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A&A
Volume 672, April 2023
Article Number A182
Number of page(s) 7
Section Interstellar and circumstellar matter
DOI https://doi.org/10.1051/0004-6361/202244057
Published online 19 April 2023

© The Authors 2023

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1 Introduction

IRAS 16293-2422 (hereinafter IRAS 16293) is a young class 0 stellar object and a protostellar system of solar masses. It is located in the ρ Ophiuchus cloud complex at a distance of ~140pc (Walker et al. 1986; Menten et al. 1987; Chen et al. 2013; Tobin et al. 2020; Dzib et al. 2018). The molecular complex IRAS 16293 has a very intricate structure on a scale of 6000–8000 AU (Crimier et al. 2010; Jacobsen et al. 2018), which includes two continuum sources, A and B, separated by a distance of ~700 AU. Source A is divided into two compact sub-sources, A1 and A2, which are separated by a distance of ~50 AU (Wootten 1989). The gas and dust disks are part of the A1 and A2 system and move around low-mass protostars (0.8 M⊙ < M⊙ < 2.2 M⊙); all but one of the disks are 12 AU in size, with the remaining being <3.6 AU (Maureira et al. 2020). IRAS 16293 is a gravitationally bound triple system, parts of which revolve around a common center of gravity; the orbital period between A1 and A2 is about 362 yr, and between A and B it is probably several thousand years (Maureira et al. 2020).

IRAS 16293 exhibits high activity accompanied by three bipolar outflows in two different directions (Fukui et al. 1986; Mizuno 1990; Chandler et al. 2005; Kristensen 2013; Chandler et al. 2005; Dzib et al. 2018). The available interferometric observations have established the presence of groups of maser clumps (spots), which are associated with outflows and are possibly connected with gas and dust disks around protostars (Wootten 1989; Imai 1999; Dzib et al. 2018). To determine the location of water masers, simultaneous monitoring observations in the regime of single radio telescopes and in inter-ferometric mode are required. Due to the difficulty of making such observations over long periods of time, they are not yet available.

As part of the program of long-term detailed monitoring of promising objects of water vapor masers, we have observed IRAS 16293 almost daily with the RT-22 radio telescope (Simeiz) since the beginning of 2020. A prolonged powerful flare phenomenon was detected, consisting of individual shorter water maser flares. Data on the flare phenomenon near 8 km s−1 in IRAS 16293 were published in Volvach (2021). That work presented, for the first time, fundamentally new unique data on the physical characteristics of the maser emission in this object. The most important conclusion was that powerful flares of unsaturated water masers are formed due to the cascade amplification of the radiation directed at the observer from several maser condensations with increasing flux densities. The maser condensations responsible for the powerful flares are located at different points on the gas and dust disk and have slightly different radial velocities. This creates a visible drift in the radial velocity of the maser lines. The high temperature of the maser radiation medium (3000 K) in combination with supersonic shock waves ensures its high density (nH ≈ 1012) and degree of ionization (ne ≈ 10−6 · nH) for the most powerful maser flares. The giant water maser flares in W49N have been shown to have characteristics similar to those of IRAS 16293.

In September 2020, a powerful flare phenomenon in IRAS 16293 reached its maximum simultaneously in the 8 km s−1 radial line and in the line near 1.5 km s−1. Almost contemporaneously with Volvach et al. (2019a), Colom et al. (2021) published independent data showing that, over the course of 2020, nine spectral density values for the flare flux in IRAS 16293 were detected in a line near 1.5 km s−1, with an average interval between data points of about 1.5 months. It should be noted that the duration of each of the powerful flares in IRAS 16293 was no more than a month. Additionally, we can note the difficulty that Colom et al. (2021) faced. The observation latitude of the Pushchino radio telescope is 12 degrees greater than that of the Simeiz radio telescope. Therefore, all observations of the source IRAS 16293 were made at an elevation of less than 10 degrees from the horizon. At such angles, the absorption of radio emission from the source by the atmosphere can reach ten times or more compared to its absence; therefore, accurate measurements of fluxes are difficult. Nevertheless, we tried to compare our results on a radial line of about 1.5 km s−1 with some of the data presented in Colom et al. (2021). The widths of the radial lines are not provided in Colom et al. (2021), but their graphical estimates give values that coincide with our data to within 10–15%.

