Luminosity of deceleration

In Astronomy, the luminosity of deceleration ( spin-down luminosity in English) is the energy radiated by a Pulsar consequently of its fast Rotation and sound high Magnetic field.

Formulate

A pulsar is a neutron star in fast rotation. Its magnetic Axis not being confondua with its Axis of rotation (like the Ground), there is emission of a electromagnetic Rayonnement in directions close to those of its magnetic poles. This radiation sweeps a cone in space because of rotation of pulsar. Its signal is thus received in the form of a short and periodic impulse, allowing of measurement its Period of rotation with a very high degree of accuracy (about 10 -12 ). This precision makes it possible to measure a weak lengthening of the period of rotation of the star, interpreted as being due to losses of energy, resulting probably partly from a magnetic dipolar Rayonnement.

Knowing the Period of rotation $P$ of pulsar, it is possible to determine its kinetic energy of rotation by the formula

E = \ frac {1} {2} I \ omega^2

where I is the Moment of inertia pulsar and ω its angular Velocity, connected to the period by the usual formula

\ Omega = \ frac {2 \ pi} {P}

The deceleration of pulsar results in a slow increase in the period during time, noted

\ dowry P

. The angular velocity of pulsar thus varies it also, according to the law

\ dowry \ Omega = - 2 \ pi \ frac {\ dowry P} {P^2}

The kinetic energy of rotation thus varies during time according to the law

\ dowry E = I \ Omega \ dowry \ omega

The luminosity of deceleration L is equal to the power dissipated by this process, that is to say

L = - \ dowry E = 4 \ pi^2 I \ frac {\ dowry P} {P^3}

Order of magnitude

The formula above utilizes the moment of inertia of pulsar. This one is not directly measurable, but can be predicted by the study of the structure of neutron stars. Calculations show that on the one hand the Masse M of a neutron star varies little from one object to another (between 1,2 and 1,5 solar Masse), and that the ray R of a neutron star decrease with its mass, also its moment of inertia, proportional to the product M R 2 it is not very depend on the mass. In practice, one assigns with pulsars a constant canonical value. Under these conditions, the luminosity of deceleration is strictly proportional to the quantity $\ dowry P/P^3$ .

Energy assessment

It is in general difficult to carry out a complete energy assessment of a pulsar and its environment. That is possible, at least partially for young pulsars still located at the threshold of the remanent of the Supernova which gave him birth. In this case, it is possible to consider the quantity of energy necessary to explain the dynamics of the remanent one. That remains however difficult, because such remanent (known as full, sometimes called Plérion S) has a relatively complex structure. In the case of the Pulsar of the Crab, whose formation goes back to a little less than 1000 years, one notices that the speed of expansion of the matter ejected during the explosion has today an high speed with that which would be necessary to give an account of an explosion being produced. Indeed, the expansion of the ejected matter is done, in the first phases, at constant speed. There thus exists a simple simple relation between the speed of expansion, the age and the physical size of the remanent one. This relation is not checked for the matter composing the matter ejected at the time of this event, forming the Nébuleuse Crab, of which the speed of expansion higher than is awaited. This dissension can be explained by the fact why the matter ejected by the explosion was gradually accelerated by the emission of radiation of central pulsar. Moreover, the luminosity of nebula is very important, and can be explained only by the presence of an important energy source in its center. With final, a minimum capacity of 1,5× 10 31 W (either close to 100 000 solar luminosities emitted uninterrupted since the explosion is necessary to explain the structure of this nebula. With a luminosity of deceleration of 1,5× 10 31 W, the pulsar of Crab is perfectly able to give an account of dynamics observed. Moreover, it is precisely by carrying out this kind of energy assessment that the Astrophysicien Italy N Franco Pacini was able to predict the existence of pulsar of Crab a few months before its discovery.

Lastly, there exist pulsars for which the luminosity of deceleration is lower than the total luminosity observed. It is the case of the pulsar class called abnormal pulsars X, whose luminosity radiated in the field of the X-rays exceeds of much the lumimnosity of deceleration. It is thus necessary to call upon another energy source that the deceleration of pulsar to explain the behavior of these objects. In fact, the dynamics of the superfluid interior at the same time and superconductive of these stars could give an account of the excess of emission observed in X.

See too

Deceleration of the pulsars
abnormal Pulsar X

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