Frequency Limits on Naked-Eye Optical Transients Lasting from Minutes to Years
aa r X i v : . [ a s t r o - ph . I M ] A ug Frequency Limits on Naked-Eye Optical Transients Lasting fromMinutes to Years
Lior Shamir
Image Informatics and Computational Biology Unit, Laboratory of Genetics, NIA, NIH, 333 Cassell Dr.,Suite 3000, Baltimore, MD 21224 [email protected] and
Robert J. Nemiroff
Department of Physics, Michigan Technological University, Houghton, MI 49931 [email protected]
ABSTRACT
How often do bright optical transients occur on the sky but go unreported? To constrain thebright end of the astronomical transient function, a systematic search for transients that becomebright enough to be noticed by the unaided eye was conducted using the all-sky monitors ofthe Night Sky Live network. Two fisheye continuous cameras (CONCAMs) operating over threeyears created a data base that was searched for transients that appeared in time-contiguousCCD frames. Although a single candidate transient was found (Nemiroff and Shamir 2006), thelack of more transients is used here to deduce upper limits to the general frequency of brighttransients. To be detected, a transient must have increased by over three visual magnitudes tobecome brighter than visual magnitude 5.5 on the time scale of minutes to years. It is concludedthat, on the average, fewer than 0.0040 ( t dur /
60 seconds) transients with duration t dur betweenminutes and hours, occur anywhere on the sky at any one time. For transients on the order ofmonths to years, fewer than 160 ( t dur / t dur / occur. Subject headings: methods: data analysis — methods: statistical
1. Introduction
Transients that become bright enough to benoticed with the unaided eye have been recordedon the night sky far back into human his-tory. Ancient records include, for example,bright supernovae such as the SN 1054 whichreached an estimated visual magnitude of − − − Night SkyLive network of all-sky cameras (Nemiroff & Rafert1999) is used to derive limits on the frequency ofnaked-eye transients. Section 2 reviews how theresults of transient searches can be converted tooccurrence limits. Section 3 describes the obser-vations, hardware, and software used to search fornaked-eye transients, and present the results ofthe search. Section 4 converts the search resultsto fundamental limits on the frequency of brightastronomical transients. Section 5 summarizes,gives discussion, and draws conclusions.
2. Theory: Connecting Transient Searchesto Transient Limits
To connect results of a transient search to ac-tual limits on the event rates of transients isstraightforward but sufficiently nuanced that abrief analysis is presented here. In sum, a hypoth-esis involving the abundance of transients is madeand statistically compared with the observationalresult. In this simple canonical model, a transientinstantly brightens by more than a given magni-tude amount from the beginning of an observingcampaign. The transient then does not dip be-low this peak brightness for its duration t dur . Asimple canonical observing campaign of duration t c is also assumed where consecutive exposures allhave exposure duration t e . For a discussion ondetecting transients that includes down time, op-timal frame rates and statistical independence, seeNemiroff (2003).The standard hypothesis that will be tested isthat N i instantaneously detectable transients ofduration t dur occur randomly on the sky at anyone time. Therefore, most simply, a hypotheticaldevice that images the entire sky would enable thedetection, on the average, of N i transients on ev-2ry all-sky image. A more realistic device wouldhave an angular efficiency factor of f a and a tem-poral efficiency factor of f t . Here f a is the fractionof sky that is being monitored, while f t is the frac-tion of time during the campaign that a transientcould actually be detected. Variable names andnomenclature will follow Nemiroff (2003).As discussed in some detail below, for givensearch parameters and transient durations t dur ,the statistically independent number of trials N trial might differ from number of exposures takenduring the observing campaign N c . The relation-ship between N trial and N i may involve f t , t dur , t e , or even t c . Once N trial is determined, however,then the grand number of transients N g detectedduring the observing campaign would be N g = f a N trial N i . (1)Note that it is not only the detection of lightfrom transients themselves that is important here.Rather, what is searched for is the change in thebrightness of a source. Otherwise, all detectedstars would be classified as transients. When each exposure duration t e in the tran-sient search observing campaign is significantlygreater than a given canonical transient duration t dur , only “single frame transients” of that dura-tion are usually expected. Single frame transientsshould generally be considered to be unreliable in-dicators of