User Manual for DUSTY - Physics and Astronomy
Contents
1. 322. 3 2 3 Otherwise the units of both radius and density are arbitrary DUSTY will transform both to dimensionless variables The number of entry data points is limited to a maximum of 1 000 but is otherwise arbitrary DUSTY will transform the table to its own radial grid with typically 20 30 points e Density profile tabulated in the file collapse dat density type 5 profile supplied in the file collapse dat This file is supplied with DUSTY and contains tabulation of the profile y x y corresponding to steady state accretion to a central mass In all cases care must be taken that 7 not become so small that roundoff errors cause spline oscillations and decrease accuracy To avoid such problems DUSTY will stop execution with a warning message whenever y dips below 107 or its dynamic range exceeds 10 This is particularly pertinent for very steep density profiles where the outer boundary should be chosen with care 3 4 Optical Depth For a given set of the parameters specified above DUSTY will generate up to 999 models with different overall optical depths The list of optical depths can be specified in two different ways DUSTY can generate a grid of optical depths spaced either linearly or logarithmically between two end points specified in the input Alternatively an arbitrary list can be entered in a file 1 Optical depths covering a specified range in linear steps Following the option selection the fiducial wavele
3. The occurrence of relevant numerical input which is entered in standard FORTRAN conventions is flagged by the equal sign The only restrictions are that all required input entries must be specified and in the correct order the most likely source of an input error is failure to comply with these requirements Recall also that FORTRAN requires a carriage return termination of the file s last line if it contains relevant input Single entries are always preceded by the equal sign and terminated by a blank which can be optionally preceded with a punctuation mark For example T 10 000 K as well as Temperature 1 E4 degrees and simply 10000 00 are all equivalent legal input entries note that comma separations of long numbers are permitted Some input is entered as a list in which case the first member is preceded by and each subsequent member must be preceded by a blank an optional punctuation can be entered before the blank for additional separation for example Temperatures 1E4 2E4 30 000 Because of the special role of as a flag for input entry care must be taken not to introduce any except when required All text following the sign is ignored as in TEX and this can be used to comment out material that includes signs For example different options for the same physical property may require a different number of input entries By commenting out with all options may be r
4. 2 3 Dust Temperature on Inner Boundary The next input entry is the dust temperature T in K on the shell inner boundary This is the only dimensional input required by the dust radiative transfer problem 9 T uniquely determines E the external flux entering the shell which is listed in DUSTY s output see 84 1 In principle different types of grains can have different temperatures at the same location However DUSTY currently treats mixtures as single type grains whose properties average the actual mix Therefore only one temperature is specified 11 3 3 Density Distribution In spherical geometry the density distribution is specified in terms of the scaled radius y ry where r is the shell inner radius This quantity is irrelevant to the radiative transfer problem 9 therefore it is never entered r scales with the luminosity L as LI when all other parameters are held fixed The explicit relation is provided as part of DUSTY s output see 84 1 The density distribution is described by the dimensionless profile n y which DUSTY normalizes according to f ndy 1 Note that the shell inner boundary is always y 1 Its outer boundary in terms of scaled radii is the shell relative thickness and is specified as part of the definition of 7 DUSTY provides three methods for entering the spherical density distribution prescribed analytical forms hydrodynamic calculation of winds driven by radiation pressure on dust par
5. B PITFALLS REAL AND IMAGINARY This appendix provides a central depository of potential programming and numerical prob lems Some were already mentioned in the text and are repeated here for completeness e FORTRAN requires termination of input records with a carriage return Make sure you press the Enter key whenever you enter a filename in the last line of dusty inp e In preparing input files the following two rules must be carefully observed 1 all required input entries must be specified and in the correct order 2 the equal sign must be entered only as a flag to numerical input When either rule is violated and DUSTY reaches the end of the input file while looking for additional input you will obtain the error message TERMINATED EOF reached by RDINP while looking for input Last line read This message is a clear sign that the input is out of order 28 e Linux apparently makes heavier demand on machine resources than Windows On any particular PC and a given value of npY DUSTY may execute properly under Windows but not under Linux dictating a smaller npY e DUSTY s execution under the Solaris operating system occasionally gives the following warning message Note IEEE floating point exception flags raised Inexact Underflow See the Numerical Computation Guide ieee_flags 3M This ominous message is triggered on Solaris also by other applications and is not unique to DUSTY The reason
6. Output Control The final input entries control DUSTY s output The first is a flag that sets the level of DUSTY s verbosity during execution With verbose 1 DUSTY will output to the screen a minimal progress report of its execution With verbose 2 you get a more detailed report that allows tracing in case of execution problems verbose 0 suppresses all messages The messages are printed to the standard output device with the FORTRAN statement write If you suspect that your system may not handle this properly choose verbose 0 All other output and its control is explained in the next section Note again that this section describes only the output for spherical models All changes necessitated by the planar geometry are described separately in 85 2 4 OUTPUT A typical DUSTY run generates an enormous amount of information and the volume of output can easily get out of hand To avoid that DUSTY s default output is a single file that lists only minimal information about the run as described next All other output is optional and fully controlled by the user 84 2 describes the optional output and its control 4 1 Default Output DUSTY always produces the output file fname out for each model input fname inp In addition to a summary of the input parameters the default output file tabulates global properties for each of the optical depths covered in the run The table s left column lists the sequential number of the model wit
7. are read from a file previous option set at 3 the present option is skipped 10 DUSTY recognizes two distribution functions for grain sizes n a the MRN 16 power law with sharp boundaries nfa xa fOr amin OG Ga 1 and its modification by Kim Martin and Hendry 14 which replaces the upper cutoff with a smooth exponential falloff n a ax a 4e 4 for a Amin 2 DUSTY contains the standard MRN parameters q 3 5 amin 0 005 wm and amax 0 25 um as a built in option In addition the user may select different cutoffs as well as power index for both distributions 1 This is the standard MRN distribution No input required other than the option flag 2 Modified MRN distribution The option flag is followed by listing of the power index q lower limit amin and upper limit amax in um e Standard MRN distribution can be entered with this option as Size distribution 2 q 3 5 a min 0 005 micron a max 0 25 micron e Single size grains with a 0 05 um Size distribution 2 q 0 it is irrelevant in this case a min 0 05 micron a max 0 05 micron 3 KMH distribution The option flag is followed by a list of the power index q lower limit Amin and the characteristic size ay in um e Size distribution for grains in the dusty envelope around IRC 10216 as obtained by Jura 13 and verified in Ivezi amp Elitzur 8 Size distribution 3 q 3 5 a min 0 005 micron a0 0 2 micron 3
