5 Time variability

The two ROSAT PSPC surveys of M 31, separated by $\sim$1 year, and the Einstein survey from $\sim$11 years before the first ROSAT survey can be used to search for long term variability within the sources. We treat this here in two different subsections. Readers who wish to investigate long term variabilities or the search for transients should refer to both sections (5.1 and 5.2), and are strongly recommended to read Sect. 4.1 in S97.

Concerning any two catalogues 1 and 2 which refer to the same sources, we used for a quantitative study of possible long term variabilities a linear significance parameter following Primini et al. (1993), which is defined as:

$$S(F_{\rm 1} - F_{\rm 2}) = \frac{\vert F_{\rm 1} - F_{\rm 2}\vert}{\sqrt{\sigma^2_{F_1} + \sigma^2_{F_2}}} \, ,$$ (1)

where $F_{\rm 1}$ and $F_{\rm 2}$ represent the X-ray flux in the first and second source catalogues and $\sigma_{F_1}$ and $\sigma_{F_2}$ give the corresponding flux errors. This definition is useful in that, in cases where an inappropriate spectral model has been used to compute the two fluxes, any systematic errors are disregarded. We state time variability only for sources with $S \ge 3\sigma$. Additionally, sources within the bulge and other confused or "handicapped'' regions (e.g. beneath the ribs of the PSPC support structure) were excluded on cautionary grounds.

   
5.1 Comparison with the ${\mathsfsl {Einstein}}$ sources

 

 

Table 2: List of X-ray sources showing flux variability between the Einstein observation and the ROSAT observations. $F_{\rm R}$ gives the ROSAT source flux using the Einstein spectral model of TF (thermal bremsstrahlung with $kT = 5~\mbox{keV}$ and $N_{\rm H} = 7\times 10^{20}~\mbox{cm}^{-2}$ in the 0.2-4.0 keV energy band) and $F_{\rm E}$ gives the Einstein source flux of the correlated Einstein source. Column "S'' lists the significance of the variability as described in the text. A "T'' in this column indicates bright transients or possible faint transients when enclosed in brackets (see Sect. 5.1 for a detailed explanation).

ROSAT	$F_{\rm R} \, (\times 10^{13})$	Ein.	$F_{\rm E} \, (\times 10^{13})$	$F_{\rm R}/F_{\rm E}$	S
RXJ-No.	(cgs)	No.	(cgs)
0040.2+4034	$19.87 \pm 0.29$		<10.00	>2.00	T
0041.7+4134	$14.38 \pm 0.49$	9	$8.72 \pm 1.08$	$1.65 \pm 0.21$	3.66
0041.8+4021	$24.25 \pm 0.76$	11	$15.54 \pm 0.88$	$1.56 \pm 0.10$	5.69
0042.2+4019	$40.38 \pm 1.23$	15	$48.83 \pm 1.61$	$0.83 \pm 0.04$	3.89
0042.2+4101	$9.53 \pm 0.32$	16	$3.88 \pm 0.75$	$2.46 \pm 0.48$	4.48
0042.2+4112	$9.04 \pm 0.25$	19	$4.26 \pm 0.54$	$2.12 \pm 0.28$	4.45
0042.2+4118	$9.71 \pm 0.32$	14	$3.23 \pm 0.51$	$3.01 \pm 0.49$	6.09
0042.6+4052	$32.45 \pm 0.53$	51	$9.16 \pm 1.01$	$3.54 \pm 0.40$	15.33
0042.8+4131	$18.62 \pm 0.45$	67	$11.95 \pm 1.10$	$1.56 \pm 0.15$	4.30
0043.1+4118	$7.54 \pm 0.24$	82	$2.03 \pm 0.31$	$3.72 \pm 0.58$	6.69
0043.3+4117	$4.44 \pm 0.25$	88	$1.31 \pm 0.34$	$3.39 \pm 0.89$	3.66
0046.4+4201	$10.08 \pm 0.31$	105	$5.52 \pm 0.89$	$1.83 \pm 0.30$	3.33
	SI: < 0.35	12	$2.56 \pm 0.50$	< 0.14	(T)
	SI: < 0.44	40	$1.59 \pm 0.62$	< 0.28	(T)
	SII: < 2.01	75	$4.02 \pm 0.56$	< 0.50	(T)
	SI: < 0.40	84	$1.99 \pm 0.49$	< 0.82	(T)
	SI: < 0.35	96	$3.50 \pm 0.94$	< 0.10	(T)
	SI: < 0.39	106	$0.71 \pm 0.22$	< 0.55	(T)