extra-terrestrial astronomical phenom-ena, as any number of local effects could mimicthem, including cosmic-ray hits, satellite glints,and meteors. Cosmic ray hits could be ruled out,however, based on image shape (Shamir 2005b)or were several cameras to record a transient in-dependently. Satellite glints (Nemiroff & Bonnell2005) and meteors could be ruled out with si-multaneous detections of sufficient parallax so asto create a minimum limiting distance of extra-terrestrial origin. Alternatively, a group of singleframe transients might be believable as a statisti-cal ensemble.Mathematically, for transients with t e >> t dur ,transients visible on one frame would not be ex-pected to be visible on any other frame. Therefore,for the purposes of statistics, a search for tran-sients on one frame should be considered statisti-cally independent of a search on any other frame. Each frame could be considered an independentstatistical “trial” in a search for transients. There-fore, for single frame transients, effectively f t = 1and N trial = N c . Therefore, Eq. (1) for the grandtotal number of transients becomes N g = f a N c N i . (2)Note that when t e >> t dur , a transient is not“on” during the entire frame or frames when it isdetected. Therefore, these fast transients wouldhave to be brighter during their short reign toappear as bright as a seemingly similar quies-cent source in the same frame Nemiroff (1998b).Given a limiting detectable brightness of a quies-cent source of l dim per frame, and assuming thetransient occurs during a single frame, the limit-ing brightness of a transient source would need tobe l transient > l dim ( t e /t dur ) to be detected abovethe quiescent limit. When a single transient is detectable on sev-eral consecutive frames, each frame should not becounted as a statistically independent trial. Thisis because a single long duration transient is muchmore likely to occur on successive frames thantwo independent transients. For time consecutiveframes, the effective number of statistically inde-pendent trials is N trial ∼ N c ( t e /t dur ). More gen-erally, given the hypothesis that on average N i transients exist instantaneously somewhere on thesky at any one time, the grand total of detectedtransients expected during an observational cam-paign is expected to be, given perfect time cover-age, N g = f a N trial N i ∼ N c f a N i t e /t dur .In many practical searches, however, there aretime lapses in time coverage due to clouds, day-light, or exposures missing for other reasons. Inthese cases the effective number of statistical trialsis reduced by a “temporal efficiency” factor quan-tized as f t , the fraction of time during a campaignthat, were a transient to start, it would be detectedduring the campaign as a transient.It is important to note that different f t factorsmay operate for different transient durations t dur .Consider, for example, a one week observing cam-paign. Further consider that due to clouds, everyother night is completely missed. For transientswith t dur ∼ f t = 3 /
7. For transients du-rations on the time scale t dur ∼ f t fraction determines the effective num-ber of trials. This is because a one week transientthat occurred any time during the week long ob-serving campaign would have been detected withnear unit efficiency. Therefore, for week long tran-sients in this example, f t ∼
1. More generally, N trial ∼ f t N c t e /t dur .For believability, an observer might demandthat a “verified” transient occur on (at least) N ver frames, quite possibly time-consecutive frames.This would primarily affect the verified detectionof transients near the exposure time of individualframes. As in the above case, this would reducethe effective number of statistically independenttrials by a factor of N ver . Therefore, the effectivenumber of trials would be N trial = f t t e N c N ver t dur . (3)Also, the grand total number of verified transientsof duration t dur expected during the observingcampaign would then be derived from Eq. (1) tobe N g = (cid:18) f a f t t e N c N ver t dur (cid:19) N i . (4)The situation is slightly more complicated wereframes co-added. Assume that N add frames areco-added so that a transient is only visible on theco-added frames – it is too dim to be significantlydetected otherwise. In this case, the effective num-ber of independent trials would again be reduced,and the resulting expressions can be found by sub-stituting N ver with N ver N add in the above expres-sions. Limits on N i can even be determined for tran-sient durations t dur greater than the entire dura-tion of the observing campaign t c . The importantfeature for detection here is that the transient’srise in brightness occurs during the observing cam-paign. It will be assumed here that a transientthat declines in brightness will not be found be-cause it will not be searched for.Consider as an example a one week observingcampaign’s effort to detect