First of all I know there is a similar question here, but I feel is wasn't answered at all.

My question is that I have seen many texts which says that Radiative Flux is equal to the Irradiance of a star. In Carroll & Ostlie book "An Introduction to Modern Astrophysics" even say that:

And Wikipedia's Irradiance on Earth's surface says this:

Average annual solar radiation arriving at the top of the Earth's atmosphere is roughly 1361 W/m².

Following this I first I assume that Irradiance and Radiative Flux are the same thing, but when searching for Irradiance on Wikipedia says that:

Which means that Irradiance is Flux divided by Area, so Radiant Flux has units of J/s and Irradiance has units of W m^-2 which I remember from my Optics class, then again Carroll & Ostlie say that:

That doesn't mean if Irradiance is equal to Radiant Flux divided by Area, so F = I*A that would make Irradiance equal Luminosity / Area^2 ? In that case the bolometric magnitude should be calculated with the integral of Irradiance, not Luminosity nor Flux right?

Probably I'm making it complicated for myself and it's not that hard to understand. I'm just sharing my confusion with you guys, please help me with that question.

It looks to me like irradiant flux is the same as radiant flux is the same as irradiance, both are energy per second divided by area. That interpretation would seem to be consistent with everything you quoted. In more precise terms, these should all be "flux density", not "flux", because flux just means the amount of something per time, but that convention is never followed much any more.

I think the confusion you're having stems from the fact that there are different terms for the same phenomena being used in different fields, and some of these terms use the same underlying words, but in different, inconsistent ways.

Specifically, in astrophysics we most commonly use the following terms

• luminosity -- total power emitted by an object, with units of energy per time (e.g. J s$$^{-1}$$ = W);

• flux -- power crossing a specific area, with units of energy per time per area (e.g. W m$$^{-2}$$);

• intensity -- flux per solid angle (e.g. W m$$^{-2}$$ ster$$^{-1}$$).

The Carroll & Ostlie book you're referencing follows the astrophysical convention, but unintentionally confuses things by (sometimes) referring to flux as "radiant flux", probably unaware that this term means something different (i.e., luminosity) in radiometry. (And thus you get confused when you look thngs up on Wikipedia and encounter the radiometric terms.)

I'm guessing Carroll & Ostlie do this to remind the reader that this is flux of light as opposed to something else (Google search within the book shows a brief discussion of "convective flux" later on). In practice, astrophysicists almost always use just "flux" for light, and will use extra words to indicate if they're talking about flux of something else (e.g. dust grains, cosmic rays, neutrinos, or whatever).

For what it's worth, the astrophysical use of "flux" is consistent with the general mathematics/physics use of the term (e.g., "flux is defined as the rate of flow of a property per unit area, which has the dimensions [quantity] $$\cdot$$ [time]$$^{−1}$$ $$\cdot$$ [area]$$^{-1}$$. The area is of the surface the property is flowing "through" or "across". For example, the magnitude of a river's current, i.e. the amount of water that flows through a cross-section of the river each second, or the amount of sunlight energy that lands on a patch of ground each second, are kinds of flux."). So the radiometric term "radiant flux" is arguably a misuse of the word "flux", though I doubt radiometrists are losing sleep over this.