Inputs

The file zphot.param contains the following input parameters for hyperz:

• A0VSED: the file-path containing the spectrum of Vega;
• FILTERS_RES: the file-path containing the filter transmission functions;
• FILTERS_FILE: the file containing information about filters. The first column is the identification number of each filter in the file FILTER.RES. The user can check it in the file filters.log (see Section A). If the user wants a combination of several filters, e.g. $n_1$ (filter) and $n_2$ (detector), write $n_1 \& n_2$ in the first column. When the magnitude system is different from the standard Vega or AB, the second column contains the correction (in magnitudes): $m_{\rm Vega} = m_{\rm cat} + m_{\rm corr}$. When the magnitude system is the standard Vega or AB, $m_{\rm corr}=0$. The user can specify the magnitude system AB using the MAG_TYPE parameter. See Fukugita et al. (1995) for typical correction values. Also, when using the Thuan-Gunn system (based on the standard BD+17 4708):

 

 

$$\begin{array}{ccccc}g({\rm Vega}) & = & g({\rm TG}) & + & 0......\z({\rm Vega}) & = & z({\rm TG}) & - & 0.762 \\\end{array}$$

The third column is the rule applied in the case of undetected objects:

0.  This filter will not be taken into account in the computation.

1.  The flux in this filter is set to $F_{\rm obs} = 0$ with an error corresponding to the flux deduced from the limiting magnitude in the fourth column, i.e. $\Delta F_{\rm obs} =F_{\rm lim}$.

2.  The flux in this filter and the associated $1\sigma$ error are set equal to $F_{\rm lim}/2$.

3.  The flux in this filter and the associated error are computed from the limiting magnitude $m_{\rm lim}$ and from the error $\Delta m_{\rm lim}$ given in columns four and five, respectively.

Undetected objects in a filter $i$ are characterized by a magnitude $m(i) > 90$ [in general $m(i) = 99$, following the convention of the photometric software SExtractor (Bertin & Arnouts 1996)]. ``Out of field'' objects, for which the photometry is not available, must be characterized by a magnitude $m(i) < 1$ (in general $m(i) = 0$); in this way the filter ``out of field'' is not taken into account in the $\chi^2$ minimization procedure.

The fourth column gives the limiting magnitude $m_{\rm lim}(i)$ in each filter $i$. The fifth column is the error value in magnitudes, $\Delta m_{\rm lim}(i)$, that will be attributed to undetected objects when option 3 is selected in column three. Lines beginning with a # or blank lines are not considered.

• TEMPLATES_FILE: the name of the file containing the path of templates that the user wants to use and their type ( BC = Bruzual & Charlot, binary, AS = ASCII); the user can select or unselect a template by placing or removing a # as the first character in the spectra.param file. The correct path of templates must be checked by the user.


The present library consists of 8 synthesis template SEDs with solar metallicity and Miller & Scalo IMF presented in Section 2.2.1, and 4 spectra from CWW and extended in UV and near-IR with the GISSEL98 library. This set of templates can be changed by the user.

