We propose a novel type filter for multicolor imaging to improve on the
photometric redshift estimation of galaxies. An extra filter - specific to a
certain photometric system - may be utilized with high efficiency. We present a
case study of the Hubble Space Telescope's Advanced Camera for Surveys and show
that one extra exposure could cut down the mean square error on photometric
redshifts by 34% over the z<1.3 redshift range.Comment: 9 pages, 3 figures, LaTeX AASTeX, accepted to A

Budavari, Tamas

Connolly, Andrew J.

Csabai, Istvan

Szalay, Alexander S.

Tsvetanov, Zlatan

English

arXiv

Tamás Budavári

Alexander S. Szalay

István Csabai

Andrew J. Connolly

Zlatan Tsvetanov

Crossref

An Optimal Multihump Filter for Photometric Redshifts

We propose a novel type of filter for multicolor imaging to improve on the photometric redshift estimation of galaxies. An extra filter-specific to a certain photometric system-may be utilized with high efficiency. We present a case study of the Hubble Space Telescope's Advanced Camera for Surveys and show that one extra exposure could cut down the mean square error on photometric redshifts by 34% over the z <1.3 redshift range

Budavari, T

Szalay, A S

Csabai, I

Connolly, A J

Tsvetanov, Z

ELTE Digital Institutional Repository (EDIT)

