# Rotational Disruption of Dust Grains by Radiative Torques in Strong Radiation Fields

Thiem Hoang, Le Ngoc Tram, Hyeseung Lee, Sang-Hyeon Ahn

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Thiem Hoang, Le Ngoc Tram, Hyeseung Lee, Sang-Hyeon Ahn. Rotational Disruption of Dust Grains by Radiative Torques in Strong Radiation Fields. Nature Astronomy, 2019, 3 (8), pp.766-775. 10.1038/s41550-019-0763-6. hal-01909596

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# Rotational disruption of dust grains by radiative torques in strong radiation fields

Thiem Hoang<sup>1,2*</sup>, Le Ngoc Tram<sup>1,3,4</sup>, Hyeseung Lee<sup>1</sup> and Sang-Hyeon Ahn<sup>1</sup>

Massive stars, supernovae, and kilonovae are among the most luminous radiation sources in the Universe. Observations usually show near- to mid-infrared (NIR–MIR, $\lambda \approx 1–5 \mu m$) emission excess from H II regions around young massive star clusters. Early-phase observations in optical-to-NIR wavelengths of type Ia supernovae also reveal unusual properties of dust extinction and dust polarization. The most common explanation for such NIR–MIR excess and unusual dust properties is the predominance of small grains (size $a \lesssim 0.05 \mu m$) relative to large grains ($a \gtrsim 0.1 \mu m$) in the local environment of these strong radiation sources. However, why small grains might be predominant in these environments is unclear. Here we report a mechanism of dust destruction based on centrifugal stress within extremely fast-rotating grains spun-up by radiative torques, which we term radiative torque disruption (RATD). We find that RATD can disrupt large grains located within a distance of about a parsec from a massive star of luminosity $L \approx 10^4 L_{\odot}$, where $L_{\odot}$ is the solar luminosity, or from a supernova. This disruption effect increases the abundance of small grains relative to large grains and successfully reproduces the observed NIR–MIR excess and anomalous dust extinction/polarization. We apply the RATD mechanism for kilonovae and find that dust within about 0.1 parsec would be dominated by small grains. Small grains produced by RATD can also explain the steep far-ultraviolet rise in extinction curves towards starburst and high-redshift galaxies, and the decrease of the escape fraction of Lyman $\alpha$ photons from H II regions surrounding young massive star clusters.

Massive (OB) stars are the most luminous stellar objects in the Universe, which can produce high luminosities of $L \approx 10^4–10^6 L_{\odot}$ over millions of years. Such a strong radiation source can have a substantial impact on the physical and chemical properties of gas and dust in the environment of the star. Observations usually show a NIR–MIR emission excess from H II regions surrounding young massive star clusters (YMSCs)<fnref n="1" />,². The NIR–MIR excess is explained by the presence of a large fraction of small grains ($a \lesssim 0.05 \mu m$) that are transiently heated to high temperatures (about 1,000 K) by ultraviolet photons (see ref. ³ and references therein). Such an explanation is difficult to reconcile with the fact that thermal sputtering is efficient in H II regions⁴, which can destroy small grains on a timescale of around $10^4$ yr, much shorter than the age of YMSCs. Therefore, the remaining question is how small grains can be rapidly replenished against thermal sputtering in H II regions.

Type Ia supernovae have been widely used as standard candles to measure the expansion of the Universe, owing to their stable intrinsic luminosity⁵. To achieve the most precise constraints on cosmological parameters, the effect of dust extinction on the intrinsic light curve of type Ia supernovae must be accurately characterized. Optical-to-near-infrared photometric observations of type Ia supernovae during the early phase (that is, within a few weeks after maximum brightness) reveal unusual properties of dust extinction, with unprecedentedly low values of the total-to-selective extinction ratio of $R_V \lesssim 2$ (refs. ⁶,⁷), much lower than the standard Milky Way value of $R_V \approx 3.1$ (ref. ⁸). Moreover, polarimetric observations also report unusually low wavelengths of the maximum polarization ($\lambda_{max} < 0.4 \mu m$) for several type Ia supernovae⁹,¹⁰. Numerical modelling of dust extinction¹¹ and polarization curves¹² towards individual type Ia supernovae demonstrate that the anomalous values

of $R_V$ and $\lambda_{max}$ can be reproduced by an enhancement in the relative abundance of small grains to large grains in the host galaxy.

Type II supernovae are considered the major source of dust formation¹³⁻¹⁶ in the early Universe where dust formation by AGB stars is not relevant¹⁷. Observational and theoretical studies show that grains in the early Universe essentially have small sizes of $a \lesssim 0.05 \mu m$ (ref. ¹⁸). Moreover, early-phase observations of individual type II-P supernovae (a special class of type II supernovae with an extended plateau in the light curve) also reveal anomalous values of $R_V \approx 1.4–1.5$ (refs. ¹⁹,²⁰), which requires an excess of small grains to resolve. Here we distinguish original dust probed by early-phase observations of supernovae from dust formed much more recently in the supernova ejecta observed at later stages, both of which might have large grains²¹⁻²³.

The previously known mechanisms of dust destruction²⁴ cannot explain why small grains are predominant along the lines of sight towards type Ia and type II-P supernovae, as revealed by early-phase observations. First, thermal sublimation, which is efficient in strong radiation fields of supernovae, would reduce rather than enhance the abundance of small grains²⁵,²⁶. Second, shattering by grain–grain collisions in supernova shocks occurs at a late stage, so that it cannot explain why early-phase observations already show the predominance of small grains¹⁰,¹². As we will see in Methods section ‘Comparison of RATD to other destruction mechanisms’, a mechanism based on grain–grain collisions induced by supernova radiation pressure¹² cannot reproduce an excess of small grains on a timescale of several months observed towards type Ia and type II-P supernovae.

Here we describe a mechanism of dust destruction based on centrifugal stress within extremely fast-rotating grains spun-up by radiative torques—the radiative torque disruption (RATD)

<footnote n="1">¹Korea Astronomy and Space Science Institute, Daejeon, Republic of Korea. ²Korea University of Science and Technology, Yuseong-gu, Daejeon, Republic of Korea. ³University of Science and Technology of Hanoi, VAST, Hanoi, Vietnam. ⁴Present address: SOFIA-USRA, NASA Ames Research Center, Moffett Field, CA, USA. *e-mail: thiemhoang@kasi.re.kr</footnote>
<figure><img src="image_2.png" /><figcaption>**Fig. 1** | Grain disruption size and disruption time versus cloud distance from the central source for massive stars and YMScs of different luminosity, assuming grain tensile strength $S_{max} = 10^9$ erg cm$^{-3}$. a, Grain disruption size versus cloud distance computed for the interstellar medium (blue lines) and H II regions (orange lines). Results obtained from an analytical formula in the absence of gas damping (equation (26) in Methods) are shown as black lines. The horizontal line at the top marks $a_{disr} = \bar{\lambda}/1.8$. b, Grain disruption time versus cloud distance computed for the interstellar medium and H II regions. The disruption time is short, below approximately one million years for YMScs of $L \approx 10^6-10^9$L$_{⊙}$.</figcaption></figure>

mechanism—which can successfully explain these observational puzzles. We also apply the RATD mechanism to study the feedback of kilonovae$^{27,28}$ on dust properties in the surrounding environments. An accurate description of dust extinction to kilonovae is needed to infer intrinsic colour and light curves, as well as a precise measurement of opacity caused by lanthanides in the kilonova ejecta$^{29}$.

## The dust destruction mechanism

**Rotational disruption by radiative torques.** A dust grain of irregular shape subject to an anisotropic radiation field experiences radiative torques as a result of differential scattering and absorption of incident photons$^{30-32}$.

