Astronomy & Astrophysics manuscript no. November 18, 2021
(DOI: will be inserted by hand later)
Probing MACHOs by observation of M31 pixel lensing
with the 1.5m Loiano telescope
S. Calchi Novati1,2, G. Covone3, F. De Paolis4, M. Dominik⋆5, Y. Giraud-Héraud6, G. Ingrosso4,
Ph. Jetzer7, L. Mancini1,2, A. Nucita4, G. Scarpetta1,2, F. Strafella4, and A. Gould8
(the PLAN⋆⋆ collaboration)
1 Dipartimento di Fisica “E. R. Caianiello”, Università di Salerno, Via S. Allende, 84081 Baronissi (SA), Italy
2 Istituto Nazionale di Fisica Nucleare, sezione di Napoli, Italy
3 INAF - Osservatorio Astronomico di Capodimonte, via Moiariello 16, Napoli, Italy
4 Dipartimento di Fisica, Università di Lecce and INFN, Sezione di Lecce, CP 193, 73100 Lecce, Italy
5 SUPA, University of St Andrews, School of Physics & Astronomy, North Haugh, St Andrews, KY16 9SS, United
Kingdom
6 APC, 10, rue Alice Domon et Léonie Duquet 75205 Paris, France
7 Institute for Theoretical Physics, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
8 Department of Astronomy, Ohio State University, 140 West 18th Avenue, Columbus, OH 43210, US
Received/ Accepted
Abstract. We analyse a series of pilot observations in order to study microlensing of (unresolved) stars in M31 with
the 1.5m Loiano telescope, including observations on both identified variable source stars and reported microlens-
ing events. We also look for previously unknown variability and discover a nova. We discuss an observing strategy
for an extended campaign with the goal of determining whether MACHOs exist or whether all microlensing events
are compatible with lens stars in M31.
Key words. Gravitational lensing - Galaxy: Halo - Galaxies: M31
1. Introduction
Following the original proposal of Paczyński (1986),
several microlensing campaigns have been undertaken in
the recent years with the purpose of unveiling the content
of galactic halos in form of MACHOs. While both the
MACHO (Alcock et al. 2000) and EROS (Tisserand et al.
2006) groups have published comprehensive results of
their respective campaigns, and an analysis of the
OGLE campaign is underway, no consensus has yet
been reached on either the density of MACHOs or
their mass spectrum, and it is still not clear whether
“self lensing” within the Magellanic Clouds (Sahu 1994;
Wu 1994) can account for most or even all of the de-
tected microlensing events (Belokurov et al. 2003, 2004;
Mancini et al. 2004; Griest & Thomas 2005; Bennett
2005; Calchi Novati et al. 2006; Evans & Belokurov
2006).
Searching for microlensing events towards the
Andromeda Galaxy (M31) not only allows one to monitor
a huge number of stars (∼ 108) within a few fields, but also
allows one to fully probe M31’s whole halo (which is not
⋆ Royal Society University Research Fellow
⋆⋆ Pixel Lensing Andromeda
possible for the Milky Way), and possibly to distinguish
more easily between self lensing and lensing by MACHOs
because M31’s tilt with respect to the line of sight in-
duces a characteristic signature in the spatial distribution
of the halo events (Crotts 1992; Baillon et al. 1993; Jetzer
1994). Observational campaigns have been carried out by
several collaborations: AGAPE (Ansari et al. 1997, 1999),
Columbia-VATT (Crotts & Tomaney 1996), POINT-
AGAPE (Aurière et al. 2001; Paulin-Henriksson et al.
2003), SLOTT-AGAPE (Calchi Novati et al. 2002, 2003),
WeCAPP (Riffeser et al. 2003), MEGA (de Jong et al.
2004), NainiTal (Joshi et al. 2005) and ANGSTROM
(Kerins et al. 2006). The detection of a handful of mi-
crolensing candidates have been reported and first, though
contradictory, conclusions on the MACHO content along
this line of sight have been reported (Calchi Novati et al.
2005; de Jong et al. 2006).
In order to go beyond these first results, it is essential
to choose an appropriate observational strategy for the
new observational campaigns. Indeed, the experience of
the previous campaigns shows that a careful assessment of
the characteristics of the microlensing signal and of poten-
tially contaminating stellar variables is crucial. Two main
phenomenological characteristics of microlensing events
http://arxiv.org/abs/0704.1408v1
2 Calchi Novati et al.: Probing MACHOs with the 1.5m Loiano telescope
must be taken into account: the duration and the flux de-
viation (e.g. Ingrosso et al. 2006a,b). Microlensing events
in M31 are expected to last only a few days (this holds in
the lens mass range 10−2 − 1 M⊙, over which self lensing
but also most of the MACHO signal is expected). Note
that here we refer to the full-duration-at-half-maximum,
t1/2, easily evaluated out of pixel lensing observations,
with t1/2 = t1/2(tE, u0), where tE, u0 are the Einstein
time and impact parameter, respectively. The degeneracy
in the parameter space tE, u0 is intrinsically linked to the
fact that the underlying sources are not resolved objects
so that the background level of the light curves is a blend
(of a huge number) of stars (Gould 1996). However, as
was shown to be the case for some of the POINT-AGAPE
microlensing candidates, extremely good sampling along
the flux variation sometimes allow one to break this de-
generacy. To gain insight into the underlying mass spec-
trum of the lens population (recall tE ∝
Mlens), it
will be essential to break the tE, u0 degeneracy beyond
what was achieved in previous campaigns. Furthermore,
the expected short duration can also be used to robustly
test the detected flux variations with respect to the vari-
able star background (Calchi Novati et al. 2005), but to
achieve this, a very tight and regular sampling is again
necessary. On the other hand, the expected duration im-
plies that to characterise the microlensing signals, the
campaign does not need to be extremely long. Besides,
the dataset of previous campaigns already allows one to
check for the expected uniqueness of microlensing signals.
