Name That Comet

As of this writing, there are 3,635 comets named SOHO, over 300 comets named LINEAR, some 179 comets named PANSTARRS, 82 comets named McNaught, 62 comets named NEAT, and so on.

Except for the comets discovered by Scottish-Australian astronomer Robert H. McNaught (1956-), all of the above comets were discovered by various automated surveys.

SOHO = Solar and Heliospheric Observatory (spacecraft)

LINEAR = Lincoln Near-Earth Asteroid Research

Pan-STARRS = Panoramic Survey Telescope and Rapid Response System

NEAT = Near-Earth Asteroid Tracking

How do we distinguish between comets having the same name?  Each has a separate comet designation.  The first Comet LINEAR has a designation of P/1997 A2, and the most recent Comet LINEAR has a designation of C/2017 B3.

A comet designation starts with one of the following prefixes:

P/ – a periodic comet (orbital period < 200 years or confirmed observations at more than one perihelion passage)

C/ – non-periodic comet (orbital period ≥ 200 years and confirmed observations at only one perihelion passage)

X/ – comet for which no reliable orbit could be calculated (generally, historical comets)

D/ – a periodic comet that has disappeared, broken up, or been lost

A/ – an object that was mistakenly identified as a comet, but is actually a minor planet (asteroid, trans-Neptunian object, etc.)

I/ – an interstellar object that did not originate in our solar system

This is then followed by the year of discovery, a letter indicating the half-month of discovery, followed by the numeric order of discovery during the half-month.

So, we can see that the first Comet LINEAR, P/1997 A2, is a periodic comet discovered in 1997, between January 1 and January 15 of that year, and it was the second comet to be discovered during that period of time.  After the second perihelion passage, P/1997 A2 (LINEAR) was subsequently given the periodic comet number prefix of 230, so the full designation for this comet is now 230P/1997 A2 (LINEAR).

Likewise, the most recent Comet LINEAR (at the time of this writing), C/2017 B3, is a non-periodic comet discovered in 2017 between January 16 and January 31, the third comet discovered during that period of time.

Interestingly, if different periodic comets have the same name, they are sequentially numbered.  Perhaps the most famous example is Comet Shoemaker-Levy 9 that broke up and crashed into Jupiter during July 1994.  There are a total of nine periodic comets named Shoemaker-Levy.  They are:

192P/1990 V1   Shoemaker-Levy 1
137P/1990 UL3  Shoemaker-Levy 2
129P/1991 C1   Shoemaker-Levy 3
118P/1991 C2   Shoemaker-Levy 4
145P/1991 T1   Shoemaker-Levy 5
181P/1991 V1   Shoemaker-Levy 6
138P/1991 V2   Shoemaker-Levy 7
135P/1992 G2   Shoemaker-Levy 8
D/1993 F2      Shoemaker-Levy 9

However, four additional non-periodic comets were discovered by the Carolyn & Gene Shoemaker and David Levy team.  They have not received a numeric suffix and are all called “Comet Shoemaker-Levy”:

C/1991 B1      Shoemaker-Levy
C/1991 T2      Shoemaker-Levy
C/1993 K1      Shoemaker-Levy
C/1994 E2      Shoemaker-Levy

This strikes me as a bit strange.  Why afford a numeric suffix to a comet name only when it is a periodic comet?  Why not give all comets named “Shoemaker-Levy” a numeric suffix.  Normally, we would number them all in order of discovery, but since the nine periodic comets have already received a number, we would have to number the four non-periodic comets as C/1991 B1 (Shoemaker-Levy 10), C/1991 T2 (Shoemaker-Levy 11), C/1993 K1 (Shoemaker-Levy 12), and C/1994 E2 (Shoemaker-Levy 13).

I would like to see all comets, both periodic and non-periodic, receive a numeric suffix to their names whenever there is more than one.  So, instead of Comet LINEAR we would have Comet LINEAR 1, Comet LINEAR 2, Comet LINEAR 3, and so on.

By the way, the days of amateur astronomers discovering a new comet will probably soon come to a close.  Though this is a little sad, it does tell us that the entire sky is being monitored much more closely than in the past, by a number of automated surveys.  And that is a good thing, because we will be much less likely to miss anything “new” in the sky.

None One of the comets this year (so far) have has been discovered by amateurs.

UPDATE – November 20, 2018: California amateur astronomer and prolific comet hunter Don Machholz, along with Japanese amateur astronomers Shigehisa Fujikawa and Masayuki Iwamoto, independently discovered a new comet on November 7.  The new long-period comet has been named C/2018 V1 (Machholz-Fujikawa-Iwamoto).  Remarkable!

