Thursday, 23 January 2020

Orion’s Shoulder Star Betelgeuse Continues to Dim, (Updated with new Data, Jan 23, 2020)


Orion’s Shoulder Star Betelgeuse Continues to Dim, (Updated with new Data)

Update, Jan 23, 2020

From the Astronomer’s Telegram, there has been a lot more dimming over the last month, about 0.2 magnitudes.  I make that to be about a 20% decline in brightness.
“Since our last report, Betelgeuse has continued to gradually decrease in brightness. Our most recent photometry secured on 17.25 UT and 18.20 UT January 2020 yields: V = +1.494 mag and 1.506 mag, respectively. This is more than ~0.2 mag fainter than previously reported in ATel #13365 on 22.25 UT Dec. 2019. However during the last week or so the decline in brightness of the star may be slowing.
Betelgeuse is currently the coolest and least luminous yet observed. Since September 2019, the star's temperature has decreased by ~100 K while its luminosity (inferred from the C-band/m-bol observations) has diminished by nearly 25%. At face value using R'/R = [(T'/T)^4 / L'/L]^0.5 (where R', T' and L' are the current values of stellar Radius, Temperature & Luminosity), this implies an increase of the star's radius of ~9%. However, as pointed out by others, the current fainting episode could also arise from expelled, cooling gas/dust partially obscuring the star. The recent changes defined by our V-band/Wing photometry seem best explained from changes in the envelop-outer convection atmosphere of this pulsating, unstable supergiant. If these recent light changes are due to an extra-large amplitude light pulse on the ~420-day period, then the next mid-light minimum is expected during late January/early February, 2020. If Betelgeuse continues to dim after that time then other possibilities will have to be considered. The unusual behavior of Betelgeuse should be closely watched.”

Previous Observations

Some recent reports via the Astronomers’ Telegram (astronomerstelegram.org) entitled “The Fainting of the Nearby Red Supergiant Betelgeuse” and “Updates on the ‘Fainting’ of Betelgeuse” comment on the continuing dimming of the star Betelgeuse, in the constellation Orion.  That would be the (normally) bright star that represents Orion’s left shoulder (left from the observer’s point of view).

“Betelgeuse and Antares are the two nearest red supergiant core-collapse Type-II supernova (SN II) progenitors.  Photometry from this season shows the star has been declining in brightness since October 2019, now reaching a modern all-time low of V = +1.12 mag on 07 December 2019 UT. Betelgeuse undergoes complicated quasi-periodic brightness variations with a dominant period of ~420 +/-15 days. But also Betelgeuse has longer-term (5 - 6 years) and shorter term (100 - 180 days) smaller brightness changes. Currently this is the faintest the star has been during our 25+ years of continuous monitoring and 50 years of photoelectric V-band observations.” ATel #13341 8 Dec 2019; 03:57 UT

A slightly later report had some further information.

“The most recent measurements made on 2019 December 19.3 UT, 20.2 UT and 22.25 UT are V = +1.273, +1.294 and +1.286 mag, respectively. This appears to be the faintest the star has been measured since photoelectric observations have been carried out of the star… At its average maximum brightness light (V ~ 0.3 - 0.4 mag), Betelgeuse is the 6 - 7th brightest star. But by 2019 mid-December the star has slipped to the ~21st brightest star. The red supergiant is now closer in brightness to Bellatrix (V =+1.64 mag) than to Rigel (V =+0.13 mag).” ATel #13365 23 Dec 2019; 20:24 UT

So Betelgeuse has dimmed from about -.4 to about 1.29.  That’s about 1.7 magnitudes reduction (the magnitude scale works backwards, with larger positive numbers indicating less bright objects).  In terms of absolute brightness (luminosity), that means the star is about 4.7 times brighter at its usual maximum than it is now (2.51 raised to the exponent 1.7).  However, it should be noted that the magnitude scale is closer to what the eye sees, so the star seems to be about 60% as bright as it does at its peak (1/1.7).

The series of iPad/iPhone photos that I have taken over the past few years shows this difference visually.  The September 2016 iPad photo shows Betelgeuse being much brighter than Bellatrix.  The 2018 picture was taken in January with an iPhone, and it shows Betelgeuse to be brighter than Bellatrix, but the difference seems to have diminished.  And the December 2019 iPhone photo definitely shows Betelgeuse to now be about the same brightness as Bellatrix.  Also, at the beginning of the sequence, Betelgeuse is quite close to Rigel in brightness, while by 2019 it is clearly much dimmer. 


For additional reference, the other set of photos below shows a very good example of astrophotography of Orion (from Wiki) in comparison with the September 2016 iPad photo.