As already described in Sect. 4.1.2, we compared the complete ROSAT PSPC source list of M 31 (Table 6) with the Einstein source list published by TF. The results are listed in Table 7, where, besides the fluxes (using the spectral model of TF), the flux ratios are also given. Here, we extend these calculations by the significance parameter given in formula (1), where catalogue 1 is set to the ROSAT source list and catalogue 2 is set to the Einstein source list. Applying the criteria mentioned above to accept sources only with $S \ge 3\sigma$ and outside confused regions, we come up with the remaining sources listed in Table 2. Additionally, this table contains potential transients (see below). The meanings of the columns are: Cols. 1 and 3 give the ROSAT source number (RXJ; see Table 6) and the correlating Einstein source (TF's source list) respectively, Cols. 2 and 4 list the (unabsorbed) flux and flux error of the sources as measured with ROSAT and Einstein respectively, the spectral model of TF having been applied (thermal bremsstrahlung with $kT = 5~\mbox{keV}$ and $N_{\rm H} = 7\times 10^{20}~\mbox{cm}^{-2}$ in the 0.2-4.0 keV energy band), Col. 5 lists the flux ratio between the ROSAT and the Einstein observations, and Col. 6 gives the significance parameter as described above, or a transient indicator "T'' (see below).

Variable sources:
Table 2 lists 11 (long term) variable sources. From a comparison between the Einstein detected sources reported by TF and the sources found in the first ROSAT survey of M 31 we reported 15 potentially variable sources in S97. Actually, 10 of the S97-reported 15 sources vanish from the variability list, and 6 new variable sources join the list. Among the 10 vanished sources, 6 lay within the bulge region (Einstein sources #33, #58, #68, #76, #79, and #80) and have therefore been rejected from our very stringent list (we were not so restrictive for Table 3 of S97). For 2 sources (Einstein sources #70 and #348), the fluxes of the corresponding ROSAT sources have been substituted with the data from the second PSPC survey, which were closer to the Einstein fluxes, and the significance of variability therefore fell below our threshold. Einstein source #2 now correlates with ROSAT source RX J0040.0+4031 (formerly ROSAT source #55) instead of ROSAT source RX J0040.0+4033 (formerly ROSAT source #57) because we obtained an improved position from the second PSPC survey data, cancelling the prior correlation. Finally, we deleted by hand the correlation pair of Einstein source #27 with ROSAT source #172 because it lies close to the bulge within a confused region.

Among the 6 new variable sources, 3 came into the list due to their newly determined fluxes from the second PSPC survey data (ROSAT sources RX J0041.8+4021, RX J0043.1+4118, and RX J0046.4+4201), 2 joined the list because of the now improved positions of the correlating ROSAT sources (RX J0042.2+4112 and RX J0042.2+4118) and the last one (RX J0043.3+4117) was newly discovered within the second survey data.

In cases where a change in determined flux (between the first and second PSPC survey) is responsible for changes in the variable source list, one should bear in mind that this might be due to a real flux change (variability) of the particular source within the time gap between the two ROSAT surveys ($\sim$1 year). In assembling Table 2, we assumed that the changes are due to the better flux determination within the data of the second PSPC survey compared to the first. Readers who wish to investigate the variable sources are therefore recommended to examine all sources in both lists.

The two variable sources reported by Collura et al. (1990) have been discussed already in S97. Including the second PSPC survey data has added nothing of significance as regards these.

