Evidence for the pulsational origin of the Long Secondary Periods: The red supergiant star V424 Lac (HD 216946)

The results of a long-term UBV photometric monitoring of the red supergiant (RSG) star V424 Lac are presented. V424 Lac shows multiperiodic brightness variations which can be attributed to pulsational oscillations. A much longer period (P = 1601 d), that allows us to classify this star as a long secondary period variable star (LSPV) has been also detected. The B − V and U − B color variations related to the long secondary period (LSP) are similar to those related to the shorter periods, supporting the pulsational nature of LSP. The long period brightness variation of V424 Lac is accompanied by a near-UV (NUV) excess, which was spectroscopically detected in a previous study [Massey, P., Plez, B., Levesque, E.M., et al., 2005. ApJ 634, 1286] and which is now found to be variable from photometry. On the basis of the results found for V424 Lac, the NUV excess recently found in a number of RSGs may be due not solely to circumstellar dust but may also have a contribution from a still undetected LSP variability.     

A new absolute magnitude calibration with 2MASS for cataclysmic variables

Using reliable trigonometric measurements, we find that the absolute magnitude of cataclysmic variables depends on the orbital period and de-reddened (J − H)₀ and (H − K _s)₀ colours of 2MASS (Two Micron All Sky Survey) photometric system. The calibration equation covers the ranges 0.032^d < P_orb ⩽ 0.454^d, −0.08 < (J − H)₀ ⩽ 1.54, −0.03 < (H − K_s)₀ ⩽ 0.56 and 2.0 < M_J < 11.7; It is based on trigonometric parallaxes with relative errors of (σ_π/π) ⩽ 0.4. By using the period-luminosity-colours (PLCs) relation, we estimated the distances of cataclysmic variables with orbital periods and 2MASS observations and compared them with distances found from other methods. We suggest that the PLCs relation can be a useful statistical tool to estimate the distances of cataclysmic variables.     

Apsidal motion elements of three eccentric eclipsing binaries: V397 Cep,V493 Car and BW Aqr

The apsidal motion analysis of the eccentric eclipsing binaries: V397 Cep, V493 Car and BW Aqr have been presented. The method described by Lacy (1992) [Lacy, C.H S., 1992. AJ 104, 2213] has been used for the apsidal motion analysis. The apsidal motion periods have been found to be 174.2 ± 1.4, 277.3 ± 21.3 and 7195 ± 174 years for V397 Cep, V493 Car and BW Aqr, respectively.     

Thermal structure and CO distribution for the Venus mesosphere/lower thermosphere: 2001–2009 inferior conjunction sub-millimeter CO absorption line observations

Sub-millimeter ¹²CO (346 GHz) and ¹³CO (330 GHz) line absorptions, formed in the mesosphere and lower thermosphere of Venus (70–120 km), have been mapped across the nightside Venus disk during 2001–2009 inferior conjunctions, employing the James Clerk Maxwell Telescope (JCMT). Radiative transfer analysis of these thermal line absorptions supports temperature and CO mixing profile retrievals, as well as Doppler wind fields (described in the companion paper, Clancy et al., 2012). Temporal sampling over the hourly, daily, weekly and interannual timescales was obtained over 2001–2009. On timescales inferred as several weeks, we observe changes between very distinctive CO and temperature nightside distributions. Retrieved nightside CO, temperature distributions for January 2006 and August 2007 observations display strong local time, latitudinal gradients consistent with early morning (2–3 am), low-to-mid latitude (0–40NS) peaks of 100–200% in CO and 20–30 K in temperature. The temperature increases are most pronounced above 100 km altitudes, whereas CO variations extend from 105 km (top altitude of retrieval) down to below 80 km in the mesosphere. In contrast, the 2004 and 2009 periods of observation display modest temperature (5–10 K) and CO (30–60%) increases, that are centered on antisolar (midnight) local times and equatorial latitudes. Doppler wind derived global (zonal and should be SSAS) circulations from the same data do not exhibit variations correlated with these CO, temperature short-term variations. However, large-scale residual wind fields not fit by the zonal, SSAS circulations are observed in concert with the strong temperature, CO gradients observed in 2006 and 2007 (Clancy et al., 2010). These short term variations in nightside CO, temperature distributions may also be related to observed nightside variations in O₂ airglow (Hueso, H., Sánchez-Lavega, A., Piccioni, G., Drossart, P., Gérard, J.C., Khatuntsev, I., Zasova, L., Migliorini, A. [2008]. J. Geophys. Res. 113, E00B02. doi:10.1029/2008JE003081) and upper mesospheric SO and SO₂ layers (Sandor, B.J., Clancy, R.T., Moriarty-Schieven, G.H., Mills, F.P. [2010]. Icarus 208, 49–60).The retrieved temperature profiles also exhibit 20 K long-term (2001–2009) variations in nightside (whole disk) average mesospheric (80–95 km) temperatures, similar to 1982–1991 variations identified in previous millimeter CO line observations (Clancy et al., 1991). Global average diurnal variations in lower thermospheric temperatures and mesospheric CO abundances decreased by a factor-of-two between 2000–2002 versus 2007–2009 periods of combined dayside and nightside observations. The infrequency and still limited temporal extent of the observations make it difficult to assign specific timescales to such longer term variations, which may be associated with longer term variations observed for cloud top SO₂ (Esposito, L.W., Bertaux, J.-L., Krasnopolsky, V., Moroz, V.I., Zasova, L.V. [1997]. Chemistry of lower atmosphere and clouds. In: Bougher, S.W., Hunten, D.M., Phillips, R.J. (Eds.), VENUS II, 1362pp) and mesospheric water vapor (Sandor, B.J., Clancy, R.T. [2005]. Icarus 177, 129–143) abundances.     