For an average diffuse interstellar radiation field in the solar neighbourhood$^{33}$, irregular grains of effective size $a \approx 0.1$ µm can be spun-up to an angular velocity of $\omega_{RAT} \approx 10^6$ rad s$^{-1}$ by radiative torques$^{31,34}$. In strong radiation fields such as near a massive star or a supernova where the radiation energy density can be increased by a factor $U \gg 1$ from the average interstellar radiation field, grains can be spun-up to extremely fast rotation with

$$ \omega_{RAT} \approx 7.6 \times 10^{10} \gamma a_{-5}^{1.7} \bar{\lambda}_{0.5}^{-1.7} U_6^{1/3} \text{ rad s}^{-1} \quad (1) $$

for $a \lesssim \bar{\lambda}/1.8$, and

$$ \omega_{RAT} \approx 1.1 \times 10^{12} a_{-5}^{-1} \gamma \bar{\lambda}_{0.5}^{-1.7} U_6^{1/3} \text{ rad s}^{-1} \quad (2) $$

for $a > \bar{\lambda}/1.8$. Here $a_{-5} = a/(10^{-5}$ cm), $\gamma$ is the anisotropy degree of radiation, $\bar{\lambda}$ is the mean wavelength of the radiation field with $\bar{\lambda}_{0.5} = \bar{\lambda}/(0.5$ µm), and $U_6 = U/10^6$ (see Methods for details).

A centrifugal force applied to a spinning grain causes it to develop a centrifugal stress that tends to tear the grain apart. The centrifugal stress averaged over the surface parallel to the spinning axis is given by $S = \rho\omega^2 a^2/4$, with $\rho$ being the grain mass density (see Methods section ‘Centrifugal stress within a spinning grain’). When the centrifugal stress exceeds the maximum tensile strength of the grain material, $S_{max}$, the grain is instantaneously disrupted into small fragments. We call this mechanism radiative torque disruption (RATD).

The critical rotation rate above which the grain is disrupted can be obtained by equating the centrifugal stress $S$ to $S_{max}$, which yields

$$ \omega_{disr} = \frac{2}{a} \left( \frac{S_{max}}{\rho} \right)^{1/2} \approx 3.6 \times 10^9 a_{-5}^{-1} \bar{\rho}^{-1/2} S_{max,9}^{1/2} \text{ rad s}^{-1}, \quad (3) $$

where $\bar{\rho} = \rho/(3\text{gcm}^{-3})$ and $S_{max,9} = S_{max}/(10^9 \text{erg cm}^{-3})$.

The critical rotation rate depends on the grain tensile strength, which is uncertain for interstellar dust. Here, we take $S_{max} = 10^9 \text{erg cm}^{-3}$ as a typical value for compact grains and $S_{max} = 10^7 \text{erg cm}^{-3}$ for composite grains (see Supplementary Information section ‘Tensile strengths of grain materials’).

Owing to the rapid increase of $\omega_{RAT}$ and decrease of $\omega_{disr}$ with the grain size $a$ (equations (1) and (3)), we expect large grains to be destroyed by RATD, whereas small grains can survive in strong radiation fields. In the following, we will calculate the critical size of grain disruption by radiative torques and its required timescale in the strong radiation fields of massive stars, supernovae and kilonovae.

**Grain disruption in massive stars and YMScs.** For a given radiation field of constant bolometric luminosity $L$ and mean wavelength $\bar{\lambda}$, one can calculate $\omega_{RAT}$ for a grid of grain sizes, assuming the gas density ($n_H$) and temperature ($T_{gas}$) of the local environment. The disruption size, $a_{disr}$, is then obtained by comparing $\omega_{RAT}$ with $\omega_{disr}$. The time required to spin-up dust grains to $\omega_{disr}$ (that is, disruption time, $t_{disr}$) is calculated by equation (27) (see Methods for details). We calculate $a_{disr}$ and $t_{disr}$ for the physical parameters of the standard interstellar medium with $n_H = 30 \text{ cm}^{-3}$ and $T_{gas} = 100$ K, and an H II region with $n_H = 1.0 \text{ cm}^{-3}$ and $T_{gas} = 10^6$ K.

Figure 1a shows the grain disruption size as a function of the cloud distance for $L = 10^4-10^9$L$_{⊙}$ for the interstellar medium (blue lines) and H II regions (orange lines). The results obtained from an analytical formula (equation (26) in Methods) where the grain rotational damping by gas collisions is disregarded (see Supplementary Information section ‘Grain rotational damping’) are shown as black lines for comparison.

The disruption size $a_{disr}$ increases rapidly with increasing cloud distance and reaches $a_{disr} \sim \bar{\lambda}/1.8 \sim 0.16$ µm (marked by a horizontal line in Fig. 1a) at some distance. Beyond this distance, grain disruption ceases to occur, owing to the decrease of radiation energy
<table><caption>**Table 1 | Grain disruption size and disruption time for dust clouds at different distances from the radiation source**</caption><thead><tr><th rowspan="2">Sources d (pc)</th><th colspan="5">a<sub>disr</sub> (μm)</th><th colspan="5">t<sub>disr</sub> (days)<sup>a</sup></th></tr><tr><th>0.1</th><th>0.5</th><th>1.0</th><th>3.0</th><th>5.0</th><th>0.1</th><th>0.5</th><th>1.0</th><th>3.0</th><th>5.0</th></tr></thead><tbody><tr><td colspan="11"><strong>Case 1<sup>b</sup></strong></td></tr><tr><td>YMSC<sup>c</sup></td><td>0.013</td><td>0.019</td><td>0.022</td><td>0.029</td><td>0.033</td><td>114</td><td>2,864</td><td>11,457</td><td>103,109</td><td>286,416</td></tr><tr><td>Type Ia supernovae</td><td>0.014</td><td>0.021</td><td>0.083</td><td>ND</td><td>ND</td><td>5.15</td><td>17.3</td><td>64.03</td><td>ND</td><td>ND</td></tr><tr><td>Type II-P supernovae</td><td>0.014</td><td>0.025</td><td>0.10</td><td>ND</td><td>ND</td><td>1.14</td><td>30.52</td><td>198.3</td><td>ND</td><td>ND</td></tr><tr><td>SLSN</td><td>0.01</td><td>0.014</td><td>0.017</td><td>0.048</td><td>ND</td><td>0.07</td><td>1.78</td><td>7.22</td><td>75.87</td><td>ND</td></tr><tr><td colspan="11"><strong>Case 2<sup>d</sup></strong></td></tr><tr><td>YMSC</td><td>0.005</td><td>0.008</td><td>0.009</td><td>0.012</td><td>0.014</td><td>11</td><td>286</td><td>1,146</td><td>10,311</td><td>28,641</td></tr><tr><td>Type Ia supernovae</td><td>0.007</td><td>0.009</td><td>0.011</td><td>0.07</td><td>ND</td><td>2.37</td><td>7.05</td><td>11.69</td><td>48.42</td><td>ND</td></tr><tr><td>Type II-P supernovae</td><td>0.006</td><td>0.009</td><td>0.012</td><td>0.085</td><td>ND</td><td>0.11</td><td>2.85</td><td>11.64</td><td>127.31</td><td>ND</td></tr><tr><td>SLSN</td><td>0.003</td><td>0.007</td><td>0.008</td><td>0.01</td><td>0.011</td><td>0.0071</td><td>0.18</td><td>0.71</td><td>6.47</td><td>18.46</td></tr></tbody></table>

density (see Fig. 1). For $L=10^4$L⊙, which is typical for OB stars, we get $a_{disr} \approx 0.1$ µm for $d \approx 1$ pc for the interstellar medium. For more luminous stars of $L=10^6$L⊙, $a_{disr} \approx 0.1$ µm for $d \approx 10$ pc (see dashed line). For a YMSC of $L=10^9$L⊙, we obtain $a_{disr} \approx 0.05$ µm for $d \approx 30$ pc and $a_{disr} \approx 0.02$ µm for $d \approx 1$ pc (see also Table 1).

For a given L, the value of $a_{disr}$ for the interstellar medium and H II regions is similar at small distances. At large distances from the source, $a_{disr}$ for H II regions is larger than for the interstellar medium and for the case without gas damping (black lines in Fig. 1). This is because at large distances, rotational damping by gas collisions becomes dominant over the rotational damping by infrared emission, resulting in the increase of $a_{disr}$ with the gas damping rate, which scales as $n_{\text{H}} T_{\text{gas}}^{1/2}$ (equation (14) in Methods). This can also be seen through the increase in the critical radiation strength required to disrupt grains with the gas damping rate (see Methods and Supplementary Fig. 1).

