Brainstorm User's manual - Observatoire de Bordeaux
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1. F does occur in Eqs 1 1 and 1 2 making the straight integration of these expressions not easy if some precision is needed Well and SQ Sy outside the source there is not such difficulty since the equality r 7 never occur in the above expressions If the surface has finite size is planar and of rectangular shape then Cartesian coor dinates are appropriate The potential is then Ex y dady U X Y Z TRS ETT 1 3 where x y z are associated to the source and X Y Z are for the field point Unfor tunately this double integral generally does not lead to a closed form i e a formula involving a finite number of analytical terms A remarkable exception however is the homogeneous rectangular sheet Actually with X x y cst the potential is indeed fully analytical we shall not give the formula here We can advantageously use this issue to numerically compute with great accuracy the potential due to any planar distribution inside the distribution How For any field point X Y Z z located onto the surface we can always form the difference surface density Then W writes Y X Y Z 6 ES PE 1 5 gt 12 User s manual for BRAINSTORM In other words the potential is the sum of two contributions i the potential Yus due to a uniform sheet with surface density Z X Y namely the value dxdy Wus X Y Z GE X Y If e 1 6 and ii the residual potential OW due to the distribu2. is stored 6 User s manual for BRAINSTORM 7 Compilation Edit the Makefile Enter the name of your Fortran 90 Compiler at the right place for instance FCOMPL f90 Possibly change the absolute path where to find the CFITSIO numerical library for instance CFITSIO usr mylibs Compile and link the source code with the command make brainstorm After the prompt you can run the main demo program like this brainstorm exe lt data brainstorm where data brainstorm is a batch file containing default parameters If you wish to enter all the parameters one by one by hand then just enter the command brainstorm exe but this may be non very confortable for repetitive uses You can compile link and run the source code with the command make rbrainstorm lt data brainstorm 8 Main intput parameters Input parameters are for the filenames input output the object the computation of and g namely the accuracy of the double integrals the computational box size and resolution see Fig 3 These input parameters are contained in the batch file data brainstorm This batch file must be of the following form line numbers are added for convenience line 1 gt gt gt FITS format file line 2 n4303_pr fits line 3 gt gt gt Mass Luminosity conversion factor line 4 1 0000E 00 line 5 gt gt gt Distance in kiloparsecs line 6 750 line 7 gt gt gt Pixel size in deg line line line lin
3. 3_pr Any other filename works 33 at line 12 is the number of source point used to perfom numerical integration in the x direction if you decrease this value then the precision will fall down The larger this value the larger the computing time the more accurate the potential 37 at line 14 is the number of source point used to perfom numerical integration in the y direction if you decrease this value then the precision will fall down The larger this value the larger the computing time the more accurate the potential with auto at line 16 the computational box automatically fits the genuine image with the same distribution of pixels lines 18 to 28 herebelow are then obsolete Three other values are allowed here With fine the computational box auto matically fits the genuine image but you can vary the number of pixels in each direction lines 19 20 23 and 24 herebelow are then obsolete With zoom the computational box still lies in the image plane but can be shorter wider than the image lines 26 to 28 herebelow are then obsolete with full you specify the full computational box at lines 18 to 28 132 at line 18 is the number of point of the computational box in the X direction namely NBOX It can be 1 0 15 at line 19 is the X coordinate of the inner edge of the computational box namely CBOX 1 0 11 at line 20 is the X coordinate of the outer edge of the computational box namely CBOX 2 134 at line 22 is the n
