visible light - Why do we not see stars during the day?

As stars always propagate light, I was thinking that we should see them even during the day. I searched a lot and I find three questions related to the current one.

1. 
   
   

   Why do two beams of light pass through one another without interacting?

   
   


2. 
   

   Can photons pass through each other?

   
   


3. 
   

   Star visibility in outer space even during the day?

   
   

I couldn't get the answers given to these questions, but I could find some clues!

I guess beams of light pass through one another without interacting (and so we should see stars during the day) because of

1. 
   

   This sentence of Anna's answer to the first question: "Thus two light beams have no measurable interactions when crossing"

   
   


2. 
   

   The "Because" in the beginning of John Duffield's answer to the first question.

   
   


3. 
   

   This sentence of Anna's answer to the second question: "Thus we can say that for all intents and purposes photons scatter on each other without interacting"

   
   
   

In other hand, I guess we cannot see stars during the day because of this sentence of udiboy1209's answer to the third question: "if you can sustain the heat and the blinding radiation from the sun, you should be able to see stars when you are facing the sun"

May someone please clarify me by (as much as possible) simple explanations?

Answer

The daylight sky has a brightness of about magnitude 3 per square arcsecond. The brightest stars have an integrated intensity of about zeroth magnitude.

If your eyes had an angular resolution approaching 1 arcsecond then you would easily be able to see bright stars in the daylight sky - they would be about 10 times as bright as the sky. Unfortunately, the resolution of the eye is more like 1 arcminute. That means when comparing the starlight to the sky, the star is blurred over an area such that the contrast ratio with the sky is no longer large enough to discern it. However, even with this, if you knew exactly where to look, you could make out the very brightest stars, if your eyesight were good and this is obviously the case of bright objects like Venus, which are visible in the daytime sky.

If you look through a telescope (which increases collection of both starlight and daylight equally) then you can easily see stars. This is because the angular resolution of the telescope is around $1.22\lambda/D$, where $\lambda$ is the wavelength and $D$ the telescope diameter. A 10cm telescope can give you an angular resolution approaching 1 arcsecond (atmospheric conditions permitting) and thus a 3rd magnitude star has a similar brightness to the daytime sky through such a telescope.