A CCD photometric study of the late type contact binary EK Comae Berenices

We present CCD photometric observations of the W UMa type contact binary EK Comae Berenices using the 2 m telescope of IUCAA Girawali Observatory, India. The star was classified as a W UMa type binary of subtype-W by Samec et al. (1996). The new V band photometric observations of the star reveal that shape of the light curve has changed significantly from the one observed by Samec et al. (1996). A detailed analysis of the light curve obtained from the high-precision CCD photometric observations of the star indicates that EK Comae Berenices is not a W-type but an A-type totally eclipsing W UMa contact binary. The photometric mass ratio is determined to be 0.349 ± 0.005. A temperature difference of ΔT = 141 ± 10 K between the components and an orbital inclination of i[°] = 89.800 ± 0.075 were obtained for the binary system. Absolute values of masses, radii and luminosities are estimated by means of the standard mass-luminosity relation for zero age main-sequence stars. The star shows O’Connell effect, asymmetries in the light curve shape around the primary and secondary maximum. The observed O’Connell effect is explained by the presence of a hot spot on the primary component.     

Photometric and spectroscopic evolution of the symbiotic nova V1016 Cygni after its outburst

We have constructed the light curves of the symbiotic nova V1016 Cyg for the period 1971–2007 in a homogeneous photometric system close to UBV using our observations with the Zeiss-600 SAI telescope. Based on the observational data obtained with the 125-cm SAI telescope in 2000–2007, we have performed absolute spectrophotometry of the star in the range λ3700–9300 Å. The derived line intensities are compared with the data of other authors in the preceding years (1965–1988). The behavior of nebular lines showed the variations in electron density and, probably, electron temperature in the [OIII] emission region caused by a variable stellar wind from the hot component. All the available observations of the star confirm the theoretical conclusion that the nova-like outburst of V1016 Cyg was produced by a thermonuclear flash in the accreted envelope of a white dwarf.     

Unstable cyclic modulation during the main outburst of KS 1731-260

We analyze the intensity modulation in the final, very broad peak of the main outburst of the neutron star low-mass X-ray binary KS 1731-260. We use ASM/RXTE observations for a time-series analysis of the long-term variations. We also investigate the X-ray color (hardness ratio) changes in the 1.5–12 keV band. The modulation with the mean cycle-length of 37 days is transient and is detected only in several time segments. It underwent significant variations of both the cycle-length and the amplitude. This cycle cannot be caused by transitions of the outer disk region between the hot and cool state that gave rise to the subsequent series of the echo outbursts. Because of its high X-ray luminosity (L_X ≈ 0.1 of the Eddington luminosity), KS 1731-260 is a promising candidate for having its accretion disk tilted and warped. The properties of the modulation can therefore be explained as due to variable (multimodal), but still detectable superorbital periods caused by a disk precession with mode switching and unstable warps. We find that a variable L_X is not the sole parameter that governs the presence of the cycle. Variable absorption of X-rays cannot be dominant in producing the modulation of the ASM flux during the cycle. Variations of the stream impact on the tilted and warped disk, hence affecting the mass flow in the inner disk region, consequently the emission components, are a promising mechanism for the observed cycle. In this scenario, the true cycle-length can be twice as long because of the double-wave profile.     