The long flare phenomena in IRAS 16293, which occurred near radial velocities of 1.5 and 8 km s−1 in 2020, were preceded by a powerful water maser flare in the same source, which occurred near a radial velocity of 6 km s−1 from October 2019 to mid-2020. Its flux density exceeded 20 kJy. Short unsaturated powerful flares originated at the top of a longer but less powerful flare with a radial line of about 3 km, which initiated their maser emission and, presumably, was in a saturated state. Volvach (2022) determined the existence of a cascade amplification of the maser in cases where powerful short flares occurred in maser condensations with a dense cluster structure.

This article presents new detailed data on the most powerful long-term complex water maser phenomenon near −1.5 km s−1 and gives an interpretation of the data obtained.

2 Observations and data processing

The observations at a frequency 22.235 GHz of the 616–523 water-vapor maser transition were carried out using the 22m telescope and a spectral-polarimetry radiometer with a parallel Fourier spectrum analyzer. Resolutions for the radial velocity in the H2O line were 8 and 2 kHz (0.105 and 0.03 km s−1), respectively (Volvach et al. 2019a; Volvach 2020). The half-width of the radiation pattern of the radio telescope (FWHM) was 2.5 arcmin; the sensitivity of the radio telescope was 13 Jy K−1. Depending on the weather conditions, the system temperature at the intermediate angles varied in the range 120–150 K. The collected spectral data were corrected for atmospheric absorption and changes in the effective area of the radio telescope at different elevation angles. Observations, registration, and primary data processing were carried out in an automatic mode, as was the motion of the radio telescope. The fluxes were calibrated using DR 21, Vir A, and Cyg A sources. The receiving system was installed at the secondary focus of the radio telescope. The heterodyne receiver was stabilized by an H-maser with a frequency of 5 MHz, and the observational data were transmitted from the radio telescope to the spectrometer and recording equipment. The cycles of observations of the maser line consisted of signal accumulation for 5–10 min on the source and 5–10 min away from it. The procedure was repeated several times to achieve the given signal-to-noise ratio.

thumbnail Fig. 1

Powerful flare phenomenon that occurred in IRAS 16293 near −1.5 km s−1. The crosses mark the values of the flux densities obtained on the RT-22 in Pushchino and published in Colom et al. (2021). The individual flares are numbered and marked with the symbol “F.”

3 Results

3.1 Observational data

The data from the long-term monitoring of the spectral flux density of the water maser in the direction of the protostellar complex IRAS 16293 at a frequency of 22.235 GHz near −1.5 km s−1 are shown in Fig. 1.

The powerful flare phenomenon that we discovered is a superposition of individual flares, each of which lasted about a month. The phenomenon began with an increase in the flux density at the beginning of March 2019, reached its maximum flux density at the end of 2020 and continued until the beginning 2021, lasting for a total of about 2 yr. The change in the flux density of the flare phenomenon has two components. The first varies slowly and is present for all 2 yr, with a maximum amplitude of about 7 kJy toward the end 2020 (Flare 0). The second component involves nine powerful flares that lasted no more than a month each (Fig. 1). It is important to note that all nine powerful flares are located at the top of Flare 0, which makes it impossible to accurately determine the amplitude of Flare 0 during each of Flares 1–9. The division of the flare phenomenon into nine shorter flares and one extremely long flare, Flare 0, is arbitrary but does not contradict the presentation of data from long-term monitoring of the flux density. The first of the nine powerful flares occurred at the beginning of 2020. Its amplitude exceeded 20 kJy. It was followed shortly by Flare 2, the increase in radiation of which coincided with the decrease in the flux density of Flare 1. At a level of about 7 kJy, minimum flux density values are observed for the short flares but the maximum flux density of Flare 0 is observed. Flares 3–9 are also located on the top of Flare 0. Then, in 4 months, the amplitude of Flare 0 decreases to values close to zero. In March 2021 the flare phenomenon disappeared.

