Table Of ContentA Search for Stellar Obscuration Events due to Dark Clouds
A. J. Drake1,2,3, K. H. Cook1
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ABSTRACT
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2 The recent detections of a large population of faint submillimetre sources, an excess
n halo γ-ray background, and the extreme scattering events observed for extragalactic
a radio sources have been explained as being due to baryonic dark matter in the form of
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small, dark, gas clouds. In this paper we present the results of a search for the transient
1
stellar obscurations such clouds are expected to cause. We examine the Macho project
1 light curves of 48×106 stars toward the Galactic bulge, LMC and SMC for the presence
v
of dark cloud extinction events. We find no evidence for the existence of a population
3
1 of dark gas clouds with A > 0.2 and masses between ∼ 10−4 and 10−2M⊙ in the
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Galactic disk or halo. However, it is possible that such dark cloud populations could
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0 exist if they are clustered in regions away from the observed lines of sight.
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h Subject headings: ISM: clouds – dust, extinction – Galaxy : halo – dark matter
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1Lawrence Livermore National Laboratory, 7000 East Ave,Livermore, CA 94550
2Dept. of Astrophysical Sciences, Princeton University,Princeton, NJ08544
3Depto. de Astronomia, P.Universidad Catolica, Casilla 104, Santiago 22, Chile
1
1. Introduction Lin 1990). Any population of gas clouds must be
much cooler than this to have escaped detection
It has been proposed that a large fraction
in previous surveys (Lawrence 2001). The pres-
of the baryonic dark matter in the halo of our
ence of a small amount of metals can assist the
Galaxy could be in the form of cold, dense gas
cooling of gas clouds (Gerhard & Silk 1996). It
clouds (de Paolis et al. 1995, Gerhard & Silk
has been suggested that, even if the clouds were
1996). Such clouds would be extremely difficult
dust-free, they could be stabilized against gravi-
to detect directly with traditional means due to
tational collapse by cosmic ray heating (Sciama
their dark nature. However, the extreme scatter-
2000). However, if the SCUBA sources are due
ing events observed by Fiedler (1987) have been
to clouds they must contain some dust to ex-
given as evidence for AU-sized, planetary-mass
hibit continuous emission in the sub-mm band
gas clouds (Henriksen& Widrow 1995, Walker &
(Lawrence 2001). The SCUBA results led to
Wardle 1998). Further evidence for the existence likely cloud masses of 10−4 −2×10−2M⊙ with
of such clouds comes from the detections of large
temperatures < 18K. Thevirial radiusof a cloud
populations of faint sub-mm sources detected by −4
with T = 18K and M= 10 M⊙ is 0.39AU, and
SCUBA (Submillimetre Common User Bolomet- −2
for a cloud with T = 10K and M = 10 M⊙
ric Array) (Lawrence 2001). Yet more evidence
the virial radius is 70AU. These radii set likely-
for sucha populationcomes fromrecent EGRET
limitsonthesizesofagascloudpopulation. Fur-
(Energetic Gamma Ray Explorer Telescope) re-
ther limits on clouds sizes and masses come from
sults which show the presence of a background
constraints on gaseous lensing events. Raficov
γ-ray emission from the Galactic halo. Kalberla,
and Draine (2001) note that no gaseous lensing
Schekinov and Dettmar (1999) have suggested
events have been observed toward the LMC by
that these results can be explained as due to the
the MACHO project, while many events are ex-
interaction ofhighenergycosmicrays withdense
pectedforasignificantpopulationofcompactgas
H2 clumps with masses ∼ 10−3M⊙ and radii clouds. Massive compact objects such as clouds,
∼ 6AU. Thesedetections andprior observational
stars, or other objects will lense stars as they
and dynamical arguments have lead to further
pass through our line-of-sight of the stars. Since
suggestions abouthow a halo dark cloud popula-
lensing is not observed any clouds present must
tion could be discovered (Kerins, Binney & Silk
exceed the projected Einstein radius. The anal-
2002,hereafterKBS;KamayaandSilk2002). Al-
ysis of Raficov and Draine (2001) suggests that
though most models place the cloud population
cloud musthave radiifrom 2to 300AU, for cloud
within the halo, Pfenniger and Combes (1994) masses between M = 10−4 and 2×10−2M⊙ for
suggested that such clouds are a natural part of
temperatures of 10 to 100K. Another constraint
the cold ISM and would exist concomitant with
on the dark clouds comes from the EGRET re-
the thin HI disk.
