all of which is due to errors of observation. There are about a dozen galaxies with a stellar mass $M \sim 10^{10}$M$_{\odot}$ and a star formation rate SFR $\geq 10$M $_{\odot}{\rm yr}^{-1}$. For such galaxies, the current burst of star formation is likely to increase the stellar mass by at least 10%, implying that the event is of considerable significance in the development of the system. These objects are reminiscent of the IRAS galaxies having high ratio of $L_{\rm FIR}/L_B$ (e.g., Sanders & Mirabel 1996 [85], their Section 2.2).

Prospects

The utility of decimetric radio luminosity as a measure of the star formation rate in a galaxy relies on observations that can be interpreted as showing that the luminosity is directly proportional to the supernova rate. Given the potential applications of this relation, it is desirable that the astrophysical interpretation of the phenomenon be explored further. Armed with the capacity to determine star formation rates from radio luminosities, we are in a position to probe the current star formation rates of galaxies to redshifts well beyond z=0.1, provided that we can obtain optical identifications and thence redshifts. Optical photometric and spectroscopic observations also help to confirm that the galaxy is not host to a "monster" and to eliminate the possibility this it is radio loud. Radio selection of the candidates will preferentially reveal objects with high rates of current star formation.

The radio frequency sensitivity of the PDS is presently being extended using the Australia Telescope, and redshifts are being sought for all the optically identified radio sources using the 2dF fibre spectrograph on the Anglo-Australian Telescope. These data will provide a significant addition to the understanding of star formation in the regime $0.1{\ifmmode\stackrel{<}{_{\sim}}\else$\stackrel{<}{_{\sim}}$\fi}z{\ifmmode\stackrel{<}{_{\sim}}\else$\stackrel{<}{_{\sim}}$\fi}1$.