arXiv:astro-ph/0106073v1  5 Jun 2001Optimal multihump filter for photometric redshiftsTamás Budavári1, Alexander S. SzalayDepartment of Physics and Astronomy, The Johns Hopkins University, Baltimore, MD 21218budavari@pha.jhu.eduIstván Csabai2Department of Physics, Eötvös University, Budapest, Pf. 32, Hungary, H-1518Andrew J. ConnollyDepartment of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260andZlatan TsvetanovDepartment of Physics and Astronomy, The Johns Hopkins University, Baltimore, MD 21218ABSTRACTWe propose a novel type filter for multicolor imaging to improve on the photomet-ric redshift estimation of galaxies. An extra filter—specific to a certain photometricsystem—may be utilized with high efficiency. We present a case study of the Hub-ble Space Telescope’s Advanced Camera for Surveys and show that one extra exposurecould cut down the mean square error on photometric redshifts by 34% over the z < 1.3redshift range.Subject headings: galaxies: distances and redshifts — galaxies: photometry — instru-mentation: miscellaneous1. IntroductionThe prediction of photometric redshifts (Koo 1985; Connolly et al. 1995a; Gwyn & Hartwick1996; Sawicki, Lin & Yee 1997; Hogg et al. 1998; Wang, Bahcall & Turner 1998; Yee 1998; Fernández-Soto, Lanzetta, & Yahil 1999; Weymann et al. 1999; Beńıtez 2000; Csabai et al. 2000; Budavári1Department of Physics, Eötvös University, Budapest, Pf. 32, Hungary, H-15182Department of Physics and Astronomy, The Johns Hopkins University, Baltimore, MD 21218– 2 –et al. 2000) is built upon global continuum features of the underlying galaxy spectrum such as theBalmer break at 4000 Å. The more precisely one can localize these features, the more accurate theredshift estimates become. However, traditional broadband filters were not designed to providethe best possible photometric redshifts, for several reasons. In theory, a set of filters optimalfor photometric redshift estimation might be designed, but this would probably be substantiallydifferent from any current standard set. Here we do not intend to solve the generic problem offinding an optimal filter set for photometric redshift estimation; this study shows how conventionalfilter sets can be extended to yield better photometric redshifts.In Section 1.1, we present the idea of an additional filter and look into why and how anextra measurement—sampling the same wavelengths—can improve significantly on photometricredshifts. In Section 2, the algorithm is developed and we make a case study of the AdvancedCamera for Surveys of the Hubble Space Telescope. Based on our analysis, we propose a novel typeof “broad-band” filter that can be effectively used for photometric redshifts.1.1. The ideaThe more general inversion problem of photometry in terms of redshift, type, and intrinsicluminosity (Koo 1985; Connolly et al. 1995a,b, 1999; Budavári et al. 1999, 2000; Csabai et al.2000) involves the study of the Jacobian matrix of fluxes as a function of the physical parametersof galaxies. Our numerical simulations show that filter sets yield more precise estimates whencontinuum spectral features are located around the overlap of two bands—both fluxes changerapidly with redshift. One way to improve the redshift estimates is to increase the number offilters and use narrower bands. This would require too many exposures and yield a non-standardphotometric system (Hickson et al. 1998). The other possibility is to put an intermediate width(IM) filter in a broad band, which would help the redshift estimation by improving the resolution.A single IM band can only help in a narrow redshift range, so additional, narrower filters are neededfor each broad band. This approach could triple the resolution but will heavily increase the totalexposure time at the same signal-to-noise ratio.We propose combining multiple IM filters located in standard photometric bands into one“broadband” filter. We call this a multihump filter. The resulting new filter will be able to improvethe redshift prediction (wavelength resolution) over a much wider redshift range and will onlyrequire a single additional exposure of comparable length.How does this really work? Our approach makes a large difference for blue galaxies. The 4000 Åbreak in their spectra shows up only as a small “bump” which makes the redshift estimation difficult.Let us consider the worst-case scenario, a toy model spectrum of a late-type galaxy that declineswith wavelength as a power law and has as its only spectral feature the approximately 500 Å widebump. Without this feature, the colors would be the same at any redshift. The flux changes withredshift within a band depending on the shape of the filter. If its gradient is too small (e.g. flat– 3 –as a top-hat), tiny photometric errors can yield large errors in the redshift prediction. In otherwords, while the bump is in a broad band, it is hard to tell precisely where it is. The measuredflux in our new filter will change in redshift regions where the spectral feature is passing throughone of the IM humps. These are the regions where the proposed filter contributes the most to theredshift estimation and where the original filter set has poor performance (small gradient). Redelliptical (E/S0) galaxies do not present a significant problem, because the strong discontinuity at4000 Å changes noticeably the fluxes as it passes through the bands with redshift. In this case theadditional