8. grain types is entered followed by the names of the data files listed separately one per line that contain the relevant optical properties These properties are specified by the index of refraction and DUSTY calculates the absorption and scattering coefficients using Mie theory Each data file must start with seven header lines arbitrary text followed by a three column tabulation of wavelength in um and real n and imaginary k parts of the index of refraction The number of table entries is arbitrary up to a maximum of 10 000 The tabulation must be ordered in wavelength but the order can be either ascending or descending DUSTY will linearly interpolate the data for n and k to its built in wavelength grid If the supplied data do not fully cover DUSTY s wavelength range the refraction index will be assumed constant in the unspecified range with a value equal to the corresponding end point of the user tabulation The file list should be followed by a list of abundances entered in the same order as the names of the corresponding data files e Draine amp Lee graphite grains with three additional grain types whose n and k are provided by the user in data files amC zb1 nk amC zb2 nk and amC zb3 nk distributed with DUSTY These files tabulate the most recent properties for amor phous carbon by Zubko et al 20 Optical properties index 2 Abundances of built in grain types Sil 0w Sil 0c Sil DL grf DL amC Hn SiC Pg x 0 00 0 00 0
9. size in arcsec of the shell inner diameter This angle depends on the observer s position and scales in proportion to F a Where Fops is the observed bolometric flux The tabulated value corresponds to Ee 107 W m7 Td Y the dust temperature in K at the envelope s outer edge err the numerical accuracy in achieved in the run Specifically if r is the ratio of smallest to largest bolometric fluxes in the shell after accounting for radial dilution then the error is 1 r 1 r Errors smaller than 1 are listed as zero When the density distribution is derived from a hydrodynamics calculation for AGB winds 3 3 2 three more columns are added to fname out listing the derived mass loss rate terminal outflow velocity and an upper bound on the stellar mass These quantities posses general scaling properties in terms of the luminosity L gas to dust mass ratio gd and dust grain bulk density ps 10 The tabulations are for L 104 Lo rea 200 and Ps 3 g cm and their scaling properties are Mdot the mass loss rate in Mo vr scales in proportion to L rgap This quantity has 30 inherent uncertainty because varying the gravitational correction from 0 up to 50 has no discernible effect on the observed spectrum 1 1 2 scales in proportion to LY r aps 71 Ve is subject to Ve the terminal outflow velocity in km s The provided solutions apply only if this velocity e
10. 00 0 22 0 00 0 00 Number of additional components 3 properties listed in files amC zb1 nk amC zb2 nk amC zb3 nk Abundances for these components 0 45 0 10 23 3 This option is similar to the previous one only the absorption and scattering coeffi cients are tabulated instead of the complex index of refraction so that the full optical properties are directly specified and there is no further calculation by DUSTY The data filename is listed in the line following the option flag This file must start with a three line header of arbitrary text followed by a three column tabulation of wavelength in um absorption Cabs and scattering sca cross sections Units for Cabs and Osea are arbitrary only their spectral variation is relevant The number of entries is arbitrary with a maximum of 10 000 The handling of the wavelength grid is the same as in the previous option e Absorption and scattering cross sections from the file ism stnd dat supplied with DUSTY listing the optical properties for the standard interstellar dust mix ture Optical properties index 3 cross sections entered in file ism stnd dat DUSTY s distribution includes a library of data files with the complex refractive indices of various compounds of common interest This library is described in appendix E 3 2 2 Grain Size Distribution The grain size distribution must be specified only when the previous option was set to 1 or 2 When the dust cross sections
11. 1 AN 1 lt A In this case after the option selection the number N is entered followed by a list of the break points A z i 1 N 1 in um and a list of the power indices k 1 1 1 N The wavelengths A must be listed in increasing order e A flat spectrum confined to the range 0 1 1 0 um Spectrum 3 N 1 lambda 0 1 1 micron k 0 All spectral points entered outside the range covered by DUSTY s wavelength grid are ignored If the input spectrum does not cover the entire wavelength range all undefined points are assumed zero The other three options are for entry in numerical form as a separate user supplied input file which lists either 4 AF vF or 5 Fy or 6 F vs A Here A is wavelength in wm and y the corresponding frequency and F or F is the external flux density in arbitrary units 4 Stellar spectrum tabulated in a file The filename for the input spectrum must be entered separately in the line following the numerical flag This input file must have a three line header of arbitrary text followed by a two column tabulation of A and AF where A is in ym and AF is in arbitrary units The number of entry data points is limited to a maximum of 10 000 but is otherwise arbitrary The tabulation must be ordered in wavelength but the order can be either ascending or descending If the shortest tabulated wavelength is longer than 0 01 um the external flux is assumed to vanish at all shorter wavelengths If the
12. 4 Optical Depths at a besch ted Se ka ne tna BO md Oe ae cn Eet 3 5 Numerical Accuracy and Internal Bounds 04 3 0 Qutp t Controles acuda 2d SA eal SY bP RY Bae PG AAD di ele OUTPUT Aa Alte e amp geb 25 Meek AA Ale Beales Bees 4 2 Optional Output y er asp ba a eke er re BAO A ee A eS 4 2 1 Properties of Emerging Spectra o 4 2 2 Detailed spectra for each model o 4 2 3 Images at specified wavelengths o 42A e EE aoe Ro a Ee ee Ae ee EE A 4 2 5 Radial profiles for each model 4 2 6 Detailed Run time Messages SLAB GEOMETRY 5 1 IMumi ating A DE ey A brut Deet r de T Geen A Zeg pat Wee Me E E e 5 2 1 Default Output sd A ee A Bee A D22 EE ele At Eh ot cr Oh ok ete ehre eae 5 2 3 Spatial Promesa aaa aaa A HENS EES USER CONTROL OF DUSTY 6 1 Array Sizes for Spatial Grid 4 eher reo ada e ia ee 6 2 Wavelength Grid 2 is a da Ske a pare PES e as aN Om ol 11 12 12 13 14 14 15 16 16 16 18 18 19 20 21 21 22 22 23 24 24 24 25 APPENDICES 28 A OUTPUT SUMMARY 28 B PITFALLS REAL AND IMAGINARY 28 C SAMPLE OUTPUT FILE spherel out 29 D SAMPLE OUTPUT FILE slab1 out 30 E LIBRARY OF OPTICAL CONSTANTS 32 1 INTRODUCTION The code DUSTY was developed at the University of Kentucky by Zeljko Ivezi Maia Nenkova and Moshe Elitzur for a commonly encountered astrophysical problem radiation from some source star gal
13. In this case the spectral shape of the source is entered as in the spherical case The only change from the spherical input is that the density profile is replaced by the following density type 0 cos angle 1 0 spectral shape entered previously R 0 no source on the right Two sided illumination is specified by a non zero R where 0 lt R lt 1 The properties of the right side source are specified following the input for R 23 e Slab illuminated from both sides The left side radiation has isotropic distribution whose spectral shape has been entered previously The right side source has a bolo metric flux half that of the left side source and a black body spectral shape with temperature 3 000 K It illuminates the slab with parallel rays incident at an angle of 60 from normal The density profile is replaced by the following density type 0 cos angle 1 0 spectral shape entered previously R 0 5 Properties of the right side source cos angle 0 5 Spectrum 1 N 1 Tbb 3000 K 5 2 Slab Output The output control flags are identical to those in the spherical case and the output files are analogous except for some changes dictated by the different geometry 5 2 1 Default Output In the default fname out the first two columns are the same as in the spherical case 4 1 and are followed by o Fei bolometric flux in W m of the left side source at the slab left boundary f1 F Fa where F is th