• FILT_M_ABS: the filter number (to be checked in the file filters.log, as before) for the absolute magnitude estimate (Vega magnitudes; with k-correction only).
• ERR_MAG_MIN: the value of the photometric error which is set if the input error from the catalogue is $<$ ERR_MAG_MIN, to avoid too small and non-realistic photometric errors. It is worth to note that SEDs computed from a catalogue are ``absolute'', in the sense that errors should include ALL the possible sources (air-mass, photometric zero-points, background noise, etc.).
• Z_MIN and Z_MAX: the limits of the redshift range the user wants to investigate. These parameters are connected to CATALOG_TYPE: if CATALOG_TYPE = 0, these limits are set for all the objects in the catalogue; if CATALOG_TYPE = 1, the limits are set individually for each object.
• Z_STEP: the step in redshift used in the first estimate of best fit. After the first minimization, the candidate solutions are refined with a step Z_STEP/10 to search for smaller $\chi^2$.
• ZSTEP_TYPE: the option for the type of step in redshift: if ZSTEP_TYPE = 0 the step is constant and equal to Z_STEP, if ZSTEP_TYPE = 1 the step is evolving as Z_STEP $\times (1+z)$. The latter is preferable if the user wants to better investigate the low redshifts region without increasing the total number of steps and consequently the CPU time.
• CATALOG_TYPE: must be set to 0 if the input catalogue has the format:
id, [$m(i),i=1,n_{\rm filt}$], [$\Delta m(i),i=1,n_{\rm filt}$] where id is the identification number, $m(i)$ are the observed magnitudes, $\Delta m(i)$ are the corresponding photometric errors and $n_{\rm filt}$ the number of filters. CATALOG_TYPE must be set to 1 if the format is id, $z_{\rm min}$, $z_{\rm max}$, [$m(i),i=1,n_{\rm filt}$], [$\Delta m(i),i=1,n_{\rm filt}$] with a redshift range $(z_{\rm min},z_{\rm max})$ that can be different for each object. In the latter case the values of Z_MIN and Z_MAX are not taken in account.
• CATALOG_FILE: the name of the input photometric catalogue.
• MAG_TYPE: the type of magnitude used in the catalogue: 0 for standard magnitudes (Vega system or others, see FILTERS_FILE), 1 for AB magnitudes.
• REDDENING_LAW: the law for internal reddening (see Section 2.3):

0.  No reddening

1.  MW from Allen (1976);

2.  MW from Seaton (1979);

3.  LMC from Fitzpatrick (1986);

4.  SMC from Prévot et al. (1984) and Bouchet et al. (1985);

5.  Starburst galaxies from Calzetti et al. (2000).

• AV_MIN, AV_MAX and AV_STEP: the values of the maximum and minimum absorption in the $V$ band (in magnitudes) and the value of the computation step to cover the range. If REDDENING_LAW = 0, these values are not taken in account.
• AGE_CHECK: the option for the control of age as a function of redshift: if this parameter is set equal to y or Y the program checks that the age of the template is less than the age of the universe (for a cosmological model assigned with H0, OMEGA_M and OMEGA_V) at the redshift under consideration.
• PROB_THRESH: the minimum value of the probability (inferred from the reduced $\chi^2$ analysis) for the study of secondary maxima. The range of permitted values is 0 - 100.
• OUTPUT_FILE: the name of output files (without extension).
• SED_OBS_FILE, SED_TEMP_FILE, LOGPHOT_FILE, ZPHOT_FILE and CATPHOT_FILE are the options y/n for the output files containing:
• OUTPUT_FILE.obs_sed: the observed SEDs, given as the mean integrated fluxes through the photometric system, and the corresponding errors (units selected by OUTPUT_TYPE).
id, [$F_{\rm obs}(i), i=1,n_{\rm filt}$], [$\Delta F_{\rm obs}(i), i=1,n_{\rm filt}$]
• OUTPUT_FILE.temp_sed: the best fit integrated SEDs (same units).
id, [$F_{\rm temp}(i), i=1,n_{\rm filt}$]
• OUTPUT_FILE.log_phot: the best fit parameters as a function of the redshift, with steps defined by Z_STEP:
id, $z_{\rm step}$, $\chi^2_\nu(z_{\rm step})$, $P(\chi^2_\nu)$, SpT, age [Gyr], $A_V$ where $z_{\rm step}$ is the redshift step, $\chi^2_\nu(z_{\rm step})$ is the minimum reduced $\chi^2$ corresponding to the considered redshift, $P(\chi^2_\nu)$ is the probability associated to the value of $\chi^2_\nu$ and the degrees of freedom involved (see Table 5), SpT, age [Gyr] and $A_V$ are the spectral type, the age and the reddening of the SED corresponding to the minimum $\chi^2$. The $\chi^2_\nu$ is defined by $\chi^2/\nu$, where $\nu$ is the number of degrees of freedom. Because we are interested in only one parameter (the photometric redshift), the degrees of freedom are $n_{\rm filt} - 1$, subtracting the degree of freedom lost with the normalization $b$ in equation 1.
 