filter plays a subsidiary role, and the improvement of the accuracy is incremental.2. Filter designThe actual throughput of a photometric system strongly depends on the instrument, differentprojects use different CCDs to gain more sensitivity in the desired wavelength range. The quantumefficiency of these devices set strict constraints on the observable wavelength regime. The filter setis selected to cover the available spectral interval according to science goals. The multihump filteris specific to a filter set, and its transmissivity is affected by the CCD’s quantum efficiency (QE).We have analyzed the photometric system of the Hubble Space Telescope’s Advanced Camerafor Surveys (ACS Ford et al. 1996)3. The two back-illuminated CCDs of the wide field channel areVIS-AR coated in order to optimize the response in the I band, and thus the U -band sensitivityhas been sacrificed. Mission specifications dictate the constraints on the multihump filter that is toextend the original set of the g’, r’, i’ and z’ bands, which span the entire observable wavelengthrange. No bluer or redder filter can be used, because the detector is not sensitive at shorter orlonger wavelengths.The framework of the algorithm is simple. We parameterize a fictitious filter curve and convolveit with the CCD’s actual QE to obtain a realistic response function. Simulated photometric catalogsof fluxes and errors are generated using the extended filter set. The goodness of a particular filterset is assessed by computing the errors on the redshift estimates.In the context of current filter manufacturing techniques (Offer & Bland-Hawthorn 1998), afeasible parameterization of the additional filter’s response function (R(λ), see Figure 1) consistsof at most two notch filters, plus a low and a high cutoff, as described byR(λ) =1πarctan(ǫ · (λ− λstart))−1πarctan(ǫ · (λ− λend))− exp[−(λ− λ1∆λ1)p]− exp[−(λ− λ2∆λ2)p]. (1)Parameters λstart and λend are the limits of the filter, and ǫ determines the gradients, the rise of theedges. The values of λ1 and λ2 correspond to the locations of the notches and p (an even number)3http://adcam.pha.jhu.edu– 4 –changes their shape.The mock catalogs were generated based on spectral energy distributions (SEDs) derived froma physical interpolation scheme applied to the spectra of Coleman, Wu & Weedman (1980), asdescribed in Connolly et al. (1999) and Budavári et al. (2000). On a high resolution redshift grid(δz = 5 × 10−3), a hundred objects were generated at each grid point with random SEDs. Thecontinuous type parameter was scaled to yield a population of galaxies in which the probabilityof having a spectral type between Ell and Sbc was 10%, Sbc–Scd 35%, Scd–Irr 35%, and bluer20%. The fluxes were modulated with 3% photometric errors taken from a Gaussian distribution.The quality of the photometric redshifts is determined by computing the rms of the estimates.The error is calculated for the desired redshift interval (or regions) meeting the actual projectrequirements—in this study, redshifts between z = 0.2 and z = 1.2.The actual optimization problem has quite a few parameters (see Equation 1) to solve for,which makes it hard to numerically find the global minimum. It is also quite time-consuming toevaluate the underlying function; a new loop of the simulation has to be completed each time. Alsoextra constraints were added to the problem. To be able to use the very same filter from the groundfor testing purposes or in follow-up observations, a design compromise due to the atmosphere hasbeen made. In the actual optimization algorithm, one of the notches was always forced to includethe 5577 Å sky line. To map the entire parameter space, a linear search on a coarse grid was usedto find the best possible filter candidates, and then from the those minima, a gradient method wasutilized with discrete, higher resolution step-sizes.3. DiscussionThe resulting shape of the multihump is shown in Figure 2. This best configuration has twohumps and its transmissivity peaks at the shortest possible wavelengths in the g’ band and, atlonger wavelength, in the i’ band. Since the ACS filters look almost like triangles (as a result ofthe strong wavelength dependency in the CCD’s QE), our additional filter tries to intensify thechanges in colors, at the lowest, z ∼ 0.2, and highest, z ∼ 1.2, redshifts. On one side, the optimalmultihump filter is essentially trying to compensate the lack of a ultraviolet filter by boosting thecontrast at the edge of the g’ band. In fact, the algorithm also finds an optimal solution of havinga U band, which is not a real option because of the CCD’s QE (see Section 2). The location ofthe hump in the i’ is clearly set by the upper redshift limit z . 1.2, when the Balmer break isat . 8800 Å.Figure 3 compares the performance of the original and extended filter sets by plotting the rmserror as a function of redshift. The accuracy of photometric redshifts for the entire catalog is shownfirst. The prediction improves at all redshifts; the overall improvement isQ =σ2orig − σ2extσ2orig= 34%. (2)– 5 –Early- and late-type subsamples are shown in the middle and right panels of Figure 3, respectively.The E/S0 estimates clearly get better at the smallest redshifts, z & 0, and at around z . 