What will happen if a ball of ice with the mass of sun is thrown into the sun? The question is a bit unrealistic with its circumstances but lets assume there is a bucket of ice cooled down to about absolute zero and is about 1000 km away (all around the sun) from sun and moving with v_0 = 1000km/sec, what will be if that all water with mass of sun  reaches the sun.
UPDATE
Basically I have read about this in gizmodo http://gizmodo.com/could-the-sun-be-extinguished-by-a-bucket-of-water-just-1669914928 but did not agreed , thats why I have decided to ask about this phenomena here, hoping to find out more precise answer
 A: If ice is "all around the sun" I fail to see how it can be moving at a velocity of 1000 m/s inwards. The mass of the sun is $2\cdot 10^{30}\mathrm{\;kg}$ and the radius $7\cdot 10^{8}\mathrm{\;m}$.
The thickness of a shell of ice with that inner radius and mass would be (assuming the usual density of ice of about 0.9x that of liquid water) approximately $10^8 \mathrm{\;m}$. That is probably sufficiently thick to withstand the gravitational attraction of the sun; certainly it will stop most solar radiation.
To take one gram of ice from absolute zero to melting takes roughly 273*4.2+334=1500 J. The sun puts out about $4\cdot 10^{26}$ W - assuming that the ice would absorb all that heat, it would take $8\cdot 10^9$ seconds to melt all the ice - a bit more than 200 years.
All that time the sun would be happily continuing to produce power - but I expect all life on earth would have ceased by the time it starts to shine again.
One obvious question - would the spherical "ice shell" be stable undertake the tremendous gravitational stress? Would it melt under the pressure? Would the pressure of the steam generated blow the water / ice outwards? It would be interesting to analyze those questions further. I suspect the over all conclusion - that a 100,000 km thick layer of water will "turn out the lights on Earth" will be unaltered by these details - because that water will still be between the Earth and the Sun, regardless of the distance and the phase.
update - a few additional thoughts.
First - the crushing strength of ice is quite low: no more than about 1000 psi (7 MPa) according to this USGS report. That is obviously many orders of magnitude smaller than the pressure on the inside of the 100,000 km thick ice shell. The average distance of the shell (mid point) is $7.5\cdot 10^8 \mathrm{\;m}$ from the center of the Sun, and will therefore experience a gravitational acceleration of 
$$a = \frac{GM}{R^2} = \frac{6.7\cdot 10^{-11} \cdot 2\cdot 10^{30}}{(7.5\cdot 10^8)^2} = 240 \mathrm{\;m/s^2}$$
Thus the pressure on the inner surface is roughly
$$P = \rho a t = 0.9E3 \cdot 240 \cdot 1E8 = 2.5 \cdot 10^{13} Pa = 22 TPa$$
An obvious question to ask: what happens to ice at that pressure? The phase diagram I could find (at this location) "only" goes up to 1 TPa, but it suggests that "really cold" ice does in fact remain solid at these pressures (unlike slightly warmer ice like we normally encounter, this would be "phase XI hexagonal" ice).

The next interesting question is that of steam formation. If we did drop a certain volume of ice into the sun (inside the closed ice shell), what happens to the pressure? Presumably the pressure would increase somewhat, but it really isn't relevant - because again, at the pressure you would have to generate to support the ice shell, the density of the water would have to be very high - in fact, it would no longer be a gas, but a solid (or at least with comparable density to a solid - we would be in a part of the phase diagram that is not given).
Finally, the question of the potential energy of the ice - and the impact of the release of this energy on the over all equation. For the purpose of this calculation, we can't just assume that things fall to the center of the sun - even photons that are generated at the center of the sun take a long time to diffuse to the surface, so we can assume the same is true for water. Let's assume therefore that the water simply falls to the surface. While the inside of the shell only falls 1000 km, on average the ice would fall 50,000 km. The force of gravity can be considered (to first order) constant over this distance, so the work done on 1 kg of ice would be 
$$W = F\cdot d = 240 N \cdot 5\cdot 10^{7} m = 12 GJ$$
The ice that fell from the inside of the shell (the first ice that melts) has less energy, namely
$$W = 240 N \cdot 10^6 m = 240 MJ$$
and I am for now ignoring the claim that the ice is moving at 1000 km/s (from the original question) as that would mean 1 kg of ice had a kinetic energy of $\frac12 m v^2 = 500 GJ$.
Whichever way you look at it, that is a very considerable amount of energy. It suggests that as the ice starts melting from the inside of the shell out, the water slamming into the surface of the sun will actually heat the sun up, speeding up the melting of the rest of the ice. The whole process will therefore take much less time than I initially estimated - there will be a runaway reaction. 
Just to calibrate us - all that ice slamming into the sun adds about 12 GJ/kg * 2E30 kg = 2.4E40 J to the sun. If none of that energy was transferred to the sun, it would lead to a temperature rise of the water of about 3 million degrees. Just from the potential energy (not the initial kinetic energy). That is much hotter than the sun - so there would be a runaway melt reaction.
So it seems that after a brief time when the sun is dark (much less than 200 years), it would shine very, very brightly? Still seems like an uncomfortable solar system.
UPDATE 2
One more thought. If the ice was a little bit less dense, so that structurally it can all fall to the surface of the sun, the 100,000 km thick layer of ice would (at an initial velocity of 1000 km/s) take just 100 seconds to fall into the sun. On average, each bit of ice would fall just 1000 km, and most of the energy dissipated would be the inital kinetic energy (500 GJ/kg - much more than the 240 MJ/kg gravitational energy).
This would briefly heat the surface of the sun to a temperature of more than 100 million degrees - hotter than the core of the sun. So in that case the sun might blink briefly (while the ice is still acting as a shield) - but very quickly, it would all be over for the earth. Of course at that temperature all kinds of fusion reactions would take place - and an immense amount of heat would radiate from the surface of the sun. 
It reminds me of Tom Lehrer's song - "We will all go together when we go"

There will be no more miserywhen the world is our rotisserieyes we will all fry together when we fry.

