Sirius and its planet SiriusAb.

The Planet Sirius Ab located 8.3 light years from Earth.

Geudes et al(2007) discusses the probability of exoplanets existing on the alpha Centauri system,which is closest to Earth at 4 light years, based on projections using a computer algorithm. [1]

In their paper are various mathematical algorithms that seem to predict over an extended period of millions of years the formation of planets that go on to stabilised orbits and with finite, rocky natures and orbits at various distances from the binary. The other companion, Proxima Centauri is not considered as the influence at 10,000AU is minor on the main pair.

In this paper, I use the projections of Guedes et al and include the Sirius star system which is binary, Sirius A being twice the mass of our Sun and Sirius B , a white dwarf companion, as massive as the Sun but about the size of the Earth. [2]

 Further, the system is a S-type where the planet orbits Sirius A only and not P-type.

For a P-type situation, the orbital mechanics would indicate a stabilised orbit at twice the separation of the binary pair and this amounts to 40 AU or more and this corresponds to being out of any habitable zone. Planets may exist at this distance but they have not been seen so far for nearby star systems. Sirius B has a closest approach distance of 7.5 AU and therefore any planet existing and orbiting around SiriusA would need to be much closer, say about 6 AU in order to be in a stable orbit not severely affected by the white dwarf.[5]

Alpha Centauri AB

The system is unique because both companions are sun-like stars with similar masses and no detectable planets as can be seen presently from Earth. Using the B companion, Guedes et al has gone on to collate probability of planet formation in the event of the formation of a protoplanetary disc, an embryonic solar system, that will go on to coalesce to form the planets.

I would suggest that in doing so, they have set a model on which my projections on the Sirian star system can be similarly used. But there are variations and complications. To avoid going into detailed orbital mechanics, I have simplified the approach, making it as least technical but nevertheless detailed enough for the professional astronomer to pursue for further study at will.

Complications

These are:

1. Sirius AB is a binary with a 50.09 year orbit of the white dwarf companion.
2. Sirius A is more luminous than the Sun and twice as massive.
3. Orbital stability considerations limit any planet formed near Sirius A to orbits which would not interfere with the returning white dwarf, Sirius B.[5]
4. This in itself means that no stable orbit or planet can exist that is suitable for life further than a certain distance from the Sirius A – the distance calculated from some papers indicate at least a separation from Sirius B by 1.5 AU.
5. Planets formed at Sirius A therefore can only be within the orbital distance from its parent at maximum of distance 6AU before serious perturbations result from Sirius B's gravitational pull.

The left figure indicates what an astronaut might see upon entering the Sirius system. The planet b orbits Sirius A whilst the orbit of Sirius B is located into the plane of the paper and the whole system then orbits around its barycenter.

Based on the projections of the paper by Guedes and Quintana, we can expect at least 1 earth analog planet for Sirius A. His paper indicates roughly the formation of bodies that are rocky at various distances from the Alpha- Centauri system and there is probability of an Earth analog which might be in the habitable zone of the star. I posit that 3 planets exist with their distances as shown in the image above. Only one planet,b, is in the habitable zone. 
The white dwarf has successfully cleared any debris resulting from planet formation.

Calculation of Habitable Zone for Sirius A

The calculations shown below are for the SiriusA system and are referenced from [4].

 

 where L is the stellar luminosity in solar units,T_eff is the stellar effective temperature in K units, in this case 9900K,T_s= 5700 K, a_i = 2.7619e-5, b_i = 3.8095e-9, a_o = 1.3786e-4, b_o = 1.4286e-9, r_is = 0.72, and r_os = 1.77. The L value for SiriusA is 25.4.

The habitable zonal exoplanets boundaries lie between both r values. The values after calculations are: ri of 2.705 AU and ro of 5.875AU respectively.

Calculation of orbital radius for planet SiriusAb

Based on an assumption that a planet exists on SiriusA and that it has a 5 year period around this star, we can determine if this theoretical planet can be in the habitable zone of the star and hence possibly have liquid water for life as we know to exist.

Using the Kepler's formula for orbital period of a body in elliptical motion

where T is period in years, a is semi-major axis and μ is standard gravitational parameter,we derive a value for a of 3.766AU for this planet.

The habitable zones distance (HZD) is given as the formula above,

where r is the distance of the exoplanet from the star in AU units and HZD is the HZD in HZU units. HZD values between -1 and +1 HZU may correspond to planets within the HZ.  

Based on the values we obtained for SiriusAb, we can punch this into the above equation and we get a value that is very close to 0. The actual value is -0.328.[4]
 A value greater than plus 1 indicates that it is out of the zone. But our planet seems to have just made it! From this reading it is quite a close value to Earth's, which has a value of -0.46.