About Betelgeuse and Supernovas

Betelgeuse is a red giant star, about 11 or so solar masses, at a distance of about 700 light years.  It is a progenitor star for a supernova – in other words, it will end its “stellar life” in a supernova, to become a neutron star or a black hole.  This is expected to happen soon by astronomical standards, which means within about 100,000 years.

So, this could happen any day, or it might be a thousand centuries from now.  It is now thought that the star is too far from the Earth to actually pose a significant threat to life on our planet, even when it does go supernova.  However, it is expected to be a good show for anyone around at that time, as it will be at least as bright as the full moon, and probably even visible during the day.

It is natural to wonder whether the current unprecedented dimming is a warning that the star will soon explode (this is within the 100,000 year window, after all).  Basically, nobody really knows.
Supernovas are rare during the current galactic epoch, with maybe one expected within the Milky Way every century or so.  Only a couple have been observed in recorded history – the 10th century event that created the Crab Nebula and another in the 17th century.  Other than that, we have had to rely on observations of supernova in nearby galaxies, such as the event in 1987 in the Magellenic Cloud, a nearby “suburb” galaxy of the Milky Way. 

Because these events are so rare, we don’t have historical observations of what the progenitor star looks like in the period of a few years before it goes supernova.  So, we don’t know if it dims before the explosion or whether it first brightens.  Perhaps it pulsates for a few centuries (as Betelgeuse does now) before exploding.  Or maybe it just goes bang with no warning.

That leaves us with theory to try to predict what a star on its way to going supernova looks like.  The theory of the evolution of massive stars goes something like this:

“For the most massive stars…the carbon core remains convective and carbon burns to oxygen and magnesium.  Finally, the star consists of an iron core surrounded by shells with silicon, oxygen, carbon, helium and hydrogen.  The nuclear fuel is now exhausted, and the star collapses on a dynamical time scale.  The result is a supernova.  The other parts explode, but the remaining core continues to contract to a neutron star or a black hole.” (Page 253 of Fundamental Astronomy by Karttunen et al)
“For example, for a 20 solar mass star, its main-sequence lifetime (core hydrogen burning) is roughly 10 million years, core helium burning requires one million years, carbon burning lasts 300 years, oxygen burning takes roughly 200 days, and silicon burning is completed in only two days!” (page 510 of Modern Astrophysics by Carroll and Ostlie)

That doesn’t really pin things down much, in terms of what we might expect to witness when Betelgeuse does go supernova.

During these various stages, dust can be thrown off that could obscure the star from our point of view, or dust could be blown away by a solar wind giving us a better view.  And of course, the intensity of the nuclear burning of various fuels could brighten or dim the star.  To be sure about these matters, we would require more observations, hopefully close enough to learn a lot about supernovas but far enough away to remain safe. 

It is always worth keeping in mind that astrophysical theory says that our sun condensed out of an enormous nebula, that was probably created by a supernova over 5 billion years ago.  The heavy elements, some of which are needed for life on Earth, were created in that supernova.  So, in a sense we owe our existence to a supernova (we really are stardust), though we hope that we won’t owe our demise to the second coming of one.

Turning and turning in the widening gyre   
The falcon cannot hear the falconer;
Things fall apart; the centre cannot hold;
Mere anarchy is loosed upon the world,
The blood-dimmed tide is loosed, and everywhere   
The ceremony of innocence is drowned;
 (Yeats, The Second Coming)

Sources:

·       The Astronomers’ Telegram  http://www.astronomerstelegram.org/
·       Fundamental Astronomy by Karttunen et al
·       Modern Astrophysics by Carroll and Ostlie
·       Wikipedia (Betelgeuse entry).

Some Related Blogs

The Orion Nebula


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Related to astronomy (sort of), if you want to see an area that is remarkably evocative of the landscape of Mars, here on Earth, try Newfoundland’s Table Lands, as described in the book below (along with plenty of other interesting features of Newfoundland):

A Drive Across Newfoundland


Newfoundland, Canada’s most easterly province, is a region that is both fascinating in its unique culture and amazing in its vistas of stark beauty. The weather is often wild, with coastal regions known for steep cliffs and crashing waves (though tranquil beaches exist too). The inland areas are primarily Precambrian shield, dominated by forests, rivers, rock formations, and abundant wildlife. The province also features some of the Earth’s most remarkable geology, notably The Tablelands, where the mantle rocks of the Earth’s interior have been exposed at the surface, permitting one to explore an almost alien landscape, an opportunity available on only a few scattered regions of the planet.
The city of St. John’s is one of Canada’s most unique urban areas, with a population that maintains many old traditions and cultural aspects of the British Isles. That’s true of the rest of the province, as well, where the people are friendly and inclined to chat amiably with visitors. Plus, they talk with amusing accents and party hard, so what’s not to like?