sults of Kalberla et al. (1999). They find that
For dark clouds to have survived until the the γ-ray results are consistent with H2 clumps
present day, they must have a mass which is sus- with masses 0.3−3×10−3M⊙ and sizes from 3
tainable over a Hubble time. Within the Galaxy to 10AU.
−6
the lower mass limit is 10 M⊙ because smaller
One consequence of the existence of a popu-
masses will evaporate due to cosmic ray heat-
lation of small dark clouds is the transient ob-
ing (Wardle & Walker 1999). It is also expected
scuration of background stars (Gerhard & Silk
that these objects will contain some metals since
1996). Such events are expected to be very rare
ithasbeensuggestedthatcloudswithprimordial
with much less than 1% of stars in any given di-
composition can not cool below 100K (Murray &
rection being obscured at any time. However,
2
even a very low rate of obscuration events is de- dard Kron-Cousins system V and R using the
tectable with the data from microlensing experi- photometric calibrations are given in Alcock et
ments, since millions of stars have been observed al. (1999). The dataset provides a consistent set
for many years (Alcock et al. 2000; Udalski et of photometry for stars spanning the duration of
al. 2000; Derue et al. 2001; Bond et al. 2002). the experiment.
Models for the obscuration event timescale dis- The observations toward the LMC and the
tribution of cloud occultation events have been SMC were taken all year round, while the Galac-
presented by KBS. They consider two hypothet- tic bulge was observed between March and Oc-
ical cloud populations, one in which the clouds tober. The median seeing of the data set is
occupy the disk and another where they reside roughly2′′ andmeasurementsreachstarswithV-
in the Halo. band magnitudes between 21 and 22. The pho-
Inthispaperwepresenttheresultsofananal- tometric sampling frequency varies greatly be-
ysis of the MACHO light curve dataset to de- tween the individual fields observed toward the
tect light curves consistent with extinction due Galactic bulge and the LMC. The least sampled
to passing dark clouds. We will search for events fields have only ∼ 50 observations while those
toward stars in the disk (Galactic bulge) and the most sampled have ∼ 2000 observations. For
Halo (LMC and SMC). To quantify our results most fields, observations are quite evenly spaced
we determineour detection efficiency for the var- over the experiments duration (apart from the
ious possible dark cloud parameters in the KBS observing gaps toward bulge fields). However,
models. a few fields in the LMC and the Galactic bulge
have variations in observation frequency because
2. Observations of changes in the observing strategy. Also, a
small number of the bulge fields were only ob-
The MACHO project repeatedly imaged ∼ 67
served in the last few years of the project.
million stars in a total of 182 observation fields
To select candidate obscuration events from
toward the Galactic bulge, the LMC and SMC,
the MACHO database we performed a number
to detect the phenomenon of microlensing (Al-
of cuts to remove data which was noisy or had a
cock et al. 1997). The data was taken in ∼
low signal-to-noise ratio. We selected stars with
90,000 individual observations, each covering a
totalareaof43′×43′ onthesky. Whenfieldover- magnitudes between 13 < V < 21 toward the
Galactic bulge and LMC and 14 < V < 22 for
lap is considered, the 182 fields observed cover
the SMC. For each of the stars in this range we
approximately 80 square degrees. These images
determined the median magnitude, M10, and the
were taken between 1992 and 2000 on the Mount
standard deviation, σ10, based on the first 10%
Stromlo and Siding Springs Observatories’ 1.3M
of the data points. However, if there were less
Great Melbourne Telescope with the 8 × 20482
than500observationsinalightcurveweusedthe
pixel dual-colour wide-field Macho camera. Ob-
first50 data points. We rejected any light curves
servations toward the Galactic bulge have expo-
where σ10 was larger than 0.7 magnitudes in ei-
sure times of 150 seconds while toward the LMC
ther passband. Altogether these cuts removed
andSMC they have 300 and600 seconds, respec-
∼ 40% of the stars observed. The parameters of
tively. The photometry was carried out using a
the analyzed dataset are given in Table 1.