Simultaneous photometric and spectral analysis of a new outburst of V1686 Cyg

We present an analysis of the optical observations of Herbig Ae/Be(HAeBe) star V1686 Cyg,which is associated with a small isolated star-forming region around HAeBe star BD+40?4124. We observed this star as a part of our project investigating young eruptive stars. Observations were conducted on the 2.6-m telescope of Byurakan Observatory from 2015 to 2017. In this period, we obtained direct images of V1686 Cyg and 14 medium-and low-resolution spectra. In the course of observations, we noticed that this star underwent an atypical brightness outburst. After data reduction, we found that the full rise and decline in the brightness of V1686 Cyg had an amplitude of almost 3 magnitudes and lasted about 3 months.We were also able to track changes in the stellar spectrum during the outburst, which are correlated with the photometric variations.     

VISTA Variables in the Via Lactea (VVV): The public ESO near-IR variability survey of the Milky Way

We describe the public ESO near-IR variability survey (VVV) scanning the Milky Way bulge and an adjacent section of the mid-plane where star formation activity is high. The survey will take 1929 h of observations with the 4-m VISTA telescope during 5 years (2010–2014), covering ～10⁹ point sources across an area of 520 deg², including 33 known globular clusters and ～350 open clusters. The final product will be a deep near-IR atlas in five passbands (0.9–2.5 μm) and a catalogue of more than 10⁶ variable point sources. Unlike single-epoch surveys that, in most cases, only produce 2-D maps, the VVV variable star survey will enable the construction of a 3-D map of the surveyed region using well-understood distance indicators such as RR Lyrae stars, and Cepheids. It will yield important information on the ages of the populations. The observations will be combined with data from MACHO, OGLE, EROS, VST, Spitzer, HST, Chandra, INTEGRAL, WISE, Fermi LAT, XMM-Newton, GAIA and ALMA for a complete understanding of the variable sources in the inner Milky Way. This public survey will provide data available to the whole community and therefore will enable further studies of the history of the Milky Way, its globular cluster evolution, and the population census of the Galactic Bulge and center, as well as the investigations of the star forming regions in the disk. The combined variable star catalogues will have important implications for theoretical investigations of pulsation properties of stars.     

Photometric study of the FUor star V 1735 Cyg (Elias 1-12)

Results from optical photometric observations of the PMS star V 1735 Cyg are reported. The star is located in the IC 5146 dark cloud complex—a region of active star formation. On the basis of observed outburst and spectral properties, V 1735 Cyg was classified as a FUor object. We present data from BVRI CCD photometric observations of the star, collected from March 2003 to January 2009. Plates from the Rozhen Schmidt telescope archive were scanned for a brightness estimation of the star. A sequence of sixteen comparison stars in the field of V 1735 Cyg was calibrated in BVRI bands. The data from photographic observations made from 1986 to 1992 show a strong light variability (ΔV=1_⋅^m2). In contrast, the recent photometric data obtained from 2003 to 2009 show only small amplitude variations (ΔI=0_⋅^m3). The analysis of existing photometric data shows a very slow decrease in star brightness—1_⋅^m8 (R) for a 44 year period. The possibilities for future photometric investigations of V 1735 Cyg using the photographical plate archives is discussed briefly.     

