A Search for Stellar Obscuration Events due to Dark Clouds A. J. Drake1,2,3, K. H. Cook1 3 ABSTRACT 0 0 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 J 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 V 0 Galactic disk or halo. However, it is possible that such dark cloud populations could 1 0 exist if they are clustered in regions away from the observed lines of sight. 3 0 / h Subject headings: ISM: clouds – dust, extinction – Galaxy : halo – dark matter p - o r t s a : v i X r a 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