fixed position PSF photometry package deriva-
tive of the DoPhot package (Schecter, Mateo &
Saha 1993) called SoDOPHOT (Bennett 1993).
The images were taken with non-standard B
M
and R bandsand can beconverted to the stan-
M
3
3. Searching for Obscuration Events
In this analysis we aimed to detect stellar oc-
cultations due to opaque dust clouds and obscu-
rations due to dark clouds with a small dust-to-
gas ratio. We also tried to detect gas cloud tran-
sitswithoutrestrictingthecloudshapestopurely
spherical morphology or isotropic dust distribu-
tion. Therefore,tofindevents duetothepassage
of dark clouds in front of stars, we were as lib-
eralaspossibleinourselection ofthelightcurves
which might exhibit extinction effects.
Firstly, we selected light curves that exhibited
a significant drop in flux that lasted > 10 days.
This selection was required to remove eclipsing
binaries and data that was affected by periods of
bad observing conditions. Secondly, we required
that the photometry points duringthe candidate
Fig. 1.— The initial obscuration event can-
obscuration event were > 0.2 magnitudes below
didates selected from all Galactic bulge light
themedianmagnitudeandhad> 4σsignificance.
curves. Stars toward the bulge fields are rep-
Theuncertainty,σ,wasbasedonthedistribution
resented by small dots while candidates are rep-
ofthephotometryvaluesratherthantheindivid-
resented by larger ringed-dots. The dashed-line
ual photometric uncertainties. As the detection
shows the selection criteria used to remove vari-
ofcandidateobscurationeventsissensitivetothe
ables from our lists.
sampling rate of a target field, we also required
atleast 10 points below themedianinany candi-
date event. To reduce the number of long period have large variability amplitudes, timescales ∼>
80 days, and red colours. However, we intended
variables detected, we only accepted light curves
to examine the light curves before applying any
with < 50% of the points below M10, (the 10%
colour selection criteria which might bias our re-
median value). However, we did not require that
sults. As none of the light curves in the AGB re-
the flux in a candidate’s light curve returned to
gion of the CMD appeared consistent with dark
the median value. In this way, we hoped to re-
cloud transit events, we chose to apply empir-
tain some of the sensitivity to dark cloud extinc-
ical colour selections to the candidates toward
tion events with timescales longer than the Ma-
cho projects baseline (∼ 8 yrs). each target direction. In Figures 1 and 2 we
present CMDs of the Galactic bulge, LMC and
ApplyingthesecriteriatotheMACHOproject
SMCstars. TheCMDsarecomposedofa∼ 1000
photometry data, 5284 (∼ 0.016%) light curves
stars from each of the 182 fields observed. In
passed our initial selection toward the Galactic
each figure we have over-plotted the M10 mag-
bulge,6427(∼ 0.050%) towardtheLMCand678
nitudes of the light curves passing our primary
(∼ 0.027%) toward the SMC. From examination
selection as obscuration events. We have also
ofthecandidate’slightcurvesandtheirpositions
plotted the colour cuts we applied to remove the
in CMDs, it was clear that most of the objects
AGB variables (to the right of the dashed-line)
passing these selections were long period vari-
whichpassedourinitialselection criteria. Ascan
ables. This was to be expected since these stars
be clearly seen, this colour selection removes al-
4
factthatthephotometry ofclumpstars ispoorer
at the distances of Magellanic cloud stars.
A large number of the candidates in the Mag-
ellanic cloud fields were found to be due to the
well known population of bright, blue, Be vari-
able stars known as bumpers(Keller et al. 2002).
