RECURRENT NOVAE IN M31

M31N 1998-06a was discovered at ${{m}_{H\alpha }}=16.3$ on 1998 June 06 UT as part of the Kitt Peak National Observatory's Research-Based Science Education (RBSE) program (Rector et al. 1999). The object lies approximately 105 from the nucleus of M31 and just 18 from the nominal position of M31N 1919-09a (Hubble 1929). The probability of a chance positional coincidence with $s\leqslant 1\buildrel{\prime\prime}\over{.} 8$ at this location is estimated to be 0.030, making the object a strong RN candidate. To confirm this possibility we have located the original discovery plate (#5054) in the Carnegie archives. The plate was taken on 1919 September 21, and shows the nova at ${{m}_{{\rm pg}}}=17.6$. Figure 2 shows a scan of the plate compared with the RBSE image of 1998-06a. The novae clearly appear to be spatially coincident. Revised astrometry of M31N 1919-09a (see Table 2) shows that the nova lies $\sim 1\buildrel{\prime\prime}\over{.} 5$ from the measured position of 1998-06a, dropping the probability of a chance coincidence to 0.016. To within the uncertainty of the measured positions, the novae are consistent with being spatially coincident, and we conclude that M31N 1919-09a is very likely a RN. We note that M31N 1998-06a was detected as a faint supersoft X-ray source (SSS) 1028 ± 92 days after the optical outburst (Pietsch et al. 2005). Owing to the low number of detected photons, no estimate of the effective temperature was possible. The SSS disappeared 1773 ± 463 days after outburst (Pietsch et al. 2007a).

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M31N 2012-01b was a rapidly fading, He/N nova that was discovered on 2012 January 21.419 UT by K. Nishiyama and F. Kabashima approximately 6'' from the nominal position of M31N 1923-12c, a nova discovered by Hubble on 1923 December 11. We located Hubble's plate (H348H) in the Carnegie archives and produced a scan of the plate, a portion of which is reproduced in Figure 3 along with a chart of 2012-01b courtesy of K. Nishiyama and F. Kabashima (Miyaki-Argenteus Observatory, Japan). Nova 1923-12c, which is indicated by Hubble's hand-drawn ink marks, appears to lie at the same position as 2012-01b. The revised astrometry of 1923-12c (see Table 2) confirms that the nova lies within 045 of 2012-01b. The probability of a chance coincidence at this location in the galaxy is estimated to be just 0.0033. We conclude, as initially reported in Shafter et al. (2012b), that 1923-12c is a RN, and that 2012-01b is a subsequent eruption of Hubble's 1923 nova.

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A possible recurrence of M31N 1926-06a, 1962-11a, was discovered by Rosino (1964) as part of his multi-year nova survey. As pointed out by Henze et al. (2008a), the recurrence was discovered independently by Börngen (1968). Our expanded screen shows that the published position of M31N 1962-11a lies $\sim 6\buildrel{\prime\prime}\over{.} 3$ from the reported position of 1926-06a (nova #62 in Hubble 1929). We were successful in locating the original discovery plates (H304D and H309D) in the Carnegie archives. Figure 4 shows a comparison of the position of M31N 1926-06a and that of 1962-11a from Henze et al. (2008a). The novae appear coincident. Revised astrometry of M31N 1926-06a (see Table 2) reveals that Hubble's nova lies within $1\buildrel{\prime\prime}\over{.} 40$ of the position of 1962-11a. The probability of a chance coincidence at this location in the galaxy is just 0.010, and we conclude that M31N 1962-11a is almost certainly a recurrence of 1926-06a.

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Our coarse screen indicated that M31N 1926-07c, nova #65 in Hubble (1929), might be coincident with a nova that erupted 54 yr later, M31N 1980-09d (Rosino et al. 1989). Examination of the finding charts for the two novae shown in Figure 5, clearly demonstrate that the novae are not spatially coincident. However, revised astrometry for M31N 1926-07c (see Table 2) and further analysis of it's precise position unexpectedly revealed that the nova was coincident with both M31N 1997-10f and 2008-08b, a nova pair also identified as a RN candidate in our coarse screen.

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M31N 1997-10f was discovered by Shafter & Irby (2001), and confirmed by Lee et al. (2012). A possible recurrence was discovered by Henze et al. (2008a), who noted that the position of M31N 2008-08b was nearly coincident with 1997-10f (${{P}_{C}}\simeq 0.045$), making the latter object likely a RN. We have located the original image from Shafter & Irby (2001) and re-measured the coordinates of M31N 1997-10f (see Table 2), confirming the association with 2008-08b.

The positions of M31N 1926-07c, 1997-10f, and 2008-08b are compared in Figure 6, which shows that all three novae are indeed spatially coincident to within the resolution of the images (${{P}_{C}}\simeq 0.024$). We also note that M31N 2008-08b was spectroscopically classified as a possible He/N nova (with a quite narrow Hα FWHM) by di Mille et al. (2008). We conclude that M31N 1926-07c is a RN with 1997-10f and 2008-08b representing subsequent outbursts.

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M31N 1975-11a was observed to erupt in the outskirts of M31 at an isophotal radius, $a\sim 29^{\prime}$, and less than 1'' from the reported position of 1945-09c (Baade & Arp 1964). At this position in the galaxy, the probability of a chance positional coincidence is negligible (∼0.0004). We conclude, as did Henze et al. (2008a), that M31N 1945-09c is a RN. Finding charts for the novae are compared in Figure 7, and confirm that the novae are indeed spatially coincident. The revised coordinates for M31N 1945-09c are given in Table 2 lie only 041 from the position of 1975-11a leading to an even smaller probability of a chance positional near coincidence, ${{P}_{C}}\simeq 0.0001$.

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M31N 1960-12a erupted relatively close to the nucleus of M31 ($a\sim 4\buildrel{\,\prime}\over{.} 4$) and our initial screen revealed two possible recurrences: 1962-11b and 2013-05b. Figure 8 shows the position of M31N 1960-12a compared with 2013-05b. Revised astrometry of M31N 1960-12a yields the coordinates given in Table 2, and shows that the nova is coincident with the published position of 2013-05b to within $\sim 0\buildrel{\prime\prime}\over{.} 9$. We estimate the probability of a chance coincidence at this location in M31 is ∼0.091, and thus we consider it very likely that M31N 2013-05b is a recurrence of 1960-12a.

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As will be discussed further below, M31N 1960-12a, 1962-11b, and 2013-05b were also flagged as a possible recurrences of 1953-11a. Of these, M31N 1962-11b was the most likely recurrence with a reported separation $s\sim 2\buildrel{\prime\prime}\over{.} 9$. A comparison of the finding charts shown in both Figure 8 and later in 27 reveals that none of these novae are coincident with M31N 1953-11a.

M31N 1963-09c, which was discovered by Rosino (1973), has been observed to have three possible recurrences. 1968-09a (Rosino 1973), 2001-07b (Lee et al. 2012), and 2010-10e (Hornochova et al. 2010) have all erupted within 132 of the reported position of 1963-09c. Rosino (1973) was first to note that M31N 1963-09c and 1968-09a appeared to be spatially coincident. Given that the novae are located rather far ($a\sim 17\buildrel{\,\prime}\over{.} 6$) from the nucleus of M31, the probability of a chance positional coincidence with $s\lt 1\buildrel{\prime\prime}\over{.} 32$ is ∼0.01. Finding charts for the eruptions of M31N 1963-09c and 1968-09a from the survey of Rosino (1973) are compared with the chart of 2010-10e (Hornochova et al. 2010) in Figure 9. The novae are clearly coincident, and we conclude, as did Shafter et al. (2010), that M31N 1963-09c is a RN in M31. Consistent with this finding, spectroscopic observations of the most recent eruption (2010-10e) by Shafter et al. (2010) revealed that the nova was a member of the He/N class. In addition, M31N 2010-10e was first detected as a bright SSS only 14 ± 1 days after outburst by Pietsch et al. (2010). Henze et al. (2014a) described an X-ray spectrum characterized by a relatively high effective (blackbody) temperature of $61_{-3}^{+6}$ eV and reported that the SSS had disappeared on day 92 ± 5 after the optical outburst. Additionally, during one of the observations of Henze et al. (2014a) the X-ray light curve of M31N 2010-10e showed strong, aperiodic variability on time scales of hours.