4. BRAINSTORM An easy to use F90 program to compute galactic potentials and ac User s manual 2005 September 1st f Jean Marc Hur X Copyright C 2005 Jean Marc Hur BRAINSTORM is free software you can redistribute it and or modify it under the terms of the GNU General Public License as published by the Free Software Foun dation either version 2 of the License or at your option any later version 2 User s manual for BRAINSTORM 1 Overview of BRAINSTORM capabilities BRAINSTORM is an easy to use Fortran 90 program devoted to the study of galaxy dy namics It reads and write FITS format files thanks to the CFITSIO numerical library The gravitational potential and field components are then computed in the rotation plane of galaxies as well as oustide it from the splitting method Hur 2005 In contrast with most methods this one uses no kind of approximation or modification of Newton s law like smoothing length or so Matter is assumed to be continuously distributed over a planar finite size rectangular surface Singularities in the Poisson kernels are exactly treated in the homogeneous limit see the appendix for a brief outline of the splitting method in Cartesian coordiantes A bi dimensional dynamical mesh ensures reliability high accuracy and a not so long computing time typical of integral based techniques BRAINSTORM is part of the NOBONES project by the same author to be released soon 2 An example Fig
5. ICH 1 orders the computation of the potential only Set this varaibale to 2 for the field only and to 12 for both e X is a vector X 1 is the potential UV X 2 is gx X 3 is gy and X 4 is gz e XERROR is a vector containing an estimate of the absolute error on X XERROR 1 is the error on potential Y XERROR 2 is gx XERROR 3 is gy and XERROR 4 is gz References Hur J M 2005 Solutions of the axi symmetric Poisson equation from elliptic integrals I Numerical splitting methods Astronomy and Astrophysics 434 1 User s manual for BRAINSTORM 11 A Brief outline of the splitting method The gravitational potential and acceleration g VW due to matter distributed over a surface S write in the integral forms w ele Ir ao ag 7 a f 2 Lei Bae ee 1 2 respectively where X is the surface density rl is the spherical vector refering to loca tion of matter i e the source and F is for the field point i e the point of space where the information are requested It is worth noting that the bare inversion of the Poisson equation in two dimension 2D would require the knowledge of the discontinuity of the vertical gravity field namely 02 U This quantity is generally not straigtforwardly avail able that is why there is no way around the integral approach for 2D objects like those considered here The difficulty with the integral formalism is the presence of singular integrands everwhere on the source r
6. License as published by the Free Software Foundation either version 2 of the License or at your option any later version This program is distributed in the hope that it will be useful but WITHOUT ANY WARRANTY without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE See the GNU General Public License for more details Web site currently at http www gnu org licenses gpl html You should have received a copy of the GNU General Public License along with this program if not write to the Free Software Foundation Inc 59 Temple Place Suite 4 User s manual for BRAINSTORM POTENTIAL ROT ENERGY 0 2 0 17 4 O J 0 07 01F gol 1 en rss fe 0 2 0 1 0 0 0 1 0 2 Xx 1 1 0 56 0 02 0 52 1 06 1 6 Fig 2 Left gravitational potential normalized log scale computed with BRAINSTORM Right steady specific kinetic energy normalized linear scale 330 Boston MA 02111 1307 USA 4 Author address Jean Marc Hur Observatoire Aquitain des Sciences de l Univers 2 rue de l Observatoire B P 89 33270 Floirac France and Universit Bordeaux 1 351 cours de la Lib ration 33405 Talence cedex France email jean marc hure obs u bordeaux1 fr User s manual for BRAINSTORM 5 5 Download and installation BRAINSTORM can be downloaded at the following Internet address http www obs u bordeaux1 fr radio pages we
7. b radio webhure Two files are required e the UNIX compressed archive file nammed brainstorm tar gz It includes the source code several modules and a demo program written in Fortran 90 a FITS format file a default batch file data brainstorm a Makefile and this user manual in PDF format e the installation script nammed installbrainstorm Once these two files have been downloaded you can install the program Make the installation script executable like this chmod x installbrainstorm and run it with the command installbrainstorm This uncompresses the archive creating a directory nammed BRAINSTORM and sev eral files within it In principle you should need to modify none of the F90 rou tines and modules except the demonstration program brainstorm f90 the batch file data brainstorm and the Makefile Reach this directory with the command cd BAINSTORM 6 Dependancy the CFITSIO numerical library The main program calls a few subroutines belonging to the CFITSIO numerical library which enables to read and write FITS format file So you need to install that library before compilation It is free You can find it at the Internet site http heasarc gsfc nasa gov docs software This provides a library nammed libcfitsio ain your environment In the following we shall assume that this library is correctly installed in the directory usr 1ib as usual otherwise you must know the absolute path where the library
