OUTBURST DUST PRODUCTION OF COMET 29P/SCHWASSMANN-WACHMANN 1

Comet SW1 was observed in two intervals spanning 2011 May 1–9 and 2012 June 6–July 3 (Table 1). Johnson–Cousins R-band images were obtained using an RCOS 0.5 m Ritchey–Chretien telescope equipped with an Apogee U16M CCD camera located at New Mexico Skies near Mayhill, NM, operated remotely from the Marshall Space Flight Center via ACP Astronomy (Denny 2011). Exposure time was 180 s, using 4 × 4 binning for an effective resolution of 184 pixel⁻¹ and field of view of 31' × 31'. Bias, dark, and twilight flat calibration frames were obtained and applied in the standard manner.

Photometry was conducted using Astrometrica (Raab, 2005) and Fotometrica Con Astrometrica (FoCAs; Roig et al. 2011). Of ∼15 images of the object obtained each night, four were chosen for photometry after being carefully examined for background stars, cosmic rays, or image artifacts within 50 arcsec of the comet which could effect the measurements. These images were then processed using Astrometrica, which uses the Carlsberg Meridian Catalog 14 (CMC-14) to identify the star field, locate any known non-stellar objects in the image, and perform photometry on a multitude of reference stars. Photometric measurements of the reference stars were compared with their catalog values in order to estimate the uncertainty in the photometric measurements. This output was then fed into FoCAs, which re-measures each identified star and again compares its calculated magnitude to its catalog value. Any stars with photometric residuals beyond a specified limit (0.3 mag in this case) were not used for analysis, in order to avoid inaccuracies caused by variable stars. Stars within a photometric aperture of the image edge or with saturated pixels were also rejected. Using the remaining reference stars, the calibrated flux and apparent magnitude of the comet was determined using 10 × 10, 20 × 20, 30 × 30, 40 × 40, 50 × 50, and 60 × 60 arcsec square apertures. The background was calculated from the mode of the entire image rather than from a sky annulus which could be contaminated with signal from the tail of the comet. The results from the four selected images were then averaged together to obtain the final apparent magnitude and flux of the comet for the night.

The FoCAs software was developed by the Internet comet forum Cometas-Obs, a group dedicated to observing and monitoring comets (http://www.astrosurf.com/cometas-obs/). All photometric measurements reported by the group use this software as part of a standardized procedure to ensure consistency across multiple observers. The Af ρ values produced from these measurements have been compared favorably with those from professional observations (Moreno et al. 2012; Moreno 2009). To qualitatively test the FoCAs software, the 10 and 20 arcsec apparent R-magnitudes measured using FoCAs during the 2011 observing session were compared with values obtained using standard aperture photometry routines in IRAF³ (Table 2). The FoCAs and IRAF measurements agree within an uncertainty of 0.1 mag for all but the night of 2011 May 8, which anomalously differed by 0.12 and 0.22 mag in the 10 and 20 arcsec apertures, respectively. The root mean square differences between the IRAF and FoCAs values across all nights were 0.06 mag in the 10 arcsec case and 0.11 mag in the 20 arcsec case. Given that primarily the 10 arcsec measurements are examined, this test gives confidence in the accuracy of the FoCAs results within the ∼0.1 mag uncertainties considered here. Further in-depth testing of the software is required to determine the accuracy of FoCAs beyond this level of uncertainty.

Dust production is calculated using the parameter Af ρ, which is the product of the object's albedo A, filling factor of grains within the field of view f, and nucleocentric distance ρ (A'Hearn et al. 1984). This can be calculated explicitly from the comet's observed brightness:

$$\begin{equation} Af\rho ({\rm cm}) = \frac{(2 \Delta R_{H})^2}{\rho }\left(\frac{F_{{\rm com}}}{F_{\odot }}\right) \end{equation} \tag{ 1 }$$

where Δ (AU) and R_H (cm) are the geocentric and heliocentric distances, ρ (cm) the nucleocentric distance, F_com the observed flux of the comet, and F_☉ the solar flux at 1 AU measured in the Johnson–Cousins R-filter. Δ and R_H were found using the JPL Horizons Web Interface,⁴ F_com determined from the apparent magnitude, and ρ calculated from the aperture radius r in arcseconds:

$$\begin{equation} \rho = \tan \left(\frac{1.12838r}{206265}\right)\Delta \end{equation} \tag{ 2 }$$

where 1.12838 represents a geometric correction factor due to the fact that FoCAs uses a square photometric aperture rather than a circular one.