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This RN is noteworthy in that the first two recorded eruptions occurred within a time span of just 5 yr. This was the shortest recurrence time measured for any RN until the discovery that M31N 2008-12a has a recurrence time of just 1 yr (see below). Williams et al. (2014) has studied the field of M31N 2010-10e in search of a potential red giant companion for the nova. Archival Hubble Space Telescope (HST) images reveal a resolved source $0.80\sigma$ away from the nominal position of the nova. According to Williams et al. (2014), the density of stars at this location suggests there is a 15.6% probability of such an alignment occurring by chance.

M31N 1966-09e, discovered as nova #71 by Henze et al. (2008a) on archival Tautenburg Schmidt plates, is noteworthy in that it was observed to erupt in the outskirts of M31 (almost a full degree from the nucleus of the galaxy). A recurrence was observed as M31N 2007-08d (Pietsch et al. 2007b). The reported positions differ by just $0\buildrel{\prime\prime}\over{.} 36$, and at this position in the galaxy the probability of a chance coincidence is negligible. Astrometry of M31N 1966-09e yields the coordinates given in Table 2. Figure 10 confirms that the two eruptions are indeed spatially coincident, and we conclude that M31N 1966-09e is a RN. The spectroscopic type and light curve properties of M31N 2007-08d was measured by Shafter et al. (2011b) as a relatively slow (${{t}_{2}}\sim 81\pm 11$d) Fe ii system. The recurrence was also observed in the infrared by the Spitzer Space Telescope but did not reveal an infrared excess that could be attributed to dust formation (Shafter et al. 2011a).

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M31N 1982-08b was discovered in the outskirts of M31 as nova #27 in the survey of Sharov & Alksnis (1992). A likely recurrence (nominally located $\sim 3^{\prime\prime}$ away) was discovered by Shafter & Irby (2001), who reported a nova discovered on 1996 August 12. Subsequently, the nova acquired the designation M31N 1996-08c. In reviewing the original data to produce a finding chart, we have determined that the nova was actually discovered a year later, on 1997 August 01 UT. Revised astrometry given in Table 2 shows that the novae are spatially coincident to less than 1'', which is less than the uncertainty in the absolute positions. Finding charts for the images are shown in Figure 11, confirming that the novae are spatially coincident. The probability of a chance positional coincidence is negligible (${{P}_{C}}\simeq 0.0001$), and we conclude that M31N 1982-08b is recurrent.

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M31N 1984-07a was discovered by Rosino et al. (1989) very close to the nucleus of M31. There have been several subsequent novae seen to erupt within 2'' of M31N 1984-07a, including 2001-10c, 2004-02a, 2004-11f, and 2012-09a. We have remeasured the position of M31N 1984-07a using the image from the survey of Rosino et al. (1989), and determined the revised coordinates given in Table 2. The revised coordinates are within 11, 23, 03, and 06 of M31N 2001-10c, 2004-02a, 2004-11f, and 2012-09a, respectively. Thus, it appears likely that M31N 2004-11f and 2012-09a are recurrences, with 2001-10c and 2004-02a being less likely to be recurrences. Pietsch et al. (2007a) have studied the positions of M31N 2001-10c, 2004-02a, and 2004-11f, and concluded that these three novae are not spatially coincident. They were not able, however, to rule out the possibility that M31N 2004-11f was a recurrence of 1984-07a. The positions of M31N 1984-07a, 2004-11f, and 2012-09a are shown in Figure 12. It appears very likely that both M31N 2004-11f and 2012-09a are recurrences of 1984-07a.

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M31N 2004-11f was detected as a bright and fast SSS by Pietsch et al. (2007a). The X-ray emission was already present 34 days after the optical outburst and had started to decline in luminosity soon afterwards, by day 55 after outburst. Pietsch et al. (2007a) reported strong indications that the X-ray emission was supersoft, but unfortunately did not detect sufficient photons to estimate the effective SSS temperature. Notably, ∼10 months prior to the discovery of M31N 2004-11f, Pietsch et al. (2007a) identified what they believed to be the "pre-nova" in archival HST images. If so, and if M31N 2012-09a is also a recurrence of 1984-07a, it is noteworthy that archival HST images of the field of 2012-09a were analyzed by Williams et al. (2014) who found no compelling evidence for a red giant companion.

M31N 1997-11k was discovered as part of the RBSE program (Rector et al. 1999) and confirmed by Lee et al. (2012). Two likely recurrences have been observed: M31N 2001-12b (Lee et al. 2012) and 2009-11b (Henze et al. 2009b). Henze et al. (2009b) discussed the possibility that M31N 1997-11k might either be a RN in M31 or a dwarf nova in the Galaxy, and urged spectroscopic observations of 2009-11b to resolve the issue. Kasliwal (2009) obtained a spectrum clearly establishing that M31N 2009-11b was an Fe ii class nova in M31. Finding charts for the three objects from the RBSE program are shown in Figure 13. We conclude, in agreement with earlier suggestions, that M31N 1997-11k is a RN. Given the relatively short recurrence time, it would appear that the mass accretion rate in this system must be relatively high. Williams et al. (2014) ruled out the presence of a luminous red giant secondary in the progenitor system of M31N 2009-11b.

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M31N 2008-12a, which was discovered by K. Nishiyama and F. Kabashima (Miyaki-Argenteus Observatory, Japan), was first seen to erupt in the outskirts of M31 ($a\simeq 49^{\prime}$). The nova has subsequently been seen to have had four additional outbursts: M31N 2009-12b (Tang et al. 2014), 2011-10e (Barsukova et al. 2011), 2012-10a (Shafter et al. 2012a), and 2013-11f (Tang et al. 2013), all four occurring within 1'' of the measured position of 2008-12a.¹⁵ At this relatively large galactocentric radius, the probability of a chance positional coincidence is negligible, and it seems clear that the novae represent brightenings of the same progenitor system (see Figure 14). It would appear that M31N 2008-12a must be either a RN with an extremely short interval between eruptions (∼1 yr), or that the 2009, 2011–2013 events are simply rebrightenings of an unusually slow nova. Recent observations have shown that the latter possibility is untenable. In particular, the He/N (Shafter et al. 2012a) spectroscopic type along with the super-soft X-ray behavior strongly suggests that the object is in fact a short recurrence time RN (Tang et al. 2014; Darnley et al. 2014a; Henze et al. 2014b). Further, as shown by Darnley et al. (2014a), the spectral energy distribution of the quiescent counterpart of M31N 2008-12a is consistent with a bright accretion disk (and thus a high accretion rate) in this system.

