All but two of these dim constellations are, at least in part, visible from southern Arizona; Chamaeleon and Mensa require a trip south to see.
The southern constellation Mensa, the Table Mountain (declination -70° to -85°) is a ghost of a constellation, exhibiting no star brighter than magnitude 5.1. That’s 17 times fainter than Polaris! In fact, that’s fainter than all the stars of the Little Dipper asterism! Mensa does have one claim to fame, however. The Large Magellanic Cloud, satellite galaxy of our Milky Way galaxy, straddles most of the border that Mensa shares with Dorado, the Swordfish.
Mensa is far and away the dimmest constellation. But Mensa is a small constellation, bested in size by 74 of the 88 constellations. So perhaps it is not too surprising that a small constellation is less likely to harbor a bright star. Another measure of faint, perhaps, is to determine which of these twelve constellations with no star brighter than 4th magnitude is largest. That might be more remarkable, because one is less likely to find no bright stars in a large area of sky than in a small area of sky. By this measure, Camelopardalis, the Giraffe, wins without a doubt. Camelopardalis is the 18th largest constellation, and yet contains no star brighter than magnitude 4.0. It is that empty region you might have not noticed midway between Capella and Polaris, best viewed at evening twilight’s end during the month of February each year.
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.
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.
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
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
The Earth orbits the Sun once every 365.256363 (mean solar) days relative to the distant stars. The Earth’s orbital speed ranges from 18.2 miles per second at aphelion, around July 4th, to 18.8 miles per second at perihelion, around January 3rd. In units we’re perhaps more familiar with, that’s 65,518 mph at aphelion and 67,741 mph at perihelion. That’s a difference of 2,223 miles per hour!
As we are on a spinning globe, the direction towards which the Earth is orbiting is different at different times of the day. When the Sun crosses the celestial meridian, due south, at its highest point in the sky around noon (1:00 p.m. daylight time), the Earth is orbiting towards your right (west) as you are facing south. Since the Earth is orbiting towards the west, the Sun appears to move towards the east, relative to the background stars—if we could see them during the day. Since there are 360° in a circle and the Earth orbits the Sun in 365.256363 days (therefore the Sun appears to go around the Earth once every 365.256363 days relative to the background stars), the Sun’s average angular velocity eastward relative to the background stars is 360°/365.256363 days = 0.9856° per day.
The constellations through which the Sun moves are called the zodiacal constellations, and historically the zodiac contained 12 constellations, the same number as the number of months in a year. But Belgian astronomer Eugène Delporte (1882-1955) drew up the 88 constellation boundaries we use today, approved by the IAU in 1930, so now the Sun spends a few days each year in the non-zodiacal constellation Ophiuchus, the Serpent Bearer. Furthermore, because the Earth’s axis is precessing, the calendar dates during which the Sun is in a particular zodiacal constellation is gradually getting later.
Astrologically, each zodiacal constellation has a width of 30° (360° / 12 constellations = 30° per constellation). But, of course, the constellations are different sizes and shapes, so astronomically the number of days the Sun spends in each constellation varies. Here is the situation at present.
Sun Travel Dates
Jan 19 through Feb 16
Feb 16 through Mar 12
Mar 12 through Apr 18
Apr 18 through May 14
May 14 through Jun 21
Jun 21 through Jul 20
Jul 20 through Aug 10
Aug 10 through Sep 16
Sep 16 through Oct 31
Oct 31 through Nov 23
Nov 23 through Nov 29
Nov 29 through Dec 18
Dec 18 through Jan 19
The apparent path the Sun takes across the sky relative to the background stars through these 13 constellations is called the ecliptic. A little contemplation, aided perhaps by a drawing, will convince you that the ecliptic is also the plane of the Earth’s orbit around the Sun. The Moon never strays very far from the ecliptic in our sky, since its orbital plane around the Earth is inclined at a modest angle of 5.16° relative to the Earth’s orbital plane around the Sun. But, relative to the Earth’s equatorial plane, the inclination of the Moon’s orbit varies between 18.28° and 28.60° over 18.6 years as the line of intersection between the Moon’s orbital plane and the ecliptic plane precesses westward along the ecliptic due to the gravitational tug of war the Earth and the Sun exert on the Moon as it moves through space. This steep inclination to the equatorial plane is very unusual for such a large moon. In fact, all four satellites in our solar system that are larger than our Moon (Ganymede, Titan, Callisto, and Io) and the one that is slightly smaller (Europa) all orbit in a plane that is inclined less than 1/2° from the equatorial plane of their host planet (Jupiter and Saturn).
Since the Moon is never farther than 5.16° from the ecliptic, its apparent motion through our sky as it orbits the Earth mimics that of the Sun, only the Moon’s angular speed is over 13 times faster, completing its circuit of the sky every 27.321662 days, relative to the distant stars. Thus the Moon moves a little over 13° eastward every day, or about 1/2° per hour. Since the angular diameter of the Moon is also about 1/2°, we can easily remember that the Moon moves its own diameter eastward relative to the stars every hour. Of course, superimposed on this motion is the 27-times-faster-yet motion of the Moon and stars westward as the Earth rotates towards the east.
Now, take a look at the following table and see how the Moon’s motion mimics that of the Sun throughout the month, and throughout the year.
