# Download PDF by Walter J. Maciel: Hydrodynamics and Stellar Winds: An Introduction

By Walter J. Maciel

Introduces hydrodynamics to undergraduate scholars in physics and astrophysics.

Stellar winds are a standard phenomenon within the lifetime of stars, from the dwarfs just like the solar to the purple giants and scorching supergiants, constituting one of many simple facets of contemporary astrophysics. Stellar winds are a hydrodynamic phenomenon during which circumstellar gases extend in the direction of the interstellar medium. This e-book offers an trouble-free advent to the basics of hydrodynamics with an program to the research of stellar winds. the rules of hydrodynamics have many different functions, in order that the ebook can be utilized as an creation to hydrodynamics for college students of physics, astrophysics and different comparable areas.

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**Example text**

4 Example: Accelerated Envelope Let us now consider the opposite situation of the previous example, in which the gravitational term is negligible compared to the pressure forces in a region of the envelope characterized by the width r. 90) We can roughly estimate the final velocity in the circumstellar envelope of a red giant star using the equation of state (see Eq. 91) where T ' 103 K is the average temperature in the envelope, and vf ' 4 km/s. This relation is simply a rough estimate, useful in order to obtain orders of magnitude.

13). 19) that is, the current density J can be obtained from the magnetic field B and viceversa. 21) From Eq. 21) we see that the term B 2 =8 corresponds to the magnetic pressure, introduced by the presence of the magnetic field. 21) is related to the tension along the magnetic field lines, that is, the magnetic field is associated to an isotropic pressure and also to a tension along the field lines. 1 Example: Solar Atmosphere As an example, we may compare the magnetic pressure B 2 =8 with the gas pressure in a few points in the solar atmosphere.

1 are closer to each other. 21) This condition is fulfilled when the interaction among the particles is small, or the gas is sufficiently rarefied. Let us consider some simple examples applied to astrophysical situations, particularly to expanding stellar envelopes, and show that in general the perfect gas hypothesis is a reasonable one, so that the ideal gas equation of state can be used as a first approximation. 21) increases as the particles are closer to each other, that is, when the gas density increases.