3.2 Interpretation of the received data

To understand the physical nature of this complex flare phenomenon, we used the spectral-time method of research. It is based on the simultaneous analysis of flux density monitoring data and spectral data. The changes in the flux density of the nine shorter but more powerful flares have an exponential character during both the increase and decrease in flux density. This spectral flux density behavior is one of the main indications that the maser was in an unsaturated state during the flare. For this case, the dependence of the spectral line width, Δυ, on the maser flux density, S, should have the form (Goldreich & Kwan 1974) Δυ≈Δυ01+lnSS0,$ {\rm{\Delta }}\upsilon \approx {{{\rm{\Delta }}{\upsilon _0}} \over {\sqrt {1 + \ln {\textstyle{S \over {{S_0}}}}} }}, $(1)

where Δυ0 is the thermal line width of the water molecule, and S0 is the input flux density into the maser condensation. We obtained an approximation of the observational data and the relation that describes the experimental dependence (Volvach 2019b): 1(Δυ)2=a+b⋅lnS.$ {1 \over {{{\left( {{\rm{\Delta }}\upsilon } \right)}^2}}} = a + b \cdot \ln S. $(2)

Here a and b are coefficients.

To convert the form of Eq. (1) into the form of Eq. (2), we swapped both parts of it (right and left) and squared them: 1(Δυ)2=1+lnSS0(Δυ0)2,$ {1 \over {{{\left( {{\rm{\Delta }}\upsilon } \right)}^2}}} = {{1 + \ln {\textstyle{S \over {{S_0}}}}} \over {{{\left( {{\rm{\Delta }}{\upsilon _0}} \right)}^2}}}, $(3)

leading to 1(Δυ)2=(1−lnS0)+lnS(Δυ0)2.$ {1 \over {{{\left( {{\rm{\Delta }}\upsilon } \right)}^2}}} = {{\left( {1 - \ln {S_0}} \right) + \ln S} \over {{{\left( {{\rm{\Delta }}{\upsilon _0}} \right)}^2}}}. $(4)

From Eq. (4), we obtain a coefficient value: a=1−lnS0(Δυ0)2,b=1(Δυ0)2.$ \matrix{ {a = {{1 - \ln {S_0}} \over {{{\left( {{\rm{\Delta }}{\upsilon _0}} \right)}^2}}},} &amp; {b = {1 \over {{{\left( {{\rm{\Delta }}{\upsilon _0}} \right)}^2}}}} \cr } . $(5)

We thus obtained the best-fit line for Flares 5 and 7 (Fig. 2), which correspond to Eq. (2), and the masers, which are in an unsaturated state. The coefficients a and b were determined, from which the values Δυ0 and S0 were calculated. For Flare 5, for example, these coefficients are a5 = −1.96, b5 = 0.81. The width of the thermal line and the input flux density obtained from these coefficients are respectively Δυ05 ≈ 1.10 km s−1 and S05 ≈ 30 kJy.

Figure 3 shows the spectral line of the most powerful flare, Flare 5, with an amplitude of about 65 kJy; its line width is Δυ05 measured ≈ 0.95 km s−1, which coincides with the model value within 15%. The input flux density obtained from the model representations, S05 ≈ 30 kJy, coincides with the input flux density created by Flare 4 and transferred to Flare 5 (Fig. 1). Flare 3 also produces an input flux of about 20 kJy for Flare 4 (Fig. 1). Thus, each previous flare creates an input flux density for the next flare that corresponds to its amplitude at a given time. This may indicate that the proposed model for fitting the observational data successfully operates under the assumption of the cascade amplification of a water maser.

Regarding the slope of the flare, where flux density decreases, it also changes exponentially. This gives a line width close to that obtained at the rising edge of the flare. Indeed, for Flare 7, the width of the spectral line is Δυ07 measured ≈ 0.96 km s−1 (Fig. 4). The measurement error of the spectral line width is close to the maximum spectral resolution of 0.03 km s−1. The difference in the widths of two spectral lines is measured as 2$\sqrt 2 $ times the greater error.

Figure 5 shows the approximation of the Flare 0 spectrum by a Gaussian dependence (red line). The Flare 0 amplitude is 4.4 kJy according to the best-fit approximation. The width of the spectral line approximation of Flare 0 is 2.75 km s−1. The kinetic temperature of H2O molecules corresponding to this value is Tk = 2875 K, in accordance with expression (10) of Goldreich & Kwan (1974).