Af ρ is advantageous in that it makes no assumptions about the dust characteristics of the comet (such as grain size or ejection velocity, often unknown) and is independent of aperture size if the surface brightness of the coma goes as ρ⁻¹ as predicted by models of quiescent dust production (Jewitt & Meech 1987). However, it is dependent on solar phase angle, for which a correction must be applied. As no standard solar phase correction exists for comets, a correction curve created by D. G. Schleicher (2012, private communication) from the combination of low phase angle observations of Halley's Comet (Schleicher et al. 1998) and a high-angle curve based on the Henyey–Greenstein function (Marcus 2007) was applied. This curve was chosen for its coverage of the low phase angle regime, which was critical since the phase angles of the observations ranged from 79 to 94. All Af ρ values are normalized to a phase angle θ = 0°, unless otherwise noted.

The brightness profile of many comets, which reveal the dust distribution of their comas, have been observed to deviate from the canonical ρ⁻¹ relationship (Jewitt & Meech, 1987; Baum et al. 1992). If this occurs, then Af ρ becomes dependent on aperture size, and the measurements must be normalized to a standard ρ when comparing values over a large range of geocentric distances (Schleicher et al. 1998; Schleicher & Blair 2011). In this case, the geocentric distance to SW1 did not change significantly over the time of the observations (5.68–5.79 AU in 2011, 5.84–6.26 AU in 2012), and so an aperture correction would change the Af ρ values by 2% at most. Since this is below photometric errors, no correction was applied. Unless specified, all reported values are measured using a 10 arcsec aperture, corresponding to ρ = 2.3 × 10⁹ cm for the 2011 observations and ρ = 2.4 × 10⁹ cm for the 2012 observations.

A significant increase in the activity of Comet 29P/Schwassmann-Wachmann 1 on 2011 May 3 indicates that an outburst occurred around that time. Its apparent R magnitude, measured through a 10 arcsec aperture, was observed to decrease from 16.4 ± 0.1 on May 1 to 14.3 ± 0.1 on May 3, accompanied with a shift in coma appearance from diffuse to stellar-like (Figure 1). This event is corroborated by Trigo-Rodriguez et al. (2011), who observe the 10 arcsec apparent R magnitude to decrease from 16.5 to 14.3 in measurements made between May 1 and May 2 using the data reduction procedure described by Kidger (2002). Af ρ is calculated to increase by a factor of ∼7, going from 2700 ± 300 cm on May 1 to 20,000 ± 1400 cm on May 3 (Figure 2). The comet continued to show distinctly heightened activity through May 9, seven days after the initial outburst.

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A second outburst was observed to occur between 2012 June 26 and July 1, during which the 10 arcsec R magnitude decreased from 16.9 ± 0.2 to 14.9 ± 0.2 (Hosek et al. 2012). As with the 2011 May 3 event, the coma was observed to shift from a diffuse to stellar-like appearance, seen in Figure 1. Af ρ is observed to increase by a factor of ∼6.5 during this period, from 2000 ± 200 cm to 12,500 ± 1100 cm, and remains at heightened values through July 3 (Figure 2), when the comet became unobservable due to its early set time and proximity to the moon. Unfortunately this outburst is not as well covered as the 2011 May 3 event, and so it is not possible to tightly constrain when the event began. These results are summarized in Table 3.

A lower limit for the dust production rate (Q_dust, kg s⁻¹) can be calculated from Af ρ (m):

$$\begin{equation} Q_{{\rm dust}} = \frac{0.67 * a * d * v_{{\rm dust}} * {Af}\rho }{A_{p}} \end{equation} \tag{ 3 }$$

where a is the average dust radius (μm), d the grain density (g cm⁻³), A_p the geometric albedo, and v_dust the ejection velocity of the dust grains (Weaver et al. 1999). An average dust radius a = 1 μm is assumed, as these grains dominate the photometric measurements since smaller grains do not strongly scatter at visible wavelengths and larger grains are expected to be small in number (Trigo-Rodriguez et al. 2008). A grain density d = 1 g cm⁻³ and geometric albedo A_p = 0.04 are adopted as typical values used for comets (Ivanova et al. 2011). There is evidence that v_dust changes when the comet is outbursting compared to when it is not; observations and theoretical models of SW1 suggest an ejection velocity of 50 m s⁻¹ when the comet is in a quiescent state (Gunnarsson et al. 2002; Fulle et al. 1998), while a velocity of 150 ± 50 m s⁻¹ was measured during an outburst (Feldman et al. 1996). Using these values, a lower limit for the dust production rate is calculated before and during each outburst from the Af ρ measurements (Table 3).