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A literature search has revealed three additional X-ray detections of M31N 2008-12a in February 1992 and January 1993 (White et al. 1995) as well as in September 2001 (Williams et al. 2004). The super-soft X-ray properties of the two earlier outbursts (short duration, relatively high effective temperature) are in agreement with the 2013 X-ray detection (Henze et al. 2014b). These authors reported a very short SSS phase, appearing on day 6 ± 1 and disappearing on day 19 ± 1 after the optical outburst, with an exceptionally high effective (blackbody) temperature of $97_{-4}^{+5}$ eV. With eight recorded outbursts, M31N 2008-12a is a very unusual object that merits continued attention. An archival study of potential previous outbursts is underway (M. Henze et al. 2015, in preparation).

M31N 1953-09b was discovered by Arp (1956) as part of his classic M31 nova study (Arp #3). A subsequent nova, M31N 2004-08a, discovered by K. Hornoch (Pietsch et al. 2007a), was seen to erupt $\sim 4\buildrel{\prime\prime}\over{.} 8$ away from the reported position of 1953-09b. At the location of the nova ($a\sim 5\buildrel{\,\prime}\over{.} 8$), the probability of a chance coincidence is quite high (${{P}_{C}}\simeq 0.640$). Nevertheless, we have located the original plate from Arp's survey (S967A) and compared the position of M31N 1953-09b with that of 2004-08a in Figure 15. A careful inspection of the charts shows that M31N 1953-09b may be just slightly south of the position of 2004-08a, but to within the limits of the seeing disks ($\sim 1\buildrel{\prime\prime}\over{.} 5$), it is possible that the novae could be spatially coincident. Revised coordinates for M31N 1953-09b are given in Table 2, lowering the probability of a chance positional coincidence to ${{P}_{C}}\simeq 0.131$.

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It is worth noting that Lee et al. (2012) judge the light curve of M31N 2004-08a to be questionable for a nova, so there remains some doubt regarding the nature of this object. That said, M31N 2004-08a was detected as a SSS by Pietsch et al. (2007a). The nova showed a very short SSS phase and was only detected around day 60 after outburst without being visible about 30 days before and after. Pietsch et al. (2007a) also estimated a high effective (blackbody) temperature of around 80 eV. In view of the available evidence, the nature of M31N 1953-09b remains uncertain, with the possibility that the object is a RN remaining viable.

M31N 1961-11a erupted near the nucleus of M31 ($a\sim 3^{\prime}$) and was discovered as nova #35 in the survey of Rosino (1973). A possible recurrence, M31N 2005-06c, discovered by K. Hornoch (Pietsch et al. 2007a), erupted ∼24 from the reported position of 1961-11a and thus passed our initial RN screening. Given the nominal separation of the two novae, and their close proximity to the nucleus, the probability of a chance positional coincidence is quite high (${{P}_{C}}\simeq 0.691$). However, a careful comparison of the finding charts for the two novae shown in Figure 16 reveals that they are in fact spatially coincident to within measurement uncertainties. Revised astrometry of M31N 1961-11a based on the published chart (see Table 2) shows that the two novae appear to be separated by just 045, with a probability of a chance coincidence, ${{P}_{C}}\simeq 0.042$. Despite the spatial coincidence, Lee et al. (2012) have identified a variable star near the position of M31N 2005-06c, and have called into question the nature of the object. In view of their findings, we hesitate to definitively classify the object as a RN, and have instead included it in our list of uncertain RNe.

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M31N 1966-08a and 1968-10c were discovered as novae #66 and #81 in the survey of Rosino (1973), who gives the coordinates of the novae as being identical. The object is located at a relatively large galactocentric radius ($a\simeq 31\buildrel{\,\prime}\over{.} 2$) and there is very little chance that the objects could be distinct systems. The positions of the two novae are shown in Figure 17, confirming that the objects are in fact spatially coincident. Sharov & Alksnis (1989) argue that given the short interval between eruptions, the system is likely a Galactic foreground U Gem star (dwarf nova). That said, the possibility that the object is a RN with a very short recurrence time cannot be ruled out, and we have classified the object as an uncertain RN. Whether or not the system is a short recurrence time RN or a Galactic dwarf nova, it is quite surprising that more eruptions of the star have not been observed!

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M31N 1990-10a was discovered on 1990 October 13.16 UT during a routine photographic patrol of M31 (Bryan 1990). Our initial screen reveals two possible recurrences. The first, M31N 1997-10b, was a faint nova candidate reported by Shafter & Irby (2001). A re-examination of the original image shows that the object was likely a CCD artifact, and not a nova, as noted by Lee et al. (2012). Another possible recurrence was M31N 2007-07a (Hatzidimitriou et al. 2007a), which erupted $\sim 0\buildrel{\prime\prime}\over{.} 8$ away from the reported position of 1990-10a. Revised astrometry of M31N 1990-10a (see Table 2) reveals that the two novae are spatially coincident to within $0\buildrel{\prime\prime}\over{.} 59$ (${{P}_{C}}\simeq 0.041$). However, as can be seen in Figure 18, it appears that M31N 2007-07a may lie just slightly to the NW of 1990-10a. The relatively poor seeing of the M31N 1990-10a discovery image makes it impossible to establish conclusively whether or not the two novae are in fact coincident. We conclude that M31N 1990-10a is a possible RN.

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M31N 1932-09d was discovered by Stratton (1936) and lies $\sim 3\buildrel{\prime\prime}\over{.} 6$ from the position of a more recent nova, 2001-07d, which was discovered by Li (2001) and independently by the Wendelstein Calar Alto Pixellensing Project (Lee et al. 2012) and in data from the POINT-AGAPE survey (Darnley et al. 2004). Unfortunately, we have not been able to locate a finding chart for M31N 1932-09d, so we are unable to definitely establish whether or not the object is a RN. We note that eruptions with a nominal separation of $3\buildrel{\prime\prime}\over{.} 6$ or less at a projected distance of $\sim 3^{\prime}$ from the nucleus of M31 have probability of a chance coincidence that is quite high (${{P}_{C}}\simeq 0.939$). We conclude that M31N 2001-07d is unlikely to be a recurrence of 1932-09d.

As noted by Alksnis & Zharova (2000), M31N 1957-10b (PT And) has exhibited several recurrences (1983, 1986, 1988, and 1998) over the past 30 yr in addition to its most recent outburst in 2010, M31N 2010-12a (Zheng et al. 2010; Ruan & Gao 2010a). Sharov & Alksnis (1989) and Alksnis & Zharova (2000) have argued based on its light curve properties that PT And is a Galactic dwarf nova system, while Cao et al. (2012) suggest based on an optical spectrum that the object may indeed be a RN in M31. We have not shown finding charts for the outbursts of PT And because it is clear that they are spatially coincident and the light curves are consistent between eruptions (Alksnis & Zharova 2000). The only question is whether the object is a RN in M31 or a Galactic dwarf nova. After reviewing available data, including a spectrum published online by Kao,¹⁶ which shows a blue continuum with no prominent emission features, we conclude that the object is most likely a foreground Galactic dwarf nova and not a RN.

M31N 1982-09a is the first of 6 novae to be discussed below that were all discovered as part of the Ciardullo et al. (1987) Hα survey for novae in M31. Unfortunately, the original CCD data for these novae have been lost, making it impossible to create the finding charts necessary to definitively test whether these novae are recurrent. Most of these novae erupted quite close to the nucleus of M31 and their putative recurrences have high probabilities of chance positional coincidence.

M31N 1982-09a was one of the Ciardullo et al. (1987) novae that erupted very close ($a\sim 1\buildrel{\,\prime}\over{.} 08$) to the nucleus of M31. A possible recurrence, M31N 2011-02b, was seen to erupt $\sim 5\buildrel{\prime\prime}\over{.} 46$ from the reported position of 1982-09a. The estimated probability of a chance positional coincidence is extremely high, with ${{P}_{C}}\simeq 0.998$. Despite the fact that a direct comparison of the finding charts is not possible, the coordinates are unlikely to be in error by as much as 5'' making it is extremely unlikely that M31N 2011-02b is a recurrence of 1982-09a.

