3 Equivalent widths

In an earlier investigation, based on smaller samples of high-redshift galaxies, we noticed an apparent anticorrelation between redshift and the strength of the C  IV 1550 Å doublet (Mehlert et al. 2001, 2002). According to Walborn et al. (1995) high-excitation lines like C  IV and Si  IV are produced mostly in stellar photospheres and winds and their strengths depend sensitively on the stellar metallicity. Although in a few cases a non-negligible ($\leq$50%) contamination of the C  IV and Si  IV features by interstellar absorption could not be excluded, Heckman et al. (1998) find for their sample of 45 nearby starburst galaxies that the C  IV and Si  IV absorption is normally produced by photospheric and stellar wind lines of the unresolved stars. We found further evidence for a close relation between the strength of these resonance lines and the metallicity of the observed starburst galaxies by measuring the equivalent widths of the C  IV 1550 Å and Si  IV 1398 Å doublets in synthetic spectra of starburst galaxies with different metallicities taken from Leitherer et al. (2001) (see Fig. 2). According to Fig. 2 for ages $\ge$10 Myr the measured equivalent widths depend strongly on the metallicity but are almost independent of the age of the starburst. Therefore, we measured for those galaxies with reliable spectroscopic redshifts z>1.35 (i.e. galaxies where the C  IV doublet was redshifted into our observed spectral range) the rest-frame equivalent widths W₀ of this feature, which is defined by

$$% W_0 = \int_{\lambda1}^{\lambda2}\left( 1-\frac{S(\lambda)}{C(\lambda)} \right){\rm d}\lambda .$$ (1)

Here we used following approximation:

$$% W_0 = \Delta \lambda - \frac{1}{C(\lambda_0)} \int_{\lambda1}^{\lambda2} S(\lambda) {\rm d}\lambda ~~ {\rm with}$$

$$\lambda_1 = \lambda_{0} - \frac{\Delta\lambda}{2};~ \lambda_2 = \lambda_{0} + \frac{\Delta\lambda}{2}\cdot$$ (2)

The central wavelength for C  IV is $\lambda_0$ = 1549.5 Å and for the width of the line window we chose $\Delta\lambda = 30$ Å. The continuum flux at the central rest frame wavelength $\lambda_0$ was approximated by the mean flux within two well defined continuum windows, one on each side of the line window. Each of these continuum windows has a width of 75 Å and is separated from the line window by 5 Å. Since the correct continuum determination is critical for the resulting W₀, its level was checked interactively. In particular it turned out that the influence of the B-band, that lies in the right continuum window of the highest-z objects is negligible with respect to the resulting W₀.

Figure 2: Measured C  IV (a) and Si  IV (b) equivalent width of the synthetic spectra of Leitherer et al. (2001) as a function of the starburst age. The model spectra are based on continuous star formation (1 $M_{\odot }$/yr) assuming the model parameter $M_{{\rm up}} = 100$ $M_{\odot }$ and $\alpha _{{\rm IMF}} = 2.35$. Circles and triangles correspond to solar and LMC metallicity, respectively.

For objects with z>1.7, where in addition the Si  IV doublet ( $\lambda_0 = 1398.3$ Å) became visible, we also measured W₀(Si  IV) with the same bandwidth and continuum window definitions as for C  IV. The same measurements were also carried out in the IUE spectra of the comparison sample of $z\approx 0$ starburst galaxies. Statistical mean errors of the individual W₀ measurements were calculated from the S/N of the individual spectra and the errors of the continuum fits ($\leq$10%). Equivalent width measurements in the spectra of faint objects can be affected severely by errors in the sky background subtraction. Therefore, during the reduction of our FORS spectra a particular effort was made to keep these errors low. Various tests showed that for all FORS spectra used in this study the errors in determining the continuum level remained below 5% (see Noll et al. 2002). Hence, systematic errors in the measured equivalent widths due to an incorrect sky subtraction are well below the statistical errors in most cases.

Another source of systematic errors in our W₀ measurements is our low spectral resolution, which in most cases did not allow us to resolve the line profiles. However, since equivalent widths measurements of strong isolated lines are in principle independent of the spectral resolution and since all our conclusions are based on differences between measurements carried out with the same procedure in spectra of the same resolution, these systematic errors are expected to cancel out and therefore are not expected to affect the results of this paper significantly. On the other hand, since the C  IV doublet is not a truly isolated feature, our numerical results for the equivalent widths should not be directly compared to results obtained from spectra with a different spectral resolution.