The long time baseline can then be exploited in order to
increase the expected rate of events. Very tight and regu-
lar sampling on a nightly basis is therefore a first crucial
feature for an optimal observational strategy. This would
represent an important improvement with respect to pre-
vious campaigns that would allow one both to better dis-
tinguish microlensing events from other background vari-
ations, and, possibly, to break some of the degeneracy in
the microlensing parameter space. As for the flux devia-
tion, the main results have been obtained using the 2.5m
INT telescope with integration times of about 20 minutes
per night, so that even smaller telescopes can be used,
provided that long enough integration times are employed
to reach the needed signal-to-noise ratio.
In this paper we present the results of the pilot sea-
son of a new observational campaign towards M31 car-
ried out with the Loiano telescope at the “Osservatorio
Astronomico di Bologna” (OAB)1. In Sect. 2 we present
the observational setup and outline data reduction and
analysis. In Sect. 3 we present the results of our follow-up
observations on previously reported microlensing candi-
dates and other variable light curves, and we report the
discovery of a new Nova variation. In Sect. 4 we estimate
the expected microlensing signal and discuss the feasibility
and objectives of a longer-term microlensing campaign.
1 http://www.bo.astro.it/loiano/index.htm
2. Data analysis
2.1. Observational setup, data acquisition and
reduction
As pilot observations for studying microlensing of stars
in the inner M31 region, we observed two fields dur-
ing 11 consecutive nights, from 5 September to 15
September 2006, with the 152cm Cassini Telescope lo-
cated in Loiano (Bologna, Italy). We make use of a CCD
EEV of 1300x1340 pixels of 0.′′58 for a total field of view
of 13′ × 12.′6, with gain of 2 e−/ADU and low read-
out noise (3.5 e−/px). Two fields of view around the in-
ner M31 region have been monitored, centered respec-
tively at RA=0h42m50s, DEC=41◦23′57′′ (“North”) and
RA=0h42m50s, DEC=41◦08′23′′ (“South”) (J2000), so as
to leave out the innermost (∼ 3′) M31 bulge region, and
with the CCD axes parallel to the north-south and east-
west directions, in order to get the maximum field overlap
with previous campaigns (Fig. 1). To test for achromatic-
ity, data have been acquired in two bandpasses (similar to
Cousins R and I), with exposure times of 5 or 6 minutes
per frame. Overall we collected about 100 exposures per
field per filter over 8 nights or about 15 images per night2.
Typical seeing values were in the range 1.5′′−2′′. Bias and
sky flats frames were taken each night and standard data
reduction was carried out using the IRAF package3. We
also corrected the I-band data for fringe effects.
2.2. Image analysis
The search for flux variations towards M31 has to deal
with the fact that sources are not resolved objects, so that
one has to monitor flux variations of every element of the
image (the so called “pixel-lensing” technique discussed
in Gould 1996). As for the preliminary image analysis, we
follow closely the strategy outlined by the AGAPE group
(Ansari et al. 1997; Calchi Novati et al. 2002), in which
each image is geometrically and photometrically aligned
relative to a reference image. To account for seeing vari-
ations we then substitute for the flux of each pixel, the
flux of the corresponding 5-pixel square “superpixel” cen-
tered on it (whose size is determined so as to cover most
of the average seeing disc) and then apply an empirical,
linear, correction in the flux, again calibrating each image
with respect to the reference image. The final expression
for the flux error accounts both for the statistical error in
the flux count and for the residual error linked to the see-
ing correction procedure. Finally, in order to increase the
signal-to-noise ratio, we combine the images taken during
the same night.
2 During the last useful night only a few R images in the
North field could be taken.
3 http://iraf.noao.edu/
Calchi Novati et al.: Probing MACHOs with the 1.5m Loiano telescope 3
Fig. 1. Projected on M31, we display the boundaries of
the two 13’x12.6’ monitored fields (inner contours), to-
gether with the larger INT fields and the centre M31
(cross). The filled circle marks the position of the Nova
variable detected (Sect. 3.3).
3. Light curve results
3.1. Variables in the POINT-AGAPE catalogue
In order to assess the quality of the present data set as
compared to that of previous campaigns we looked into
observations of ∼ 40000 stars identified as variables by
the POINT-AGAPE group (An et al. 2004). Besides the
position, each variation in this catalogue is characterised
by three quantities: the magnitude corresponding to the
flux deviation at maximum R(∆φ), with values down to
R(∆φ) ∼ 23, the period (P ) as evaluated using a Lomb
algorithm, and an estimator of the probability of a false
detection (Lf ) (high absolute values of Lf indicate a sure
identification). We note that most of the variations in the
catalogue are rather faint and only a few have short peri-
We want to investigate which fraction of variables
found by POINT-AGAPE can be identified by our ob-
servations. (Preliminary to the analysis, we must evalu-
ate the relative geometrical and photometrical transfor-
mation between the two data sets. In particular, we find
that ∼ 30% of the original sample belongs also to our field
of view). Since our observations cover only 11 days, we re-
strict our attention to the shortest periods (P < 30 d),
which encompasses a ∼ 2% subset of the POINT-AGAPE
catalogue. Note that our limited baseline does not allow
us to properly characterise the shape parameters of the
detected variations. Therefore, in order to cross-identify
the flux variations detected with those belonging to the
Period (days)
Period (days)
0 5 10 15 20 25 30
0 5 10 15 20 25 30
Fig. 2. R(∆φ) vs. Period for short-period (P < 30 d)
variable stars reported in the POINT-AGAPE catalogue
(top panel shows the subset with log(Lf) < −30), where
filled circles indicate the flux variations identified within
the OAB data set.
POINT-AGAPE catalogue we only test for the offset be-
tween the position evaluated through our selection and
the transformed POINT-AGAPE position.
For our analysis, we first identify a “clean” set of
variable stars (selected by demanding log(Lf) < −30),
which includes ∼ 25% of the POINT-AGAPE sam-
ple. Restricting ourselves to short-period variables with
P < 30 d, leaves us with 169 stars within our field of view,
among which 68 fall into the “clean” sample. For the lat-
ter, we detect most of the bright variations (R(∆φ) < 21),
namely ∼ 70%, and about 40% of all of the variations.
When we consider the total sample of short-period vari-
ables we arrive at values that are about 10% smaller. This
partly results from the fact that the total sample con-
tains a larger fraction of faint objects, while our detection
threshold, though varying with the position in the fields,
is typically about R(∆φ) ∼ 22. In Fig. 2 we show flux
deviation vs. period for the the full set of short-period
POINT-AGAPE variables, where solid circles mark those
that were found by our analysis. In Fig. 3, we show the
lightcurve of a POINT-AGAPE variable recovered within
the OAB data, with its OAB extension.
3.2. Identified microlensing candidates
Since microlensing variations are quite unlikely to re-
peat, measuring a constant flux from follow-up obser-
vations provides further evidence that the previously
observed signal has indeed been caused by microlens-
ing. Our target fields contain three of the six can-
4 Calchi Novati et al.: Probing MACHOs with the 1.5m Loiano telescope
t (days)
t (days)
t (JD-2449624.5)
t (JD-2449624.5)
0 2.5 5 7.5 10 12.5 15 17.5 20 22.5
0 2.5 5 7.5 10 12.5 15 17.5 20 22.5
4350 4355 4360 4365 4370 4375
4350 4355 4360 4365 4370 4375
Fig. 3. The light curve of a POINT-AGAPE flux varia-
tion (P = 11.14 days and R(∆φ) = 21.1), together with
its extension in the OAB data. Top to bottom, the INT
R and color light curves, folded by their period (for visual
aid, two cycles are plotted); and the OAB R and color
light curves. The “color” is evaluated as −2.5 log(φr/φi),
where φ is the observed flux. Flux is in ADU s−1.
didates reported by the POINT-AGAPE collaboration
(Calchi Novati et al. 2005), PA-N1, PA-S3 and PA-S7; be-
side PA-N1, two more among the 14 reported by the
MEGA collaboration (de Jong et al. 2006), MEGA-ML-
3 and MEGA-ML-15; beside PA-S3, the second candidate
reported by the WeCAPP collaboration, WeCAPP-GL2
(Riffeser et al. 2003). All of the light curve extensions
within our data set of the previous variations appear to
be stable, namely, we do not observe any flux variation
beyond the background noise level compatible with the
observed microlensing flux variation. As an example, in
Fig. 4 we show the PA-S3 light curve together with its
extension in the OAB data.
3.3. A Nova like variation
Lastly, we discuss the result of a search for very bright
flux variations (R(∆φ) < 19). One flux variation sur-
vives this selection (Fig. 5), and this appears to be a
nova-like variable (its extension on the POINT-AGAPE
data set appears to be stable) located in RA=0h42m33s,
DEC=41◦10′06′′ (J2000). We estimate the magnitude and
color at maximum to be R(∆φ) ∼ 17.5 and R− I ∼ −0.1.
The rate of decline, about 2 magnitudes during the 7
nights of our observational period, puts this nova among
the “very fast” ones in the speed classes defined in Warner
(1989). The (strong) color evolution is rather unusual, as
it got redder during descent. In the POINT-AGAPE nova
t (JD-2449624.5)
t (JD-2449624.5)
t (JD-2449624.5)
t (JD-2449624.5)
2140 2160 2180 2200 2220 2240 2260 2280 2300
2140 2160 2180 2200 2220 2240 2260 2280 2300
4350 4355 4360 4365 4370 4375
4350 4355 4360 4365 4370 4375
Fig. 4. The light curve of the POINT-AGAPE PA-
S3 microlensing candidate (Paulin-Henriksson et al. 2003;
Calchi Novati et al. 2005) together with its extension in
the OAB data. In the INT data the dotted line is the best
Paczyński (1986) fit; in the OAB data, the solid lines indi-
cate the background level, while the dotted lines represent
the flux deviation corresponding to the observed flux devi-
ation at maximum for the POINT-AGAPE variation. The
ordinate axis units are flux in ADU s−1.
t (JD-2449624.5)
t (JD-2449624.5)
t (JD-2449624.5)
4345 4350 4355 4360 4365 4370 4375 4380
4345 4350 4355 4360 4365 4370 4375 4380
4345 4350 4355 4360 4365 4370 4375 4380
Fig. 5. The light curve of the Nova detected within the
OAB data. Top to bottom, R, I bands and color data (as
defined in Fig. 3) are shown. The solid lines (R and I data)
indicate the estimate of the background level.
Calchi Novati et al.: Probing MACHOs with the 1.5m Loiano telescope 5
catalogue (Darnley et al. 2004), there was only one such
object, PACN-00-07, showing a similar color evolution but
also characterised by a fainter magnitude at maximum and
a slower speed of descent.
The issue of the expected novæ rate in M31 is still
a matter of debate. Darnley et al. (2006) evaluate a rate
of ∼ 38 (∼ 27) novæ/years for the bulge (disc) respec-
tively, while previous works pointed to somewhat smaller
values (e.g. Capaccioli et al. 1989; Shafter & Irby 2001).
Our detection of 1 nova during an overall period of 11
days is in any case in good agreement with these expec-
tations (restricted to the bulge region only and using the
first estimate, we derive an expected number of novæ of
∼ 1.1).