These stars occupy a restricted region of the
CMDandcanshow longdipssimilar tothoseex-
Fig. 2.— LMC and SMC dark cloud obscura- pected for a cloud transit. However, many also
tion event candidates. Left panel: the median exhibit outbursts similar to dwarf novae. Such
magnitudesforcandidatelight curves toward the flaresarenoteasily explainableinacloud transit
LMC. Right panel: same as the left, but for can- model. We removed an additional 89, 280, and
didates toward theSMC.Thesmalldots arenor- 55 (Galactic bulge, LMC, SMC) exhibit either
mal stars within the Magellanic cloud fields and obvious flares or multiple dipsbelow thebaseline
largerringed-dotsarethecandidates. Thecandi- magnitude. Although it is possible that a star
dates to the right of the dashed-line are deemed could be eclipsed by more than one cloud within
to be due to normal stellar variability. a period of a few years, this seems extremely un-
likely given the the small number of candidates
relative to the total number of stars analyzed.
most all the initial candidates. However, these
Of the candidate cloud transit events 45, 18
colour cuts only remove ∼1% of all stars toward
and 1 (Galactic bulge, LMC, SMC) were discov-
any of the target fields, so they do not signifi-
eredtobeduetohighpropermotionstars. These
cantly change our total exposure. After applying
objectshaveverycharacteristiclightcurvesshapes.
the red variable star cuts there were 372, 441
In such curves the dip in magnitude is actually
and 98 remaining candidates toward the Galac-
due to the movement of the star away from the
tic bulge, LMC and SMC, respectively. Many of
fixed position where photometry is performed
these objects were also clearly variable stars.
(Alcock et al. 2001). These light curves show
Toward the Galactic bulge many of the candi-
increased scatter with time and never return to
date events had clump star sources. Almost all
the baseline flux level. In our selection process
of these light curves exhibit sinusoidal modula-
we only removed the light curves which exhib-
tions superimposed on a varying baseline mag-
ited increasing scatter with time to a degree sig-
nitude. The oscillation periods were found to
nificantly larger than expected for stars of their
be between 11 and 90 days with amplitudes be-
measured magnitudes. After removing the vari-
tween 0.02 and 0.2 magnitudes. These stars ex-
able stars, etc, 83 Galactic bulge, 133 LMC, and
hibitedbaselinemagnitudechangesofupto∼0.5
36 SMC candidates remained.
magnitudes. All these features are typical of
Ifthedipsobservedincandidate’s light curves
chromospherically-active stars (Fekel, Henry, &
are dueto extinction caused by dusty clouds, the
Eaton 2002) and can not be explained simply by
obscuredstarsshouldbecomeredderastheyfade
a transiting dark cloud. Of the candidate events
along the extinction vector. The exact amount
155, 10, and2lightcurves(Galactic bulge,LMC,
of reddening should depend on the quantity and
SMC) were clearly due to chromospherically-
nature of the dust present. To test this scenario,
active stars and were removed. The variation in
we assumed that the detected drop in flux was
the number of objects toward the target fields is
purely due to dust extinction. In this case the
due to stellar populations differences and to the
magnitude during an obscuration event should
5
be well represented by,
V = C +R ∆(V −R), (1)
VR
where C is the baseline flux, ∆(V − R) is the
changeinthestar’scolourandR = A /E(V−
VR V
R) is the ratio of total to selective extinction
for the bands we observed. The V-band light
curve of each candidate was fitted to determine
the value of R .
VR
We expect that, if the drop in flux was only
due to varying amounts of dust (producing vary-
2
ing degrees of extinction), the reduced χ of
this fit should be close to 1. However, if the
drop in flux is caused by variability which is
not consistent in the two passbands the fit will
be poor. Furthermore, if the dust composition
within a cloud follows standard dust proper- Fig. 3.— Reddening fit values for candidate
ties, the value of the extinction should be sim- cloud obscuration events. The dotted line show
ilar to that expected for standard reddening law the expected limits if the dips on the light curves
RV = AV/E(B−V) = 3.1 (Cardelli, Clayton, & areduetodustreddening. Thedashedlineshows
Mathis 1989). However, there is some evidence maximum χ2 expected for the fit in the presence
r
for variations from the standard extinction law of underestimated errors and varying dust com-
toward the Galactic bulge. For example, Udalski position along the line-of-sight through a cloud.