a transient with a one year duration, such that N i = 1, meaning thatsuch a transient is likely to occur somewhere onthe sky at any particular time. On average onemeasurable event will occur during that year –the rise of the transient. The chance that the riseoccurs during any one week during that year isabout 1 in 52, so that, effectively, for transients of t dur ∼ f t ∼ / N trial can be convolved with an f t that dips toless than one such that N trial = f t = t c /t dur . (5)Therefore Eq. (1) becomes N g = f t f a N i = (cid:18) f a t c t dur (cid:19) N i . (6) What is the greatest number of instantaneoustransients N i that is consistent with no transientsbeing found ( N act = 0) during the observationalcampaign? To find N i , one might start with theintermediate question: How different is this N g from zero? Now the number of σ that N g differsfrom zero is σ = p N g . Therefore, the differencebetween N g and zero in terms of σ is s = ( N g − p N g = p N g . (7)Choosing s as quantifying the upper limit on howhigh N g can become gives N g < s . (8)Given now the relation Eq. (1) this becomes N i < s f a N trial . (9)Now N trial can be expanded for each of thethree cases discussed above. For the single frametransient, N trial = N c so that N i < s f a N c . (10)For the multiple frame transient, one substitutesEq. (3) into Eq. (9) to get N i < N ver t dur s N c f a f t t e . (11)4or transients longer than entire observing cam-paign, one substitutes Eq. (5) into Eq. (9) to get N i < t c s f a t dur . (12) What is the greatest number of instantaneoustransients N i that is consistent with the results ofa campaign that observed N act actual transients?To find out, the logic of the above subsection isfollowed focusing on the question: How differentis this N g from N act ? As above, the standard devi-ation of the predicted N g is σ = p N g . Therefore,the difference between N g and zero in terms of σ is s = ( N g − N act ) p N g . (13)Choosing s as quantifying the upper limit on howhigh N g can become gives s > ( N g − N act ) N g . (14)This equation is quadratic in N g and has a physi-cal solution for N act > N g < ( N act + s /
2) + p N act s + s / . (15)Substituting in Eq. (1) into the above equationyields N i < ( N act + s /
2) + p N act s + s / f a N trial . (16)Single frame transients are again first consid-ered. Plugging in N trial = N c for single frametransients into Eq. (16) yields N i < ( N act + s /
2) + p N act s + s / f a N c . (17)For multiple frame transients, using the N trial ofEq. (3) yields N i < (cid:18) N ver t dur f t t e N c (cid:19) [( N act + s / p N act s + s / . (18)For transients with durations greater than the ob-serving campaign, using the N trial of Eq. (5)yields N i < (cid:18) t dur t c (cid:19) [( N act + s /
2) + p N act s + s / . (19)
3. Observations: A Three Year Search forBright Astronomical Transients3.1. Hardware
Two CONtinuous CAMeras (CONCAMs) fromthe Night Sky Live network were used for thisproject. These CONCAMs were located in CerroPachon, Chile, and the Canary Islands, off thewest coast of northern Africa. Although otherCONCAMs were running, transient detection soft-ware was only applied to data taken by these twocameras. Reasons that other cameras were notused include bandwidth, hardware, and remotecomputing power limitations. Each CONCAM in-cludes a CCD camera, a fisheye lens and an indus-trial PC running Linux Red-Hat. The CCD cam-eras used were SBIG ST-1001E. The lenses usedwere the SIGMA F4-EX. However, clouds, occlu-sions, and reduced sensitivity very near the hori-zon limited the search to approximately π steradi-ans per clear frame.The CONCAM hardware would typically runcontinuously from nautical sunset to nauticalsunrise. The resulting images are 1024 × gray-scale levelsand recorded in FITS format. Each CONCAMrecorded a 180-second exposure every 236 seconds.The reason for the 180 exposure duration relatedto the time before stars began to trail significantlyon the image. The reason for the 236-second timebetween the beginnings of exposures is to allowfor data read-out and to allow each CONCAMto begin exposures separated in time by exactlyone sidereal day. The reason for separating expo-sures by exactly one sidereal day is to allow starsto return to known positions in the sky and onthe CCD, allowing fewer and more manageablesystematic effects.The CONCAM all-sky cameras were passiveand did not track the sky. The wide-angle lensesallow recording full 2 π steradians in one frame,and quiescent stars as dim as visual magnitude 6.8are visible near the image center (Shamir 2005a). Once taken, the images were transmittedto a central computer at Michigan Technolog-ical University, where they were made pub-licly available over a web server accessible at5ttp://nightskylive.net/ . Data for this projectwere then analyzed for new astronomical tran-sients.The detection of optical transients in all-sky im-ages requires several