Scary Asteroids! How huge sky surveys and little pushes will save the Earth.

When I was growing up in the 70’s and 80’s, the opportunities available to the amateur for making useful scientific observations  were somewhat limited.   One could observe variable stars,  record stellar occultations by the moon, planets, or asteroids, or hunt for comets and supernovae.  While such activities will continue to appeal to backyard observers, large automated survey telescopes that can repeatedly image the entire night sky to extremely faint magnitudes will certainly change the role of the amateur and the potential for novel discoveries by those of us with more modest equipment.   However, with future surveys promising to produce  petabytes of data annually and the creation of massive catalogs containing hundreds of millions of objects, new and important discoveries await the desktop-bound amateur with a penchant for data analysis.

For example, it was widely reported last year that a group of undergraduate astronomy students out of the University of Washington went looking for supernova using images obtained by the Sloan Digital Sky Survey as part of a class project.   What they found instead were 1,300 newly discovered asteroids.  From the original press release:

“We started searching for supernovae using data from the second phase of the Sloan Digital Sky Survey and all these asteroids were in the way,” said Andrew Becker, a UW research assistant professor in astronomy.  “We decided that rather than get frustrated by the asteroids we should do some science and note details about our observations. I kept asking the students what they had found and they kept saying, ‘More asteroids. No supernovae, but lots of asteroids.’”

This is a story that underscores the exciting opportunities for novel discoveries and scientific contributions available to the amateur as we enter the age of high-throughput digital astronomy.   The story got me to thinking about what we know about asteroids, and the dangers they pose to life on Earth.   Asteroids are small rocky objects revolving around the sun, mostly between the orbits of Mars and Jupiter in the so-called asteroid belt between 2.1 and 3.3 A.U from the sun.  The majority of these have shallow orbital eccentricities.   Over time, some of these asteroids have been purturbed gravitationally by Mars or more particularly Jupiter into more highly eccentric orbits.

Asteroid 243 Ida, imaged by the Galileo spacecraft

Of particular concern are the Near-Earth Asteroids (NEA’s) which cross the orbit of the Earth and thus have the potential for major devastation.

Some notable impacts from both recent and ancient history:

• Asteroid 2008 TC3 (October 7, 2008).   The first case of an asteroid’s impact time and location being predicted in advance.   The entry of the asteroid, estimated to be no more than 5 meters in diameter, generated a spectacular fireball over Northern Sudan.   The event was even capture by satellite imaging.  Energy release: 1 kiloton TNT.
• Hodges Meteorite.   (1954) The only documented case of a human getting hit from a rock from outerspace.   The 4 Kg meteorite crashed through the roof of 31-year old Ann Hodges of Sylacauga, Alabama, bouncing off her radio before striking her on the left hip.   She was badly bruised.   The radio was destroyed.   Energy: 16 lbs TNT (personal rough estimate based on size), with the roof and radio absorbing the brunt of the impact!
• The Tunguska Event (1908) flattened 2000 sq kilometers of trees in a remote region of Siberia.   It is believed to have been caused by an asteroid about 60 meters in diameter.   Energy: 10 Megatons TNT.
• Meteor crater Arizona (50,000 years ago.)    A 45-50 meter asteroid left a 1.2 km diameter crater and probably leveling everything within about 16 km (10 miles).  Energy: 2.5 megatons TNT.
• Cretaceous-Tertiary Extinction Event (65.5 million years ago).   A 10 km asteroid striking the Yucatan leading to the immediate extinction of the dinosaurs and 70% of the life on Earth.   Energy: 100 million Megatons TNT.

NASA’s Jet Propulsion Laboratory (JPL) has an on-going program to study Near Earth Objects.  There you can obtain orbital elements for some 5800+ catalogued NEAs.   Of these, a little over 1000 are designated as potentially hazardous, having an MOID (minimum orbit intersection distance) of less than 0.05 AU (about 5 million miles).

The site also lists upcoming close approaches.   For example, the asteroid 2008 XC1, a Tunguska-sized asteroid, will pass within about 1 million miles of the Earth, or about 4 times the distance to the moon in the next couple of days (Friday December 12, 2008).

You can also plot the orbit of any of the 437 thousand asteroids whose orbital elements have been catalogued.  The figure below depicts Earth’s upcoming close encounter with 2008 XC1.

Although only about 1000 potentially hazardous asteroids (PHAs) have been identified, it has been estimated that there may be as many as 10-20,000 such objects awaiting discovery by larger more powerful survey telescopes such as the LSST due to come online in the coming decade.