(2002) found RV values between 1.8 and 3.3 in The filled squares show Galactic bulge candidate
theextinctionratioforGalacticbulgefields. Low fits, while the circles and crosses present results
RV valueshavealsobeenobservedbySzomoru& for LMC and SMC candidates, respectively.
Guhathakurta (1999), whom found RV ∼< 2 for a
sample of Galactic cirrus clouds. However, Clay-
well the magnitude uncertainties are determined
ton & Cardelli (1988) reported that extinction
and whether the dust composition varies within
values aretypically between 2.6 and5.5. Theob-
a cloud. The flux measurement uncertainties are
served differences in R from the standard value
V
highly unlikely to be incorrect by more than a
have been attributed to variations in silicate and
factor of 3. The degree of variation in the dust
graphite grain size distributions (Kim, Martin,
composition within a cloud is completely un-
& Hendry 1994, Larson et al. 2000). To be com-
known, butitseems unlikely tobelarge. Most of
prehensive in our candidate event selection, we
the light curves are well sampled with a few hun-
selected light curves having fit coefficients cor-
dred data points. Therefore, it seems unlikely
responding to RV between 1.8 and 5.5. Using 2
that a χ value greater than 12 could occur even
the relative extinction for our passbandsfrom by r
with poorly estimated photometric uncertainties
Schlegel, Finkbeiner, & Davis (1998) we trans-
and varying dust composition within a cloud. In
form our results from R to R We adopted
VR V
Figure 3 we plot the values of R for the MA-
VR
thesameRV limits forthecandidate light curves 2
CHO V-band light curves against the reduced χ
toward all targets.
values of the fit.
2
The reduced χ fit value is sensitive to how
Oftheremainingcandidates,10bulge,2LMC
6
and0SMClightcurvespassedourextinctioncri- good, the photometry of the faint data points
teria. InTable2wepresentthenumberof candi- is very uncertain. Almost all of the other can-
date obscuration events remaining after each se- didate’s light curves exhibit drops < 1 magni-
lection criterion was applied. From examination tude. However, the Galactic bulge light curve
of their light curves it seems likely that most, if with MACHO ID number 120.21786.958 has a
notall, oftheselight curvesareduetovariability drop > 3.5 magnitudes and is also a good candi-
ratherthanextinctioneffects. Furthermore,they date obscuration event. If any of the the other
do not appear to be near the location represen- candidates were due to dark cloud events they
tative of the most common stars. This suggests wouldhave tohave avery smalldust-to-gas ratio
that they are simply outliers among the thou- compared to molecular clouds. The lack of a sig-
sands of variable stars present in the fields. nificant number of obscuration event detections
is significant, but must be quantified to provide
a useful limit on cloud models.