logical steps. Before even thefirst transient was sought, it was useful to build adatabase of canonical images that are known not to have a transient that can then be compared toimages that might contain a transient. For thisproject, this was done by co-adding several im-ages taken on a clear night at the same siderealtime. A detailed description of this mechanism isdescribed in (Shamir & Nemiroff 2005b).Each source that is detected above 40 σ on a pa-trol frame is compared to the same source positionon the comparison frame. A threshold of 40 σ wasfound to give a resultant rate of candidate single-frame transients that could be checked by humans.If that source is not detected on the comparisonframe, meaning specifically that no source above2 σ is detected there, then it has passed the firstcut and is a candidate transient.Note that the high 40 σ change insures a min-imum amount of variability in actually detectedtransients. Surely every source is variable at somelow level, but the transient sources searched forhere must be variable above some minimum levelto be detectable here. What is that level? Givena background level of 1000 counts, a typical level,40 σ over background corresponds to about 1200additional counts, or about 2200 raw counts. As-sume a quiescent source was as bright as 2 σ overbackground previously and had gone undetected.The source would then have undergone a changefrom 64 to 1200 counts. This corresponds to a fac-tor of about 18.75, or a variability of about threemagnitudes at minimum.After the comparison frame cut, any survivingcandidate transient is then searched for in an on-Color Visual MagnitudeA 5.1F 5.2G 5.3K 5.6M 5.8Table 1: CONCAM stellar visual magnitude of a40 σ PSF line catalog. The catalog used for comparison wasthe Hipparcos catalog (Perryman et al. 1997). Inthis way, several candidate transients were lateridentified as variable stars.Even after the catalog comparison cut, mostcandidate transients turned out to be single frameevents that were not astronomical in origin. Thereare many routes to creating single-frame “back-ground” transients that may initially appear to beastronomical in nature. Hot stuck pixels, cosmicrays, Moon-ghosts, satellite glints all provided abackground for single frame transients, while plan-ets provided a background for multiple frame tran-sients.One important step in rejecting backgroundsingle-frame events was the rejection of pix-els dominated by cosmic-ray generated counts(Shaw & Horn 1992; Fixsen et al. 2000), typicallymade use of the non-point source nature of cosmicray splashes (Shamir & Nemiroff 2005c). Brightplanets are also rejected using a star recognitionalgorithm designed to find astronomical objects inwide angle frames (Shamir & Nemiroff 2005a).Due to the relatively high density of artificialobjects in orbit around the earth, one can expectthat many single-frame candidate transients areactually sun glints from these artificial objects(Schaefer et al. 1987a; Varady & Hudec 1992). Infact, some flashes that were suspected to be trueastronomical transients (Halliday, Feldman & Blackwell1987) appeared later to be nothing but foregroundnear-earth flashes (Schaefer et al. 1987b). An-other source of background flashes is bright me-teors and fireballs (Shamir & Nemiroff 2005c).When the trajectory of a meteor is oriented to-ward the camera, the meteor might have a pointspread function (PSF) that appears similar to thatof a star (Brosch & Manulis 2002).Even given these rejections, the non-astronomicalbackground remained so high that little trust wasplaced on the hypothesis that any transient thatappeared on a single frame was astronomical inorigin. Therefore, subsequent cuts by the softwaredemanded that candidate transients be signifi-cantly brighter than frame background and werefound in more than one consecutive CONCAMframe. Frames taken at the same time from otherCONCAMs were compared as well, but this stepwas only used to confirm candidate transients.6lthough the CONCAM exposure duration waschosen to be just long enough so that most starsdon’t trail significantly, in fact most star centroidsdo trail by a few pixels each exposure. This seem-ingly disadvantage was used here to find transientsthat rotated with the sky. If the PSF of the flashseems to trail to the same direction of nearby stars,this is an indication that the transient had littleangular motion relative to these stars, and so thetrail might be caused by the rotation of the Earth.Flashes with non-trailing PSFs were interpretedas either very short flashes or flashes from tran-sients that rotated with the Earth, such as geosyn-chronous satellites (Shamir 2005b).Once a flash is recorded it is compared to pre-vious images to check if the flash is persistent androtates with the sky. If a flash appears to be ro-tating with the sky for at least two images, thesystem alerts on that flash as an optical transientcandidate (Shamir et al. 2006).