Here is the current tally of comet discoveries (or recoveries) this year:

Pan-STARRS (Panoramic Survey Telescope and Rapid Response System)
C/2018 A1 (PANSTARRS)
364P/2018 A2 (PANSTARRS)
C/2018 A4 (PANSTARRS)
P/2018 A5 (PANSTARRS)
C/2018 F4 (PANSTARRS)
P/2018 H2 (PANSTARRS)
P/2018 L1 (PANSTARRS)
P/2018 L4 (PANSTARRS)
P/2018 P3 (PANSTARRS)
P/2018 P4 (PANSTARRS)
C/2018 P5 (PANSTARRS)
372P/2018 P6 (McNaught) [recovery of P/2008 O2]

ATLAS (Asteroid Terrestrial-impact Last Alert System)
C/2018 A3 (ATLAS)
C/2018 E1 (ATLAS)
C/2018 K1 (Weiland) [H. Weiland, ATLAS]
C/2018 L2 (ATLAS)
C/2018 O1 (ATLAS)

MLS (Mt. Lemmon Survey)
C/2018 A6 (Gibbs) [A.R. Gibbs, MLS]
C/2018 B1 (Lemmon)
P/2018 C1 (Lemmon-Read) [M.T. Read, Spacewatch, Kitt Peak]
C/2018 C2 (Lemmon)
C/2018 EF9 (Lemmon)  [originally classified as an asteroid]
C/2018 F1 (Grauer) [A.D. Grauer, MLS]
C/2018 F3 (Johnson) [J.A. Johnson, MLS]
C/2018 KJ3 (Lemmon) [originally classified as an asteroid]
P/2018 L5 (Leonard) [G. Leonard, MLS]
C/2018 R3 (Lemmon)
C/2018 R5 (Lemmon)

SONEAR (Southern Observatory for Near Earth Asteroid Research)
C/2018 E2 (Barros) [Joao Barros, SONEAR]

NEOWISE (Near-Earth Object Wide-field Infrared Survey Explorer)
C/2018 EN4 (NEOWISE)  [originally classified as a Centaur asteroid]
C/2018 N1 (NEOWISE)

Spacewatch
366P/2018 F2 (Spacewatch)

CSS (Catalina Sky Survey)
367P/2018 H1 (Catalina)
C/2018 M1 (Catalina)
C/2018 R4 (Fuls) [D.C. Fuls, CSS]

NEAT (Near-Earth Asteroid Tracking)
368P/2018 L3 (NEAT)
370P/2018 P2 (NEAT)

ASAS-SN (All Sky Automated Survey for SuperNovae)
C/2018 N2 (ASASSN)

OGS (ESA Optical Ground Station)
369P/2018 P1 (Hill) [recovery of P/2010 A1]
371P/2018 R1 (LINEAR-Skiff) [recovery of P/2001 R6]

373P/2018 R2 (Rinner)  [Jean-Francois Soulier, Maisoncelles, and Krisztian Sarneczky, University of Szeged, Piszkesteto Station (Konkoly), independently recovered P/2011 W2]

374P/2018 S1 (Larson) [Krisztian Sarneczky and Robert Szakats, University of Szeged, Piszkesteto Station (Konkoly), recovered P/2007 V1]

375P/2018 T1 (Hill) [Krisztian Sarneczky, University of Szeged, Piszkesteto Station (Konkoly), recovered P/2006 D1]

Cosmology: The History and Nature of Our Universe

Mark Whittle, Professor of Astronomy at the University of Virginia, has put together the most comprehensive and comprehensible treatment on the subject of cosmology that I have ever encountered.  Cosmology: The History and Nature of Our Universe, a series of 36 thirty-minute video lectures for The Great Courses (Course No. 1830), is a truly remarkable achievement.

Even though this course was released ten years ago in 2008, all of the material is still completely relevant.  This is the course on cosmology that I’ve always wanted but never had.  Enjoy!

Cosmology has come a long ways since I was a physics and astronomy student at Iowa State University from 1975-1980, and again in 1981, 1984, and 2000-2005.  I’m glad to see a course specifically about cosmology is now offered at a number of universities.  When I was an undergraduate student at ISU, it was unheard of.  The University of Wisconsin at Madison Department of Astronomy currently offers both an undergraduate and a graduate course in cosmology: Astronomy 335 – Cosmology, and Astronomy 735 – Observational Cosmology.  And the Department of Physics & Astronomy at Iowa State University now offers an undergraduate/graduate dual-listed cosmology course: Astro 405/505 – Astrophysical Cosmology.