Figure 6 shows the approximation of the Flare 0 spectrum by a Gaussian dependence (red line). The Flare 0 amplitude is 4.8 kJy according to the best-fit approximation. The width of the spectral line approximation of Flare 0 is 2.80 km s−1. The kinetic temperature of H2O molecules corresponding to this value is Tk = 2980 K, in accordance with expression (10) of Goldreich & Kwan (1974).

Flare 0 has a much longer duration than each of Flares 1–9, beginning before the onset of Flare 1 and continuing past the conclusion of Flare 9. It also has several times wider spectral lines. During the action of each of Flares 1–9, the amplitude of Flare 0, over which they are visible, changes. The amplitude of Flare 0 during the action of each of Flares 1–9 we can approximate with a Gaussian dependence, choosing its width and amplitude. We used a least squares optimization of the entire spectrum via the MATLAB package. The procedure was carried out to approximate the first Gaussian for a broad line (under software constraints on the flux density of the second component). Then, the Gaussian fitting procedure was performed for the flare component with a narrow line.

Flare 0 has no narrowed spectral lines, which mean they most likely belong to a saturated maser. The degree of the line narrowing in unsaturated masers is about a factor of 3 (Δυunsatur ≈ 0.95 km s−1).

The narrowing of the lines in unsaturated masers that we have found is within the limits of theoretical predictions (Shmeld 1976). The kinetic temperature of this saturated Flare 0 line is close to 3000 K. This provides a high degree of ionization and the necessary population of signal levels in the rotational transitions of the water molecule to create a powerful maser activation. Flare 0 supplies a significant input flux for all the unsaturated flares, Flares 1–9, providing a cascade amplification mode for the water masers. This is one of the most important results we obtained.

thumbnail Fig. 2

Dependences between the spectral line width in the power of minus two, (Δυ)−2, and the natural logarithm of the flux density, ln(5), for Flare 5 and Flare 7.
thumbnail Fig. 3

Spectrum of Flare 5 for the phenomenon at about −1.5 km s−1.
thumbnail Fig. 4

Spectrum of Flare 7 for the phenomenon at about −1.5 km s−1.
thumbnail Fig. 5

Approximation of the Flare 0 spectrum by a Gaussian dependence (red line). Flare 7 (black line) is on top of Flare 0. Flare 0 is better seen when the flux density is limited to 6 kJy. The spectral line near 2.5 km s−1 is visible on the right.
thumbnail Fig. 6

Approximation of the Flare 0 spectrum by a Gaussian dependence (red line). Flare 5 (black line) is on top of Flare 0. Flare 0 is better seen when the flux density is limited to 6 kJy. The spectral line near 2.5 km s−1 is visible on the right.

4 Discussion

4.1 The CC(r) maser pumping model and its implications for IRAS 16293

Some suggest that the powerful flares of a water maser are explained by the collisional-collisional pumping mechanism at rotational levels (CCr) since certain difficulties arise with other mechanisms, in particular radiative ones (Strelnitskiy 1980; Palma 1988). No current models can naturally explain the very large fluxes of maser radiation from small emitting regions (Litvak 1969; Jong 1973; Goldreich & Kwan 1974; Norman & Silk 1979). There are four main points that lend support to the idea of CCr maser pumping during the generation of extremely powerful flares (Strelnitskiy 1980).

First, CCr pumping works at arbitrarily high gas densities. Its speed increases with increasing density, which is realized in a medium where powerful supersonic shock waves propagate.

Second, such pumping is extremely economical, since a negligible amount of energy, about one rotational quantum, is expended to create a water maser photon.

Third, there is no problem of energy sink here, which exists with the radiative pumping mechanism in rotational lines. The energy sink from the pumping region is carried out by photons of vibrational transitions, although during the pumping cycle, cold particles take energy from the working molecules via rotational quanta. For vibrational photons, the effective thickness of maser condensation is much smaller than for rotational photons, which accelerates the exit of vibrational photons from the medium of maser radiation generation.

Fourth, in this case, vibrational photons are more strongly absorbed by cold dust (Walker et al. 1986), which, in combination with a shallower optical depth, reduces the probability of their scattering and ensures an efficient energy sink from the water maser pumping medium.

The radiatively pumped scheme generally operates at a higher dust temperature, and a lower kinetic temperature, than the collisional scheme (Gray et al. 2022). Therefore, we do not consider the scheme of radiatively maser pumping to be preferable.