Figure 1b shows the disruption time $t_{disr}$ of $a=a_{disr}$ grains as a function of the cloud distance for the different values of L. The disruption time increases rapidly with the cloud distance and decreases with increasing L. For grains at 10 pc, we obtain $t_{disr} \approx 50-30,000$ yr for $L \approx 10^9-10^6$L⊙. This disruption time is much shorter than the age of YMSCs (a few million years).

**Grain disruption in supernovae and kilonovae.** For time-varying radiation sources such as supernovae and kilonovae, we first solve equation (12) to obtain the time-dependent angular velocity $\omega(t)$. We then compare $\omega(t)$ with $\omega_{disr}$ (equation (3)) to determine grain disruption size and disruption time (see more details in Methods and Supplementary Fig. 2).

Figure 2a–d shows $a_{disr}$ as a function of the cloud distance for supernovae and kilonovae, assuming a range of the grain tensile strength from $S_{max}=10^7-10^{11}$ erg cm$^{-3}$. For a given $S_{max}$, $a_{disr}$ increases rapidly with the cloud distance owing to the decrease of radiation strength U with d. Moreover, for a fixed distance, the disruption size increases rapidly with $S_{max}$. This is because larger grains experience stronger radiation torques and rotate faster (see equation (1)) such that the centrifugal stress can exceed the maximum tensile strength $S_{max}$. For $S_{max}=10^9$ erg cm$^{-3}$ (for example, compact grains), one obtains $a_{disr} \approx 0.1$ µm for a dust cloud at a distance of $d \approx 1$ pc. For a lower strength of $S_{max}=10^7$ erg cm$^{-3}$ (for example, composite grains; see Supplementary Table 1), large grains can be disrupted at large distances of $d \approx 4$ pc. The results for type II-P supernovae are similar to those for type Ia supernovae, but SLSNs can destroy large grains to farther distances owing to their stronger radiation intensity, as expected. The disruption by kilonovae is efficient within a short distance of $d \lesssim 0.1$ pc owing to their lower luminosity.

Figure 3a–d shows the disruption time $t_{disr}$ as a function of the disruption size $a_{disr}$ for supernovae, SLSNs and kilonovae. When the grain size increases to the critical value $a_{disr}$, the disruption time starts to decrease rapidly with increasing grain size as a result of stronger radiation torques (see equation (27) in Methods). Large grains ($a \gtrsim 0.1$ µm) are destroyed within 50 days from the type Ia supernovae explosion for $S_{max}=10^9$ erg cm$^{-3}$, and the disruption time becomes shorter, within 10 days, for $S_{max}=10^7$ erg cm$^{-3}$ (blue line in Fig. 3a). The disruption time for SLSNs (Fig. 3c) is shorter than that for type Ia and type II-P supernovae owing to the higher luminosity of SLSNs.

Table 1 lists the grain disruption size and disruption time (estimated for a typical grain size of $a=0.1$ µm) for the different cloud distances illuminated by the various radiation fields.

## Discussion

In Table 2, we compare the characteristic timescale of RATD with that of other destruction mechanisms, including grain–grain collisions and non-thermal sputtering induced by supernova radiation pressure¹² (see Supplementary Information section ‘Comparison of RATD to other destruction mechanisms’). The RATD mechanism is clearly far more efficient than other mechanisms in destroying large grains (that is, $a \gtrsim 0.1$ µm) in strong radiation fields of radiation strength $U \gg 1$.

**RATD reproduces small grains in H II regions around YMSCs.** Using the numerical results presented in Fig. 1a and in Fig. 4a, we illustrate the expected range of grain sizes and grain number density present in a H II region surrounding a YMSC of luminosity $L=10^7$L⊙ as a result of RATD. Large grains of $a>0.2$ µm are destroyed within a large distance of $d \approx 30$ pc from the source, producing smaller grains of $a \lesssim 0.08-0.2$ µm within a shell of $d \approx 10-30$ pc. Similarly, RATD destroys large grains of $a>0.08$ µm within a distance of 10 pc, increasing the abundance of small grains of $a \lesssim 0.04-0.08$ µm in a shell of $d \approx 1-10$ pc. Within 1 pc from the source, all large grains are destroyed to further increase the abundance of small grains of $a \lesssim 0.04$ µm. A more luminous cluster of $L=10^9$L⊙ can destroy grains of $a \gtrsim 0.02$ µm within approximately 1 pc (see Fig. 1a. Therefore, as a result of the destruction of large grains by RATD, the abundance of small grains is predicted to increase towards the central cluster, as illustrated in Fig. 4a.

The production of small grains by RATD can explain the NIR–MIR emission excess observed in H II regions around YMCSs²,³. If large grains are constantly formed in dense regions (for example, stellar winds and supernova ejecta) and injected into the interstellar medium, then it takes less than a million years (see Fig. 1b).

<footnote>SLSN, superluminous supernovae. ND, no disruption. <sup>a</sup>Estimated for $a=0.1$ µm. <sup>b</sup>$S_{max}=10^9$ erg cm$^{-3}$ (compact grains). <sup>c</sup>Results for luminosity $L=10^7$ L⊙. <sup>d</sup>$S_{max}=10^7$ erg cm$^{-3}$ (composite grains).</footnote>
<figure><img src="image_3.png" /></figure>

<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /><figcaption>**Fig. 2** | Grain disruption size versus cloud distance for the time-varying radiation sources, assuming different tensile strength $S_{max}$. a-d. Results obtained for type Ia supernovae, type II-P supernovae with $L=L_{SNI}$, SLSNs with $L=16L_{SNI}$ (where $L_{SNI}$ is the luminosity of a type II supernova) and kilonovae. The disruption size increases rapidly with increasing cloud distance, but it decreases with decreasing grain tensile strength.</figcaption></figure>

for RATD to destroy these grains, thus producing small grains. Moreover, RATD can explain the increase in the abundance of small grains relative to large grains toward the cluster centre, as observed in H II regions around massive stars³⁵ and YMCS (NGC 3603)³⁶,³⁷.

**RATD enhances small grains in the regions surrounding supernovae.** Figure 4b shows a schematic illustration of the size range and density of dust grains in a cloud surrounding a type Ia supernova due to RATD. The structure is similar to YMCSs, but the extent is smaller owing to the shorter shining time of type Ia supernovae. Large grains of $a \approx 0.08-0.2$ µm can be present within a shell of $d \approx 1-1.5$ pc. However, these large grains are destroyed within $d \approx 0.5-1$ pc, thus increasing the abundance of small grains of $a \lesssim 0.02-0.08$ µm. Below $d \approx 0.5$ pc, large and small grains are destroyed, such that only very small grains of $a < 0.02$ µm are present.

Numerous works suggest that the anomalous values of $R_V$ observed toward type Ia supernovae$^{6,38}$ are produced by the predominance of small grains in the host galaxy$^{39}$.

The inverse modelling for both extinction and polarization curves demonstrates that grains are essentially small, with the peak mass distribution at $a_{peak} \approx 0.07-0.08$ µm for supernovae SN 1986G, SN 2006X and SN 2014J (ref. ¹²). A detailed modelling of the extinction curve for SN 2014J (ref. ⁴⁰) yields $a_{peak} \approx 0.04-0.06$ µm. Moreover, maximum cutoff values of the power-law size distribution of $a_{max} \approx 0.094$ µm and 0.057 µm can be inferred for type Ia supernovae with $R_V=1.5$ and $R_V=1$ (ref. ¹¹). One can see from Fig. 4b that the RATD mechanism can successfully produce such small grains if the dust cloud is located at distance $d \approx 1$ pc, assuming compact grains of $S_{max} = 10^9$ erg cm⁻³. For composite grains of

$S_{max} = 10^7$ erg cm⁻³, the dust cloud that contains such small grains can be farther from the explosion, at $d \approx 3$ pc.