When I retire in a few years, I would love to be a “fly on the wall” at the UW-Madison astronomy department.  Wonder if they could use an expert SAS programmer to help analyze the massive quantities of data they surely must have?  (Though the last time I interviewed for an astronomy job, at the McDonald Observatory in Texas, the interviewers had never heard of SAS but asked if I knew Python, which of course is what nearly everyone is looking for and using these days.  Tomorrow, it will be something else…).  In retirement, at the very least I would love to immerse myself in a few astronomy courses at UW-Madison.  Something to look forward to!

Effective Diameter of an Irregularly-Shaped Object

A diameter of a circle in 2D is defined as any straight line segment that intersects the center of the circle with endpoints that lie on the circle.  Since all diameters of a circle have the same length, the diameter is the length of any diameter.

Likewise, a diameter of a sphere in 3D is defined as any straight line segment that intersects the center of the sphere with endpoints that lie on the surface of the sphere, and the diameter is its associated length.

But how do we define the diameter of an irregularly-shaped object such as a typical asteroid or trans-Neptunian object?

For a well-characterized object such as 951 Gaspra—the first asteroid to be photographed up close by a spacecraft—we’ll see the dimensions of the best fitting triaxial ellipsoid given in terms of “principal diameters”.  In the case of Gaspra, that is 18.2 × 10.5 × 8.9 km.

In certain circumstances, however, it would advantageous to characterize an irregularly-shaped object using a single “mean diameter”.  How should we calculate that?

There are two good approaches, provided you have enough information about the object.  The first is to determine the “volume equivalent diameter” which is the diameter of a sphere having the same volume as the asteroid.  This is particularly relevant to mass and density.

For purposes of illustration only, let’s assume Gaspra’s dimensions are exactly the same as its best-fitting triaxial ellipsoid.  If that were true, the volume of Gaspra would be

V = \frac{{4\pi abc }}{3}

where V is the volume, and a, b, and c are the principal radii of the triaxial ellipsoid.

Plugging in the numbers 9.1 km, 5.25 km, and 4.45 km (half the principal diameters), we get a volume of 890.5 km3.

The volume equivalent diameter is

d_{vol} = \left (\frac{6V_{obj}}{\pi } \right )^{1/3}

where dvol is the volume equivalent diameter, and Vobj is the volume of the object.

Plugging in the volume of 890.5 km3 gives us a volume equivalent diameter of 11.9 km.

The second approach is to determine the “surface equivalent diameter” which is the diameter of a sphere having the same surface area as the asteroid.  This is most relevant to reflectivity or brightness.

Once again using our triaxial ellipsoid as a stand-in for the real 951 Gaspra, we find that the general solution for the surface area of an ellipsoid requires the use of elliptic integrals.  However, there is an approximation that is more straightforward to calculate and accurate to within about 1%:

S\approx 4\pi\left ( \frac{a^{p}b^{p}+a^{p}c^{p}+b^{p}c^{p}}{3} \right )^{1/p}

where S is the surface area, p ≈ 1.6075 can be used, and a, b, and c are the principal radii of the triaxial ellipsoid.

Once again plugging in the numbers, we get a surface area of of 478.5 km2.

The surface equivalent diameter is

d_{sur} = \left (\frac{S_{obj}}{\pi } \right )^{1/2}

where dsur is the surface equivalent diameter, and Sobj is the surface area of the object.

Plugging in the surface area of 478.5 km3 gives us a surface equivalent diameter of 12.3 km.

You’ll notice that the surface equivalent diameter for 951 Gaspra (triaxial ellipsoid approximation) is 12.3 km which is larger than the volume equivalent diameter of 11.9 km.  The surface equivalent diameter is apparently always larger than the volume equivalent diameter, though I leave it as an exercise for the mathematically-inclined reader to prove that this is so.

References
Herald, David (2018, October 23).  [Online forum comment].  Message
posted to https://groups.yahoo.com/neo/groups/IOTAoccultations/conversations/messages/65158

Thomas, P.C., Veverka, J., Simonelli, D., et al.: 1994, Icarus 107The Shape of Gaspra, 23-26.

Eclipsing Binaries

With the advent of relatively inexpensive CCD cameras, amateur astronomers with modest-sized telescopes are in an excellent position to contribute valuable scientific data to the astronomical community.  One type of object that can be very interesting and useful to observe is the eclipsing binary.  And there are a lot of them.