M31N 1983-09c was also discovered as part of the Ciardullo et al. (1987) nova survey. A possible recurrence, M31N 1997-11c (Rector et al. 1999), erupted $\sim 6^{\prime\prime}$ from the reported position of 1983-09c, and thus just passed our RN screening criterion. The novae erupted with $a\sim 8^{\prime}$ from the nucleus, and probability of a chance positional coincidence is estimated to be ∼0.5. Since a finding chart for M31N 1983-09c is not available, we cannot test whether these novae might be spatially coincident. However, given that both novae were registered with CCD detectors and their positions computed directly from the images, it is highly unlikely that a positional error of $\sim 6^{\prime\prime}$ would be possible if M31N 1997-11c was a recurrence of 1983-09c.

M31N 1984-09b was another nova found in the survey by Ciardullo et al. (1987), and like 1982-09a quite close to the nucleus of the galaxy ($a\simeq 1\buildrel{\,\prime}\over{.} 27$). A possible recurrence, M31N 2012-12a, was flagged by our screen. The latter nova was discovered by Hornoch & Galad (2012), and found to be a member of the Fe ii spectroscopic class by Shafter et al. (2012b). Despite the fact that M31N 2012-12a has a reported position that is only $1\buildrel{\prime\prime}\over{.} 5$ from that of 1984-09b, the probability of a chance positional coincidence so close to the nucleus of M31 is relatively high (${{P}_{C}}\simeq 0.450$). Unfortunately, since a finding chart for M31N 1984-09b no longer exists, once again we cannot evaluate whether the objects are spatially coincident. Williams et al. (2014) studied the field of M31N 2012-12a and found that there is a source within $3\sigma$ (1.532 ACS/WFC pixels or 0077) of the nova's position. According to Williams et al. (2014), the local stellar density suggests a probability of chance coincidence with this separation is 19.9%, and it is unclear whether the source might be associated with the nova progenitor.

As with two of the three the previous Ciardullo et al. (1987) novae, M31N 1985-09d was discovered close to the nucleus of M31 ($a\simeq 0\buildrel{\,\prime}\over{.} 81$). A possible recurrence, M31N 2009-08d, located $\sim 4\buildrel{\prime\prime}\over{.} 12$ away was discovered by K. Hornoch (Henze et al. 2009a). Despite the fact that without a finding chart we cannot definitively rule out the possibility that M31N 1985-09d is recurrent, it seems highly unlikely given that the coordinates differ by more than 4'' and the probability of a chance positional coincidence with this separation at this location in the galaxy is very high (${{P}_{C}}\simeq 0.993$). We note that another nova, M31N 2005-05b was also flagged by our screen, and lies 46 away from the nominal position of 2009-08d. As shown below M31N 2005-05b and 2009-08d are not spatially coincident. Given that the reported position of M31N 1985-09d is even further from 2005-05b than it is from 2009-08d, it is even less likely that 2005-05b could be a recurrence of 1985-09d. Finally, we note that M31N 2009-08d was determined to be an Fe ii nova by di Mille et al. (2009), and no evidence for a red giant companion often associated with RNe was found in the search for M31 nova progenitors by Williams et al. (2014).

M31N 1985-10c, another nova discovered by Ciardullo et al. (1987), was again found extremely close to the nucleus of M31 ($a\simeq 0\buildrel{\,\prime}\over{.} 30$). Two possible recurrences have been subsequently noted, M31N 1995-12a and 2003-10b. In addition to lacking a finding chart for M31N 1985-10c, we were also unable to locate a chart for M31N 1995-12a despite re-examining an image from the survey of Shafter & Irby (2001) taken on 1996 January 14, 27 days after the nova was discovered by Ansari et al. (2004). A chart does exits for M31N 2003-10b (Fiaschi et al. 2003), but given the extremely close proximity to the nucleus, it is unlikely that finding charts, even if available for all three novae, would be useful in definitively establishing the spatial coincidence of the objects. Based on the published coordinates, M31N 1995-12a and 2003-10b have probabilities of chance coincidence with 1985-10c of ${{P}_{C}}\simeq 0.708$ and ${{P}_{C}}\simeq 0.422$, respectively, while 1995-12a and 2003-10b have a probability of chance coincidence with respect to each other of ${{P}_{C}}\simeq 0.953$. We conclude that there is no compelling evidence that M31N 1985-10c is a RN.

M31N 1986-09a, the final nova from the Ciardullo et al. (1987) survey to be discussed, was also discovered relatively close to the nucleus of M31 ($a\simeq 1\buildrel{\,\prime}\over{.} 63$). A possible recurrence is M31N 2006-09b, which was seen to erupt $\sim 4\buildrel{\prime\prime}\over{.} 8$ away. Despite the fact that a comparison of the finding charts for these novae is not possible, as with the previous two systems, it is unlikely that the coordinates would be in error by as much as 48 if the system was a RN. At this separation, the probability of a chance positional near coincidence, ${{P}_{C}}\simeq 0.994$.

The relatively recent nova M31N 2009-02b (Pietsch et al. 2009a) erupted $\sim 4\buildrel{\prime\prime}\over{.} 2$ SSW of the nominal position of M31N 1909-09b. M31N 1909-09b is the second nova listed by Hubble (1929), and was discovered on the rise on 1909 September 12 on a plate taken by Ritchey using the Mount Wilson 60-in reflector (Ritchey 1917). The nova reached a maximum brightness of ${{m}_{{\rm pg}}}=16.7$ on September 15, and faded slowly to ${{m}_{{\rm pg}}}=18.0$ on November 07. The available photometry places a lower limit on the t₂ time of at least 55 days, making M31N 1909-09b a very slow nova. A comparison of the position of M31N 1909-09b from plate S19-Ri (1.5 hr exposure) taken by Ritchey on 1909 September 13 and the position of 2009-02b from the SuperLOTIS project clearly shows that the two novae are in fact distinct objects separated by $10\buildrel{\prime\prime}\over{.} 5$ (see Figure 19). Astrometry of M31N 1909-09b based on a scan of the Ritchey plate yields the revised coordinates given in Table 2.

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Our screen has revealed that the recent Fe ii nova M31N 2013-10g, which reached a peak brightness of R = 17.5 (Fabrika et al. 2013), erupted within $\sim 12^{\prime\prime}$ of nova #9 in Hubble's survey (Hubble 1929). The latter nova was discovered on 1918 February 10 UT (plate S162-Ri), and reached a similar peak brightness (${{m}_{{\rm pg}}}=17.5$). Despite the relatively large nominal separation, given the uncertainty in the coordinates derived from these early photographic surveys, we took a closer look at the positions of these two novae. As can be seen in Figure 20, the novae clearly represent eruptions from distinct progenitors, and we conclude that M31N 2013-10g is not a recurrence of 1918-02b. Updated astrometry for M31N 1918-02b yields the revised coordinates given in Table 2.

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M31N 1923-02a, nova #22 in the survey of Hubble (1929), erupted close to the nucleus of M31 ($a\simeq 1\buildrel{\,\prime}\over{.} 74$). Since then, there have been three potential recurrences M31N 1967-12a (Rosino 1973), 1993-11c (Shafter & Irby 2001) and 2013-08b (Hornoch & Vrastil 2013). Finding charts for the novae are shown in Figure 21. It is clear that M31N 1923-02a, 1967-12a, and 1993-11c are different novae. It is less obvious that M31N 2013-08b is distinct from 1967-12a, but the comparison image clearly shows that the novae are not spatially coincident. Revised astrometry of M31N 1923-02a and 1967-12a are given in Table 2, confirming that all four novae are distinct objects.

