drw_utils

Module Contents

Functions

get_drw(t_rest, tau, z, SF_inf[, xmean, rng])	Generate a damped random walk light curve
get_drw_torch(t_rest, tau, z, SF_inf[, xmean])	Generate a damped random walk light curve

drw_utils.get_drw(t_rest, tau, z, SF_inf, xmean=0, rng=None)

Generate a damped random walk light curve This uses a damped random walk model to generate a light curve similar to that of a QSO [1]_. Taken with minor modification from https://github.com/astroML/astroML/blob/main/astroML/time_series/generate.py

t_restarray_like

rest-frame time. Should be in increasing order

taufloat

relaxation time

zfloat

redshift

xmeanfloat (optional)

mean value of random walk; default=0

SF_inffloat (optional

Structure function at infinity; default=0.3

random_stateGenerator instance

random seed or random number generator

xndarray

the sampled values corresponding to times t_rest

The differential equation is (with t = time/tau):

dX = -X(t) * dt + sigma * sqrt(tau) * e(t) * sqrt(dt) + b * tau * dt

where e(t) is white noise with zero mean and unit variance, and

Xmean = b * tau SFinf = sigma * sqrt(tau / 2)

so

dX(t) = -X(t) * dt + sqrt(2) * SFint * e(t) * sqrt(dt) + Xmean * dt

1

Kelly, B., Bechtold, J. & Siemiginowska, A. (2009) Are the Variations in Quasar Optical Flux Driven by Thermal Fluctuations? ApJ 698:895 (2009)

drw_utils.get_drw_torch(t_rest, tau, z, SF_inf, xmean=0)

Generate a damped random walk light curve This uses a damped random walk model to generate a light curve similar to that of a QSO [1]_. Taken with minor modification from https://github.com/astroML/astroML/blob/main/astroML/time_series/generate.py

t_restarray_like

rest-frame time. Should be in increasing order

taufloat

relaxation time in days

zfloat

redshift

xmeanfloat (optional)

mean value of random walk; default=0

SF_inffloat (optional

Structure function at infinity, in mag; default=0.3

random_stateint

random seed or random number generator

xndarray

the sampled values corresponding to times t_rest

The differential equation is (with t = time/tau):

dX = -X(t) * dt + sigma * sqrt(tau) * e(t) * sqrt(dt) + b * tau * dt

where e(t) is white noise with zero mean and unit variance, and

Xmean = b * tau SFinf = sigma * sqrt(tau / 2)

so

dX(t) = -X(t) * dt + sqrt(2) * SFint * e(t) * sqrt(dt) + Xmean * dt

1

Kelly, B., Bechtold, J. & Siemiginowska, A. (2009) Are the Variations in Quasar Optical Flux Driven by Thermal Fluctuations? ApJ 698:895 (2009)