A CCr maser pumping behind the front of the shock wave was proposed in Shmeld (1976) and Kylafis & Norman (1986). Taking the four arguments listed above into account, we chose to use the CCr pump model to analyze the powerful flares in IRAS 16293.

The main condition for the operation of this model is the presence in the maser medium of at least two types of particles (molecules or atoms of hydrogen and electrons) with different temperatures, which contribute comparable shares to the excitation of the H2O levels (Sobolev et al. 2018). On the whole, CCr pumping works at all densities, but its effective operation requires a sufficiently high density of the medium and a high degree of ionization. The pump power needed for the observed flux density from IRAS 16293 in the water line can be determined from Eq. (3.8a) of Strelnitskij (1984), from which the relation nl⋅ΔPCCr≥nl⋅ΔP${n_l} \cdot {\rm{\Delta }}{P_{C{C_r}}} \ge {n_l} \cdot {\rm{\Delta }}P$ is obtained: n1⋅ne⋅qer⋅Erk⋅Te⋅TH−TeTH≥10⋅l−3⋅D2⋅S⋅ΔvH2OvH2O,or$ {n_1} \cdot {n_{\rm{e}}} \cdot q_{\rm{e}}^r \cdot {{{E_{\rm{r}}}} \over {k \cdot {T_{\rm{e}}}}} \cdot {{{T_{\rm{H}}} - {T_{\rm{e}}}} \over {{T_{\rm{H}}}}} \ge 10 \cdot {l^{ - 3}} \cdot {D^2} \cdot S \cdot {{{\rm{\Delta }}{v_{{{\rm{H}}_2}}}_{\rm{O}}} \over {{v_{{{\rm{H}}_2}}}_{\rm{O}}}},{\rm{or}} $(6) n1⋅ne≥10⋅l−3⋅D2⋅S⋅ΔvH2OvH2Oqer⋅Erk⋅Te⋅TH−TeTH.$ {n_1} \cdot {n_{\rm{e}}} \ge {{10 \cdot {l^{ - 3}} \cdot {D^2} \cdot S \cdot {\textstyle{{{\rm{\Delta }}{v_{{{\rm{H}}_2}{\rm{O}}}}} \over {{v_{{{\rm{H}}_2}{\rm{O}}}}}}}} \over {q_{\rm{e}}^r \cdot {\textstyle{{{E_{\rm{r}}}} \over {k \cdot {T_{\rm{e}}}}}} \cdot {\textstyle{{{T_{\rm{H}}} - {T_{\rm{e}}}} \over {{T_{\rm{H}}}}}}}}. $(7)

Here, n1 is the population density of the lower signal level, ne is the electronic density, qer$q_{\rm{e}}^r$ is the electronic shock decontamination coefficient, Er=h⋅vH2O${E_{\rm{r}}} = h \cdot {v_{{{\rm{H}}_2}{\rm{O}}}}$, Te is the kinetic electronic temperature, TH is the kinetic temperature of H2 molecules, l is a maser amplification length (in units of AU), D is the distance to the source (in kpc), S is the flux density of the source (in Jy), and ΔvH2OvH2O${\textstyle{{{\rm{\Delta }}{v_{{{\rm{H}}_2}{\rm{O}}}}} \over {{v_{{{\rm{H}}_2}{\rm{O}}}}}}}$ is the ratio of the maser line width to its frequency (in units of 10−6).

According to Strelnitskij (1984), the CCr maser pumping begins to operate effectively at TH−TeTH=0.1${\textstyle{{{T_{\rm{H}}} - {T_{\rm{e}}}} \over {{T_{\rm{H}}}}}} = 0.1$. Substituting known and measured values into Eq. (7), we have: qer≈10−6$q_{\rm{e}}^r \approx {10^{ - 6}}$ cm3 s−1 (Itikawa 1972); Er = 1.5 × 10−16 erg, Te ≈ 2700 K, TH−TeTH≈0.1${\textstyle{{{T_{\rm{H}}} - {T_{\rm{e}}}} \over {{T_{\rm{H}}}}}} \approx 0.1$, l ≈ 3 × 1013 cm ≈ 2 AU (three condensations on the visual beam of 1013 cm, or 0,6 AU each), and D ≈ 0.14 kpc, S ≈ 6.5 × 104 Jy, ΔvH2OvH2O≈2.4×10−1${\textstyle{{{\rm{\Delta }}{v_{{{\rm{H}}_2}{\rm{O}}}}} \over {{v_{{{\rm{H}}_2}{\rm{O}}}}}}} \approx 2.4 \times {10^{ - 1}}$. Then we have nl · ne ≥ 4.4 × 1015 cm−6. The lower estimates that we obtain for n1 and ne (n1 ≈ 6.5 × 107 cm−3 and ne ≈ 6.5 × 107 cm3) are an order of magnitude higher than the values of physical parameters in the emission regions of water masers in Strelnitskij (1984).