Transients:
Table 2 lists 7 possible (bright) transient sources. We define bright transients as those sources which are detected in one catalogue, and are bright enough to be detected in the other, but which are not seen. ROSAT sources with fluxes $\ge$ $10^{-12} \mbox{ erg cm}^{-2} \mbox{ s}^{-1}$(applying the spectral model of TF) should have been seen during the Einstein observations. Conversely, Einstein sources with fluxes $\ge$ $10^{-12} \mbox{ erg cm}^{-2} \mbox{ s}^{-1}$ should have been seen in the ROSAT surveys.

From a comparison between the Einstein detected sources reported by TF and the sources found in the first ROSAT survey of M 31, we reported 9 potentially transient sources in S97. In detail, we have now "lost'' 5 of these transients, 3 of them because the relevant Einstein sources (#81, #93, and #100) were found to correlate with sources detected within the second PSPC survey data, and the other two because they lay within confused regions. On the other hand, we included 3 new transients in our list (Einstein sources #12, #75, and #84) because, within the first PSPC survey their positions were near the PSPC support structure and therefore we formally excluded them from the list at that time. With the help of the second PSPC survey and its more homogeneous exposure, we were able to verify their potential transient nature. For all transients, we list in Table 2 a flux upper limit. In the case of the ROSAT fluxes, we compute these limits from the known background fluxes at the source positions making use of the most sensitive survey (indicated by SI/SII for the first/second PSPC survey). Although 3 sources were partially obstructed by the PSPC support structure within the first survey (see above), for 2 of them we calculated their upper limits from these data because these positions still received more exposure within the first survey than within the second. In these cases, we simply used the second survey and its homogeneity as a proof to clarify their transient nature.

We list all 6 transients at the bottom of Table 2 as faint transients ("T'' within brackets) as they have luminosities below our bright transient threshold given above, even though their Einstein luminosities are above the detection threshold of the ROSAT surveys.

For the one transient in Table 2 not seen by Einstein (ROSAT source RX J0040.2+4034), we give our transient threshold of $10^{-12}~\mbox{erg~cm}^{-2}~\mbox{s}^{-1}$ as an upper limit because TF did not mention the limiting flux of the individual Einstein observations. With this value, we are surely above the sensitivity of the Einstein observations.

   
5.2 Comparison between the two ROSAT PSPC surveys

In Sect. 3.3 we described the merge of the two source lists assembled from the first and second PSPC surveys of M 31. Sources which were found in both lists have been tested for variability in flux. To indicate a possible variability we have applied the following criteria: (1) The source must reside outside the bulge and outside other confused regions, (2) the significance parameter (Eq. (1)) must hold with $S \ge 3$($F_{\rm 1}$ and $F_{\rm 2}$ being the fluxes of the source determined from the first and second surveys), (3) sources with an upper limit to the count rate in the B-band in either of the two surveys have been excluded (in other words, the count rate must have been determinable), (4) sources behind/near the PSPC support structure within the first survey have been excluded (i.e. sources marked with a $\dagger$-symbol in Table 5 of S97, (5) the sources have to belong to source class "1'' in both surveys, and (6) the detection likelihood of the source has to be $\ge$20 in both surveys. Criterion (1) prevents any pseudo-variability occurring due to uncertain flux determinations within confused regions, criterion (2) ensures a sufficient significance, and with criteria (3) to (6), the influence of any systematic errors should be widely excluded.

 

 

Table 3: List of all the potentially long term variable sources found via a comparison of the first and second ROSAT PSPC surveys of M 31. Column "S'' lists the significance of the variability as described in text. Additionally, possible transients are tabled, marked with "T'' in this column.

