4 Comparison with previous investigations

Other groups have carried out similar studies already, either time-series spectroscopy (O'Toole et al. 2000; O'Toole et al. 2002; Woolf et al. 2002) or photometry (Kilkenny et al. 1999). O'Toole et al. (2000) have collected monochromatic photometric data, too, but they are not strictly simultaneous. We shall compare our results with their results in this section.

The photometric multi-site campaign of Kilkenny et al. (1999) discovered more than 50 frequencies in their frequency analysis of PG 1605+072. The five frequencies (2.076, 1.9865, 2.102, 2.2695 and 1.8912 mHz) detected in all BUSCA bands of our data were already present in their data. Some of the others which we found additionally (e.g. 4.0631 mHz) can be identified with frequencies from Kilkenny et al. (1999) and others can not (in particular at 2.7866 mHz). A closer inspection of these frequencies shows that all of them are very close to one-day aliases ($\pm$11.57  $\mu{\rm Hz}$) of the extracted frequencies of our or of Kilkenny's data to within the frequency resolution of 5.68  $\mu{\rm Hz}$. Small deviations of our measurements from those of Kilkenny et al. (1999) can be explained by the shorter time spanned by our data ($\approx$48 h compared to $\approx$217.6 h, frequency resolution: 5.68  $\mu{\rm Hz}$ compared to 1.28  $\mu{\rm Hz}$). In contrast to our analysis, Kilkenny et al. (1999) were able to resolve closely spaced frequencies, e.g. at 2.1017 $\mu$Hz and 2.1033 $\mu$Hz (see Table 2). Since 1997 the relative power within one blend of frequencies may have changed so that the frequency of unresolved peaks in the periodogram changes slightly because the contribution of the weaker feature at that time may have grown in the meantime. We conclude that the frequencies measured in the BUSCA light curves are consistent with those of Kilkenny et al. (1999). The frequencies are stable in time to within our measurement errors.

 

 

Table 1: Radial velocities (RV) of PG 1605+072 derived for ${\rm H}_{\beta }$ and ${\rm H}_{\gamma }$and for comparison of the other radial velocity studies. Woolf et al. (2002) measured their radial velocities from shifts of the whole spectrum. The radial velocities of O'Toole et al. (2002) are measured for all Balmer lines (velocity error: $\approx$0.4 km s^-1).

	${\rm H}_{\beta }$			${\rm H}_{\gamma }$		Woolf et al. (2002)		O'Toole et al. (2002)
f	P	RV	f	P	RV	P	RV	P	RV
${\rm [mHz]}$	[s]	[km s-1]	[mHz]	[s]	[km s-1]	[s]	[km s-1]	[s]	[km s-1]
2.078	481.28	12.7	2.076	481.66	14.3	481.7/475.3	3.9/4.0	480/475	4.3/8.5
2.756	362.89	8.0	2.753	363.21	6.5	363.2/366.2	3.0/6.1	365	7.2
1.985	503.79	7.9	1.978	505.77	7.2	502.0	3.9	504	4.1
						527.1	2.7

 

 

Table 2: Frequencies and corresponding periods as well as amplitudes for PG 1605+072 in the first two BUSCA wavebands (" $UV_{\rm {B}}$'' and " $B_{\rm {B}}$''). The errors of the periods and amplitudes are the formal fit errors from the sine fit procedure. The left column shows the corresponding values derived in Kilkenny et al. (1999) as a comparison to the values found in this work. The two frequencies marked with a star can not be resolved in our data but can in the data of Kilkenny (see Sect. 4 for the discussion). The phases derived within the sine fit procedure are denoted by $\phi$ and are discussed in Sect. 3 as well as the determination of the phase errors.

Kilk.'99				" $UV_{\rm {B}}$''			" $B_{\rm {B}}$''
${f_{\rm Kilk99}}$	${P_{\rm Kilk99}}$	${A_{\rm Kilk99}}$	f	P	A	$\phi$	P	A	$\phi$
${\rm [mHz]}$	[s]	[mmag]	[mHz]	[s]	[mmag]		[s]	[mmag]
2.0758	481.75	27.4	2.0760	481.69$~\pm~$0.02	36.88$~\pm~$0.12	0.684$~\pm~$0.006	481.69$~\pm~$0.02	29.27$~\pm~$0.07	0.700$~\pm~$0.008
1.9853	503.70	3.3	1.9861	503.51$~\pm~$0.03	22.59$~\pm~$0.09	0.953$~\pm~$0.010	503.60$~\pm~$0.02	22.45$~\pm~$0.06	0.951$~\pm~$0.010
$\star$2.1017	475.82	15.4	2.1020	475.74$~\pm~$0.04	19.76$~\pm~$0.11	0.026$~\pm~$0.011	475.82$~\pm~$0.03	16.94$~\pm~$0.07	0.000$~\pm~$0.013
$\star$2.1033	475.45	15.9
2.7613	362.15	1.8	2.7631	361.92$~\pm~$0.03	16.01$~\pm~$0.16	0.051$~\pm~$0.014	361.97$~\pm~$0.03	10.54$~\pm~$0.07	0.043$~\pm~$0.021
2.7663	361.49	2.0	2.7668	361.43$~\pm~$0.06	10.94$~\pm~$0.15	0.192$~\pm~$0.020
-	-	-	2.7554				363.10$~\pm~$0.02	14.97$~\pm~$0.07	0.080$~\pm~$0.015
2.2701	440.51	5.2	2.2700	440.52$~\pm~$0.05	8.92$~\pm~$0.08	0.144$~\pm~$0.025	440.54$~\pm~$0.04	6.85$~\pm~$0.05	0.148$~\pm~$0.032
1.8914	528.70	13.9	1.8915	528.69$~\pm~$0.09	7.65$~\pm~$0.09	0.675$~\pm~$0.029	528.79$~\pm~$0.05	8.25$~\pm~$0.05	0.643$~\pm~$0.027
2.7173	368.01	0.6	2.7191	367.77$~\pm~$0.06	7.45$~\pm~$0.10	0.897$~\pm~$0.029
2.3920	418.05	2.2	2.3921				418.05$~\pm~$0.04	7.87$~\pm~$0.05	0.833$~\pm~$0.028
-	-	-	4.0748				245.41$~\pm~$0.02	4.39$~\pm~$0.05	0.549$~\pm~$0.049

