The Nature of V838 Mon and its Light Echo ASP Conference Series, Vol. 363, 2007 R. L. M. Corradi and U. Munari eds. An Introduction to Scattered-Light Echoes BenE.K.Sugerman Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 2128 USA Abstract. Scattered light echoes offer one of the most effective means to probe the structure and composition of circumstellar and interstellar media. Of note, light echoes provide exact three-dimensional positions of scattering dust. However, they are also very rare, and have only been unambiguously resolved around a handful of sources. I will discuss the history of light echo astronomy, and how they can be used to study the environments around variable stars and cataclysmic events. I will also show results from most of the existing known echo sources, showing how they have been used to map out star’s circumstellar environments, probe the disks of galaxies, and determine the distance to variable stars. 1. History The history of scattered-light echoes is well summarized in Couderc (1939); even though the scanned version is now on ADS, we don’t all read French, so I give a brief synopsis here. Nova Persei 1901 was first discovered by Naegamvala (1901) on 1901 Feb 25. On 20 Sep and 10 Nov, Ritchey (1901) imaged the surrounding region, only to discover a complex network of ring-like nebulosities that appeared to have moved 1′ in 6 weeks. Kapteyn (1902) proposed this is not bulk motion of gas (which required the nova to be less than 2 lt-yr away) but rather, reflection of the nova light pulse from surrounding, stationary media. This hypothesis was confirmed by Perrine (1903) in a remarkable 35-hour spectrum that verified the light was indeed reflected from the nova. The problem is that Kapteyn’s hypothesis demanded the echoes propagate at c, forcing the nova to be 290 lt-yr away. Barnard (1917) soonafter observed bulk motion of ejecta, with spectral velocities of 1200 km s−1 and proper motion on the sky of 0′′. 4yr−1, yielding a distance of 2000 lt-yr. A nasty debate ensued between proponents of the near and far distances, until Couderc (1939) deduced the correct light-echo physics, by which an echo can be observed to propagate superluminally on the sky. 2. Light Echo Basics Consider the left-hand panel of Fig. 1, in which the earth and some light source are separated by distance d. If the source emits a light pulse that scatters off some dust, that light will arrive at earth at a time t later than the original light pulse. When a particular echo (say, echo 2) is observed, we could equally well have seen an echo from any point in space (e.g. echo 1) with the same optical 121 122 Sugerman Echo 2 Echo 2 Source Ellipsoid Echo ρ z d ρ Earth Source Echo 1 Echo 1 View from space Image on the sky Figure 1. Cartoon showing the geometry of light echoes. The positions of echoes on the sky and the time delay between the source and echo flux arriving at earth yield one-to-one mappings between observed echo positions (right) and the 3-D positions of the scattering dust (left). ∆ρ Figure 2. Cartoon geometry of a simple echo. A sheet z of dust is perpendicular to the line of sight, located a distance z from the source. The dust sheet has thickness ∆z and grain number density nd. The two curves rep- nd dust resent the parabolae marking the beginning and end of ∆ z the light pulse, which causes an observed echo (darker r grey) to have a thickness ∆ρ, dependent on the light θ pulse duration ∆t and dust thickness ∆z. This observed echo can be described as having a position (ρ, z)from the source in cylindrical coordinates, or (r, θ) in spher- ρ ical coordinates. Note that θ is also scattering angle between the r and the observer. path length, that is, along an ellipsoid with the earth and source at the foci. If we know d,thent constrains the size of the ellipsoid, so that at any given time, any observed echo must lie on an ellipsoid of known geometry. Thus, given t and measuring the distance ρ between the echo and the source on the plane of the sky (right panel), we know the exact line-of-sight distance z from the source to the echo. In other words, echoes provide exact three-dimentional positions. Ellipsoids are analytically cumbersome to work with, so we generally adopt cylindrical geometry and approximate the ellipsoid in the neighborhood of the source by a paraboloid. Since, in general, d ≫ z, this approximation is excellent. Consider a sheet of dust located a distance z in front of a source. An echo at time