 

Table:Values of the reduced $\chi^2$ corresponding to the probability $P(\chi^2\vert\nu)$ of exceeding the value $\chi^2$ by chance, as a function of the number of degrees of freedom $\nu$.

 

$\nu$	P=0.99	0.95	0.90	0.75	0.68	0.50
1	0.00016	0.00393	0.0158	0.1015	0.170	0.455
2	0.0100	0.0515	0.105	0.288	0.386	0.693
3	0.0383	0.117	0.195	0.404	0.503	0.789
4	0.0742	0.178	0.266	0.481	0.576	0.839
5	0.111	0.229	0.322	0.535	0.626	0.870
6	0.145	0.273	0.367	0.576	0.663	0.891
7	0.177	0.310	0.405	0.608	0.691	0.907
8	0.206	0.342	0.436	0.634	0.713	0.918
9	0.232	0.369	0.463	0.655	0.732	0.927
10	0.256	0.394	0.487	0.674	0.747	0.934

• OUTPUT_FILE.z_phot: the best fit redshift and corresponding parameters for each object:
id, $z_{\rm phot}$, $\chi^2_\nu$, $P(\chi^2)$, SpT, $N_{\rm age}$, age [Gyr], $A_V$, $b$$z_{\rm inf}(99\%)$, $z_{\rm sup}(99\%)$, $z_{\rm inf}(90\%)$, $z_{\rm sup}(90\%)$, $z_{\rm inf}(68\%)$, $z_{\rm sup}(68\%)$, $z_{\rm wm}$, $P(\chi^2_{\rm wm})$, $M_{\rm abs}$, $z_{\rm phot}(2)$, $P[\chi^2(2)]$ where $z_{\rm phot}$ is the redshift corresponding to the minimum $\chi^2$, $N_{\rm age}$ is the age record number, as listed in Table 4, followed by the other SED characteristics corresponding to the best fit spectrum. $z_{\rm inf}$ and $z_{\rm sup}$ are the extrema of confidence intervals defined by the $\Delta\chi^2$ method, being the number of ``interesting parameters'' equal to 1, i.e. the photometric redshift. In this case the values of $\Delta\chi^2$ defining the confidence intervals at 99%, 90% and 68% are 1.00, 2.71 and 6.63 respectively (Avni 1976). The other quantities are the weighted mean $z_{\rm wm}$, computed in the confidence interval at 99% around the main solution, the associated probability, the Vega absolute magnitude $M_{\rm abs}$ in the FILT_M_ABS filter. $z_{\rm phot}(2)$ and $P[\chi^2(2)]$ are the secondary solution and its $\chi^2$ probability.

If the user switches on the Z_CLUSTER option three columns are added: the absolute magnitude in the FILT_M_ABS filter if the object is at Z_CLUSTER, the probability at Z_CLUSTER and the apparent magnitude in the redshifted filter closest to FILT_M_ABS (used to estimate the absolute magnitude).

• OUTPUT_FILE.cat_phot: the best fit and secondary solutions (if any) for each object. CATPHOT_FILE contains ZPHOT_FILE, and it has the same format, without the columns regarding the secondary solution and the cluster option, and with an additional column to display the solution rank.

 

 

Note that looking at the OUTPUT_FILE.log_phot file the user can find that the secondary maximum has a higher probability than the first one. This is because of the refinement around the $\chi^2$ minima: the main photometric redshift and the secondary solution are written after the refinement, whereas the file OUTPUT_FILE.log_phot contains probabilities before the refinement, with the step Z_STEP. After refinement, some solutions can change their rank in the solution classification.
• OUTPUT_TYPE : selects the flux units for the output SEDs in files with extension .spe, .temp_sed and .obs_sed:

0.  $2\times 10^{-17}{\rm erg/cm^2/s/\AA}$;