14. Similar to the fTot column of the spherical case the spectral shape of the right emerging half flux is printed in column fRight It consists of three components whose fractional con tributions are listed next as in the spherical case xAtt for the left source attenuated radia tion xDs and xDe for the diffuse scattered and emitted components respectively Subsequent columns are as in the spherical case The tables for the spectral shape of the left emerging half flux fLeft are analogous 5 2 3 Spatial Profiles The output for spatial profiles is similar to the spherical case The radial distance y and density profile eta are removed The relative distance in optical depth from the left boundary t becomes the running variable and the tabulations of tauF epsilon and Td are the same see 4 2 5 The tabulation for Frad Ferav is dropped replaced by three components of the overall bolometric flux febol is the local net bolometric flux of external radiation fRbol and fLbol are respectively the rightward and leftward half fluxes of the local diffuse radiation All components are normalized by Fei so that the flux conservation relation is febol fRbol fLbol f1 everywhere in the slab Note that fRbol vanishes on the slab left face fLbol on the right face DUSTY s distribution contains two sample input files slab1 inp and slab2 inp which can be used as templates for the slab geometry The output generated with slab1 inp is shown in appendi
15. USER MANUAL FOR DUSTY Zeljko Ivezi Maia Nenkova amp Moshe Elitzur Department of Physics and Astronomy University of Kentucky Lexington KY 40506 0055 October 1999 Abstract DUSTY solves the problem of radiation transport in a dusty environment The code can handle both spherical and planar geometries The user specifies the proper ties of the radiation source and dusty region and the code calculates the dust tem perature distribution and the radiation field in it The solution method is based on a self consistent equation for the radiative energy density including dust scattering absorption and emission and does not introduce any approximations The solution is exact to within the specified numerical accuracy DUSTY has built in optical properties for the most common types of astronomical dust and comes with a library for many other grains It supports various analytical forms for the density distribution and can perform a full dynamical calculation for radiatively driven winds around AGB stars The spectral energy distribution of the source can be specified analytically as either Planckian or broken power law In addi tion arbitrary dust optical properties density distributions and external radiation can be entered in user supplied files Furthermore the wavelength grid can be modified to accommodate spectral features A single DUSTY run can process an unlimited number of models with each input set producing a run of optical de
16. Ultra 1 and 6 min on SPARC20 These run times should provide an indication of what to expect on your machine If DUSTY compiles properly but the execution seems to be going nowhere and the output is not produced in the expected time in all likelihood the problem reflects insufficient amount of machine memory As a first measure try to close all programs with heavy demand on system resources such as ghostview and Netscape before running DUSTY If this does not help the problem may be alleviated by reducing DUSTY s memory requirements Section 6 1 describes how to do that 3 INPUT A single DUSTY run can process an unlimited number of models To accomplish this DUSTY s input is always the master input file dusty inp which lists the names of the actual input files for all models These filenames must have the form fname inp where fname is arbitrary and can include a full path so that a single run may produce output models in different directories In dusty inp each input filename must be listed on a separate line with the implied extension inp omitted Since FORTRAN requires termination of input records with a carriage return make sure you press the Enter key after every filename you enter especially if it is in the last line of dusty inp Empty lines are ignored as is all text following the sign as in TeX This enables you to enter comments and conveniently switch on and off the running of any particular model The sampl
17. actic nucleus etc viewed after processing by a dusty region The original radiation is scattered absorbed and reemitted by the dust and the emerging pro cessed spectrum often provides the only available information about the embedded object DUSTY can handle both planar and centrally heated spherical density distributions The so lution is obtained through an integral equation for the spectral energy density introduced in 9 The number of independent input model parameters is minimized by fully implementing the scaling properties of the radiative transfer problem and the spatial temperature profile is found from radiative equilibrium at every point in the dusty region On a Convex Exemplar machine the solution for spherical geometry is produced in a minute or less for visual optical depth ty up to 10 increasing to 5 10 min for ty higher than 100 In extreme cases ty 1000 the run time may reach 30 min or more Run times for the slab case are typically five times shorter All run times are approximately twice as long on a 300 MHz Pentium PC The purpose of this manual is to help users get quickly acquainted with the code Follow ing a short description of the installation procedure 2 the input and output are described in full for the spherical case in 83 and 34 All changes pertaining to the plane parallel case are described separately in 85 Finally Sp describes user control of DUSTY itself This new version of DUSTY is significant
18. different components to the total luminosity e A single black body Spectrum 1 Number of BB 1 Temperature 10 000 K This could also be entered on a single line as type 1 N 1 T EA e Two black bodies e g a binary system with the first one contributing 80 of the total luminosity note that the distance between the stars must be sufficiently small that the assumption of a central point source remain valid Spectrum 1 Number of BB 2 Temperatures Luminosities 4 10 000 2 500 K 1 2 Engelke Marengo function This expression improves upon the black body description of cool star emission by incorporating empirical corrections for the main atmospheric effects Engelke 3 found that changing the temperature argument of the Planck function from T to 0 738 T 1 79450 AT where T is in K and A is wavelength in wm adequately accounts for the spectral effect of H7 Massimo Marengo 15 devised an additional empirical correction for molecular SiO absorption around 8 um and has kindly made his results available to DUSTY The selection of this combined Engelke Marengo function requires as input the temperature and the relative to the continuum SiO absorption depth in e Stellar spectrum parametrized with Engelke Marengo function Spectrum Temperature SiO0 absorption depth 3 Broken power law of the form 0 ATEC ATEL Ab x AH 0 2 2500 K 10 percents A N lt ASA N
19. e dusty inp supplied with the program points to the five actual input files sphereN inp N 1 3 and slabM inp M 1 2 Only spherel and slab1 will be executed since the others are commented out providing samples of DUSTY s simplest possible input and output Once they have been successfully run you may wish to remove the signs from the other entries which demonstrate more elaborate input and output and check the running of a full sequence Your output can be verified against the corresponding sample output files accessible on DUSTY s homepage Each model is characterized by properties of the radiation source and the dusty region and DUSTY produces a set of up to 999 solutions for all the optical depths specified in the input The output file for fname inp is fname out containing a summary of the run and a ldusty inp must be kept with the DUSTY executable file in the same directory table of the main output results Additional output files containing more detailed tables of radiative and radial properties may be optionally produced The input file has a free format text and empty lines can be entered arbitrarily All lines that start with the sign are echoed in the output and can be used to print out notes and comments This option can also be useful when the program fails for some mysterious reason and you want to compare its output with an exact copy of the input line as it was read in before processing by DUSTY