Due to a sometimes fortuitous alignment of the orbital plane of a binary star along or near our line of sight, one or both stars pass directly in front of the other periodically, and this type of object is known as an eclipsing binary.

The brightest eclipsing binary in our sky is Algol (Beta (β) Persei).  Known to vary in brightness since antiquity, astute ancient Arab astronomers gave Beta Persei the name “al Ghul” which, loosely translated, means “the Demon Star”.  Today, we know that Algol’s brightness variations are caused by a hot blue B8V star (Algol A) going behind and in front of its cooler and less massive but larger K0IV companion (Algol B).  Since the two stars orbit each other once every 2.867328 days (they are very close, separated by just a little over 5½ million miles), every 2 days, 20 hours, 48 minutes, and 57 seconds Algol B passes in front of much-brighter Algol A for a few hours, and the single point of light we see from Earth dims by 1.3 magnitudes.  This is the primary eclipse.  A secondary eclipse also occurs half a period before or after each primary eclipse.  When Algol A passes in front of Algol B, the brightness of the point of light we see drops by only 0.05 magnitude.  This shallow secondary minimum occurs because Algol B is not nearly as bright as Algol A.

Eclipsing binaries like Algol (which are close enough to each other to form an interacting pair) are interesting subjects for amateur astronomers to monitor.  Periods can change, phases can shift, and unexpected events can occur, such as when Dr. Jim Pierce (now Emeritus Professor of Astronomy at Minnesota State University in Mankato) and I were the first to observe ultraviolet flare events from the eclipsing binary V471 Tau at Iowa State University’s Erwin W. Fick Observatory in 1978.

So, how do you know when eclipses will occur, how deep they will be, and how long to monitor the star before, during, and after the event?  A great starting point is the Eclipsing Binary Ephemeris Generator by Shawn Dvorak which shows you a number of stars that will be in eclipse and observable from your location on any given night.  The Timing Database at Krakow (TIDAK), maintained by Jerzy M. Kreiner at the Mt. Suhora Astronomical Observatory in Poland, is another great source of eclipsing binary information.

A schedule, if you will, of eclipsing binary primary eclipses (like other astronomical events) is called an ephemeris.  Eclipsing binary ephemerides look like this one for Algol:

HJD = 2452500.21 + E × 2.867315

Here, HJD is the heliocentric Julian date of minimum light.  Julian date is a continuous count of days and fractions thereof elapsed since an arbitrary starting date of noon Universal Time (UT) on January 1, 4713 B.C.  The heliocentric Julian date removes the orbital motion of the Earth from the ephemeris calculations, centering the times of events on the Sun rather than the Earth.  An event could be observed to occur as much as 8.3 minutes earlier or later than calculated depending on where the Earth is in her orbit relative to the star.  The first number in the equation above, in this case 2452500.21, refers to the heliocentric Julian date of some arbitrary starting minimum.  The E stands for epoch, simply a consecutive integer count of successive minima, and the second number, in this case 2.867315, refers to the orbital period of the eclipsing binary in days.  The Kreiner website takes the chore out of choosing the appropriate value of E for the time you want to observe by calculating the HJDs (and corresponding Earth-based UT dates and times) of the eclipsing binary you choose over the next several days.

You should monitor a star before, during, and after the eclipse, so having a rough of idea of what object you should observe and when does not require you convert heliocentric Julian date to the Julian date at the telescope. However, any event times from data you record at the telescope must be converted to HJD for it to be useful.  There is an online tool to do this for you.  Of course, you not only need to know the UT date and time of an event, but also the equatorial coordinates (right ascension and declination) of the object you were observing to calculate the heliocentric Julian date.

We’re not even going to get into barycentric Julian date (BJD), or the fact that the distance between the Sun (or the barycenter of the solar system) and the eclipsing binary of interest is growing (radial velocity > 0) or shrinking (radial velocity < 0), and that this means that the period we measure is not exactly the same as the true orbital period of the system.  But it is very close.

Historical Astronomy Magazines Online and DVD

Excellent astronomy magazines have come and gone throughout the past several hundred years, and the time has come to start digitizing microfilm, microfiche, or printed copies of all these magazines and journals, and make them available at an affordable price to individuals and institutions on DVD and via the Internet.  First on my list? Popular Astronomy, which was published from 1893 until 1951 at Carleton College in Northfield, Minnesota, a worthy predecessor to Sky & Telescope.