4. The expected microlensing signal
To predict the number and characteristics of the ex-
pected microlensing signal for the different lens popula-
tions (Galactic halo and components of M31), we need
both an astrophysical model for all the physical quantities
that determine the microlensing events (which includes
brightness profile, spatial mass density, velocity distribu-
tions, luminosity function for the sources, and mass spec-
trum for the lenses) and a model reproducing both the ob-
servational setup and the selection pipeline. Because of the
huge parameter space involved, we use a Monte Carlo sim-
ulation to carry out this program. In particular, we make
use of the simulation described in Calchi Novati et al.
(2005), adapted to the OAB observational setup.
In Fig. 6 we report the results, obtained using the fidu-
cial astrophysical model discussed in Calchi Novati et al.
(2005), for the flux deviation at maximum and duration
distributions expected for self-lensing events (the corre-
sponding distributions for 0.5 M⊙ MACHOs are almost
indistinguishable) and, for both self lensing and MACHOs,
the expected distance from the M31 center distribution.
In particular we recover the well known results that most
of the microlensing events are expected to last only a
few days. We also stress the difference, already apparent
within our relatively small field of view, between the spa-
tial distributions due to luminous and MACHO lenses.
The latter is much broader, implying that this diagnostic
can be used to distinguish between the two populations.
Note that here we are considering the distance-from-the-
M31-center statistics rather than the expected asymmetry
in the spatial distribution of M31 halo lenses (Crotts 1992;
Jetzer 1994). The M31-center-distance statistic is sensitive
to the different mass distributions of stars and dark mat-
ter, although it is a zeroth order approximation since it
ignores the additional difference due to the expected asym-
metry of the microlensing signal. We adopt this zeroth-
order approach because the refinement needed to include
the asymmetry information would require substantial ad-
ditional analysis: as was pointed out by An et al. (2004),
the study of variable stars demonstrates that differential
extinction could induce a similar asymmetric signal on the
spatial distribution of self-lensing events. Note also that
Self lensing: R(∆φ)
Self lensing: t1/2 (days)
Self lensing: distance from M31 center (arcmin)
MACHO: distance from M31 center (arcmin)
18 19 20 21 22 23 24
0 5 10 15 20 25 30
0 2 4 6 8 10 12 14
0 2 4 6 8 10 12 14
Fig. 6. Results of the Monte Carlo simulation: from top
to bottom we show the histograms of the expected flux de-
viation at maximum, duration distribution for self-lensing
events, and the distance (from the M31 center) distribu-
tions for self-lensing and for MACHOs. The units on the
ordinate axes are the number of events.
our choice for the field position has not been chosen in or-
der to optimise such an analysis, but rather to maximise
the overlap with the fields of previous campaigns. Let us
note that a real “second generation” pixel lensing experi-
ment should cover a much larger field of view than ours,
both to increase, for a given time baseline, the expected
rate of events but especially in order to better disentangle
the self-lensing signal from the MACHO signal.
To estimate the number of expected events, we repro-
duce the actual sampling of this pilot season and imple-
ment a basic selection for microlensing events (asking for
the presence of a significant bump), and take into account
the results of the analysis carried out in Sect. 3.1 by re-
stricting to the subsample of R(∆φ) < 22 variations. As
a results, we predict ∼ 0.17 self-lensing events and ∼ 0.54
MACHOs (for full M31 and Galactic halos with 0.5 M⊙
MACHO objects). As discussed in Calchi Novati et al.
(2005), the predictions of the Monte Carlo simulation are
quantifiable as “over-optimistic”, so that these figures, for
the given astrophysical model, should be taken as an up-
per limit to the actual number of expected events because
we have not factored in the efficiency of the pipeline.
In order to increase the available statistics we need
a longer time baseline. An aspect here deserves to be
stressed. As the expected duration of the events we are
looking for is of the same order of the length of our present
baseline, because of “boundary” effects, the number of ex-
pected events should increase more than linearly with the
overall baseline length (of course, this is no longer true
6 Calchi Novati et al.: Probing MACHOs with the 1.5m Loiano telescope
as soon as the baseline is long enough). This holds un-
der the condition that no gaps are introduced into the
sampling, clearly showing the importance of an appropri-
ate observational strategy. For example, for a full two-
month campaign we predict, again for the sub sample of
R(∆φ) < 22 variations, ∼ 1.3 (5.1) self-lensing (0.5 M⊙
MACHO) events, respectively. Finally, we note that we
have obtained similar results within a parallel analysis car-
ried out following the approach outlined in Ingrosso et al.
(2006a,b).
As for the astrophysical model, we recall that
de Jong et al. (2006), using a different model for the lumi-
nous components of M31, obtained a significantly higher
expected contribution of the self-lensing signal relative
to that evaluated with the fiducial model discussed in
Calchi Novati et al. (2005), which we are also using in the
present analysis. Hence, the full-fledged campaign that we
are planning will be important for understanding the dis-
puted issue of M31 self-lensing as well as MACHO dark
matter.
5. Conclusions
Based on pilot season observations of M31 during 11 con-
secutive nights in September 2006 and a Monte Carlo sim-
ulation for the expected properties of microlensing events
caused by lenses in the Galactic halo or M31, respectively,
we have shown the feasibility of an extended campaign
with the 1.5m Loiano telescope being able to resolve the
current puzzle of the origin of microlensing events involv-
ing extragalactic sources.
In particular, we were able to identify known variable
stars from our data thanks to the tight sampling and de-
spite the short time range covered. Reported microlensing
candidates within our field of view have shown no fur-
ther variation, therefore the microlensing interpretation
was confirmed. Moreover, a nova variable showed up in
our data.
As for the microlensing signal, we have stressed the im-
portance of an appropriate sampling for the observations,
and discussed the results of a Monte Carlo simulation
of the present experiment. In particular, we have shown
how the expected spatial distribution for self-lensing and
MACHO events can allow us to disentangle the two con-
tributions. Finally, we have provided an evaluation of the
expected number of microlensing events for the present
pilot season and discussed quantitatively the possible out-
put of a longer baseline campaign.