So what can we do about mitigating the risk of death-by-asteroid?   Obviously cataloging asteroids in order to assess the risk is a critical first step.   To avert an imminent collision, a number of ideas have been proposed.   Simply nuking the asteroid might actually be problematic.   One particularly interesting idea involves the use of a “tugboat” spacecraft which would rendezvous with the asteroid and by applying a small but steady force, would physically nudge the asteroid just enough to avert disaster.   In an article by Schweickart, Lu, Hut, and Chapman describing the concept, they note that with an asteroid with an orbital period of two years, a 1 cm per second velocity change would increase the period by 45 seconds, creating a delay of 225 seconds over 10 years, enough to insure a near miss, but a miss nevertheless (Scientific American, 2003).   Of course, such a scheme underscores the importance of early detection with decades of advance notice.

So ultimately it turns out the the new generation of deep-sky surveys not only leads to unprecendented insights into the nature of the universe, but may even one day save the world!

Gravitational lensing as a dark matter probe

A competition is underway to develop new algorithms to quantify the gravitational lensing effect of the mysterious dark matter that pervades the Universe.  The competition known as GREAT08 (GRavitational lEnsing Accuracy Test 2008) has recently been opened up to the public and aims at developing methods for understanding the nature and distribution of dark energy.   As noted in a short blurb about the competition in the 31 October 2008 issue of Science, new image analysis and machine learning techniques coming out of GREAT08 could be key to the analysis of the billions of galaxies that future surveys will catalog in the coming years.  The site also contains a very nice and informative screencast.

Observable long-period variables of high scientific interest

In my last post, I presented a high-level analysis looking at some of the factors leading to high observation counts in the AAVSO database.   That analysis made use of information from the General Catalog of Variable Stars (GCVS) as well as spreadsheets provided by the AAVSO containing observation counts and estimates of citations for all long-period variables (LPVs) in the AAVSO database.   We found, for example, that observation counts are highly skewed towards a relatively few LPVs, that these popular stars occur almost exclusively above zero degrees declination, and that the magnitude of the star at maximum (brightest) strongly influences the popularity (observation counts) – LPVs whose maximum falls below 10m (an approximate binocular limit – at least here in the light-polluted skies of Boston suburbia) rarely have large numbers of observations.

There are of course many other factors that observers take into account when selecting stars of interest.   Variables that are close together in the sky seem more likely to be observed because it is easier to knock them both off at once.   Stars with more interesting light-curves that offer “surprises” are I suspect going to garner greater attention, all else being equal.   A star may be difficult to observer because charts are lacking or because there are no convenient comparison stars.   And we should not forget the important influence of the AAVSO in making special requests of the user community via special bulletins, or regular articles such as “Variable of the Season.”    Indeed, one of the most important functions of the AAVSO, in my view, is to help align amateurs with the scientific goals of the professional astronomical community.

With the recent announcement that the AAVSO was forming a special section dedicated to long-period variables, an important task before the section is to choose LPVs of scientific and community interest.   Citation counts estimated by the AAVSO provide some measure of the overall scientific importance of an individual star.   We use these citation counts together with the observation counts to propose a methodology for selecting candidate LPVs for the new section.

The most obvious thing to do is to consider references per 1000 observations (RefPerKObs).   For example, Y Cas with 6,604 observerations has accumulated 100 citations giving it a RefPerKObs of 15.1.   By comparison, RV Her (Obs=10219, Refs=34) has a RefPerKObs of only 3.3.  The problem with this statistic is that it is undefined for near 3/4ths of the LPV stars in the AAVSO database having 0 observation counts, and tends to be highly skewed when the observation counts are very low.  (The difference between having 1 observation and 2 observations is a factor of two difference in RefPerKObs!)

So instead we consider computing two percentiles – one based on its ranking (1,2,3…) with respect to observations, the other with respect to number of citations.    Then we define a score:

(1)   RankPercentileDiff = CitationRankPercentile – ObservationRankPercentile

The resulting score varies from [-1...+1], and a high (>.5) RankPercentile suggests an under-observed star  with relatively high scientific interesest worthy perhaps of being added to the LPV program.   It turns out this score is actually quite bad because of what I noted in the last time: observation counts are highly skewed towards a relatively few popular stars.   As a result the M-type star, LX  Cyg, ranks in the 50th percentile in observations with a paltry 1700+ observations.  But over 92% of the 6.7 million LPV observations in the AAVSO database are associated with higher-ranking stars.  The RankPercentile defined above tends to underestimate the importance of a star.    LX Cyg achieve a maximum magnitude of only 11.5, so as I noted above, it’s low observation counts are to be expected.    We address these observability issues below.   Nor have we taken into account how its 23 citations stack up.

