1. LSST, the Spatial Cross-Match Challenge
Maria Nieto-Santisteban
Alexander Szalay
Ani Thakar
The Johns Hopkins University
Jim Gray
Microsoft Research

2. What is Cross-Matching?
Identify point(s) in A with point(s) in B
Cones: Find points nearby one point
Distance from few arcseconds to few degrees
Neighborhood: points nearby points
Distance from few arcseconds to very few arcminutes
Decide whether those points share more than just their position
Points:
Search around single position versus All-to-All match with arbitrary distance.
Radius:
Cone searches may go from small to very big
All-to-All tend to be small. Otherwise we face combinatorial explosion.
It is not a matter of radius but density, number of objects
Whether is better to use cones or neighbors it may depend on the ratio between cardinalities and relative dispersion
Maria A. Nieto-Santisteban / ADASS 2006

3. Maria A. Nieto-Santisteban / ADASS 2006
Zones
Bin the data
ZoneID = floor ((dec ) /zoneHeight)
Place the data close on disk
Cluster Index on ZoneID, Ra
Trick required to handle the (360,0)
Efficient
Cones
Neighbors (especially)
Useful
Partition the data
Distribute workload
Maria A. Nieto-Santisteban / ADASS 2006

4. Maria A. Nieto-Santisteban / ADASS 2006
Zone Table
ObjID
ZoneID* RA
Dec CX CY CZ … 1
0.0
-90.0 2
20250
180.0 3
181.0 4
40500
360.0
+90.0
* Using a zone height of 8 arcsec in this example
Maria A. Nieto-Santisteban / ADASS 2006

5. Maria A. Nieto-Santisteban / ADASS 2006
Declination vs. Zone, RA
Order by Dec
This slide shows two ways of ordering (“clustering”) catalog data on disk: by DECLINATION or by (ZONE, RA)
(WHAT DO THE NUMBERS AND THEIR LOCATIONS MEAN?)
The numbers in the figures are indexes that indicate the order on the disk.
The positions of the indexes in the figure indicate the location of the object in a simulated LSST image of the Galactic center.
The LSST image extends 3 degrees to the right and up off the top of the screen.
(WHAT PROBLEM ARE WE TRYING TO SOLVE?)
Now imagine we want to find neighbors within 8 arcsec of the object in blue.
(WHAT IS THE WORST APPROACH?)
The worst approach would be to calculate the distance from the blue object to all 2.5 million sources in the image.
This would be very expensive because only 7 out of the 2.5 million distances would be within 8 arcsec
(WHAT ABOUT ORDERING BY DECLINATION? FEWER CALCULATIONS.)
We can do much better by using DECLINATION as a cluster index, as in the figure on the left.
The indexes increase from bottom to top in the figure.
There are big jumps between neighbors because stars off the right edge have intermediate declinations.
Using the declination index, we limit the search range to +/-8 arcsec, as shown by the horizontal red lines.
Then we only have to calculate distances for about 8000 sources, which is much better than 2.5 million.
(WHAT ABOUT ORDERING BY ZONE AND RA? THE FEWEST CALCULATIONS.)
We can do even better by using ZONE and RA as a cluster index , as in the figure on the right.
Zone index increases in coarse bins from the bottom of the figure to the top.
Within each zone, index increases monotonically from left to right.
See how the indexes go 1, 2, 3, 4, … in the bottom zone. Then 3925, 3926,… in the next zone. And so on.
Using the cluster index, we limit the search to a (different) narrow range in right ascension for each zone.
We only have to calculate distances for 8 objects, which is much better than 8000 and much, much better than 2.5 million
(DISK I/O AND SEEK TIME ARE ALSO BETTER WITH ZONES.)
The other key point is that with a zone index, data for the neighbors are concentrated in a few disk blocks.
With the DECLINATION index, data for the neighbors is spread over many disk blocks, with only one neighbor per disk block.
In other words, the ZONE approach requires less CPU, less physical I/O, and less seeking by the disk.
Order by RA within Zone
Maria A. Nieto-Santisteban / ADASS 2006

