**4. The formation of homochiral ice crystals**

#### **4.1 Sources of circularly polarized light**

One-handed circularly polarized light (CPL) from an astronomical source could play an essential role in the homochirality of ice crystals. Neutron stars have been suggested as possible sources of CPL [51]; however, CPL at visible and UV wavelengths has not been observed [52], and it is unlikely that a neutron star could encounter a molecular cloud where our solar system was born [53]. In contrast, CPL produced in star-forming regions is considered to be more important because CPL has been observed [54], and the possibility of a star-forming region and a molecular cloud occurring together is very large. Therefore, our discussion of the homochirality of ice crystals assumes that the CPL originated in a star-forming region.

#### **4.2 CPL flux in a molecular cloud**

We estimated the CPL photon flux in a molecular cloud based on a simplified model. We assumed two cases: i) a molecular cloud illuminated by the interstellar radiation field and ii) a molecular cloud illuminated by radiation from a nearby massive star. Case i) assumed an isolated star formation, while case ii) assumed a clustered star formation in a massive star-forming region. In both cases, we assumed a 0.1 pc diameter molecular cloud with a hydrogen density of 2 x 10<sup>5</sup> cm<sup>3</sup> . We used Weingartner and Draine's [55] standard dust extinction curve with an *R*<sup>V</sup> parameter of 5.5 to mimic dust in dense clouds [56].

For i), a standard interstellar radiation field model [57] was assumed for the incident radiation spectrum. For (ii), the incident radiation field was simulated by blackbody radiation from a B3-type star (mass = 8 solar mass, luminosity = 2.8 x 10<sup>3</sup> solar luminosity, and surface effective temperature = 2.3 x 10<sup>4</sup> K), which was located 0.1 pc away from the molecular cloud. IR observations have indicated that circularly polarized IR emissions with a degree of circular polarization of up to 20% extend in a 0.1–0.7 pc area in high/intermediate-mass star-forming regions [58, 59].

We assumed that the CPL was generated within the molecular cloud by the dichroic extinction of incident radiation [60]. A theoretical study predicted that dichroic extinction can produce a degree of circular polarization of up 10% in starforming clouds [61]. Here, we assumed that the radiation penetrating the molecular cloud resulted in a 10% degree of circular polarization.

The estimated flux of the CPL in the molecular cloud is summarized in **Figure 6**. On the surface of the molecular cloud, the photon flux reflects sources of radiation and does not change with wavelength. At the middle points (r = 0.025 pc), however, the photon flux decreases with decreasing wavelength. The intensities of the photon fluxes at 200 nm in the cases of i) and ii) were <sup>10</sup><sup>1</sup> and <sup>10</sup><sup>3</sup> photons cm<sup>2</sup> <sup>s</sup> 1 , respectively, suggesting that the photon flux of case i) was too weak for a photochemical reaction but that of case ii) was effective.

We noted that cosmic-ray-induced UV (CRUV) is a dominant source of UV photons in well-shielded regions [62, 63]. The total photon flux of CRUV is estimated to be 10<sup>4</sup> photons cm<sup>2</sup> s <sup>1</sup> [64], which is orders of magnitude higher than the estimated photon fluxes at the middle and core points in cases i) and ii). However, because

#### **Figure 6.**

*The wavelength dependence of the flux of circularly polarized light in the molecular cloud. For incident radiation sources, (A) and (B) assume an interstellar radiation field and blackbody radiation from a massive star, respectively. The respective colored marks represent the photon fluxes integrated over the following wavelength regions: Cyan, 90–150 nm; blue, 150–250 nm; green, 400–700 nm; magenta, 800–1200 nm; and red, 1000–2600 nm.*

CRUV photons are produced in dense regions, they would be irradiated to icy grains before experiencing dichroic extinction. Thus, we did not consider CRUV to be a source of CPL. If circularly polarized UV light plays an important role in the production of enantiomeric excess, then relevant photo processing would occur on the shallow molecular cloud surface, where the external UV overwhelms the CRUV. Because the volume fraction of the middle part of the molecular cloud is 0.88, we discuss the asymmetric nucleation of ice crystals using a curve at the middle points (r = 0.025 pc) in the following section.