Some of the volumes of Popular Astronomy are available online, thanks to the HathiTrust Digital Library:

Volume 1, 1893
Volume 2, 1894
Volume 3, 1895
Volume 4, 1896
Volume 5, 1897
Volume 6, 1898
Volume 7, 1899
Volume 8, 1900
Volume 9, 1901
Volume 10, 1902
Volume 11, 1903
Volume 12, 1904
Volume 13, 1905
Volume 14, 1906
Volume 15, 1907
Volume 16, 1908
Volume 17, 1909
Volume 18, 1910
Volume 19, 1911
Volume 20, 1912
Volume 21, 1913
Volume 22, 1914
Volume 23, 1915
Volume 24, 1916
Volume 25, 1917
Volume 26, 1918
Volume 27, 1919
Volume 28, 1920
Volume 29, 1921
Volume 30, 1922
Volume 31, 1923
Volume 32, 1924
Volume 33, 1925
Volume 34, 1926
Volume 35, 1927
Volume 36, 1928
Volume 37, 1929
Volume 38, 1930
Volume 39, 1931
Volume 40, 1932
Volume 41, 1933
Volume 42, 1934
Volume 43, 1935
Volume 44, 1936
Volume 45, 1937
Volume 46, 1938
Volume 47, 1939
Volume 48, 1940
Volume 49, 1941
Volume 50, 1942
Volume 51, 1943
Volume 52, 1944
Volume 53, 1945
Volume 54, 1946
Volume 55, 1947
Volume 56, 1948
Volume 57, 1949
Volume 58, 1950
Volume 59, 1951

The Anthropic Question

George F. R. Ellis writes in Issues in the Philosophy of Cosmology:

9.1 Issue G: The anthropic question: Fine tuning for life
One of the most profound fundamental issues in cosmology is the Anthropic question: why does the Universe have the very special nature required in order that life can exist?  The point is that a great deal of “fine tuning” is required in order that life be possible.  There are many relationships embedded in physical laws that are not explained by physics, but are required for life to be possible; in particular various fundamental constants are highly constrained in their values if life as we know it is to exist:

Ellis goes on to quote Martin Rees.

A universe hospitable to life—what we might call a biophilic universe—has to be special in many ways … Many recipes would lead to stillborn universes with no atoms, no chemistry, and no planets; or to universes too short lived or too empty to evolve beyond sterile uniformity.

Physics does not tell us anything (yet) about why the fundamental constants and other parameters have the values they do.  These parameters include, for example, the speed of light, the Planck constant, the four fundamental forces and their relative strengths, the mass ratio of the proton and the electron, the fine-structure constant, the cosmological density parameter, Ωtot, relative to the critical density, and so on.  And, why are there four fundamental forces?  Why not five?  Or three?

Also, why do we live in a universe with three spatial dimensions and one time dimension?  Others are possible—even universes with two or more time dimensions.

But it appears that only three spatial dimensions and one time dimension is conducive to life (at least life as we know it), as shown in the diagram above (Whittle 2008).

In fact, altering almost any of the parameters would lead to a sterile universe and we could not exist.  Is the universe fine-tuned for our existence?

Let’s assume for the moment it is.  Where does that lead us?

  1. As our understanding of physics advances, we will eventually understand why these parameters must have the values that they do. -or-
  2. We will eventually learn that some of these parameters could have been different, and still support the existence of life. -or-
  3. God created the universe in such a way that life could exist -or-
  4. We’re overthinking the problem.  We live in a life-supporting universe, so of course we find the parameters are specially tuned to allow life. -or-
  5. There exist many universes with different parameters and we just happen to find ourselves in one that is conducive to life. (The multiverse idea.)

#4 is the anthropic explanation, but a deeper scientific understanding will occur if we find either #1, #2, or #5 to be true.  #3 is problematic for a couple of reasons.  First of all, how was God created?  Also, deism has a long history of explaining phenomena we don’t understand (“God of the gaps”), but in time we are able to understand each phenomenon in turn as science progresses.

The anthropic explanation itself is not controversial.  What is controversial is deciding to what degree fine tuning has occurred and how to explain it.

In recent years, the multiverse idea has become more popular because, for example, if there were a billion big bangs and therefore a billion different universes created, then it should not be at all surprising that we find ourselves in  one with just the right set of parameters to allow our existence.  However, there is one big problem with the multiverse idea.  Not only do we have no physical evidence that a multiverse exists, but we may never be able to obtain evidence that a multiverse exists, due to the cosmological horizon problem1.  If physical evidence of a multiverse is not forthcoming, then in that sense it is not any better than the deistic explanation.