20. e offered for the modeling of objects such as AGB stars where the envelope expansion is driven by radiation pressure on the dust grains DUSTY can compute the wind structure by solving the hydrodynamics equations including dust drift and the star s gravitational attraction as a set coupled to radiative transfer This solution is triggered with density type 3 while density type 4 utilizes an analytic approximation for the dust density profile which is appropriate in most cases and offers the advantage of a much shorter run time 3 An exact calculation of the density structure from a full dynamics calculations see 6 and references therein The calculation is performed for a typical wind in which the final expansion velocity exceeds 5 km s but is otherwise arbitrary The only input parameter that needs to be specified is the shell thickness Y rout 11 e Numerical solution for radiatively driven winds extending to a distance 10 times the inner radius density type 3 Y 1 e4 The steepness of the density profile near the wind origin increases with optical depth and with it the numerical difficulties DUSTY handles the full dynamics calculation for models that have ty lt 1 000 corresponding to M 4x10 4 Mo yr 4 When the variation of flux averaged opacity with radial distance is negligible the problem can be solved analytically 10 In the limit of negligible drift the analytic solution takes the form 1 7 1 2 a
21. e overall bolometric flux Values at and below the internal accuracy of DUSTY s flux computation 1073 when dace 0 05 are listed as zero ri cm the distance at which a point source with luminosity 104 Lo produces the bolometric flux ba o Td K the dust temperature at the slab right boundary Te L the effective temperature in K obtained from F oTe When the slab is illuminated also from the right a column is added next for Te R the effective temperature obtained similarly for the right side flux o err the flux conservation error defined as in the spherical case 5 2 2 Spectral Profiles Unlike the spherical case the slab optional spectral files list properties of the half fluxes emerging from both sides of the slab calculated over the forward and backward hemispheres perpendicular to the slab faces The magnitudes of the bolometric half fluxes on the slab right and left faces can be obtained from tabulated quantities via Fright R 1 Fel Fie 1 1 Fet 24 The right emerging radiation replaces the spherical output in fname spp fname stb and fname s analogous tables for the left emerging radiation are simply added to the ap propriate output files Setting the relevant selection flags to 3 places these additional tables in their own separate files fname zpp for spectral properties and fname z for the detailed spectra of model number in the optical depth sequence
22. es In models that utilize these standard properties the only input required is the fractional abundance of the relevant grains In addition optical properties for other grains can be supplied by the user In this case the user can either specify directly the absorption and scattering coefficients or have DUSTY calculate them from provided index of refraction The various alternatives are selected by a flag as follows 1 DUSTY contains data for six common grain types warm and cold silicates from Ossenkopff et al 17 Sil Ow and Sil Oc silicates and graphite grains from Draine and Lee 2 Sil DL and grf DL amorphous carbon from Hanner 4 amC Hn and SiC by Pegourie 18 SiC Pg Fractional number abundances must be entered for all these grain types in the order listed e Mixture containing only dust grains with built in data for optical properties optical properties index 1 Abundances for supported grain types standard ISM mixture Sil Ow Sil Oc Sil DL grf DL amC Hn SiC Pg x 0 00 0 00 0 53 0 47 0 00 0 00 The overall abundance normalization is arbitrary In this example the silicate and graphite abundances could have been entered equivalently as 53 and 47 respectively 2 With this option the user can introduce up to ten additional grain types on top of those built in First the abundances of the six built in types of grains are entered as in the previous option Next the number lt 10 of additional
23. etained in the input file with only the relevant one switched on The input contains three types of data physical parameters numerical accuracy pa rameters and flags for optional output files The physical parameters include characteristics of the external radiation properties of the dust grains and the envelope density distribu tion Detailed description of the program input follows including examples marked with the e sign Each example contains a brief explanation followed by sample text typeset in typewriter font as it would appear in the input file The sample input files sphereN inp and slabM inp supplied with DUSTY are heavily commented to ease initial use and can be used as templates 3 1 External Radiation In the spherical case DUSTY assumes that the external radiation comes from a point source at the center of the density distribution Thanks to scale invariance the only relevant property of the external radiation under these circumstances is its spectral shape see 9 Six different flag selected input options are available The first three involve entry in analytical form 1 A combination of up to 10 black bodies each described by a Planck function of a given temperature Following the spectrum flag the number of black bodies is specified followed by a list of the temperatures When more then one black body is specified the temperature list must be followed by a list of the fractional contributions of the
24. for it is not yet clear and it is not issued on other platforms In spite of this statement the code performs fine and produces results identical to those on machines that do not issue this warning e CRAY J90 machines have specific requirements on FORTRAN programs which prevent DUSTY from running in its present form If you plan to run DUSTY on this platform you ll have to introduce some changes in the source code such as replacing all DOUBLE PRECISION statements with REAL 4 C SAMPLE OUTPUT FILE sphere1 out Output from program Dusty Version 2 0 INPUT parameters from file spherel inp NOTES This is a simple version of an input file producing a minimal output Central source spectrum described by a black body with temperature 2500 K Abundances for supported grains Sil 0w Sil Oc Sil DL grf DL amC Hn SiC Pg 1 000 0 000 0 000 0 000 0 000 0 000 MRN size distribution Power q 3 5 29 Minimal size 5 00E 03 microns Maximal size 2 50E 01 microns Density described by 1 r k with k 2 0 Relative thickness 1 000E 03 Optical depth at 5 5E 01 microns 1 00E 00 Required accuracy 5 For compliance with the point source assumption the following results should only be applied to sources whose effective temperature exceeds 1737 K tauo F1 W m2 ri cm r1 rc thetal Td Y err HHH 1 2 3 4 5 6 7 1 Optical depth at 5 5E 01 microns 2 Bolometric flux at the inner radius 3 Inner radius for L 1E4 Lsun 4 Ratio
25. h the fiducial optical depth tauo listed in the next column Subsequent columns list quantities calculated by DUSTY for that tauo o F1 the bolometric flux in W m at the inner radius y 1 Only the external source contributes to F1 since the diffuse flux vanishes there under the point source assumption Note that F1 is independent of overall luminosity fully determined by the scaled solution see 9 The bolometric flux emerging from the spherical distribution is F1 Y Any measure of the shell dimension is irrelevant to the radiative transfer problem and thus not part of DUSTY s calculations Still the shell size can be of considerable interest in many applications For convenience the next three output items list differ ent measures of the shell size expressed in terms of redundant quantities such as the luminosity ri cm the shell inner radius where the dust temperature is T1 specified in the input 3 2 3 This radius scales in proportion to L where L is the luminosity The tabulated value corresponds to L 104 Lo r1 rc where rc is the radius of the central source This quantity scales in proportion to T T where T is the external radiation effective temperature The listed value is for T 10 000 K with two exceptions when the spectral shape of the external radiation is the Planck or Engelke Marengo function the arguments of those functions are used for T 16 o thetal the angular