In the RATD paradigm, large grains ($a \gtrsim 0.1$ µm) in a cloud of distance $d < 2-3$ pc are destroyed first by RATD, followed by destruction of smaller grains (see Fig. 3). As a result, the colour excess ($E(B-V)$) of type Ia supernovae is expected to increase with time owing to the increase of small grains if there are dust clouds located within $d < 2-3$ pc. This poses a critical challenge for inferring accurate intrinsic light curves of type Ia supernovae because type Ia supernovae also experience intrinsic colour variation⁴¹.

A time-varying colour excess has already been found towards many highly reddened type Ia supernovae with anomalous $R_V$ values$^{42}$. Those authors estimated the distance of dust clouds $d \approx 0.7-18$ pc for 13 out of the 15 type Ia supernovae with time-varying $E(B-V)$. We note that their cloud distances are estimated assuming the standard grain size distribution of the Milky Way. The inclusion of the smaller grain size cutoff due to RATD is expected to reduce the cloud distance (M. Bulla, personal communication).

**RATD can modify dust properties around kilonovae.** In Figs. 2 and 3, we showed that large grains within 0.1 pc of the merger location can be destroyed by kilonovae through RATD. Therefore, the surrounding environment should be dominated by small grains. The time-varying colour excess due to RATD would be a critical problem for deriving the intrinsic colour of kilonovae because the latter also varies with time$^{43}$.

While large grains can be destroyed by kilonovae, small grains receiving weaker torques can be spun-up to suprathermal rotation and be aligned with the magnetic field by radiative torques$^{12}$.
<figure><img src="image_7.png" /><figcaption>**Fig. 3** | Disruption time versus grain size for the time-varying radiation sources, assuming different tensile strength $S_{max}$. a-d. Results obtained for type Ia supernovae, type II-P supernovae with $L = L_{SNII}$ for a dust cloud at 1 pc, SLSNs with $L = 16L_{SNII}$ for a dust cloud at 3 pc and kilonovae with a dust cloud at 0.02 pc. The disruption time decreases rapidly with increasing grain size and with decreasing tensile strength. Large grains can be rapidly destroyed within 100 days, but the smallest grains are not disrupted and $t_{disr}$ is set to be 200 days.</figcaption></figure>

<table><caption>**Table 2** | Characteristic timescales of dust destruction by different mechanisms</caption><thead><tr><td>Mechanisms</td><td>Timescales (yr)</td></tr></thead><tbody><tr><td>RATD</td><td>1.0a<sub>-5</sub><sup>-0.7</sup>χ<sub>0.5</sub><sup>1.7</sup>U<sub>6</sub><sup>-1</sup>S<sub>max,9</sub><sup>1/2</sup></td></tr><tr><td>Thermal sputtering</td><td>9.8 × 10<sup>3</sup>a<sub>-5</sub>n<sub>1</sub><sup>-1</sup>T<sub>6</sub><sup>-1/2</sup>(0.1W<sub>sp</sub>)</td></tr><tr><td>Non-thermal sputtering</td><td>5.7 × 10<sup>3</sup>ρa<sub>-5</sub>n<sub>1</sub><sup>-1</sup>v<sub>drift,3</sub><sup>-1</sup>(0.1W<sub>sp</sub>)</td></tr><tr><td>Grain-grain collision</td><td>7.6 × 10<sup>4</sup>ρa<sub>-5</sub>n<sub>1</sub><sup>-1</sup>v<sub>drift,3</sub><sup>-1</sup></td></tr></tbody></table>

$a_{-5} = a/(10^{-5} \text{cm})$, $U_6 = U/10^6 S_{max,9} = S_{max}/(10^9 \text{erg cm}^{-3})$, $n_1 = n_{1\text{II}}/(10 \text{cm}^{-3})$, $T_6 = T_{6\text{II}}/(10^6 \text{K})$

$v_{drift,3} = v_{drift}/(10^3 \text{km s}^{-1})$, and $Y_{sp}$ is the sputtering yield.

Polarized dust emission from aligned grains can be used to trace magnetic fields in the environment where the merger occurs.

Recently, the properties of the interstellar medium around the gravitational wave source GW170817 were studied, where a low value of $E(B-V) = 0.08$ was reported, assuming the typical $R_V = 3.1$ (ref. $^{41}$). If there is some dust cloud in the vicinity of the kilonova, then we expect a lower value of $R_V$ owing to the excess of small grains produced by RATD, resulting in a larger colour excess. Finally, polarimetric observations of GW170817 reveal a low degree of polarization$^{45}$, suggesting that most polarization is produced by aligned grains in the interstellar medium than from scattering in the ejecta. Therefore, polarimetric observations of kilonovae are useful for probing dust properties around gravitational wave sources.

**Implications of RATD for other astrophysical conditions.** In star-burst galaxies with star-formation activities and supernova explosions, observations usually show peculiar extinction curves with a steep far-ultraviolet rise$^{46}$. Such a feature is usually explained by grain shattering due to supernova shocks. However, this mechanism requires a long timescale to be efficient and cannot explain the absence of the 2,175 Å extinction bump, which is presumed to be produced by very small carbonaceous grains$^{8}$.

Here we suggest that the steep far-ultraviolet rise in starburst galaxies can be produced by the excess of small grains arising from RATD in intense radiation of massive stars and supernovae. Moreover, it is well known that tiny grains are efficiently destroyed by extreme ultraviolet and X-rays of intense radiation fields. Therefore, the RATD mechanism can successfully explain both the observed steep far-ultraviolet rise and the lack of the 2,175 Å extinction bump.

The RATD mechanism can also have implications for the study of the escape fraction of Lyα photons, $f_{esc}$, from star-forming galaxies. As shown in Fig. 4a, dust grains of $a \gtrsim 0.08$ µm can be disrupted to a distance of 10 pc in the intense radiation field of YMSCs. The resulting enhancement of small grains will increase the far-ultraviolet dust extinction, which can reduce $f_{esc}$, as previously observed$^{47}$ (see Methods section ‘Effect of RATD on Lyα photon escape from star-forming galaxies’).

Last but not least, the RATD mechanism naturally works in other intense radiation fields such as those around red giant stars, AGNs, quasars and gamma-ray-burst afterglows, resulting in the excess of small grains in their environments. Therefore, the RATD
<figure><img src="image_8.png" /><figcaption>**Fig. 4** | Schematic illustration for the properties of dust grains in a cloud surrounding an intense radiation source modified by RATD, assuming that original dust grains have the same size. a, Illustration for the case of a YMSC with $L = 10^7 L_\odot$. Within the distance $d \approx 0.1-1$ pc, only small grains of $a \lesssim 0.02-0.04$ µm can survive, while larger grains are disrupted by RATD. b, Illustration for the case of type Ia supernovae observed at early times (within a few weeks after explosion). Within the distance of $d \approx 0.5-1$ pc, only small grains $a \lesssim 0.02-0.08$ µm are present, while larger grains are disrupted. The density of small grains increases towards the centre owing to the disruption of large grains. Here the tensile strength $S_{\text{max}} = 10^9 \text{ erg cm}^{-3}$ is assumed.</figcaption></figure>

mechanism can explain the origin of a steep far-ultraviolet rise in the SMC-like extinction curves towards the host galaxies of gamma-ray bursts⁴⁸, quasars⁴⁹ and high-$z$ star-forming galaxies⁵⁰.

## Conclusions

We have introduced a mechanism of dust destruction that is based on the fact that extremely fast-rotating grains spun-up by radiative torques would be disrupted when the centrifugal stress exceeds the maximum tensile strength of grains. This RATD mechanism is more efficient than previously known mechanisms at destroying large grains in strong radiation fields.

Using the RATD mechanism, we quantified the critical size of rotational disruption for grains and its required disruption time for YMSCs, supernovae and kilonovae. We find that the RATD mechanism can rapidly replenish small grains, as is required to reproduce the NIR-MIR emission excess as well as the increase in abundance of small grains towards the centre observed in YMSCs.

We show that RATD can destroy large grains of $a \gtrsim 0.1$ µm within distance of $d \approx 1$ pc (compact grains) and approximately 3 pc (composite grains) from type Ia and type II-P supernovae, which can successfully explain the excessive abundance of small grains towards supernovae as demonstrated by the anomalous dust extinction and polarization.