Acknowledgements. The observational campaign has been pos-
sible thanks to the generous allocation of telescope time by the
TAC of the Bologna Observatory and to the invaluable help of
the technical staff. In particular, we thank Ivan Bruni for accu-
rate and precious assistance during the observations. We thank
the POINT-AGAPE collaboration for access to their database.
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Warner, B. 1989, in Bode M. F., Evans A., eds, Classical
Novæ. Wiley, Chichester, p.1
Wu, X.-P. 1994, ApJ, 435, 66
	Introduction
	Data analysis
	Observational setup, data acquisition and reduction
	Image analysis
	Light curve results
	Variables in the POINT-AGAPE catalogue
	Identified microlensing candidates
	A Nova like variation
	The expected microlensing signal
	Conclusions

  We analyse a series of pilot observations in order to study microlensing of
(unresolved) stars in M31 with the 1.5m Loiano telescope, including
observations on both identified variable source stars and reported microlensing
events. We also look for previously unknown variability and discover a nova. We
discuss an observing strategy for an extended campaign with the goal of
determining whether MACHOs exist or whether all microlensing events are
compatible with lens stars in M31.

Introduction
Following the original proposal of Paczyński (1986),
several microlensing campaigns have been undertaken in
the recent years with the purpose of unveiling the content
of galactic halos in form of MACHOs. While both the
MACHO (Alcock et al. 2000) and EROS (Tisserand et al.
2006) groups have published comprehensive results of
their respective campaigns, and an analysis of the
OGLE campaign is underway, no consensus has yet
been reached on either the density of MACHOs or
their mass spectrum, and it is still not clear whether
“self lensing” within the Magellanic Clouds (Sahu 1994;
Wu 1994) can account for most or even all of the de-
tected microlensing events (Belokurov et al. 2003, 2004;
Mancini et al. 2004; Griest & Thomas 2005; Bennett
2005; Calchi Novati et al. 2006; Evans & Belokurov
2006).
Searching for microlensing events towards the
Andromeda Galaxy (M31) not only allows one to monitor
a huge number of stars (∼ 108) within a few fields, but also
allows one to fully probe M31’s whole halo (which is not
⋆ Royal Society University Research Fellow
⋆⋆ Pixel Lensing Andromeda
possible for the Milky Way), and possibly to distinguish
more easily between self lensing and lensing by MACHOs
because M31’s tilt with respect to the line of sight in-
duces a characteristic signature in the spatial distribution
of the halo events (Crotts 1992; Baillon et al. 1993; Jetzer
1994). Observational campaigns have been carried out by
several collaborations: AGAPE (Ansari et al. 1997, 1999),
Columbia-VATT (Crotts & Tomaney 1996), POINT-
AGAPE (Aurière et al. 2001; Paulin-Henriksson et al.
2003), SLOTT-AGAPE (Calchi Novati et al. 2002, 2003),
WeCAPP (Riffeser et al. 2003), MEGA (de Jong et al.
2004), NainiTal (Joshi et al. 2005) and ANGSTROM
(Kerins et al. 2006). The detection of a handful of mi-
crolensing candidates have been reported and first, though
contradictory, conclusions on the MACHO content along
this line of sight have been reported (Calchi Novati et al.
2005; de Jong et al. 2006).
In order to go beyond these first results, it is essential
to choose an appropriate observational strategy for the
new observational campaigns. Indeed, the experience of
the previous campaigns shows that a careful assessment of
the characteristics of the microlensing signal and of poten-
tially contaminating stellar variables is crucial. Two main
phenomenological characteristics of microlensing events
http://arxiv.org/abs/0704.1408v1
2 Calchi Novati et al.: Probing MACHOs with the 1.5m Loiano telescope
must be taken into account: the duration and the flux de-
viation (e.g. Ingrosso et al. 2006a,b). Microlensing events
in M31 are expected to last only a few days (this holds in
the lens mass range 10−2 − 1 M⊙, over which self lensing
but also most of the MACHO signal is expected). Note
that here we refer to the full-duration-at-half-maximum,
t1/2, easily evaluated out of pixel lensing observations,
with t1/2 = t1/2(tE, u0), where tE, u0 are the Einstein
time and impact parameter, respectively. The degeneracy
in the parameter space tE, u0 is intrinsically linked to the
fact that the underlying sources are not resolved objects
so that the background level of the light curves is a blend
(of a huge number) of stars (Gould 1996). However, as
was shown to be the case for some of the POINT-AGAPE
microlensing candidates, extremely good sampling along
the flux variation sometimes allow one to break this de-
generacy. To gain insight into the underlying mass spec-
trum of the lens population (recall tE ∝
Mlens), it
will be essential to break the tE, u0 degeneracy beyond
what was achieved in previous campaigns. Furthermore,
the expected short duration can also be used to robustly
test the detected flux variations with respect to the vari-
able star background (Calchi Novati et al. 2005), but to
achieve this, a very tight and regular sampling is again
necessary. On the other hand, the expected duration im-
plies that to characterise the microlensing signals, the
campaign does not need to be extremely long. Besides,
the dataset of previous campaigns already allows one to
check for the expected uniqueness of microlensing signals.
The long time baseline can then be exploited in order to
increase the expected rate of events. Very tight and regu-
lar sampling on a nightly basis is therefore a first crucial
feature for an optimal observational strategy. This would
represent an important improvement with respect to pre-
vious campaigns that would allow one both to better dis-
tinguish microlensing events from other background vari-
ations, and, possibly, to break some of the degeneracy in
the microlensing parameter space. As for the flux devia-
tion, the main results have been obtained using the 2.5m
INT telescope with integration times of about 20 minutes
per night, so that even smaller telescopes can be used,
provided that long enough integration times are employed
to reach the needed signal-to-noise ratio.
