THEY'RE CLOSING IN!!
------------------
John Pazmino
NYSkies Astronomy Inc
nyskies@nyskies.org
www.nyskies.org
2005 March 28
Introduction
----------
In April 2000 I wrote a historical piece about the star Porrima,
or gamma Virginis. I related its discovery as a double star and the
studies of its orbit over the centuries. I reissued it thru NYSkies in
April 2005 as a companion article. Please read that first, 'A star on
the move', as a prerequisite for this update here.
Porrima is now in the evening sky attaining a maximum altitude of
about 49 degrees in the course of the night. It'll be with us in the
evening sky thru late summer, when it recedes into twilight.
Some of us watched gamma Virginis when it was in the morning sky
since late fall of 2004, but the bulk of NYSkiers waited until March
for the more convenient hours of viewing.
Amazing star
----------
The 'A star on the move' piece has the detailed description of
gamma Virginis. Here I give a brief summary. It was first noticed as a
double star in 1689 but real study wasn't started until 1718. By 1800
Porrima was recognized as a true binary system, not just a chance
lineup of unrelated stars.
An orbit was first worked up in 1833, revealing that the two stars
in Porrima would round periastron in 1834. Periastron is analogous to
perigee or perihelion; it's the 'near' end of the orbit's major axis.
This event was closely observed. The stars swang so close, angularly,
that no telescopes of the era could resolve them. The stars appeared
to merge into a single dot! By reverse calculation in the 20th
century, periastron actually occurred in spring of 1836.
Facts and figures
---------------
Some catalog names for Porrima are
Aitken ADS 8630 Bayer gamma
Bonner D'g BD-00:2601 Boss GC 17170
Bright Star HR 4825, 4826 Flamsteed 29
Draper HD 110379, 110380 Hipparchos HIP 61491
Hubble GSC 4949-1113 Smithsonian SAO 138917
Struve STF 1870 P & P M PPM 400177
3rd Fundamtl Kat FK3 477 Tycho TYC 4949-1120-2
Washington WDS 12417-0127 Zodiacal ZC 1821
Catalogs may give data for only one component, a blend of the two,
or each separately.
The celestial parameters are, for epoch 2000:
Right ascension 12h 41.6s Declination -01d 26.9m
Ecliptic long 190.13 Ecliptic lat +02.79
Galactic long 297.77 Galactic lat +61.33
The two stars are nearly equal in size, brilliance, diameter, and
other properties as follows
diameter 2 Sun mass 2.1 Sun
output 4.6 Sun surf temp 7,100K
spectrum F0 lum class V (main seq)
tot app magn +2.7 ind app magn +3.4, +3.5
tot abs magn +2.4 ind abs magn +3.1, 3.2
Sun magn +5.2 dist 38.6ly, 11.8pc
Normal binary
-----------
Thruout most of the 20th century, when most of us began our
astronomy lifes, gamma Virginis was well separated, several arcseconds
apart, in even quite small telescopes. It was a favorite target for
spring and summer public starviewings.
Porrima was for the early 2000s a favorite star for occultations
by the Moon. It sits near the ecliptic about 60% from Denebola to
Spica. Each component suffers its own occultation, allowing for tight
bounds on their orientation and separation. The first such occasion so
exploited was in 1720 for the first good measurements of the pair.