1.2, whenthe 4000 Å break is in one of the humps. However, the redshift prediction also improves in anotherredshift region, around z ∼ 0.55, as a result of the H β and Mg i absorption as it passes throughthe second hump. In according with our expectations, redshift estimates of the late-type galaxieschange much more drastically then those estimated for early types.The large number of parameters makes it difficult to estimate the errors or covariances. InTable 1, the rms errors computed for different set of filters are shown. The original ACS filter setgives σz = 0.075. If we try additional multihump filters with humps centered on the g’r’i’ andg’r’z’ bands, the performance just slightly improves; σz = 0.072 and 0.073, respectively. Centeringhumps on the gaps between the original bands (off-band multihump filter) does not improve onthe accuracy of the estimates either; σz = 0.073. The optimized filter yields much better redshifts,σz = 0.058. The gain in the entire catalog is comparable to what would be achievable by usingseparate IM filters. The redshift accuracy can be marginally increased by splitting the optimalmultihump into two separate filters (σz = 0.055), but the additional exposure time would be morethan twice as long as in our approach.4. ConclusionWe propose the use of multihump filters extending standard photometric systems to makephotometric redshift estimation much more efficient. Our simulations have shown that an optimizedextra filter could improve the redshift prediction by 34% for the Advanced Camera for Surveys.The improvement takes place over the z < 1.3 redshift range. The filter’s effective width is about1500 Å, comparable to the existing photometric bands, so the measurement would require onlyabout 25% more exposure time. Such a filter can be built with today’s technology; in fact, similarfilters have been utilized to suppres atmospheric features at near-infrared wavelengths (Offer &Bland-Hawthorn 1998). The shape of the extra filter can be tuned to different goals and missions.It can be optimized for different filter sets and adjusted to desired redshift ranges.I. C. and T. B. acknowledge partial support from the Hungarian Academy of Sciences–NSFgrant 124 and the Hungarian National Scientific Research Foundation grant T030836, A. J. C. ac-knowledges support from NASA through a Long Term Space Astrophysics grant (NAG 5-7934) andthrough grant GO-07817.06-96A from the Space Telescope Science Institute. A. S. acknowledgessupport from the NSF (AST 98-02980) and the NASA Long Term Space Astrophysics program(NAG 5-3503).– 6 –REFERENCESBeńıtez, N., 2000, ApJ, 536, 571Budavári, T., Szalay, A.S., Connolly, A.J., Csabai, I. & Dickinson, M.E., 1999, in Photometric Red-shifts and High Redshift Galaxies, eds. R.J. Weymann, L.J. Storrie–Lombardi, M. Sawicki,& R. Brunner, (San Francisco: ASP), 19Budavári, T., Szalay, A.S., Connolly, A.J., Csabai, I. & Dickinson, M.E., 2000, AJ, 120, 1588Coleman, G.D., Wu., C.-C., & Weedman, D.W., 1980, ApJS, 43, 393Connolly, A.J., Csabai, I., Szalay, A.S., Koo, D.C., Kron, R.G., & Munn, J.A., 1995a, AJ, 110,2655Connolly, A.J., Szalay, A.S., Bershady, M.A., Kinney, A.L., & Calzetti, D., 1995b, AJ, 110, 1071Connolly, A.J., Budavári, T., Szalay, A.S., Csabai, I., & Brunner, R.J., 1999, in Photometric Red-shifts and High Redshift Galaxies, eds. R.J. Weymann, L.J. Storrie–Lombardi, M. Sawicki,& R. Brunner, (San Francisco: ASP), 13Csabai, I., Connolly, A.J., Szalay, A.S., & Budavári, T., 2000, AJ, 119, 69Fernández-Soto, A., Lanzetta, K.M., & Yahil, A., 1999, ApJ, 513, 34Ford, H.C., et al., 1996, SPIE, 2807, 184Gwyn, S.D.J., & Hartwick, F.D.A., 1996, ApJ, 468, L77Hickson, P., et al., 1998, SPIE, 3352, 226Hogg, D.W, et al., 1998, AJ, 115, 1418Koo, D.C., 1985, AJ, 90, 148Offer, A.R., & Bland-Hawthorn, J., 1998, MNRAS, 229, 176Sawicki, M.J., Lin, H., & Yee, H.K.C, 1997, AJ, 113, 1Wang, Y., Bahcall, N., & Turner, E.L., 1998, AJ, 116, 2081Weymann, R.J., Storrie–Lombardi, L.J., Sawicki, M., & Brunner, R., (editors), 1999, PhotometricRedshifts and High–Redshift Galaxies (San Francisco: ASP)Yee, H.K.C., 1998, in Proc. 10th Recontres de Blois, in press (astro-ph/9809347)This preprint was prepared with the AAS LATEX macros v5.0.– 7 –Table 1. Errors on Photometric RedshiftsFilter Set ∆zrms λstart λend λ1 ∆λ1 λ2 ∆λ2 p ǫOriginal 0.075 ... ... ... ... ... ... ... ...g’r’i’ 0.072 4800 7900 5700 450 7000 600 8 0.05g’r’z’ 0.073 4900 8900 5700 450 7550 900 8 0.05Off-band 0.073 5200 8800 6200 400 7800 400 8 0.05Optimized 0.058 4000 8500 6250 1750 ... ... 20 0.05Separate 0.055 ... ... ... ... ... ... ... ...Fig. 1.— Illustration of the filter’s response curve, as defined by Equation 1.– 8 –Fig. 2.— The throughput of the filters as used in convolutions. The original g’,r’,i’, and z’ bandsare represented by solid lines (left to right). The add-on multihump filter (dotted line) is scaleddown by 30% for illustration.– 9 –Fig. 3.— The rms error on photometric redshifts using the original filter set (solid line) andthe extended set (dotted line). Left to right: The improvement for the entire population in thesimulation and for the red (E/S0) and blue subsamples, respectively. The large errors at lowredshifts are due to the lack of the U band; at redshift z > 1, one would need a J band or higher.

An optimal multihump filter for photometric redshifts

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Optimal multihump filter for photometric redshifts

Optimal multihump filter for photometric redshifts

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