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While we still do not have a velocity-delay map in hand, we certainly know how to get one. More than a dozen years of experience in reverberation mapping have led to a reasonably good understanding of the timescales for response of various lines as a function of luminosity and of how the continuum itself varies with time. On the basis of this information, we have carried out extensive simulations to determine the observational requirements to obtain high-fidelity velocity-delay maps for emission lines in moderate luminosity Seyfert galaxies (quantities that follow are based specifically on NGC 5548, by far the AGN best studied by reverberation). A sample numerical simulation is shown in Figure 6. As described more completely by Horne et al. (2004), the principal requirements are:

  1. High time resolution, (less than 0.2 - 1 day, depending on the emission line). The interval between observations translates directly into the resolution in the time-delay axis.

  2. Long duration (several months). A rule of thumb in time series analysis is that the duration of the experiment should exceed the maximum timescale to be probed by at least a factor of three. The lag for Hbeta in NGC 5548 is typically around 20 days, so the longest timescale to be probed is 2r / c. The duration should thus be at least ~ 120 days to map the Hbeta-emitting region. However, since C IV seems to respond twice as fast as Hbeta, the C IV-emitting region might be mapped in as little as ~ 60 days. A more important consideration, however, is detection in the time series a strong continuum signal, such as a change in sign of the derivative of the light curve. This produces a similarly strong emission-line response. We find that ~ 200 days of observations are required to be certain that such an event occurs, and to observe its consequences in the emission lines.

  3. Moderate spectral resolution (leq 600 km s-1). While higher spectral resolution is always desirable, AGN emission lines show little additional structure at resolution better than several hundred kilometers per second. Higher resolution does, however, make it in principle possible to detect a gravitational redshift (e.g., Kollatschy 2004), providing an independent and complementary measure of the black hole mass.

  4. High homogeneity and signal-to-noise ratios (S/N propto 100). Both continuum and emission-line flux variations are small on short time scales, typically no more than a few percent on diurnal timescales. Excellent relative flux calibration and signal-to-noise ratios are necessary to make use of the high time resolution.

Figure 6

Figure 6. Numerical simulations of velocity - delay map recovery. An arbitrary but complex geometry was chosen to show that a complicated BLR structure can be recovered. The left column shows the BLR geometry in four lines, Lyalpha lambda1215, C IV lambda1549, He II lambda1640, and Hbeta lambda4861, from top to bottom. The middle column shows the BLR model mapped into velocity - delay space. The right column shows the recovered velocity - delay map recovered from simulated data. From Horne et al. (2004).

The final point makes it clear that this will be difficult to do with ground-based observations: it is hard to maintain such high levels of homogeneity and thus accurate relative flux calibration with a variable point-spread function, such as one dominated by the effects of atmospheric seeing. Space-based observations are much more likely to succeed, and moreover, the ultraviolet part of the spectrum gives access to the important strong lines Lyalpha, N V lambda1240, Si IV lambda1400, C IV lambda1549, and He II lambda1640, all of which vary strongly.

We have carried out a series of simulations assuming specifically observation of NGC 5548 with the Space Telescope Imaging Spectrograph (STIS) on HST. We assume that the typical BLR response times are as observed during the first major monitoring campaign in 1989, as these values appear to be typical. We also assume for practical reasons that we can obtain only one observation per day (mostly on account of restrictions against the use of the STIS UV detectors during orbits when HST passes through the South Atlantic Anomaly) which we must complete in one HST orbit, using the typical time that NGC 5548 is observable per orbit. Furthermore, we included in the simulations nominal spacecraft and instrument safing events of typical duration (generally a few days) and frequency. We also considered the effects of early termination of the experiment due, for example, to a more catastrophic failure. We carried out 10 individual simulations, with each one using a different continuum model; all of the continuum models were "conservative" in the sense that the continuum activity is weaker and less pronounced than it is usually observed to be.

Given our assumptions, we find that all 10 of the simulated experiments succeed within 200 days. For the most favorable continuum behavior, success can be achieved in as little as ~ 60 days, though this is rare, or more commonly in around ~ 150 days. We also find that these results are robust against occasional random data losses.

These generally conservative assumptions argue strongly that velocity-delay maps for all the strong UV lines in NGC 5548 could be obtained in a 200-orbit HST program based on one orbit per day. There are clearly elements of risk associated with the program, the most obvious being early termination on account of a systems failure or a major safing event that would end the time series prematurely. This risk is somewhat mitigated by the conservatism of our simulations; it is possible that the experiment could succeed in much less time. Indeed, if we define "success" as obtaining a velocity-delay map that is stable for 50 days, we find that the probability of success is as high as ~ 90% in 150 days.

Finally, one might also ask about the scientific risk: for example, what if the velocity-delay map, though of high fidelity, cannot be interpreted? In other words, what if the velocity-delay map is a "mess" and has no discernible structure? First of all, this is not a likely outcome since long-term monitoring shows persistent features in emission-line profiles that imply there is some order or symmetry to the BLR. Moreover, even if the BLR turns out to be a "mess" we'll still have learned an important fact about the BLR structure, namely that it is basically chaotic. But the bottom line is that right now we have nearly complete ignorance about the BLR structure. We cannot even assess to any level of confidence how many velocity-delay maps of AGNs we will need to solve the problem until we have obtained at least one velocity-delay map of at least one emission line. Until we have that, our knowledge of the role of the BLR in AGN fueling and outflows will remain based on theoretical speculation alone, historically a very dangerous situation for astrophysicists.

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