t illuminates a particular point at (r, θ)or(ρ, z). The difference in arrival times between the original light pulse and the echo is just the difference in optical path lengths, t = z(sec θ − 1)/c, which simplifies to ρ2 ct z = − (1) 2ct 2 which we call the light-echo equation. For simplicity, we generally adopt uncon- ventional units of years and lt-yr, such that c = 1. To understand superluminal motion, consider the change dρ/dt for the dust sheet shown in Fig. 2. Using Eq. (1), dρ/dt = ρ/2t + t/2ρ, and since t and ρ are always positive, dρ/dt > 1(orc in physical units). I cannot stress enough that one must be careful when interpreting by eye the 3-D positions of echoes based on their 2-D projections on the sky. This is Light Echoes 123 Figure 3. — Example of how light echoes illuminate a geometric structure, in this case, the bipolar nebula depicted at top. Five echo parabolae are drawn, each occuring at the time (in years) indicated next to each curve. Below, renderings show the positions of light echoes for the first two parabolae (first column), third parabola (second column), last two parabolae (third column), and all parabolae (last column). In this rendering, echo positions are discretized as dots, where larger points are closer to the observer. Axes are: x toward west, y toward north, z toward the observer, with the origin indicated by the longest tick along each axis. Here, major tick marks denote a distance of 2 lt-yr. Top row: Face-on view (the plane of the sky). Middle row: Oblique view rotated 45◦. Bottom row: Side view from far to the east. Note that the geometry of this nebula (or any other structure) cannot be determined from only 1–2 observations, but is only discernable by combining observations of many echoes. because echoes are parabolic slices through continuous structures, and we rarely think in parabolic spaces. Figure 3 shows five echoes through a bipolar nebula with lobes of radius 5 lt-yr and centers separated by 8 lt-yr. The echo positions 124 Sugerman on the plane of the sky and at different orientations are shown below. Note how the correlation between the echoes as viewed on the sky and from the side are far from obvious. Also note that a single observation is insufficient to deduce the true geometry of the nebula. Since a single echo only illuminates a thin subset of a complete structure, multiple observations are mandatory if one wishes to learn the true geometry of this structure. The spectrum of an echo is a function of the scattering efficiency of the dust, the input light spectrum, and the scattering geometry. For an observed nova or supernova (SN), we are in the unique position of knowing the latter two and can thus derive dust properties, such as the grain-size distribution, density, and chemical composition, since (in broad terms): small grains tend to scatter isotropically, while large grains predominantly forward scatter; silicate grains tend to scatter more green light and less blue light than carbonaceous grains; and with increasing number density of grains, more light is scattered to the observer (provided the dust is not optically thick, at which point multiple scatterings make things reasonably complicated). To show this, consider the flux scattered off one dust grain of radius a at position r (Chevalier 1986; Emmering & Chevalier 1989) ′ CSC(λ, a)L(λ, t )Φ(θ, λ, a) dFSC(λ, t, r, a)= (2) 16π2d2r2 ′ where CSC is the grain-scattering cross section; L(λ, t ) is the luminosity at λ and t′ that scattered off the dust; and Φ is the scattering phase function for a given scattering angle. One often adopts the Henyey & Greenstein (1941) phase function 1 − g2(λ, a) Φ(µ, λ, a)= 3 2 (3) [1 + g2(λ, a) − 2g(λ, a)µ] / with g(λ, a) measuring the degree of forward scattering for a given grain. The total flux FSC from a single scattering is found by multiplying equation (2) by the dust density nd( r, a) and integrating over the scattering volume and all grain sizes. Treating the dust as a thin sheet (Fig. 2), and expressing the dust number density nd( r, a)=nH( r)f(a) as a function of the local gas density nH and a grain-size distribution funcion f (Mathis et al. 1977), one can express the light- echo surface brightness as c∆z BSC(λ, t, φ)=F (λ)nH(r) CSC(λ, a)Φ(θ, λ, a)f(a)da (4) 4πrρ∆ρ where F (λ) is the integrated fluence of the light pulse over its duration ∆t,and the integral is the “average scattering function.” Since the observed flux F (λ) and area element ρ∆ρ diminish as d−2, Eq.