We just ended a season of Porrima occultations but most of the
events were not visible from New York City. The next season begins in
2016 with the next City event in 2017:
UT date event
----------- ----------------
2003 Aug 03 previous occultation over NYC
2005 Jan 03 last occultation of old season
2016 Feb 25 first occultation of new season
2017 Jan 18 next occultation over NYC
Orbit
---
Orbits were calculated in 1908 and 1935. The latter, by Strand, is
still in wide circulation in reference books from the mid to late 20th
century. New orbits were issued by Heintz in 1990 and Soderhjeim in
1999. The latter gives orbit elements as follows
Period = 168.9y SMAxis = 3.68" Inclination = 148
AscNode = 37 PeriT = 1836.4 Excentricity = 0.89
ArgPeri = 257
From the Soderhjeim orbit comes this ephemeris of gamma:
Year dec dist ang dec dist ang dec dist ang dec dist ang
---- --- ---- --- --- ---- --- --- ---- --- --- ---- ---
2003 .00 0.87 236 .25 0.82 232 .50 0.76 228 .75 0.69 222
2004 .00 0.63 216 .25 0.56 208 .50 0.50 198 .75 0.43 185
2005 .00 0.38 168 .25 0.35 147 .50 0.35 124 .75 0.38 103
2006 .00 0.44 86 .25 0.51 73 .50 0.58 64 .75 0.65 56
2007 .00 0.73 50 .25 0.80 46 .50 0.87 42 .75 0.93 38
2008 .00 1.00 35 .25 1.06 33 .50 1.12 30 .75 1.18 28
2009 .00 1.24 26 .25 1.29 24 .50 1.35 23 .75 1.40 21
2010 .00 1.46 20 .25 1.51 19 .50 1.56 18 .75 1.61 16
The year is given in decimals. .00 is January 1st; .25, about
April 1st; .50, about July 1st; .75, about Oct 1st. 'Dist' is the
angular distance in arcseconds between the pair. 'Ang' is the direction
from the main, primary, star and the comes. North is 0; east, 90;
south, 180; west, 270.
Orbital parameters
----------------
Altho the names of the elements look familiar, the definitions are
quite different from the usual ones in solar system orbits. You have
to be versed in double star work to make proper use fo these figures.
The semimajor axis is given in arcseconds, not linear measure.
This is simply due to the initially uncertain or unknown remoteness of
the star.
The linear separation is obtained once the distance to the star is
known. It wasn't until the mid 1990s, quite ten years ago!, that clean
distance measures were in hand from the HIPPARCOS spaceprobe. Porrima
stands 38.6 lightyears, or 11.8 parsecs, away.
By the definition of a parsec, the linear equivalent of an angular
extent on the sky is
(lin sep in AU) = (ang sep in arcsec) * (dist in pc)
This gives the projected value, as if the two stars were placed flat
against the celestial sphere. It ignores the inclination of the orbit.
So, for Porrima at the start of 2005, we have
(lin sep) = (0.38 arcsec) * (11.8pc)
= 4.13 AU
The ascending node, argument of periastron, and inclination are
defined on the plane of the celestial sphere. There is no common base
plane for all binaries, such as the equatorial plane of the Milky Way.
Thus, you can not directly compare orbits among double stars like you
can with, say, planets or comets in the solar system.
Orbits and orbits
---------------
None of the orbits prove out! We can excuse the earlier
computations, but why are there problems with a star so well and
continuously monitored for over 250 years? The answer is partly in the
the observations of the 1830s. Porrima's orbit is strongly elongated,
like a long period comet. It spends most of its period near apoastron,
where the pair moves slowly for decades.
Near periastron, things get weird. Despite the valiant efforts of
the 1830s, the instruments and skills were too crude. There are no
firm measurements in the critical years surrounding the periastron. To
the early astronomers, the stars comgealed into one. Alas, like for a
comet, the section of orbit close to periastron is the most sensitive
to errors.
Be wary of articles still citing the Strand orbit from 1935. This
offers a periastron in 2008! If you're not with it, you may sleep off
the years until then and miss completely the periastron right now in
progress!!
Even the Soderhjeim calculations are already out of spec. The
closest separation is 0.35 arcsecond. Measurements in 2004 showed the
stars were nearer than 0.30 arcsecond! Such a small periastron, and a
well documented apoastron, pushes the excentricity to the Moon. The
extant orbits posit excentricity of 0.85 or so. It looks like it may
be as high as 0.92!
Proximity vs periastron
---------------------
Many authors treat these two as alternate terms for the closest
approach of the two stars. In the general case this is totally wrong.
The dip and strike and sweep of the orbit on the celestial sphere puts
the physical closest approach, periastron, away from the angular
closest approach, proximity. Think of a comet in our sky. Its smallest
angular separation from the Sun is not at all its perihelion passage.
We have to work with TWO orbits. The first is the apparent path on
the sky, which is the projection of the other, true, orbit in space.
The latter is not directly observable, unless by chance we happen to
view it face on from its pole.
Elements in binary star catalogs are always for the true orbit.