Using the RATD mechanism, we study the feedback of kilonovae on surrounding dust and predict that the environments in the vicinity of the mergers would be dominated by small grains.

Finally, we suggest that the steep far-ultraviolet rise in the extinction curves of star-forming galaxies, quasars, and high-$z$ galaxies can be explained by the enhanced abundance of small grains due to grain disruption. The low escape fraction of Ly$\alpha$ photons from star-forming galaxies can also originate from the enhanced dust extinction owing to an excess of small grains as a result of RATD.

## Methods

**Radiation fields and radiative torques of irregular grains.** Let $u_i$ be the spectral energy density of a radiation field. The energy density of the radiation field is then $u_{\text{rad}} = \int u_i d\lambda$. The radiation strength is characterized by $U = u_{\text{rad}}/u_{\text{ISRF}}$ with $u_{\text{ISRF}} = 8.64 \times 10^{-13} \text{ erg cm}^{-3}$ being the energy density of the average interstellar radiation field in the solar neighbourhood³³.

For a point source of radiation field with bolometric luminosity $L$, the radiation energy density at distance $d_{\text{pc}}$ in units of pc is given by

$$u_{\text{rad}} = \int u_i d\lambda = \int \frac{L_i e^{-\tau_i}}{4\pi c d^2} d\lambda \approx 1.06 \times 10^{-6} \left( \frac{L_9 e^{-\tau}}{d_{\text{pc}}^2} \right) \text{erg cm}^{-3} \quad (4)$$

where $L_9 = L/(10^9 L_\odot)$, $\tau_i$ is the optical depth induced by intervening dust, and $\tau$ is defined as $e^{-\tau} = \int L_i e^{-\tau} d\lambda/L$. The radiation strength is then

$$U_6 = \frac{U}{10^6} \approx 1.2 \left( \frac{L_9 e^{-\tau}}{d_{\text{pc}}^2} \right). \quad (5)$$

Thus, at distance $d=1$ pc, a massive star of $L \approx 10^9 L_\odot$ can produce radiation strength of $U \approx 10^2$ and a supernova of $L \approx 10^9 L_\odot$ gives $U \approx 10^6$.

Dust grains of irregular shape subject to an anisotropic radiation field experience radiative torques due to differential scattering and absorption of incident photons³⁰. Numerical calculations of radiative torques for several irregular shapes³¹ found that grains can be spun-up to suprathelial rotation. The spin-up by radiative torques was subsequently tested in laboratory experiments³¹. An analytical model of radiative torques and their alignment was developed³²,⁵², which is supported by numerous observations³³,⁵⁴.

Let $a$ be the effective size of the irregular grain, which is defined as the radius of an equivalent sphere of the same volume as the irregular grain. The radiative torque of the irregular grain produced by the illumination of the anisotropic radiation is written as

$$\Gamma_{\lambda} = \pi a^2 \gamma u_{\lambda} \left(\frac{\lambda}{2\pi}\right) Q_{\Gamma} \quad (6)$$

where $\gamma$ is the anisotropy degree of the radiation field, and $Q_\Gamma$ is the radiative torque efficiency³¹,³².

The value of $Q_\Gamma$ depends on the radiation wavelength, grain shape and grain size, but it seems to weakly depend on the grain composition and internal structure³²,⁵⁵. The radiative torque efficiency can be approximately described by a power law³²:

$$Q_{\Gamma} \approx 0.4 \left( \frac{\lambda}{1.8a} \right)^{\eta} \quad (7)$$

where $\eta = 0$ for $\lambda \lesssim 1.8a$, and $\eta = -3$ for $\lambda > 1.8a$.

Let $\bar{\lambda} = \int \lambda u_i d\lambda / u_{\text{rad}}$ be the mean wavelength of the radiation spectrum. The radiative torque efficiency averaged over the radiation spectrum is defined as

$$\bar{Q}_{\Gamma} = \frac{\int \lambda Q_{\Gamma} u_{i} d\lambda}{\int \lambda u_{i} d\lambda} \quad (8)$$
For dust grains of size $a \lesssim \bar{\lambda}/1.8$, the averaged radiative torque efficiency, $\bar{Q}_r$, can be approximated to$^{56}$

$$ \bar{Q}_r \approx 2 \left( \frac{\bar{\lambda}}{a} \right)^{-2.7} \approx 2.6 \times 10^{-2} \bar{\lambda}_{0.5}^{-2.7} a_{-5}^{2.7} \quad (9) $$

where $a_{-5} = a/(10^{-5} \text{ cm})$, $\bar{\lambda}_{0.5} = \bar{\lambda}/(0.5 \text{ µm})$, and $\bar{Q}_r \approx 0.4$ for $a > \bar{\lambda}/1.8$. As a result, the averaged radiative torque can be written as

$$ I_{\text{RAT}} = \pi a^2 \gamma u_{\text{rad}} \left( \frac{\bar{\lambda}}{2\pi} \right) \bar{Q}_r \approx 5.6 \times 10^{-23} \gamma a_{-5}^{4.7} \bar{\lambda}_{0.5}^{-1.7} U_6 \quad \text{erg} \quad (10) $$

for $a \lesssim \bar{\lambda}/1.8$, and

$$ I_{\text{RAT}} \approx 8.6 \times 10^{-22} \gamma a_{-5}^{2} \bar{\lambda}_{0.5} U_6 \quad \text{erg} \quad (11) $$

for $a > \bar{\lambda}/1.8$

**Maximum grain angular velocity spun-up by radiative torques.** RATs can spin-up dust grains to fast rotation. However, faster grain rotation induces faster rotational damping owing to both gas collisions and emission of infrared photons. The equation of motion for irregular grains subject to radiation torques and rotational damping is described by

$$ \frac{I d\omega}{dt} = I_{\text{RAT}} - \frac{I\omega}{\tau_{\text{damp}}} \quad (12) $$

where $I = 8\pi\rho a^2/15$ is the grain inertia moment, and

$$ \tau_{\text{damp}}^{-1} = \tau_{\text{gas}}^{-1}(1 + F_{\text{IR}}) \quad (13) $$

where $\tau_{\text{gas}}$ is the characteristic rotational damping time due to gas collisions (see Supplementary Information section 'Grain rotational damping'):

$$ \tau_{\text{gas}} = \frac{3}{4\sqrt{\pi}} \frac{I}{1.2 n_{\text{H}} m_{\text{H}} v_{\text{th}} a^4} \approx 8.74 \times 10^4 a^{-5} \hat{\rho} \left( \frac{30 \text{ cm}^{-3}}{n_{\text{H}}} \right) \left( \frac{100 \text{ K}}{T_{\text{gas}}} \right)^{1/2} \gamma R \quad (14) $$

where $v_{\text{th}} = (2k_B T_{\text{gas}}/m_{\text{H}})^{1/2}$ is the thermal velocity of hydrogen atoms of mass $m_{\text{H}}$ (ref. $^{31}$).

In equation (13), $F_{\text{IR}}$ is a dimensionless parameter that describes the relative importance of rotational damping by infrared emission with respect to the damping by gas collisions, as given by (see ref. $^{37}$)

$$ F_{\text{IR}} \approx \left( \frac{0.4 V^{2/3}}{a_{-5}} \right) \left( \frac{30 \text{ cm}^{-3}}{n_{\text{H}}} \right) \left( \frac{100 \text{ K}}{T_{\text{gas}}} \right)^{1/2} \quad (15) $$

For the radiation source of constant luminosity (for example, massive stars or YMSCs), $I_{\text{RAT}}$ is constant. From equation (12), one can solve for the grain angular velocity as a function of time

$$ \omega(t) = \omega_{\text{RAT}} \left[ 1 - \exp\left(-\frac{t}{\tau_{\text{damp}}}\right) \right] \quad (16) $$

where

$$ \omega_{\text{RAT}} = \frac{I_{\text{RAT}} \tau_{\text{damp}}}{I} \quad (17) $$

is the terminal angular velocity at $t \gg \tau_{\text{damp}}$, which is considered the maximum rotational rate spun-up by radiation torques.