26. he normal b Isotropic radiation where fF is the bolometric flux of the left side source at slab entry is another unknown variable determined by the solution The slab geometry is selected by specifying density type 0 The dust properties are entered as in the spherical case with the dust temperature specified on the slab left surface instead of the shell inner boundary The range of optical depths too is chosen as in the spherical case The only changes from the spherical case involve the external radiation and the output 5 1 Illuminating Source s External radiation is incident from the left side The presence of an optional right side source is specified by a non zero value for R the ratio of the right side bolometric flux at slab entry to that of the left side source Each input radiation is characterized by its spectral shape which is entered exactly as in the spherical case 3 1 and angular distribution The only angular distributions that do not break the planar symmetry involve parallel rays falling at some incident angle and isotropic radiation see figure 2 The parallel rays distribution is specified by the cosine gt 0 05 of the illumination angle the isotropic distribution is selected by setting this input parameter to 1 Since oblique angles effectively increase the slab optical depth run times will increase with incidence angle e Slab geometry with illumination by parallel rays normal to the left surface
27. ic expressions for these integrations Since this grid becomes redundant npP can be set to unity allowing a larger maximum npY The procedure is described in userpar inc 6 2 Wavelength Grid DUSTY s wavelength grid is used both in the internal calculations and for the output of all wavelength dependent quantities The number of grid points is set in userpar inc by the parameter npL the grid itself is read from the file lambda_grid dat This file starts with an arbitrary number of text lines the beginning of the wavelength list is signaled by an entry for the number of grid points This number must be equal to npL entered in userpar inc and to the actual number of entries in the list The grid supplied with DUSTY contains 105 points from 0 01 to 3 6 x 104 um The short wavelength boundary is to ensure adequate coverage of input radiation from an O star for example which peaks at 0 1 wm Potential effects on the grain material by such hard radiation are not included in DUSTY The long wavelength end is to ensure adequate coverage at all wavelengths where dust emission is potentially significant Wavelengths can be added and removed provided the following rules are obeyed 1 Wavelengths are specified in um 2 The shortest wavelength must be lt 0 01 um the longest gt 3 6 x 104 um 3 The ratio of each consecutive pair must be lt 1 5 The order of entries is arbitrary DUSTY sorts them in increasing wavelength and the sorted list is u
28. ing parameter W see 9 for the model The subsequent columns list fluxes f A AF F where F Fd for various wavelengths of interest fV relative emerging flux at 0 55 wm fK relative emerging flux at 2 2 um 12 relative emerging flux at 12 um convolved with the IRAS filter for this wave length 18 Next are the IRAS colors defined for wavelengths A and Az in um as Ae A E A2 O 6 AFA On G Columns 5 7 list in this order C21 25 12 C31 60 12 and C43 100 60 They are followed by tabulations of b8 13 the IRAS defined spectral slope 3 13 between 8 and 13 um Ag Se l 1 log f 13 _13 4 74log 1 0 Ps 13 08 F 8 b14 22 the IRAS defined spectral slope B14 22 between 14 and 22 um f 22 _92 5 09 log 1 0 Pya 29 08 FAA o B9 8 the relative strength of the 9 8 um feature defined as f 9 8 Bog 1 La where f 9 8 is the continuum interpolated flux across the feature B11 3 the relative strength of the 11 3 um feature defined as above for B9 8 R9 8 18 the ratio of the fluxes at 9 8 wm and 18 um f 9 8 f 18 4 2 2 Detailed spectra for each model The next output flag triggers listing of detailed spectra for each model in the run Setting this flag to 1 produces tables for the emerging spectra of all models in the single output file fname stb Setting the flag to 2 places each table in
29. its own separate file where file fname s contains the tabulation for model number in the optical depth sequence listed in the default output file 84 1 In addition to the emerging spectrum the table for each model lists separately the contri butions of various components to the overall flux the spectral shape of the input radiation and the wavelength dependence of the total optical depth The following quantities are tabulated lambda the wavelength in um fTot the spectral shape of the total emerging flux f A AF SE1dA Values smaller than 107 are listed as 0 xAtt fractional contribution of the attenuated input radiation to fTot xDs fractional contribution of the scattered radiation to fTot xDe fractional contribution of the dust emission to fTot fInp the spectral shape of the input unattenuated radiation tauT overall optical depth at wavelength lambda albedo the albedo at wavelength lambda 19 OF Vi Figure 1 Notation for imaging output 4 2 3 Images at specified wavelengths The surface brightness is a luminosity independent self similar distribution 7 of b r the impact parameter scaled by the envelope inner radius fig 1 note that r is listed in the default output file 84 1 for a source luminosity 104 Lo DUSTY can produce maps of the surface brightness at up to 20 wavelengths specified in the input file Setting the option flag to 1 prod
30. les are standardized in the format DUSTY accepts Included are the optical constants for the seven built in dust types as well as other frequently encountered astronomical dust components This library will be updated continuously at the DUSTY site The following table lists all the files currently supplied Table 2 Optical Constants Library Supplied with Dusty File Name Compound Range um Ref A1203 comp nk Al203 compact 7 8 200 12 A1203 por nk Al203 porous 7 8 500 12 amC hann nk amorphous carbon 0 04 905 4 amC zb1 nk amorphous carbon BE 0 05 1984 20 amC zb2 nk amorphous carbon ACAR 0 04 1984 20 amC zb3 nk amorphous carbon ACH2 0 04 948 20 crbr300 nk crystalline bronzite 6 7 487 4 5 crMgFeSil nk crystalline silicate 6 7 584 9 12 Fe0 nk FeO 5 7g ccm 0 2 500 12 gloliMg50 nk glassy olivine 0 2 500 1 glpyr300 nk glassy pyroxene at 300 K 6 7 487 5 glpyrMg50 nk glassy pyroxene 0 2 500 1 glSil nk glassy silicate 0 4 500 11 grphi dl nk graphite E Lc 0 001 103 2 grph2 dl nk graphite E c 0 001 10 2 opyr pwd nk ortho pyroxenes powder 5 0 25 19 opyr slb nk ortho pyroxenes slab 5 0 25 19 OssOdef ok O deficient CS silicate 0 4 10 17 OssOrich nk O rich IS silicate 0 4 10 17 SiC peg nk a SiC 0 03 2000 18 Sil dlee nk Astronomical silicate 0 03 2000 2 Sil oss1 nk warm O deficient silicates 0 4 10 17 Sil oss2 nk cold O rich silicate 0 4 10 17
31. longest tabulated wavelength is shorter than 3 6 cm DUSTY will extrapolate the rest of the spectrum with a Rayleigh Jeans tail e Spectrum tabulated in file quasar dat Spectrum 4 quasar dat 5 Stellar spectrum read from a file as in the previous option but F is specified in arbitrary units instead of AF e Kurucz model atmosphere tabulated in file kurucz10 dat Spectrum 5 kurucz10 dat 6 Stellar spectrum read from a file as in the previous option but F is specified in arbitrary units instead of F In the last three entry options the filename for the input spectrum must be entered separately in the line following the numerical flag Optionally you may separate the flag line and the filename line by an arbitrary number of lines that are either empty or commented out starting with The files quasar dat and kurucz10 dat are distributed with DUSTY 3 2 Dust Properties Dust optical properties are described by the dust absorption and scattering cross sections which depend on the grain size and material Currently DUSTY supports only single type grains namely a single size and chemical composition Grain mixtures can still be treated simulated by a single type grain constructed from an appropriate average This approximation will be removed in future releases which will provide full treatment of grain mixtures 3 2 1 Chemical Composition DUSTY contains data for the optical properties of six common grain typ
