II. Limitations upon the usefulness of L_IR/L_B and SB_IR

Before we can test whether or not (L_IR/L_B) and SB_IR can be used as an indicator of the current to integrated star formation rate, we need to highlight a number of limitations upon their usefulness.

i) Increasing bulge contribution

Figure 1a shows the median Log(L_IR/L_B) ratio for all Hubble types from Sa (T=1) through to Sdm (T=8), for the 90 non-interacting spirals (i.e. excluding pairs and mergers) listed in the sample of Young et al.1996. Figure 1b shows the comparable plot of the median Log(SB_IR) versus Hubble type. Error bars are shown for the first and third quartile values. The spiral galaxies in the sample of Young et al. 1996 were specifically selected to cover a wide range in Hubble type, intrinsic size (4 –100 kpc, H_o= 50 km/sec/Mpc) and blue luminosity (9.15 < Log(L_B/L_O) < 11.29).

We can see from figures 1a and 1b that both parameters increase slowly with Hubble type as you move from Sdm (T=8) to Sbc (T=4), before dropping off significantly for Hubble types Sa – Sb (T=1 – 3).

The simplest explanation for the marked downward trend in (L_IR /L _B) for the earlier Hubble types is the increasing bulge contribution to the galaxy’s integrated optical light. An increase in the bulge contribution increases the galaxy’s blue luminosity
but the extra blue light is not accompanied by a comparable increase in the amount of infra-red radiation, since this radiation primarily comes from the disk and not the bulge.

Similarly, an increasing bulge contribution can also be used to explain the downturn in SB_IR as you move to earlier Hubble types i.e. since the infrared luminosity primarily comes from the galactic disk, the S_IR decreases as the galacticbulge makes an increasing contribution to the overall surface area of the galactic disk.

Hence, if we want to minimize (though not eliminate) the effects of the changing bulge contribution upon (L _IR/L_B) and SB _IR , we need to limit the range in Hubble type for the spiral galaxies in our sample. Consequently, we limit the spiral galaxies in our sample to those with Hubble type lying between Sbc (T=4) and Sdm (T=8).

ii) HI gas depletion

Since the 40 - 120 micron infrared radiation emitted by spiral galaxies is almost exclusively the result of starlight being re-emitted by dust, their L _IR/L_B ratios and their SB_IR are implicitly linked to the properties of the gas and dust in these galaxies. Hence, there is a need to identify galaxies that have unusual or extreme HI gas fractions that are caused by environment.

It has been known for some time that spirals near the centres of large galaxyclusters (e.g. the Virgo cluster) have lost significant amounts of their HI gas because of evaporation and/or stripping in the dense cluster environments (Giovanelli and Haynes 1983, Giovanelli and Haynes 1985, Kenny and Young 1986, and Hashimoto and Oemler 1998). Giovanelli and Haynes (1983) quantified this loss of HI gas using a deficiency parameter:

HI def = <log(M^*_HI)> - log(M _HI)         (3)

where M^*_HI is the HI mass expected for a “normal” galaxy for a given Hubble type (T), luminosity class (L) and optical diameter (D _L ), and M _HI is the observed HI mass for a galaxy. Haynes and Giovanelli (1984) found that for a given Hubble
type (T):

<log(M^*_HI)> = c₁ + c ₂ log(D_L²)                 (4)

where c₁ and c₂ are constant coefficients. This relationship is almost independent of L­ _B .

UGC blue major diameters are needed to obtain HI deficiency values that are consistent with those of Haynes and Giovanelli (1984) . Unfortunately, direct measurements of these diameters are not available for many the spirals so we have to use an alternative indicator.

Haynes and Giovanelli’s (1984) also found that for a given T:

<log(M ^*_HI)> = c₁ + c₂ log(L_B)             (5)

though this relationship has a significantly greater dispersion than that of equation (4) and it is affected by growing bulge contribution to the blue light as you move towards earlier Hubble types.

This alternate measure of the HI gas deficiency is much more widely available as it is listed for many galaxies in the RC3 catalogue (de Vaucouleurs et al 1991) as a parameter called the HI index, given by:

HI Index = m ₂₁ - B ^o _T                         (6)

where m₂₁ is the HI line magnitude (defined in terms of the HI flux density) corrected for red shift and B^o_T is the B-band magnitude corrected for red shift, internal extinction and galactic extinction. Note: we do not correct the HI linemagnitudes for 21 cm self-absorption.

Figure 2 shows the HI deficiency of Giovanelli and Haynes (Kenny and Young 1986,1988) plotted against HI index for Sbc-Sdm spirals in the Virgo cluster (de Vaucouleurs et al 1991). We can see from this figure that the HI index is an excellent measure of HI gas deficiency (with a linear correlation coefficient r = 0.88).

For the purposes of this study, we shall assume that all Sbc-Sdm galaxies with a HI mass that is factor of 3 (HI def = 0.48) below that of a “normal” galaxy of similar Hubble type (T), luminosity class (L) and optical diameter (D _L), are gas deficient. Using figure 2, this defines gas deficient Sbc-Sdm spirals as those with an HI index greater than 2.9 ( ± 0.1). All spirals with values greater than this are placed in the HI gas depleted sample.