To decide whether or not there is only one combination of parameters that can lead to life we need to rule out all the other combinations, and that is a tall order.  Recent work in this field suggests that there is more than one combination of parameters that could create a universe that is hospitable to life (Hossenfelder 2018).

Thinking now about why our universe is here at all, it seems there are just two possibilities:

(1)  Our universe has a supernatural origin.

(2)  Our universe has a natural origin.

If our universe has a supernatural origin, then what is the origin of the supernatural entity (e.g. God)?  If, on the other hand, our universe had a natural origin (e.g. something was created out of nothing), didn’t something have to exist (laws of physics or whatever) before the universe came into existence?  If so, what created those pre-conditions?

In either case, we are facing an infinite regression.  However, we could avoid the infinite regression by stating that something has to exist outside of time, that is to say, it has no beginning and no ending.  But isn’t this just replacing one infinity with another?

Perhaps there’s another possibility.  Just as a chimpanzee cannot possibly understand quantum mechanics, could it be that human intellect is also fundamentally limited?  Are the questions in the previous two paragraphs meaningless or nonsensical in the context of some higher intelligence?

1We appear to live in a universe that is finite but very much larger than the region that is visible to us now, or ever.

References
G.F.R. Ellis, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
[http://arxiv.org/abs/astro-ph/0602280]

Sabine Hossenfelder, Lost in Math: How Beauty Leads Physics Astray (Basic Books, 2018).

M. J. Rees, Our Cosmic Habitat (Princeton and Oxford, 2003).

Mark Whittle, “Fine Tuning and Anthropic Arguments”, Lecture 34, Course No. 1830.  Cosmology: The History and Nature of Our Universe.  The Great Courses, 2008.  DVD.
[https://www.thegreatcourses.com/courses/cosmology-the-history-and-nature-of-our-universe.html]

Help Save WWV and WWVH!

Read these articles about the proposed elimination of radio time services WWV (Fort Collins, Colorado) and WWVH (Kekaha, Kauai, Hawaii) in 2019:

https://www.voanews.com/a/time-may-be-running-out-for-millions-of-clocks/4554376.html

https://www.nist.gov/fy-2019-presidential-budget-request-summary/scientific-and-technical-research-and-services-3

And please sign this petition by September 15:

https://petitions.whitehouse.gov/petition/maintain-funding-nist-stations-wwv-wwvh

WWV continuously broadcasts time signals at 2.5, 5, 10, 15, and 20 MHz, and WWVH does the same at 5, 10, and 15 MHz.

There are many uses for these radio stations.  For example, I have a shortwave radio in my observatory and use the WWV voice time broadcasts on 2.5, 5, and 10 MHz to make sure my GPS clock is properly synchronized, and also use it to set my computer clocks accurately and well as my wristwatch.

WWV and WWVH are an important and reliable “low tech” backup to the Global Positioning System (GPS) satellite constellation which can be used to derive accurate times.

Well over 50 million devices use the 60 kHz signal provided by WWVB to allow them to maintain accurate time, and eliminating this particular service would be devastating.  Whether or not shutting down WWVB is part of the proposed budget cuts remains to be seen.

These U.S. Government radio stations have been announcing accurate time since World War II.  We must do all we can to ensure their continued operation.

Black Hole Conundrums

Last night I re-watched the excellent two-hour PBS NOVA special Black Hole Apocalypse, and this time I jotted a few questions down.

  • Has Gaia DR2 improved our knowledge of the distance to the O-star black hole binary system Cygnus X-1 (6000 ly) and the mass of the black hole (15M)?
  • Are there any known pulsar black hole binary systems?
  • Could LIGO (and now Virgo in Italy) detect a stellar-mass black hole infalling into a supermassive black hole at the center of the Milky Way galaxy or another galaxy?
  • Do supermassive black holes play a role in galaxy formation?  If so, how does a supermassive black hole interact with dark matter?
  • Wouldn’t material infalling into a black hole undergo extreme time dilation and from our vantage point take millions or even billions of years to cross the event horizon?  If so, don’t all black holes—even supermassive ones—form from rapid catastrophic events such as core-collapse supernovae and black hole collisions?

Gaia DR2 (Gaia Data Release 2) has indeed measured the distance to the Cygnus X-1 system.  The “normal” star component of Cygnus X-1 (SIMBAD gives spectral type O9.7Iabpvar) is the 8.9-magnitude star HDE 226868.  Gaia DR2 shows a parallax of 0.42176139325365936 ± 0.032117130282281664 mas (not sure why they show so many digits!).