Equation (17) allows us to calculate the maximum rotation rate enabled by radiation torques for arbitrary environments with given $n_{\text{H}}$, $T_{\text{gas}}$ and U. For the case of strong radiation fields with $U \gg 1$, infrared damping is dominant over gas damping (that is, $F_{\text{IR}} \gg 1$), such that $\tau_{\text{damp}} \approx \tau_{\text{gas}} F_{\text{IR}}$. As a result, by plugging $\tau_{\text{damp}}$ and $I_{\text{RAT}}$ into equation (17), we can derive analytical formulae for $\omega_{\text{RAT}}$ as given by equations (1) and (2).

For the time-varying radiation sources such as supernovae and kilonovae, the grain angular velocity can be obtained by numerically solving the equation of motion

$$ I d\omega = \left( I_{\text{RAT}}(t) - \frac{I\omega}{\tau_{\text{damp}}} \right) dt \quad (18) $$

where the initial conditions $\omega=0$ at $t=0$ can be chosen.

We note that equations (16)–(18) can be used for specific shapes of irregular grains$^{4,25,58}$ by replacing I with the principal inertia moment along the axis of maximum inertia. The reason is that, for suprathermally rotating grains spun-up by intense radiation, internal relaxation can rapidly dissipate the grain rotational energy to the minimum level, resulting in the perfect alignment of the axis of maximum inertia moment with the grain angular momentum$^{59}$.

**Centrifugal stress within a spinning grain.** For an equivalent spherical grain spinning around a z-axis with angular velocity $\omega$, the centrifugal stress on a circular slab of thickness dx located at distance $x_0$ from the mass centre is equal to

$$ dS = \frac{\omega^2 x dx}{\pi (a^2 - x_0^2)} = \frac{\rho \omega^2 (a^2 - x^2) x dx}{a^2 - x_0^2} \quad (19) $$

where the mass of the slab $dm = \rho dAdx$ with $dA = \pi(a^2 - x^2)$ the area of the circular slab

The average centrifugal stress is then given by

$$ \begin{aligned} S &= \int_{x_0}^{a} dS = \frac{\rho \omega^2 a^2}{2} \int_{x_0/a}^{1} \frac{(1-u)du}{1-u_0} \\ &= \frac{\rho \omega^2 a^2}{4} \left[ \frac{(1-u_0)^2}{1-u_0} \right] = \frac{\rho \omega^2 a^2}{4} \left[ 1 - \left( \frac{x_0}{a} \right)^2 \right] \end{aligned} \quad (20) $$

where $u = x^2/a^2$. The centrifugal stress is the maximum value of $S = \rho\omega^2 a^2/4$ for $x_0 = 0$.

**Radiation fields of massive stars, supernovae, and kilonovae.** Massive OB stars can produce strong radiation fields of $L \approx 10^4-10^6 L_{\odot}$. A YMSC of mass exceeding $10^4 M_{\odot}$ contains several thousand OB stars and its luminosity is in the range $10^6-10^9 L_{\odot}$ (ref. $^{60}$).

A massive star can be considered as a blackbody radiation source, such that its radiation spectrum can be described by the Planck function, assuming an effective temperature $T_* = 20,000$ K. The mean wavelength of the radiation spectrum is then

$$ \bar{\lambda} = \frac{\int_{u_0}^{u_1} u_2(t) d\lambda}{\int_{u_0}^{u_1} (T_*) d\lambda} \approx 0.28 \ \mu\text{m} \quad (21) $$

Thus, for massive stars and YMSCs, we can assume a constant radiation field over the lifetime of massive stars with the anisotropy degree of radiation $\gamma=1$.

Supernova explosions can release radiation energy of $L \approx 10^8-10^{10} L_{\odot}$ over a timescale of about 100–150 days. Radiation energy of type Ia supernovae is produced mostly by conversion of the kinetic energy of ejecta interacting with surrounding environments (that is, shocked regions). Most of the radiative energy is concentrated in ultraviolet–optical wavelengths, especially in early epochs after the explosion$^{61}$.

An analytical formula for fitting the optical luminosity of the type Ia supernovae light curve is introduced$^{62}$. The formula appears to fit the B and g bands well during the first 50 days$^{62}$. For RATs, we are interested only in ultraviolet–optical wavelengths, so we can use their analytical fit for our numerical calculations of grain rotation rate, which consists of two power laws

$$ L_{\text{SN}\text{I}}(t) = L_0 \left[ \frac{t-t_0}{t_b} \right]^{a_r} \left[ 1 + \left( \frac{t-t_0}{t_b} \right)^{s a_d} \right]^{-2/s} \quad (22) $$

where $L_0$ is the scaling parameter, the first power law describes the rising period in the luminosity$^{63}$, and the second power law (in square brackets) describes the falling stage after the peak luminosity. The parameters $\alpha$, and $\alpha_d$ are the power-law indices before and after the peak, $t_0$, $t_b$ is the first-light time and the break time, and $s$ is the smooth transition parameter. We adopt $\alpha_r \approx 2$, $\alpha_d \approx 2.5$, $s \approx 1$, and $t_0 \approx 23$ days, which are the best-fit parameters$^{63}$, and $L_0 = 2 \times 10^{10} L_{\odot}$. For convenience, we set the first-light time at $t_0 = 0$, so that $t$ corresponds to the time interval that dust grains in a nearby cloud are illuminated by supernova radiation.

We now consider the case of type II-P supernovae. We use the arbitrary power-law fits for the light curve of the supernova SN 2015ba (ref. $^{64}$), which consists of three components

$$ L_{\text{SNII}}(t) = \begin{cases} 10^{-0.002t+9.17} L_{\odot}, & \text{for } t \le 60 \text{ days} \\ 1.1 \times 10^9 L_{\odot}, & \text{for } 60 < t \le 120 \text{ days} \\ 10^{-0.0067t+9.84} L_{\odot}, & \text{for } t > 120 \text{ days.} \end{cases} \quad (23) $$

Recently, a new class of supernovae, SLSNs, was discovered$^{65}$. Their luminosity can be two orders of magnitude higher than that of the standard type Ia supernovae$^{66}$. For the sake of completeness, we calculate the disruption size and
disruption time for an SLSN that has a peak luminosity 16 times larger than $L_{SNID}$ given by equation (23).

A kilonova emits electromagnetic radiation mostly in the ultraviolet, optical and near-infrared parts of the spectrum, which is produced by the decay of radioactive nuclei in the relativistic ejecta after the mergers of black holes and neutron stars$^{28,67}$.

The bolometric luminosity of kilonovae can reach the peak of $L_{peak} \approx 3 \times 10^8 L_{\odot}$ after 0.5–5 days from the merger moment. After the peak, the luminosity decreases with time as

$$L_{KN}(t) = L_{\text{peak}} t^{-\alpha} \quad (24)$$

where the time $t$ is given in units of days, $\alpha \approx 0.2$ for $t \le 3$ days (shallow slope), and $\alpha = 1.3$ for $t > 3$ days (steep slope)$^{67}$.

The radiation spectrum of type Ia supernovae is also assumed to be a blackbody radiation source of effective temperature $T_*$. This is especially valid during the rising phase of the type Ia supernovae light curve$^{63}$. Thus, for $T_* = 1.5 \times 10^4$ K, one obtains $\bar{\lambda} \approx 0.35$ µm for type Ia supernovae. For type II-P supernovae and SLSNs, which are assumed to have similar spectra with $T_* \approx 2 \times 10^4$ K except that the luminosity of SLSNs is 16 times larger, one obtains $\bar{\lambda} \approx 0.28$ µm. The radiation spectrum of kilonovae can also be approximated by a temperature of $T_* = 10^4$ K (ref. $^{63}$), which yields $\bar{\lambda} \approx 0.53$ µm.