To estimate the angular fraction of the sky f a visible during each frame, it is noted that each CONCAM all-sky camera sees the entire sky overthe horizon, which amounts to 2 π steradian. How-ever, the area nearest the horizon has low visibil-ity, and the automated source search only oper-ated at 20 degrees over the horizon. This meansthat about 34 percent of the sky is ignored, yield-ing an effective search area, per CONCAM, wasabout 4.1 steradians. Together, the two CON-CAMs had a higher search area, but for sake ofconservative limits the total search area will beconsidered to be 4.1 steradians. Dividing by thetotal angular area of the sky, 4 π steradians, it isfound that the total fraction of sky monitored perexposure is about f a ∼ . / (4 π ) ∼ . The transient detection mechanism started op-erating in October 2003 in La Palma, Canary Is-lands, and another station started operating inCerro Pachon, Chile in September 2004.The present search was not uniformly sensitiveto transients of all durations. Here the sensitiv-ity of the search to transients of all durations t dur will be assessed. The search sensitivity to tran-sients of the shortest durations will be evaluated first: those lasting less than 12 minutes. Thesemight be seen on individual campaign frames butcould not exist on three consecutive and indepen-dent frames. Transients this short would thereforebe considered unverified and hence not reported asa discovery, so that f t ∼ f t is evaluated fora transient with t dur of 12 minutes. A 12 minutetransient would likely not be missed were it to oc-cur during a clear, moon-free time when a CON-CAM was operating. On the average, CONCAMsrun 8 hours during any 24 hour period, which is0 .
33 of a day. Also, on the average, CONCAMs areable to record transients only about one night infour, due to weather, bright moon time when thesoftware is not running, and equipment problems(Pereira et al. 2005). Therefore, were a 12 minutetransient to occur in the field of a CONAM duringthis three year campaign, the chance of it actuallybeing recorded is about f t ∼ . / ∼ . f t ∼ . / ∼ . .
33 of a day factor should be ex-cluded. The other efficiency factor, that CON-CAMs obtain useful data only one night in four,is still important, however. Therefore, for the oneday time scale, f t ∼ . f t ∼ f t = 1.Note, however, that a transient that started beforethe campaign started – or on the first day of thecampaign, might not have been recorded by thiscampaign because it would have been included inthe canonical frames against which transients arecompared and hence discovered.For transients of durations of t dur = 3 years,the logic is the same as for t dur = 1 year, so that f t ∼ t dur = 10 years. Transients of durations longerthan three years last longer than the entire ob-serving campaign. There is a chance the tran-sient remained constant within the quiescence cri-teria all during the observing campaign, as so wasidentified as a star and not a transient. For thisreason, as discussed in an above Section, f t willbe less than unity for transient durations greaterthan the duration of the observing campaign. Here f t = t c /t dur ∼ /
10 = 0 .
3. Similarly, for tran-sients of t dur = 100 and 1000 years, f t is equal to0.03 and 0.003 respectively. The relation between f t and t dur is shown in Table 1 and depicted graph-ically in Figure 1. To estimate the total number of exposurestaken during the campaign, N c , it is noted thateach CONCAM camera takes on average ∼ ∼
35 clear imagesper calendar day (Shamir & Nemiroff 2006b). Fora campaign time of three years, this yields approx-imately m ∼ Only a single multi-frame transient survivedboth software detection and vetting by the au-thors (Nemiroff & Shamir 2006a). This candidatetransient lasted about 12 minutes, was seen onthree time-consecutive CONCAM frames from theCerro Pachon CONCAM and the (only) two time- coincident frames from the Canary Island CON-CAM. The event was labeled OT060420 where“OT” stood for optical transient, and the num-bers corresponded to the date the candidate tran-sient occurred. The transient software describedabove alerted on OT060420 in near real time andthe possibility that the event was a real astro-nomical transient was considered high enough oninitial inspection to release the images and po-sition of the transient immediately to the GCNglobal network for follow-up observations. Soonthereafter a second report indicated that the tran-sient was not recorded by a somewhat-inferiorthird all-sky camera (Smette 2006) led to thehypothesis that the recorded source was not as-tronomical (Nemiroff & Shamir 2006b). The na-ture of the transient remains controversial, withsome astronomers interpreting the event as a newtype of astronomical transient (Paczynski 2006).A detailed analysis of this event is described in(Shamir & Nemiroff 2006b).