1.  $\mu$Jy;

2.  AB magnitudes.

• OMEGA_M: the matter density parameter; used if the age check is switched on and for absolute magnitude computation.
• OMEGA_V: the cosmological constant density parameter; used if the age check is switched on and for absolute magnitude computation.
• H0: the Hubble constant; used if the age check is switched on and for absolute magnitude computation.
• Z_CLUSTER: optional parameter; if the user selects this option, the program computes the probability of each object to lie at Z_CLUSTER and writes it in the .z_phot file.
• M_ABS_MIN: optional parameter; the minimum absolute magnitude (bright).
• M_ABS_MAX: optional parameter; the maximum absolute magnitude (faint).
• MATRIX: optional parameter. The user can choose y/Y or n/N (default is n): if the user selects y/Y the program will write for each object a file #id.m containing the $\chi^2$ value over the parameter space:
id, z, SpT, $N_{\rm age}$, age [Gyr], $A_V$, $\chi^2$. If the catalogue contains more than 100 objects the program asks to confirm, because these are large files.
• SPECTRUM: optional parameter as MATRIX. If the user chooses y/Y (default is n), files named #id.spe containing the spectrum of the best fit model $\lambda, F(\lambda)$ are written for each galaxy.
• EBV_MW: optional parameter. The colour excess $E(B-V)$ for the galactic dereddening of data (default is EBV_MW = 0). The reddening law used for the dereddening is number 1 (Allen 1976).

 

 

The file OUTPUT_FILE.out_phot is a fixed output, summarizing the main parameters used running hyperz:

• the name of the photometric catalogue file;
• the name and associated number of template files;
• the characteristics of filters:
• n is the number of filter in the file FILTER.RES;
• wl_eff is the effective wavelength of the filter, computed as:
$$\lambda_{\rm eff}= \frac{\int \lambda R(\lambda)\,d\lambda}{\int R(\lambda)\,d\lambda} \:,$$


where $R(\lambda)$ is the filter transmission normalized at $R_{\rm max}=1$;

• surface is the integral of the normalized filter transmission:
$$S = \int R(\lambda)\,d\lambda\: ;$$
• bandpass1 is the effective bandpass computed with a Gaussian approximation:
$$\Delta\lambda = 2\,\sqrt{\frac{\int (\lambda -\lambda_{\rm eff})^2 R(\lambda)\,d\lambda}{S}} \: ;$$
• conv_AB is the conversion between AB and Vega magnitudes (see Section A):
$$m_{\rm Vega} = m_{\rm AB} - {\tt conv\_AB} \: ;$$
• mag_lim is the limiting magnitude (selected in FILTERS_FILE);
• nd is the non detection law (selected in FILTERS_FILE);
• the range and step in redshift;
• the range and step in $A_V$ and reddening law;
• the range of absolute magnitudes and the filter used to compute it;
• the cosmological parameters.

The user must check the maximum number of steps in redshift and reddening and the maximum number of templates and filters in the file ~ /ZPHOT/src/dimension.dec. The program will stop if the user requests a number exceeding the maximum. If the user wants to change some dimensions (because of problems of memory in the user's machine if the size of the executable is too large or if the user wants to increase the array dimensions), he/she must edit the file and recompile the program.

Here we report an example of the parameter files zphot.param, UBVRI.param, spectra.param and of the photometric catalogue UBVRI.cat:
::::::::::::::
zphot.param
:::::::::::::: 