ROSAT	${\rm Rate}_{\rm SI}$	${\rm Rate}_{\rm SII}$	${\rm Rate}_{\rm SI/SII}$	S
No.	( $\mbox{ct} * \mbox{ks}^{-1}$)	( $\mbox{ct} * \mbox{ks}^{-1}$)
RX J0038.4+4012	$12.61 \pm 0.66$	$9.03 \pm 0.78$	$1.40 \pm 0.14$	3.51
RX J0040.7+3959	<2.81	$5.54 \pm 1.01$	<0.51	T
RX J0041.1+4002	$1.96 \pm 0.64$	$5.57 \pm 1.01$	$0.35 \pm 0.13$	3.04
RX J0041.5+4105	<1.27	$12.36 \pm 0.69$	<0.10	T
RX J0041.6+4101	$1.49 \pm 0.31$	$3.10 \pm 0.40$	$0.48 \pm 0.12$	3.20
RX J0041.8+4015	$3.18 \pm 0.58$	$7.02 \pm 1.04$	$0.45 \pm 0.11$	3.24
RX J0041.8+4021	$60.52 \pm 1.22$	$90.56 \pm 2.85$	$0.67 \pm 0.02$	9.68
RX J0041.8+4101	$11.73 \pm 0.71$	$6.25 \pm 0.51$	$1.88 \pm 0.19$	6.28
RX J0041.8+4122	$6.11 \pm 0.58$	$2.69 \pm 0.43$	$2.27 \pm 0.42$	4.75
RX J0042.1+4110	$4.20 \pm 0.46$	$6.83 \pm 0.65$	$0.62 \pm 0.09$	3.28
RX J0042.1+4118	$13.85 \pm 0.79$	$35.01 \pm 1.21$	$0.40 \pm 0.03$	14.68
RX J0042.2+4039	$3.90 \pm 0.39$	$8.12 \pm 0.71$	$0.48 \pm 0.06$	5.24
RX J0042.2+4055	$10.13 \pm 0.69$	$6.59 \pm 0.52$	$1.54 \pm 0.16$	4.10
RX J0042.2+4101	$35.60 \pm 1.18$	$29.59 \pm 1.02$	$1.20 \pm 0.06$	3.85
RX J0042.2+4112	$24.95 \pm 1.02$	$33.74 \pm 0.95$	$0.74 \pm 0.04$	6.33
RX J0042.2+4118	$11.31 \pm 0.73$	$36.25 \pm 1.21$	$0.31 \pm 0.02$	17.64
RX J0042.3+4113	$18.74 \pm 0.87$	$66.18 \pm 0.96$	$0.28 \pm 0.01$	36.58
RX J0042.4+4104	$6.95 \pm 0.56$	$17.85 \pm 0.83$	$0.39 \pm 0.04$	10.87
RX J0042.4+4112	$22.09 \pm 0.94$	$44.15 \pm 0.76$	$0.50 \pm 0.02$	18.34
RX J0042.5+4048	$1.69 \pm 0.32$	$3.91 \pm 0.46$	$0.43 \pm 0.10$	3.97
RX J0042.6+4052	$121.17 \pm 1.99$	$58.12 \pm 1.50$	$2.08 \pm 0.06$	25.28
RX J0042.8+4125	$14.75 \pm 0.84$	$21.27 \pm 0.98$	$0.69 \pm 0.05$	5.05
RX J0042.9+4146	$3.55 \pm 0.53$	$7.64 \pm 0.72$	$0.46 \pm 0.08$	4.57
RX J0043.1+4048	<2.27	$5.53 \pm 0.62$	<0.41	T
RX J0043.1+4112	$3.06 \pm 0.41$	$5.63 \pm 0.56$	$0.54 \pm 0.09$	3.69
RX J0043.1+4118	$5.58 \pm 0.57$	$28.17 \pm 0.91$	$0.20 \pm 0.02$	21.05
RX J0043.3+4120	$6.74 \pm 0.62$	$10.07 \pm 0.91$	$0.67 \pm 0.09$	3.02
RX J0043.4+4118	$6.86 \pm 0.62$	$11.96 \pm 0.76$	$0.57 \pm 0.06$	5.20
RX J0043.4+4126	<1.50	$5.87 \pm 0.52$	<0.26	T
RX J0043.7+4124	<1.53	$3.72 \pm 0.50$	<0.41	T
RX J0043.7+4136	$7.04 \pm 0.56$	$2.16 \pm 0.36$	$3.26 \pm 0.60$	7.35
RX J0043.9+4122	$4.82 \pm 0.48$	$2.07 \pm 0.36$	$2.33 \pm 0.47$	4.56
RX J0044.3+4145	$1.17 \pm 0.35$	$3.07 \pm 0.42$	$0.38 \pm 0.12$	3.51
RX J0044.4+4121	$29.77 \pm 1.12$	$25.10 \pm 1.02$	$1.19 \pm 0.07$	3.08
RX J0044.8+4225	<2.74	$4.85 \pm 1.11$	<0.56	T
RX J0045.6+4208	$19.18 \pm 0.92$	$25.83 \pm 1.11$	$0.74 \pm 0.05$	4.63
RX J0045.7+4139	$147.96 \pm 1.91$	$134.43 \pm 1.96$	$1.10 \pm 0.02$	4.95
RX J0046.4+4201	$29.58 \pm 1.14$	$37.64 \pm 1.15$	$0.79 \pm 0.04$	4.99
RX J0046.4+4204	$20.61 \pm 0.99$	$33.17 \pm 1.16$	$0.62 \pm 0.04$	8.24
RX J0047.4+4152	<2.08	$3.35 \pm 0.54$	<0.62	T
RX J0047.8+4142	<2.70	$7.02 \pm 1.15$	<0.38	T
RX J0048.4+4157	$46.28 \pm 1.64$	$35.30 \pm 2.16$	$1.31 \pm 0.09$	4.05