To address the above concern, we modify the Observation and Citation percentiles based on actual counts rather than a simple ranking.    Thus for each LPV:

AAVSO_Obs_Percentile = percent of observations occurring in stars with fewer observations.

NumRefs_Percentile = percent of citations associated with stars having fewer citations.

Note that stars having the same number of observations or references have the same observational or reference percentiles, respectively.

Finally:

(2)  PercentileDiff = AAVSO_Obs_Percentile – NumRefs_Percentile

Figure 1 below plots the observational percentile vs. the reference percentile, with redder stars having a higher percentile difference.   (Click on each image to see ful size).

Observational -vs- Reference percentiles

As noted in my last post, sometimes stars like CW Leo, a proto-planetary nebula surrounded by water-containing comets, generates high scientific interest outside of its variability.   But by way of example, compare RS Virginis (marked, upper left) to AF Cyg (right).   RS Vir has garnered far fewer observations (6469 -vs- 57799) but has far more citations (164 -vs- 68), a victim perhaps of the declination effect where more southerly stars tend to be neglected.   Am I suggesting that AF Cyg should be excluded from the LPV section?  Absolutely not!   But if I’m trying to get members to focus their attention, I’m focussing them more towards RS Vir – a star that seems to have high scientific interest, but has been relatively neglected by observers.

To account for observability, we filter out stars having declination south of -20 degrees, and a maximum magnitude below 10.0m    We further exclude LPVs having amplitudes less than 1.0.   We also limit ourselves to visual (V) and photographic (p) bands.   One might choose different cutoffs.  The point is simply to demonstrate that reasonable cutoffs still lead to a goodly number of focus candidates.  The above constraints still leave about 600 candidates to choose from (about 5%)

Figure 2 is a revised scatter plot with the above constraints in place.   These are stars that are more accessible to the observing community.

Observational -vs- Reference percentiles for accessible LPVs

Figure 3 below shows the distribution on PercentileDifference for the 600 or so remaining candidates.    I would argue that the 154 stars in the marked should all be included in the LPV section.

Distribution of PercentileDiff for 600 Accessible LPV Stars

The table below lists these 154 stars and their basic properties.   I emphasize that this list isn’t intended to be exclusive.    Furthermore, the final selection process should ensure that different LPV types (irregulars, semi-regulars, miras) are well represented.    Finally, it should be noted that U Herculis at the top of the list appears to be the result of an observation count error in the AAVSO spreadsheets, and that there may be a systemic error in the counts involving variable designations with Greek letters, or names that can be confused with greek letters (U = u = mu?).   This table isn’t intended to be the final word, but rather a demonstration of a methodology for narrowing down candidates.

rachlin_154_lpv_candidates.pdf

Addendum: Another thought occurred to me this afternoon. You might ask – why consider low observation counts as a factor?  Why not just look at the stars with the highest scientific interest?   It would certainly be reasonable to include such stars if they are overlooked in the table above.   What I’m focussing on here is finding stars where increases in the observation counts could potentially have the greatest scientific impact.   Adding five or ten thousand observations to stars with a few hundred in the books might provide novel scientific insights – a new dimension of understanding to a star whose scientific importance has already been established.   Adding more observations to a star already teaming with tens of thousands of observations may have less potential for impact, in my opinion.   For this reason, I consider stars currently having fewer observations as an important selection criteria.

AAVSO/RJB

Long-Period Variables and the AAVSO

As described in my last post, I recently became interested in variable stars.   The American Association of Variable Star Observers (AAVSO) provides a terrific amount of information and guidance about observing variable stars, and the underlying science.   My own excursion into this area began with a somewhat randomly chosen variable known as XZ Cyg, an RR Lyra – type variable with a magnitude amplitude of 1.3 in the Visual band and a period of 0.46 days.   As a beginning observer, I have become increasingly interested in selecting variable stars as part of a personal “observing program.”    There are tens of thousands of catalogued variables.  Where to begin?  A number of personal considerations include:

- the nature of the light curve – for me, and I think for most observers, a certain degree of unpredictability is more interesting.

- The star needs to be obviously visible from my northern latitutude (42 degrees N), and I have trees and houses to contend with as well!

- The magnitude range needs to fall within the observing range of my available equipment which includes:

a) my naked eye, which achieves a limit of 5.95m here in the light-polluted skies of metro-west Boston area,
b) Pentax 10×50 binoculars (mag limit approx 9.50 – 10.0)
c) 10″ Meade SCT (mag limit approx. 13.5-13.7).