——— Moon’s Phase and Path ———
New = New Moon
near the Sun
FQ = First Quarter
90° east of the Sun
Full = Full Moon
180°, opposite the Sun
LQ = Last Quarter
90° west of the Sun
= crosses the celestial equator heading north
= rides high (north) across the sky
= crosses the celestial equator heading south
= rides low (south) across the sky
So, if you aren’t already doing so, take note of how the Moon moves across the sky at different phases and times of the year. For example, notice how the full moon (nearest the summer solstice) on June 27/28 rides low in the south across the sky. You’ll note the entry for the “Jun 21” row and “Full” column is “Low”. And, the Sun entry for that date is “High”. See, it works!
Fermilab is a name well known to all physicists. When I was an astrophysics undergraduate student at Iowa State University in Ames, Iowa in the mid-to-late 1970s, I remember that several members of our large high energy physics group made frequent trips to Fermilab, including Bill Kernan and Alex Firestone. At the time, it was the best place in the world to do high energy physics. What is high energy physics? Basically, it is the creation and study of new and normally unseen elementary particles formed by colliding subatomic particles into one another at very high velocities (kinetic energies).
On Sunday, March 4, a group of us from the Iowa County Astronomers met up at Fermilab for an afternoon tour of this amazing facility. We were all grateful that John Heasley had organized the tour, and that Lynda Schweikert photo-documented our visit.
Our afternoon began with an engaging talk by Jim Annis, Senior Scientist with the Experimental Astrophysics Group: “Kilonova-2017: The birth of multi-messenger astronomy using gravitational waves, x-rays, optical, infrared and radio waves to see and hear neutron stars”. Here he is showing a computer simulation of an orbiting pair of neutron stars coalescing, an event first observed by the LIGO and Virgo gravitational wave detectors on 17 August 2017 (GW170817), and subsequently studied across the entire electromagnetic spectrum.
One of the amazing factinos I remember from his talk: even though neutrinos were not directly detected from the GW170817 event, the matter in colliding neutron stars is so dense that neutrinos push material outwards in what is called a neutrino wind. Yes, these are the same neutrinos that could pass through a light year of solid lead and only have a 50% chance of being absorbed or deflected, and pass through your body at the rate of 100 trillion every second with nary a notice.
Even though CERN has now eclipsed Fermilab as the world’s highest-energy particle physics laboratory, Fermilab is making a new name for itself as the world’s premier facility for producing and studying neutrinos. This is a fitting tribute to Enrico Fermi (1901-1954)—after whom Fermilab is named—as Fermi coined (or at least popularized) the term “neutrino” for these elusive particles in July 1932.
Basic research is so important to the advancement of human knowledge, and funding it generally requires public/government funding because practical benefits are often years or decades away; therefore such work is seldom taken up by businesses interested in short term profit. However, as our tour guide informed us, the equipment and technology that has to be developed to do the basic research often leads to practical applications in other fields on a much shorter time frame.
Thoughts Inspired by Leon Lederman: A Footnote
I had the great privilege in October 2004 of attending a talk given by Leon Lederman (1922-), winner of the 1988 Nobel Prize in Physics and director emeritus of Fermilab. I listened intently and took a lot of notes, but what I remember best besides his charm and engaging speaking style was his idea for restructuring high school science education. The growing scientific illiteracy in American society, and the growth of dogmatic religious doctrine, is alarming. Lederman advocates that all U.S. high school students should be required to take a conceptual physics & astronomy course in 9th grade, chemistry in 10th grade, and biology in 11th grade. Then, in 12th grade, students with a strong interest in science would take one or more advanced science courses.
Teaching conceptual physics (and astronomy) first would better develop scientific thinking skills and lay a better groundwork for chemistry, which in turn would lay a better groundwork for biology. Whether or not a student chooses a career in science, our future prosperity as a society depends, in large part, on citizens being well-informed about science & technology matters that affect all of our lives. We also need to be well-equipped to assimilate new information as it comes along.
It is in this context that I was delighted to read Leon Lederman’s commentary, “Science education and the future of humankind” as the last article in the first biweekly issue of Science News (April 21, 2008). He writes:
Can we modify our educational system so that all high school graduates emerge with a science way of thinking? Let me try to be more specific. Consider Galileo’s great discovery (immortalized as Newton’s First Law): “An isolated body will continue its state of motion forever.” What could be more counterintuitive? The creative act was to realize that our experience is irrelevant because in our normal experience, objects are never isolated—balls stop rolling, horses must pull carts to continue the motion. However, Galileo’s deeper intuition suspected simplicity in the law governing moving bodies, and his insightful surmise was that if one could isolate the body, it would indeed continue moving forever. Galileo and his followers for the past 400 years have demonstrated how scientists must construct new intuitions in order to know how the world works.
I’d like to take Lederman’s comments one step further. Whether it be science, politics, economics, philosophy, or religion, we must realize that most ignorance is learned. We all have blind spots you could drive a truck through. Our perceptions masquerade as truth but sometimes upon closer inspection prove to be faulty. Therefore, we must learn to question everything, accepting only those tenets that survive careful, ongoing scrutiny. We must learn to reject, unlearn if you will, old intuitions and beliefs that are harmful to others or that have outlived their usefulness in the world. We must develop new intuitions, even though at first they might seem counterintuitive, that are well supported by facts and that emphasize the greater good. We must, all of us, construct new intuitions in order to make our world a better place—for everyone.