A: You can't have a "ball of ice with the mass of sun", because the ice in the middle of the ball wouldn't be strong enough to support the weight of the ice on top of it.  Instead, the ice would collapse under its own gravity.
This would cause the pressure and temperature inside the ball to increase until the water molecules that make up the ice would break up into a plasma of free oxygen and hydrogen atoms (possibly a bit after the ice first melted and then evaporated, although, honestly, I'm not sure if anyone knows how water behaves at such extreme pressures), and the hydrogen would start to fuse (presumably, given the abundant oxygen, via the CNO cycle).  This would increase the temperature and pressure at the core even further, and the increased pressure from the fusion reaction would finally stop the gravitational collapse.
Basically, if you had a ball of ice with the mass of sun, it would very quickly turn into a sun.  A rather odd sun, to be sure (at least if you're an astrophysicist), because of the absurdly high oxygen content, but a sun nonetheless.
Of course, the fact that your ball of ice has turned into a ball of glowing plasma doesn't stop you from dropping it into the sun.  What you get, if you do that, is basically a stellar collision.  Unfortunately, we still don't know much about the details of what happens in such collisions, because they're fairly rare and brief events, but one likely outcome is that the stars will merge and form a single, bigger and hotter star.  With lots of oxygen from the ice.
A: Short term, the ice would be vapourised as it fell. It would mix with the sun and form a bizarrely metal-rich star of twice the mass. Such a star would have a much more opaque envelope. This leads to (once an equilibrium is reached) the final star being much less luminous and cooler than a 2 solar mass star of more normal composition.
It would probably be cooler and less luminous than the Sun (and therefore much longer lived), but by just how much is difficult to say without a detailed stellar evolution calculation. The qualitative result is correct, but extrapolation of the usual formulae for main sequence stars to these bizarre metallicities cannot be quantitatively accurate.
An interesting complication could be gravitational settling and separation of oxygen and the lighter elements. I think there are various sources of turbulence (e.g. thermohaline mixing) that would prevent this, but I doubt this has been tested theoretically in a star with such crazy abundances.
Edit: The above would be true for a collision in freefall. I missed the point about 1000 km/s, which completely dominates the energetics of the whole scenario. This is enough energy to completely unbind the Sun (by an order of magnitude), so it is difficult to provide any non speculative answer.
A: The first thing you'll notice is that the Sun stops shining. It still produces heat and light, but everything is stopped by the thick layer of cold ice.
The Sun however is not completely cold. The core is still active, even more than before. You doubled the mass, so the Sun has a higher pressure and thus can fuse easily hydrogen atoms together. The net result is more heat produced and a shorter lifespan.
In the long run the heat will trickle to the surface and the Sun will shine again. I admit I haven't done any calculations, but I think it can take up to a few million years for the Sun to shine again.
Scientist on Earth could tell that the Sun is still active. When I said that everything is stopped, it wasn't completely accurate. Neutrinos aren't particularly affected by the new layer and they can be measured on Earth as before. Not that it can give any hope, if I guessed the time scale correctly. Almost every life form on Earth would be extinct long before the Sun starts shining again.
A: This would be a highly energenic event, a gravitational collapse in combination with the initial inward velocity of 1000km/s (which is greater than the escape velocity at the surface of the sun).  
There would be some type of nova event initially because the hydrogen already present in the sun would be compressed by the infalling new material, greatly enhancing fusion. Some material may be ejected and become a nebula in the nova event; rebouding energy would be a factor in addition to enhanced fusion, as in a core collapse supernova.  
The water would dissociate into atomic hydrogen and oxygen.
Of the material not ejected in the nova event, the oxygen would eventually form a core at the center of a star, with lighter elements (H, He) being a shell around the core. 
What happens from there depends upon the mass remaining.  
If the remaining mass is less than 1.39 solar masses (the Chandrasekhar limit), the star would eventually become an inert white dwarf star, with the oxygen core being sustained by electron degeneracy pressure and unable to undergo oxygen fusion. If more than 1.39 solar mass remain, the star could become a neutron star.
A: First and most important effect of having two sun sized bodies in our solar system very close to each other is that this new system will throw the planetary motion off its course, and there will be chaos(Noticeable chaos right at the moment when lets us assume the ice appeared 1000 km away from sun out of nowhere). Gravitational pull will be twice as much as it is now, Earth including all planets will start revolving in spiral instead of elliptical routes until they find "peace"(equilibrium between orbital velocity and gravitational pull) in new orbit. We might not be there to see the after effects of the collision.
But below is what i think will happen after collision:
Since water is nothing but 2 parts hydrogen and 1 part oxygen, And at Hydrogen is basic fuel  in fusion reaction occurring on sun. So basically sun will shine brighter as Hydrogen and Oxygen from water(Ice) will break down which result into increased amount of reactants and hence the rate of reaction(hydrogen + hydrogen -> Helium + Energy) will increase significantly.