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M31N 1924-02b was flagged as a potential RN candidate because nova 1995-09d was observed to lie $5\buildrel{\prime\prime}\over{.} 2$ from its reported position. M31N 1924-02b was a faint (${{m}_{{\rm pg}}}=19$) transient discovered on 1924 February 03 UT by Hubble (1929) who noted that the object varied between ${{m}_{{\rm pg}}}=19.0$ and 19.5 for several years. Given its long-term photometric behavior, it seems clear that M31N 1924-02b is not a nova in M31, but likely a fainter LPV.

M31N 1987-12a was discovered at ${{m}_{{\rm pg}}}=16.8$ on 1987 December 20.13 UT (Bryan 1987). Our screen revealed that the nova erupted $3\buildrel{\prime\prime}\over{.} 1$ from the reported position of M31N 1924-08a. At an isophotal radius of just $a\sim 2\buildrel{\,\prime}\over{.} 61$, the probability of a chance coincidence is quite high (${{P}_{C}}\simeq 0.900$). Fortunately, we were able to recover both the original 35 mm negative from the 1987 observation as well as the original Mt. Wilson plates, H241D and H246D, from 1924 August 26 and 28, respectively. Figure 22 shows the field of M31N 1924-08a taken from plate H246D compared with the position of 1987-12a from a 35 mm photographic negative taken on 1987 December 20.13 UT. The two novae are clearly not spatially coincident. Updated astrometry has been performed, and revised coordinates measured, for both M31N 1924-08a and 1987-12a, and are given in Table 2.

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M31N 2011-12b (PNV J00435583+4121265), which was discovered by K. Nishiyama and F. Kabashima on 2011 December 27.448 UT at m = 17.4 (unfiltered), was found to lie $\sim 7\buildrel{\prime\prime}\over{.} 5$ from the position of Nova #49 in Hubble's survey (Hubble 1929). Despite the relatively large reported separation, our expanded initial screen for early photographic surveys flagged this pair of novae for closer inspection. Figure 23 shows a comparison of the positions of M31N 1925-07c and 2011-12b, revealing that the novae to be distinct objects. Revised coordinates for M31N 1925-07c are given in Table 2.

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M31N 1976-12a was discovered at B = 18.3 by Rosino et al. (1989) as the 115th nova in his survey. Our coarse screen reveals that Rosino #115 lies within $9\buildrel{\prime\prime}\over{.} 7$ of a very bright nova (${{m}_{{\rm pg}}}=15.3$), which is nova #54 in the survey of Hubble (1929). Given the disparity in peak brightness, and the relatively large apparent separation, we considered it unlikely that the 1976 eruption was a recurrence of Hubble #54. Nevertheless, given that the novae are relatively far from the nucleus of M31 ($a\simeq 20^{\prime}$), the probability for a chance coincidence is relatively low (${{P}_{C}}\simeq 0.155$), and we decided to take a closer look at the positions of these two novae. The positions are compared in Figure 24, confirming that the novae are in fact distinct objects. Revised coordinates for M31N 1925-07c are given in Table 2.

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M31N 1927-08a was discovered as nova #76 in the survey of (Hubble 1929), reaching a magnitude of ${{m}_{{\rm pg}}}=17.1$ on 1927 August 23 UT. A possible, but unlikely recurrence with a reported position $\sim 8^{\prime\prime}$ from 1927-08a, the R = 17.4 nova M31N 2009-11e (Pietsch et al. 2009b), was flagged by our screen. Figure 25 shows finding charts for the two novae, and clearly establishes that they are in fact distinct objects.

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M31N 1930-06b was reported by Mayall (1931). The object was detected on Mount Wilson plates taken on 1929 November 30 and 1930 June 19. Both times the apparent nova was seen at $m\sim 18$. A possible recurrence, M31N 2008-08e, was discovered by D. Balam on 2008 August 31. Unpublished observations by one of us (K. H.) at the Ondřejov Observatory, establish that the object is visible on multiple images taken over a 2 yr period from 2007 March to 2008 August. Given its photometric behavior, the object appears to be a LPV star and not a nova in M31.

M31N 1996-08a (Shafter & Irby 2001) was observed to erupt within $s\sim 7\buildrel{\prime\prime}\over{.} 2$ of the reported position of M31N 1930-06c (nova #92 in Mayall 1931) and made it through our coarse screen for RN candidates. A review of plate H1155H in the Carnegie archives taken on 1930 June 28 fails to reveal a source at the reported position of M31N 1930-06c. Instead, an object labeled "nova 92" is found far from the reported position of M31N 1930-06c on the opposite (south) side of the nucleus of M31. A comparison of the position of Hubble's nova #92 with that of M31N 1996-08a is shown in Figure 26. We conclude that an error was made in the conversion of Hubble's original X and Y position of the nova to the equatorial coordinates for M31N 1930-06c given in the online M31 nova catalog. Revised coordinates for both novae are given in Table 2.

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M31N 1953-11a was discovered by Arp (1956) as nova #19 in his survey. Three subsequent novae were seen to erupt nearby and passed our coarse screen: M31N 1960-12a, 1962-11b, and 2013-05b. Of these, M31N 1962-11b (Rosino 1964) was the closest to 1953-11a, with a reported position lying just $\sim 2\buildrel{\prime\prime}\over{.} 9$ away. These novae are all relatively close to the nucleus of M31 ($a\sim 4\buildrel{\,\prime}\over{.} 4$), making the probability of a chance positional coincidence between M31N 1953-11a and 1962-11b relatively high (${{P}_{C}}\simeq 0.622$). As with M31N 1953-09b, we were able to locate the original Arp plate (S1137A) in the Carnegie archives. A reproduction of the nova field, along with that of M31N 1962-11b, is shown in Figure 27. The novae are clearly not spatially coincident. Furthermore, as expected, a comparison of Figure 27 with Figure 8 shows that both M31N 1953-11a and 1962-11a are also not coincident with either M31N 1960-12a or 2013-05b. However, as discussed earlier and shown in Figure 8, the latter two novae are in fact spatially coincident to within observational uncertainties, strongly suggesting that M31N 1960-12a is a RN. Revised coordinates for M31N 1953-11a have been included, along with those of 1960-12a and 1961-11b, in Table 2.

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M31N 2010-01b was discovered by Nishiyama et al. (2010) on 2010 January 17.438 UT at m = 18.1. The position of the nova lies $\sim 8\buildrel{\prime\prime}\over{.} 8$ (just inside our coarse screen) from the position of M31N 1954-06c, which is Nova #28 in Arp's nova survey (Arp 1956). The light curve of M31N 1954-06c is very slow, with Arp (1956) finding a "duration" (the number of days where the nova is brighter than m = 20) of 115 days. In contrast, light curve information on 2010-01b is much more sparse; however, photometry by Pietsch & Henze (2010) shows that the nova remained near m = 17.7 between 2010 January 25 and February 02. As with the previous two novae from Arp's survey, we located the discovery plate (S1335A) in the Carnegie archives, and re-measured the coordinates of the nova (see Table 2). The field of M31N 1954-06c is compared with that of 2010-01b in Figure 28, clearly showing that the two novae are not spatially coincident.