32. ly faster than its previous public release Because of the addition of many features the structure of the input has changed and old input files will not run on the current version 2 INSTALLATION The FORTRAN source dusty f along with additional files including five sample input files come in a single compressed file dusty tar gz This file and its unpacking instructions are available at DUSTY s homepage at http www pa uky edu moshe dusty Alter natively anonymous ftp gradj pa uky edu cd dusty distribution and retrieve all files and sub directories DUSTY was developed on a Pentium PC and has been run also on a variety of Unix workstations It is written in standard FORTRAN 77 and producing the executable file is rather straightforward For example on a Unix machine 77 dusty f o dusty If the compilation is successful you can immediately proceed to run DUSTY without any further action It should produce the output files sphere1 out and slab1 out printed in appendices C and D respectively On a 300 MHz Pentium PC with DUSTY compiled by Visual FORTRAN under Windows these files are produced in just under 2 minutes Execution times under Linux are roughly three times longer the Linux FORTRAN imple mentation on the Digital alpha machine appears to be especially poor the execution may be as much as ten times longer Execution times on SUN workstations vary greatly with the model about 1 30 min on an Enterprise 3000 3 min on SPARC
33. mp Elitzur M in preparation Jager C et al 1994 A amp A 292 641 Jena St Petersburg database of optical constants accessible at http www astro uni jena de Users database entry html Jura M 1994 ApJ 434 713 Kim S H Martin P G amp Hendry P D 1994 ApJ 422 164 Marengo M 1999 in preparation Mathis J S Rumpl W amp Nordsieck K H 1977 ApJ 217 425 Ossenkopf V Henning Th amp Mathis J S 1992 A amp A 261 567 Pegourie B 1988 A amp A 194 335 Roush T et al 1991 Icarus 94 191 Zubko V G et al 1996 MNRAS 282 1321 27 APPENDICES A OUTPUT SUMMARY DUSTY s default output is the file fname out described in 84 1 Additional output is op tionally produced through selection flags summarized in the following table The second column lists the section number where a detailed description of the corresponding output is provided Table 1 Summary of all Output Options Output Listing 8 Output File Triggered by Flag 1 2 3 Spectral properties all models 4 2 1 fname spp fname spp fname spp Slab left face spectra 5 2 fname zpp Detailed spectra each model 4 2 2 fname stb fname s fname s Slab left face spectra 5 2 fname z Images 4 2 3 fname itb fname i fname i Visibilities 4 2 4 fname v Radial profiles 4 2 5 fname rtb fname r Error messages 4 2 6 fname mtb fname m
34. ngth An in wm of optical depth To is entered The 7 grid is then specified by its two ends and the number of points lt 999 14 e Models with 2 2 um optical depths including all the integers from 1 to 100 tau grid 1 lambda0 2 2 micron tau min 1 tau max 100 number of models 100 2 Same as the previous option only the To range is covered in logarithmic steps e Three models with visual optical depth ty 0 1 1 and 10 tau grid 2 lambda0 0 55 micron tau min 0 1 tau max 10 number of models 3 3 Optical depths list entered in a file The file name is entered on a single line after the option selection The arbitrary header text of the supplied file must end with the fiducial wavelength Ay preceded by the equal sign The list of optical depths one per line up to a maximum of 999 entries is entered next in arbitrary order DUSTY will sort and run it in increasing To e Optical depths from the file taugrid txt supplied with the DUSTY distribution tau grid 3 grid supplied in file taugrid dat The file taugrid dat is used in the sample input files slab2 inp and sphere3 inp 3 5 Numerical Accuracy and Internal Bounds The numerical accuracy and convergence of DUSTY s calculations are controlled by the next input parameter dacc The accuracy is closely related to the set of spatial and wavelength grids employed by DUSTY The wavelength grid can be modified by users to meet their s
35. ntrolled through flags entered at the end of the input file fname inp that turn on and off the optional tabulations Setting all flags to 0 as in sphere1 inp and slab1 inp suppresses all optional tabulations and results in minimal output A non zero output flag triggers the production of corresponding output occasionally requiring additional input Further user control is provided by the value of the output flag When a certain flag is set to 1 the corresponding output is listed in a single file that contains the tabulations for all the optical depth solutions Setting the flag to 2 splits the output when appropriate tabulating the solution for each optical depth in its own separate file This may make it more convenient for plotting purposes for example at the price of many small files A few flags can also be set to 3 splitting the output even further Each of the following subsections describes in detail the optional tabulations triggered by one of the output flags and any additional input it may require Appendix A summarizes all the output flags and the corresponding output files they trigger and can be used for quick reference 4 2 1 Properties of Emerging Spectra Setting the first optional flag to 1 outputs a variety of spectral properties for all the model solutions to the file fname spp The tabulation has four header lines and starts with the model sequential number The following columns list the corresponding tau0 and the scal
36. o the radiation field see 9 Td radial profile of the dust temperature 21 rg radial profile of the ratio of radiation pressure to gravitational force where both forces are per unit volume Fs 3L Y man Ion dA rg Foray 16nGMCrya ara j Here fy F f F1dA is the local spectral shape ps is the material solid density and na the number density of grains with size a The gas to dust ratio rga appears since the gas is collisionally coupled to the dust The tabulated value is for ps 3 g cm L M 10 Lo Mo and rga 200 In the case of radiatively driven winds rq varies in the envelope because of the dust drift and this effect is properly accounted in the solution When the dust optical properties are entered using optical properties 3 grain sizes are not specified 3 2 1 This case is handled as described in the last paragraph of 84 1 In the case of dynamical calculation with density type 3 for AGB stars 3 3 2 the following additional profiles are tabulated u the dimensionless radial velocity profile normalized to the terminal velocity Ve which is tabulated for the corresponding overall optical depth in file fname out 84 1 drift the radial variation of v v4 the velocity ratio of the gas and dust components of the envelope This quantity measures the relative decrease in dust opacity due to dust drift 4 2 6 Detailed Run time messages In case of an error the default
37. of the inner to the stellar radius 5 Angular size in arcsec when Fbol 1E 6 W m2 6 Dust temperature at the outer edge in K 7 Maximum error in flux conservation Output from program Dusty Version 2 0 INPUT parameters from file slab1 inp 30 NOTES This is a simple version of an input file for calculation in planar geometry with single source illumination Left side source spectrum described by a black body with temperature 2500 K Abundances for supported grains Sil 0w Sil 0c Sil DL grf DL amC Hn SiC Pg 1 000 0 000 0 000 0 000 0 000 0 000 MRN size distribution Power q 3 5 Minimal size 5 00E 03 microns Maximal size 2 50E 01 microns Calculation in planar geometry cos of left illumination angle 1 000E 00 R 0 000E 00 Optical depth at 5 5E 01 microns 1 00E 00 Required accuracy 5 tau0 Fe1 W m2 f1 ri cm Td K Te L err HHH 1 2 3 4 5 6 7 1 Optical depth at 5 5E 01 microns 2 Bol flux of the left side source at the slab left boundary 3 f1 F Fel where F is the overall bol flux in the slab 4 Position of the left slab boundary for L 1E4 Lsun 5 Dust temperature at the right slab face 6 Effective temperature of the left source in K 7 Maximum error in flux conservation Everything is OK for all models 31 E LIBRARY OF OPTICAL CONSTANTS DUSTY s distribution includes a library of data files with the complex refractive indices of various compounds of interest The fi
