Variable stars magnitudes estimations exploiting the eye physiology

arXiv:1106.6356v1 [astro-ph.IM] 30 Jun 2011 Einstein 120 Conference, Kyrgyz State University, Bishkek, 2000. Sigismondi1 VARIABLE STARS MAGNITUDES ESTIMATIONS EXPLOITING THE EYE PHYSIOLOGY COSTANTINO SIGISMONDI Department of Physics, University of Rome ”La Sapienza” and ICRA, International Center for Relativistic Astrophysics, P.le A.Moro 2 00185 Rome Italy The physiology of the dark adaption process of the eye is revisited from an astronomical point of view. A new method for the magnitude estimation of a star is presented. It is based upon the timing of the physiological cycle of the rhodopsin during the eye dark adaption process. The limits of the application of the method are discussed. This method is suitable for bright stars as Betelgeuse, Antares or Delta Scorpii or stars at the limiting magnitude observed with a telescope. 1. Introduction: the observations of variable stars Professional astronomers and astronomical observatories have not enough time for following all the light curves of the variable stars and novae appearing in the sky. Such work is carried out by amateurs astronomers with very good skills, and they are gathered in the AAVSO international organization.a They use mainly naked- eye observations, because of the relatively high cost of CCD devices for amateur equipments. The method of magnitude estimation of the star magnitude presented here (section two) is useful for observations near the telescope limiting magnitude (section three). The source of error in this method is outlined in section four. The efficiency of this method with the altitude is also taken into account (section five). 2. The response to the darkness of the eye as magnitude estimator The physiology of the eye dark adaption is composed by two mechanisms: • the mechanical one in which the pupil reaches its maximum diameter (∼ 7 mm) • the chemical one where the rhodopsin and iodopsin (for the cones) are regenerated in the retinal receptors. The rods and the cones have different time scales of chemical regeneration (5 minutes the former and 30 minutes the latter). Moreover the sensitivity to small intensity of light is much better in rods with respect to the cones (that are sensitive to the colours). Therefore the combination asee http://www.aavso.org 1 Einstein 120 Conference, Kyrgyz State University, Bishkek, 2000. Sigismondi1 Fig. 1. The y axis is the logarithm of luminous intensity threshold visible to the naked eye measured in µµ lux. The x axis, in minutes, is the time during which the eye remains in the darkness. Vega, a star of mv=0.03 has an intensity of 2.5 × 10−6 lux, i. e. 6.4 in the scale here represented. A star of mv=6.5, considered the fainter star detectable at the naked eye, corresponds to 3.8 in this scale. The eye is sensitive to even fainter signals (3.3 in the y scale of this figure, i. e. 1.25 magnitudes fainter) but it is difficult to discern it as a star for its low signal-to-noise ratio. Figure adapted from Lerman (1980). of all those factors gives the curve describing the dark adaption versus time shown in the figure 1 (adapted from Lerman (1980)1). Such figure needs of a more extended comment with respect to the medical text- book, for an astronomical application. The factor of 4 in logarithm of the intensity gained after 30 minutes of darkness corresponds to a gain of 10 magnitudes according to the Pogson’s law. Under optimal optical conditions the naked-eye limiting magni- tude is considered as mlim = 6.5 (see e.g. Jenniskens (1994)2 for naked-eye meteor observations) for point-like sources. The initial point of such curve corresponds to mv ∼−3. It corresponds indeed to daylight. A point-like object of mv ∼−3 is indis- tinguishable from the background when the latter has a brightness of 5 mag arcsec2 (see appendix), say within ∼10o apart of the Sun with clear sky. We can also consider this value as the ”bleaching (dazzling)” intensity of the light. That is a condition never occurring in the night because the home illumination does not reach that one of the sky near the Sun. The only one case of sudden decrease of luminosity is during the last stages of a total eclipse of the Sun, when the eye is not protected by appropriate filters. So for astronomical use in figure 1 we can start directly by the knee occurring after 7 minutes of dark adaptions, with the reasonable assumption of do not start astronomical observations when bleached (dazzled). Moreover, when we start to observe the stars we are immediately able to distinguish the colours of the most bright, so the cones are already ready to detect and to analyse the star’s 2 Einstein 120 Conference, Kyrgyz State University, Bishkek, 2000. Sigismondi1 light. We can approximate the second part of the curve with the exponen- tial law: mlim(t) = m0 + 3 · (1 −exp(−t τ )) (1) with τ = 5 minutes and m0 the minimum magnitude visible at the beginning of the observation. For small time intervals eq. (1) be- comes mlim(∆t) = m0 + 3 · ∆t τ (2) It is to remark that t

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