An Introduction to Scattered-Light Echoes

The Nature of V838 Mon and its Light Echo ASP Conference Series, Vol. 363, 2007 R. L. M. Corradi and U. Munari eds.

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. (4) for surface brightness is distance independent, as expected. As described above, Eq. (4) shows that surface brightness is indeed dependent on the source spectrum (known), dust density (constrained by echo fluxes), dust geometry (known), and grain-scattering properties (constrained by echo colors). A more detailed derivation of these formulae, as well as detailed descriptions of calculating the average scattering function are given in Sugerman (2003). The reader is also referred to Chevalier (1986), Xu et al. (1994), and Patat (2005). Light Echoes 125

Figure 4. A 50′′ × 50′′ image showing all light echoes from SN 1987A from 1469 days after outburst. North is up, east is left, and major tick marks denote 10′′. The position of the SN and two nearby stars are marked with stars. The inset shows the cen- tral 12′′at a diﬀerent color stretch to resolve the innermost echoes. Crosshairs mark positions of iden- tiﬁed echoes.

3. Some Observed Echoes

3.1. SN 1987A Until the echoes from V838 Mon came along, the best known were those of SN 1987A. Located about 50 kpc away in the LMC, SN 1987A is the nearest SN in 400 years. Echoes located arcmin from the SN were discovered in the late 80’s (Bond et al. 1989) and have been followed intensely by A. Crotts and collaborators ever since. These have been used by Xu et al. (1995) to trace out a pencil-beam survey of the structure of the LMC in front of the SN, revealing many sheets and superbubbles, and placing the SN almost 1 kpc deep within the LMC. Following the original study of echoes within 30′′of the SN by Crotts et al. (1995), I performed a much more detailed analysis of 15 years’ worth of imaging to fully reconstruct the circumstellar environment within 30 lt-yr of the SN (Sugerman et al. 2005). Extensive geometric analyses of these echoes (Fig. 5a–b) reveals a richly-structured bipolar nebula, whose complete structure is rendered in Fig. 5(c–d).

3.2. SN 1993J SN 1993J in M81 was the closest SN (d=3.6 Mpc) between 1987 and 2004. Sugerman & Crotts (2002) reported the discovery of two echo structures in archival HST/WFPC2 imaging, which are 260 and 770 lt-yr in front of the SN. The more distant echo has an inclination very similar to that of the host galaxy, and our analysis suggested this dust is part of its stellar disk. Modelling of the ﬂuxes and colors show the dust is highly carbon-rich and fairly dense, with gas 126 Sugerman on the of extended, equatorial an structures ositions y an p b form ) a probable probable the surrounded (panel the of es are ho n views ec w hourglass, sho cut-out inner ) Also an c–d t). ( igh largest-distance r and along is he T lie er . ) b ly 1987A, 2 observ SN ark (panel the m es from ks up, ho es tic ec is ho jor ec Ma ed (north east observ circumstellar depth. the all ) this, to of a–b ( far indicates of Inside from size t ). ed views c oin P view as (panel ). ut Rendered d lie, nebula. ean p 5. they (panel h olar Figure three-ring whic bip disk Light Echoes 127

Figure 6. HST images of SN 1993J taken in 2001, showing a the direct image, and b adif- ference image made from data taken in 1995. Two echo arcs are clearly visible in the diﬀerence image (light curves have been drawn (a) (b) outside these to guide the eye). Notice that a nearby variable star (arrowed) is not an echo feature.

Figure 7. HST images of a 1′′. 4 ﬁeld surrounding SN 2003gd. North is up and east is left. The SN (or progenitor) is at the cen- ter of each frame. Circles of radii 0′′. 225 and 0′′. 375 roughly delimit the radial extent of the echoes. (a) ACS/HRC F435W image from 2004. (b) WFPC2 F606W image of the progenitor. number densities around ∼ 10 cm−3. By contrast, our own ISM has a large fraction of silicates, and much lower gas densities.

4. SN 2003gd

SN 2003gd in M74 (d =9.3 Mpc) is unusual in that its progenitor was observed by HST before it exploded, leading Hendry et al. (2005) to conclude the progenitor mass was 10–12 M⊙. The progenitor is shown in Fig. 7(b). An archival ACS image taken 632 days after outburst (panel a) reveals a light echo to the northwest, which I presented in Sugerman (2005). Its 3-D position is rendered in Fig. 8. From the side, this is a very thick (∆z = 300 − 400 lt-yr) sheet of material that is roughly perpendicular to the line of sight. Quite likely, this is the disk of the host galaxy, with the SN located roughly 400 lt-yr behind it. Comparison of the echo ﬂuxes and colors to my dust models show the dust has a roughly Galactic composition, but with smaller grains than our ISM.

5. Conclusions

In this talk, I have summarized the key points of light echoes, namely, that they provide exact 3-D positions of the scattering materials, that they can constrain the properties of that dust, and as such, can be used to probe the structure and composition of circumstellar and interstellar media. Note, in particular, that a single observation with multiple wavelengths was suﬃcient in the cases of SNe 1993J and 2003gd to constrain the properties of the host galaxy’s interstellar media, while a decade of observations of SN 1987A have revealed the ﬁrst, complete map of any star’s circumstellar environment. Although rare, light echoes 128 Sugerman

Figure 8. Three-dimensional renderings of the observed echo location of the SN 2003gd echo, as viewed from the side. Axes are defined in Fig. 3, with the z axis running from 400–900 lt-yr in front of the SN. are extremely powerful tools, and their potential to study the physical processes surrounding V 838 Mon are enormous. Acknowledgments. I offer sincere thanks to the organizers for inviting me to give this introductory talk, and for financial support to facilitate my atten- dance. This work was also supported by the Space Telescope Science Institute and HST grant GO-10607.

References

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Discussion

Skodaˇ : How do you distinguish between the light echo and Einstein ring (gravi- tational lensing)? Can it be done from a single image? Sugerman: Two answers are possible. First, an Einstein ring won’t expand in time like an echo. Secondly, they are ultra-rare so just by probability, one would doubt it is an Einstein ring in a single image, but obviously follow-up is required to ascertain what the observed ring actually is. Hirschi: How difficult is it to determine the composition of the circumstellar material with light echoes? Sugerman: It isn’t trivial but the methods are straightforward. See Sugerman (2003). Using the broad-band fluxes and colours of the echo as a function of position and time we can constrain the dust density, grain sizes and composition. V838Mon offers one of the most comprehensive data sets so , in fact, determining the properties should be much more robust than our previous efforts (eg, SN 1987A, SN 1993J, etc). Retter: There was a report on a light echo in V1974 Cyg (Nova Cygni 1992). I wonder whether you or anyone else can elaborate about it. Sugerman: “Motion in the Light Echo from Nova Cygni 1992” P. Garnavich, J Raymond, IAUC 6648 (1997) is the only reference I’ve seen for it.