38. output file issues a warning Optionally additional more detailed run time error messages can be produced and might prove useful in tracing the program s progress in case of a failure Setting the corresponding flag to 1 produces messages for all the models in the single output file fname mtb setting the flag to 2 puts the messages for model number in its own separate file fname m 5 SLAB GEOMETRY DUSTY offers the option of calculating radiative transfer through a plane parallel dusty slab The slab is always illuminated from the left additional illumination from the right is optional As long as the surfaces of equal density are parallel to the slab boundaries the density profile is irrelevant location in the slab is uniquely specified by the optical depth from the left surface Unlike the spherical case there is no reference to spatial variables since the problem can be solved fully in optical depth space The other major difference involves the bolometric flux F In the spherical case the diffuse flux vanishes at y 1 and F F 1 y where Fe is the external bolometric flux at the shell inner boundary 9 In contrast F is constant in the slab and the diffuse flux does not vanish on either face Therefore H E 22 A e DN ANA To 0 a o a b Figure 2 The two possible schemes for a slab illuminated from the left a Parallel rays impinging at an arbitrary angle to t
39. pecific needs see 6 2 and it does not change during execution The spatial grids are automatically generated and refined until the fractional error of flux conservation at every grid point is less than ga Whenever DUSTY calculates also the density profile y the numerical accuracy of that calculation is also controlled by dace The recommended value is dace 0 05 entered in all the sample input files The accuracy level that can be accomplished is related to the number of spatial grid points and the model s overall optical depth When ty lt 100 fewer than 30 points will usually produce a flux error of lt 1 already in the first iteration However as Ty increases the solution accuracy decreases if the grid is unchanged and finer grids are required to maintain a constant level of accuracy This is done automatically by DUSTY The maximum number of grid points is bound by DUSTY s array dimensions which are controlled by the parameter npY whose default value is 40 This internal limit suffices to ensure convergence at the 5 level for most models with ty lt 1000 If higher levels of accuracy or larger Ty are needed DUSTY s internal limits on array sizes must be expanded by increasing npY as described in 86 1 Convergence and execution speed can be affected by the input radiation spectral shape A hard spectrum heavily weighed toward short wavelengths where the opacity is high can have an effect similar to large Ty 15 3 6
40. pths as specified The user controls the detail level of the output which can include both spectral and imaging properties as well as other quantities of interest Current address Department of Astrophysical Sciences Princeton University Princeton NJ 08544 This code is copywrited 1996 99 by Moshe Elitzur and may not be copied without acknowledging its origin Use of this code is not restricted provided that acknowledgement is made in each publication The bibliographic reference to this version of DUSTY is Ivezi Z Nenkova M amp Elitzur M 1999 User Manual for DUSTY University of Kentucky Internal Report accessible at http www pa uky edu moshe dusty Make sure that you have the current version with the latest options and problem fixes by checking the DUSTY Web site To be automatically notified of these changes ask to be placed on the DUSTY mailing list by sending an e mail to moshe pa uky edu Contents 1 2 INTRODUCTION INSTALLATION INPUT 3 1 External Radiation lt A A A o e ae 2 amp 2 Dust o lA se ce Oe A owe Ga A H 3 2 1 Chemical Composition ooa 3 2 2 Grain Size Distribution AAN EE 3 2 3 Dust Temperature on Inner Boundary 3 3 Density Distribution es E ee e ew ce ae as ee ae eee BO ed eh ee okt ad 3 3 1 Analytical Profiles at aia PE a DO BT eke Se ke E 3 3 2 Radiatively Driven Winds day ie i A E AN Be KA Braco Fabul ted Pronles A maris ee wih oe oe ad GS AA 3
41. sed for all internal calculations and output This provides a simple convenient method for increasing the resolution at selected spectral regions just add points at the end of the supplied grid until the desired resolution is attained Make sure you update both entries of npL and recompile DUSTY In practice tinkering with the wavelength grid should be reserved for adding spectral features Specifying the optical properties of the grains at a resolution coarser than that of the wavelength grid defeats the purpose of adding grid points The optical properties of grains supported by DUSTY are listed on the default wavelength grid Therefore modeling of very narrow features requires both the entry of a finer grid in lambda_grid dat and the input of user supplied optical properties see 3 2 1 defined on that same grid 4lambda_grid dat must always stay with the DUSTY executable file in the same directory 26 References 10 11 12 13 14 15 16 17 18 19 20 Dorschner J et al 1995 A amp A 300 503 Draine B T amp Lee H M 1984 ApJ 285 89 Engelke C W 1992 AJ 104 1248 Hanner M S 1988 NASA Conf Pub 3004 22 Henning Th et al 1997 A amp A 327 743 Ivezi Z amp Elitzur M 1995 ApJ 445 415 Ivezi Z amp Elitzur M 1996 MNRAS 279 1011 Ivezi Z dz Elitzur M 1996 MNRAS 279 1019 Ivezi Z amp Elitzur M 1997 MNRAS 287 799 Erratum MNRAS 303 864 1999 Ivezi Z a
42. sumption implies that the output is meaningful only for sources whose effective temperature obeys eq 5 For assistance with this requirement fname out lists the lower bound on Te obtained from this relation for optically thin sources Since F decreases with optical depth see 9 the listed bound 17 ensures compliance for all the models in the series However in optically thick cases F may become so small that the listed bound will greatly exceed the actual limit from eq 5 In those cases the true bounds can be obtained if desired from eq 5 and the model tabulated F1 note again that with the point source assumption F1 Fa Black body emission provides an absolute upper bound on the intensity of any thermal source Therefore input radiation whose spectral shape is the Planck function at tempera ture T is subject to the limit T lt T even though T is arbitrary in principle In such cases T must comply with eq 5 otherwise DUSTY s output is suspect and in fact could be mean ingless DUSTY issues a stern warning after the tabulation line of any model with input spectral shape that is either the Planck or Engelke Marengo function whose temperature violates eq 5 4 2 Optional Output In addition to the default output the user can obtain numerous tabulations of spectra imaging profiles and radial distributions of various quantities of interest for each of the optical depths included in the run This additional output is co
43. tains a narrow central spike of width be 2r r where re is the radius of the central source 7 Since this feature is unresolved in most observations it is usually of limited interest This spike is the only feature of the emerging intensity that depends on the effective temperature T of the central source which is irrelevant to DUSTY s calculations The width of the spike scales in proportion to T gt its height in proportion to T The listed value is for Te 10 000 K with two exceptions when the spectral shape of the external radiation is the Planck or Engelke Marengo function the arguments of those functions are used for Ty 4 2 4 Visibilities Visibility is the two dimensional spatial Fourier transform of the surface brightness distri bution for definition and discussion see 7 Since the surface brightness is a self similar function of b r the visibility is a self similar function of q9 where q is the spatial frequency 0 2r D and D is the distance to the source note that 0 is listed in the default output file for the location where Fops 107 W m 84 1 When imaging tables are produced DUSTY can calculate from them the corresponding visibility functions The only required input is the flag triggering this option if images are not requested in the first place this entry is skipped When the visibility option flag is different from zero it must be the same as the one for imaging Setting both flags to 1 will add
