# A Superfluid Perspective on Neutron Star Dynamics

## Abstract

**:**

## 1. Neutron Star Superfluidity

## 2. The Essence of the Two-Fluid Model

#### 2.1. The Equations of Motion

#### 2.2. The Crust and the Chemical Gauge

#### 2.3. Thermal Excitations

## 3. Vortex Dynamics

#### 3.1. Mutual Friction

#### 3.2. Pulsar Glitches

#### 3.3. Superfluid Turbulence

## 4. Oscillations and Instabilities

#### Decoupling the Degrees of Freedom

## 5. Final Remarks

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**A sketch of the critical temperatures for superfluidity/superconductivity as a function of density. The indicated critical temperatures ${T}_{n}$ (black), ${T}_{{n}^{\prime}}$ (red), and ${T}_{p}$ (blue) represent neutron singlet, neutron triplet, and proton singlet pairing, respectively. The least “secure” of these critical curves is that for neutron triplet pairing. The edges of the coloured regions indicate the boundaries between the core and the inner crust (at just above half the nuclear saturation density) as well as the inner and outer crusts (at neutron drip; $\rho \approx 4\times {10}^{11}$ g cm${}^{-3}$). The main message is that superfluid aspects come into play already at a temperature close to ${10}^{10}$ K (about 1 MeV), very early in a neutron star’s life. The results provide a phenomenological representation of actual gap calculations within the BCS approximation, see [6] for details.

**Figure 2.**An indication of the dependence of the effective neutron mass—encoding the superfluid entrainment—on the baryon number density, ${n}_{\mathrm{b}}$. In the crust, the curve has been fitted to the data points from Chamel and collaborators [50,51,52] (shown as filled circles). The results in the core are obtained by assuming that the dynamical effective mass is equal to the Landau effective mass from nuclear physics (which should be a good approximation as the proton fraction is small).

**Figure 3.**Temperature profiles for a neutron star cooling model with superfluidity and no additional heating (thin black curves). Six (redshifted) temperature profiles are shown, representing ages ${10}^{-4}$ (top), 1, 100, 500, ${10}^{3}$, and ${10}^{4}\mathrm{yr}$ (bottom), respectively. The critical temperatures for superfluidity/superconductivity, as well as the different regions in the star, are also shown. The stellar model is the same as is Figure 1 (reproducing the results from [6].)

**Figure 4.**A sketch of the vectors involved in the representation of the induced flow for a curved vortex.

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Andersson, N.
A Superfluid Perspective on Neutron Star Dynamics. *Universe* **2021**, *7*, 17.
https://doi.org/10.3390/universe7010017

**AMA Style**

Andersson N.
A Superfluid Perspective on Neutron Star Dynamics. *Universe*. 2021; 7(1):17.
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2021. "A Superfluid Perspective on Neutron Star Dynamics" *Universe* 7, no. 1: 17.
https://doi.org/10.3390/universe7010017