Here we took the value of the kinetic temperature H2O = 3000 K for the saturated Flare 0 (Fig. 6). If the gas is heated by a shock wave (Pikelner & Strelnitsky 1976), or Alfven turbulence (Norman & Silk 1979), then the dissipated energy is transferred primarily to heavy particles – H2O and H2 molecules or hydrogen ions. In this case, the electrons can be stably in a colder state (Strelnitskiy 1980; Strelnitskij 1984). Therefore, it is natural to assume a temperature of 2700 K for them, which results in the ratio (TH–Te)/TH ≈ 0.1. If the ratio is larger, then the efficiency of the maser will be higher (Kylafis & Norman 1986, 1987). There are no exact data on the sizes of the maser condensations responsible for the giant flares of the water maser in IRAS 16293; therefore, we adopted a conditional value of 0.6 AU. This value does not contradict the observational data on the sizes of condensations in another source obtained for a much weaker flare, 1 ≈ 0.3 AU (Sobolev et al. 2018).

Our result is also in agreement with earlier works on maser emission in Orion KL, where the values ne/nH ≈ 10−5 and nH ≈ 2 × 1011 cm−3 were obtained based on reasonable assumptions (Strelnitskiy 1980). If we assume the same degree of ionization in the condensations of IRAS 16293 as adopted in other sources (Strelnitskiy 1980), then we get the density nH ≈ 6.5 × 1012 cm−3. This clearly shows that powerful water maser flares occur in spots with a high density of matter and a high ionization level, which is also a consequence of the high temperature of the environment during flares.

A legitimate question arises as to how the line width of a supposedly saturated water maser, which has a half-width of about 3 km s−1, changes. To do this, we looked at the parameters of the maser line at the beginning of Flare 0 (Fig. 7). We obtained the values of these parameters: amplitude SFlare0 ≈ 1.8 kJy ± 0.2 kJy, vH2O≈−1.7 km s−1±0.1 km s−1${v_{{{\rm{H}}_2}{\rm{O}}}} \approx - 1.7\,{\rm{km}}\,{{\rm{s}}^{ - 1}} \pm 0.1\,{\rm{km}}\,{{\rm{s}}^{ - 1}}$, and the half-width ≈2.9 km s−1 ± 0.1 km s−1. The error in determining the line velocity and its width for wide lines corresponds to a lower spectral resolution, as indicated in Sect. 2. The error in determining the flux density is about 10%. The resulting half-width of the spectral line of water at the beginning of Flare 0 is almost the same as at the maximum of Flare 0. This may indicate that the temperature increase during the flare phenomenon is explosive. This is an important physical conclusion. Outside the duration of the flare phenomenon under consideration, Flare 0, whose maser is in a saturated state, does not exist at all, although there is a narrow spectral line (≅0.5 km s−1) of much lower amplitude at this spot (Fig. 8). This suggests that Flares 0–9 were all initiated by the same agent.

It should be noted that during Flare 0, shorter flares occur with a rapid increase and decrease in flux density. For example, Figs. 5 and 6 show shorter flares with amplitudes of about 54 and 63 kJy, respectively, located on top of Flare 0. This can also be interpreted in such a way that the distribution of maser spots (not spatially resolved by our observations) is dense. Sometimes some of these spots blend together in the spectrum of a single dish, making the shorter flares be located on top of the longer Flare 0.