With these criteria, 34 possible long term variable sources were found, as listed in Table 3. Column (1) gives the ROSAT RXJ-number of the source, Cols. (2) and (3) list the count rate in the B-band determined from the data of the first and second surveys respectively, Col. (4) gives the ratio in count rate between the first and second survey, and Col. (5) gives the value of the significance parameter, following Eq. (1).

Additionally, Table 3 contains possible transients, marked with a "T'' in Col. (5). For this, the sensitive flux limit was determined within the survey in which the source was not found, using the source position from the other survey (i.e. where the source was detected). If this value was below the count rate minus the $1\sigma$ count rate error determined from the survey where the source was found, then this source was considered as a possible transient. To prevent false diagnoses being made, the same criteria as above for the variable source search were applied except for criterion (2) which was dropped, and criterion (3), which was substituted as just described. With this, no transients were found which could be seen only in the first survey but not in the second. This is mainly due to the exclusion of regions near the PSPC support structure within the first survey which results in a reduction in area and may have removed a few transient candidates from our (conservative) list. Additionally, the second survey with its homogeneous exposure is more sensitive in the outer region of M 31 than the first survey. As a consequence of these two effects, we found 8 transients which were seen in the second survey but not in the first. Because of the very different conditions of both surveys (mainly the influence of the PSPC support structure in the first survey), we desist from a quantitative analysis of a transient rate and its comparison with expected theoretical values.

If we readopt criterion (2) in a slightly changed form, that the upper flux limit for transient sources also represents the error in flux, we would come up with values for the significance parameter always below our threshold of 3 except for source RX J0041.5+4105 where S = 7.67. Here, we could quote source RX J0041.5+4105 as a strong candidate for a transient, whereas all the others must be considered as weak candidates.

Some words concerning ROSAT source RX J0040.2+4034: In Sect. 5.1, from a comparison with the Einstein source list of TF, we have indicated this source as a possible transient. If the increase in flux between the Einstein observations and the first ROSAT survey is based on a short-time outburst of this transient source, we would expect this source to appear much fainter during the second PSPC survey or even disappear. Actually, with the criteria applied to merge both source lists as described in Sect. 3.3, the source seemed to disappear, as no correlating source could be found within the second survey. Nevertheless, a visual inspection suggested an identification of ROSAT source RX J0040.2+4034, only found within the first survey (source #69, Table 5 in S97), with ROSAT source RX J0040.2+4033, only detected within the second survey. Both sources are listed separately in Table 6. Under the assumption that these two sources are the same source we note a large decrease in count rate (by over a factor of 40) between the first and second surveys. This would tie in with the possible transient nature of this source. On the other hand, the fact that these two sources are separated by $57 \hbox{$^{\prime\prime}$ }$ and are both good quality detections argues against this treatement. We therefore list both sources as individual sources in our list.