A0VSED	~/ZPHOT/filters/A0V_KUR_BB.SED	# Vega SED
FILTERS_RES	~/ZPHOT/filters/FILTER.RES	# filters' transmission
FILTERS_FILE	~/ZPHOT/filters/UBVRI.param	# filters' file
TEMPLATES_FILE	spectra.param	# models file
FILT_M_ABS	91	# filter for absolute magnitude
ERR_MAG_MIN	0.05	# err_min
Z_MIN	0.00	# minimum redshift
Z_MAX	6.00	# maximum redshift
Z_STEP	0.20	# step in redshift
ZSTEP_TYPE	0	# 0 step = Z_STEP
		# 1 step = Z_STEP*(1+z)
CATALOG_TYPE	0	# cat.type
		# 0 z/cat
		# 1 z/obj
CATALOG_FILE	~/ZPHOT/models/UBVRI.cat	# cat file
MAG_TYPE	0	# 0 standard Vega mag, 1 AB mag
REDDENING_LAW	5	# reddening law
		# 0 no reddening
		# 1 Allen (1976) MW
		# 2 Seaton (1979) MW
		# 3 Fitzpatrick (1983) LMC
		# 4 Prevot (1984) Bouchet (1985) SMC
		# 5 Calzetti (2000)
AV_MIN	0.00	# Av_min
AV_MAX	1.20	# Av_max
AV_STEP	0.20	# Av_err
AGE_CHECK	y	# check age gal. $<$ age universe
PROB_THRESH	10.00	# prob. thresh. for second. max. (0,100)
OUTPUT_FILE	UBVRI	# name of output files (no extension)
OUTPUT_TYPE	0	# 0 2.E-17 erg/cm^2/s/A, 1 microJy, 2 mag_AB
SED_OBS_FILE	n	# file .obs_sed
SED_TEMP_FILE	n	# file .temp_sed
LOGPHOT_FILE	n	# file .log_phot
CATPHOT_FILE	n	# file .cat_phot
ZPHOT_FILE	y	# file .z_phot
H0	50.	# Hubble constant
		# used to compute absolute magnitude and
		# ages if AGE_CHECK = y
OMEGA_M	1.	# density parameter (matter)
		# used to compute absolute magnitude and
		# ages if AGE_CHECK = y
OMEGA_V	0.	# density parameter (Lambda)
		# used to compute absolute magnitude and
		# ages if AGE_CHECK = y
############	########## cluster option	##########################
#Z_CLUSTER	1.	# redshift of cluster
##################	####### optional parameters	##########################
#M_ABS_MIN	-28.	# minimum absolute magnitude (bright)
#M_ABS_MAX	-9.	# maximum absolute magnitude (faint)
MATRIX	n	# file .m for each object
SPECTRUM	n	# file .spe for each object
EBV_MW	0.	# E(B-V) for galactic dereddening

::::::::::::::
UBVRI.param
:::::::::::::: 

12	0.00	1	30.0	0.5
108	0.00	1	30.0	0.5
111	0.00	1	29.0	0.5
112	0.00	1	28.0	0.5
113	0.00	1	27.0	0.5

::::::::::::::
spectra.param
:::::::::::::: 

~/ZPHOT/templates/Burst.ised	BC
~/ZPHOT/templates/E.ised	BC
#~/ZPHOT/templates/S0.ised	BC
~/ZPHOT/templates/Sa.ised	BC
#~/ZPHOT/templates/Sb.ised	BC
~/ZPHOT/templates/Sc.ised	BC
#~/ZPHOT/templates/Sd.ised	BC
~/ZPHOT/templates/Im.ised	BC
#~/ZPHOT/templates/CWW_E_ext.sed	AS
#~/ZPHOT/templates/CWW_Sbc_ext.sed	AS
#~/ZPHOT/templates/CWW_Scd_ext.sed	AS
#~/ZPHOT/templates/CWW_Im_ext.sed	AS

::::::::::::::
UBVRI.cat
::::::::::::::

1	24.660	25.239	24.588	23.581	22.745	0.051	0.052	0.051	0.050	0.050
2	99.000	99.000	29.498	25.686	23.100	1.000	1.000	0.336	0.054	0.050
3	28.018	27.582	25.930	25.241	24.309	0.175	0.122	0.056	0.051	0.050
4	28.524	26.291	24.674	24.140	23.493	0.349	0.060	0.051	0.050	0.050
5	99.000	99.000	27.048	25.204	24.048	1.000	1.000	0.087	0.052	0.050

2000-12-10