The first high-precision radial velocity search for extra-solar planets

The reflex motion of a star induced by a planetary companion is too small to detect by photographic astrometry. The apparent discovery in the 1960s of planetary systems around certain nearby stars, in particular Barnard’s star, turned out to be spurious. Conventional stellar radial velocities determined from photographic spectra at that time were also too inaccurate to detect the expected reflex velocity changes. In the late 1970s and early 1980s, the introduction of solid-state, signal-generating detectors and absorption cells to impose wavelength fiducials directly on the starlight, reduced radial velocity errors to the point where such a search became feasible. Beginning in 1980, our team from UBC introduced an absorption cell of hydrogen fluoride gas in front of the CFHT coudé spectrograph and, for 12 years, monitored the radial velocities of some 29 solar-type stars. Since it was assumed that extra-solar planets would most likely resemble Jupiter in mass and orbit, we were awarded only three or four two-night observing runs each year. Our survey highlighted three potential planet hosting stars, γ Cep (K1 IV), β Gem (K0 III), and ? Eri (K2 V). The putative planets all resembled Jovian systems with periods and masses of: 2.5 years and 1.4 M_J, 1.6 years and 2.6 M_J, and 6.9 years and 0.9 M_J, respectively. All three were subsequently confirmed from more extensive data by the Texas group led by Cochran and Hatzes who also derived the currently accepted orbital elements.None of these three systems is simple. All five giant stars and the supergiant in our survey proved to be intrinsic velocity variables. When we first drew attention to a possible planetary companion to γ Cep in 1988 it was classified as a giant, and there was the possibility that its radial velocity variations and those of β Gem (K0 III) were intrinsic to the stars. A further complication for γ Cep was the presence of an unseen secondary star in an orbit with a period initially estimated at some 30 years. The implication was that the planetary orbit might not be stable, and a Jovian planet surviving so close to a giant then seemed improbable. Later observations by others showed the stellar binary period was closer to 67 years, the primary was only a sub-giant and a weak, apparently synchronous chromospheric variation disappeared. Chromospheric activity was considered important because κ¹ Cet, one of our program stars, showed a significant correlation of its radial velocity curve with chromospheric activity.? Eri is a young, magnetically active star with spots making it a noisy target for radial velocities. While the signature of a highly elliptical orbit (e = 0.6) has persisted for more than three planetary orbits, some feel that even more extensive coverage is needed to confirm the identification despite an apparent complementary astrometric acceleration detected with the Hubble Space Telescope.We confined our initial analyses of the program stars to looking for circular orbits. In retrospect, it appears that some 10% of our sample did in fact have Jovian planetary companions in orbits with periods of years.     

Multiwavelength modelling the SED of supersoft X-ray sources I. The method and examples

Radiation of supersoft X-ray sources (SSS) dominates both the supersof X-ray and the far-UV domain. A fraction of their radiation can be reprocessed into the thermal nebular emission, seen in the spectrum from the near-UV to longer wavelengths. In the case of symbiotic X-ray binaries (SyXBs) a strong contribution from their cool giants is indicated in the optical/near-IR. In this paper I introduce a method of multiwavelength modelling the spectral energy distribution (SED) of SSSs from the supersoft X-rays to the near-IR with the aim to determine the physical parameters of their composite spectra. The method is demonstrated on two extragalactic SSSs, the SyXB RX J0059.1-7505 (LIN 358) in the Small Magellanic Cloud (SMC), RX J0439.8-6809 in the Large Magellanic Cloud (LMC) and two Galactic SSSs, the classical nova RX J2030.5+5237 (V1974 Cyg) during its supersoft phase and the classical symbiotic star RX J1601.6+6648 (AG Dra) during its quiescent phase. The multiwavelength approach overcomes the problem of the mutual dependence between the temperature, luminosity and amount of absorption, which appears when only the X-ray data are fitted. Thus, the method provides an unambiguous solution. It was found that selection of the model (a blackbody or an atmospheric model) is not of crucial importance in fitting the global X-ray/IR SED. The multiwavelength modelling of the SED of SSSs is essential in determining their physical parameters.     

A comprehensive photometric study of the Algol-type eclipsing binary: BG Pegasi

This study presents new photometric observations of classical Algol type binary BG Peg with a δ Scuti component. The light curve modeling was provided with the physical parameters of the component stars in the BG Peg system for the first time. After modeling light curves in B and V filters, the eclipse and proximity effects were removed from the light curve to analyze intrinsic variations caused by the hotter component of the system. Frequency analysis of the residuals light represents the multi-mode pulsation of the more massive component of the BG Peg system at periods of 0.039 and 0.047 days. Two frequencies could be associated with non-radial (l = 2) modes. The total amplitude of the pulsational variability in the V light curve was found to be about 0.045 mag. The long-term orbital period variation of the system was also investigated for the first time. The O–C analysis indicates periodic variation superimposed on a downward parabola. The secular period variation means that the orbital period of the system is decreasing at a rate of ?5.5 seconds per century, probably due to the magnetic activity of the cooler component. The tilted sinusoidal O–C variation may be caused by the gravitational effect of an unseen component around the system.     

Is V899 Herculis an unsolved quadruple system containing double close binary stars?