It takes a bit of fancy maths to convert the plotted apparent
orbit into a path in 3D space. This exercise occupied a whole weekend
in the age before home computers and calculettes. Today, I tickle a
handheld computer, while I type out this article, with a binary star
orbit calculator program. A couple pecks with the stylus and I can
play with gamma Virginis to my heart's content.
Due to the high excentricity of gamma Virginis and the as-yet
still fuzzy true orbit, proximity and periastron are near together,
within 1/10 year. The Soderhjeim orbit offers a periastron of 0.40
arcsec on 2005.30 and a proximity of 0.35 on 2005.37. Lo here the
details:
year proxim perias | year proxim perias
------- ------ ------ | ------- ------ ------
2005.28 0.3476 0.4049 | 2005.35 0.3453 0.4053
2005.29 0.3471 0.4048 | 2005.36 0.3452 0.4055
2005.30 0.3467 0.4048 | 2005.37 0.3452 0.4057
2005.31 0.3463 0.4048 | 2005.38 0.3452 0.4060
2005.32 0.3460 0.4049 | 2005.39 0.3453 0.4063
2005.33 0.3457 0.4050 | 2005.40 0.3454 0.4067
2005.34 0.3455 0.4051 | 2005.41 0.3456 0.4071
The 2005 periastron
-----------------
Some binary star enthusiasts, in the lack of a valid orbit, took
to brute comparison of the 1836 experience with theirs of the 1990s and
early 2000s. From this it appears that the periastron occurs in mid
May 2005 with a proximity of about 0.25 arcsecond.
As the stars closed up in the 2000s, they fell out of range of
ever larger home telescopes. For my own experience with a variety of
instruments of my own and at starviewings, I followed Porrima as two
stars thru early 2003. Then they merged in my totable scopes. By early
2004 I lost them in almost every home telescope that crossed my path.
Never the less, I was thrilled as the months rolled by that I could
see for myself two suns in dynamic motion.
In 2003 and 2004 gamma Virginis required not only major aperture
but also stable air and sharp eyesight. On a typical turbulent night
it was impossible to tell that the smeared blob had two stars in it.
By mid 2006 the stars are receding enough for the midsize scopes
to discern. Then year by year, the star returns to duplicity in ever
smaller telescopes. By the New York Super Bowl, in 2010, Porrima is a
close but resolvable star in 100mm scopes. By 2012, the New York
Olympics, it is a trivially easy binary in the smaller scopes. There
after, until the next periastron in 2174, gamma Virginis is a pleasing
pair to admire, along with others in the spring sky.
A star on the move
----------------
A typical binary star that is seen as two stars in home
telescopes has a period so long that during a lifetime there is little
motion of the components. This causes some observers to keep old
figures for the distance and orientation thruout their astronomy life.
The long period comes from the necessary immense linear separation of
the stars to be seen as two in small scopes. Kepler's laws and all
that, you know.
Porrima is one rare exception. Within a lifetime (provided it's
not centered around apoastron!) real spatial motion of stars can be
witnessed within a couple years. Near periastron the shift in position
is discernible within months, and, now, weeks. The downside is that
you will need some huge scope, like the largest Dobsons or a major
observatory.
By late 2006 more and more telescopes will start seeing the return
of the double Porrima. During this phase, the stars are still in
revolution, so they will continuously change their orientation. Be
sure to watch for that!
Observing tips
------------
Naively the stars at periastron should be resolvable in a scope of
480mm aperture, based on the (120)/(diam) rule. This is an ideal value
with the stars as perfect optical images. In fact, the atmosphere
never allows such perfect images. The stars may blur to a half to a
full arcsecond diameter, thoroly smearing them together.
It may be a challenge project to capture digital videos during
instants of good seeing and combine the best of the frames. This is
routinely done for planet and lunar pictures, so why not try it for
double stars?
When the stars start reproaching and become a pair in the
eyepiece, inspection should be made with some particular magnification
repeatedly to experience the widening separation at the same visual
scale. If you use various scopes and oculars, keep within 10% of this
nominal power.
The angular rotation is harder to appreciate because of field and
optical rotation. Unless you fix the field orientation, you won't know
which way the stars are turning. For sure, here's a star that can
justify a permanently set up rig.
I haven't heard of any ongoing observations from space
observatories. I expect at least a couple of poster or publicity shots
by Hubble, no? Same wish with the new supersize machines in Chile with
their adaptive optics.