4. Fundamental Limits on Bright OpticalTransients
The below discussed results were obtained byincluding the above discussed search parametersand efficiencies into Eqs. (11, 12, 18, 19). Limitson the all sky prevalence of optical transients N i were placed demanding s = 2 σ upper limit.Table 2 summarizes the limiting maximumnumber of transients instantaneously visible onthe sky at any one time: N i , as a function oftransient duration t dur . The first column of Table2 shows the transient duration t dur to which thecurrent campaign was sensitive. The second col-umn of Table 2 shows the angular efficiency factor f a , which holds for all transients in the transientsearch campaign reported here. The third columnof Table 2 shows the temporal efficiency factor f t for a transient of duration t dur in the observingcampaign reported here.The fifth column of Table 2 shows N i , themaximum number of transients that can be ex-pected to be on the entire sky at any one timewith the duration listed in the first column, giventhat the single successful candidate reported inShamir & Nemiroff (2006b) is considered real. Asindicated above, this is a 2 σ upper limit. In otherwords, it is possible to have fewer transients on the8ky than this limit, but not more. The fourth col-umn in Table 2 similarly shows N i , but this timeassumes that the observing campaign found notransients, essentially assuming that the candidatetransient reported in Shamir & Nemiroff (2006b)was not astronomical in nature.The relations between t dur and N i are showngraphically in Figure 2. Generalizing the aboveresults, it is concluded that, on the average, lessthan 0.0040 ( t dur /
60 seconds) transients with du-ration t dur occur on the sky at any one time, when t dur is on the order of minutes to hours. For tran-sients on the order of months to years, fewer than160 ( t dur / t dur / exist.
5. Discussion and Conclusions
An automated digital search was conducted foroptical transients that would have been visible tothe unaided eye. The search lasted for three years,involved two CCD cameras, and thousands of fish-eye frames. Transients that brightened by morethan three magnitudes to become visual magni-tude 5.5 or brighter were detectable. Only a sin-gle candidate optical transient was found. It istherefore concluded that such transients on the or-der of minutes are rare, with N i < .
004 ( t dur / N i ∼ . f a ∼ .
33 and f t ∼ .
25 for a transient of one week duration, thegrand total number of transients expected in thiscampaign would be N g ∼ f a f t N i ∼ . χ Cygnus, and β Lyra were detectedby the automated software, but excluded by theauthors because their origin was known.9ransient Angular Temporal Maximum MaximumDuration Efficiency Efficiency Transients Transients(units) f a f t N i , N act = 0 N i ; N act = 112 minutes 0.33 0.0825 0.062 0.0461 hour 0.33 0.0825 0.345 0.2308 hours 0.33 0.0825 2.76 1.841 week 0.33 0.25 19.1 12.81 month 0.33 1.0 20.5 13.71 year 0.33 1.0 250 1663 years 0.33 1.0 749 49910 years 0.33 0.3 8,320 5,550100 years 0.33 0.03 8.32E5 5.55E51,000 years 0.33 0.003 8.32E7 5.55E7Table 2: A table of transient durations and their corresponding maximum number of transients possible onthe sky.In the future, it would be possible for CONCAM-like devices to search for objects fainter than“naked-eye”, but this campaign did not do so.Possibly the simplest methods would involvelonger exposures and co-adding exposures. Suchmethods would become significantly more difficultat the background brightness of an empty pixel(Nemiroff 2003), which corresponds to about vi-sual magnitude 8 for the CONCAMs used in thiscampaign. Other methods geared toward discover-ing fainter transients might increase the aperturesize of the system or decrease the pixel size andhence the background noise. REFERENCES
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