In this paper we present the results of the pilot sea-
son of a new observational campaign towards M31 car-
ried out with the Loiano telescope at the “Osservatorio
Astronomico di Bologna” (OAB)1. In Sect. 2 we present
the observational setup and outline data reduction and
analysis. In Sect. 3 we present the results of our follow-up
observations on previously reported microlensing candi-
dates and other variable light curves, and we report the
discovery of a new Nova variation. In Sect. 4 we estimate
the expected microlensing signal and discuss the feasibility
and objectives of a longer-term microlensing campaign.
1 http://www.bo.astro.it/loiano/index.htm
2. Data analysis
2.1. Observational setup, data acquisition and
reduction
As pilot observations for studying microlensing of stars
in the inner M31 region, we observed two fields dur-
ing 11 consecutive nights, from 5 September to 15
September 2006, with the 152cm Cassini Telescope lo-
cated in Loiano (Bologna, Italy). We make use of a CCD
EEV of 1300x1340 pixels of 0.′′58 for a total field of view
of 13′ × 12.′6, with gain of 2 e−/ADU and low read-
out noise (3.5 e−/px). Two fields of view around the in-
ner M31 region have been monitored, centered respec-
tively at RA=0h42m50s, DEC=41◦23′57′′ (“North”) and
RA=0h42m50s, DEC=41◦08′23′′ (“South”) (J2000), so as
to leave out the innermost (∼ 3′) M31 bulge region, and
with the CCD axes parallel to the north-south and east-
west directions, in order to get the maximum field overlap
with previous campaigns (Fig. 1). To test for achromatic-
ity, data have been acquired in two bandpasses (similar to
Cousins R and I), with exposure times of 5 or 6 minutes
per frame. Overall we collected about 100 exposures per
field per filter over 8 nights or about 15 images per night2.
Typical seeing values were in the range 1.5′′−2′′. Bias and
sky flats frames were taken each night and standard data
reduction was carried out using the IRAF package3. We
also corrected the I-band data for fringe effects.
2.2. Image analysis
The search for flux variations towards M31 has to deal
with the fact that sources are not resolved objects, so that
one has to monitor flux variations of every element of the
image (the so called “pixel-lensing” technique discussed
in Gould 1996). As for the preliminary image analysis, we
follow closely the strategy outlined by the AGAPE group
(Ansari et al. 1997; Calchi Novati et al. 2002), in which
each image is geometrically and photometrically aligned
relative to a reference image. To account for seeing vari-
ations we then substitute for the flux of each pixel, the
flux of the corresponding 5-pixel square “superpixel” cen-
tered on it (whose size is determined so as to cover most
of the average seeing disc) and then apply an empirical,
linear, correction in the flux, again calibrating each image
with respect to the reference image. The final expression
for the flux error accounts both for the statistical error in
the flux count and for the residual error linked to the see-
ing correction procedure. Finally, in order to increase the
signal-to-noise ratio, we combine the images taken during
the same night.
2 During the last useful night only a few R images in the
North field could be taken.
3 http://iraf.noao.edu/
Calchi Novati et al.: Probing MACHOs with the 1.5m Loiano telescope 3
Fig. 1. Projected on M31, we display the boundaries of
the two 13’x12.6’ monitored fields (inner contours), to-
gether with the larger INT fields and the centre M31
(cross). The filled circle marks the position of the Nova
variable detected (Sect. 3.3).
3. Light curve results
3.1. Variables in the POINT-AGAPE catalogue
In order to assess the quality of the present data set as
compared to that of previous campaigns we looked into
observations of ∼ 40000 stars identified as variables by
the POINT-AGAPE group (An et al. 2004). Besides the
position, each variation in this catalogue is characterised
by three quantities: the magnitude corresponding to the
flux deviation at maximum R(∆φ), with values down to
R(∆φ) ∼ 23, the period (P ) as evaluated using a Lomb
algorithm, and an estimator of the probability of a false
detection (Lf ) (high absolute values of Lf indicate a sure
identification). We note that most of the variations in the
catalogue are rather faint and only a few have short peri-
We want to investigate which fraction of variables
found by POINT-AGAPE can be identified by our ob-
servations. (Preliminary to the analysis, we must evalu-
ate the relative geometrical and photometrical transfor-
mation between the two data sets. In particular, we find
that ∼ 30% of the original sample belongs also to our field
of view). Since our observations cover only 11 days, we re-
strict our attention to the shortest periods (P < 30 d),
which encompasses a ∼ 2% subset of the POINT-AGAPE
catalogue. Note that our limited baseline does not allow
us to properly characterise the shape parameters of the
detected variations. Therefore, in order to cross-identify
the flux variations detected with those belonging to the
Period (days)
Period (days)
0 5 10 15 20 25 30
0 5 10 15 20 25 30
Fig. 2. R(∆φ) vs. Period for short-period (P < 30 d)
variable stars reported in the POINT-AGAPE catalogue
(top panel shows the subset with log(Lf) < −30), where
filled circles indicate the flux variations identified within
the OAB data set.
POINT-AGAPE catalogue we only test for the offset be-
tween the position evaluated through our selection and
the transformed POINT-AGAPE position.
For our analysis, we first identify a “clean” set of
variable stars (selected by demanding log(Lf) < −30),
which includes ∼ 25% of the POINT-AGAPE sam-
ple. Restricting ourselves to short-period variables with
P < 30 d, leaves us with 169 stars within our field of view,
among which 68 fall into the “clean” sample. For the lat-
ter, we detect most of the bright variations (R(∆φ) < 21),
namely ∼ 70%, and about 40% of all of the variations.
