Proca stars (arXiv:1508.05395) are everywhere regular, asymptotically flat self-gravitating solitons composed of complex, massive vector bosons, forming a macroscopic, star-sized, Bose-Einstein condensate. They have been suggested as a classical, dynamical model of exotic compact objects, black hole mimickers and dark matter candidates. In spherical symmetry, they are qualitatively similar to their scalar cousins, the standard (scalar) boson stars in all respects studied so far. Here we study the tidal deformability and the quadrupolar tidal Love numbers, both electric-type and magnetic-type, of spherically symmetric Proca stars. The equations for the perturbations are derived and the numerical values of the Love numbers for some concrete background solutions are computed. We observe that both Love numbers are qualitatively similar to the ones of the scalar boson stars; in particular, the electric-type (magnetic-type) quadrupolar Love numbers are positive (negative) for Proca stars. Quantitatively, for the same compactness, the electric and magnetic Love numbers in the Proca case are closer (in magnitude) than in the scalar case, with the electric Love numbers having a slightly larger magnitude than the magnetic ones.

中文翻译：

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Proca 明星的潮汐爱情数字

Proca 星 (arXiv:1508.05395) 到处都是规则的、渐近平坦的自引力孤子，由复杂的大质量矢量玻色子组成，形成宏观的、恒星大小的玻色-爱因斯坦凝聚体。它们被认为是奇异致密物体、黑洞模拟物和暗物质候选物的经典动力学模型。在球对称性方面，它们在性质上类似于它们的标量表亲，即迄今为止所研究的所有方面的标准（标量）玻色子星。在这里，我们研究了球对称 Proca 星的潮汐变形能力和四极潮汐洛夫数，包括电型和磁型。推导了扰动方程，并计算了一些具体背景解的洛夫数的数值。我们观察到，这两个洛夫数在性质上都与标量玻色子星的数相似；特别是，普罗卡星的电型（磁型）四极洛夫数为正（负）。从数量上讲，对于相同的致密性，Proca 情况下的电洛夫数和磁洛夫数比标量情况下的更接近（在数量上），其中电洛夫数的数量略大于磁洛夫数。