 

 

Table 3: Frequencies and corresponding periods as well as amplitudes for PG 1605+072 in the last two BUSCA wavebands (" $R_{\rm {B}}$'' and " $NIR_{\rm {B}}$''). The errors of the periods and amplitudes are the formal fit errors from the sine fit procedure. The left column shows the corresponding values derived in Kilkenny et al. (1999) as a comparison to the values found in this work. The phases derived within the sine fit procedure are denoted by $\phi$ and are discussed in Sect. 3 as well as the determination of the phase errors.

Kilk.'99				" $R_{\rm {B}}$''			" $NIR_{\rm {B}}$''
${f_{\rm Kilk99}}$	${P_{\rm Kilk99}}$	${A_{\rm Kilk99}}$	f	P	A	$\phi$	P	A	$\phi$
${\rm [mHz]}$	[s]	[mmag]	[mHz]	[s]	[mmag]		[s]	[mmag]
2.0758	481.75	27.4	2.0759	481.71$~\pm~$0.01	28.45$~\pm~$0.05	0.691$~\pm~$0.006	481.73$~\pm~$0.02	28.72$~\pm~$0.07	0.684$~\pm~$0.007
1.9853	503.70	3.3	1.9858	503.58$~\pm~$0.01	18.79$~\pm~$0.04	0.948$~\pm~$0.009	503.61$~\pm~$0.02	18.02$~\pm~$0.05	0.936$~\pm~$0.011
2.1017	475.82	15.4	2.1020	475.76$~\pm~$0.02	16.68$~\pm~$0.05	0.028$~\pm~$0.010	475.70$~\pm~$0.03	17.18$~\pm~$0.07	0.057$~\pm~$0.012
-	-	-	2.7530	363.23$~\pm~$0.01	17.15$~\pm~$0.04	0.054$~\pm~$0.010
-	-	-	2.7866	358.87$~\pm~$0.03	6.22$~\pm~$0.04	0.213$~\pm~$0.026
2.7427	364.60	15.1	2.7427				364.60$~\pm~$0.02	10.37$~\pm~$0.06	0.043$~\pm~$0.019
-	-	-	2.7637				361.84$~\pm~$0.02	13.40$~\pm~$0.06	0.057$~\pm~$0.015
2.2701	440.51	5.2	2.2700	440.56$~\pm~$0.03	6.85$~\pm~$0.04	0.133$~\pm~$0.024	440.60$~\pm~$0.04	6.66$~\pm~$0.05	0.183$~\pm~$0.030
1.8914	528.70	13.9	1.8914	528.71$~\pm~$0.04	6.79$~\pm~$0.04	0.670$~\pm~$0.024	528.90$~\pm~$0.06	6.88$~\pm~$0.05	0.625$~\pm~$0.029
2.3920	418.05	2.2	2.3920	418.06$~\pm~$0.03	5.80$~\pm~$0.04	0.811$~\pm~$0.028	417.94$~\pm~$0.04	6.44$~\pm~$0.05	0.821$~\pm~$0.031
4.0618	246.19	1.2	4.0624	246.16$~\pm~$0.01	4.47$~\pm~$0.04	0.458$~\pm~$0.036	246.17$~\pm~$0.02	5.38$~\pm~$0.05	0.413$~\pm~$0.037

Figure 6: Relative semi amplitudes of the four frequencies from Fig. 5. These are calculated by $\Delta{y} = \left({y}-{\bar{y}}\right)/{\bar{y}}$. y is the semi amplitude of the wavebands. The error bars are the formal 1$\sigma$ errors of the sine fit procedure.

Figure 7: Deviation of the phases from the mean value calculated from the four frequency bands for the frequencies given in Fig. 5. The error bars are calculated from the amplitude errors as described in the text.

Also the frequencies discovered in the radial velocity curves are consistent with both the BUSCA and the Kilkenny values. The time basis of the spectroscopic data is too short in comparison to the long-term photometry to resolve the frequencies. This is also true for most of the other spectroscopic feasibility studies mentioned before. Only O'Toole et al. (2002) had a sufficiently long baseline of $\approx$70 d. Thus, we discuss only the relative distribution of the power of the pulsation frequencies. As can be seen in Fig. 3 the main power is located around 2.076 mHz. Significant power arises in the frequency range 2.74-2.78 mHz but it falls off compared to the former. The same distribution of pulsation power was detected by the multi-site photometric campaign of Kilkenny et al. (1999) who carried out their observations in April and May 1997. Two years later, in July and August 1999, O'Toole et al. (2000) recovered the same frequency pattern but discovered that the amplitudes had changed and, in particular, that no power was detected at 2.076 mHz. Another year later (in May 2000) O'Toole et al. (2002) and Woolf et al. (2002) gathered data again. Both groups discovered a drastic change in the relative power distribution: The power at 2.076 mHz appeared again and was at that time weaker than that in the frequency range 2.74-2.78 mHz. This means that the power switches within a few years. Our data which were taken in May 2001, i.e. another year later, show that the power distribution switched back to that of 1997 measured by Kilkenny et al. (1999).