6. “Circular” Regions Near the Poles
d = cos1{sin(1) sin(2) + cos(1) cos(2) cos(1 1)}
Maria A. Nieto-Santisteban / ADASS 2006

7. Maria A. Nieto-Santisteban / ADASS 2006
SQL CrossNeighbors
SELECT *
FROM prObj1 z1
JOIN zoneZone ZZ
ON ZZ.zoneID1 = z1.zoneID
JOIN prObj2 z2
ON ZZ.ZoneID2 = z2.zoneID
WHERE
z2.ra BETWEEN z1.ra-ZZ.alpha AND z2.ra+ZZ.alpha
AND
z2.dec BETWEEN AND
(z1.cx*z2.cx+z1.cy*z2.cy+z1.cz*z2.cz) >
Maria A. Nieto-Santisteban / ADASS 2006

8. Number of Rows in LSST Catalogs
Single Exposure
Single Night
End of Survey
Objects
N/A
51010
Variable Objects
105
108
3108
Source Detections
3106
3109
81012
DIA Source Detections
( 105 )
( 108 )
31011
Data access will require good data organization
Data partitioned and placed according their position in the sky
Sources: Single Night = DR20 / 3000 because there are 300 night/year * 10 years = 3000 nights in the survey
Sources: Single Exposure = Single Night / 900 because there are 900 exposures/night.
There are 10 hours = seconds/night. Each exposure takes 40 seconds ( [+2]), so there are 36000/40=900 exposures/night
Maria A. Nieto-Santisteban / ADASS 2006

9. LSST Cross-Match’s challenges
Issue alerts within 60 seconds
Challenge: Heavily time constrained
Nightly archive
Challenge: Database consistency
Deep Processing
Challenge: Volume of data to process
Association complexity
User queries:
Challenge: Many users, many types of users, many types of queries, a lot of data to look through
Maria A. Nieto-Santisteban / ADASS 2006

10. Maria A. Nieto-Santisteban / ADASS 2006
Alert Processing
1. Start alert clock when 2nd exposure ends
3 second readout while slewing to next field
2. Calibrate images (dark subtract, flat field)
201 CCDs = 3.2 Gpixel
3. Difference image analysis
Identify and extract variable sources
4. Cross-match with object catalog
Distinguish known variables and new objects
Point
- Time to do the cross-match and issue the alert is a small fraction of the 60 seconds budget.
Maria A. Nieto-Santisteban / ADASS 2006

11. Maria A. Nieto-Santisteban / ADASS 2006
Alerts Data Flow
Variable
Catalog
Deep
Catalog
Moving
Objects
125K 6M ?
Known
Variable ?
Known
Object ?
Known
Mover ?
DIA
Sources No No
Yes
128K 3K 1K
Yes
Yes No
Alerts trigger on DIA sources
Variables are a small fraction of all objects
Alert ?
Alert ?
Alert ?
Examples:
Cataclysmic
Variable
Supernova
Gamma Ray
Burst
Maria A. Nieto-Santisteban / ADASS 2006

12. Alert Simulation for Galactic Center
Extrapolate USNO-B
LSST FOV of 10 deg2
6 Million Stars (DR20)
126 K Variable Stars
128 K DIA sources
3200 New Variables
1000 Un-matched
Moving Objects,
New Objects,
Transients (GRB)
Match distance = 1 arcsec
Maria A. Nieto-Santisteban / ADASS 2006

13. Alert Cross-Match Performance
We can detect alerts in 40 seconds on my desktop computer.
Partition by FOVs
Maria A. Nieto-Santisteban / ADASS 2006

14. Maria A. Nieto-Santisteban / ADASS 2006
Summary
Cone search != Neighbors
Zones efficiently index and “join” spatial data
e.g., SDSS DR5 vs. 2MASS in 80 minutes
Zones are a convenient for partitioning data
Simulated a LSST FOV in Galactic Center
Cross-match catalogs smallest to largest
Finds possible alerts in 40 sec on desktop
Maria A. Nieto-Santisteban / ADASS 2006