4. Detection Efficiencies
To determine the significance of our result
it is necessary to know how the selections we
have made will affect our efficiency of detec-
tion. Any obscuration event will have a start
time, a timescale, a maximum extinction, and
an impact parameter. The expected occultation
timescale distribution for viralized dark clouds
with T= 10K and R = 7AU in fields toward
the Galactic bulge, LMC, and SMC, is given
by KBS. The KBS models consider two possi-
ble dark cloud populations, a halo one and a
disk one. The halo model consists of clouds
in an isothermal halo with a core radius of 5
−3
Fig. 4.— The light curve for the best dark kpc, a local density of 0.01M⊙pc and a Gaus-
−1
cloud transit candidate (MACHO object ID sian velocity dispersion of 156km s . The disk
119.20740.1031). In the upper panel we present model consists of a sech-squared disk with scale-
theV-bandlightcurveandinthelower panelthe length 2.5 kpc, scale height 190pc and density
−3
colour curve. Over-plotted on the lower panel is 0.03M⊙pc . HeretheGalacticrotationalveloc-
the fitted colour coefficient for this light curve. ity of the clouds and stars is taken to be 220km
−1 −1
s with 25km s dispersion. Although our
In Figure 4 we present the light and colour analysis should be sensitive to a broader range
curves for the Galactic bulge candidate which of possible cloud parameters than those of KBS,
appears the most like that expected for a cloud their models are well constrained. Therefore, we
transit event. In this case, the object gets red- will determine how efficiently dark clouds follow-
der when it fades as expected for a cloud tran- ing the KBS models would have been detected
sit. For the standard reddening law (R = 3.1), in our analysis. For simplicity, we assumed that
V
we expect to measure R = 5.2 in our filters. thedustwasisotropicallydistributedwithineach
VR
The fit of the light curve of this candidate gives cloud and that the obscuring clouds should not
R = 5.1±0.1. Althoughtheagreement is very exhibit any preference in their alignment with
VR
7
background stars. We have, therefore, selected found toward each target in our survey. We have
cloud-star obscuration impactparameters froma not attempted to parameterize and implement
uniformdistributionbetween0and1cloudradii. the additional selections here since this would be
To determine our sensitivity to varying amounts a very complex and somewhat contrived process.
of dust we assumed a uniform distribution of the However, we believe the selections we made to
dust-to-gas fraction relative to Galactic molec- remove the variable stars, etc, were fairly robust
ular clouds, f, to be between 0 and 0.1. This and would have little effect on our calculated de-
ratio correspondsto a visual extinctions between tection efficiency.
0and12magnitudes(Binney&Merrifield1998).
For our analysis, an extinction of 12 magnitudes
corresponds to the opaque cloud limit since even
the brightest stars in our fields would become
undetectable.
For ustohavedetected anyoccultation events
within our analysis it would have to either start
or finish within the observing period of the MA-
CHO project. Therefore, we produced a ran-
domlydistributedsetofartificialextinctionevents
lying within the observational time frame. For
eachoftheGalacticbulge,LMCandSMCdatasets
we produced∼ 10 million artificial events. Many
events were added to the same light curves in
one dataset (corresponding to a 2′ × 2′ region)
for each of the 182 fields we analyzed. Each of
these datasets typically contain the photometry
for a few thousand stars. Although this is only
Fig. 5.— Number of recovered events R as
a small fraction of the stars within a field, we
a function of their input obscuration event
believe this number was sufficient to represent
timescales. Solid-lines show obscuration events
the overall properties of a field since the obser-
detection efficiencies toward Galactic bulge
vational properties will be the same throughout
fields, dotted-line, toward LMC fields, dashed-
a field. As there were less than 10 million stars
line, toward SMC fields.
chosentowardeach target, weaddedanumberof
artificial obscuration events to each light curve.
In Figure 5 we show the distribution of artifi-
These extinction events were added to both red
cial obscuration events recovered for the Galac-
and blue Macho light curves. The observed drop
tic bulge, LMC and SMC. For all targets the
in flux for each light curve was calculated from
peak detection efficiency is around 350 days.
theoptical depththroughthecloud at thecloud-
In general, as the timescale of the obscuration
starimpactparameter. Theextinctionwastaken
events increases, the signal-to noise ratio of even
tofollow thestandardreddeninglaw (R = 3.1).
V
asmalldropinfluxincreases. However, atlonger
Light curves with the artificial cloud obscuration
timescales theevents aremore likely to beoccur-
events were processed through the same selec-
ringatthebeginningof thelight curvewherethe
tionsastherealdataupuntilthethepointwhere
baseline is determined. Therefore, no dipis mea-
we removed the chromospherically active stars.
sured relative to the median magnitude. At very
At this point there were a few hundred objects
long timescales such clouds are more likely to be
8
transiting throughout the observation time. Al- have gone undetected in the data. For clouds in
most all obscuration events lasting less than ten the KBS isothermal halo model, the maximum
days are not detected because of the minimum number of events would have been observed to-
timescale cut we imposed. wardthetheGalacticbulgeratherthantheLMC
or SMC.Thisis somewhat surprising,butis sim-
ply dueto the fact that twice as many stars were
observed toward the Galactic bulge as the LMC.