The difference between pre- and post-outburst Af ρ values is amplified by the difference in v_dust. As a result, Q_dust is found to increase from 22 ± 8 kg s⁻¹ on 2011 May 1 to 500 ± 200 kg s⁻¹ on May 3, a factor of ∼23. Although the dust production rate decreased after the initial outburst observation, the comet still produced dust at 230 ± 80 kg s⁻¹ seven days later, ∼10 times the amount of dust produced in the quiescent state. Similarly, the dust production rate was observed to increase by a factor of ∼18 during the 2012 event, from 16 ± 6 kg s⁻¹ on June 26 to 300 ± 100 kg s⁻¹ on July 1, and remained ∼14 times higher than quiescent levels two days later.

Previous studies measuring the dust production rate through various methods have yielded a wide range of values for SW1. Jewitt (1990) estimated a dust production rate on the order of 10 kg s⁻¹ using differences in apparent R magnitude in different-sized photometric apertures, Stansberry et al. (2004) determined an upper limit of 50 kg s⁻¹ based on IR color observations, and Ivanova et al. (2011) found a value of ∼50 kg s⁻¹ using Af ρ measurements and assuming 1 μm radius spherical grain particles. These values generally agree with the quiescent dust production rates found here, given the uncertainties in this calculation. Dramatically higher dust production rates of 600 ± 300 kg s⁻¹ and 300 ± 100 kg s⁻¹ were found by Fulle (1992) and Moreno (2009), respectively, based on numerical models of the observed dust coma. Values in this range are found during outbursts in this study, but are significantly higher than the quiescent dust production rates. As a whole, better constraints on the nuclear properties of SW1 are needed to evaluate these results, as uncertainties in parameters such as dust grain size and ejection velocity can lead to large differences in dust production rate.

The relationship between Af ρ and ρ yields information about the dust brightness profile of the comet. The profile can be described as a power law going as ρ^γ, where γ can be found from the slope of a log(Af ρ)–log(ρ) plot (Milani et al. 2007):

$$\begin{equation} \frac{d[{\rm log}({Af}\rho)]}{d[{\rm log}(\rho)]} = \gamma + 1 \end{equation} \tag{ 4 }$$

The value of γ is calculated using 10, 20, 30, 40, and 50 arcsec aperture measurements (Table 3). Values were determined for all observations except for 2012 June 9–18 and 26, where scatter made unreasonable to use a linear fit. In several cases, the dust profile exhibited curvature as the inner 10 and 20 arcsec measurements appeared significantly lower than would be expected from a linear fit of the larger aperture measurements, discussed below. For these, the slope presented was derived from the larger aperture measurements, which could still be well described by a linear fit. Note that γ decreases significantly at the beginning of both outbursts, dropping from a nearly quiescent value of −0.87 ± 0.09 to −1.59 ± 0.07 in 2011 and from −0.8 ± 0.1 to −1.7 ± 0.2 in 2012. After the initial decrease, γ begins to return to its original value, mirroring the behavior of Af ρ (Figure 3). This indicates that the steepening of the profile is connected to the increase in dust production during the 2011 and 2012 outbursts. These observations are consistent with Nakamura et al. (1991), who reported similar behavior during an outburst of SW1 and attribute it to the outburst. It is interesting to note that γ <−1 for 2012 June 6–8, suggesting non-quiescent dust production. Perhaps this is caused by the tail-end of another outburst or heightened dust activity, although it is not possible to determine from these observations.

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Trigo-Rodriguez et al. (2010) describe SW1 outburst events as massive releases of relatively large dust grains into the coma which subsequently fragment into μm-sized grains via sublimation. These grains, which strongly scatter visible light, are responsible for the observed increase in magnitude and shift in dust brightness profile. As the dust expands outward and continues to sublimate, the spatial density of the light-scattering grains decreases and the outburst fades away. This is consistent with our observations of γ, which would be expected to decrease as the amount of scattered light in the inner coma increased due to the introduction of large amounts of dust close to the nucleus. After the initial outburst γ would begin to return to quiescent values as the high concentration of dust moved outward and dissipated. During this process an outbound "ripple" in the dust brightness profile might be created as the injection of fresh dust grains slows to quiescent levels but the outburst material remains fairly concentrated as it moves outward. The beginning of such a ripple may be present in the dust profile for both outbursts, in the curvature of the 10 and 20 arcsec measurements relative to the other apertures (Figure 4). If true, the fact that an apparent ripple is already present in the first observation of the 2012 event would indicate that the initial event occurred a few days before. Unfortunately, observing conditions prevented the full evolution of the dust profile from being observed, and so this interpretation is uncertain.

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