Orbital period variation of the W UMa-type eclipsing binary, V899 Herculis, discovered by the Hipparcos satellite was investigated based on all available photoelectric and CCD times of light minimum. It is discovered that the orbital period of the binary shows a cyclic change with an amplitude of 0.0117 days. The cyclic period change can be explained as the light-travel time orbit of a tertiary component in the system, which is in agreement with the spectroscopic result obtained by Lu et al. [Lu, W., Rucinski, S.M., Ogloza, W., 2001. AJ 122, 402] who found that the system, of which V899 Herculis is a fainter component (B), is a triple, even quadruple and with the photometric result obtained by Özdemir et al. [Özdemir, S., Demircan, O., Erdem, A., Cicek, C., Bulut, I., Soydugan, E., Soydugan, F., 2002. A&A 387, 240] who reported a large amount of third light (L₃ ∼ 0.68) of the system. The third body (A) rotates around the eclipsing pair in a period of 3.7 years. Lu et al. [Lu, W., Rucinski, S.M., Ogloza, W., 2001. AJ 122, 402] reported that the tertiary component is F5-type main-sequence star. However, the present analysis shows that the mass of the third component is no less than 2.8 M_⊙, which is larger than the mass of an F5-type main-sequence star suggesting that the tertiary component may be a non-eclipsing close binary. Therefore, the system may be a possible unsolved quadruple system containing double close binary stars. It is a good astrophysical laboratory to study the formation and evolution of binary and multiple system. The timescale for the formation of the G-type overcontact binary (V899 Herculis) via AML should be shorter than the main-sequence time of an F5-type star.     

New aspects of spectral behavior of SS Cyg and WX Hyi between quiescence and outburst states in the UV

We present low-resolution UV spectra of the dwarf novae SS Cyg and WX Hyi in both quiescence and outburst states from observations taken by the International Ultraviolet Explorer (IUE) during the period between 1978–1994 and 1979–1993 for two systems respectively. Both SS Cyg and WX Hyi are characterized by emission lines in quiescence physical states and absorption lines in states of outburst. We concentrated on calculating the line fluxes and line widths of the C IV 1550 Å emission line arising from the disk around the white dwarf of SS Cyg and WX Hyi. We found that there is spectral variability for these physical parameters at different times, similar to that known for their light curves (Voloshina and Khruzina, 2006, Kuulkers et al., 1991). We attribute it to the variations of both density and temperature as a result of changing the mass transfer rate (Long et al., 2005, Patterson, 1984, Meyer and Meyer-Hofmeister, 1994, Cannizzo, 2001, Schwope et al., 2002). Also we found that both line fluxes and line widths of SS Cyg are greater than the line fluxes and line widths of WX Hyi.     

Infrared photometric study of SDSS selected narrow line Seyfert 1 galaxies

The infrared photometric study of SDSS selected Narrow Line Seyfert 1 Galaxies (NLS1s) is presented in this paper. We have made cross-identifications for such NLS1s with 2MASS and WISE observations. Finally 992 NLS1s have 2MASS and WISE counterparts. Comparisons of NLS1s with the Broad Line Seyfert 1 (BLS1s) and Seyfert 2 galaxies are made. It is shown that from 1 µm to 5 µm NLS1s are redder than BLS1s and Seyfert 2 galaxies possibly due to the richer dust environment in NLS1 nuclei or to the orientation effect while in the longer wavelengths those three kinds of sources have quite similar behavior indicative of radiation mainly from the similar warm starburst-related dust and the related AGN dust.In addition, relations between infrared colors and related (to H_β) strengths of some important lines are also investigated. The results show that the related strengths of [FeII] 4570 Å are positively correlated with infrared colors in the 1–5 µm region, but negatively correlated with infrared colors in the 12–22 µm region; the related strength of [OIII] 5007 Å are negatively correlated with infrared colors in the 1–5 µm region, but positively correlated with infrared colors in the 12–22 µm region; the related strength of [NII]6583 Å are also negatively correlated with infrared colors in the 1–5 µm region, but positively correlated with infrared colors in the 12–22 µm region. Therefore it is indicated that the behavior of [FeII] 4570 Å is just opposed to that for [OIII] 5007 Å and [NII] 6583 Å This result may be caused by different origins of such lines.     