The distance to an object in parsecs is just the reciprocal of the parallax angle in arcseconds, but since the parallax angle is given in milliarcseconds, we must divide parallax into 1000.  This gives us a best-estimate distance of 2,371 parsecs or 7,733 light years.  Adding and subtracting the uncertainty to the parallax value and then doing the arithmetic above gives us a distance range of 2,203 to 2,566 parsecs or 7,186 to 8,371 light years.  (To get light years directly, just divide the parallax in millarcseconds into 3261.564.)

This is 20% to 40% further than the distance to Cygnus X-1 given in the NOVA program, and looking at the source for that distance (Reid et al. 2011) we find that the Gaia DR2 distance (7,186-8,371 ly) is outside the range given by Reid’s VLBA radio trigonometric parallax distance of 5,708-6,458 ly.  It remains to be seen what effect the Gaia DR2 distance, if correct, will have on the estimate of the mass of the black hole.

The estimate of the mass of the black hole in Cygnus X-1 is calculated using modeling which requires as one of its input parameters the distance to the system.  This distance is used to determine the size of the companion star which then constrains the scale of the binary system.  Because the Cygnus X-1 system is not an eclipsing binary, nor does the companion star fill its Roche equipotential lobe, traditional methods of determining the size of the companion star cannot be used.  However, once we use the distance to the system to determine the distance between the black hole and the companion star, as well as the orbital velocity of the companion star, we can determine the mass of the black hole.

Now, moving along to the next question, have any pulsar black-hole binary systems been discovered yet?  The answer is no, not yet, but the hunt is on because  such a discovery would provide us with an exquisite laboratory for black hole physics and gravity.  Something to look forward to!

Could LIGO ( and Virgo) detect a stellar-mass black hole infalling into a supermassive black hole at the center of the Milky Way galaxy or another galaxy?  No.  That would require a space-based system gravitational wave detector such as the Laser Interferometer Space Antenna (LISA)—see “Extreme mass ratio inspirals” in the diagram below.

http://gwplotter.com/

The above diagram illustrates that gravitational waves come in different frequencies depending on the astrophysical process that creates them.  Ground-based detectors such as LIGO and Virgo detect “high” frequency gravitational waves (on the order of 100 Hz) resulting from the mergers of stellar-mass black holes and neutron stars.  To detect the mergers of more massive objects will require space-based gravitational wave observatories (millihertz band) or pulsar timing arrays (nanohertz band) in the case of  supermassive black holes binaries within merging galaxies.  The future of gravitational wave astronomy looks very bright, indeed!

Do supermassive black holes play a role in galaxy formation?  Probably.  We are not yet able to explain how supermassive black holes form, especially so soon after the Big Bang.  Does dark matter play a major role?  Probably.  The formation of supermassive black holes, their interaction with dark matter, and their role in galaxy formation are all active topics or current research.  Stay tuned.

To succinctly restate my final and most perplexing question, “How can anything ever fall into a black hole as seen from  an outside observer?”  A lot of people have asked this question.  Here’s the best answer I have been able to find, from Ben Crowell:

The conceptual key here is that time dilation is not something that happens to the infalling matter.  Gravitational time dilation, like special-relativistic time dilation, is not a physical process but a difference between observers.  When we say that there is infinite time dilation at the event horizon we don’t mean that something dramatic happens there.  Instead we mean that something dramatic appears to happen according to an observer infinitely far away.  An observer in a spacesuit who falls through the event horizon doesn’t experience anything special there, sees her own wristwatch continue to run normally, and does not take infinite time on her own clock to get to the horizon and pass on through.  Once she passes through the horizon, she only takes a finite amount of clock time to reach the singularity and be annihilated.  (In fact, this ending of observers’ world-lines after a finite amount of their own clock time, called geodesic incompleteness, is a common way of defining the concept of a singularity.)

When we say that a distant observer never sees matter hit the event horizon, the word “sees” implies receiving an optical signal.  It’s then obvious as a matter of definition that the observer never “sees” this happen, because the definition of a horizon is that it’s the boundary of a region from which we can never see a signal.

People who are bothered by these issues often acknowledge the external unobservability of matter passing through the horizon, and then want to pass from this to questions like, “Does that mean the black hole never really forms?” This presupposes that a distant observer has a uniquely defined notion of simultaneity that applies to a region of space stretching from their own position to the interior of the black hole, so that they can say what’s going on inside the black hole “now.”  But the notion of simultaneity in GR is even more limited than its counterpart in SR.  Not only is simultaneity in GR observer-dependent, as in SR, but it is also local rather than global.