When we consider the total sample of short-period vari-
ables we arrive at values that are about 10% smaller. This
partly results from the fact that the total sample con-
tains a larger fraction of faint objects, while our detection
threshold, though varying with the position in the fields,
is typically about R(∆φ) ∼ 22. In Fig. 2 we show flux
deviation vs. period for the the full set of short-period
POINT-AGAPE variables, where solid circles mark those
that were found by our analysis. In Fig. 3, we show the
lightcurve of a POINT-AGAPE variable recovered within
the OAB data, with its OAB extension.
3.2. Identified microlensing candidates
Since microlensing variations are quite unlikely to re-
peat, measuring a constant flux from follow-up obser-
vations provides further evidence that the previously
observed signal has indeed been caused by microlens-
ing. Our target fields contain three of the six can-
4 Calchi Novati et al.: Probing MACHOs with the 1.5m Loiano telescope
t (days)
t (days)
t (JD-2449624.5)
t (JD-2449624.5)
0 2.5 5 7.5 10 12.5 15 17.5 20 22.5
0 2.5 5 7.5 10 12.5 15 17.5 20 22.5
4350 4355 4360 4365 4370 4375
4350 4355 4360 4365 4370 4375
Fig. 3. The light curve of a POINT-AGAPE flux varia-
tion (P = 11.14 days and R(∆φ) = 21.1), together with
its extension in the OAB data. Top to bottom, the INT
R and color light curves, folded by their period (for visual
aid, two cycles are plotted); and the OAB R and color
light curves. The “color” is evaluated as −2.5 log(φr/φi),
where φ is the observed flux. Flux is in ADU s−1.
didates reported by the POINT-AGAPE collaboration
(Calchi Novati et al. 2005), PA-N1, PA-S3 and PA-S7; be-
side PA-N1, two more among the 14 reported by the
MEGA collaboration (de Jong et al. 2006), MEGA-ML-
3 and MEGA-ML-15; beside PA-S3, the second candidate
reported by the WeCAPP collaboration, WeCAPP-GL2
(Riffeser et al. 2003). All of the light curve extensions
within our data set of the previous variations appear to
be stable, namely, we do not observe any flux variation
beyond the background noise level compatible with the
observed microlensing flux variation. As an example, in
Fig. 4 we show the PA-S3 light curve together with its
extension in the OAB data.
3.3. A Nova like variation
Lastly, we discuss the result of a search for very bright
flux variations (R(∆φ) < 19). One flux variation sur-
vives this selection (Fig. 5), and this appears to be a
nova-like variable (its extension on the POINT-AGAPE
data set appears to be stable) located in RA=0h42m33s,
DEC=41◦10′06′′ (J2000). We estimate the magnitude and
color at maximum to be R(∆φ) ∼ 17.5 and R− I ∼ −0.1.
The rate of decline, about 2 magnitudes during the 7
nights of our observational period, puts this nova among
the “very fast” ones in the speed classes defined in Warner
(1989). The (strong) color evolution is rather unusual, as
it got redder during descent. In the POINT-AGAPE nova
t (JD-2449624.5)
t (JD-2449624.5)
t (JD-2449624.5)
t (JD-2449624.5)
2140 2160 2180 2200 2220 2240 2260 2280 2300
2140 2160 2180 2200 2220 2240 2260 2280 2300
4350 4355 4360 4365 4370 4375
4350 4355 4360 4365 4370 4375
Fig. 4. The light curve of the POINT-AGAPE PA-
S3 microlensing candidate (Paulin-Henriksson et al. 2003;
Calchi Novati et al. 2005) together with its extension in
the OAB data. In the INT data the dotted line is the best
Paczyński (1986) fit; in the OAB data, the solid lines indi-
cate the background level, while the dotted lines represent
the flux deviation corresponding to the observed flux devi-
ation at maximum for the POINT-AGAPE variation. The
ordinate axis units are flux in ADU s−1.
t (JD-2449624.5)
t (JD-2449624.5)
t (JD-2449624.5)
4345 4350 4355 4360 4365 4370 4375 4380
4345 4350 4355 4360 4365 4370 4375 4380
4345 4350 4355 4360 4365 4370 4375 4380
Fig. 5. The light curve of the Nova detected within the
OAB data. Top to bottom, R, I bands and color data (as
defined in Fig. 3) are shown. The solid lines (R and I data)
indicate the estimate of the background level.
Calchi Novati et al.: Probing MACHOs with the 1.5m Loiano telescope 5
catalogue (Darnley et al. 2004), there was only one such
object, PACN-00-07, showing a similar color evolution but
also characterised by a fainter magnitude at maximum and
a slower speed of descent.
The issue of the expected novæ rate in M31 is still
a matter of debate. Darnley et al. (2006) evaluate a rate
of ∼ 38 (∼ 27) novæ/years for the bulge (disc) respec-
tively, while previous works pointed to somewhat smaller
values (e.g. Capaccioli et al. 1989; Shafter & Irby 2001).
Our detection of 1 nova during an overall period of 11
days is in any case in good agreement with these expec-
tations (restricted to the bulge region only and using the
first estimate, we derive an expected number of novæ of
∼ 1.1).
4. The expected microlensing signal
To predict the number and characteristics of the ex-
pected microlensing signal for the different lens popula-
tions (Galactic halo and components of M31), we need
both an astrophysical model for all the physical quantities
that determine the microlensing events (which includes
brightness profile, spatial mass density, velocity distribu-
tions, luminosity function for the sources, and mass spec-
trum for the lenses) and a model reproducing both the ob-
servational setup and the selection pipeline. Because of the
huge parameter space involved, we use a Monte Carlo sim-
ulation to carry out this program. In particular, we make
use of the simulation described in Calchi Novati et al.
(2005), adapted to the OAB observational setup.
In Fig. 6 we report the results, obtained using the fidu-
cial astrophysical model discussed in Calchi Novati et al.