8. e line line line line line line line line line line line line line line line line line 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 CBOX 6 CBOX 5 User s manual for BRAINSTORM 7 Z axis oe oe aes ee CBOX 4 CBOX 3 X axis Y axis CBOX 1 CBOX 2 Fig 3 The computational box X Y Z 7 4E 4 gt gt gt Generic name for output files auto auto gt gt gt Number of source point x axis 33 gt gt gt gt Number of source point y axis 37 gt gt gt Computational box auto zoom full zoom gt gt gt x axis box sampling NBOX and edges CBOX 1 CBOX 2 132 0 15E0 0 11E0 gt gt gt y axis box sampling LBOX and edges CBOX 3 CBOX 4 134 0 12E0 0 23E0 gt gt gt z axis box sampling MBOX and edges CBOX 5 CBOX 6 3 0 0EO 0 3E0 All lines beginning with gt gt gt are unread line or used for comment only Let us analyze this file line by line e n4303_pr fits at line 2 is the name of the FITS format file containing the image This file must has the suffix fits e 1 0000E 00 at line 4 is the mass luminosity ratio the flux or count must be con verted into surface density e 750 at line 6 is the remote distance from the galaxy expressed in kiloparsecs User s manual for BRAINSTORM 7 4E 4 at line 8 is the angular size of a image pixel with auto at line 10 output filenames are of the form n430
9. tion 65 the difference bewteen the true surface density and the local value namely 60 X Y Z G opiate 1 7 S VOZIS A Since 02 0 at the field point the integral in 6W has a regular integrand contrary to the integral in Eq 1 1 This means that Y can be computed numerically with great precision depending on the numerical quadrature Similar considerations hold for the gravitational field g BRAINSTORM computes and g on any rectangular inhomogeneous sheet using this efficient technique The splitting method in cylindrical plar coordinates is described in details in Hur 2005
10. umber of point of the computational box in the Y direction namely LBOX It can be 1 0 12 at line 23 is the Y coordinate of the inner edge of the computational box namely CBOX 3 0 23 at line 24 is the Y coordinate of the outer edge of the computational box namely CBOX 4 1 at line 26 is the number of point of the computational box in the Z direction namely MBOX It can be more than 1 0 0 at line 27 is the Z coordinate of the bottom edge of the computational box namely CBOX 5 0 3 at line 28 is the Z coordinate of the top edge of the computational box namely CBOX 6 User s manual for BRAINSTORM 9 0 galactic plane Z axis _ 0 x axis 1 Fig 4 Coordinate system x y z linked to the source Here the image is square 9 Calling sequence Within the main program brainstorm f90 the F90 calling sequence is the following inputs XF 3 0 YF 0 3 ZF 1 123 N 65 L 73 WHICH 1 calling sequence CALL NOBONES2XYZ XF YF ZF N L WHICH X XERROR output PSI X 1 GX X 2 GY X 3 GZ X 4 where e XF YF and ZF denote the coordinates of the field point belonging to the computa tional box i e X Y and Z e N and L are the number of source points effectively used in the computation of the double integrals N is for the X axis and L is for the Y axis The larger these numbers the more accurate the results the larger the computing time 10 User s manual for BRAINSTORM e WH
11. ure 1 shows an optical deprojected image of the galaxy NGC 4303 a FITS format image 561 x 561 pixels This image is mapped into a square 1 1 in both X and Y directions The zone where the potential is requested is marked by a white square It is 0 2 0 2 in both directions The selection can be a single point a surface a cube a coplanar or an off plane region The number of pixels inside this computational box is also user defined Here it is a 64 x 64 box the more the pixels the longer the computing time User s manual for BRAINSTORM 3 TE Y axis 0 X axis Fig 1 Optical g band image of the galaxy NGC4303 from The Galaxy Catalog by Z Frei amp J E Gunn see http www astro princeton edu frei galaxy_catalog html This FITS format image is a square image with 561 x 561 pixels The small white square is the selected computational box Figure 2 displays the gravitational potential log scale and the rotational energy normal scale in the plane of the galaxy NGC 4303 as output by BRAINSTORM The computing time is of the order of one minute on a low cost 1 5 GHz personal computer no optimization option no paralellization BRAINSTORM also computes the error on the computed potential as well as field components not shown here 3 Copyright BRAINSTORM Copyright C 2005 Jean Marc Hur BRAINSTORM is free software you can redistribute it and or modify it under the terms of the GNU General Public
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