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M31N 2012-03b erupted $2\buildrel{\prime\prime}\over{.} 5$ from the reported position of M31N 1955-09b, nova #1 in the extensive survey of Rosino (1964). The pair of novae are located at an isophotal radius of $a\sim 10\buildrel{\,\prime}\over{.} 5$ from the center of M31, resulting in a relatively low probability of chance coincidence, ${{P}_{C}}\simeq 0.032$. Finding charts for the two novae are shown in Figure 29. The two novae are clearly not spatially coincident, and thus M31N 2012-03b is not a recurrence of 1955-09b.

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M31N 1964-12b (Rosino 1973) erupted very close to the nucleus of M31 ($a\simeq 0\buildrel{\,\prime}\over{.} 71$). A possible recurrence, M31N 1998-07b (Rector et al. 1999), lying $3\buildrel{\prime\prime}\over{.} 74$ from that of 1964-12b was flagged by our screen. After re-analyzing the original data from the RBSE project, we have determined that M31N 1998-07b was a spurious detection, and the nova does not exist.

M31N 1967-11a was discovered on archival plates by Henze et al. (2008a). A possible recurrence, M31N 2006-02a, was later discovered by K. Hornoch (Pietsch et al. 2007a). Charts for the two novae are shown in Figure 30. Although the positions of the novae appear close, a careful inspection reveals that the positions differ, with M31N 2006-02a located $\sim 4^{\prime\prime}$ WSW of the position of 1967-11a, in agreement with their reported positions.

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M31N 1967-12b is another nova discovered by Rosino (1973). Its reported position is close to that of M31N 1999-06b discovered later as part of the RBSE program (Rector et al. 1999). Charts for the two novae are shown in Figure 31. The novae are clearly not spatially coincident, with M31N 1999-06b lying $\sim 6^{\prime\prime}$ ESE of 1967-12b. Refined coordinates for M31N 1967-12b are given in Table 2.

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M31N 2007-12b erupted very close to the reported position of M31N 1969-08a. Nevertheless, as discussed by Bode et al. (2009), the objects have been shown to be distinct novae. Interestingly however, Bode et al. (2009) were able to show that M31N 2007-12b has a red giant companion star. This discovery, combined with its He/N spectroscopic type, makes it likely that M31N 2007-12b has a short recurrence time. Thus, it is possible that it will be revealed to be a RN in the not too distant future. We also note that Pietsch et al. (2011) found a 1110 s coherent periodicity in the X-ray light curve of M31N 2007-12b, which they interpreted as the rotation period of a magnetized white dwarf in the system, and suggested that the nova erupted from a intermediate polar progenitor.

M31N 1975-09a was discovered by Henze et al. (2008a) from an analysis of the Tautenburg Schmidt plates. Henze et al. (2008a) explored the possibility that M31N 1999-01a was a recurrence of 1975-09a and determined that the novae were not spatially coincident. We confirm their conclusion as can be seen in Figure 32.

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M31N 1977-12a is nova #119 from Rosino et al. (1989). A possible recurrence is M31N 1998-08a, which was reported to erupt only $2\buildrel{\prime\prime}\over{.} 1$ from the nominal position of 1977-12a. Given that the novae were observed at a relatively large galactocentric radius ($a=10\buildrel{\,\prime}\over{.} 8$), the probability of a chance positional coincidence is small (${{P}_{C}}\simeq 0.054$). Despite the likelihood that the novae are related, comparison of the finding charts (Figure 33) shows that the novae are in fact distinct. Revised astrometry of M31N 1977-12a (see Table 2) reveals that the separation between the eruptions is slightly larger, with 1977-12a lying $\sim 2\buildrel{\prime\prime}\over{.} 9$ ESE of 1998-08a.

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M31N 1992-12b was discovered by Shafter & Irby (2001) at an isophotal radius of $a\simeq 12\buildrel{\,\prime}\over{.} 91$ from the center of M31. A possible recurrence, M31N 2001-10f was seen to erupt $\sim 5\buildrel{\prime\prime}\over{.} 31$ from the position of 1992-12b. Given this large separation, it is unlikely that M31N 2001-10f is related to 1992-12b, despite the modest probability of a chance positional coincidence (${{P}_{C}}\simeq 0.256$). Revised astrometry of M31N 1992-12b given in Table 2 shows that the position is within $\sim 0\buildrel{\prime\prime}\over{.} 8$ of that given in Shafter & Irby (2001). The positions of M31N 1992-12b and 2001-10f are shown in Figure 34, making it clear that the two novae are distinct objects.

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M31N 1993-09b was another nova discovered in the Hα survey of Shafter & Irby (2001). Approximately 3 yr later, a possible recurrence, M31N 1996-08g (Sharov & Alksnis 1997; Henze et al. 2008a), was observed $\sim 5\buildrel{\prime\prime}\over{.} 47$ away from the position of 1993-09b. The probability of a chance positional coincidence is relatively high with ${{P}_{C}}\simeq 0.843$. Figure 35 clearly establishes that the two novae are distinct objects. Revised coordinates for M31N 1993-09b are given in Table 2.

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M31N 2001-08d was discovered in the bulge of M31 ($a\simeq 4\buildrel{\,\prime}\over{.} 34$) by Fiaschi et al. (2001) on an Hα image of M31 taken on 2001 September 02.93 UT. A possible recurrence, M31N 2008-07a (Henze et al. 2008b), was observed within $\sim 3\buildrel{\prime\prime}\over{.} 5$ of the reported position of 2001-08d with an estimated probability of change positional coincidence given by ${{P}_{C}}\simeq 0.774$. A comparison of finding charts for the two novae (Figure 36) shows that the novae are not positionally coincident.

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M31N 2004-11b (Lee et al. 2012) and 2010-07b (Hornoch et al. 2010b) represent two nova outbursts in the bulge of M31 ($a\simeq 5^{\prime}$) with reported positions within $\sim 5\buildrel{\prime\prime}\over{.} 9$ of one another. Not surprisingly, given that the coordinates are unlikely to be in error by more than an arcsecond, Figure 37 confirms that the two novae are not spatially coincident.

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M31N 2005-05b (Lee et al. 2012) and M31N 2009-08d (Henze et al. 2009a) erupted within $\sim 5^{\prime\prime}$ of one another, and very close to the nucleus ($a\sim 0\buildrel{\,\prime}\over{.} 8$), resulting in a relatively high probability of a chance positional coincidence (${{P}_{C}}\simeq 0.998$). The finding charts from the RBSE data shown in Figure 38 reveal, as expected, that the objects are distinct systems.

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M31N 2006-11b and M31N 2006-12d (Lee et al. 2012) are two cataloged novae observed near the nucleus of M31 with reported positions within $0\buildrel{\prime\prime}\over{.} 34$ of one another. The probability of a chance coincidence is small (${{P}_{C}}\simeq 0.029$). The objects appear to be spatially coincident, but it seems clear that M31N 2006-12d, observed just 38 days later, is a re-brightening of 2006-11b, and not a distinct eruption.

M31N 2006-12c and M31N 2007-07e (Lee et al. 2012) erupted close to the nucleus ($a\sim 2^{\prime}$), and within $\sim 4\buildrel{\prime\prime}\over{.} 4$ of one another resulting in a high probability of a chance positional coincidence. Once again, finding charts for the objects (see Figure 39) reveal that they are distinct systems.

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M31N 2010-01a (Burwitz et al. 2010) was discovered close to the nucleus of M31 ($a\simeq 2\buildrel{\,\prime}\over{.} 7$), and observed to have a possible recurrence less than a year later, M31N 2010-12c (Hornoch et al. 2010a; Ruan & Gao 2010b), which was reported just $0\buildrel{\prime\prime}\over{.} 82$ away. Despite a probability of a chance positional coincidence of just ${{P}_{C}}\simeq 0.141$, a careful inspection of the images for each nova shows that they are in fact distinct objects (see Figure 40). This conclusion is supported by the work of Hornoch et al. (2010a), who performed careful astrometry of both novae and also came to the conclusion that they are in fact distinct systems. Revised coordinates based on astrometry performed on the charts shown in Figure 40 are given in Table 2. We conclude that M31N 2010-01a is not a RN.