This leads to the question of what processes can result in these specified values of temperature, ambient density, and ionization level for the medium. One effective mechanism for increasing the density of a medium is the action of the stellar wind (Strelnitskiy 1980; Pikelner & Strelnitsky 1976; Norman & Silk 1979). In this case, H2O maser sources are the sites of interaction between the stellar wind of a nascent star and gas clumps in its envelope. One more source that can provide a high gas density and suitable conditions for the emergence of maser radiation should be mentioned: magnetohydrodynamic gas turbulence. Turbulence can provide energy for CCr pumping in small-scale stochastic shock waves (Strelnitski et al. 2002).

The slope of the “line width–flux” dependence for Flares 5 and 7 (Fig. 2) suggests that flares behave like radiation from unsaturated masers and possibly have the same excitation source. This source should lead to an explosive increase in temperature, the density of maser condensations, and the evaporation of ice from the surface of dust grains. At the same time, there must be conditions for the evacuation of emitting quanta from the maser region by colder dust or quanta of the vibrational transition of the H2O molecule, which have a smaller optical thickness.

If we assume that CCr pumping is the most probable mechanism for powerful flares, then shock waves may be the source of its initiation. If this is so, then the velocity of the shock wave propagation will be υpropagation = r/15 days. Here r is the size of the maser condensation, and 15 days is the duration of Flare 5 or 7, for example. If we take the condensation size to be 0.5 × 1013 cm (as in Orion KL), we get υ ≈ 60 km s−1. This velocity is more than an order of magnitude higher than the velocity of sound in the considered radiation medium of the water maser. This means that supersonic shock waves are really a source of maser radiation generation here.

thumbnail Fig. 7

Approximation of the spectrum of Flare 0 by the Gaussian dependence (red line) at the beginning of Flare 0.
thumbnail Fig. 8

Spectrum of the background flare that occurred before the analyzed phenomenon near −1.5 km s−1.
thumbnail Fig. 9

Temporal evolution of the radial velocity and flux density in the −1.5 km s−1 water maser component.

4.2 Indirect maser localization

The most important issue is the localization of water masers in the gas and dust complex IRAS 16293. Compact sources A1 and A2 in IRAS 16293 have radial velocities relative to the local standard of rest of 2.1 and 5.8 km s−1, respectively (Dzib et al. 2018; Maureira et al. 2020). According to interferometric observations of this source, the emission of a water maser with radial velocities of 1.9 km s−1 (near the center of A1) and 2.1 and 2.8 km s−1 (at the center of A2) has been recorded. Taking the velocities and nature of the velocity drift of our flare masers into account (Figs. 9 and 10), we can assume that the masers are located on the protoplanetary disk and rotate around the protostar. Masers are approaching us, and in 1.3 yr their radial velocity has increased by about 1.1 km s−1, moving toward zero from the negative side, but not yet reaching zero. Thus, we have registered a change in the velocity of maser spots at a level of (0.85 ±0.1) km s−1 per year (Figs. 8 and 9).

There are physical processes that lead to a visible distortion of the shape of the water maser line. One such process involves the existence of a hyperfine structure of the H2O line. The frequencies of the 616–523 rotational transitions are 22.235044, 22.235077, and 22.235120 GHz (Bluyssen 1967). The frequency difference between the two extreme lines is about 1 km s−1. Accounting for the hyperfine structure of the H2O maser line with λ0 = 1.35 cm can explain some line broadening within 20%, as well as the line shift of 0.1–0.3 km s−1 observed in some cases (Varshalovich 2006). The amount and direction of the shift depend critically on the state of saturation of the maser and whether or not the pumping mechanism for the maser equally affects all hyperfine transitions (Sullivan 1971). The inversion of hyperfine components to explain the frequency drift of the H2O line has never been explicitly discovered. In addition, the magnitude of the possible shift in the centroid of the H2O line due to changes in the intensities of the fine structure components is much less than the line drift we detected (Figs. 9 and 10).

