Pixel Boundaries for NTPCkr of SETI@home

Example usage of HEALPix pixel boundaries using Google Sky Maps with NTPCkr.The Near-Time Persistency Checker (NTPCkr) recently went online, which allows SETI@home to publish an up-to-date list of their best candidates for persistent extraterrestrial signals. The dynamic NTPCkr top-10 list also contains a “skyplot” link for each candidate, which shows a picture of the candidate’s location on the sky using a Google Sky Map with a custom crosshair marker indicating the center of the pixel region where the signals were detected. As pointed out by Jon Golding (in this forum comment), the NTPCkr should “perhaps show the region of interest on a skymap (i.e., not crosshairs)” to illustrate this more clearly. Joe Segur shared this sentiment, stating that “plotting would ideally show the boundaries of the pixels”. The equations needed for calculating these SETI@home pixel boundaries are given below, along with an example JavaScript implementation, making such an enhancement straightforward.

From the pixel identification (ID) numbers on the NTPCkr list, along with their Right Ascension (RA) and Declination (Dec) data, it is evident that SETI@home (or at least the NTPCkr aspect of SETI) digitizes the sky using a HEALPix sphere with Nside = 2048 (that is, with resolution level k = 11) where the pixel ID numbers correspond exactly with the nested scheme of HEALPix pixel indexing; this divides the celestial sphere into over 50.3 million equal-area pixels (3 × 224 to be exact). Furthermore, from what I can determine, the signals analyzed by SETI (as recorded by the Arecibo Observatory) should all be located well-within the HEALPix equatorial belt (that is, with pixel-center declinations within about 41.80 degrees either side of the equator, thus also excluding the two transitional rings). This would mean that all the candidate pixel regions are approximately shaped like simple upright diamonds on the sky maps that are centered at their respective pixel centers, since none of the weirder shaped polar pixels are involved. Each pixel region is outlined by four corner points to form the diamond around its center (for example, connecting the east point to the north point, then to the west point, south point and back to east point to close the diamond), and the coordinates of the outlining boundary points can be calculated as follows:

Point Location Right Ascension (RA) Declination (Dec)
Center RAcenter  (know, in hours) Deccenter  (known)
East RAeast = RAcenter + 3 / 2048 Deceast = Deccenter
West RAwest = RAcenter - 3 / 2048 Decwest = Deccenter
South RAsouth = RAcenter Decsouth = arcsin( 4 / 3 - ( i + 1 ) / 3072 )
North RAnorth = RAcenter Decnorth = arcsin( 4 / 3 - ( i - 1 ) / 3072 )

where i represents the HEALPix ring index of the pixel, which can be calculated for an equatorial pixel from its center declination:

   i = 3072 . ( 4 / 3 - sin( Deccenter ) )  .

Note that the “3 / 2048” constants for the east and west points in the RA column of the table represent the half-widths of each equatorial pixel in hours (which is calculated in general as 3 / Nside), resulting in a total east-west pixel-width of just under 0.044 degrees. Furthermore, the “3072” constants in the ring-index equation and in the declination column for the south and north points can be calculated from the general expression 3 × Nside / 2.

The tabulated equations should be sufficient for calculating the NTPCkr pixel regions until SETI starts analyzing pixels in the HEALPix polar caps (in which case one can expand on this). An example implementation in JavaScript is shown below, which assumes access to the Google Maps API (version 2) to draw the pixel region using a GPolyline overlay object. It should be trivial to incorporate this into the existing NTPCkr skymap implementation. The example code also includes a conditional test, such that the pixel outline would only be calculated and shown when the size of Deccenter is less than 41.80° (thus thoroughly being an equatorial pixel); the pixel center is always shown. The RA_center and Dec_center parameters of the drawHEALPixAreaOnMap function represent the RAcenter (in hours) and Deccenter (in degrees) pixel-center variables, respectively, and the googleMap parameter specifies a Google Maps GMap2 object.

function drawHEALPixAreaOnMap(RA_center, Dec_center, googleMap) {
var baseIcon = new GIcon();
baseIcon.iconSize = new GSize(29, 29);
baseIcon.iconAnchor = new GPoint(14, 14);
var crosshair = new GIcon(baseIcon,
"http://setiathome.berkeley.edu/images/crosshair.gif");
var mark = new GMarker(
new GLatLng(Dec_center, 180-15*RA_center), {
icon : crosshair,
title : "Telescope Pointing (RA: " +
RA_center + " DEC: " + Dec_center + ")" });
googleMap.addOverlay(mark);
var i = 0;
if (Math.abs(Dec_center) < 41.80) {
i = 3072 * (4/3 - Math.sin(Dec_center * Math.PI/180));
var RA_east = RA_center + 3/2048;
var Dec_east = Dec_center;
var RA_west = RA_center - 3/2048;
var Dec_west = Dec_center;
var RA_south = RA_center;
var Dec_south = Math.asin(4/3 - (i + 1)/3072) * 180/Math.PI;
var RA_north = RA_center;
var Dec_north = Math.asin(4/3 - (i - 1)/3072) * 180/Math.PI;
var polyline = new GPolyline([
new GLatLng(Dec_east, 180-15*RA_east), // Convert RA
new GLatLng(Dec_north, 180-15*RA_north), // to longitude
new GLatLng(Dec_west, 180-15*RA_west),
new GLatLng(Dec_south, 180-15*RA_south),
new GLatLng(Dec_east, 180-15*RA_east)
], "#00ff00", 2, 0.35);
googleMap.addOverlay(polyline);
}
return i;
}

Comments

NTPCkr Now Updated

The SETI team has indeed implemented the pixel-boundary suggestion, which was available online when I looked at the NTPCkr on September 29th. You need to zoom in if you want to see the candidate’s HEALpix region clearly.

An interesting example image is included below for the candidate with ID 920891, which is the pixel centered at RA: 2.645508 hours, Dec: 26.547533° (in ICRS J2000.0). Inside the pixel there is a relatively bright orange star, located at about 02:38:43.71+26:32:05.5. I believe this is the star referred to as TYC 1775-1429-1 (from the Tycho-2 catalogue, also identified as VizieR catalogue number I/239), and, according to SIMBAD, it is also known as AG+26 260, BD+25 431, GSC 01775-01429, PPM 91859, SAO 75492, YZ 26 1395 and 2MASS J02384371+2632055.

One should be able to see this star with a small telescope and a dark sky (perhaps even with binoculars), since it has a Johnson photometric visual magnitude of approximately 9.3 (the optical V-band magnitude is about 9.4 and the B-band about 10.9). It would have been nice to know how far away this star is from earth, but, unfortunately, there is no corresponding entry for the star in the Hipparcos catalogue where one could have found a trigonometric parallax value to calculate the distance.

SETI candidate 920891 with HEALPix boundary.

Available for Sky in Google Earth

The NTPCkr candidates can now also be visualized through downloadable content for Sky in Google Earth. Refer to this new blog post for detail.