References
K. Liu, R. P. Eatough, N. Wex, M. Kramer; Pulsar–black hole binaries: prospects for new gravity tests with future radio telescopes, Monthly Notices of the Royal Astronomical Society, Volume 445, Issue 3, 11 December 2014, Pages 3115–3132, https://doi.org/10.1093/mnras/stu1913

Mingarelli, Chiara & Joseph W. Lazio, T & Sesana, Alberto & E. Greene, Jenny & A. Ellis, Justin & Ma, Chung-Pei & Croft, Steve & Burke-Spolaor, Sarah & Taylor, Stephen. (2017). The Local Nanohertz Gravitational-Wave Landscape From Supermassive Black Hole Binaries. Nature Astronomy. 1. 10.1038/s41550-017-0299-6.
https://doi.org/10.1038/s41550-017-0299-6
https://arxiv.org/abs/1708.03491

Jerome A. Orosz et al 2011 ApJ 742 84
https://doi.org/10.1088/0004-637X/742/2/84

Mark J. Reid et al 2011 ApJ 742 83
https://doi.org/10.1088/0004-637X/742/2/83

Brian C. Seymour, Kent Yagi, Testing General Relativity with Black Hole-Pulsar Binaries (2018)
https://arxiv.org/abs/1808.00080

J. Ziółkowski; Determination of the masses of the components of the HDE 226868/Cyg X-1 binary system, Monthly Notices of the Royal Astronomical Society: Letters, Volume 440, Issue 1, 1 May 2014, Pages L61–L65, https://doi.org/10.1093/mnrasl/slu002

Perseids Ahoy!

Already early this week you will see an occasional Perseid meteor gracing the sky, but next weekend the real show begins.  The absolute peak of this year’s Perseids is favorable to observers in North America, and with no moonlight interference we are in for a real treat—provided you escape cloudy weather.  I highly recommend “going mobile” if the weather forecast 24-48 hours before the peak night indicates less than ideal conditions at your location.

The Perseids this year are expected to peak Sunday night August 12/13.   Highest observed rates will likely be between 2 a.m. and 4 a.m. Monday, August 13.  Here’s a synopsis of the 2018 Perseids.

Fri/Sat
Aug 10/11
respectable activity
Sat/Sun
Aug 11/12
strong activity

Sun/Mon

Aug 12/13

very strong activity

Mon/Tue
Aug 13/14
strong activity
Tue/Wed
Aug 14/15
respectable activity

Largest Satellites of Our Solar System

Here is a table of the 12 largest satellites in our solar system.  In addition to the size of each satellite, its home planet, its median distance from that planet, and discovery information, its median distance from its home planet is given in terms of the median lunar distance from the Earth.  Remarkably, Pluto’s moon Charon is just 0.05 lunar distances from Pluto, only 19,591 km.  Only one other of the largest satellites orbits closer to its home planet than the Moon orbits around the Earth, and that is Neptune’s moon Triton at 92% of the Earth-Moon distance.  At the other end of the scale, Saturn’s moon Iapetus orbits Saturn over nine times further away than the Moon orbits the Earth.

Now let’s look at the orbital eccentricity of each of the largest moons, and the orbital inclination relative to the equator of its home planet.

Our familiar Moon is really an oddball: it has the greatest orbital eccentricity of all the largest satellites, and, with the exception of Triton and Iapetus, by far the greatest orbital inclination relative to the equator of its home planet.  Triton is the oddball among oddballs as it is the only large satellite in our solar system that has a retrograde orbit: it orbits Neptune in a direction opposite the planet’s rotation.  Iapetus has an orbital inclination relative to Saturn’s equator almost as much as the Moon’s orbital inclination relative to the Earth’s equator, but this anomaly can perhaps be forgiven because Iapetus orbits so very far away from Saturn.  Its orbital period is over 79 days.

Note that the Moon’s orbital inclination relative to the equator of the Earth varies between 18.33˚ and 28.60˚.  This occurs because the intersection between the plane of the Moon’s orbit around the Earth and the plane of the Earth’s orbit around the Sun precesses westward, making an entire circuit every 18.6 years.

Ganymede
Titan
Callisto
Io
The Moon
Europa
Triton
Titania
Rhea
Oberon
Iapetus
Charon