Forthismodelweshouldhavedetected∼ 50,000
events due to cloud extinctions.
Fig. 6.— Theexpected cumulative event rate for
theKBSmodelofdarkcloudoccultationstoward
the Galactic bulge, LMC, and SMC when detec-
tion efficiencies are taken into account. Solid-
lines represent halo clouds and the dashed-lines
are for the disk cloud model. Fig. 7.— Cumulative number of cloud obscu-
ration events expected with our analysis for the
In Figure 6 we plot the cumulative number of KBS models. The solid-lines present the halo
events expected for the KBS models. For disk cloud numbersandthedashed-lines the thosefor
clouds, the largest number of events per star is disk cloud models.
expected toward the Galactic bulge, while for
a halo cloud population, the largest number of
4.1. Efficiencies at Low Extinction
events per star is expected toward the SMC. In
Figure 7, we plot the number of event detections Thenumberofeventsthatweexpecttodetect
expected when the stellar exposure time is con- is strongly dependent on the amount of extinc-
sidered. Thetotal exposurefor each target is the tion they cause. For extinctions greater than ∼1
sum of the number of stars monitored in a field magnitude (f ∼ 0.08) the obscuration event de-
multiplied by the number of years it was mon- tection efficiency is approximately constant for
itored. If dark clouds following the KBS disk all targets. To better quantify the number of
model contribute a third of disk mass density obscuration events expected if the dark clouds
(0.03M⊙pc−3),then∼ 100,000extinctionevents have very small dust concentrations (< 1% that
should have been discovered toward the Galactic of molecular clouds), we performed a second set
bulge. Such a large number of events could not of detection efficiency simulations for extinctions
9
less than one magnitude.
Fig. 9.— Obscuration event detection efficiency
number for the KBS model when A < 1. The
V
Fig. 8.— Cumulative number of cloud obscura- solid-lines present the halo cloud numbers and
tion events expected for the KBS model when the dashed-lines those for disk cloud models.
A < 1. The solid-lines present the halo cloud
V
numbersandthedashed-linesthosefordiskcloud
ysis we have assumed the KBS model values
models. −3
(T= 10K, M = 10 M⊙, and R = 7AU). For
different dark cloud models the extinction events
In Figure 8 we present the number of low ex-
mayappearasmanyshorteventsorasmallnum-
tinction clouds weexpect to have detected in our
ber of longer timescale events. For the adopted
analysis for the KBS models. In this case we still
model, halo events peak in number at around
expecttohave detected 20,000 events toward the
60 days, while for disk clouds the peak is near
bulge for disk clouds, or 9,000, if the clouds ex-
100 days. From our efficiencies we should still
ist in an isothermal halo population. In Figure
have been able to detect obscuration events due
9 we present the obscuration event detection ef-
tosmallclouds(withmaximum∼10days)ordue
ficiency as a function of the extinction caused
to large clouds (with maximum number ∼1000
by the cloud. The differences between the plot-
days), because the cloud transit timescale distri-
ted detection efficiencies are mainly due to the
butions are broad. However, de Paolis (private
different timescale distributions. The expected
communication) suggests that there are models
number of detections only falls to zero near the
0.2 magnitudes (f ∼ 0.2%) because of thecutwe in which large halo clouds would take 10 to 100
years to transit a background star. In such cases
imposedinourselection. Anon-standardextinc-
we still expect to have discovered a few clouds
tion law would allow a larger amount of dust to
as they began to obscure stars (provided they
go unnoticed. However, this would only change
the result by a factor of ∼ 2. producedmore than 0.2 magnitudes of visual ex-
tinction). Our results do not show any trace of a
The dark cloud occultation event timescale is
low-mass dark cloud population.
proportional to the cloud size R and the event
−1 −1
rate is proportional to T R . In this anal-
10