To better appreciate the distribution of variable star properties, we can turn to The General Catalog of Variable Stars (GCVS) which currently lists over 40,000 variables.   By coincidence, the AAVSO announced one week ago that they were going to start a section dedicated to long-period variables.   These LPV’s include the famous Omicron Ceti, or “MIRA”, a pulsating red giant star with an amplitude of over 8m, and a period of about 332 days.   One of the first goals of the AAVSO’s LPV section is to identify a selection of stars to be the focus of their observing program and in so doing, provide guidence and direction to the AAVSO member community.    In short, they want to make sure that observers are well-aligned with the scientific objectives of the astronomical community.   Towards that end, the AAVSO has also put together data on all of the LPV’s in their database including the number of observations as well as the number of known publications about each star.   In combination with the GCVS catalog data, one can gain some insight into how observers choose their stars. Note: Click on each image to see full size!

1.  The figure below plots the 70 LPVs having more than 20,000 observations a piece.   The larger the circle, the more observations.   The redder the circle, the more scientific references.   One notices immediately that almost all of the most popular stars occur in the northern celestial hemisphere (>0 degrees declination) because most of the observers live in the Northern hemisphere.   And while in theory my horizon might extend down to -48 degrees if I lived on a volcano in the middle of the ocean, the practical limit here in New England is probably about -20 degrees.   It is worth noting that the six southern exceptions, which includes Omicron Ceti itself, all achieve naked eye visibility at maximum, perhaps enabling more frequent observations.

LPVs with greater than 20,000 Observations

Also interesting is the fact that these 70 LPV’s (out of 16,860 in the AAVSO database) garner over 35% of the LPV observations (2,414,998 /6,856,617).

2.   The next figure plots 59 of the (scientifically) hottest stars,  each having more than 200 references.   I’ve also highlighted (dark green small circles) those stars having fewer than 1000 observations as potential neglected candidates.   One is QX Pup, the focus of a recent AAVSO observing campaign, others however have very small amplitudes or are primarily infrared-band sources.   A strange example of a “neglected star” is U Her, but I believe this is simply a data error in the AAVSO spreadsheets, as there are in fact over 30,000 observations of this star. [11/15/08 Addendum - 18 stars reported to have fewer than about 1000 observations and more than 100 scientific references all have greek letter names - so this is probably a confusion between u (greek mu) and U, for example.   Thanks due to John Greaves for pointing out the likely cause of the discrepancy.]

The scientifically hottest LPVs

3. The above figure does suggest that observation counts aren’t always aligned with the scientific interest in the star based on the number of known references -  see figure 3 below:  R-squared = 0.3029.

Observations -vs- References

Sometimes the discrepancy is simply the result of the fact that the scientific interest in the star is largely outside the scope of its variability.   For example, CW Leonis with over 1500 references is believed to be a rare example of a proto-planetary nebula and surrounded by a cloud of water-bearing comets.

4.  Another major factor influencing observation counts is the maximum magnitude.   This in itself is probably not too surprising, but the steepness of the curve is remarkable.

Number of observations -vs- Peak magnitude

Note in particular that below 10m, my own binocular limit, few stars have more than 10,000 observations  a piece.

5.  We look now at the diversity of M-type stars.    In trying to find interesting LPV candidates for my own observing program, I thought a good starting point would be to better understand how such stars are distributed in terms of period and amplitude.   Being an impatient novice variable observer, I thought it would be cool to note large changes in brightness over the shortest time possible.   Here I have included only M-type stars with magnitudes in the V band (ignoring infrared and photographic), and excluding stars flagged in the GCVS as having uncertain (or missing) min/max magnitude or type.   Again, size is by number of observations in the AAVSO database, and redder means more references.

M-type, V-Band, Amplitude -vs- Period

There does seem to be a shared preference for larger amplitude stars, though not a strong preference for shorter periods.  If you plot number of observations -vs- the Amplitude/Period ratio (plot not shown), there does not appear to be a strong correlation.   On a side note, one of the goals of astronomical data mining is to identify interesting outliers.    R Vulpeculae (marked) along with the southern star W Puppis have  the highest amplitude/period ratios for an M-type star.   R Vul varies over 7 magnitudes in just 137 days!   Lowly V0384 Persei has an Amplitude/Period ratio a factor of 10 smaller (2.9m range in 535 days) which makes it interesting in its own right, though understandably not to your average observer.   Repeating the excercise for other types of variables having well-defined periods is interesting too.

Final thoughts:

Many other kinds of analyses are possible.   I would like to see the AAVSO identify not only the total number of observations, but also the number of unique observers as way of better understanding general community interest.   I’d also recommend additional documentation of the spreadsheets including details on how the observation and reference counts are performed so that the data can be further checked.   I’d also love to see this data provided for every star in the AAVSO database.    I hope the above analysis gives some improved insight into how individuals choose an observing program and what stars might be of interest both to observers and the scientific community.

AAVSO/RJB