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The history of nova discoveries in M31 is shown in Figure 43. A few notable features are apparent. The first clump of discoveries centered in the 1920s is due largely to Hubble's pioneering survey (Hubble 1929). Nova discoveries tailed off precipitously in the 1930s and essentially dropped off completely during World War II. Nova discoveries picked up significantly in the 1950s and 1960s as a result of the Arp (1956) and Rosino (1964, 1973) photographic surveys. Then, after a short lull in the 1970s, nova discoveries began a steady increase due primarily to the CCD surveys of Ciardullo et al. (1987), Shafter & Irby (2001), Darnley et al. (2006), and others. In recent years the number of novae discovered in M31 has exploded thanks to the contributions from automated surveys such as the Palomar Transient Factory (Law et al. 2009), and amateur astronomers throughout the world.

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In addition to the overall number of novae discovered over the past century, Figure 43 also shows the distribution of RN outbursts observed over time. As expected, the number of outbursts of RN systems has increased roughly in proportion to the number of nova discoveries. However, despite the dramatic increase in the overall number of nova discoveries in recent years, the first recorded eruptions of our 12 RNe and our 4 possible RNe are spread relatively evenly over time. This result is not surprising. If surveys had been uniform over time, with the discovery of novae increasing at a steady rate, we would have expected the percentage of novae identified as recurrent to be higher for systems discovered early on, where more would be available for the discovery of subsequent outbursts. The fact that the density of observations has increased over time has blunted this effect and resulted in what we see, namely that the identification of new RN systems is approximately evenly distributed over the past century.

In addition to the sporadic temporal coverage, the uneven spatial coverage of the various surveys can be expected to impact the relative discovery efficiencies of RNe and CNe. In particular, the discovery efficiency of RNe should be biased toward the bulge of the galaxy where the temporal coverage is more extensive. From a theoretical standpoint, it is unclear whether the recurrence times of novae (and hence the relative populations of RNe and CNe) should vary with spatial position in M31. Population synthesis models predict that younger stellar populations should produce nova progenitors that have on average more massive white dwarfs than do older stellar populations (e.g., de Kool 1992; Politano 1996). Since the recurrence times of novae are strongly dependent on the mass of the white dwarf (e.g., Yaron et al. 2005; Wolf et al. 2013), younger stellar populations should not only produce a higher observed nova rate (Yungelson et al. 1997), but also a higher fraction of systems classified as RNe. Despite these predictions, observations have consistently shown that novae are more prominent in older bulge populations (e.g., Ciardullo et al. 1987; Shafter & Irby 2001; Darnley et al. 2006). The fact that the observed spatial distribution of RNe does not differ significantly from that of novae generally (see Figure 42) suggests that an unbiased survey (with more complete disk coverage) may find that RNe are more spatially extended than novae in general. If so, such a finding would be consistent with the predictions of the population synthesis models.

Aside from the temporal and spatial uncertainties, we must also consider how variations in the limiting magnitudes of the observations will impact the discovery of novae in M31. Limiting magnitudes for most of the M31 surveys vary significantly, both between surveys and within the surveys themselves. Thus, it is not possible to determine any single limiting magnitude representative of the full M31 nova sample. Nevertheless, we can get an idea of the limiting magnitude of the "average" survey by referring to Figure 44, which shows the distribution of discovery magnitudes for the 964 M31 nova candidates in the Pietsch et al. (2007a) online database. Here we assume that the average survey reaches a limiting magnitude down to the point where the discovery magnitude distribution turns over and begins to drop precipitously. Based on the distribution of discovery magnitudes, it appears that a limiting magnitude of ${{m}_{{\rm lim} }}\sim 18$ is representative of the typical M31 nova survey. Given the considerable uncertainty in ${{m}_{{\rm lim} }}$, in the simulations described below we have also considered how our results are affected by adopting limiting magnitudes of ${{m}_{{\rm lim} }}=17$ and 19.

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We have performed a series of Monte Carlo simulations to predict the discovery efficiencies of both CN and RN outbursts in M31 under a variety of scenarios. In the simulations, we produce a total of 6500 synthetic novae erupting at random times over a 100 yr time span.¹⁷ Model nova light curves are based on the the maximum magnitudes and rates of decline from the "high quality" M31 sample of Capaccioli et al. (1989) and from the Galactic RN sample from Schaefer (2010) for CNe and RNe, respectively. Table 5 gives the values of ${{m}_{B}}({\rm max} )$ and ${{\nu }_{B}}$ (mag d⁻¹) assuming a distance and foreground reddening for M31 of ${{(m-M)}_{o}}=24.38$ and A_B = 0.25 (Freedman et al. 2001; Schlegel et al. 1998). For CNe, an eruption reaches a maximum brightness and then fades at a rate that is chosen at random from the CN light curve parameters given in Table 5. A model nova is considered "detected" if it remains brighter than the adopted limiting magnitude (${{m}_{{\rm lim} }}$=17, 18, or 19) on the nearest survey date immediately following the date of the simulated eruption. The fraction of the 6500 novae that are detected is reported as the discovery efficiency for CNe.

Table 5.  Model Light Curve Properties

Nova	mB(max)	${{\nu }_{B}}$(mag d−1)
Classical Novaea
A04	18.2	0.200
A06	16.0	0.230
A07	15.9	0.150
A12	16.1	0.180
A13	17.0	0.077
A19	17.6	0.070
A20	17.2	0.060
A21	17.4	0.075
A24	17.8	0.059
A25	17.6	0.061
A26	18.0	0.043
A29	18.0	0.017
R06	16.5	0.140
R12	17.6	0.050
R18	17.1	0.090
R20	16.9	0.090
R28	14.9	0.250
R30	16.2	0.170
R38	16.9	0.110
R43	16.3	0.220
R52	16.4	0.125
R53	17.0	0.040
R57	15.0	0.220
R67	16.2	0.130
R77	15.9	0.220
R80	17.4	0.034
R85	15.7	0.120
Recurrent Novaeb
T Pyx	17.6	0.055
IM Nor	17.9	0.039
CI Aql	17.0	0.087
V2487 Oph	17.3	0.340
U Sco	16.2	1.410
V394 CrA	15.8	0.705
T CrB	17.2	0.500
RS Oph	16.4c	0.254
V745 Sco	16.7	0.328
V3890 Sgr	15.9	0.260

^aFrom Capaccioli et al. (1989). ^bFrom Schaefer (2010). Apparent magnitudes at the distance of M31 have been computed assuming ${{(m-M)}_{o}}=24.38$ (Freedman et al. 2001) and a foreground extinction of A_B = 0.25 (Schlegel et al. 1998). ^cPeak brightness for RS Oph is based on the distance (d = 1.4 kpc) and reddening ($E(B-V)=0.7$) given in Darnley et al. (2012).

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As a lower limit on the temporal coverage of M31 we have simply taken the discovery dates of the nova candidates that have been discovered in M31 over the past century. Then, to explore the sensitivity of our simulations to the temporal coverage, we have also considered the possibility that the actual survey coverage extended one or two days on either side of each of the dates were a nova was reported to be discovered. We refer to the temporal coverage estimates either as "Clump 1" (discovery dates only), "Clump 3" (discovery dates plus the day immediately preceding and following each discovery date), or "Clump 5" (discovery date plus the 2 days preceding and the 2 days following all discovery days). It is also possible that there were more extended intervals of coverage where no novae were discovered, but we have no way of accurately accounting for this possibility.