Orbital resonances

Drawing from our own solar system, we have the inner planets having a resonance of 1:2:4 for Earth,Venus and Mercury. Gliese 876 with planets e,b and c are similarly in a 1:2:4 resonance.[6] It can be assumed, although prematurely' that a similar resonance does seem possible for SiriusA. Therefore I postulate the existence of at least 2 more planets with periods of 2.5 years, and 1.25 years on Sirius A and these can be called planets c and d respectively.[6] 

Planet SiriusAc is 2.37AU and planet SiriusAd is 1.5AU. The values are calculated from the formula from Kepler's 2nd Law.

The planetary systems showing Habitable Zones in green.
(Courtesy Astronomy Magazine 2014).

Life in High Light Intensity Environments

Any life in the system must be heavily screened by the presence of a thicker ozone layer as well as an X-ray deflection or scatterer.

The amount of UV given off by Sirius A would be very large and to protect the planet's ecosystem, a thicker atmospheric coat of ozone would be very important. A thick atmosphere would also shield the planet by scattering harmful radiation such as X-rays which will be at a peak every time the Dwarf companion returns every 40 years or so (period is 50.09 years). Sirius B is an X-ray source.

In order to prevent overheating of the planet, the presence of oceans and hence water will act as a heat sink as well as moderate the temperature of the planet. Any greenhouse gases will play a significant role in the heat cycle on the planet.

From this information it can be realized that the planet SiriusAb is therefore about 20 to 40 % larger than Earth.

Thermal infrared spectra of Venus, Earth, and Mars. The 9.6-micron band of ozone is a potential bioindicator. (From R. Hanel, NASA Goddard Space Flight Center.)[3]

At very high light intensities, we could expect that life would take several options in order to exist and these are:

1. The production of very strong pigmentation to prevent cellular damage by the star's intense radiation.
2. Going underground or deeper into seas to shield from harmful rays.
3. Production of special exostructures that would shield the organism.
4. DNA repair mechanisms that can repair damage and enhance protection in ways unknown to humans at present.
5. Cocoon life that would go into hibernation for years especially when the dark star companion, Sirius B, approaches. Its orbital period is 50.09 years. This means that upon its closest approach its time to swing past Sirius A could be in the region of a few years. This would be a “Dark Phase” in this planet's history as Sirius B is an X-ray source. 
    
   

   Presence of moons on this planet will result in significant shielding in the planetary ecosystem as this will limit the chaos caused by shifting tectonic plates as the white dwarf approaches as well as limiting tidal fluctuations be they magma or water.

   
   
   
   Theory becomes Dogma!

Many astrobiologists suffer from the Billion-year syndrome. Yes, its a billion or more years for a star to form a planetary system that can go on to produce possible life.

Were they there to see it? Just as the theory of evolution has now become a fact in most scientific circles because this makes the NO GOD NO MAN genesis all the more believable.

There is absolutely NO PROOF that the theory of evolution is fact. Just as there is absolutely no proof that a planet takes a billion years or more to form!

Planets form when conditions that favor formation are there. They can form in deep space without even a star present for light years. These are the rogue planets. There have been quite a few discovered so far. Were they from other star systems and were ejected out? Were they from a supernova explosion which cooled to reform a main pulsar possibly and then some planets? Theory again. Then let me make a good guess.

The Crab Nebula and Pulsars

Magnetar illustration

The Crab Nebula in Taurus, exploded in 1054 AD and has a pulsar present. It is no large imagination to realize that the seeds of this supernova have sown planetary debris which will have accumulated into planetesimals. I would urge all astronomers to look at this system and it will be confirmed that there are planets forming or already existing. 

This therefore will confirm that Planets do NOT take billions of years to form.

 Evidence from supernova explosions indicate that planets form geologically very soon after and there is evidence to suggest that the time period is in the  thousands of years! This will account for the existence of 2 billion planets as projected in some estimates. 

 In 2006, an  MIT scientist, using the Spitzer telescope, and colleagues discovered a planetary circumstellar disc orbiting a magnetar as shown above (courtesy wikipedia). The star went nova about 100,000 years ago and is about 13,000 ly from Earth.

REFERENCES

1. Formation and detectability of terrestrial planets around αCentauri B. Geudes et al(2007). Astrophysics Journal,679:1582-1587.2008 June 1st.
2. Piercing the glare: A direct imaging search for planets in the Sirius system. Thalman et al , Astrophysical Journal Letters, 732:L34(5pp), 2011 May 10^th.
3. Kasting, J. F., Whitmire, D. P., and Reynolds, R. T. (1993). Habitable zones around main sequence stars. Icarus, 101, 108-108.
4. Habitable Zone Distance (HZD) A habitability metric for exoplanets - Planetary Habitability Laboratory.
5. The ultimate cataclysm: the orbital(in)stability of terrestrial planets in
   exoplanet systems including planets in binaries.Elke Pilat-Lohinger. Intl Journal of Astrobiology8 (3): 175–182 (2009).
6. Rivera, Eugenio J.; Laughlin, Gregory; Butler, R. Paul; Vogt, Steven S.; Haghighipour, Nader; Meschiari, Stefano (June 2010). "The Lick-Carnegie Exoplanet Survey: A Uranus-mass Fourth Planet for GJ 876 in an Extrasolar Laplace Configuration"