A set of astrophysical data has established that the mass of each protostar in the compact formations A1 and A2 is 0.8 M⊙ (Pineda et al. 2012; Oya et al. 2016; Jacobsen et al. 2018; Maureira et al. 2020). We adopted this value. In addition, we assumed that the masers are located on the outer sides of the disks. Then, for the disk at <3.6 AU, the velocities of the maser spots on the disk will be 18 km s−1, and for the disk at 12 AU they will be 10 km s−1. In any case, the range of observed projections of maser spot radial velocities on the observer’s line of sight is suitable both for the disk in A1 and for the disk located in A2. We then needed to determine if the rotation periods of the disks are suitable for the observational data in this case. For a disk in A1 (<3.6 AU), the period of circulation of the disk in accordance with the laws of celestial mechanics (M* = 0.8 M⊙) will be less than 8.7 yr, and for a disk in A2 (12 AU) it will be about 50 yr. If we focus on the obtained value of the velocity drift (0.85 km s−1 per year) and their velocities on the disk (18 km s−1 for A1 and 10 km s−1 for A2), we can assume that the localization of our masers on the gas and dust disk in the A1 formation is preferable. The uncertainties of the obtained period values can be tens of percent, so they can be taken as estimates of these periods. Additionally, we took into account the presence of a possible period of activity of 8 yr, as indicated in Colom et al. (2021).

thumbnail Fig. 10

Drift of the radial velocity of maser flares in the phenomenon near −1.5 km s−1.

5 Conclusions

In this work, we have presented data from more than 2yr of monitoring of the water maser in the direction of the protostellar complex IRAS 16293-2422. Our main conclusions are as follows:

For the first time, a flare phenomenon unusual in terms of power and duration was registered near −1.5 km s−1. It consisted of nine short powerful flares emanating from maser spots close to one another, possibly located in the same maser cluster.

We determined new important physical parameters of maser flares: from the observational data we derived the shape of the flares in detail, the state of the water masers, and the motion parameters of the maser spots responsible for the flares. Furthermore, we inferred the temperature of the gas, the density of the medium, and the degree of ionization by assuming the CCr pumping mechanism is at play.

We have established the presence of a cascade amplification of the maser in the observer’s line of sight.

The flares of the water maser follow one another with a partial overlap in time, leading to each subsequent flare having a higher flux density.

The presence of powerful flares indicates that the masers themselves are in an unsaturated state.

We suggest that water masers are preferentially localized in the gas and dust protoplanetary disk of the young protostellar complex IRAS 16293-2422 in the A1 formation.

Acknowledgements

A.V. and L.V. are supported by Ministry of Science and Higher Education of the Russian Federation Grant 075-15-2020-780. We wish to thank the Maser Monitoring Organisation (M2O). We express our gratitude to the anonymous reviewer for his constructive comments during the preparation of the article.

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All Figures

thumbnail Fig. 1

Powerful flare phenomenon that occurred in IRAS 16293 near −1.5 km s−1. The crosses mark the values of the flux densities obtained on the RT-22 in Pushchino and published in Colom et al. (2021). The individual flares are numbered and marked with the symbol “F.”
In the text
thumbnail Fig. 2

Dependences between the spectral line width in the power of minus two, (Δυ)−2, and the natural logarithm of the flux density, ln(5), for Flare 5 and Flare 7.
In the text
thumbnail Fig. 3

Spectrum of Flare 5 for the phenomenon at about −1.5 km s−1.
In the text
thumbnail Fig. 4

Spectrum of Flare 7 for the phenomenon at about −1.5 km s−1.
In the text
thumbnail Fig. 5

Approximation of the Flare 0 spectrum by a Gaussian dependence (red line). Flare 7 (black line) is on top of Flare 0. Flare 0 is better seen when the flux density is limited to 6 kJy. The spectral line near 2.5 km s−1 is visible on the right.
In the text
thumbnail Fig. 6

Approximation of the Flare 0 spectrum by a Gaussian dependence (red line). Flare 5 (black line) is on top of Flare 0. Flare 0 is better seen when the flux density is limited to 6 kJy. The spectral line near 2.5 km s−1 is visible on the right.
In the text
thumbnail Fig. 7

Approximation of the spectrum of Flare 0 by the Gaussian dependence (red line) at the beginning of Flare 0.
In the text
thumbnail Fig. 8

Spectrum of the background flare that occurred before the analyzed phenomenon near −1.5 km s−1.
In the text
thumbnail Fig. 9

Temporal evolution of the radial velocity and flux density in the −1.5 km s−1 water maser component.
In the text
thumbnail Fig. 10

Drift of the radial velocity of maser flares in the phenomenon near −1.5 km s−1.
In the text

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