In the case of RNe, our simulations must produce multiple outbursts, and the RN discovery efficiencies will clearly depend on the assumed recurrence time, or the distribution of recurrence times, adopted in the simulations. To explore this dependence, we have initially considered several trial recurrence times ranging from as short as 1 yr (the shortest observed RN recurrence time) to a maximum of 90 yr (longer recurrence times have a negligible chance of being detected in our simulations that span just 100 yr). As for CNe, the light curve parameters for RNe have also been chosen randomly, this time from the RN sample given given in Schaefer (2010) and summarized here in Table 5.

To qualify as a RN outburst in our simulations, a particular system must be detected at least twice over the 100 yr time span of the simulation. The RN discovery efficiency is computed as the ratio of the total number of multiple outbursts detected to the total number of outbursts generated in the RN simulation (i.e., 6500 simulated nova outbursts plus all recurrences in the 100 yr interval). The entire simulation for both CNe and RNe has been repeated a total of 100,000 times, with the CN outburst fraction, the RN outburst fraction recorded as the respective discovery efficiencies.

The results of our Monte Carlo simulations of the RN outburst discovery efficiencies and their ratio to that of CNe are shown in Figure 45. Not surprisingly, the discovery efficiencies are strongly dependent on the assumed limiting magnitude of the surveys, with the deeper surveys resulting in higher RN discovery efficiencies. The assumed density of the temporal coverage is also important, with the discovery efficiencies increasing with increasing temporal coverage, as expected. It is interesting to note that at the shortest recurrence times, the discovery efficiencies for RNe relative to CNe for ${{m}_{{\rm lim} }}=18$ slightly exceeds that for ${{m}_{{\rm lim} }}=19$ for the "Clump 3" and "Clump 5" temporal distributions. This behavior results from the fact that the CN light curves have generally slower rates of decline when compared with the RN light curve sample. A fainter limiting magnitude thus increases the CN discovery efficiency more than it increases the RN discovery efficiency. This effect is most pronounced for the shorter recurrence times and denser temporal coverage where the RN discovery efficiency is already quite high.

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Regardless of the limiting survey magnitude or the temporal coverage, these simulations confirm that the observed RN recurrence time distribution for known RNe should strongly favor the discovery of RNe having shorter recurrence times. To verify this prediction, in Figure 46 we have plotted the observed outburst distribution for Galactic and M31 RNe, and compared it with the ${{m}_{{\rm lim} }}=18$, "Clump 3" discovery efficiencies from Figure 45. Since we simulated the same number of RNe across all recurrence times, the qualitative agreement shown in Figure 46 is consistent with the hypothesis that the observed bias toward the discovery of short recurrence time RNe can be explained solely by selection bias from an intrinsically flat distribution of RN recurrence times.

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Under the assumption that the intrinsic RN recurrence time distribution is flat over the range of 1–100 yr, we have conducted two composite recurrence time RN simulations. In the first composite simulation we choose recurrence times at random from the full range of ${{t}_{{\rm rec}}}\;=\;$ 1–100 yr. Then, we consider a restricted range with recurrence times ranging from ${{t}_{{\rm rec}}},=\;$ 5–100 yr that would be more appropriate for a population of RNe where ultra-short recurrence time RNe such as M31N 2008-12a are extremely rare.

The results of the Monte Carlo simulation are reported in Table 6 and shown in Figures 47 and 48 for the various input parameters. Columns 3 and 4 of Table 6 give the fractions of CN and RN outbursts that are detected in the simulation, with column 5 giving the principal result of our simulation, the ratio of RN to CN outbursts detected (see Figures 47, 48). Column 6 gives our estimate of the true ratio of RN to CN outbursts, ${{N}_{{\rm out}}}({\rm RNe})/{{N}_{{\rm out}}}({\rm CNe})$, after the observed outburst ratio given in Equation (5) is corrected for the relative outburst discovery efficiencies. Columns 7 and 8 then give our estimates of the expected numbers of RN and CN outbursts produced in M31 each year assuming a combined annual nova rate of 65 yr⁻¹ (Darnley et al. 2006).

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Table 6.  Monte Carlo Results

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
Coverage	${{m}_{{\rm lim} }}$	CN Fraction	RN Fraction	RN/CN Dis. Efficiency	${{N}_{{\rm out}}}({\rm RNe})/{{N}_{{\rm out}}}({\rm CNe})$	CN (yr−1)	RN (yr−1)
${{t}_{{\rm rec}}}\;=\;$ 1–100 yr
Clump1	17	0.0415	0.0034	0.0825	0.485	44	21
...	18	0.1335	0.0360	0.2665	0.150	57	8
...	19	0.2457	0.0936	0.3825	0.105	59	6
Clump3	17	0.0547	0.0095	0.1736	0.230	53	12
...	18	0.1532	0.0563	0.3680	0.109	59	6
...	19	0.2586	0.1119	0.4328	0.092	60	5
Clump5	17	0.0670	0.0162	0.2427	0.165	56	9
...	18	0.1702	0.0758	0.4459	0.090	60	5
...	19	0.2721	0.1287	0.4732	0.085	60	5
${{t}_{{\rm rec}}}\;=\;$ 5–100 yr
Clump1	17	...	0.0010	0.0244	1.640	25	40
...	18	...	0.0167	0.1237	0.323	49	16
...	19	...	0.0564	0.2311	0.173	55	10
Clump3	17	...	0.0032	0.0592	0.676	39	26
...	18	...	0.0295	0.1926	0.208	54	11
...	19	...	0.0704	0.2726	0.147	57	8
Clump5	17	...	0.0062	0.0931	0.430	45	20
...	18	...	0.0428	0.2518	0.159	56	9
...	19	...	0.0839	0.3083	0.130	58	7

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As a check on our simulations, we note that the CN discovery efficiency predicted by our Monte Carlo simulations is in qualitative agreement with observations. Given an annual nova rate of 65 yr⁻¹, we estimate that approximately 6500 novae have erupted in M31 over the past century. Our standard model (${{m}_{{\rm lim} }}=18$, "Clump 3") produces a CN discovery fraction of 0.15 and predicts that approximately 975 novae will have been discovered over the past century, in very good agreement with the number of novae discovered in M31. It is also worth noting that our values for the true ratio of RN to CN outbursts, ${{N}_{{\rm out}}}({\rm RNe})/{{N}_{{\rm out}}}({\rm CNe})$, for our ${{m}_{{\rm lim} }}=18,19$ models are consistent with the ratio estimated by Della Valle & Livio (1996) in their study of the RN populations in the Galaxy, the LMC, and M31.

Under the assumption that the recurrence time distribution is flat in the range of 1–100 yr, we predict that RN outbursts make up ∼10% of nova eruptions generally. For an annual nova rate of 65 yr⁻¹, as many as 5-10 outbursts per year are expected to arise from RN progenitors. If ultra-short recurrence time (${{t}_{{\rm rec}}}\lt 5\;{\rm yr}$) RNe are relatively rare, our $5\lt {{t}_{{\rm rec}}}\;{\rm y}{{{\rm r}}^{-1}}\lt 100$ models suggest that as many as one out of three (∼20) nova eruptions observed annually in M31 could arise from RN systems. This result is consistent with that found recently by Pagnotta & Schaefer (2014) for that fraction of Galactic novae that are recurrent, and Williams et al. (2014) and S. C. Williams et al. (2015, in preparation) for the fraction of M31 novae with evolved secondary stars.