The results of our $W_{0}(\mbox{C~{\sc iv}})$ measurements are listed in Table 1 and plotted in Fig. 3. In order to avoid a crowding of data points at $z\approx 0$, we plotted for the local (IUE) starburst galaxies only the average value and indicate the $1\sigma$ scatter of the individual values by a bar. For the high-redshift galaxies the individual data points and their mean errors are given.

Figure 3: Measured C  IV $\lambda$ 1550 rest-frame equivalent widths as a function of redshift. The various symbols have the following meaning: Open star at $z\approx 0$: Average and $1\sigma$ rms scatter for the 36 (Heckman et al. 1998) local starburst galaxies. Open triangles: FDF galaxies. Filled triangles: Galaxies in the field of the cluster 1E0657-558 (Mehlert et al. 2001). Filled circle and square: Galaxies in the HDF-S and the AXAF Deep Field, respectively (Cristiani et al. 2000).

 

 

Table 1: Measured C  IV and Si  IV rest-frame equivalent widths for the 57 high-z galaxies. The absolute B-magnitudes derived and discussed in Sect. 5 are also listed.

No.	z	I	$W_{0}(\mbox{C~{\sc iv}})$	d $W_{0}(\mbox{C~{\sc iv}})$	$W_{0}(\mbox{Si~{\sc iv}})$	d $W_{0}(\mbox{Si~{\sc iv}})$	MB
		[mag]	[Å]	[Å]	[Å]	[Å]	[mag]
FDF-1208	2.18	23.68	3.92	0.41	3.31	0.44	-22.45
FDF-1331	3.39	23.89	1.80	0.90	-	-	-23.30
FDF-1555	3.26	23.88	1.16	0.74	1.29	0.69	-22.36
FDF-1578	2.71	24.25	3.545	0.90	2.97	0.81	-21.98
FDF-1691	2.34	23.89	3.65	0.57	4.30	0.60	-21.53
FDF-1709	1.67	24.33	6.07	0.75	-	-	-20.46
FDF-1744	2.37	24.10	2.34	0.58	4.27	0.56	-22.21
FDF-1922	1.83	23.36	3.62	0.28	0.95	0.38	-21.64
FDF-2033	2.75	24.08	5.51	0.65	4.05	0.52	-21.62
FDF-2274	2.25	23.34	1.62	0.31	2.66	0.33	-21.66
FDF-2418	2.33	23.16	6.57	0.47	6.36	0.46	-23.19
FDF-2495	2.45	23.31	3.98	0.32	3.24	0.32	-22.32
FDF-2636	2.25	23.43	5.21	0.63	6.41	0.70	-22.77
FDF-3005	2.25	23.51	6.95	0.38	8.18	0.43	-22.63
FDF-3163	2.44	23.35	4.80	0.33	5.45	0.33	-22.97
FDF-3173	3.27	23.91	2.59	0.48	4.24	0.44	-22.51
FDF-3300	2.37	23.91	2.14	0.42	2.16	0.41	-21.79
FDF-3374	2.38	23.34	5.05	0.30	5.21	0.27	-22.65
FDF-3810	2.37	22.67	4.95	0.25	5.59	0.26	-23.18
FDF-3874	2.48	23.30	2.66	0.43	3.83	0.43	-23.15
FDF-3875	2.24	24.53	4.19	0.51	3.38	0.52	-20.73
FDF-3958	2.13	23.87	4.40	0.53	1.43	0.57	-20.98
FDF-3999	3.39	24.00	3.74	0.65	7.89	0.56	-22.70
FDF-4049	1.48	23.00	4.42	0.53	-	-	-21.76
FDF-4795	2.16	23.31	5.80	0.36	5.93	0.39	-22.35
FDF-4871	2.47	23.39	7.14	0.35	6.05	0.34	-22.62
FDF-4996	2.03	23.25	3.35	0.37	1.19	0.44	-21.77
FDF-5058	2.03	23.34	4.82	0.25	3.40	0.27	-21.57
FDF-5072	1.39	22.45	3.27	0.57	-	-	-21.88
FDF-5135	2.34	23.62	2.31	0.71	1.99	0.77	-22.73
FDF-5152	1.37	22.65	3.91	0.50	-	-	-21.55
FDF-5165	2.35	23.26	5.73	0.55	6.02	0.53	-23.02
FDF-5190	2.35	24.39	2.73	0.68	2.65	0.64	-22.74
FDF-5215	3.15	22.98	2.54	0.47	2.45	0.40	-23.18
FDF-5227	2.40	23.85	4.73	0.72	2.02	0.79	-21.79
FDF-5504	3.38	23.63	3.29	1.00	7.19	0.73	-23.65
FDF-5550	3.38	23.12	2.44	0.41	5.23	0.31	-23.23
FDF-5903	2.77	22.33	4.02	0.21	4.32	0.16	-23.23
FDF-6024	2.37	22.00	4.93	0.20	5.71	0.19	-23.34
FDF-6063	3.40	22.56	1.36	0.49	4.24	0.42	-23.35
FDF-6069	2.68	24.22	5.36	0.81	3.45	0.70	-21.74
FDF-6287	2.68	24.11	1.61	0.82	-	-	-22.04
FDF-6372	2.35	23.38	3.20	0.37	3.43	0.35	-22.18
FDF-6407	2.16	23.59	5.29	0.59	4.26	0.72	-22.31
FDF-6864	1.39	23.41	4.93	0.71	-	-	-20.87
FDF-6934	2.44	22.90	4.71	0.56	3.01	0.60	-23.05
FDF-6947	2.36	23.83	5.91	0.42	4.90	0.45	-21.94
FDF-7029	2.37	23.63	6.88	0.42	5.82	0.42	-23.07
FDF-7307	2.44	24.07	2.51	0.60	3.05	0.62	-21.20
FDF-7342	2.37	23.80	6.13	0.76	4.58	0.75	-22.06
FDF-7539	3.29	23.51	1.92	0.46	4.22	0.41	-22.41
ES0657-A	2.34	24.50	5.88	0.48	3.98	0.45	-
ES0657-C	3.08	24.89	2.30	1.00	7.07	0.62	-
ES0657-J	2.61	22.98	3.81	0.42	2.41	0.26	-
ES0657-Core	3.24	24.31	2.01	0.63	3.45	0.53	-
HDFS-047	2.79	-	2.50	0.30	4.40	0.17	-
AXAF-028	3.13	-	2.84	1.00	3.45	0.97	-