The cyclic variation of the outburst recurrence time in GRS 1747–312

We present an analysis of the long-term evolution of outbursts in the neutron star soft X-ray transient GRS 1747–312. Observations taken from ASM/RXTE, in the 1.5–12 keV passband, are utilized. We reveal a cyclic behavior in the residuals of the outburst recurrence time with respect to the mean value of T_C = 136 ± 2 days. The profile of this cycle is approximately sinusoidal; the remaining cycle-to-cycle fluctuations possess a considerably smaller amplitude. We find that, although the peak flux of the outbursts displays a significant scatter at a given phase of the cycle, the most luminous outbursts occur after the longest T_C. The fluence displays a large scatter for the individual outbursts and tends to decrease with time. We argue that although the cycle-length of ～5.4 yr is compatible with that of the presumed magnetic activity of the late-type donor, it cannot be explained by variations of the mass outflow from the donor to the disk. In our interpretation, the stellar activity is translated to variations of T_C via interaction of the magnetic field of the spots on the donor with the magnetic field of the disk. This gives rise to a variable efficiency of the removal of the angular momentum from the quiescent disk during the activity cycle of the donor. This mechanism can be strengthened by accompanying variations of the radius of the optically thin advection-dominated accretion flow in quiescence. We show that the peak mass accretion rate onto the neutron star in the individual outbursts of GRS 1747–312 is considerably more stable than in two other similar systems with frequent outbursts, Aql X-1 and 4U 1608–52; this allows the cyclic modulation of T_C to show itself in GRS 1747–312.     

Stochastic variability of luminous blue variables

Using the archives of the American Association of Variable Stars Observers and our own data, we analyse the long-term variability of several well-studied luminous blue variables (LBVs) aiming on a general picture of stochastic variability of these objects. The power density spectra of all the selected objects may be generally described by a single power law contaminated by observational noise at higher frequencies. The slopes of the power-law component are close to p = 2 (where PDS ∝ f^?p, and f is frequency) for strongly variable flaring objects like AG Car and significantly smaller (p ～ 1.3) for P Cyg where brightness variation amplitude is ? 1^m and dominated by slow low-amplitude variability. The slope holds for about two orders of magnitude in the frequency domain, though peaks and curvatures are present at f ? 10^?2–10^?3 d^?1. We show that pseudo-photosphere approach to variability may explain the power-law shape of the variability spectrum at higher frequencies. However, the observed spectra are actually rather “red” than “brown”: flux variations are correlated up to tens of years that is much longer than the characteristic refreshment time scales of the pseudo-photosphere. We propose that several stochastic noise components produce the power spectra of LBVs.     

Spectral behavior of the symbiotic nova AG Pegasi observed with IUE and HST

Ultraviolet spectra from the International Ultraviolet Explorer (IUE) and from the Hubble Space Telescope (HST) of the symbiotic novae AG Peg during the period 1978–1996 are analyzed. Some spectra showing the modulations of spectral lines at different times are presented. We determined the reddening from the 2200 Å feature, finding that E(B−V) = 0.10 ± 0.02. We studied N IV] at 1486 Å, C IV 1550 Å, and O III] at 1660 Å, produced in the fast wind from the hot white dwarf. The mean wind velocity of the three emission lines is 1300 km s⁻¹ (FWHM). The mean wind mass loss rate is ∼6 × 10⁻⁷ M_⊙ yr⁻¹. The mean temperature is ∼6.5 × 10⁵ K. The mean ultraviolet luminosity is ∼5 × 10³³ erg s⁻¹. The modulations of line fluxes in the emitting region at different times are attributed to the variations of density and temperature of the ejected matter as a result of variations in the rate of mass loss.     

Main Belt Comet P/2008 R1 Garradd: Duration of activity

In this work we investigated changes of the water emission from a model comet of the size and orbital elements of Comet P/2008 R1 (Garradd). We performed simulations for model cometary nuclei of different compositions and two different orientations in space. Our simulations indicate, that the emission of water decreases from one orbital period to another one, but in some cases slowly. When the rotation axis of the nucleus lies in the orbital plane the seasonal maximum of water production during the first two orbital periods can be as high as about 10²⁶ mol s^?1, but decreases by two orders of magnitude during only 50 orbital periods. The highest rate of water production after many orbital periods is expected when the rotation axis is perpendicular to the orbital plane – the seasonal maximum of water production can be about 5 × 10²⁵ mol s^?1 during the first two orbital periods after activation of the comet and no more than 0.8 × 10²⁵ mol s^?1 500 orbital periods later. The upper estimate for the production of water derived from observations of P/2008 R1 (Garradd) by Jewitt et al. (Jewitt, D., Yang, B., Haghighipour, N. [2009]. Astron. J. 137, 4313–4321) is 5 × 10²⁵.