**Critical radiation strength for RATD.** For strong radiation fields for which infrared damping dominates over the gas damping (that is, $F_{IR} \gg 1$), from equations (1) and (3), one can derive the minimum radiation strength required to disrupt irregular grains of $a \lesssim \bar{\lambda}/1.8$ as follows

$$U \ge U_{\text{disr}} \approx 118\gamma^{-3} a_{-5}^{8.1} \lambda_{0.5}^{3.1} S_{\text{max},9}^{3/2} \quad (25)$$

The above equation reveals that the critical radiation strength depends on the anisotropy of the radiation field $\gamma$, the mean wavelength, the grain size and especially the grain mechanical property or tensile strength. Compact grains with high $S_{\text{max}}$ are more difficult to disrupt than fluffy or composite grains. We note that radiative torques from solar radiation may be able to disrupt fluffy, submicrometre-sized interplanetary grains$^{68}$.

For a general case, one can find $U_{\text{disr}}$ by comparing $\omega_{\text{RAT}}$ obtained from numerical calculations using equation (17) with $\omega_{\text{disr}}$ (see equation (3)). Supplementary Fig. 1a shows the critical radiation strength $U_{\text{disr}}$ as a function of the grain size for the diffuse interstellar radiation field ($\gamma = 0.1, \bar{\lambda} = 1.2$ µm) and unidirectional radiation sources ($\gamma = 1, \bar{\lambda} = 0.2–0.8$ µm). The radiation strength $U_{\text{disr}}$ decreases rapidly with increasing $a$ as $a \approx 8^{-1}$, then it starts to rise slowly from $a \sim \bar{\lambda}/1.8$ because the radiative torque efficiency increases rapidly with $a$ and becomes constant for $a > \bar{\lambda}/1.8$ (see equation (7)). For the diffuse interstellar medium with $\gamma = 0.1$ and $\bar{\lambda} = 1.2$ µm, it requires $U_{\text{disr}} \approx 900$ to disrupt grains $a \approx 0.3$ µm. However, for the case of unidirectional radiation from a distant star with $\gamma = 1$, one only requires $U_{\text{disr}} \approx 0.9$ to disrupt similar-sized grains.

In Supplementary Fig. 1b, we show the results computed for the photodissociation region conditions with $n_{\text{H}} = 10^5$ cm$^{-3}$ and $T_{\text{gas}} = 10^3$ K. The enhanced gas damping means that the required radiation strength is much larger.

**Grain disruption size and disruption time.** For strong radiation fields of $U \gg 1$ such that the gas damping can be disregarded owing to the dominance of infrared damping, using equations (1) and (3), one can obtain the critical size $a_{\text{disr}}$ above which all grains would be disrupted (that is, disruption size), for $a_{\text{disr}} \lesssim \bar{\lambda}/1.8$, as follows

$$\left( \frac{a_{\text{disr}}}{0.1 \, \mu\text{m}} \right)^{2.7} \approx 0.046 \gamma^{-1} \lambda_{0.5}^{-1.7} \left( \frac{U_6}{1.2} \right)^{-1/3} S_{\text{max},9}^{1/2} \quad (26)$$

For a cloud at distance $d = 1$ pc and $\bar{\lambda} = 0.5$ µm, equation (26) gives $a_{\text{disr}} \approx 0.03$ µm for $U = 10^6$ and $S_{\text{max}} = 10^9$ erg cm$^{-3}$. At $d = 10$ pc, one obtains $a_{\text{disr}} \approx 0.08$ µm for the similar parameters, and $a_{\text{disr}} \approx 0.13$ µm for $d = 50$ pc. We note in dense environments or not-strong radiation fields where gas damping is dominant over infrared damping, there exists an upper cutoff of the grain disruption sizes by RATD because $\omega_{\text{RAT}}$ decreases faster than $\omega_{\text{disr}}$ for $a > \bar{\lambda}/1.8$ (ref. $^{63}$).

The disruption time of grains of size $a_{\text{disr}}$ can be defined as the time required to spin-up grains to $\omega_{\text{disr}}$:

$$t_{\text{disr}} = \frac{I_{\text{disr}}}{dJ/dt} = \frac{I_{\text{disr}}}{I_{\text{RAT}}} \approx 368 \bar{\lambda}_{0.5}^{1.7} \left( \frac{a_{\text{disr}}}{0.1 \, \mu\text{m}} \right)^{-0.7} U_6^{-1} S_{\text{max},9}^{1/2} \, \text{days} \quad (27)$$

For a dust cloud at $d = 1$ pc from a supernova with $U \approx 10^6$, the disruption time $t_{\text{disr}} \approx 161$ days for $a_{\text{disr}} \approx 0.25$ µm, assuming $\bar{\lambda} = 0.5$ µm. The disruption time decreases with the grain size, such that large grains are disrupted faster than smaller ones.

For supernovae and kilonovae with the time-dependent luminosity, we solve the equation of motion (equation (12)) to obtain $\omega(t)$. The disruption size and disruption time is determined by comparing $\omega(t)$ with the critical disruption limit $\omega_{\text{disr}}$ (see Supplementary Fig. 2).

**Comparison of RATD to other destruction mechanisms in strong radiation fields.** To facilitate the comparison of RATD to other destruction mechanisms, we first describe the basic properties of the RATD mechanism.

The efficiency of the RATD mechanism in destroying dust grains in general depends on the radiation strength ($U$), the anisotropy degree of the radiation field ($\gamma$), local gas properties ($n_{\text{H}}$, $T_{\text{gas}}$), and the maximum tensile strength of dust grains. In the absence of gas rotational damping, the radiation strength required for grain disruption is not too high, such as $U_{\text{disr}} < 118\gamma^{-3} S_{\text{max}}^{3/2}$ for $a \gtrsim 0.1$ µm. In the presence of gas damping, $U_{\text{disr}}$ increases with increasing the gas rotational damping rate. For a very dense and hot environment such as in photodissociation regions, the disruption occurs when $10^4 < U_{\text{disr}} < 10^5$, assuming $\gamma = 1$ (see Supplementary Fig. 1). The typical radiation strength of photodissociation regions $U \approx 3 \times 10^4$, which is sufficient to disrupt large grains. We note that the radiation strength can vary in the range $U \approx 0.1–10^7$ in galaxies$^{10}$. Therefore, the effect of RATD by strong radiation fields should be accounted for in dust modelling and galaxy evolution research. Moreover, in dense regions with weak radiation fields, such as the dense starless cores or the interior of protoplanetary disks, RATD is inefficient. On the other hand, in dense regions that have intense radiation fields such as around young stellar objects, the RATD mechanism can be efficient$^{69}$.

The efficiency of RATD depends strongly on the maximum tensile strength of dust grains, which is determined by internal structures of dust grains. Compact grains tend to have high $S_{\text{max}}$ up to $10^{11}$ erg cm$^{-3}$, while porous/composite grains have much lower tensile strength (see Supplementary Table 1). If large grains are an aggregate of nanoparticles$^{11}$, we can expect $S_{\text{max}}$ as low as $10^7 (1-P)$ erg cm$^{-3}$ (see Supplementary equation (9)). Therefore, RATD is more efficient at disrupting aggregates than compact grains. Furthermore, the efficiency of RATD mechanism is expected to be weakly dependent on grain compositions (that is, silicate and carbonaceous materials) because RATs are found not to vary very much with grain composition$^{55}$.

Now we compare the RATD mechanism with other destruction mechanisms that can work in strong radiation fields, including thermal sublimation, thermal sputtering, and grain shattering caused by grain–grain collisions induced by radiation pressure$^{72}$. The thermal sublimation is previously known to be the dominant mechanism of dust destruction by intense radiation fields$^{26,73}$.

For a point source of radiation, the sublimation distance of dust grains, $r_{\text{sub}}$ from the central source is given by

$$r_{\text{sub}} \approx 0.015 \left( \frac{L_{\text{UV}}}{10^9 L_{\odot}} \right)^{1/2} \left( \frac{T_{\text{sub}}}{1,800 \, \text{K}} \right)^{-5.6/2} \, \text{pc} \quad (28)$$

where $L_{\text{UV}}$ is the luminosity in the optical and ultraviolet, which is roughly one half of the bolometric luminosity, and $T_{\text{sub}}$ is the dust sublimation temperature in the range $1,500–1,800$ K for silicate and graphite material$^{25,74}$.