Figure 4: Averages of the measured C  IV $\lambda$ 1550 rest frame equivalent widths within selected redshift bins (see Table 2) as a function of redshift for all galaxies shown in Fig. 3 (asterisks). The bars indicate the mean errors of the averages. Open triangles show all FDF galaxies brighter than MB = -22.28 mag, open squares all FDF galaxies with $-21.52~{\rm mag} \leq M_{B} \leq -20.38~{\rm mag}$(see Sect. 5 for discussion).

As demonstrated by Fig. 3 our high-redshift galaxies with z<2.5 show about the same average C  IV equivalent widths and about the same scatter around the average as the local starburst galaxies. However, for redshifts larger than about 2.5 the average C  IV equivalent widths and their scatter clearly decrease with zin our sample. As described in Sect. 2 this decrease is not driven by any selection effect since the spectroscopic redshift distribution of the included FDF galaxies is in good agreement with the photometric redshift distribution.

Figure 3 obviously confirms the effect suspected by Steidel et al. (1996a) quantitatively. In order to estimate (in view of the observed scatter) the statistical significance of the effect, we calculated averages and their mean errors of the W₀(C  IV) values for selected redshift bins. The results are listed in Table 2 and plotted in Fig. 4. The table confirms that there is no statistically significant difference between the results for the first three bins while the difference between the local sample and our starburst galaxies with z>3.0 is highly significant (>$9 \sigma$). Tests with other bin sizes and binning intervals showed that the high significance of the result persists for any reasonable bin distribution.