44. ticles and numerical tabulation in a file 3 3 1 Analytical Profiles DUSTY can handle three types of analytical profiles piecewise power law exponential and an analytic approximation for radiatively driven winds The last option is described in the next subsection on winds 1 Piecewise power law y PD 1 lt y lt y 1 y yD lt y lt y ny xy y 2 lt y lt y 3 y PS y N 1 lt y lt y N After the option selection the number JN is entered followed by a list of the break points y i i 1 N and a list of the power indices p i i 1 N The list must be ascending in y Examples e Density falling off as y in the entire shell as in a steady state wind with constant velocity The shell extends to 1000 times its inner radius density type 1 N 1 Y 1 e3 p 2 e Three consecutive shells with density fall off softening from y to a constant distribution as the radius increases by factor 10 density type 1 N 3 transition radii 10 100 1000 power indices i N O 12 2 Exponentially decreasing density distribution gt 3 no exp deg 3 where Y is the shell s outer boundary and o determines the fall off rate Following the option flag the user enters Y and o 4 e Exponential fall off of the density to e of its inner value at the shell s outer boundary Y 100 density type 2 Y 100 sigma 4 3 3 2 Radiatively Driven Winds The density distribution options 3 and 4 ar
45. uces imaging tabulations for all the models of the run in the single output file fname itb setting the flag to 2 puts the table for model number in its separate file fname i Following the option selection flag the number lt 20 of desired wavelengths is entered first followed by a list of these wavelengths in um e Example of additional input data required in fname inp for imaging output imaging tables all models in one file 1 number of wavelengths 8 wavelengths 0 55 1 0 2 2 4 10 50 100 1000 micron Whenever a specified wavelength is not part of DUSTY s grid the corresponding image is obtained by linear interpolation from the neighboring wavelengths in the grid If the nearest wavelengths are not sufficiently close the interpolation errors can be substantial For accurate modeling all wavelengths specified for imaging should be part of the grid modifying it if necessary see 6 2 Each map is tabulated with a single header line as follows o b hir where b is the impact parameter t b 7 b 7 0 where 7 b is the overall optical depth along a path with impact parameter b Note that 7 0 is simply the overall radial optical depth tauT listed in the file fname s 4 2 2 and that t b doubles its value across the shell once the impact parameter exceeds the stellar radius 2 The intensity in Jy arcsec at each of the wavelengths listed in the header line 20 A typical image con
46. visibility tables for all models to the single file fname itb Setting the flags to 2 puts the imaging and visibility tables of each model in the separate file fname i setting them to 3 further splits the output by putting each visibility table in the separate additional file fname v t Each visibility table starts with a single header line which lists the specified wavelengths in the order they were entered The first column lists the dimensionless scaled spatial fre quency q q and is followed by the visibility tabulation for the various wavelengths 4 2 5 Radial profiles for each model The next option flag triggers tabulations of the radial profiles of the density optical depth and dust temperature Setting the flag to 1 produces tabulations for all the models of the run in the single output file fname rtb setting the flag to 2 places the table for model number in its own separate file fname r The tabulated quantities are y dimensionless radius o eta the dimensionless normalized radial density profile 3 3 t radial profile of the optical depth variation At any wavelength A the optical depth at radius y measured from the inner boundary is t tauT where tauT is the overall optical depth at that wavelength tabulated in the file fname s 4 2 2 tauF radial profile of the flux averaged optical depth epsilon the fraction of grain heating due to the contribution of the envelope t
47. x TP ly 14 01 02 This density profile provides an excellent approximation under all circumstances to the actual results of detailed numerical calculations previous option The ratio of initial to final velocity e v1 Ue is practically irrelevant as long as lt 0 2 The selection density type 4 invokes this analytical solution with the default value e 0 2 As for the previous option the only input parameter that needs to be specified in this case is the outer boundary Y 13 e Analytical approximation for radiatively driven winds the shell relative thickness is Y 104 density type 4 Y 1 e4 Run times for this option are typically 2 3 times shorter and it can handle larger optical depths than the previous one Although this option suffices for the majority of cases of interest for detailed final fitting you may wish to switch to the former 3 3 3 Tabulated Profiles Arbitrary density profiles can be entered in tabulated form in a file The tabulation could be imported from another dynamical calculation e g star formation and DUSTY would produce the corresponding IR spectrum 5 The input filename must be entered separately in the line following the numerical flag This input file must consist of a three line header of arbitrary text followed by a two column tabulation of radius and density ordered in increasing radius The inner radius first entry corresponds to the dust temperature Ty entered previously
48. x D 6 USER CONTROL OF DUSTY DUSTY allows the user control of some of its inner working through tinkering with actual code statements that control the spatial and spectral grids The appropriate statements were placed in the file userpar inc separate from the main dusty f and are imbedded during compilation by the FORTRAN statement INCLUDE After modifying statements in userpar inc DUSTY must be recompiled to enable the changes 6 1 Array Sizes for Spatial Grid The maximum size of DUSTY s spatial grid is bound by array dimensions These are con trolled by the parameter npY which sets the limit on the number of radial points The default value of 40 must be decreased when DUSTY is run on machines that lack sufficient memory see 1 and increased when DUSTY fails to achieve the prescribed accuracy see 83 5 This parameter is defined in userpar inc via PARAMETER npY 40 3userpar inc must always stay with the source code in the same directory 25 To modify npY simply open userpar inc change the number 40 to the desired value save your change and recompile That s all Every other modification follows a similar procedure Since DUSTY s memory requirements vary roughly as the second power of npY the maximum value that can be accommodated on any given machine is determined by the system memory The parameter npY defines also the size npP of the grid used in angular integrations In the case of planar geometry DUSTY uses analyt
49. xceeds 5 km s the same inherent uncertainty as Mdot M gt an upper limit in M on the stellar mass M scales in proportion to L rgaps The effect of gravity is negligible as long as M is less than 0 5 M gt and the density profile is then practically independent of M There is a slight complication with these tabulations when the dust optical properties are entered using optical properties 3 3 2 1 With this option the scattering and ab sorption cross sections are entered in a file tabulated using arbitrary units since only their spectral shape is relevant for the solution of the radiative transfer problem However the conversion to mass loss rate requires also the grain size and this quantity is not specified when optical properties 3is used DUSTY assumes that the entered values correspond to a V the cross section per grain volume in um If that is not the case in the above scaling relations replace req with Ted Vie Finally DUSTY assumes that the external radiation originates in a central point source This assumption can be tested with eqs 27 and 28 of 9 which give expressions for the central source angular size and occultation effect From these it follows that the error introduced by the point source assumption is no worse than 6 whenever T gt 2 ad Fao 5 Thanks to scaling T need not be specified and is entirely arbitrary as far as DUSTY is concerned However compliance with the point source as
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