Equation (28) reveals that thermal sublimation is efficient for grains at much smaller distances compared to RATD (see, for example, Fig. 2). Moreover, at the same distance, the radiation strength required for thermal sublimation of $U_{\text{sub}} > 8 \times 10^7 (T_{\text{sub}}/1,800 \, \text{K})^{5.6}$ (see equation (28)), which is much larger than $U_{\text{disr}}$. The dominance of rotational disruption over thermal sublimation can be understood by considering the energy. Indeed, in order to heat the dust grain to the sublimation temperature, $T_{\text{sub}}$, the radiation energy must be $E_{\text{rad}} \sim T_{\text{sub}}^4$. On the other hand, in order to spin-up dust grains to the critical rotation rate $\omega_{\text{disr}}$, the radiation energy required is $E_{\text{rad}} \approx \omega_{\text{disr}}$. Owing to the fourth-order dependence, the sublimation energy is much higher than the energy required for grain disruption.

Thermal sputtering is usually thought to be important in hot ionized gas such as YSMCs. Let $Y_{\text{sp}}$ be the average sputtering yield by impinging H with mean thermal velocity $\langle v \rangle$. Then, the sputtering rate is given by

$$\frac{4\pi a^2 da}{dt} = n_H \langle v \rangle \pi a^2 Y_{\text{sp}} m_H \quad (29)$$

which leads to the sputtering time:

$$\begin{gathered} \tau_{\text{sp}} = \frac{a}{da/dt} \\ \approx 9.8 \times 10^3 a_{-5} n_{-1}^{-1} \left( \frac{10^6 \, \text{K}}{T_{\text{gas}}} \right)^{1/2} \left( \frac{0.1}{Y_{\text{sp}}} \right) \, \text{yr} \end{gathered} \quad (30)$$

where $n_{-1} = n_{\text{H}}/(1 \, \text{cm}^{-3})$, and $Y_{\text{sp}}$ falls rapidly after its peak value of about 0.1 at the Bohr velocity owing to the decrease of the nucleon–nucleon cross-section$^{26}$.

In the case of supernovae, grains can be destroyed by grain–grain collisions and non-thermal sputtering due to drift of accelerated grains through the gas$^{72}$.
The destruction time by grain–grain collisions can be estimated as the mean time between two collisions

$$\tau_{gg} = \frac{1}{\pi a^2 n_{gr} v_{drift}} = \frac{4 \rho a M_{g/d}}{3 n_{H} m_{H} v_{drift}} \approx 7.6 \times 10^4 \hat{\rho} a_{-5} n_{1}^{-1} v_{drift}^{-1} \text{ yr} \quad (31)$$

where $n_{gr}$ is the number density of dust grains, $M_{g/d}=100$ is the gas-to-dust mass ratio, and we have assumed the single-grain size distribution.

Grains initially located at distance of $r_i=1$ pc can be accelerated to $v \approx 1,700 \text{ km s}^{-1}$ by supernova radiation pressure$^{72}$. Thus, grain–grain collisions require a much longer timescale to form small grains compared to RATD (see equation (27)). In order for grain–grain collisions to reproduce small grains as required by early-phase observations towards type Ia supernovae, that is, $\tau_{gg} < 100$ days, one needs $n_{H} > 10^{8} \text{ cm}^{-3}$, which corresponds to extremely dense clouds.

The destruction time by non-thermal sputtering is equal to:

$$\begin{align}
t_{\text{nontherm-sp}} &= \frac{\rho a}{n_{H} v_{\text{drift}} m_{H} Y_{\text{sp}}} \nonumber \\
&\approx 5.7 \times 10^3 \hat{\rho} \left( \frac{a_{-5}}{n_{1}} \right) \left( \frac{0.1}{Y_{\text{sp}}} \right) \left( \frac{10^3 \text{ kms}^{-1}}{v_{\text{drift}}} \right) \text{yr} \tag{32}
\end{align}$$

Finally, we note again that a popular mechanism of grain shattering due to supernova shocks is expected to work at a much later stage when the supernova ejecta already reaches the interstellar medium. This is different from our RATD mechanism that works within a few weeks after the explosion.

**Effect of RATD on Lyα photon escape from star-forming galaxies.** The hydrogen Lyα line ($\lambda=1,216 \AA$) in the spectra of star-forming galaxies, either nearby or high-z, carries a wealth of information about both photon sources and surrounding media. Since Lyα photons experience a large number of local scatterings before escape in these objects, the emergent line profile and flux are heavily dependent upon local properties such as kinematics, column densities of neutral hydrogen, clumpy structures, and dust properties, more than the global properties of the interstellar medium in the host galaxy. The physical quantities, such as Lyα escape fraction ($f_{\text{esc}}(\text{Ly}\alpha)$) and the star-formation rate, are usually inferred from the dust-corrected rest-frame ultraviolet/infrared flux and/or from the dust-corrected Hα emission flux. The dust-correction depends on the ultraviolet dust extinction, which is dependent upon the grain size distribution, especially the population of small grains that dominates the ultraviolet extinction.

The Lyα-selected and Hα-selected galaxies show disjoint quantities of extinction, Lyα escape fraction, and star-formation rate$^{75}$. In addition, the Lyα-selected sample is much less dusty and exhibits a higher escape fraction than the Hα-selected sample owing to the fact that dust extinction is larger at shorter wavelengths. It is well known that the escape fraction is anti-correlated with the dust reddening$^{75,76}$. Moreover, a detailed study$^{77}$ reveals that the low value of $f_{\text{esc}}(\text{Ly}\alpha)$ can be better fitted with the SMC-like extinction curve, and many galaxies have $f_{\text{esc}}$ even below the fit by SMC-like extinction (see figure 7a of ref. $^{78}$). This demonstrates the greater enhancement of small grains in these star-forming galaxies. Furthermore, direct measurements of dust properties in high-z Lyα break galaxies indicate the typical grain size $a \approx 0.05 \mu\text{m}$ (ref. $^{18}$), which is much smaller than the interstellar medium dust. Owing to the dominance of massive stars and supernovae in the star-forming galaxies, either nearby or high-z, the efficient RATD mechanism is expected to be important in disrupting large grains to produce such small grains.

Another issue is the observation of the singly peaked Lyα emission lines observed in these starburst galaxies. To explain this feature, usually a central cavity of dust grains inside a supershell/superbubble is suggested to efficiently suppress the secondary, tertiary and even higher-order peaks redshifted with respect to the rest-frame Lyα line centre$^{77}$. The size and the age of the supershell/superbubble was roughly estimated to be $1.8 \text{ pc} < R < 180 \text{ pc}$ and $10^2 \text{ yr} < t < 5 \times 10^4 \text{ yr}$, respectively, for a range of input energy as a free parameter from stellar radiation and explosions$^{78}$. A young massive star cluster has $L \approx 10^6-10^9 \text{ L}_\odot$. Thus, for an intense radiation field of $L=10^9 \text{ L}_\odot$, RATD can destroy large grains to form very small grains of $a < 0.1216/2\pi \approx 0.02 \mu\text{m}$. This reduces the absorption of Lyα photons, resulting in a cavity size of 1 pc (see Fig. 4 for compact grains). The central cavity can be larger if grains are composite.

## Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Received: 12 October 2018; Accepted: 19 March 2019; Published online: 6 May 2019

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## Acknowledgements

We thank B.-G. Andersson, M. Bulla, B. Burkhart, B. T. Draine, A. Goobar, V. Guillet, A. Lazarian, P. Lesaffre, R. Smith, and W. Zheng for comments and discussions. This work was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (2017R1D1A1B03035359).

## Author contributions

All authors contributed to the work presented in this paper. T.H. formulated the problem, carried out analytical calculations, and led the writing of the manuscript. L.N.T. carried out numerical calculations for supernovae and kilonovae. H.L. carried out calculations for massive stars. S.H.A. contributed to the discussion of the RATD mechanism on Lyα photon escape.

## Competing interests

The authors declare no competing interests.

## Additional information

Supplementary information is available for this paper at https://doi.org/10.1038/s41550-019-0763-6.

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