In Fig. 5 we present analogously to Fig. 3 the observed Si  IV equivalent width values as a function of redshift. Similarly as in the case of the C  IV doublet the average Si  IV strength does not change with redshift for z<2.5. However, unlike the average C  IV strength the average Si  IV W₀ values remain at the local value even beyond z>2.5. As a result, the ratio between the Si  IV and C  IV resonance doublets, which is practically constant for low z, varies for high redshifts in our sample. This is demonstrated quantitatively by Table 3 and Fig. 6.

 

 

Table 2: Averages and mean errors of the measured C  IV $\lambda$ 1550 rest frame equivalent widths within selected redshift bins for all galaxies listed in Table 1. N is the number of objects within each bin.

z interval	<z>	$<\mbox{C~{\sc iv}}>$	m.e.(C  IV)	N
		[Å]	[Å]
0.00 - 0.02	0.01	6.31	0.41	36
1.00 - 1.99	1.52	4.37	0.41	6
2.00 - 2.49	2.32	4.51	0.27	32
2.50 - 2.99	2.71	3.77	0.53	7
$\geq 3.00$	3.28	2.33	0.22	12

Figure 5: Measured Si  IV $\lambda$ 1400 rest-frame equivalent width as a function of redshift. Symbols as is Fig. 3.

As noted above, for local starburst galaxies the C  IV doublet as well as the Si  IV doublet are good metallicity indicators. Since both elements are produced during the evolution and explosion of massive stars, a greatly different relative chemical abundance of C and Si in the high-zstarburst galaxies appears very unlikely. In spite of the unsatisfactory state of present SN II models and the remaining large uncertainties concerning the intermediate mass element yields for different initial stellar masses, it seems very difficult to enhance Si production relative to C. On the other hand, it is well known that individual hot stars of the same metallicity show a wide range of C  IV to Si  IV line ratios. Strong C  IV absorption is well known to be universally present in O stars of all luminosity classes, while $W_{0}(\mbox{Si~{\sc iv}})$ is luminosity dependent and decreases rapidly from supergiant stars to dwarfs (Walborn & Panek 1984; Pauldrach et al. 1990; Leitherer et al. 1995). This line is, therefore, used as a luminosity indicator in UV stellar classification schemes. Moreover, Si  IV has a pronounced maximum in early B stars while C  IV changes monotonically with temperature. Finally the Si  IV strength is more strongly affected by population differences (i.e. stellar age differences) than the C  IV doublet. A scatter in these population differences can easily mask any metallicity dependence in the Si  IV line strength.

Hence, assuming that the observed absorption lines are dominated by contributions of the stellar photospheres and winds, the $W_{0}(\mbox{Si~{\sc iv}})/W_{0}(\mbox{C~{\sc iv}})$ ratio can, in principle, be used to derive informations on the star formation history (instantaneous or continuous) and/or the stellar mass distribution (see also Mas-Hesse & Kunth 1991). Therefore, Fig. 6 can possibly be understood by assuming that at the epochs corresponding to z>3 (i.e. during the first two Gyrs of the universe) instantaneous star bursts played an important role while "continuous star formation'' is the normal mode for local and lower redshift starburst galaxies. However, since the different parameters which determine the value of $W_{0}(\mbox{Si~{\sc iv}})/W_{0}(\mbox{C~{\sc iv}})$ cannot be disentangled reliably without including additional lines in the analysis, spectra of higher resolution and higher S/N are required to finally settle this issue.

The investigation of the purely interstellar lines of lower ionisation like e.g. Si  II $\lambda$ 1260, O  I/Si  II $\lambda$ 1303 and C  II $\lambda$ 1335 is in progress and the results will be published in a separate paper.

Figure 6: Averages of the ratios between the measured Si  IV and C  IV rest frame equivalent widths as a function of redshift for all galaxies shown in Fig. 5. The mean error of each average, calculated from the scatter of the individual values, is indicated by a bar.

 

 

Table 3: Average and mean error of the ratios between the measured Si  IV and C  IV rest frame equivalent widths within selected redshift bins for all high-z galaxies for which $W_{0}(\mbox{Si~{\sc iv}})$ has been measured. N is the number of galaxies within each bin.

<z>	$<\mbox{Si~{\sc iv}}/\mbox{C~{\sc iv}}>$	m.e.(Si  IV/C  IV)	N
0.00	0.76	0.04	36
2.30	0.94	0.06	33
2.72	0.95	0.18	6
3.27	1.95	0.22	11