This account focusses on a two-week road trip in October 2007, from St. John’s in the southeast, to L’Anse aux Meadows in the far northwest, the only known Viking settlement in North America. It also features a day hike visit to The Tablelands, a remarkable and majestic geological feature. Even those who don’t normally consider themselves very interested in geology will find themselves awe-struck by these other-worldly landscapes.

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And now that you have read about some real cutting-edge science, you should think about reading some Science Fiction (because all work and no play can make you a dull person, or so they say).  This one includes a sequence where a neutron star plays an important role in the action.

The Witches' Stones, Book 1 - Rescue from the Planet of the Amartos

Young Earth woman and spaceship mechanic, Sarah Mackenzie, has unwittingly triggered a vast source of energy, the Witches' Stones, via her psychic abilities, of which she was unaware. She becomes the focal point of a desperate contest between the authoritarian galactic power, known as The Organization, and the democratic Earth-based galactic power, known as The Terran Confederation. The Organization wants to capture her, and utilize her powers to create a super-weapon; the Terra Confederation wants to prevent that at all costs. The mysterious psychic aliens, the Witches of Kordea also become involved, as they see her as a possible threat, or a possible ally, for the safety of their own world.

A small but fast scout-ship, with its pilot and an agent of the Terra Confederation, Coryn Leigh, are sent to rescue her from a distant planet at the very edge of the galaxy, near space claimed by The Organization.  Battles, physical and mental, whirl around the young woman, as the agent and pilot strive at all costs to keep her from the clutches of the Organization.

Saturday, 18 January 2020

How do I do a statistical analysis of survey data?


How do I do a statistical analysis of survey data?

I have analyzed a lot of surveys over the years, and can say that it all depends on your purpose. For example, do you have some specific research questions in mind? Or, is this purely exploratory, perhaps a summary report for management?

If you have specific research questions, you might be able to skip quickly to more advanced techniques such as regression analysis. If you are doing a first level summary analysis, you might stop at the descriptive analysis stage.

Nonetheless, here are some basic steps to consider (it is a sort of ladder of complexity, so you might stop and any point, depending on your experience, your client and your resources of time or money):
  • If you weren’t involved with designing the survey, research what its overall purpose was and how it was constructed. If it is a survey that gets repeated on an annual basis (or some other basis) there may be research papers published on the results, to guide your thinking. If it is a one-off survey that you are given to analyze, find out what you can from the people who sponsored and designed the survey.
  • Read the instrument thoroughly and consider the target population. Think about how you might answer the questions yourself, if it is a general survey.
  • Consult subject-matter experts, if you aren’t one yourself (and even if you are one, it is good to get other opinions). Keep in mind what the goals of your clients are - they pay your salary. That said, don’t be afraid to give them advice or set them straight if they are recommending things that don’t make sense to you.
  • Go through the items with a statistical package, summarizing them with descriptive univariate measures, like means, standard deviations, and other distributional measures. Have a look at the actual distributions with histograms (you may have to bin numerical variables first), to see if they are normally distributed (important for many statistical methods), have skew, seem to be a power law or whatever.
  • For categorical data, look at the counts for each category, see whether they should be re-coded to make for a more manageable number of categories. Graphs if various kinds (box-plots, histograms, bar graphs, etc.) are very helpful - as they say “you can learn a lot just by looking”.
  • If there are open-ended text based questions, skim at least a sample of responses, to get a feel for things. You might later consider text analysis (e.g. word clouds, sentiment analysis, content analysis) at some later stage.
  • Consider whether some variables that “go together” can be collapsed into a single measure (a scale). For example, you might sum a number of variables that all seemed to be related to social status into one measure. Advanced techniques like factor analysis would be helpful here, though common sense will often take you a long way.
  • Try some bi-variate stats, such as X-Y charts on variables that seem likely to show interesting and relevant relationships.
  • If you have a primary dependent variable of interest in the survey (e.g. income), you might use advanced methods to explore which of your other variables have significant influences on that variable.
  • You might also consider methods like cluster analysis, to see if there are some unknown grouping factors in your population.
  • Don’t neglect the step of writing up the results. That can be anything from a formal research paper/corporate white paper to a list of comments/observations on a spreadsheet tab. It is a good idea to have some sort of “executive summary”, since your clients might be busy people. Also, keep in mind the sophistication of the clients. A very technical explanation might not be very useful to a non-quantitative client, while and oversimplified one won’t do for a technical audience.
  • If you come up with a real knock-out graph that summarizes/supports your case, keep it front and center. That may be the item that actually gets around to an important audience (e.g. a Board of Directors, Deans’ Council, Assistant Deputy Minister or whatever).
Anyway, good luck with your survey analysis.

How NOT to use survey results: