function lsf_rotate, deltav, vsini, EPSILON = epsilon, VELGRID = velgrid ;+ ; NAME: ; LSF_ROTATE: ; ; PURPOSE: ; Create a 1-d convolution kernel to broaden a spectrum from a rotating star ; ; EXPLANATION: ; Can be used to derive the broadening effect (line spread function; LSF) ; due to rotation on a synthetic stellar spectrum. Assumes constant ; limb darkening across the disk. ; ; CALLING SEQUENCE ; lsf = LSF_ROTATE(deltav, vsini, EPSILON=, VELGRID=) ; ; INPUT PARAMETERS: ; deltaV - numeric scalar giving the step increment (in km/s) in the output ; rotation kernel. ; Vsini - the rotational velocity projected along the line of sight (km/s) ; ; OUTPUT PARAMETERS: ; LSF - The convolution kernel vector for the specified rotational velocity. ; The number of points in LSF will be always be odd (the kernel is ; symmetric) and equal to either ceil(2*Vsini/deltav) or ; ceil(2*Vsini/deltav) +1 (whichever number is odd). LSF will ; always be of type FLOAT. ; ; To actually compute the broadening. the spectrum should be convolved ; with the rotational LSF. ; OPTIONAL INPUT PARAMETERS: ; Epsilon - numeric scalar giving the limb-darkening coefficient, ; default = 0.6 which is typical for photospheric lines. The ; specific intensity I at any angle theta from the specific intensity ; Icen at the center of the disk is given by: ; ; I = Icen*(1-epsilon*(1-cos(theta)) ; ; OPTIONAL OUTPUT PARAMETER: ; Velgrid - Vector with the same number of elements as LSF ; EXAMPLE: ; (1) Plot the LSF for a star rotating at 90 km/s in both velocity space and ; for a central wavelength of 4300 A. Compute the LSF every 3 km/s ; ; IDL> lsf = lsf_rotate(3,90,velgrid=vel) ;LSF will contain 61 pts ; IDL> plot,vel,lsf ;Plot the LSF in velocity space ; IDL> wgrid = 4300*(1+vel/3e5) ;Speed of light = 3e5 km/s ; IDL> oplot,wgrid,lsf ;Plot in wavelength space ; ; NOTES: ; Adapted from rotin3.f in the SYNSPEC software of Hubeny & Lanz ; .http://nova.astro.umd.edu/index.html Also see Eq. 17.12 in ; "The Observation and Analysis of Stellar Photospheres" by D. Gray (1992) ; REVISION HISTORY: ; Written, W. Landsman November 2001 ;- On_error,2 compile_opt idl2 if N_params() LT 1 then begin print,'Syntax - rkernel = lsf_rotate(deltav, vsini)' print,' Input Keyword: Epsilon' print,' Output Keyword: Velgrid' return,-1 endif if N_elements(epsilon) EQ 0 then epsilon = 0.6 e1 = 2.0d*(1.0d - epsilon) e2 = !dpi*epsilon/2.0d e3 = !dpi*(1.0d - epsilon/3.0d) npts = ceil(2*vsini/deltav) if npts mod 2 EQ 0 then npts = npts +1 nwid = npts/2 x = (dindgen(npts)- nwid) x = x*deltav/vsini if arg_present(velgrid) then velgrid = x*vsini x1 = abs(1.0d - x^2) return, float((e1*sqrt(x1) + e2*x1)/e3) end