Under the Sirian Sun

Under the Sirian Sun.

The search for planets on Sirius star system which lies at 2.64 parsecs (8.3 ly) from Earth has proven so far to be unfruitful. Over a period of over 1.5 centuries since the discovery of Sirius B in 1862, a white dwarf companion, many astronomers had hoped that the star would reveal its third companion, a brown dwarf , which has been projected to exist by gravitational perturbations as according to Devant et al(1).

Alvan Clark's discovery in 1862 of Sirius B was a watershed in the use of gravitational computations to infer presence of a companion. Now we have satellites to peer even more but still this star system has kept itself veiled from the discovery of its children.

I would posit that there are several reasons for the inability so far to detect planets on Sirius. These are:

1. Brightness of Sirius A causes too much 'noise' in the electronics.
2. The use of filters affects the system as well and any light from the planets are also filtered.
3. Focus is on a putative third star instead of possible planetary system.
4. Looking for transits across the star which is not detectable due to 1. and also the the line of sight may not correspond to the star's protoplanetary disc formed millions of years ago and aligned not to the Earth's point of view.
5. There is the possibility that the planets are in a polar orbit i.e. 90 degrees to our point of view, see ellipse fig.1.
6. the white dwarf with its immense gravity would have in its lifetime destroyed any planets that would have formed in the system
7. gravitational stability of the system indicates that planets are possible at certain locations see Devant(1), and figure 2.
8. The use of gravitational microlensing is recommended.
9. The launch in December 2013 of the Gaia spacecraft offers a good opportunity to look for the Einstein ring effect on Sirius.
10. Gaia will study 1 billion stars and take readings on every star every six seconds. This will enable a large number of planets to be detected as the Einstein time will have been in effect for many stars.

 Gaia spacecraft launched into solar orbit period of 180 days. For more information go to http://sci.esa.int/gaia/

In their paper, Thalmann et al(2) has stipulated that precision astrometry suffers from many insidious faults which result in errors. These include changes in differential atmospheric refraction from ground based systems, changes in pixel scale and orientation and other ambient conditions. Thalmann has also confirmed the absence of dust around Sirius B and this possibly indictates a planet sterile environment as far as the orbit of Sirius B is concerned.

Sirius and the “missing” planets.

The sketch of the ellipse (courtesy wikipedia) above indicates to an observer out in space that the star system of Sirius, has possibly a planet that swings past 2 stars. The small black square represents the planet(s) and the 2 blue rectangles Sirius A and B. The Y plane rectangle is Sirius B and the X plane one is Sirius A.

Assuming the Earth lies somewhere along or near the Y plane then it is very obvious that the planet cannot be seen as a transit feature as it is very close to the extremly luminous Sirius A.

Sirius B

Companion	α CMa B
Period (P)	50.090 ± 0.055 yr
Semi-major axis (a)	7.50 ± 0.04"
Eccentricity (e)	0.5923 ± 0.0019
Inclination (i)	136.53 ± 0.43°
Longitude of the node (Ω)	44.57 ± 0.44°
Periastron epoch (T)	1894.130 ± 0.015
Argument of periastron (ω) (secondary)	147.27 ± 0.54°

Courtesy wikipedia.

I would posit that the probability of life occurring near this white dwarf is quite unlikely as in reaching that stage of stellar evolution it has essentially destroyed any planets it had in the past. It has tremendous gravity and is only slightly larger than the Earth. If it has any planets they are likely to be captured from free-floating planets.

Further, Sirius B is an X-ray source unlike Sirius A which resembles more like our sun but is twice as large and more luminous.

α CMa A
Mass	2.02M☉
Radius	1.711R☉
Luminosity	25.4L☉
Surface gravity (logg)	4.33cgs
Temperature	9,940K
Metallicity [Fe/H]	0.50dex
Rotation	16 km/s
Age	2–3 × 108years
α CMa B
Mass	0.978M☉
Radius	0.0084 ± 3%R☉
Luminosity	0.026L☉
Surface gravity (logg)	8.57cgs
Temperature	25200K

Credit: NASA/SAO/CXC/McDonald Observatory

Sirius B is an X-ray source.

Gravitational microlensing and Sirius

With a white dwarf in tow the complexities of this system are many. The historical viewpoint that sometime in the very distant past, Sirius B went into a red giant phase and then collapsed into a white dwarf would indicate that the possibility of Sirius A being a captured star exists. Sirius A may have been captured along with its putative planets and some of these then settled into stable orbits that would not cause escape from or collisions with Sirius B.

Alternatively, accretion of stellar matter from the Sirius B or A stars may have resulted in the unique protoplanetary disc being formed at such alignments as to make it compatible with the combined gravitational impulses from both stars see Fig.2.

Hence this unique alignment is one that is unexpected. But in space, expect the unexpected.

The best possible option therefore to see the planets on Sirius is the use of gravitational microlensing which would at the appropriate angle provide theoretically up to 1000 times magnification of the planets brightness.(3)

Planets in the lensing zone can be detected from 1 to 4 AU from the main star(3).  
 I predict that there are planets within this region based on the 90% probability given by Devant(1) for a massive brown dwarf to exist. And, drawing from Kepler's laws the period would be about 5 years around the primary.

The expected brown dwarf is replaced by a system of planets as well as asteroid belts as in the case of the star Vega which so far seems to have 2 of these belts.

Mathematics of Microlensing.

As the maths is theoretically founded on some assumptions and to make it easier to understand, I have posted the equation below :

The angle theta represents the size of the Einstein ring and since the sensitivity of the Gaia instruments are reading to values of microarcseconds, then the microlensing events are recordable.

The einstein ring itself has been worked out to be about 2 AU and this means that it is easily observable provided the microlensing event takes place at the einstein time, which normally lasts for a few hours to several months.

Planets in a lensing zone normally around 1 to 4 AU from the primary are detectable.(3)

For the Sirius system, accretion of ejected material from the primary may have severely

affected planet formation in the proper plane because the white dwarf's gravity would have aligned the protoplanets so much off the normal ecliptic as to be not in the line of sight as seen from Earth.

With time, the planets form at angles that are severely off the ecliptic.

Numerical stability algorithms show that material is stable in Binary stars to about 3 AU from the primary as long as the inclination of the protoplanetary disc is around 60^°(4).

But this has not accounted for gravitational pertubations from white dwarf companions as in the case of Sirius.

Please do read my references for further details.

References:

1. Is Sirius a triple star? D.Benest and JL Duvent. Astron.Astrophys. 299, 621-628(1995).
2. Piercing the glare: A direct imaging search for planets in the Sirius system. 

   C Thalman et al. Astrophysical Journal Letters, 732:L34, May 10, 2011.
3. Detecting Earth-mass planets with gravitational microlensing. DP Bennett and Sun Hong Rhee. Astrophysical Journal 472:660-664, 1996 Dec 1^st.  
4. Discovery of a Jupiter/Saturn analog using gravitational microlensing. Gaudi et al.
   

   Science 319, 927 (2008).

    

For mathematics of gravitational microlensing please read :

Strong gravitational lensing: relativity in action.

Joachim Wambsganss,¹ and B Paczynski ²

¹Astronomisches Rechen-Institut, Zentrum f¨ur Astronomie der Universit¨at Heidelberg,

M¨onchhofstr. 12-14, 69120 Heidelberg, Germany email: jkw@uni-hd.de

²Visitor, Dept. of Astrophysical Sciences, Princeton University,Princeton, NJ 08540, USA.

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