(2005), for the flux deviation at maximum and duration
distributions expected for self-lensing events (the corre-
sponding distributions for 0.5 M⊙ MACHOs are almost
indistinguishable) and, for both self lensing and MACHOs,
the expected distance from the M31 center distribution.
In particular we recover the well known results that most
of the microlensing events are expected to last only a
few days. We also stress the difference, already apparent
within our relatively small field of view, between the spa-
tial distributions due to luminous and MACHO lenses.
The latter is much broader, implying that this diagnostic
can be used to distinguish between the two populations.
Note that here we are considering the distance-from-the-
M31-center statistics rather than the expected asymmetry
in the spatial distribution of M31 halo lenses (Crotts 1992;
Jetzer 1994). The M31-center-distance statistic is sensitive
to the different mass distributions of stars and dark mat-
ter, although it is a zeroth order approximation since it
ignores the additional difference due to the expected asym-
metry of the microlensing signal. We adopt this zeroth-
order approach because the refinement needed to include
the asymmetry information would require substantial ad-
ditional analysis: as was pointed out by An et al. (2004),
the study of variable stars demonstrates that differential
extinction could induce a similar asymmetric signal on the
spatial distribution of self-lensing events. Note also that
Self lensing: R(∆φ)
Self lensing: t1/2 (days)
Self lensing: distance from M31 center (arcmin)
MACHO: distance from M31 center (arcmin)
18 19 20 21 22 23 24
0 5 10 15 20 25 30
0 2 4 6 8 10 12 14
0 2 4 6 8 10 12 14
Fig. 6. Results of the Monte Carlo simulation: from top
to bottom we show the histograms of the expected flux de-
viation at maximum, duration distribution for self-lensing
events, and the distance (from the M31 center) distribu-
tions for self-lensing and for MACHOs. The units on the
ordinate axes are the number of events.
our choice for the field position has not been chosen in or-
der to optimise such an analysis, but rather to maximise
the overlap with the fields of previous campaigns. Let us
note that a real “second generation” pixel lensing experi-
ment should cover a much larger field of view than ours,
both to increase, for a given time baseline, the expected
rate of events but especially in order to better disentangle
the self-lensing signal from the MACHO signal.
To estimate the number of expected events, we repro-
duce the actual sampling of this pilot season and imple-
ment a basic selection for microlensing events (asking for
the presence of a significant bump), and take into account
the results of the analysis carried out in Sect. 3.1 by re-
stricting to the subsample of R(∆φ) < 22 variations. As
a results, we predict ∼ 0.17 self-lensing events and ∼ 0.54
MACHOs (for full M31 and Galactic halos with 0.5 M⊙
MACHO objects). As discussed in Calchi Novati et al.
(2005), the predictions of the Monte Carlo simulation are
quantifiable as “over-optimistic”, so that these figures, for
the given astrophysical model, should be taken as an up-
per limit to the actual number of expected events because
we have not factored in the efficiency of the pipeline.
In order to increase the available statistics we need
a longer time baseline. An aspect here deserves to be
stressed. As the expected duration of the events we are
looking for is of the same order of the length of our present
baseline, because of “boundary” effects, the number of ex-
pected events should increase more than linearly with the
overall baseline length (of course, this is no longer true
6 Calchi Novati et al.: Probing MACHOs with the 1.5m Loiano telescope
as soon as the baseline is long enough). This holds un-
der the condition that no gaps are introduced into the
sampling, clearly showing the importance of an appropri-
ate observational strategy. For example, for a full two-
month campaign we predict, again for the sub sample of
R(∆φ) < 22 variations, ∼ 1.3 (5.1) self-lensing (0.5 M⊙
MACHO) events, respectively. Finally, we note that we
have obtained similar results within a parallel analysis car-
ried out following the approach outlined in Ingrosso et al.
(2006a,b).
As for the astrophysical model, we recall that
de Jong et al. (2006), using a different model for the lumi-
nous components of M31, obtained a significantly higher
expected contribution of the self-lensing signal relative
to that evaluated with the fiducial model discussed in
Calchi Novati et al. (2005), which we are also using in the
present analysis. Hence, the full-fledged campaign that we
are planning will be important for understanding the dis-
puted issue of M31 self-lensing as well as MACHO dark
matter.
5. Conclusions
Based on pilot season observations of M31 during 11 con-
secutive nights in September 2006 and a Monte Carlo sim-
ulation for the expected properties of microlensing events
caused by lenses in the Galactic halo or M31, respectively,
we have shown the feasibility of an extended campaign
with the 1.5m Loiano telescope being able to resolve the
current puzzle of the origin of microlensing events involv-
ing extragalactic sources.
In particular, we were able to identify known variable
stars from our data thanks to the tight sampling and de-
spite the short time range covered. Reported microlensing
candidates within our field of view have shown no fur-
ther variation, therefore the microlensing interpretation
was confirmed. Moreover, a nova variable showed up in
our data.
As for the microlensing signal, we have stressed the im-
portance of an appropriate sampling for the observations,
and discussed the results of a Monte Carlo simulation
of the present experiment. In particular, we have shown
how the expected spatial distribution for self-lensing and
MACHO events can allow us to disentangle the two con-
tributions. Finally, we have provided an evaluation of the
expected number of microlensing events for the present
pilot season and discussed quantitatively the possible out-
put of a longer baseline campaign.
Acknowledgements. The observational campaign has been pos-
sible thanks to the generous allocation of telescope time by the
TAC of the Bologna Observatory and to the invaluable help of
the technical staff. In particular, we thank Ivan Bruni for accu-
rate and precious assistance during the observations. We thank
the POINT-AGAPE collaboration for access to their database.
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	Introduction
	Data analysis
	Observational setup, data acquisition and reduction
	Image analysis
	Light curve results
	Variables in the POINT-AGAPE catalogue
	Identified microlensing candidates
	A Nova like variation
	The expected microlensing signal
	Conclusions
